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GitLab

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<h3>

Andreas Tille pushed to branch master

at <a href="https://salsa.debian.org/med-team/python-skbio">Debian Med / python-skbio</a>

</h3>

<h4>

Commits:

</h4>

<ul>

<li>

<strong><a href="https://salsa.debian.org/med-team/python-skbio/commit/ee541afd060a47c69a82a7edb6b3009d43663cc6">ee541afd</a></strong>

<div>

<span>by Andreas Tille</span>

<i>at 2018-08-28T16:13:43Z</i>

</div>

<pre class="commit-message" style="white-space: pre-wrap; margin: 0;">New upstream version 0.5.4</pre>

</li>

<li>

<strong><a href="https://salsa.debian.org/med-team/python-skbio/commit/d9b8192adb2f14bf84713aab82d806e1766dc5b9">d9b8192a</a></strong>

<div>

<span>by Andreas Tille</span>

<i>at 2018-08-28T16:14:04Z</i>

</div>

<pre class="commit-message" style="white-space: pre-wrap; margin: 0;">Update upstream source from tag 'upstream/0.5.4'

Update to upstream version '0.5.4'

with Debian dir 9bec36a983712c49f50e01e1b526064b2342432c</pre>

</li>

<li>

<strong><a href="https://salsa.debian.org/med-team/python-skbio/commit/59737a89a9cfea9e36f5487d037b6dc5e014ee74">59737a89</a></strong>

<div>

<span>by Andreas Tille</span>

<i>at 2018-08-28T17:47:56Z</i>

</div>

<pre class="commit-message" style="white-space: pre-wrap; margin: 0;">New upstream version

</pre>

</li>

</ul>

<h4>12 changed files:</h4>

<ul>

<li class="file-stats">

<a href="#ab09011fa121d0a2bb9fa4ca76094f2482b902b7">

CHANGELOG.md

</a>

</li>

<li class="file-stats">

<a href="#9c96da0e9f91d7d8937b69b524702c106258f0d1">

debian/changelog

</a>

</li>

<li class="file-stats">

<a href="#4f527af5768c903b0fd5e66c83e25933c74fb224">

skbio/__init__.py

</a>

</li>

<li class="file-stats">

<a href="#c6f587411e1fff773305a7254f17b301583ab8f7">

skbio/stats/ordination/__init__.py

</a>

</li>

<li class="file-stats">

<a href="#c443397cd3ce71f204a6fa99ac24c98e5fcc8b14">

skbio/stats/ordination/_principal_coordinate_analysis.py

</a>

</li>

<li class="file-stats">

<a href="#4d8189dc1208d6c1d04848c3380fd81155a62c20">

skbio/stats/ordination/_utils.py

</a>

</li>

<li class="file-stats">

<a href="#0d49b2580a40a2f0585d51a5139beb0883d13f33">

<span class="new-file">

+

skbio/stats/ordination/tests/data/PCoA_sample_data_12dim

</span>

</a>

</li>

<li class="file-stats">

<a href="#b017992412f66f9ba72318f0343f890bc2b9eea2">

<span class="new-file">

+

skbio/stats/ordination/tests/data/PCoA_sample_data_3_eigh_ref_3dim

</span>

</a>

</li>

<li class="file-stats">

<a href="#740117d7edce46bbec55dd903f85d2656e72915c">

<span class="new-file">

+

skbio/stats/ordination/tests/data/PCoA_sample_data_3_fsvd_ref_3dim

</span>

</a>

</li>

<li class="file-stats">

<a href="#125936fde92c0e77b23cf33bdd140af1c8be8e27">

skbio/stats/ordination/tests/test_principal_coordinate_analysis.py

</a>

</li>

<li class="file-stats">

<a href="#941ac564379c7746c712dca1c7187329b868b6cc">

skbio/stats/ordination/tests/test_util.py

</a>

</li>

<li class="file-stats">

<a href="#21f22f46349a2970cbaac9ddeaee97358aee79b5">

skbio/util/_testing.py

</a>

</li>

</ul>

<h4>Changes:</h4>

<li id="ab09011fa121d0a2bb9fa4ca76094f2482b902b7">

<a href="https://salsa.debian.org/med-team/python-skbio/compare/3d3c45f3254533f7a7055537dba85e12078e2138...59737a89a9cfea9e36f5487d037b6dc5e014ee74#ab09011fa121d0a2bb9fa4ca76094f2482b902b7"><strong>CHANGELOG.md</strong></a>

<hr>

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<td class="diff-line-num old_line" data-linenumber="1" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

1

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<td class="diff-line-num new_line" data-linenumber="1" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

1

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<td class="line_content noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;">

<pre style="margin: 0;"> <span id="LC1" class="line" lang="markdown"><span class="gh" style="color: #999;"># scikit-bio changelog</span></span>

</pre>

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<tr class="line_holder" id="" style="line-height: 1.6;">

<td class="diff-line-num old_line" data-linenumber="2" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

2

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<td class="diff-line-num new_line" data-linenumber="2" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

2

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<td class="line_content noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;">

<pre style="margin: 0;"> <span id="LC2" class="line" lang="markdown"></span>

</pre>

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<tr class="line_holder new" id="" style="line-height: 1.6;">

<td class="diff-line-num new old_line" data-linenumber="3" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="3" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

3

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<pre style="margin: 0;">+<span id="LC3" class="line" lang="markdown"><span class="gu" style="color: #800080; font-weight: 600;">## Version 0.5.4 (2018-08-23)</span></span>

</pre>

</td>

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<tr class="line_holder new" id="" style="line-height: 1.6;">

<td class="diff-line-num new old_line" data-linenumber="3" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

</td>

<td class="diff-line-num new new_line" data-linenumber="4" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

4

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC4" class="line" lang="markdown"></span>

</pre>

</td>

</tr>

<tr class="line_holder new" id="" style="line-height: 1.6;">

<td class="diff-line-num new old_line" data-linenumber="3" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

</td>

<td class="diff-line-num new new_line" data-linenumber="5" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

5

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<pre style="margin: 0;">+<span id="LC5" class="line" lang="markdown"><span class="gu" style="color: #800080; font-weight: 600;">### Features</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="3" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

</td>

<td class="diff-line-num new new_line" data-linenumber="6" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

6

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC6" class="line" lang="markdown"></span>

</pre>

</td>

</tr>

<tr class="line_holder new" id="" style="line-height: 1.6;">

<td class="diff-line-num new old_line" data-linenumber="3" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

</td>

<td class="diff-line-num new new_line" data-linenumber="7" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

7

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC7" class="line" lang="markdown"><span class="p">*</span> Added <span class="sb" style="color: #d14;">`FSVD`</span>, an alternative fast heuristic method to perform Principal Coordinates Analysis, to <span class="sb" style="color: #d14;">`skbio.stats.ordination.pcoa`</span>.</span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="3" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

</td>

<td class="diff-line-num new new_line" data-linenumber="8" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

8

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC8" class="line" lang="markdown"></span>

</pre>

</td>

</tr>

<tr class="line_holder new" id="" style="line-height: 1.6;">

<td class="diff-line-num new old_line" data-linenumber="3" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

</td>

<td class="diff-line-num new new_line" data-linenumber="9" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

9

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<pre style="margin: 0;">+<span id="LC9" class="line" lang="markdown"><span class="gu" style="color: #800080; font-weight: 600;">### Backward-incompatible changes [stable]</span></span>

</pre>

</td>

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<td class="diff-line-num new old_line" data-linenumber="3" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

</td>

<td class="diff-line-num new new_line" data-linenumber="10" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

10

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC10" class="line" lang="markdown"></span>

</pre>

</td>

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<td class="diff-line-num new old_line" data-linenumber="3" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

</td>

<td class="diff-line-num new new_line" data-linenumber="11" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

11

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC11" class="line" lang="markdown"><span class="gu" style="color: #800080; font-weight: 600;">### Backward-incompatible changes [experimental]</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="3" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

</td>

<td class="diff-line-num new new_line" data-linenumber="12" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

12

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC12" class="line" lang="markdown"></span>

</pre>

</td>

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<td class="diff-line-num new old_line" data-linenumber="3" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

</td>

<td class="diff-line-num new new_line" data-linenumber="13" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

13

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC13" class="line" lang="markdown"><span class="gu" style="color: #800080; font-weight: 600;">### Performance enhancements</span></span>

</pre>

</td>

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<td class="diff-line-num new old_line" data-linenumber="3" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

</td>

<td class="diff-line-num new new_line" data-linenumber="14" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

14

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC14" class="line" lang="markdown"></span>

</pre>

</td>

</tr>

<tr class="line_holder new" id="" style="line-height: 1.6;">

<td class="diff-line-num new old_line" data-linenumber="3" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

</td>

<td class="diff-line-num new new_line" data-linenumber="15" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

15

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC15" class="line" lang="markdown"><span class="p">*</span> Added optimized utility methods <span class="sb" style="color: #d14;">`f_matrix_inplace`</span> and <span class="sb" style="color: #d14;">`e_matrix_inplace`</span> which perform <span class="sb" style="color: #d14;">`f_matrix`</span> and <span class="sb" style="color: #d14;">`e_matrix`</span> computations in-place and are used by the new <span class="sb" style="color: #d14;">`center_distance_matrix`</span> method in <span class="sb" style="color: #d14;">`skbio.stats.ordination`</span>.</span>

</pre>

</td>

</tr>

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<td class="diff-line-num new old_line" data-linenumber="3" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

</td>

<td class="diff-line-num new new_line" data-linenumber="16" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

16

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC16" class="line" lang="markdown"></span>

</pre>

</td>

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<td class="diff-line-num new old_line" data-linenumber="3" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

</td>

<td class="diff-line-num new new_line" data-linenumber="17" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

17

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<pre style="margin: 0;">+<span id="LC17" class="line" lang="markdown"><span class="gu" style="color: #800080; font-weight: 600;">### Bug fixes</span></span>

</pre>

</td>

</tr>

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<td class="diff-line-num new old_line" data-linenumber="3" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

</td>

<td class="diff-line-num new new_line" data-linenumber="18" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

18

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC18" class="line" lang="markdown"></span>

</pre>

</td>

</tr>

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<td class="diff-line-num new old_line" data-linenumber="3" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

</td>

<td class="diff-line-num new new_line" data-linenumber="19" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

19

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<pre style="margin: 0;">+<span id="LC19" class="line" lang="markdown"><span class="gu" style="color: #800080; font-weight: 600;">### Deprecated functionality [stable]</span></span>

</pre>

</td>

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<td class="diff-line-num new old_line" data-linenumber="3" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

</td>

<td class="diff-line-num new new_line" data-linenumber="20" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

20

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC20" class="line" lang="markdown"></span>

</pre>

</td>

</tr>

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<td class="diff-line-num new old_line" data-linenumber="3" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

</td>

<td class="diff-line-num new new_line" data-linenumber="21" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

21

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC21" class="line" lang="markdown"><span class="gu" style="color: #800080; font-weight: 600;">### Deprecated functionality [experimental]</span></span>

</pre>

</td>

</tr>

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<td class="diff-line-num new old_line" data-linenumber="3" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

</td>

<td class="diff-line-num new new_line" data-linenumber="22" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

22

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC22" class="line" lang="markdown"></span>

</pre>

</td>

</tr>

<tr class="line_holder new" id="" style="line-height: 1.6;">

<td class="diff-line-num new old_line" data-linenumber="3" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

</td>

<td class="diff-line-num new new_line" data-linenumber="23" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

23

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<pre style="margin: 0;">+<span id="LC23" class="line" lang="markdown"><span class="gu" style="color: #800080; font-weight: 600;">### Miscellaneous</span></span>

</pre>

</td>

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<td class="diff-line-num new old_line" data-linenumber="3" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

</td>

<td class="diff-line-num new new_line" data-linenumber="24" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

24

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC24" class="line" lang="markdown"></span>

</pre>

</td>

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<td class="diff-line-num old_line" data-linenumber="3" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

3

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<td class="diff-line-num new_line" data-linenumber="25" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

25

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<td class="line_content noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;">

<pre style="margin: 0;"> <span id="LC25" class="line" lang="markdown"><span class="gu" style="color: #800080; font-weight: 600;">## Version 0.5.3 (2018-08-07)</span></span>

</pre>

</td>

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<td class="diff-line-num old_line" data-linenumber="4" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

4

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<td class="diff-line-num new_line" data-linenumber="26" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

26

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<td class="line_content noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;">

<pre style="margin: 0;"> <span id="LC26" class="line" lang="markdown"></span>

</pre>

</td>

</tr>

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<td class="diff-line-num old_line" data-linenumber="5" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

5

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<td class="diff-line-num new_line" data-linenumber="27" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

27

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<td class="line_content noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;">

<pre style="margin: 0;"> <span id="LC27" class="line" lang="markdown"><span class="gu" style="color: #800080; font-weight: 600;">### Features</span></span>

</pre>

</td>

</tr>

</table>

<br>

</li>

<li id="9c96da0e9f91d7d8937b69b524702c106258f0d1">

<a href="https://salsa.debian.org/med-team/python-skbio/compare/3d3c45f3254533f7a7055537dba85e12078e2138...59737a89a9cfea9e36f5487d037b6dc5e014ee74#9c96da0e9f91d7d8937b69b524702c106258f0d1"><strong>debian/changelog</strong></a>

<hr>

<table class="code white" style="font-family: monospace; font-size: 90%;" bgcolor="#fff" width="100%" cellpadding="0" cellspacing="0">

<tr class="line_holder old" id="" style="line-height: 1.6;">

<td class="diff-line-num old old_line" data-linenumber="1" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

1

</td>

<td class="diff-line-num new_line old" data-linenumber="1" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<pre style="margin: 0;">-<span id="LC1" class="line" lang="plaintext">python-skbio (0.5.<span class="idiff left right">3</span>-1) UNRELEASED; urgency=medium</span>

</pre>

</td>

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<td class="diff-line-num new old_line" data-linenumber="2" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

</td>

<td class="diff-line-num new new_line" data-linenumber="1" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

1

</td>

<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC1" class="line" lang="plaintext">python-skbio (0.5.<span class="idiff left right">4</span>-1) UNRELEASED; urgency=medium</span>

</pre>

</td>

</tr>

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<td class="diff-line-num old_line" data-linenumber="2" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

2

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<td class="diff-line-num new_line" data-linenumber="2" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

2

</td>

<td class="line_content noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;">

<pre style="margin: 0;"> <span id="LC2" class="line" lang="plaintext"></span>

</pre>

</td>

</tr>

<tr class="line_holder" id="" style="line-height: 1.6;">

<td class="diff-line-num old_line" data-linenumber="3" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

3

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<td class="diff-line-num new_line" data-linenumber="3" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

3

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<td class="line_content noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;">

<pre style="margin: 0;"> <span id="LC3" class="line" lang="plaintext">  * New upstream version</span>

</pre>

</td>

</tr>

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<td class="diff-line-num old_line" data-linenumber="4" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

4

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<td class="diff-line-num new_line" data-linenumber="4" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

4

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<td class="line_content noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;">

<pre style="margin: 0;"> <span id="LC4" class="line" lang="plaintext">  * Standards-Version: 4.2.0</span>

</pre>

</td>

</tr>

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<td class="diff-line-num old_line" data-linenumber="5" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

5

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<td class="diff-line-num new_line" data-linenumber="5" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

5

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<td class="line_content noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;">

<pre style="margin: 0;"> <span id="LC5" class="line" lang="plaintext">  * Build-Depends: python3-hdmedians</span>

</pre>

</td>

</tr>

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<td class="diff-line-num old_line" data-linenumber="6" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

6

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<td class="diff-line-num new_line" data-linenumber="6" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

6

</td>

<td class="line_content noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;">

<pre style="margin: 0;"> <span id="LC6" class="line" lang="plaintext"></span>

</pre>

</td>

</tr>

<tr class="line_holder old" id="" style="line-height: 1.6;">

<td class="diff-line-num old old_line" data-linenumber="7" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

7

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<td class="diff-line-num new_line old" data-linenumber="7" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<pre style="margin: 0;">-<span id="LC7" class="line" lang="plaintext"> -- Andreas Tille <tille@debian.org>  <span class="idiff left right">Wed, 15 Aug 2018 15:21:02</span> +0200</span>

</pre>

</td>

</tr>

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<td class="diff-line-num new old_line" data-linenumber="8" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

</td>

<td class="diff-line-num new new_line" data-linenumber="7" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

7

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<pre style="margin: 0;">+<span id="LC7" class="line" lang="plaintext"> -- Andreas Tille <tille@debian.org>  <span class="idiff left right">Tue, 28 Aug 2018 18:14:05</span> +0200</span>

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<pre style="margin: 0;"> <span id="LC8" class="line" lang="plaintext"></span>

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<pre style="margin: 0;"> <span id="LC9" class="line" lang="plaintext">python-skbio (0.5.2-1) unstable; urgency=medium</span>

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<pre style="margin: 0;"> <span id="LC10" class="line" lang="plaintext"></span>

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<li id="4f527af5768c903b0fd5e66c83e25933c74fb224">

<a href="https://salsa.debian.org/med-team/python-skbio/compare/3d3c45f3254533f7a7055537dba85e12078e2138...59737a89a9cfea9e36f5487d037b6dc5e014ee74#4f527af5768c903b0fd5e66c83e25933c74fb224"><strong>skbio/__init__.py</strong></a>

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<td class="diff-line-num unfold js-unfold old_line" data-linenumber="26" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">...</td>

<td class="diff-line-num unfold js-unfold new_line" data-linenumber="26" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">...</td>

<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -26,7 +26,7 @@ __all__ = ['Sequence', 'DNA', 'RNA', 'Protein', 'GeneticCode',</td>

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<pre style="margin: 0;"> <span id="LC26" class="line" lang="python">           <span class="s" style="color: #d14;">'TreeNode'</span><span class="p">,</span> <span class="s" style="color: #d14;">'nj'</span><span class="p">,</span> <span class="s" style="color: #d14;">'read'</span><span class="p">,</span> <span class="s" style="color: #d14;">'write'</span><span class="p">,</span> <span class="s" style="color: #d14;">'OrdinationResults'</span><span class="p">]</span></span>

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<pre style="margin: 0;"> <span id="LC27" class="line" lang="python"></span>

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<pre style="margin: 0;"> <span id="LC28" class="line" lang="python"><span class="n" style="color: #333;">__credits__</span> <span class="o" style="font-weight: 600;">=</span> <span class="s" style="color: #d14;">"https://github.com/biocore/scikit-bio/graphs/contributors"</span></span>

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<pre style="margin: 0;">-<span id="LC29" class="line" lang="python"><span class="n" style="color: #333;">__version__</span> <span class="o" style="font-weight: 600;">=</span> <span class="s" style="color: #d14;">"0.5.<span class="idiff left right">3</span>"</span></span>

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<pre style="margin: 0;">+<span id="LC29" class="line" lang="python"><span class="n" style="color: #333;">__version__</span> <span class="o" style="font-weight: 600;">=</span> <span class="s" style="color: #d14;">"0.5.<span class="idiff left right">4</span>"</span></span>

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<pre style="margin: 0;"> <span id="LC30" class="line" lang="python"></span>

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<pre style="margin: 0;"> <span id="LC31" class="line" lang="python"><span class="n" style="color: #333;">mottos</span> <span class="o" style="font-weight: 600;">=</span> <span class="p">[</span></span>

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<pre style="margin: 0;"> <span id="LC32" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># 03/15/2014</span></span>

</pre>

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</li>

<li id="c6f587411e1fff773305a7254f17b301583ab8f7">

<a href="https://salsa.debian.org/med-team/python-skbio/compare/3d3c45f3254533f7a7055537dba85e12078e2138...59737a89a9cfea9e36f5487d037b6dc5e014ee74#c6f587411e1fff773305a7254f17b301583ab8f7"><strong>skbio/stats/ordination/__init__.py</strong></a>

<hr>

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<td class="diff-line-num unfold js-unfold old_line" data-linenumber="129" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">...</td>

<td class="diff-line-num unfold js-unfold new_line" data-linenumber="129" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">...</td>

<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -129,10 +129,11 @@ from ._correspondence_analysis import ca</td>

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<pre style="margin: 0;"> <span id="LC129" class="line" lang="python"><span class="kn" style="font-weight: 600;">from</span> <span class="nn" style="color: #555;">._canonical_correspondence_analysis</span> <span class="kn" style="font-weight: 600;">import</span> <span class="n" style="color: #333;">cca</span></span>

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<pre style="margin: 0;"> <span id="LC130" class="line" lang="python"><span class="kn" style="font-weight: 600;">from</span> <span class="nn" style="color: #555;">._principal_coordinate_analysis</span> <span class="kn" style="font-weight: 600;">import</span> <span class="n" style="color: #333;">pcoa</span><span class="p">,</span> <span class="n" style="color: #333;">pcoa_biplot</span></span>

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<pre style="margin: 0;"> <span id="LC131" class="line" lang="python"><span class="kn" style="font-weight: 600;">from</span> <span class="nn" style="color: #555;">._ordination_results</span> <span class="kn" style="font-weight: 600;">import</span> <span class="n" style="color: #333;">OrdinationResults</span></span>

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<pre style="margin: 0;">-<span id="LC132" class="line" lang="python"><span class="kn" style="font-weight: 600;">from</span> <span class="nn" style="color: #555;">._utils</span> <span class="kn" style="font-weight: 600;">import</span> <span class="p">(</span><span class="n" style="color: #333;">mean_and_std</span><span class="p">,</span> <span class="n" style="color: #333;">scale</span><span class="p">,</span> <span class="n" style="color: #333;">svd_rank</span><span class="p">,</span> <span class="n" style="color: #333;">corr</span><span class="p">,</span> <span class="n" style="color: #333;">e_matrix</span><span class="p">,</span> <span class="n" style="color: #333;">f_matrix</span><span class="p">)</span></span>

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<pre style="margin: 0;">+<span id="LC132" class="line" lang="python"><span class="kn" style="font-weight: 600;">from</span> <span class="nn" style="color: #555;">._utils</span> <span class="kn" style="font-weight: 600;">import</span> <span class="p">(</span><span class="n" style="color: #333;">mean_and_std</span><span class="p">,</span> <span class="n" style="color: #333;">scale</span><span class="p">,</span> <span class="n" style="color: #333;">svd_rank</span><span class="p">,</span> <span class="n" style="color: #333;">corr</span><span class="p">,</span> <span class="n" style="color: #333;">e_matrix</span><span class="p">,</span> <span class="n" style="color: #333;">f_matrix</span><span class="p">,</span></span>

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<pre style="margin: 0;">+<span id="LC133" class="line" lang="python">                     <span class="n" style="color: #333;">center_distance_matrix</span><span class="p">)</span></span>

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<pre style="margin: 0;"> <span id="LC134" class="line" lang="python"></span>

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<pre style="margin: 0;"> <span id="LC135" class="line" lang="python"><span class="n" style="color: #333;">__all__</span> <span class="o" style="font-weight: 600;">=</span> <span class="p">[</span><span class="s" style="color: #d14;">'ca'</span><span class="p">,</span> <span class="s" style="color: #d14;">'rda'</span><span class="p">,</span> <span class="s" style="color: #d14;">'cca'</span><span class="p">,</span> <span class="s" style="color: #d14;">'pcoa'</span><span class="p">,</span> <span class="s" style="color: #d14;">'pcoa_biplot'</span><span class="p">,</span> <span class="s" style="color: #d14;">'OrdinationResults'</span><span class="p">,</span></span>

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<pre style="margin: 0;"> <span id="LC136" class="line" lang="python">           <span class="s" style="color: #d14;">'mean_and_std'</span><span class="p">,</span> <span class="s" style="color: #d14;">'scale'</span><span class="p">,</span> <span class="s" style="color: #d14;">'svd_rank'</span><span class="p">,</span> <span class="s" style="color: #d14;">'corr'</span><span class="p">,</span></span>

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<pre style="margin: 0;">-<span id="LC136" class="line" lang="python">           <span class="s" style="color: #d14;">'e_matrix'</span><span class="p">,</span> <span class="s" style="color: #d14;">'f_matrix'</span><span class="p">]</span></span>

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<pre style="margin: 0;">+<span id="LC137" class="line" lang="python">           <span class="s" style="color: #d14;">'e_matrix'</span><span class="p">,</span> <span class="s" style="color: #d14;">'f_matrix'</span><span class="p"><span class="idiff left">,</span></span><span class="idiff"> </span><span class="s" style="color: #d14;"><span class="idiff right">'center_distance_matrix'</span></span><span class="p">]</span></span>

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<pre style="margin: 0;"> <span id="LC138" class="line" lang="python"></span>

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<pre style="margin: 0;"> <span id="LC139" class="line" lang="python"><span class="n" style="color: #333;">test</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">TestRunner</span><span class="p">(</span><span class="n" style="color: #333;">__file__</span><span class="p">)</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">test</span></span></pre>

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<br>

</li>

<li id="c443397cd3ce71f204a6fa99ac24c98e5fcc8b14">

<a href="https://salsa.debian.org/med-team/python-skbio/compare/3d3c45f3254533f7a7055537dba85e12078e2138...59737a89a9cfea9e36f5487d037b6dc5e014ee74#c443397cd3ce71f204a6fa99ac24c98e5fcc8b14"><strong>skbio/stats/ordination/_principal_coordinate_analysis.py</strong></a>

<hr>

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<pre style="margin: 0;"> <span id="LC6" class="line" lang="python"><span class="c" style="color: #998; font-style: italic;"># The full license is in the file COPYING.txt, distributed with this software.</span></span>

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<pre style="margin: 0;"> <span id="LC7" class="line" lang="python"><span class="c" style="color: #998; font-style: italic;"># ----------------------------------------------------------------------------</span></span>

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<pre style="margin: 0;"> <span id="LC8" class="line" lang="python"></span>

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<pre style="margin: 0;">-<span id="LC9" class="line" lang="python"><span class="kn" style="font-weight: 600;">from</span> <span class="nn" style="color: #555;">warnings</span> <span class="kn" style="font-weight: 600;">import</span> <span class="n" style="color: #333;">warn</span></span>

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<pre style="margin: 0;">-<span id="LC10" class="line" lang="python"></span>

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<pre style="margin: 0;">-<span id="LC11" class="line" lang="python"><span class="kn" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">pandas</span> <span class="k" style="font-weight: 600;">as</span> <span class="n" style="color: #333;">pd</span></span>

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<pre style="margin: 0;"> <span id="LC9" class="line" lang="python"><span class="kn" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">numpy</span> <span class="k" style="font-weight: 600;">as</span> <span class="n" style="color: #333;">np</span></span>

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<pre style="margin: 0;">+<span id="LC10" class="line" lang="python"><span class="kn" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">pandas</span> <span class="k" style="font-weight: 600;">as</span> <span class="n" style="color: #333;">pd</span></span>

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<pre style="margin: 0;">+<span id="LC11" class="line" lang="python"><span class="kn" style="font-weight: 600;">from</span> <span class="nn" style="color: #555;">numpy</span> <span class="kn" style="font-weight: 600;">import</span> <span class="n" style="color: #333;">dot</span><span class="p">,</span> <span class="n" style="color: #333;">hstack</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="13" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

</td>

<td class="diff-line-num new new_line" data-linenumber="12" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC12" class="line" lang="python"><span class="kn" style="font-weight: 600;">from</span> <span class="nn" style="color: #555;">numpy.linalg</span> <span class="kn" style="font-weight: 600;">import</span> <span class="n" style="color: #333;">qr</span><span class="p">,</span> <span class="n" style="color: #333;">svd</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="13" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="13" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC13" class="line" lang="python"><span class="kn" style="font-weight: 600;">from</span> <span class="nn" style="color: #555;">numpy.random</span> <span class="kn" style="font-weight: 600;">import</span> <span class="n" style="color: #333;">standard_normal</span></span>

</pre>

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<td class="diff-line-num old_line" data-linenumber="13" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<td class="diff-line-num new_line" data-linenumber="14" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<pre style="margin: 0;"> <span id="LC14" class="line" lang="python"><span class="kn" style="font-weight: 600;">from</span> <span class="nn" style="color: #555;">scipy.linalg</span> <span class="kn" style="font-weight: 600;">import</span> <span class="n" style="color: #333;">eigh</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="14" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

</td>

<td class="diff-line-num new new_line" data-linenumber="15" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC15" class="line" lang="python"><span class="kn" style="font-weight: 600;">from</span> <span class="nn" style="color: #555;">warnings</span> <span class="kn" style="font-weight: 600;">import</span> <span class="n" style="color: #333;">warn</span></span>

</pre>

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<td class="diff-line-num old_line" data-linenumber="14" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<td class="diff-line-num new_line" data-linenumber="16" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<td class="line_content noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;">

<pre style="margin: 0;"> <span id="LC16" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num old_line" data-linenumber="15" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<td class="diff-line-num new_line" data-linenumber="17" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<pre style="margin: 0;"> <span id="LC17" class="line" lang="python"><span class="kn" style="font-weight: 600;">from</span> <span class="nn" style="color: #555;">skbio.stats.distance</span> <span class="kn" style="font-weight: 600;">import</span> <span class="n" style="color: #333;">DistanceMatrix</span></span>

</pre>

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<td class="diff-line-num old_line" data-linenumber="16" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<td class="diff-line-num new_line" data-linenumber="18" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<pre style="margin: 0;"> <span id="LC18" class="line" lang="python"><span class="kn" style="font-weight: 600;">from</span> <span class="nn" style="color: #555;">skbio.util._decorator</span> <span class="kn" style="font-weight: 600;">import</span> <span class="n" style="color: #333;">experimental</span></span>

</pre>

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<td class="diff-line-num old_line" data-linenumber="17" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<td class="diff-line-num new_line" data-linenumber="19" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<pre style="margin: 0;"> <span id="LC19" class="line" lang="python"><span class="kn" style="font-weight: 600;">from</span> <span class="nn" style="color: #555;">._ordination_results</span> <span class="kn" style="font-weight: 600;">import</span> <span class="n" style="color: #333;">OrdinationResults</span></span>

</pre>

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<td class="diff-line-num old old_line" data-linenumber="18" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<td class="diff-line-num new_line old" data-linenumber="20" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<pre style="margin: 0;">-<span id="LC18" class="line" lang="python"><span class="kn" style="font-weight: 600;">from</span> <span class="nn" style="color: #555;">._utils</span> <span class="kn" style="font-weight: 600;">import</span> <span class="n" style="color: #333;">e_matrix</span><span class="p">,</span> <span class="n" style="color: #333;">f_matrix</span><span class="p">,</span> <span class="n" style="color: #333;">scale</span></span>

</pre>

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<td class="diff-line-num old old_line" data-linenumber="19" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<td class="diff-line-num new_line old" data-linenumber="20" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<pre style="margin: 0;">-<span id="LC19" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num old old_line" data-linenumber="20" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<td class="diff-line-num new_line old" data-linenumber="20" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<pre style="margin: 0;">-<span id="LC20" class="line" lang="python"><span class="c" style="color: #998; font-style: italic;"># - In cogent, after computing eigenvalues/vectors, the imaginary part</span></span>

</pre>

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<td class="diff-line-num old old_line" data-linenumber="21" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<td class="diff-line-num new_line old" data-linenumber="20" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<pre style="margin: 0;">-<span id="LC21" class="line" lang="python"><span class="c" style="color: #998; font-style: italic;">#   is dropped, if any. We know for a fact that the eigenvalues are</span></span>

</pre>

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<td class="diff-line-num old old_line" data-linenumber="22" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<td class="diff-line-num new_line old" data-linenumber="20" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<pre style="margin: 0;">-<span id="LC22" class="line" lang="python"><span class="c" style="color: #998; font-style: italic;">#   real, so that's not necessary, but eigenvectors can in principle</span></span>

</pre>

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<td class="diff-line-num old old_line" data-linenumber="23" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<td class="diff-line-num new_line old" data-linenumber="20" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<pre style="margin: 0;">-<span id="LC23" class="line" lang="python"><span class="c" style="color: #998; font-style: italic;">#   be complex (see for example</span></span>

</pre>

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<td class="diff-line-num old old_line" data-linenumber="24" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<td class="diff-line-num new_line old" data-linenumber="20" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<pre style="margin: 0;">-<span id="LC24" class="line" lang="python"><span class="c" style="color: #998; font-style: italic;">#   http://math.stackexchange.com/a/47807/109129 for details) and in</span></span>

</pre>

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<td class="diff-line-num old old_line" data-linenumber="25" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<td class="diff-line-num new_line old" data-linenumber="20" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<pre style="margin: 0;">-<span id="LC25" class="line" lang="python"><span class="c" style="color: #998; font-style: italic;">#   that case dropping the imaginary part means they'd no longer be</span></span>

</pre>

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<td class="diff-line-num old old_line" data-linenumber="26" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<td class="diff-line-num new_line old" data-linenumber="20" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<pre style="margin: 0;">-<span id="LC26" class="line" lang="python"><span class="c" style="color: #998; font-style: italic;">#   so, so I'm not doing that.</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="27" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="20" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC20" class="line" lang="python"><span class="kn" style="font-weight: 600;">from</span> <span class="nn" style="color: #555;">._utils</span> <span class="kn" style="font-weight: 600;">import</span> <span class="n" style="color: #333;">center_distance_matrix</span><span class="p">,</span> <span class="n" style="color: #333;">scale</span></span>

</pre>

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<pre style="margin: 0;"> <span id="LC21" class="line" lang="python"></span>

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<pre style="margin: 0;"> <span id="LC22" class="line" lang="python"></span>

</pre>

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<pre style="margin: 0;"> <span id="LC23" class="line" lang="python"><span class="nd">@experimental</span><span class="p">(</span><span class="n" style="color: #333;">as_of</span><span class="o" style="font-weight: 600;">=</span><span class="s" style="color: #d14;">"0.4.0"</span><span class="p">)</span></span>

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<pre style="margin: 0;">-<span id="LC30" class="line" lang="python"><span class="k" style="font-weight: 600;">def</span> <span class="nf" style="color: #900; font-weight: 600;">pcoa</span><span class="p">(</span><span class="n" style="color: #333;">distance_matrix</span><span class="p">):</span></span>

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<pre style="margin: 0;">+<span id="LC24" class="line" lang="python"><span class="k" style="font-weight: 600;">def</span> <span class="nf" style="color: #900; font-weight: 600;">pcoa</span><span class="p">(</span><span class="n" style="color: #333;">distance_matrix</span><span class="p">,</span> <span class="n" style="color: #333;">method</span><span class="o" style="font-weight: 600;">=</span><span class="s" style="color: #d14;">"eigh"</span><span class="p">,</span> <span class="n" style="color: #333;">number_of_dimensions</span><span class="o" style="font-weight: 600;">=</span><span class="mi" style="color: #099;">0</span><span class="p">,</span></span>

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<pre style="margin: 0;">+<span id="LC25" class="line" lang="python">         <span class="n" style="color: #333;">inplace</span><span class="o" style="font-weight: 600;">=</span><span class="bp" style="color: #999;">False</span><span class="p">):</span></span>

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<pre style="margin: 0;"> <span id="LC26" class="line" lang="python">    <span class="s" style="color: #d14;">r"""Perform Principal Coordinate Analysis.</span></span>

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<pre style="margin: 0;"> <span id="LC27" class="line" lang="python"></span>

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<pre style="margin: 0;">-<span id="LC33" class="line" lang="python"><span class="s" style="color: #d14;">    Principal Coordinate Analysis (PCoA) is a method similar to PCA</span></span>

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<pre style="margin: 0;">-<span id="LC34" class="line" lang="python"><span class="s" style="color: #d14;">    that works from distance matrices, and so it can be used with</span></span>

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<td class="diff-line-num new_line old" data-linenumber="28" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<pre style="margin: 0;">-<span id="LC35" class="line" lang="python"><span class="s" style="color: #d14;">    ecologically meaningful distances like UniFrac for bacteria.</span></span>

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<pre style="margin: 0;">+<span id="LC28" class="line" lang="python"><span class="s" style="color: #d14;">    Principal Coordinate Analysis (PCoA) is a method similar</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="36" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="29" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC29" class="line" lang="python"><span class="s" style="color: #d14;">    to Principal Components Analysis (PCA) with the difference that PCoA</span></span>

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<td class="diff-line-num new old_line" data-linenumber="36" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="30" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC30" class="line" lang="python"><span class="s" style="color: #d14;">    operates on distance matrices, typically with non-euclidian and thus</span></span>

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<td class="diff-line-num new new_line" data-linenumber="31" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC31" class="line" lang="python"><span class="s" style="color: #d14;">    ecologically meaningful distances like UniFrac in microbiome research.</span></span>

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<pre style="margin: 0;"> <span id="LC32" class="line" lang="python"></span>

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<pre style="margin: 0;"> <span id="LC33" class="line" lang="python"><span class="s" style="color: #d14;">    In ecology, the euclidean distance preserved by Principal</span></span>

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<pre style="margin: 0;"> <span id="LC34" class="line" lang="python"><span class="s" style="color: #d14;">    Component Analysis (PCA) is often not a good choice because it</span></span>

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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -44,10 +40,36 @@ def pcoa(distance_matrix):</td>

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<pre style="margin: 0;"> <span id="LC40" class="line" lang="python"><span class="s" style="color: #d14;">    species is present in two sites, that means that the sites are</span></span>

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<pre style="margin: 0;"> <span id="LC41" class="line" lang="python"><span class="s" style="color: #d14;">    similar.).</span></span>

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<pre style="margin: 0;"> <span id="LC42" class="line" lang="python"></span>

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<pre style="margin: 0;">+<span id="LC43" class="line" lang="python"><span class="s" style="color: #d14;">    Note that the returned eigenvectors are not normalized to unit length.</span></span>

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<pre style="margin: 0;">+<span id="LC44" class="line" lang="python"></span>

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<pre style="margin: 0;"> <span id="LC45" class="line" lang="python"><span class="s" style="color: #d14;">    Parameters</span></span>

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<pre style="margin: 0;"> <span id="LC46" class="line" lang="python"><span class="s" style="color: #d14;">    ----------</span></span>

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<pre style="margin: 0;"> <span id="LC47" class="line" lang="python"><span class="s" style="color: #d14;">    distance_matrix : DistanceMatrix</span></span>

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<pre style="margin: 0;"> <span id="LC48" class="line" lang="python"><span class="s" style="color: #d14;">        A distance matrix.</span></span>

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<pre style="margin: 0;">+<span id="LC49" class="line" lang="python"><span class="s" style="color: #d14;">    method : str, optional</span></span>

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<pre style="margin: 0;">+<span id="LC50" class="line" lang="python"><span class="s" style="color: #d14;">        Eigendecomposition method to use in performing PCoA.</span></span>

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<pre style="margin: 0;">+<span id="LC51" class="line" lang="python"><span class="s" style="color: #d14;">        By default, uses SciPy's `eigh`, which computes exact</span></span>

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<pre style="margin: 0;">+<span id="LC52" class="line" lang="python"><span class="s" style="color: #d14;">        eigenvectors and eigenvalues for all dimensions. The alternate</span></span>

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<pre style="margin: 0;">+<span id="LC53" class="line" lang="python"><span class="s" style="color: #d14;">        method, `fsvd`, uses faster heuristic eigendecomposition but loses</span></span>

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<pre style="margin: 0;">+<span id="LC54" class="line" lang="python"><span class="s" style="color: #d14;">        accuracy. The magnitude of accuracy lost is dependent on dataset.</span></span>

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<pre style="margin: 0;">+<span id="LC55" class="line" lang="python"><span class="s" style="color: #d14;">    number_of_dimensions : int, optional</span></span>

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<pre style="margin: 0;">+<span id="LC56" class="line" lang="python"><span class="s" style="color: #d14;">        Dimensions to reduce the distance matrix to. This number determines</span></span>

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<pre style="margin: 0;">+<span id="LC57" class="line" lang="python"><span class="s" style="color: #d14;">        how many eigenvectors and eigenvalues will be returned.</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC58" class="line" lang="python"><span class="s" style="color: #d14;">        By default, equal to the number of dimensions of the distance matrix,</span></span>

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<pre style="margin: 0;">+<span id="LC59" class="line" lang="python"><span class="s" style="color: #d14;">        as default eigendecomposition using SciPy's `eigh` method computes</span></span>

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<pre style="margin: 0;">+<span id="LC60" class="line" lang="python"><span class="s" style="color: #d14;">        all eigenvectors and eigenvalues. If using fast heuristic</span></span>

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<pre style="margin: 0;">+<span id="LC61" class="line" lang="python"><span class="s" style="color: #d14;">        eigendecomposition through `fsvd`, a desired number of dimensions</span></span>

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<pre style="margin: 0;">+<span id="LC62" class="line" lang="python"><span class="s" style="color: #d14;">        should be specified. Note that the default eigendecomposition</span></span>

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<pre style="margin: 0;">+<span id="LC63" class="line" lang="python"><span class="s" style="color: #d14;">        method `eigh` does not natively support a specifying number of</span></span>

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<pre style="margin: 0;">+<span id="LC64" class="line" lang="python"><span class="s" style="color: #d14;">        dimensions to reduce a matrix to, so if this parameter is specified,</span></span>

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<pre style="margin: 0;">+<span id="LC65" class="line" lang="python"><span class="s" style="color: #d14;">        all eigenvectors and eigenvalues will be simply be computed with no</span></span>

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<pre style="margin: 0;">+<span id="LC66" class="line" lang="python"><span class="s" style="color: #d14;">        speed gain, and only the number specified by `number_of_dimensions`</span></span>

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<pre style="margin: 0;">+<span id="LC67" class="line" lang="python"><span class="s" style="color: #d14;">        will be returned. Specifying a value of `0`, the default, will</span></span>

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<pre style="margin: 0;">+<span id="LC68" class="line" lang="python"><span class="s" style="color: #d14;">        set `number_of_dimensions` equal to the number of dimensions of the</span></span>

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<pre style="margin: 0;">+<span id="LC69" class="line" lang="python"><span class="s" style="color: #d14;">        specified `distance_matrix`.</span></span>

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<pre style="margin: 0;">+<span id="LC70" class="line" lang="python"><span class="s" style="color: #d14;">    inplace : bool, optional</span></span>

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<pre style="margin: 0;">+<span id="LC71" class="line" lang="python"><span class="s" style="color: #d14;">        If true, centers a distance matrix in-place in a manner that reduces</span></span>

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<pre style="margin: 0;">+<span id="LC72" class="line" lang="python"><span class="s" style="color: #d14;">        memory consumption.</span></span>

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<pre style="margin: 0;"> <span id="LC73" class="line" lang="python"></span>

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<pre style="margin: 0;"> <span id="LC74" class="line" lang="python"><span class="s" style="color: #d14;">    Returns</span></span>

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<pre style="margin: 0;"> <span id="LC75" class="line" lang="python"><span class="s" style="color: #d14;">    -------</span></span>

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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -62,37 +84,56 @@ def pcoa(distance_matrix):</td>

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<pre style="margin: 0;"> <span id="LC84" class="line" lang="python"></span>

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<pre style="margin: 0;"> <span id="LC85" class="line" lang="python"><span class="s" style="color: #d14;">    Notes</span></span>

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<pre style="margin: 0;"> <span id="LC86" class="line" lang="python"><span class="s" style="color: #d14;">    -----</span></span>

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<pre style="margin: 0;">-<span id="LC65" class="line" lang="python"><span class="s" style="color: #d14;">    It is sometimes known as metric multidimensional scaling or</span></span>

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<pre style="margin: 0;">-<span id="LC66" class="line" lang="python"><span class="s" style="color: #d14;">    classical scaling.</span></span>

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<pre style="margin: 0;">-<span id="LC67" class="line" lang="python"></span>

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<pre style="margin: 0;">-<span id="LC68" class="line" lang="python"><span class="s" style="color: #d14;">    .. note::</span></span>

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<pre style="margin: 0;">-<span id="LC69" class="line" lang="python"></span>

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<pre style="margin: 0;">-<span id="LC70" class="line" lang="python"><span class="s" style="color: #d14;">       If the distance is not euclidean (for example if it is a</span></span>

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<pre style="margin: 0;">-<span id="LC71" class="line" lang="python"><span class="s" style="color: #d14;">       semimetric and the triangle inequality doesn't hold),</span></span>

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<pre style="margin: 0;">-<span id="LC72" class="line" lang="python"><span class="s" style="color: #d14;">       negative eigenvalues can appear. There are different ways</span></span>

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<pre style="margin: 0;">-<span id="LC73" class="line" lang="python"><span class="s" style="color: #d14;">       to deal with that problem (see Legendre & Legendre 1998, \S</span></span>

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<pre style="margin: 0;">-<span id="LC74" class="line" lang="python"><span class="s" style="color: #d14;">       9.2.3), but none are currently implemented here.</span></span>

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<pre style="margin: 0;">-<span id="LC75" class="line" lang="python"></span>

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<pre style="margin: 0;">-<span id="LC76" class="line" lang="python"><span class="s" style="color: #d14;">       However, a warning is raised whenever negative eigenvalues</span></span>

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<pre style="margin: 0;">-<span id="LC77" class="line" lang="python"><span class="s" style="color: #d14;">       appear, allowing the user to decide if they can be safely</span></span>

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<pre style="margin: 0;">-<span id="LC78" class="line" lang="python"><span class="s" style="color: #d14;">       ignored.</span></span>

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<pre style="margin: 0;">+<span id="LC87" class="line" lang="python"><span class="s" style="color: #d14;">    .. note:: If the distance is not euclidean (for example if it is a</span></span>

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<pre style="margin: 0;">+<span id="LC88" class="line" lang="python"><span class="s" style="color: #d14;">        semimetric and the triangle inequality doesn't hold),</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC89" class="line" lang="python"><span class="s" style="color: #d14;">        negative eigenvalues can appear. There are different ways</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC90" class="line" lang="python"><span class="s" style="color: #d14;">        to deal with that problem (see Legendre & Legendre 1998, \S</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="91" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC91" class="line" lang="python"><span class="s" style="color: #d14;">        9.2.3), but none are currently implemented here.</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="79" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="92" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC92" class="line" lang="python"><span class="s" style="color: #d14;">        However, a warning is raised whenever negative eigenvalues</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="79" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="93" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC93" class="line" lang="python"><span class="s" style="color: #d14;">        appear, allowing the user to decide if they can be safely</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="94" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC94" class="line" lang="python"><span class="s" style="color: #d14;">        ignored.</span></span>

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<pre style="margin: 0;"> <span id="LC95" class="line" lang="python"><span class="s" style="color: #d14;">    """</span></span>

</pre>

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<pre style="margin: 0;"> <span id="LC96" class="line" lang="python">    <span class="n" style="color: #333;">distance_matrix</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">DistanceMatrix</span><span class="p">(</span><span class="n" style="color: #333;">distance_matrix</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num new_line" data-linenumber="97" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<pre style="margin: 0;"> <span id="LC97" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num old old_line" data-linenumber="82" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<td class="diff-line-num new_line old" data-linenumber="98" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<pre style="margin: 0;">-<span id="LC82" class="line" lang="python">    <span class="n" style="color: #333;">E_matrix</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">e_matrix</span><span class="p">(</span><span class="n" style="color: #333;">distance_matrix</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">data</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num old old_line" data-linenumber="83" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<td class="diff-line-num new_line old" data-linenumber="98" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<pre style="margin: 0;">-<span id="LC83" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num old old_line" data-linenumber="84" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<td class="diff-line-num new_line old" data-linenumber="98" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<pre style="margin: 0;">-<span id="LC84" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># If the used distance was euclidean, pairwise distances</span></span>

</pre>

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<td class="diff-line-num old old_line" data-linenumber="85" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<td class="diff-line-num new_line old" data-linenumber="98" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<pre style="margin: 0;">-<span id="LC85" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># needn't be computed from the data table Y because F_matrix =</span></span>

</pre>

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<td class="diff-line-num old old_line" data-linenumber="86" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<td class="diff-line-num new_line old" data-linenumber="98" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<pre style="margin: 0;">-<span id="LC86" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># Y.dot(Y.T) (if Y has been centred).</span></span>

</pre>

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<td class="diff-line-num old old_line" data-linenumber="87" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<td class="diff-line-num new_line old" data-linenumber="98" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<pre style="margin: 0;">-<span id="LC87" class="line" lang="python">    <span class="n" style="color: #333;">F_matrix</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">f_matrix</span><span class="p">(</span><span class="n" style="color: #333;">E_matrix</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num old old_line" data-linenumber="88" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<td class="diff-line-num new_line old" data-linenumber="98" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<pre style="margin: 0;">-<span id="LC88" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num old old_line" data-linenumber="89" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<td class="diff-line-num new_line old" data-linenumber="98" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<pre style="margin: 0;">-<span id="LC89" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># If the eigendecomposition ever became a bottleneck, it could</span></span>

</pre>

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<td class="diff-line-num new_line old" data-linenumber="98" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<pre style="margin: 0;">-<span id="LC90" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># be replaced with an iterative version that computes the</span></span>

</pre>

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<td class="diff-line-num old old_line" data-linenumber="91" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<td class="diff-line-num new_line old" data-linenumber="98" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<pre style="margin: 0;">-<span id="LC91" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># largest k eigenvectors.</span></span>

</pre>

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<td class="diff-line-num old old_line" data-linenumber="92" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<pre style="margin: 0;">-<span id="LC92" class="line" lang="python">    <span class="n" style="color: #333;">eigvals</span><span class="p">,</span> <span class="n" style="color: #333;">eigvecs</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">eigh</span><span class="p">(</span><span class="n" style="color: #333;">F_matrix</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num old old_line" data-linenumber="93" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<td class="diff-line-num new_line old" data-linenumber="98" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<pre style="margin: 0;">-<span id="LC93" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num old old_line" data-linenumber="94" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<td class="diff-line-num new_line old" data-linenumber="98" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<pre style="margin: 0;">-<span id="LC94" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># eigvals might not be ordered, so we order them (at least one</span></span>

</pre>

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<td class="diff-line-num old old_line" data-linenumber="95" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<td class="diff-line-num new_line old" data-linenumber="98" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<pre style="margin: 0;">-<span id="LC95" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># is zero). cogent makes eigenvalues positive by taking the</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="96" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="98" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC98" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># Center distance matrix, a requirement for PCoA here</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="96" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="99" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC99" class="line" lang="python">    <span class="n" style="color: #333;">matrix_data</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">center_distance_matrix</span><span class="p">(</span><span class="n" style="color: #333;">distance_matrix</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">data</span><span class="p">,</span> <span class="n" style="color: #333;">inplace</span><span class="o" style="font-weight: 600;">=</span><span class="n" style="color: #333;">inplace</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="100" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

100

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<pre style="margin: 0;">+<span id="LC100" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="96" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="101" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

101

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<pre style="margin: 0;">+<span id="LC101" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># If no dimension specified, by default will compute all eigenvectors</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="96" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="102" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC102" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># and eigenvalues</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="96" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="103" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

103

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<pre style="margin: 0;">+<span id="LC103" class="line" lang="python">    <span class="k" style="font-weight: 600;">if</span> <span class="n" style="color: #333;">number_of_dimensions</span> <span class="o" style="font-weight: 600;">==</span> <span class="mi" style="color: #099;">0</span><span class="p">:</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="96" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="104" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

104

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<pre style="margin: 0;">+<span id="LC104" class="line" lang="python">        <span class="k" style="font-weight: 600;">if</span> <span class="n" style="color: #333;">method</span> <span class="o" style="font-weight: 600;">==</span> <span class="s" style="color: #d14;">"fsvd"</span> <span class="ow" style="font-weight: 600;">and</span> <span class="n" style="color: #333;">matrix_data</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">shape</span><span class="p">[</span><span class="mi" style="color: #099;">0</span><span class="p">]</span> <span class="o" style="font-weight: 600;">></span> <span class="mi" style="color: #099;">10</span><span class="p">:</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="96" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="105" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC105" class="line" lang="python">            <span class="n" style="color: #333;">warn</span><span class="p">(</span><span class="s" style="color: #d14;">"FSVD: since no value for number_of_dimensions is specified, "</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="96" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="106" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC106" class="line" lang="python">                 <span class="s" style="color: #d14;">"PCoA for all dimensions will be computed, which may "</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="96" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="107" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

107

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<pre style="margin: 0;">+<span id="LC107" class="line" lang="python">                 <span class="s" style="color: #d14;">"result in long computation time if the original "</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="96" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="108" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC108" class="line" lang="python">                 <span class="s" style="color: #d14;">"distance matrix is large."</span><span class="p">,</span> <span class="nb" style="color: #0086b3;">RuntimeWarning</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="109" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

109

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<pre style="margin: 0;">+<span id="LC109" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="96" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="110" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC110" class="line" lang="python">        <span class="c" style="color: #998; font-style: italic;"># distance_matrix is guaranteed to be square</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="111" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC111" class="line" lang="python">        <span class="n" style="color: #333;">number_of_dimensions</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">matrix_data</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">shape</span><span class="p">[</span><span class="mi" style="color: #099;">0</span><span class="p">]</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="96" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="112" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

112

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<pre style="margin: 0;">+<span id="LC112" class="line" lang="python">    <span class="k" style="font-weight: 600;">elif</span> <span class="n" style="color: #333;">number_of_dimensions</span> <span class="o" style="font-weight: 600;"><</span> <span class="mi" style="color: #099;">0</span><span class="p">:</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="96" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="113" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

113

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<pre style="margin: 0;">+<span id="LC113" class="line" lang="python">        <span class="k" style="font-weight: 600;">raise</span> <span class="nb" style="color: #0086b3;">ValueError</span><span class="p">(</span><span class="s" style="color: #d14;">'Invalid operation: cannot reduce distance matrix '</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="96" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="114" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

114

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<pre style="margin: 0;">+<span id="LC114" class="line" lang="python">                         <span class="s" style="color: #d14;">'to negative dimensions using PCoA. Did you intend '</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="96" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="115" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

115

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<pre style="margin: 0;">+<span id="LC115" class="line" lang="python">                         <span class="s" style="color: #d14;">'to specify the default value "0", which sets '</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="96" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="116" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

116

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<pre style="margin: 0;">+<span id="LC116" class="line" lang="python">                         <span class="s" style="color: #d14;">'the number_of_dimensions equal to the '</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="96" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="117" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

117

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<pre style="margin: 0;">+<span id="LC117" class="line" lang="python">                         <span class="s" style="color: #d14;">'dimensionality of the given distance matrix?'</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="96" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="118" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC118" class="line" lang="python"></span>

</pre>

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<pre style="margin: 0;">+<span id="LC119" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># Perform eigendecomposition</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC120" class="line" lang="python">    <span class="k" style="font-weight: 600;">if</span> <span class="n" style="color: #333;">method</span> <span class="o" style="font-weight: 600;">==</span> <span class="s" style="color: #d14;">"eigh"</span><span class="p">:</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="121" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC121" class="line" lang="python">        <span class="c" style="color: #998; font-style: italic;"># eigh does not natively support specifying number_of_dimensions, i.e.</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC122" class="line" lang="python">        <span class="c" style="color: #998; font-style: italic;"># there are no speed gains unlike in FSVD. Later, we slice off unwanted</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC123" class="line" lang="python">        <span class="c" style="color: #998; font-style: italic;"># dimensions to conform the result of eigh to the specified</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="124" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC124" class="line" lang="python">        <span class="c" style="color: #998; font-style: italic;"># number_of_dimensions.</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC125" class="line" lang="python"></span>

</pre>

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<pre style="margin: 0;">+<span id="LC126" class="line" lang="python">        <span class="n" style="color: #333;">eigvals</span><span class="p">,</span> <span class="n" style="color: #333;">eigvecs</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">eigh</span><span class="p">(</span><span class="n" style="color: #333;">matrix_data</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="127" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC127" class="line" lang="python">        <span class="n" style="color: #333;">long_method_name</span> <span class="o" style="font-weight: 600;">=</span> <span class="s" style="color: #d14;">"Principal Coordinate Analysis"</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="128" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC128" class="line" lang="python">    <span class="k" style="font-weight: 600;">elif</span> <span class="n" style="color: #333;">method</span> <span class="o" style="font-weight: 600;">==</span> <span class="s" style="color: #d14;">"fsvd"</span><span class="p">:</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="129" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC129" class="line" lang="python">        <span class="n" style="color: #333;">eigvals</span><span class="p">,</span> <span class="n" style="color: #333;">eigvecs</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">_fsvd</span><span class="p">(</span><span class="n" style="color: #333;">matrix_data</span><span class="p">,</span> <span class="n" style="color: #333;">number_of_dimensions</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="130" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC130" class="line" lang="python">        <span class="n" style="color: #333;">long_method_name</span> <span class="o" style="font-weight: 600;">=</span> <span class="s" style="color: #d14;">"Approximate Principal Coordinate Analysis "</span> \</span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="131" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC131" class="line" lang="python">                           <span class="s" style="color: #d14;">"using FSVD"</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="132" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC132" class="line" lang="python">    <span class="k" style="font-weight: 600;">else</span><span class="p">:</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC133" class="line" lang="python">        <span class="k" style="font-weight: 600;">raise</span> <span class="nb" style="color: #0086b3;">ValueError</span><span class="p">(</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="134" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC134" class="line" lang="python">            <span class="s" style="color: #d14;">"PCoA eigendecomposition method {} not supported."</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">format</span><span class="p">(</span><span class="n" style="color: #333;">method</span><span class="p">))</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="135" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC135" class="line" lang="python"></span>

</pre>

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<pre style="margin: 0;">+<span id="LC136" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># cogent makes eigenvalues positive by taking the</span></span>

</pre>

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<pre style="margin: 0;"> <span id="LC137" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># abs value, but that doesn't seem to be an approach accepted</span></span>

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<pre style="margin: 0;"> <span id="LC138" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># by L&L to deal with negative eigenvalues. We raise a warning</span></span>

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<pre style="margin: 0;"> <span id="LC139" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># in that case. First, we make values close to 0 equal to 0.</span></span>

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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -109,18 +150,14 @@ def pcoa(distance_matrix):</td>

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<pre style="margin: 0;"> <span id="LC150" class="line" lang="python">            <span class="s" style="color: #d14;">" {0} and the largest is {1}."</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">format</span><span class="p">(</span><span class="n" style="color: #333;">eigvals</span><span class="o" style="font-weight: 600;">.</span><span class="nb" style="color: #0086b3;">min</span><span class="p">(),</span></span>

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<pre style="margin: 0;"> <span id="LC151" class="line" lang="python">                                                  <span class="n" style="color: #333;">eigvals</span><span class="o" style="font-weight: 600;">.</span><span class="nb" style="color: #0086b3;">max</span><span class="p">()),</span></span>

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<pre style="margin: 0;"> <span id="LC152" class="line" lang="python">            <span class="nb" style="color: #0086b3;">RuntimeWarning</span></span>

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<pre style="margin: 0;">-<span id="LC112" class="line" lang="python">            <span class="p">)</span></span>

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<pre style="margin: 0;">+<span id="LC153" class="line" lang="python">        <span class="p">)</span></span>

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<pre style="margin: 0;">+<span id="LC154" class="line" lang="python"></span>

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<pre style="margin: 0;">+<span id="LC155" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># eigvals might not be ordered, so we first sort them, then analogously</span></span>

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<pre style="margin: 0;">+<span id="LC156" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># sort the eigenvectors by the ordering of the eigenvalues too</span></span>

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<pre style="margin: 0;"> <span id="LC157" class="line" lang="python">    <span class="n" style="color: #333;">idxs_descending</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">eigvals</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">argsort</span><span class="p">()[::</span><span class="o" style="font-weight: 600;">-</span><span class="mi" style="color: #099;">1</span><span class="p">]</span></span>

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<pre style="margin: 0;"> <span id="LC158" class="line" lang="python">    <span class="n" style="color: #333;">eigvals</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">eigvals</span><span class="p">[</span><span class="n" style="color: #333;">idxs_descending</span><span class="p">]</span></span>

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<pre style="margin: 0;"> <span id="LC159" class="line" lang="python">    <span class="n" style="color: #333;">eigvecs</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">eigvecs</span><span class="p">[:,</span> <span class="n" style="color: #333;">idxs_descending</span><span class="p">]</span></span>

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<pre style="margin: 0;"> <span id="LC160" class="line" lang="python"></span>

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<pre style="margin: 0;">-<span id="LC117" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># Scale eigenvalues to have lenght = sqrt(eigenvalue). This</span></span>

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<pre style="margin: 0;">-<span id="LC118" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># works because np.linalg.eigh returns normalized</span></span>

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<pre style="margin: 0;">-<span id="LC119" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># eigenvectors. Each row contains the coordinates of the</span></span>

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<pre style="margin: 0;">-<span id="LC120" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># objects in the space of principal coordinates. Note that at</span></span>

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<pre style="margin: 0;">-<span id="LC121" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># least one eigenvalue is zero because only n-1 axes are</span></span>

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<pre style="margin: 0;">-<span id="LC122" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># needed to represent n points in an euclidean space.</span></span>

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<pre style="margin: 0;">-<span id="LC123" class="line" lang="python"></span>

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<pre style="margin: 0;"> <span id="LC161" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># If we return only the coordinates that make sense (i.e., that have a</span></span>

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<pre style="margin: 0;"> <span id="LC162" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># corresponding positive eigenvalue), then Jackknifed Beta Diversity</span></span>

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<pre style="margin: 0;"> <span id="LC163" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># won't work as it expects all the OrdinationResults to have the same</span></span>

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<pre style="margin: 0;"> <span id="LC167" class="line" lang="python">    <span class="n" style="color: #333;">eigvecs</span><span class="p">[:,</span> <span class="n" style="color: #333;">num_positive</span><span class="p">:]</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">np</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">zeros</span><span class="p">(</span><span class="n" style="color: #333;">eigvecs</span><span class="p">[:,</span> <span class="n" style="color: #333;">num_positive</span><span class="p">:]</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">shape</span><span class="p">)</span></span>

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<pre style="margin: 0;"> <span id="LC168" class="line" lang="python">    <span class="n" style="color: #333;">eigvals</span><span class="p">[</span><span class="n" style="color: #333;">num_positive</span><span class="p">:]</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">np</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">zeros</span><span class="p">(</span><span class="n" style="color: #333;">eigvals</span><span class="p">[</span><span class="n" style="color: #333;">num_positive</span><span class="p">:]</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">shape</span><span class="p">)</span></span>

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<pre style="margin: 0;"> <span id="LC169" class="line" lang="python"></span>

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<pre style="margin: 0;">+<span id="LC170" class="line" lang="python">    <span class="k" style="font-weight: 600;">if</span> <span class="n" style="color: #333;">method</span> <span class="o" style="font-weight: 600;">==</span> <span class="s" style="color: #d14;">"fsvd"</span><span class="p">:</span></span>

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<pre style="margin: 0;">+<span id="LC171" class="line" lang="python">        <span class="c" style="color: #998; font-style: italic;"># Since the dimension parameter, hereafter referred to as 'd',</span></span>

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<pre style="margin: 0;">+<span id="LC172" class="line" lang="python">        <span class="c" style="color: #998; font-style: italic;"># restricts the number of eigenvalues and eigenvectors that FSVD</span></span>

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<pre style="margin: 0;">+<span id="LC173" class="line" lang="python">        <span class="c" style="color: #998; font-style: italic;"># computes, we need to use an alternative method to compute the sum</span></span>

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<pre style="margin: 0;">+<span id="LC174" class="line" lang="python">        <span class="c" style="color: #998; font-style: italic;"># of all eigenvalues, used to compute the array of proportions</span></span>

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<pre style="margin: 0;">+<span id="LC175" class="line" lang="python">        <span class="c" style="color: #998; font-style: italic;"># explained. Otherwise, the proportions calculated will only be</span></span>

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<pre style="margin: 0;">+<span id="LC176" class="line" lang="python">        <span class="c" style="color: #998; font-style: italic;"># relative to d number of dimensions computed; whereas we want</span></span>

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<pre style="margin: 0;">+<span id="LC177" class="line" lang="python">        <span class="c" style="color: #998; font-style: italic;"># it to be relative to the entire dimensionality of the</span></span>

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<pre style="margin: 0;">+<span id="LC178" class="line" lang="python">        <span class="c" style="color: #998; font-style: italic;"># centered distance matrix.</span></span>

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<pre style="margin: 0;">+<span id="LC179" class="line" lang="python"></span>

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<pre style="margin: 0;">+<span id="LC180" class="line" lang="python">        <span class="c" style="color: #998; font-style: italic;"># An alternative method of calculating th sum of eigenvalues is by</span></span>

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<pre style="margin: 0;">+<span id="LC181" class="line" lang="python">        <span class="c" style="color: #998; font-style: italic;"># computing the trace of the centered distance matrix.</span></span>

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<pre style="margin: 0;">+<span id="LC182" class="line" lang="python">        <span class="c" style="color: #998; font-style: italic;"># See proof outlined here: https://goo.gl/VAYiXx</span></span>

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<pre style="margin: 0;">+<span id="LC183" class="line" lang="python">        <span class="n" style="color: #333;">sum_eigenvalues</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">np</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">trace</span><span class="p">(</span><span class="n" style="color: #333;">matrix_data</span><span class="p">)</span></span>

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<pre style="margin: 0;">+<span id="LC184" class="line" lang="python">    <span class="k" style="font-weight: 600;">else</span><span class="p">:</span></span>

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<pre style="margin: 0;">+<span id="LC185" class="line" lang="python">        <span class="c" style="color: #998; font-style: italic;"># Calculate proportions the usual way</span></span>

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<pre style="margin: 0;">+<span id="LC186" class="line" lang="python">        <span class="n" style="color: #333;">sum_eigenvalues</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">np</span><span class="o" style="font-weight: 600;">.</span><span class="nb" style="color: #0086b3;">sum</span><span class="p">(</span><span class="n" style="color: #333;">eigvals</span><span class="p">)</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC187" class="line" lang="python"></span>

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<pre style="margin: 0;">+<span id="LC188" class="line" lang="python">    <span class="n" style="color: #333;">proportion_explained</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">eigvals</span> <span class="o" style="font-weight: 600;">/</span> <span class="n" style="color: #333;">sum_eigenvalues</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC189" class="line" lang="python"></span>

</pre>

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<pre style="margin: 0;">+<span id="LC190" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># In case eigh is used, eigh computes all eigenvectors and -values.</span></span>

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<pre style="margin: 0;">+<span id="LC191" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># So if number_of_dimensions was specified, we manually need to ensure</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC192" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># only the requested number of dimensions</span></span>

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<pre style="margin: 0;">+<span id="LC193" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># (number of eigenvectors and eigenvalues, respectively) are returned.</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC194" class="line" lang="python">    <span class="n" style="color: #333;">eigvecs</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">eigvecs</span><span class="p">[:,</span> <span class="p">:</span><span class="n" style="color: #333;">number_of_dimensions</span><span class="p">]</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC195" class="line" lang="python">    <span class="n" style="color: #333;">eigvals</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">eigvals</span><span class="p">[:</span><span class="n" style="color: #333;">number_of_dimensions</span><span class="p">]</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC196" class="line" lang="python">    <span class="n" style="color: #333;">proportion_explained</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">proportion_explained</span><span class="p">[:</span><span class="n" style="color: #333;">number_of_dimensions</span><span class="p">]</span></span>

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<pre style="margin: 0;">+<span id="LC197" class="line" lang="python"></span>

</pre>

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<pre style="margin: 0;">+<span id="LC198" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># Scale eigenvalues to have length = sqrt(eigenvalue). This</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC199" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># works because np.linalg.eigh returns normalized</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC200" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># eigenvectors. Each row contains the coordinates of the</span></span>

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<pre style="margin: 0;">+<span id="LC201" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># objects in the space of principal coordinates. Note that at</span></span>

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<pre style="margin: 0;">+<span id="LC202" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># least one eigenvalue is zero because only n-1 axes are</span></span>

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<pre style="margin: 0;">+<span id="LC203" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># needed to represent n points in a euclidean space.</span></span>

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<pre style="margin: 0;"> <span id="LC204" class="line" lang="python">    <span class="n" style="color: #333;">coordinates</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">eigvecs</span> <span class="o" style="font-weight: 600;">*</span> <span class="n" style="color: #333;">np</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">sqrt</span><span class="p">(</span><span class="n" style="color: #333;">eigvals</span><span class="p">)</span></span>

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<pre style="margin: 0;">-<span id="LC134" class="line" lang="python">    <span class="n" style="color: #333;">proportion_explained</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">eigvals</span> <span class="o" style="font-weight: 600;">/</span> <span class="n" style="color: #333;">eigvals</span><span class="o" style="font-weight: 600;">.</span><span class="nb" style="color: #0086b3;">sum</span><span class="p">()</span></span>

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<pre style="margin: 0;"> <span id="LC205" class="line" lang="python"></span>

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<pre style="margin: 0;">-<span id="LC136" class="line" lang="python">    <span class="n" style="color: #333;">axis_labels</span> <span class="o" style="font-weight: 600;">=</span> <span class="p">[</span><span class="s" style="color: #d14;"><span class="idiff left">'PC</span></span><span class="si" style="color: #d14;"><span class="idiff">%</span></span><span class="s" style="color: #d14;"><span class="idiff">d'</span></span><span class="idiff"> </span><span class="o" style="font-weight: 600;"><span class="idiff">%</span></span><span class="idiff"> </span><span class="n" style="color: #333;"><span class="idiff">i</span></span><span class="idiff"> </span><span class="k" style="font-weight: 600;"><span class="idiff">for</span></span><span class="idiff"> </span><span class="n" style="color: #333;"><span class="idiff">i</span></span><span class="idiff"> </span><span class="ow" style="font-weight: 600;"><span class="idiff">in</span></span><span class="idiff"> </span><span class="nb" style="color: #0086b3;"><span class="idiff">range</span></span><span class="p"><span class="idiff">(</span></span><span class="mi" style="color: #099;"><span class="idiff">1</span></span><span class="p"><span class="idiff">,</span></span><span class="idiff"> </span><span class="n" style="color: #333;"><span class="idiff">eigvals</span></span><span class="o" style="font-weight: 600;"><span class="idiff">.</span></span><span class="n" style="color: #333;"><span class="idiff right">size</span></span> <span class="o" style="font-weight: 600;">+</span> <span class="mi" style="color: #099;">1</span><span class="p">)]</span></span>

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<pre style="margin: 0;">+<span id="LC206" class="line" lang="python">    <span class="n" style="color: #333;">axis_labels</span> <span class="o" style="font-weight: 600;">=</span> <span class="p">[</span><span class="s" style="color: #d14;"><span class="idiff left">"PC</span></span><span class="si" style="color: #d14;"><span class="idiff">%</span></span><span class="s" style="color: #d14;"><span class="idiff">d"</span></span><span class="idiff"> </span><span class="o" style="font-weight: 600;"><span class="idiff">%</span></span><span class="idiff"> </span><span class="n" style="color: #333;"><span class="idiff">i</span></span><span class="idiff"> </span><span class="k" style="font-weight: 600;"><span class="idiff">for</span></span><span class="idiff"> </span><span class="n" style="color: #333;"><span class="idiff">i</span></span><span class="idiff"> </span><span class="ow" style="font-weight: 600;"><span class="idiff">in</span></span><span class="idiff"> </span><span class="nb" style="color: #0086b3;"><span class="idiff">range</span></span><span class="p"><span class="idiff">(</span></span><span class="mi" style="color: #099;"><span class="idiff">1</span></span><span class="p"><span class="idiff">,</span></span><span class="idiff"> </span><span class="n" style="color: #333;"><span class="idiff right">number_of_dimensions</span></span> <span class="o" style="font-weight: 600;">+</span> <span class="mi" style="color: #099;">1</span><span class="p">)]</span></span>

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<pre style="margin: 0;"> <span id="LC207" class="line" lang="python">    <span class="k" style="font-weight: 600;">return</span> <span class="n" style="color: #333;">OrdinationResults</span><span class="p">(</span></span>

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<pre style="margin: 0;">-<span id="LC138" class="line" lang="python">        <span class="n" style="color: #333;">short_method_name</span><span class="o" style="font-weight: 600;">=</span><span class="s" style="color: #d14;"><span class="idiff left right">'PCoA'</span></span><span class="p">,</span></span>

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<pre style="margin: 0;">-<span id="LC139" class="line" lang="python">        <span class="n" style="color: #333;">long_method_name</span><span class="o" style="font-weight: 600;">=</span><span class="s" style="color: #d14;"><span class="idiff left right">'Principal Coordinate Analysis'</span></span><span class="p">,</span></span>

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<pre style="margin: 0;">+<span id="LC208" class="line" lang="python">        <span class="n" style="color: #333;">short_method_name</span><span class="o" style="font-weight: 600;">=</span><span class="s" style="color: #d14;"><span class="idiff left right">"PCoA"</span></span><span class="p">,</span></span>

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<pre style="margin: 0;">+<span id="LC209" class="line" lang="python">        <span class="n" style="color: #333;">long_method_name</span><span class="o" style="font-weight: 600;">=</span><span class="n" style="color: #333;"><span class="idiff left right">long_method_name</span></span><span class="p">,</span></span>

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<pre style="margin: 0;"> <span id="LC210" class="line" lang="python">        <span class="n" style="color: #333;">eigvals</span><span class="o" style="font-weight: 600;">=</span><span class="n" style="color: #333;">pd</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">Series</span><span class="p">(</span><span class="n" style="color: #333;">eigvals</span><span class="p">,</span> <span class="n" style="color: #333;">index</span><span class="o" style="font-weight: 600;">=</span><span class="n" style="color: #333;">axis_labels</span><span class="p">),</span></span>

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<pre style="margin: 0;"> <span id="LC211" class="line" lang="python">        <span class="n" style="color: #333;">samples</span><span class="o" style="font-weight: 600;">=</span><span class="n" style="color: #333;">pd</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">DataFrame</span><span class="p">(</span><span class="n" style="color: #333;">coordinates</span><span class="p">,</span> <span class="n" style="color: #333;">index</span><span class="o" style="font-weight: 600;">=</span><span class="n" style="color: #333;">distance_matrix</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">ids</span><span class="p">,</span></span>

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<pre style="margin: 0;"> <span id="LC212" class="line" lang="python">                             <span class="n" style="color: #333;">columns</span><span class="o" style="font-weight: 600;">=</span><span class="n" style="color: #333;">axis_labels</span><span class="p">),</span></span>

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<pre style="margin: 0;"> <span id="LC214" class="line" lang="python">                                       <span class="n" style="color: #333;">index</span><span class="o" style="font-weight: 600;">=</span><span class="n" style="color: #333;">axis_labels</span><span class="p">))</span></span>

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<pre style="margin: 0;"> <span id="LC215" class="line" lang="python"></span>

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<pre style="margin: 0;"> <span id="LC216" class="line" lang="python"></span>

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<pre style="margin: 0;">+<span id="LC217" class="line" lang="python"><span class="k" style="font-weight: 600;">def</span> <span class="nf" style="color: #900; font-weight: 600;">_fsvd</span><span class="p">(</span><span class="n" style="color: #333;">centered_distance_matrix</span><span class="p">,</span> <span class="n" style="color: #333;">number_of_dimensions</span><span class="o" style="font-weight: 600;">=</span><span class="mi" style="color: #099;">10</span><span class="p">):</span></span>

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<pre style="margin: 0;">+<span id="LC218" class="line" lang="python">    <span class="s" style="color: #d14;">"""</span></span>

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<pre style="margin: 0;">+<span id="LC219" class="line" lang="python"><span class="s" style="color: #d14;">    Performs singular value decomposition, or more specifically in</span></span>

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<pre style="margin: 0;">+<span id="LC220" class="line" lang="python"><span class="s" style="color: #d14;">    this case eigendecomposition, using fast heuristic algorithm</span></span>

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<pre style="margin: 0;">+<span id="LC221" class="line" lang="python"><span class="s" style="color: #d14;">    nicknamed "FSVD" (FastSVD), adapted and optimized from the algorithm</span></span>

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<pre style="margin: 0;">+<span id="LC222" class="line" lang="python"><span class="s" style="color: #d14;">    described by Halko et al (2011).</span></span>

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<pre style="margin: 0;">+<span id="LC223" class="line" lang="python"></span>

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<pre style="margin: 0;">+<span id="LC224" class="line" lang="python"><span class="s" style="color: #d14;">    Parameters</span></span>

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<pre style="margin: 0;">+<span id="LC225" class="line" lang="python"><span class="s" style="color: #d14;">    ----------</span></span>

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<pre style="margin: 0;">+<span id="LC226" class="line" lang="python"><span class="s" style="color: #d14;">    centered_distance_matrix : np.array</span></span>

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<pre style="margin: 0;">+<span id="LC227" class="line" lang="python"><span class="s" style="color: #d14;">       Numpy matrix representing the distance matrix for which the</span></span>

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<pre style="margin: 0;">+<span id="LC228" class="line" lang="python"><span class="s" style="color: #d14;">       eigenvectors and eigenvalues shall be computed</span></span>

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<pre style="margin: 0;">+<span id="LC229" class="line" lang="python"><span class="s" style="color: #d14;">    number_of_dimensions : int</span></span>

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<pre style="margin: 0;">+<span id="LC230" class="line" lang="python"><span class="s" style="color: #d14;">       Number of dimensions to keep. Must be lower than or equal to the</span></span>

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<pre style="margin: 0;">+<span id="LC231" class="line" lang="python"><span class="s" style="color: #d14;">       rank of the given distance_matrix.</span></span>

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<pre style="margin: 0;">+<span id="LC232" class="line" lang="python"></span>

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<pre style="margin: 0;">+<span id="LC233" class="line" lang="python"><span class="s" style="color: #d14;">    Returns</span></span>

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<pre style="margin: 0;">+<span id="LC234" class="line" lang="python"><span class="s" style="color: #d14;">    -------</span></span>

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<pre style="margin: 0;">+<span id="LC235" class="line" lang="python"><span class="s" style="color: #d14;">    np.array</span></span>

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<pre style="margin: 0;">+<span id="LC236" class="line" lang="python"><span class="s" style="color: #d14;">       Array of eigenvectors, each with number_of_dimensions length.</span></span>

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<pre style="margin: 0;">+<span id="LC237" class="line" lang="python"><span class="s" style="color: #d14;">    np.array</span></span>

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<pre style="margin: 0;">+<span id="LC238" class="line" lang="python"><span class="s" style="color: #d14;">       Array of eigenvalues, a total number of number_of_dimensions.</span></span>

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<pre style="margin: 0;">+<span id="LC239" class="line" lang="python"></span>

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<pre style="margin: 0;">+<span id="LC240" class="line" lang="python"><span class="s" style="color: #d14;">    Notes</span></span>

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<pre style="margin: 0;">+<span id="LC241" class="line" lang="python"><span class="s" style="color: #d14;">    -----</span></span>

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<pre style="margin: 0;">+<span id="LC242" class="line" lang="python"><span class="s" style="color: #d14;">    The algorithm is based on 'An Algorithm for the Principal</span></span>

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<pre style="margin: 0;">+<span id="LC243" class="line" lang="python"><span class="s" style="color: #d14;">    Component analysis of Large Data Sets'</span></span>

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<pre style="margin: 0;">+<span id="LC244" class="line" lang="python"><span class="s" style="color: #d14;">    by N. Halko, P.G. Martinsson, Y. Shkolnisky, and M. Tygert.</span></span>

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<pre style="margin: 0;">+<span id="LC245" class="line" lang="python"><span class="s" style="color: #d14;">    Original Paper: https://arxiv.org/abs/1007.5510</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC246" class="line" lang="python"></span>

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<pre style="margin: 0;">+<span id="LC247" class="line" lang="python"><span class="s" style="color: #d14;">    Ported from MATLAB implementation described here:</span></span>

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<pre style="margin: 0;">+<span id="LC248" class="line" lang="python"><span class="s" style="color: #d14;">    https://stats.stackexchange.com/a/11934/211065</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC249" class="line" lang="python"><span class="s" style="color: #d14;">    """</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC250" class="line" lang="python"></span>

</pre>

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<pre style="margin: 0;">+<span id="LC251" class="line" lang="python">    <span class="n" style="color: #333;">m</span><span class="p">,</span> <span class="n" style="color: #333;">n</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">centered_distance_matrix</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">shape</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="252" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC252" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="253" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC253" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># Number of levels of the Krylov method to use.</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="254" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC254" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># For most applications, num_levels=1 or num_levels=2 is sufficient.</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="255" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC255" class="line" lang="python">    <span class="n" style="color: #333;">num_levels</span> <span class="o" style="font-weight: 600;">=</span> <span class="mi" style="color: #099;">1</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="256" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC256" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="257" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC257" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># Changes the power of the spectral norm, thus minimizing the error).</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC258" class="line" lang="python">    <span class="n" style="color: #333;">use_power_method</span> <span class="o" style="font-weight: 600;">=</span> <span class="bp" style="color: #999;">False</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="259" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC259" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="260" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC260" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># Note: a (conjugate) transpose is removed for performance, since we</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="261" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC261" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># only expect square matrices.</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="262" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC262" class="line" lang="python">    <span class="k" style="font-weight: 600;">if</span> <span class="n" style="color: #333;">m</span> <span class="o" style="font-weight: 600;">!=</span> <span class="n" style="color: #333;">n</span><span class="p">:</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="263" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC263" class="line" lang="python">        <span class="k" style="font-weight: 600;">raise</span> <span class="nb" style="color: #0086b3;">ValueError</span><span class="p">(</span><span class="s" style="color: #d14;">'FSVD expects square distance matrix'</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="264" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC264" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="147" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="265" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC265" class="line" lang="python">    <span class="k" style="font-weight: 600;">if</span> <span class="n" style="color: #333;">number_of_dimensions</span> <span class="o" style="font-weight: 600;">></span> <span class="n" style="color: #333;">m</span> <span class="ow" style="font-weight: 600;">or</span> <span class="n" style="color: #333;">number_of_dimensions</span> <span class="o" style="font-weight: 600;">></span> <span class="n" style="color: #333;">n</span><span class="p">:</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="266" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC266" class="line" lang="python">        <span class="k" style="font-weight: 600;">raise</span> <span class="nb" style="color: #0086b3;">ValueError</span><span class="p">(</span><span class="s" style="color: #d14;">'FSVD: number_of_dimensions cannot be larger than'</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="267" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC267" class="line" lang="python">                         <span class="s" style="color: #d14;">' the dimensionality of the given distance matrix.'</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="268" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC268" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="269" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC269" class="line" lang="python">    <span class="k" style="font-weight: 600;">if</span> <span class="n" style="color: #333;">number_of_dimensions</span> <span class="o" style="font-weight: 600;"><</span> <span class="mi" style="color: #099;">0</span><span class="p">:</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="270" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

270

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<pre style="margin: 0;">+<span id="LC270" class="line" lang="python">        <span class="k" style="font-weight: 600;">raise</span> <span class="nb" style="color: #0086b3;">ValueError</span><span class="p">(</span><span class="s" style="color: #d14;">'Invalid operation: cannot reduce distance matrix '</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="147" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="271" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC271" class="line" lang="python">                         <span class="s" style="color: #d14;">'to negative dimensions using PCoA. Did you intend '</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="147" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="272" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC272" class="line" lang="python">                         <span class="s" style="color: #d14;">'to specify the default value "0", which sets '</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="273" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

273

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<pre style="margin: 0;">+<span id="LC273" class="line" lang="python">                         <span class="s" style="color: #d14;">'the number_of_dimensions equal to the '</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="147" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="274" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

274

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<pre style="margin: 0;">+<span id="LC274" class="line" lang="python">                         <span class="s" style="color: #d14;">'dimensionality of the given distance matrix?'</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="147" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="275" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC275" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="147" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="276" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC276" class="line" lang="python">    <span class="n" style="color: #333;">k</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">number_of_dimensions</span> <span class="o" style="font-weight: 600;">+</span> <span class="mi" style="color: #099;">2</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="277" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC277" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="278" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC278" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># Form a real nxl matrix G whose entries are independent, identically</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="279" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC279" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># distributed Gaussian random variables of zero mean and unit variance</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="280" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC280" class="line" lang="python">    <span class="n" style="color: #333;">G</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">standard_normal</span><span class="p">(</span><span class="n" style="color: #333;">size</span><span class="o" style="font-weight: 600;">=</span><span class="p">(</span><span class="n" style="color: #333;">n</span><span class="p">,</span> <span class="n" style="color: #333;">k</span><span class="p">))</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="281" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

281

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<pre style="margin: 0;">+<span id="LC281" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="147" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="282" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC282" class="line" lang="python">    <span class="k" style="font-weight: 600;">if</span> <span class="n" style="color: #333;">use_power_method</span><span class="p">:</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="147" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="283" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC283" class="line" lang="python">        <span class="c" style="color: #998; font-style: italic;"># use only the given exponent</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="147" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="284" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC284" class="line" lang="python">        <span class="n" style="color: #333;">H</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">dot</span><span class="p">(</span><span class="n" style="color: #333;">centered_distance_matrix</span><span class="p">,</span> <span class="n" style="color: #333;">G</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="147" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="285" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC285" class="line" lang="python"></span>

</pre>

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<pre style="margin: 0;">+<span id="LC286" class="line" lang="python">        <span class="k" style="font-weight: 600;">for</span> <span class="n" style="color: #333;">x</span> <span class="ow" style="font-weight: 600;">in</span> <span class="nb" style="color: #0086b3;">range</span><span class="p">(</span><span class="mi" style="color: #099;">2</span><span class="p">,</span> <span class="n" style="color: #333;">num_levels</span> <span class="o" style="font-weight: 600;">+</span> <span class="mi" style="color: #099;">2</span><span class="p">):</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="287" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC287" class="line" lang="python">            <span class="c" style="color: #998; font-style: italic;"># enhance decay of singular values</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC288" class="line" lang="python">            <span class="c" style="color: #998; font-style: italic;"># note: distance_matrix is no longer transposed, saves work</span></span>

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<pre style="margin: 0;">+<span id="LC289" class="line" lang="python">            <span class="c" style="color: #998; font-style: italic;"># since we're expecting symmetric, square matrices anyway</span></span>

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<pre style="margin: 0;">+<span id="LC290" class="line" lang="python">            <span class="c" style="color: #998; font-style: italic;"># (Daniel McDonald's changes)</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC291" class="line" lang="python">            <span class="n" style="color: #333;">H</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">dot</span><span class="p">(</span><span class="n" style="color: #333;">centered_distance_matrix</span><span class="p">,</span> <span class="n" style="color: #333;">dot</span><span class="p">(</span><span class="n" style="color: #333;">centered_distance_matrix</span><span class="p">,</span> <span class="n" style="color: #333;">H</span><span class="p">))</span></span>

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<pre style="margin: 0;">+<span id="LC292" class="line" lang="python"></span>

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<pre style="margin: 0;">+<span id="LC293" class="line" lang="python">    <span class="k" style="font-weight: 600;">else</span><span class="p">:</span></span>

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<pre style="margin: 0;">+<span id="LC294" class="line" lang="python">        <span class="c" style="color: #998; font-style: italic;"># compute the m x l matrices H^{(0)}, ..., H^{(i)}</span></span>

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<pre style="margin: 0;">+<span id="LC295" class="line" lang="python">        <span class="c" style="color: #998; font-style: italic;"># Note that this is done implicitly in each iteration below.</span></span>

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<pre style="margin: 0;">+<span id="LC296" class="line" lang="python">        <span class="n" style="color: #333;">H</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">dot</span><span class="p">(</span><span class="n" style="color: #333;">centered_distance_matrix</span><span class="p">,</span> <span class="n" style="color: #333;">G</span><span class="p">)</span></span>

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<pre style="margin: 0;">+<span id="LC297" class="line" lang="python">        <span class="c" style="color: #998; font-style: italic;"># to enhance performance</span></span>

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<pre style="margin: 0;">+<span id="LC298" class="line" lang="python">        <span class="n" style="color: #333;">H</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">hstack</span><span class="p">(</span></span>

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<pre style="margin: 0;">+<span id="LC299" class="line" lang="python">            <span class="p">(</span><span class="n" style="color: #333;">H</span><span class="p">,</span></span>

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<pre style="margin: 0;">+<span id="LC300" class="line" lang="python">             <span class="n" style="color: #333;">dot</span><span class="p">(</span><span class="n" style="color: #333;">centered_distance_matrix</span><span class="p">,</span> <span class="n" style="color: #333;">dot</span><span class="p">(</span><span class="n" style="color: #333;">centered_distance_matrix</span><span class="p">,</span> <span class="n" style="color: #333;">H</span><span class="p">))))</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC301" class="line" lang="python">        <span class="k" style="font-weight: 600;">for</span> <span class="n" style="color: #333;">x</span> <span class="ow" style="font-weight: 600;">in</span> <span class="nb" style="color: #0086b3;">range</span><span class="p">(</span><span class="mi" style="color: #099;">3</span><span class="p">,</span> <span class="n" style="color: #333;">num_levels</span> <span class="o" style="font-weight: 600;">+</span> <span class="mi" style="color: #099;">2</span><span class="p">):</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC302" class="line" lang="python">            <span class="n" style="color: #333;">tmp</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">dot</span><span class="p">(</span><span class="n" style="color: #333;">centered_distance_matrix</span><span class="p">,</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC303" class="line" lang="python">                      <span class="n" style="color: #333;">dot</span><span class="p">(</span><span class="n" style="color: #333;">centered_distance_matrix</span><span class="p">,</span> <span class="n" style="color: #333;">H</span><span class="p">))</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC304" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="305" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC305" class="line" lang="python">            <span class="n" style="color: #333;">H</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">hstack</span><span class="p">(</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="306" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC306" class="line" lang="python">                <span class="p">(</span><span class="n" style="color: #333;">H</span><span class="p">,</span> <span class="n" style="color: #333;">dot</span><span class="p">(</span><span class="n" style="color: #333;">centered_distance_matrix</span><span class="p">,</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="147" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="307" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC307" class="line" lang="python">                        <span class="n" style="color: #333;">dot</span><span class="p">(</span><span class="n" style="color: #333;">centered_distance_matrix</span><span class="p">,</span> <span class="n" style="color: #333;">tmp</span><span class="p">))))</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="147" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="308" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC308" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="309" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC309" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># Using the pivoted QR-decomposition, form a real m * ((i+1)l) matrix Q</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="310" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC310" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># whose columns are orthonormal, s.t. there exists a real</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="147" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="311" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC311" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># ((i+1)l) * ((i+1)l) matrix R for which H = QR</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="312" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC312" class="line" lang="python">    <span class="n" style="color: #333;">Q</span><span class="p">,</span> <span class="n" style="color: #333;">R</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">qr</span><span class="p">(</span><span class="n" style="color: #333;">H</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="313" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC313" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="147" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="314" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC314" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># Compute the n * ((i+1)l) product matrix T = A^T Q</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="315" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC315" class="line" lang="python">    <span class="n" style="color: #333;">T</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">dot</span><span class="p">(</span><span class="n" style="color: #333;">centered_distance_matrix</span><span class="p">,</span> <span class="n" style="color: #333;">Q</span><span class="p">)</span>  <span class="c" style="color: #998; font-style: italic;"># step 3</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="316" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC316" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="317" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC317" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># Form an SVD of T</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="318" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC318" class="line" lang="python">    <span class="n" style="color: #333;">Vt</span><span class="p">,</span> <span class="n" style="color: #333;">St</span><span class="p">,</span> <span class="n" style="color: #333;">W</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">svd</span><span class="p">(</span><span class="n" style="color: #333;">T</span><span class="p">,</span> <span class="n" style="color: #333;">full_matrices</span><span class="o" style="font-weight: 600;">=</span><span class="bp" style="color: #999;">False</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="319" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC319" class="line" lang="python">    <span class="n" style="color: #333;">W</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">W</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">transpose</span><span class="p">()</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="147" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="320" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC320" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="147" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="321" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC321" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># Compute the m * ((i+1)l) product matrix</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC322" class="line" lang="python">    <span class="n" style="color: #333;">Ut</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">dot</span><span class="p">(</span><span class="n" style="color: #333;">Q</span><span class="p">,</span> <span class="n" style="color: #333;">W</span><span class="p">)</span></span>

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<pre style="margin: 0;">+<span id="LC323" class="line" lang="python"></span>

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<pre style="margin: 0;">+<span id="LC324" class="line" lang="python">    <span class="n" style="color: #333;">U_fsvd</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">Ut</span><span class="p">[:,</span> <span class="p">:</span><span class="n" style="color: #333;">number_of_dimensions</span><span class="p">]</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC325" class="line" lang="python"></span>

</pre>

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<pre style="margin: 0;">+<span id="LC326" class="line" lang="python">    <span class="n" style="color: #333;">S</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">St</span><span class="p">[:</span><span class="n" style="color: #333;">number_of_dimensions</span><span class="p">]</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="327" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC327" class="line" lang="python"></span>

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<pre style="margin: 0;">+<span id="LC328" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># drop imaginary component, if we got one</span></span>

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<pre style="margin: 0;">+<span id="LC329" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># Note:</span></span>

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<pre style="margin: 0;">+<span id="LC330" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;">#   In cogent, after computing eigenvalues/vectors, the imaginary part</span></span>

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<pre style="margin: 0;">+<span id="LC331" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;">#   is dropped, if any. We know for a fact that the eigenvalues are</span></span>

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<pre style="margin: 0;">+<span id="LC332" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;">#   real, so that's not necessary, but eigenvectors can in principle</span></span>

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<pre style="margin: 0;">+<span id="LC333" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;">#   be complex (see for example</span></span>

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<pre style="margin: 0;">+<span id="LC334" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;">#   http://math.stackexchange.com/a/47807/109129 for details)</span></span>

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<pre style="margin: 0;">+<span id="LC335" class="line" lang="python">    <span class="n" style="color: #333;">eigenvalues</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">S</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">real</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC336" class="line" lang="python">    <span class="n" style="color: #333;">eigenvectors</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">U_fsvd</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">real</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC337" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="338" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC338" class="line" lang="python">    <span class="k" style="font-weight: 600;">return</span> <span class="n" style="color: #333;">eigenvalues</span><span class="p">,</span> <span class="n" style="color: #333;">eigenvectors</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC339" class="line" lang="python"></span>

</pre>

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<pre style="margin: 0;">+<span id="LC340" class="line" lang="python"></span>

</pre>

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<pre style="margin: 0;"> <span id="LC341" class="line" lang="python"><span class="nd">@experimental</span><span class="p">(</span><span class="n" style="color: #333;">as_of</span><span class="o" style="font-weight: 600;">=</span><span class="s" style="color: #d14;">"0.5.3"</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num old_line" data-linenumber="148" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<td class="diff-line-num new_line" data-linenumber="342" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<pre style="margin: 0;"> <span id="LC342" class="line" lang="python"><span class="k" style="font-weight: 600;">def</span> <span class="nf" style="color: #900; font-weight: 600;">pcoa_biplot</span><span class="p">(</span><span class="n" style="color: #333;">ordination</span><span class="p">,</span> <span class="n" style="color: #333;">y</span><span class="p">):</span></span>

</pre>

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<td class="diff-line-num old_line" data-linenumber="149" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<td class="diff-line-num new_line" data-linenumber="343" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<pre style="margin: 0;"> <span id="LC343" class="line" lang="python">    <span class="s" style="color: #d14;">"""Compute the projection of descriptors into a PCoA matrix</span></span>

</pre>

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<td class="diff-line-num unfold js-unfold old_line" data-linenumber="171" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">...</td>

<td class="diff-line-num unfold js-unfold new_line" data-linenumber="365" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">...</td>

<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -171,7 +365,7 @@ def pcoa_biplot(ordination, y):</td>

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<td class="diff-line-num old_line" data-linenumber="171" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<pre style="margin: 0;"> <span id="LC365" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># acknowledge that most saved ordinations lack a name, however if they have</span></span>

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<td class="diff-line-num old_line" data-linenumber="172" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<pre style="margin: 0;"> <span id="LC366" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># a name, it should be PCoA</span></span>

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<td class="diff-line-num old_line" data-linenumber="173" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<pre style="margin: 0;"> <span id="LC367" class="line" lang="python">    <span class="k" style="font-weight: 600;">if</span> <span class="p">(</span><span class="n" style="color: #333;">ordination</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">short_method_name</span> <span class="o" style="font-weight: 600;">!=</span> <span class="s" style="color: #d14;">''</span> <span class="ow" style="font-weight: 600;">and</span></span>

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<td class="diff-line-num new_line old" data-linenumber="368" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<pre style="margin: 0;">-<span id="LC174" class="line" lang="python">       <span class="n" style="color: #333;">ordination</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">short_method_name</span> <span class="o" style="font-weight: 600;">!=</span> <span class="s" style="color: #d14;">'PCoA'</span><span class="p">):</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="175" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC368" class="line" lang="python">       <span class="idiff left right">     </span><span class="n" style="color: #333;">ordination</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">short_method_name</span> <span class="o" style="font-weight: 600;">!=</span> <span class="s" style="color: #d14;">'PCoA'</span><span class="p">):</span></span>

</pre>

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<td class="diff-line-num old_line" data-linenumber="175" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<pre style="margin: 0;"> <span id="LC369" class="line" lang="python">        <span class="k" style="font-weight: 600;">raise</span> <span class="nb" style="color: #0086b3;">ValueError</span><span class="p">(</span><span class="s" style="color: #d14;">'This biplot computation can only be performed in a '</span></span>

</pre>

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<td class="diff-line-num new_line" data-linenumber="370" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<pre style="margin: 0;"> <span id="LC370" class="line" lang="python">                         <span class="s" style="color: #d14;">'PCoA matrix.'</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num old_line" data-linenumber="177" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<td class="diff-line-num new_line" data-linenumber="371" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<pre style="margin: 0;"> <span id="LC371" class="line" lang="python"></span>

</pre>

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<br>

</li>

<li id="4d8189dc1208d6c1d04848c3380fd81155a62c20">

<a href="https://salsa.debian.org/med-team/python-skbio/compare/3d3c45f3254533f7a7055537dba85e12078e2138...59737a89a9cfea9e36f5487d037b6dc5e014ee74#4d8189dc1208d6c1d04848c3380fd81155a62c20"><strong>skbio/stats/ordination/_utils.py</strong></a>

<hr>

<table class="code white" style="font-family: monospace; font-size: 90%;" bgcolor="#fff" width="100%" cellpadding="0" cellspacing="0">

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<td class="diff-line-num unfold js-unfold old_line" data-linenumber="196" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">...</td>

<td class="diff-line-num unfold js-unfold new_line" data-linenumber="196" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">...</td>

<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -196,3 +196,86 @@ def f_matrix(E_matrix):</td>

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<td class="diff-line-num old_line" data-linenumber="196" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<td class="diff-line-num new_line" data-linenumber="196" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<pre style="margin: 0;"> <span id="LC196" class="line" lang="python">    <span class="n" style="color: #333;">col_means</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">E_matrix</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">mean</span><span class="p">(</span><span class="n" style="color: #333;">axis</span><span class="o" style="font-weight: 600;">=</span><span class="mi" style="color: #099;">0</span><span class="p">,</span> <span class="n" style="color: #333;">keepdims</span><span class="o" style="font-weight: 600;">=</span><span class="bp" style="color: #999;">True</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num old_line" data-linenumber="197" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<td class="diff-line-num new_line" data-linenumber="197" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<pre style="margin: 0;"> <span id="LC197" class="line" lang="python">    <span class="n" style="color: #333;">matrix_mean</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">E_matrix</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">mean</span><span class="p">()</span></span>

</pre>

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<td class="diff-line-num old_line" data-linenumber="198" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<td class="diff-line-num new_line" data-linenumber="198" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<pre style="margin: 0;"> <span id="LC198" class="line" lang="python">    <span class="k" style="font-weight: 600;">return</span> <span class="n" style="color: #333;">E_matrix</span> <span class="o" style="font-weight: 600;">-</span> <span class="n" style="color: #333;">row_means</span> <span class="o" style="font-weight: 600;">-</span> <span class="n" style="color: #333;">col_means</span> <span class="o" style="font-weight: 600;">+</span> <span class="n" style="color: #333;">matrix_mean</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="199" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="199" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC199" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="199" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="200" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC200" class="line" lang="python"></span>

</pre>

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<pre style="margin: 0;">+<span id="LC201" class="line" lang="python"><span class="k" style="font-weight: 600;">def</span> <span class="nf" style="color: #900; font-weight: 600;">center_distance_matrix</span><span class="p">(</span><span class="n" style="color: #333;">distance_matrix</span><span class="p">,</span> <span class="n" style="color: #333;">inplace</span><span class="o" style="font-weight: 600;">=</span><span class="bp" style="color: #999;">False</span><span class="p">):</span></span>

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<pre style="margin: 0;">+<span id="LC202" class="line" lang="python">    <span class="s" style="color: #d14;">"""</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC203" class="line" lang="python"><span class="s" style="color: #d14;">    Centers a distance matrix.</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC204" class="line" lang="python"></span>

</pre>

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<pre style="margin: 0;">+<span id="LC205" class="line" lang="python"><span class="s" style="color: #d14;">    Note: If the used distance was euclidean, pairwise distances</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC206" class="line" lang="python"><span class="s" style="color: #d14;">    needn't be computed from the data table Y because F_matrix =</span></span>

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<pre style="margin: 0;">+<span id="LC207" class="line" lang="python"><span class="s" style="color: #d14;">    Y.dot(Y.T) (if Y has been centered).</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC208" class="line" lang="python"><span class="s" style="color: #d14;">    But since we're expecting distance_matrix to be non-euclidian,</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC209" class="line" lang="python"><span class="s" style="color: #d14;">    we do the following computation as per</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC210" class="line" lang="python"><span class="s" style="color: #d14;">    Numerical Ecology (Legendre & Legendre 1998).</span></span>

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<pre style="margin: 0;">+<span id="LC211" class="line" lang="python"></span>

</pre>

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<pre style="margin: 0;">+<span id="LC212" class="line" lang="python"><span class="s" style="color: #d14;">    Parameters</span></span>

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<pre style="margin: 0;">+<span id="LC213" class="line" lang="python"><span class="s" style="color: #d14;">    ----------</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC214" class="line" lang="python"><span class="s" style="color: #d14;">    distance_matrix : 2D array_like</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC215" class="line" lang="python"><span class="s" style="color: #d14;">        Distance matrix.</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC216" class="line" lang="python"><span class="s" style="color: #d14;">    inplace : bool, optional</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC217" class="line" lang="python"><span class="s" style="color: #d14;">        Whether or not to center the given distance matrix in-place, which</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="218" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC218" class="line" lang="python"><span class="s" style="color: #d14;">        is more efficient in terms of memory and computation.</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC219" class="line" lang="python"><span class="s" style="color: #d14;">    """</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC220" class="line" lang="python">    <span class="k" style="font-weight: 600;">if</span> <span class="n" style="color: #333;">inplace</span><span class="p">:</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC221" class="line" lang="python">        <span class="k" style="font-weight: 600;">return</span> <span class="n" style="color: #333;">_f_matrix_inplace</span><span class="p">(</span><span class="n" style="color: #333;">_e_matrix_inplace</span><span class="p">(</span><span class="n" style="color: #333;">distance_matrix</span><span class="p">))</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC222" class="line" lang="python">    <span class="k" style="font-weight: 600;">else</span><span class="p">:</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC223" class="line" lang="python">        <span class="k" style="font-weight: 600;">return</span> <span class="n" style="color: #333;">f_matrix</span><span class="p">(</span><span class="n" style="color: #333;">e_matrix</span><span class="p">(</span><span class="n" style="color: #333;">distance_matrix</span><span class="p">))</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC224" class="line" lang="python"></span>

</pre>

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<pre style="margin: 0;">+<span id="LC225" class="line" lang="python"></span>

</pre>

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<pre style="margin: 0;">+<span id="LC226" class="line" lang="python"><span class="k" style="font-weight: 600;">def</span> <span class="nf" style="color: #900; font-weight: 600;">_e_matrix_inplace</span><span class="p">(</span><span class="n" style="color: #333;">distance_matrix</span><span class="p">):</span></span>

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<pre style="margin: 0;">+<span id="LC227" class="line" lang="python">    <span class="s" style="color: #d14;">"""</span></span>

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<pre style="margin: 0;">+<span id="LC228" class="line" lang="python"><span class="s" style="color: #d14;">    Compute E matrix from a distance matrix inplace.</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC229" class="line" lang="python"><span class="s" style="color: #d14;">    Squares and divides by -2 the input element-wise. Eq. 9.20 in</span></span>

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<pre style="margin: 0;">+<span id="LC230" class="line" lang="python"><span class="s" style="color: #d14;">    Legendre & Legendre 1998.</span></span>

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<pre style="margin: 0;">+<span id="LC231" class="line" lang="python"></span>

</pre>

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<pre style="margin: 0;">+<span id="LC232" class="line" lang="python"><span class="s" style="color: #d14;">    Modified from :func:`skbio.stats.ordination.e_matrix` function,</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC233" class="line" lang="python"><span class="s" style="color: #d14;">    performing row-wise operations to avoid excessive memory allocations.</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC234" class="line" lang="python"></span>

</pre>

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<pre style="margin: 0;">+<span id="LC235" class="line" lang="python"><span class="s" style="color: #d14;">    Parameters</span></span>

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<pre style="margin: 0;">+<span id="LC236" class="line" lang="python"><span class="s" style="color: #d14;">    ----------</span></span>

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<pre style="margin: 0;">+<span id="LC237" class="line" lang="python"><span class="s" style="color: #d14;">    distance_matrix : 2D array_like</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC238" class="line" lang="python"><span class="s" style="color: #d14;">        Distance matrix.</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC239" class="line" lang="python"><span class="s" style="color: #d14;">    """</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC240" class="line" lang="python">    <span class="n" style="color: #333;">distance_matrix</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">distance_matrix</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">astype</span><span class="p">(</span><span class="n" style="color: #333;">np</span><span class="o" style="font-weight: 600;">.</span><span class="nb" style="color: #0086b3;">float</span><span class="p">)</span></span>

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<pre style="margin: 0;">+<span id="LC241" class="line" lang="python"></span>

</pre>

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<pre style="margin: 0;">+<span id="LC242" class="line" lang="python">    <span class="k" style="font-weight: 600;">for</span> <span class="n" style="color: #333;">i</span> <span class="ow" style="font-weight: 600;">in</span> <span class="n" style="color: #333;">np</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">arange</span><span class="p">(</span><span class="nb" style="color: #0086b3;">len</span><span class="p">(</span><span class="n" style="color: #333;">distance_matrix</span><span class="p">)):</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC243" class="line" lang="python">        <span class="n" style="color: #333;">distance_matrix</span><span class="p">[</span><span class="n" style="color: #333;">i</span><span class="p">]</span> <span class="o" style="font-weight: 600;">=</span> <span class="p">(</span><span class="n" style="color: #333;">distance_matrix</span><span class="p">[</span><span class="n" style="color: #333;">i</span><span class="p">]</span> <span class="o" style="font-weight: 600;">*</span> <span class="n" style="color: #333;">distance_matrix</span><span class="p">[</span><span class="n" style="color: #333;">i</span><span class="p">])</span> <span class="o" style="font-weight: 600;">/</span> <span class="o" style="font-weight: 600;">-</span><span class="mi" style="color: #099;">2</span></span>

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<pre style="margin: 0;">+<span id="LC244" class="line" lang="python">    <span class="k" style="font-weight: 600;">return</span> <span class="n" style="color: #333;">distance_matrix</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC245" class="line" lang="python"></span>

</pre>

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<pre style="margin: 0;">+<span id="LC246" class="line" lang="python"></span>

</pre>

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<pre style="margin: 0;">+<span id="LC247" class="line" lang="python"><span class="k" style="font-weight: 600;">def</span> <span class="nf" style="color: #900; font-weight: 600;">_f_matrix_inplace</span><span class="p">(</span><span class="n" style="color: #333;">e_matrix</span><span class="p">):</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC248" class="line" lang="python">    <span class="s" style="color: #d14;">"""</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC249" class="line" lang="python"><span class="s" style="color: #d14;">    Compute F matrix from E matrix inplace.</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC250" class="line" lang="python"><span class="s" style="color: #d14;">    Centering step: for each element, the mean of the corresponding</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC251" class="line" lang="python"><span class="s" style="color: #d14;">    row and column are subtracted, and the mean of the whole</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC252" class="line" lang="python"><span class="s" style="color: #d14;">    matrix is added. Eq. 9.21 in Legendre & Legendre 1998.</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC253" class="line" lang="python"></span>

</pre>

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<pre style="margin: 0;">+<span id="LC254" class="line" lang="python"><span class="s" style="color: #d14;">    Modified from :func:`skbio.stats.ordination.f_matrix` function,</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC255" class="line" lang="python"><span class="s" style="color: #d14;">    performing row-wise operations to avoid excessive memory allocations.</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC256" class="line" lang="python"></span>

</pre>

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<pre style="margin: 0;">+<span id="LC257" class="line" lang="python"><span class="s" style="color: #d14;">    Parameters</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC258" class="line" lang="python"><span class="s" style="color: #d14;">    ----------</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC259" class="line" lang="python"><span class="s" style="color: #d14;">    e_matrix : 2D array_like</span></span>

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<pre style="margin: 0;">+<span id="LC260" class="line" lang="python"><span class="s" style="color: #d14;">        A matrix representing the "E matrix" as described above.</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC261" class="line" lang="python"><span class="s" style="color: #d14;">    """</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC262" class="line" lang="python">    <span class="n" style="color: #333;">e_matrix</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">e_matrix</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">astype</span><span class="p">(</span><span class="n" style="color: #333;">np</span><span class="o" style="font-weight: 600;">.</span><span class="nb" style="color: #0086b3;">float</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="263" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC263" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="264" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC264" class="line" lang="python">    <span class="n" style="color: #333;">row_means</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">np</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">zeros</span><span class="p">(</span><span class="nb" style="color: #0086b3;">len</span><span class="p">(</span><span class="n" style="color: #333;">e_matrix</span><span class="p">),</span> <span class="n" style="color: #333;">dtype</span><span class="o" style="font-weight: 600;">=</span><span class="nb" style="color: #0086b3;">float</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="265" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC265" class="line" lang="python">    <span class="n" style="color: #333;">col_means</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">np</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">zeros</span><span class="p">(</span><span class="nb" style="color: #0086b3;">len</span><span class="p">(</span><span class="n" style="color: #333;">e_matrix</span><span class="p">),</span> <span class="n" style="color: #333;">dtype</span><span class="o" style="font-weight: 600;">=</span><span class="nb" style="color: #0086b3;">float</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="266" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC266" class="line" lang="python">    <span class="n" style="color: #333;">matrix_mean</span> <span class="o" style="font-weight: 600;">=</span> <span class="mf" style="color: #099;">0.0</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC267" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="268" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC268" class="line" lang="python">    <span class="k" style="font-weight: 600;">for</span> <span class="n" style="color: #333;">i</span> <span class="ow" style="font-weight: 600;">in</span> <span class="n" style="color: #333;">np</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">arange</span><span class="p">(</span><span class="nb" style="color: #0086b3;">len</span><span class="p">(</span><span class="n" style="color: #333;">e_matrix</span><span class="p">)):</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="269" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC269" class="line" lang="python">        <span class="n" style="color: #333;">row_means</span><span class="p">[</span><span class="n" style="color: #333;">i</span><span class="p">]</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">e_matrix</span><span class="p">[</span><span class="n" style="color: #333;">i</span><span class="p">]</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">mean</span><span class="p">()</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="270" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC270" class="line" lang="python">        <span class="n" style="color: #333;">matrix_mean</span> <span class="o" style="font-weight: 600;">+=</span> <span class="n" style="color: #333;">e_matrix</span><span class="p">[</span><span class="n" style="color: #333;">i</span><span class="p">]</span><span class="o" style="font-weight: 600;">.</span><span class="nb" style="color: #0086b3;">sum</span><span class="p">()</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="271" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC271" class="line" lang="python">        <span class="n" style="color: #333;">col_means</span> <span class="o" style="font-weight: 600;">+=</span> <span class="n" style="color: #333;">e_matrix</span><span class="p">[</span><span class="n" style="color: #333;">i</span><span class="p">]</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="272" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC272" class="line" lang="python">    <span class="n" style="color: #333;">matrix_mean</span> <span class="o" style="font-weight: 600;">/=</span> <span class="nb" style="color: #0086b3;">len</span><span class="p">(</span><span class="n" style="color: #333;">e_matrix</span><span class="p">)</span> <span class="o" style="font-weight: 600;">**</span> <span class="mi" style="color: #099;">2</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="273" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC273" class="line" lang="python">    <span class="n" style="color: #333;">col_means</span> <span class="o" style="font-weight: 600;">/=</span> <span class="nb" style="color: #0086b3;">len</span><span class="p">(</span><span class="n" style="color: #333;">e_matrix</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="274" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC274" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="275" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC275" class="line" lang="python">    <span class="k" style="font-weight: 600;">for</span> <span class="n" style="color: #333;">i</span> <span class="ow" style="font-weight: 600;">in</span> <span class="n" style="color: #333;">np</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">arange</span><span class="p">(</span><span class="nb" style="color: #0086b3;">len</span><span class="p">(</span><span class="n" style="color: #333;">e_matrix</span><span class="p">)):</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC276" class="line" lang="python">        <span class="n" style="color: #333;">v</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">e_matrix</span><span class="p">[</span><span class="n" style="color: #333;">i</span><span class="p">]</span></span>

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<td class="diff-line-num new new_line" data-linenumber="277" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

277

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<pre style="margin: 0;">+<span id="LC277" class="line" lang="python">        <span class="n" style="color: #333;">v</span> <span class="o" style="font-weight: 600;">-=</span> <span class="n" style="color: #333;">row_means</span><span class="p">[</span><span class="n" style="color: #333;">i</span><span class="p">]</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="278" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

278

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<pre style="margin: 0;">+<span id="LC278" class="line" lang="python">        <span class="n" style="color: #333;">v</span> <span class="o" style="font-weight: 600;">-=</span> <span class="n" style="color: #333;">col_means</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="279" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC279" class="line" lang="python">        <span class="n" style="color: #333;">v</span> <span class="o" style="font-weight: 600;">+=</span> <span class="n" style="color: #333;">matrix_mean</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="280" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

280

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<pre style="margin: 0;">+<span id="LC280" class="line" lang="python">        <span class="n" style="color: #333;">e_matrix</span><span class="p">[</span><span class="n" style="color: #333;">i</span><span class="p">]</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">v</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="281" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

281

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<pre style="margin: 0;">+<span id="LC281" class="line" lang="python">    <span class="k" style="font-weight: 600;">return</span> <span class="n" style="color: #333;">e_matrix</span></span></pre>

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<br>

</li>

<li id="0d49b2580a40a2f0585d51a5139beb0883d13f33">

<a href="https://salsa.debian.org/med-team/python-skbio/compare/3d3c45f3254533f7a7055537dba85e12078e2138...59737a89a9cfea9e36f5487d037b6dc5e014ee74#0d49b2580a40a2f0585d51a5139beb0883d13f33"><strong>skbio/stats/ordination/tests/data/PCoA_sample_data_12dim</strong></a>

<hr>

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1

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<pre style="margin: 0;">+<span id="LC1" class="line" lang="plaintext">      1       2       3       4       5       6       7       8       9       10      11      12</span>

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<td class="diff-line-num new new_line" data-linenumber="2" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

2

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<pre style="margin: 0;">+<span id="LC2" class="line" lang="plaintext">1     0.0     0.909636950834479       0.9869428157422727      0.7190893636533138      0.6960053958431593      0.6477238596907942      0.30557161358653495     0.8946966124829346      0.12780699944110363     0.39915339691165386     0.7641239434153432      0.6248070796484706</span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="3" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

3

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<pre style="margin: 0;">+<span id="LC3" class="line" lang="plaintext">2     0.909636950834479       0.0     0.3871354292850083      0.6881160960373599      0.5550593584027527      0.5855786600007656      0.4843215561734061      0.20448304199758327     0.4067028703340123      0.2754701840044086      0.6269219445617967      0.05629366991581264</span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="4" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

4

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<pre style="margin: 0;">+<span id="LC4" class="line" lang="plaintext">3     0.9869428157422727      0.3871354292850083      0.0     0.6088130886750466      0.8611896463567201      0.2815827949525225      0.6500535832888426      0.8196046614443331      0.356410088497226       0.05164123821334954     0.7110953188954077      0.32855281988632934</span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="5" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

5

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<pre style="margin: 0;">+<span id="LC5" class="line" lang="plaintext">4     0.7190893636533138      0.6881160960373599      0.6088130886750466      0.0     0.7453215102240474      0.9916540031629704      0.14394284428694282     0.8388378539413649      0.15115603934799038     0.13871462268568635     0.1934605692727246      0.9804118301943398</span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="6" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

6

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<pre style="margin: 0;">+<span id="LC6" class="line" lang="plaintext">5     0.6960053958431593      0.5550593584027527      0.8611896463567201      0.7453215102240474      0.0     0.7996611932937304      0.30579824243478326     0.5227960305398314      0.8564730629853469      0.7786384040043949      0.06843106040159719     0.7715973816221341</span>

</pre>

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7

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<pre style="margin: 0;">+<span id="LC7" class="line" lang="plaintext">6     0.6477238596907942      0.5855786600007656      0.2815827949525225      0.9916540031629704      0.7996611932937304      0.0     0.8869204659721949      0.1619378942802252      0.10200764546980268     0.17805335055828198     0.8796559972720953      0.20933243431218862</span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="8" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

8

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<pre style="margin: 0;">+<span id="LC8" class="line" lang="plaintext">7     0.30557161358653495     0.4843215561734061      0.6500535832888426      0.14394284428694282     0.30579824243478326     0.8869204659721949      0.0     0.9489770186788868      0.9531210051205121      0.5834385348164726      0.31984891724102216     0.5852822100268925</span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="9" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

9

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<pre style="margin: 0;">+<span id="LC9" class="line" lang="plaintext">8     0.8946966124829346      0.20448304199758327     0.8196046614443331      0.8388378539413649      0.5227960305398314      0.1619378942802252      0.9489770186788868      0.0     0.16681381452925792     0.9281238242741929      0.604480007052297       0.43978806925866687</span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="10" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

10

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<pre style="margin: 0;">+<span id="LC10" class="line" lang="plaintext">9    0.12780699944110363     0.4067028703340123      0.356410088497226       0.15115603934799038     0.8564730629853469      0.10200764546980268     0.9531210051205121      0.16681381452925792     0.0     0.10766387594368387     0.9552101788877516      0.6135541732435132</span>

</pre>

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11

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<pre style="margin: 0;">+<span id="LC11" class="line" lang="plaintext">10   0.39915339691165386     0.2754701840044086      0.05164123821334954     0.13871462268568635     0.7786384040043949      0.17805335055828198     0.5834385348164726      0.9281238242741929      0.10766387594368387     0.0     0.4157921207508062      0.31997143485314194</span>

</pre>

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</tr>

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<td class="diff-line-num new new_line" data-linenumber="12" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

12

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<pre style="margin: 0;">+<span id="LC12" class="line" lang="plaintext">11   0.7641239434153432      0.6269219445617967      0.7110953188954077      0.1934605692727246      0.06843106040159719     0.8796559972720953      0.31984891724102216     0.604480007052297       0.9552101788877516      0.4157921207508062      0.0     0.11189976154475101</span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="13" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

13

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<pre style="margin: 0;">+<span id="LC13" class="line" lang="plaintext">12   0.6248070796484706      0.05629366991581264     0.32855281988632934     0.9804118301943398      0.7715973816221341      0.20933243431218862     0.5852822100268925      0.43978806925866687     0.6135541732435132      0.31997143485314194     0.11189976154475101     0.0</span></pre>

</td>

</tr>

</table>

<br>

</li>

<li id="b017992412f66f9ba72318f0343f890bc2b9eea2">

<a href="https://salsa.debian.org/med-team/python-skbio/compare/3d3c45f3254533f7a7055537dba85e12078e2138...59737a89a9cfea9e36f5487d037b6dc5e014ee74#b017992412f66f9ba72318f0343f890bc2b9eea2"><strong>skbio/stats/ordination/tests/data/PCoA_sample_data_3_eigh_ref_3dim</strong></a>

<hr>

<table class="code white" style="font-family: monospace; font-size: 90%;" bgcolor="#fff" width="100%" cellpadding="0" cellspacing="0">

<tr class="line_holder new" id="" style="line-height: 1.6;">

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<td class="diff-line-num new new_line" data-linenumber="1" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

1

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC1" class="line" lang="plaintext">Eigvals       3</span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="0" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="2" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

2

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC2" class="line" lang="plaintext">0.5123672604605051    0.30071909442702155     0.26791206600414047</span>

</pre>

</td>

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<td class="diff-line-num new old_line" data-linenumber="0" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="3" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

3

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC3" class="line" lang="plaintext"></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="4" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

4

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<pre style="margin: 0;">+<span id="LC4" class="line" lang="plaintext">Proportion explained  3</span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="5" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

5

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<pre style="margin: 0;">+<span id="LC5" class="line" lang="plaintext">0.26757383277657976   0.15704469604990076     0.13991186377402365</span>

</pre>

</td>

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<td class="diff-line-num new new_line" data-linenumber="6" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

6

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC6" class="line" lang="plaintext"></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="7" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

7

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC7" class="line" lang="plaintext">Species       0       0</span>

</pre>

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8

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC8" class="line" lang="plaintext"></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="9" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

9

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC9" class="line" lang="plaintext">Site  9       3</span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="10" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

10

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<pre style="margin: 0;">+<span id="LC10" class="line" lang="plaintext">PC.636       -0.2584654611828421     0.17399954688273872     -0.03828757925519412</span>

</pre>

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</tr>

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<td class="diff-line-num new old_line" data-linenumber="0" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="11" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

11

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC11" class="line" lang="plaintext">PC.635       -0.27100113539100934    -0.018595131906339258   0.08648419263485663</span>

</pre>

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</tr>

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<td class="diff-line-num new old_line" data-linenumber="0" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="12" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

12

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC12" class="line" lang="plaintext">PC.356       0.23507789817473093     0.09625192544887005     0.34579272671386985</span>

</pre>

</td>

</tr>

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<td class="diff-line-num new old_line" data-linenumber="0" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="13" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

13

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC13" class="line" lang="plaintext">PC.481       0.026140766432533755    -0.011145967653319655   -0.14766060301460787</span>

</pre>

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</tr>

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<td class="diff-line-num new old_line" data-linenumber="0" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="14" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

14

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC14" class="line" lang="plaintext">PC.354       0.2850075522831216      -0.019254988848331687   -0.062326337538532166</span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="0" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="15" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

15

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC15" class="line" lang="plaintext">PC.593       0.20463632624145514     -0.13936115093164073    -0.29151381962286704</span>

</pre>

</td>

</tr>

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<td class="diff-line-num new old_line" data-linenumber="0" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="16" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

16

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC16" class="line" lang="plaintext">PC.355       0.23348240321199026     0.22525797406849954     0.018862309626814944</span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="17" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

17

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC17" class="line" lang="plaintext">PC.607       -0.09496319113225934    -0.4209748024953033     0.15486945486941445</span>

</pre>

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18

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<pre style="margin: 0;">+<span id="LC18" class="line" lang="plaintext">PC.634       -0.35991515863772167    0.11382259543482587     -0.06622034441375392</span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="19" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

19

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC19" class="line" lang="plaintext"></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="20" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

20

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC20" class="line" lang="plaintext">Biplot       0       0</span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="21" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

21

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC21" class="line" lang="plaintext"></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="22" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

22

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<pre style="margin: 0;">+<span id="LC22" class="line" lang="plaintext">Site constraints     0       0</span></pre>

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<br>

</li>

<li id="740117d7edce46bbec55dd903f85d2656e72915c">

<a href="https://salsa.debian.org/med-team/python-skbio/compare/3d3c45f3254533f7a7055537dba85e12078e2138...59737a89a9cfea9e36f5487d037b6dc5e014ee74#740117d7edce46bbec55dd903f85d2656e72915c"><strong>skbio/stats/ordination/tests/data/PCoA_sample_data_3_fsvd_ref_3dim</strong></a>

<hr>

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<td class="diff-line-num new new_line" data-linenumber="1" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

1

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC1" class="line" lang="plaintext">Eigvals       3</span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="2" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

2

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<pre style="margin: 0;">+<span id="LC2" class="line" lang="plaintext">0.5123672604605054    0.3007190944270222      0.2679120660041405</span>

</pre>

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3

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC3" class="line" lang="plaintext"></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="4" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

4

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<pre style="margin: 0;">+<span id="LC4" class="line" lang="plaintext">Proportion explained  3</span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="5" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

5

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<pre style="margin: 0;">+<span id="LC5" class="line" lang="plaintext">0.2675738327765797    0.15704469604990098     0.13991186377402356</span>

</pre>

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6

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC6" class="line" lang="plaintext"></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="7" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

7

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<pre style="margin: 0;">+<span id="LC7" class="line" lang="plaintext">Species       0       0</span>

</pre>

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8

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC8" class="line" lang="plaintext"></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="9" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

9

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<pre style="margin: 0;">+<span id="LC9" class="line" lang="plaintext">Site  9       3</span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="10" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

10

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<pre style="margin: 0;">+<span id="LC10" class="line" lang="plaintext">PC.636       -0.2584654611828421     0.17399954688273822     -0.03828757925519378</span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="11" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

11

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<pre style="margin: 0;">+<span id="LC11" class="line" lang="plaintext">PC.635       -0.2710011353910087     -0.018595131906339074   0.08648419263485721</span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="0" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="12" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

12

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<pre style="margin: 0;">+<span id="LC12" class="line" lang="plaintext">PC.356       0.23507789817473107     0.0962519254488692      0.3457927267138707</span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="0" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="13" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

13

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC13" class="line" lang="plaintext">PC.481       0.026140766432533644    -0.011145967653318808   -0.14766060301460796</span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="14" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

14

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC14" class="line" lang="plaintext">PC.354       0.28500755228312136     -0.019254988848331694   -0.06232633753853236</span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="15" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

15

</td>

<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC15" class="line" lang="plaintext">PC.593       0.20463632624145525     -0.13936115093164014    -0.2915138196228672</span>

</pre>

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<pre style="margin: 0;">+<span id="LC16" class="line" lang="plaintext">PC.355       0.23348240321199093     0.22525797406849954     0.018862309626815132</span>

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<pre style="margin: 0;">+<span id="LC17" class="line" lang="plaintext">PC.607       -0.09496319113225955    -0.4209748024953044     0.1548694548694131</span>

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<pre style="margin: 0;">+<span id="LC18" class="line" lang="plaintext">PC.634       -0.35991515863772144    0.1138225954348267      -0.06622034441375402</span>

</pre>

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<pre style="margin: 0;">+<span id="LC19" class="line" lang="plaintext"></span>

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<pre style="margin: 0;">+<span id="LC20" class="line" lang="plaintext">Biplot       0       0</span>

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<pre style="margin: 0;">+<span id="LC21" class="line" lang="plaintext"></span>

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<pre style="margin: 0;">+<span id="LC22" class="line" lang="plaintext">Site constraints     0       0</span></pre>

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<br>

</li>

<li id="125936fde92c0e77b23cf33bdd140af1c8be8e27">

<a href="https://salsa.debian.org/med-team/python-skbio/compare/3d3c45f3254533f7a7055537dba85e12078e2138...59737a89a9cfea9e36f5487d037b6dc5e014ee74#125936fde92c0e77b23cf33bdd140af1c8be8e27"><strong>skbio/stats/ordination/tests/test_principal_coordinate_analysis.py</strong></a>

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<pre style="margin: 0;"> <span id="LC6" class="line" lang="python"><span class="c" style="color: #998; font-style: italic;"># The full license is in the file COPYING.txt, distributed with this software.</span></span>

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<pre style="margin: 0;"> <span id="LC7" class="line" lang="python"><span class="c" style="color: #998; font-style: italic;"># ----------------------------------------------------------------------------</span></span>

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<pre style="margin: 0;"> <span id="LC8" class="line" lang="python"></span>

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<pre style="margin: 0;">-<span id="LC9" class="line" lang="python"><span class="kn" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">pandas</span> <span class="k" style="font-weight: 600;">as</span> <span class="n" style="color: #333;">pd</span></span>

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<pre style="margin: 0;"> <span id="LC9" class="line" lang="python"><span class="kn" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">numpy</span> <span class="k" style="font-weight: 600;">as</span> <span class="n" style="color: #333;">np</span></span>

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<pre style="margin: 0;"> <span id="LC10" class="line" lang="python"><span class="kn" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">numpy.testing</span> <span class="k" style="font-weight: 600;">as</span> <span class="n" style="color: #333;">npt</span></span>

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<pre style="margin: 0;">+<span id="LC11" class="line" lang="python"><span class="kn" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">pandas</span> <span class="k" style="font-weight: 600;">as</span> <span class="n" style="color: #333;">pd</span></span>

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<pre style="margin: 0;"> <span id="LC12" class="line" lang="python"><span class="kn" style="font-weight: 600;">from</span> <span class="nn" style="color: #555;">copy</span> <span class="kn" style="font-weight: 600;">import</span> <span class="n" style="color: #333;">deepcopy</span></span>

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<pre style="margin: 0;"> <span id="LC13" class="line" lang="python"><span class="kn" style="font-weight: 600;">from</span> <span class="nn" style="color: #555;">unittest</span> <span class="kn" style="font-weight: 600;">import</span> <span class="n" style="color: #333;">TestCase</span><span class="p">,</span> <span class="n" style="color: #333;">main</span></span>

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<pre style="margin: 0;"> <span id="LC14" class="line" lang="python"></span>

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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -27,7 +27,7 @@ class TestPCoA(TestCase):</td>

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<pre style="margin: 0;"> <span id="LC27" class="line" lang="python"></span>

</pre>

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<pre style="margin: 0;"> <span id="LC28" class="line" lang="python">    <span class="k" style="font-weight: 600;">def</span> <span class="nf" style="color: #900; font-weight: 600;">test_simple</span><span class="p">(</span><span class="bp" style="color: #999;">self</span><span class="p">):</span></span>

</pre>

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<td class="diff-line-num old_line" data-linenumber="29" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<pre style="margin: 0;"> <span id="LC29" class="line" lang="python">        <span class="n" style="color: #333;">eigvals</span> <span class="o" style="font-weight: 600;">=</span> <span class="p">[</span><span class="mf" style="color: #099;">0.51236726</span><span class="p">,</span> <span class="mf" style="color: #099;">0.30071909</span><span class="p">,</span> <span class="mf" style="color: #099;">0.26791207</span><span class="p">,</span> <span class="mf" style="color: #099;">0.20898868</span><span class="p">,</span></span>

</pre>

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<td class="diff-line-num old old_line" data-linenumber="30" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<td class="diff-line-num new_line old" data-linenumber="30" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<pre style="margin: 0;">-<span id="LC30" class="line" lang="python">                   <span class="mf" style="color: #099;">0.19169895</span><span class="p">,</span> <span class="mf" style="color: #099;">0.16054235</span><span class="p">,</span> <span class="idiff left"> </span><span class="mf" style="color: #099;"><span class="idiff">0.15017696</span></span><span class="p"><span class="idiff">,</span></span><span class="idiff right"> </span> <span class="mf" style="color: #099;">0.12245775</span><span class="p">,</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="31" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="30" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC30" class="line" lang="python">                   <span class="mf" style="color: #099;">0.19169895</span><span class="p">,</span> <span class="mf" style="color: #099;">0.16054235</span><span class="p">,</span> <span class="mf" style="color: #099;"><span class="idiff left">0.15017696</span></span><span class="p"><span class="idiff right">,</span></span> <span class="mf" style="color: #099;">0.12245775</span><span class="p">,</span></span>

</pre>

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<td class="diff-line-num old_line" data-linenumber="31" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<pre style="margin: 0;"> <span id="LC31" class="line" lang="python">                   <span class="mf" style="color: #099;">0.0</span><span class="p">]</span></span>

</pre>

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<td class="diff-line-num old_line" data-linenumber="32" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<td class="diff-line-num new_line" data-linenumber="32" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<pre style="margin: 0;"> <span id="LC32" class="line" lang="python">        <span class="n" style="color: #333;">proportion_explained</span> <span class="o" style="font-weight: 600;">=</span> <span class="p">[</span><span class="mf" style="color: #099;">0.2675738328</span><span class="p">,</span> <span class="mf" style="color: #099;">0.157044696</span><span class="p">,</span> <span class="mf" style="color: #099;">0.1399118638</span><span class="p">,</span></span>

</pre>

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<td class="diff-line-num old_line" data-linenumber="33" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<pre style="margin: 0;"> <span id="LC33" class="line" lang="python">                                <span class="mf" style="color: #099;">0.1091402725</span><span class="p">,</span> <span class="mf" style="color: #099;">0.1001110485</span><span class="p">,</span></span>

</pre>

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<td class="diff-line-num unfold js-unfold old_line" data-linenumber="53" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">...</td>

<td class="diff-line-num unfold js-unfold new_line" data-linenumber="53" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">...</td>

<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -53,6 +53,73 @@ class TestPCoA(TestCase):</td>

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<pre style="margin: 0;"> <span id="LC53" class="line" lang="python">        <span class="n" style="color: #333;">assert_ordination_results_equal</span><span class="p">(</span><span class="n" style="color: #333;">results</span><span class="p">,</span> <span class="n" style="color: #333;">expected_results</span><span class="p">,</span></span>

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<pre style="margin: 0;"> <span id="LC54" class="line" lang="python">                                        <span class="n" style="color: #333;">ignore_directionality</span><span class="o" style="font-weight: 600;">=</span><span class="bp" style="color: #999;">True</span><span class="p">)</span></span>

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<pre style="margin: 0;"> <span id="LC55" class="line" lang="python"></span>

</pre>

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<pre style="margin: 0;">+<span id="LC56" class="line" lang="python">    <span class="k" style="font-weight: 600;">def</span> <span class="nf" style="color: #900; font-weight: 600;">test_fsvd_inplace</span><span class="p">(</span><span class="bp" style="color: #999;">self</span><span class="p">):</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="57" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC57" class="line" lang="python">        <span class="n" style="color: #333;">dm1</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">DistanceMatrix</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">read</span><span class="p">(</span><span class="n" style="color: #333;">get_data_path</span><span class="p">(</span><span class="s" style="color: #d14;">'PCoA_sample_data_3'</span><span class="p">))</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="56" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="58" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC58" class="line" lang="python">        <span class="n" style="color: #333;">dm2</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">DistanceMatrix</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">read</span><span class="p">(</span><span class="n" style="color: #333;">get_data_path</span><span class="p">(</span><span class="s" style="color: #d14;">'PCoA_sample_data_3'</span><span class="p">))</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="56" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="59" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC59" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="60" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC60" class="line" lang="python">        <span class="n" style="color: #333;">expected_results</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">pcoa</span><span class="p">(</span><span class="n" style="color: #333;">dm1</span><span class="p">,</span> <span class="n" style="color: #333;">method</span><span class="o" style="font-weight: 600;">=</span><span class="s" style="color: #d14;">"eigh"</span><span class="p">,</span> <span class="n" style="color: #333;">number_of_dimensions</span><span class="o" style="font-weight: 600;">=</span><span class="mi" style="color: #099;">3</span><span class="p">,</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC61" class="line" lang="python">                                <span class="n" style="color: #333;">inplace</span><span class="o" style="font-weight: 600;">=</span><span class="bp" style="color: #999;">True</span><span class="p">)</span></span>

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<pre style="margin: 0;">+<span id="LC62" class="line" lang="python"></span>

</pre>

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<pre style="margin: 0;">+<span id="LC63" class="line" lang="python">        <span class="n" style="color: #333;">results</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">pcoa</span><span class="p">(</span><span class="n" style="color: #333;">dm2</span><span class="p">,</span> <span class="n" style="color: #333;">method</span><span class="o" style="font-weight: 600;">=</span><span class="s" style="color: #d14;">"fsvd"</span><span class="p">,</span> <span class="n" style="color: #333;">number_of_dimensions</span><span class="o" style="font-weight: 600;">=</span><span class="mi" style="color: #099;">3</span><span class="p">,</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="64" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC64" class="line" lang="python">                       <span class="n" style="color: #333;">inplace</span><span class="o" style="font-weight: 600;">=</span><span class="bp" style="color: #999;">True</span><span class="p">)</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC65" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="66" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC66" class="line" lang="python">        <span class="n" style="color: #333;">assert_ordination_results_equal</span><span class="p">(</span><span class="n" style="color: #333;">results</span><span class="p">,</span> <span class="n" style="color: #333;">expected_results</span><span class="p">,</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="67" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC67" class="line" lang="python">                                        <span class="n" style="color: #333;">ignore_directionality</span><span class="o" style="font-weight: 600;">=</span><span class="bp" style="color: #999;">True</span><span class="p">,</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="68" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC68" class="line" lang="python">                                        <span class="n" style="color: #333;">ignore_method_names</span><span class="o" style="font-weight: 600;">=</span><span class="bp" style="color: #999;">True</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="69" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC69" class="line" lang="python"></span>

</pre>

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<pre style="margin: 0;">+<span id="LC70" class="line" lang="python">    <span class="k" style="font-weight: 600;">def</span> <span class="nf" style="color: #900; font-weight: 600;">test_fsvd</span><span class="p">(</span><span class="bp" style="color: #999;">self</span><span class="p">):</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC71" class="line" lang="python">        <span class="n" style="color: #333;">dm1</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">DistanceMatrix</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">read</span><span class="p">(</span><span class="n" style="color: #333;">get_data_path</span><span class="p">(</span><span class="s" style="color: #d14;">'PCoA_sample_data_3'</span><span class="p">))</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC72" class="line" lang="python">        <span class="n" style="color: #333;">dm2</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">DistanceMatrix</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">read</span><span class="p">(</span><span class="n" style="color: #333;">get_data_path</span><span class="p">(</span><span class="s" style="color: #d14;">'PCoA_sample_data_3'</span><span class="p">))</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="73" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC73" class="line" lang="python">        <span class="n" style="color: #333;">dm3</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">DistanceMatrix</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">read</span><span class="p">(</span><span class="n" style="color: #333;">get_data_path</span><span class="p">(</span><span class="s" style="color: #d14;">'PCoA_sample_data_3'</span><span class="p">))</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC74" class="line" lang="python"></span>

</pre>

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<pre style="margin: 0;">+<span id="LC75" class="line" lang="python">        <span class="c" style="color: #998; font-style: italic;"># Test eigh vs. fsvd pcoa and inplace parameter</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="76" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC76" class="line" lang="python">        <span class="n" style="color: #333;">expected_results</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">pcoa</span><span class="p">(</span><span class="n" style="color: #333;">dm1</span><span class="p">,</span> <span class="n" style="color: #333;">method</span><span class="o" style="font-weight: 600;">=</span><span class="s" style="color: #d14;">"eigh"</span><span class="p">,</span> <span class="n" style="color: #333;">number_of_dimensions</span><span class="o" style="font-weight: 600;">=</span><span class="mi" style="color: #099;">3</span><span class="p">,</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="77" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC77" class="line" lang="python">                                <span class="n" style="color: #333;">inplace</span><span class="o" style="font-weight: 600;">=</span><span class="bp" style="color: #999;">False</span><span class="p">)</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC78" class="line" lang="python"></span>

</pre>

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<pre style="margin: 0;">+<span id="LC79" class="line" lang="python">        <span class="n" style="color: #333;">results</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">pcoa</span><span class="p">(</span><span class="n" style="color: #333;">dm2</span><span class="p">,</span> <span class="n" style="color: #333;">method</span><span class="o" style="font-weight: 600;">=</span><span class="s" style="color: #d14;">"fsvd"</span><span class="p">,</span> <span class="n" style="color: #333;">number_of_dimensions</span><span class="o" style="font-weight: 600;">=</span><span class="mi" style="color: #099;">3</span><span class="p">,</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC80" class="line" lang="python">                       <span class="n" style="color: #333;">inplace</span><span class="o" style="font-weight: 600;">=</span><span class="bp" style="color: #999;">False</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="81" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

81

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<pre style="margin: 0;">+<span id="LC81" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="82" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC82" class="line" lang="python">        <span class="n" style="color: #333;">results_inplace</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">pcoa</span><span class="p">(</span><span class="n" style="color: #333;">dm2</span><span class="p">,</span> <span class="n" style="color: #333;">method</span><span class="o" style="font-weight: 600;">=</span><span class="s" style="color: #d14;">"fsvd"</span><span class="p">,</span> <span class="n" style="color: #333;">number_of_dimensions</span><span class="o" style="font-weight: 600;">=</span><span class="mi" style="color: #099;">3</span><span class="p">,</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="83" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

83

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<pre style="margin: 0;">+<span id="LC83" class="line" lang="python">                               <span class="n" style="color: #333;">inplace</span><span class="o" style="font-weight: 600;">=</span><span class="bp" style="color: #999;">True</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="84" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

84

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<pre style="margin: 0;">+<span id="LC84" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="85" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

85

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<pre style="margin: 0;">+<span id="LC85" class="line" lang="python">        <span class="n" style="color: #333;">assert_ordination_results_equal</span><span class="p">(</span><span class="n" style="color: #333;">results</span><span class="p">,</span> <span class="n" style="color: #333;">expected_results</span><span class="p">,</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="86" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

86

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<pre style="margin: 0;">+<span id="LC86" class="line" lang="python">                                        <span class="n" style="color: #333;">ignore_directionality</span><span class="o" style="font-weight: 600;">=</span><span class="bp" style="color: #999;">True</span><span class="p">,</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="87" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

87

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<pre style="margin: 0;">+<span id="LC87" class="line" lang="python">                                        <span class="n" style="color: #333;">ignore_method_names</span><span class="o" style="font-weight: 600;">=</span><span class="bp" style="color: #999;">True</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="88" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

88

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<pre style="margin: 0;">+<span id="LC88" class="line" lang="python"></span>

</pre>

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<pre style="margin: 0;">+<span id="LC89" class="line" lang="python">        <span class="n" style="color: #333;">assert_ordination_results_equal</span><span class="p">(</span><span class="n" style="color: #333;">results</span><span class="p">,</span> <span class="n" style="color: #333;">results_inplace</span><span class="p">,</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="90" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC90" class="line" lang="python">                                        <span class="n" style="color: #333;">ignore_directionality</span><span class="o" style="font-weight: 600;">=</span><span class="bp" style="color: #999;">True</span><span class="p">,</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="91" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC91" class="line" lang="python">                                        <span class="n" style="color: #333;">ignore_method_names</span><span class="o" style="font-weight: 600;">=</span><span class="bp" style="color: #999;">True</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="92" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC92" class="line" lang="python"></span>

</pre>

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<pre style="margin: 0;">+<span id="LC93" class="line" lang="python">        <span class="c" style="color: #998; font-style: italic;"># Test number_of_dimensions edge cases</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="94" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC94" class="line" lang="python">        <span class="n" style="color: #333;">results2</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">pcoa</span><span class="p">(</span><span class="n" style="color: #333;">dm3</span><span class="p">,</span> <span class="n" style="color: #333;">method</span><span class="o" style="font-weight: 600;">=</span><span class="s" style="color: #d14;">"fsvd"</span><span class="p">,</span> <span class="n" style="color: #333;">number_of_dimensions</span><span class="o" style="font-weight: 600;">=</span><span class="mi" style="color: #099;">0</span><span class="p">,</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="95" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

95

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<pre style="margin: 0;">+<span id="LC95" class="line" lang="python">                        <span class="n" style="color: #333;">inplace</span><span class="o" style="font-weight: 600;">=</span><span class="bp" style="color: #999;">False</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="96" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC96" class="line" lang="python">        <span class="n" style="color: #333;">expected_results2</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">pcoa</span><span class="p">(</span><span class="n" style="color: #333;">dm3</span><span class="p">,</span> <span class="n" style="color: #333;">method</span><span class="o" style="font-weight: 600;">=</span><span class="s" style="color: #d14;">"fsvd"</span><span class="p">,</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="97" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

97

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<pre style="margin: 0;">+<span id="LC97" class="line" lang="python">                                 <span class="n" style="color: #333;">number_of_dimensions</span><span class="o" style="font-weight: 600;">=</span><span class="n" style="color: #333;">dm3</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">data</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">shape</span><span class="p">[</span><span class="mi" style="color: #099;">0</span><span class="p">],</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="98" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

98

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<pre style="margin: 0;">+<span id="LC98" class="line" lang="python">                                 <span class="n" style="color: #333;">inplace</span><span class="o" style="font-weight: 600;">=</span><span class="bp" style="color: #999;">False</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="99" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

99

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<pre style="margin: 0;">+<span id="LC99" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="100" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

100

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<pre style="margin: 0;">+<span id="LC100" class="line" lang="python">        <span class="n" style="color: #333;">assert_ordination_results_equal</span><span class="p">(</span><span class="n" style="color: #333;">results2</span><span class="p">,</span> <span class="n" style="color: #333;">expected_results2</span><span class="p">,</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="101" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

101

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<pre style="margin: 0;">+<span id="LC101" class="line" lang="python">                                        <span class="n" style="color: #333;">ignore_directionality</span><span class="o" style="font-weight: 600;">=</span><span class="bp" style="color: #999;">True</span><span class="p">,</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="102" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

102

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<pre style="margin: 0;">+<span id="LC102" class="line" lang="python">                                        <span class="n" style="color: #333;">ignore_method_names</span><span class="o" style="font-weight: 600;">=</span><span class="bp" style="color: #999;">True</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="103" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

103

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<pre style="margin: 0;">+<span id="LC103" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="104" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC104" class="line" lang="python">        <span class="k" style="font-weight: 600;">with</span> <span class="bp" style="color: #999;">self</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">assertRaises</span><span class="p">(</span><span class="nb" style="color: #0086b3;">ValueError</span><span class="p">):</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="105" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

105

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<pre style="margin: 0;">+<span id="LC105" class="line" lang="python">            <span class="n" style="color: #333;">dim_too_large</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">dm1</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">data</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">shape</span><span class="p">[</span><span class="mi" style="color: #099;">0</span><span class="p">]</span> <span class="o" style="font-weight: 600;">+</span> <span class="mi" style="color: #099;">10</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="106" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

106

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<pre style="margin: 0;">+<span id="LC106" class="line" lang="python">            <span class="n" style="color: #333;">pcoa</span><span class="p">(</span><span class="n" style="color: #333;">dm2</span><span class="p">,</span> <span class="n" style="color: #333;">method</span><span class="o" style="font-weight: 600;">=</span><span class="s" style="color: #d14;">"fsvd"</span><span class="p">,</span> <span class="n" style="color: #333;">number_of_dimensions</span><span class="o" style="font-weight: 600;">=</span><span class="n" style="color: #333;">dim_too_large</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="107" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

107

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<pre style="margin: 0;">+<span id="LC107" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="108" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC108" class="line" lang="python">        <span class="k" style="font-weight: 600;">with</span> <span class="bp" style="color: #999;">self</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">assertRaises</span><span class="p">(</span><span class="nb" style="color: #0086b3;">ValueError</span><span class="p">):</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="109" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

109

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<pre style="margin: 0;">+<span id="LC109" class="line" lang="python">            <span class="n" style="color: #333;">pcoa</span><span class="p">(</span><span class="n" style="color: #333;">dm2</span><span class="p">,</span> <span class="n" style="color: #333;">method</span><span class="o" style="font-weight: 600;">=</span><span class="s" style="color: #d14;">"fsvd"</span><span class="p">,</span> <span class="n" style="color: #333;">number_of_dimensions</span><span class="o" style="font-weight: 600;">=-</span><span class="mi" style="color: #099;">1</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="110" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

110

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<pre style="margin: 0;">+<span id="LC110" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="111" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

111

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<pre style="margin: 0;">+<span id="LC111" class="line" lang="python">        <span class="k" style="font-weight: 600;">with</span> <span class="bp" style="color: #999;">self</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">assertRaises</span><span class="p">(</span><span class="nb" style="color: #0086b3;">ValueError</span><span class="p">):</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="112" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

112

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<pre style="margin: 0;">+<span id="LC112" class="line" lang="python">            <span class="n" style="color: #333;">dim_too_large</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">dm1</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">data</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">shape</span><span class="p">[</span><span class="mi" style="color: #099;">0</span><span class="p">]</span> <span class="o" style="font-weight: 600;">+</span> <span class="mi" style="color: #099;">10</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="113" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC113" class="line" lang="python">            <span class="n" style="color: #333;">pcoa</span><span class="p">(</span><span class="n" style="color: #333;">dm2</span><span class="p">,</span> <span class="n" style="color: #333;">method</span><span class="o" style="font-weight: 600;">=</span><span class="s" style="color: #d14;">"eigh"</span><span class="p">,</span> <span class="n" style="color: #333;">number_of_dimensions</span><span class="o" style="font-weight: 600;">=</span><span class="n" style="color: #333;">dim_too_large</span><span class="p">)</span></span>

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<pre style="margin: 0;">+<span id="LC114" class="line" lang="python"></span>

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<td class="diff-line-num new new_line" data-linenumber="115" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC115" class="line" lang="python">        <span class="k" style="font-weight: 600;">with</span> <span class="bp" style="color: #999;">self</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">assertRaises</span><span class="p">(</span><span class="nb" style="color: #0086b3;">ValueError</span><span class="p">):</span></span>

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<td class="diff-line-num new new_line" data-linenumber="116" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC116" class="line" lang="python">            <span class="n" style="color: #333;">pcoa</span><span class="p">(</span><span class="n" style="color: #333;">dm2</span><span class="p">,</span> <span class="n" style="color: #333;">method</span><span class="o" style="font-weight: 600;">=</span><span class="s" style="color: #d14;">"eigh"</span><span class="p">,</span> <span class="n" style="color: #333;">number_of_dimensions</span><span class="o" style="font-weight: 600;">=-</span><span class="mi" style="color: #099;">1</span><span class="p">)</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC117" class="line" lang="python"></span>

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<pre style="margin: 0;">+<span id="LC118" class="line" lang="python">        <span class="n" style="color: #333;">dm_big</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">DistanceMatrix</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">read</span><span class="p">(</span><span class="n" style="color: #333;">get_data_path</span><span class="p">(</span><span class="s" style="color: #d14;">'PCoA_sample_data_12dim'</span><span class="p">))</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC119" class="line" lang="python">        <span class="k" style="font-weight: 600;">with</span> <span class="bp" style="color: #999;">self</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">assertWarnsRegex</span><span class="p">(</span><span class="nb" style="color: #0086b3;">RuntimeWarning</span><span class="p">,</span></span>

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<pre style="margin: 0;">+<span id="LC120" class="line" lang="python">                                   <span class="s" style="color: #d14;">"no value for number_of_dimensions"</span><span class="p">):</span></span>

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<pre style="margin: 0;">+<span id="LC121" class="line" lang="python">            <span class="n" style="color: #333;">pcoa</span><span class="p">(</span><span class="n" style="color: #333;">dm_big</span><span class="p">,</span> <span class="n" style="color: #333;">method</span><span class="o" style="font-weight: 600;">=</span><span class="s" style="color: #d14;">"fsvd"</span><span class="p">,</span> <span class="n" style="color: #333;">number_of_dimensions</span><span class="o" style="font-weight: 600;">=</span><span class="mi" style="color: #099;">0</span><span class="p">)</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC122" class="line" lang="python"></span>

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<pre style="margin: 0;"> <span id="LC123" class="line" lang="python">    <span class="k" style="font-weight: 600;">def</span> <span class="nf" style="color: #900; font-weight: 600;">test_extensive</span><span class="p">(</span><span class="bp" style="color: #999;">self</span><span class="p">):</span></span>

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<pre style="margin: 0;"> <span id="LC124" class="line" lang="python">        <span class="n" style="color: #333;">eigvals</span> <span class="o" style="font-weight: 600;">=</span> <span class="p">[</span><span class="mf" style="color: #099;">0.3984635</span><span class="p">,</span> <span class="mf" style="color: #099;">0.36405689</span><span class="p">,</span> <span class="mf" style="color: #099;">0.28804535</span><span class="p">,</span> <span class="mf" style="color: #099;">0.27479983</span><span class="p">,</span></span>

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<pre style="margin: 0;"> <span id="LC125" class="line" lang="python">                   <span class="mf" style="color: #099;">0.19165361</span><span class="p">,</span> <span class="mf" style="color: #099;">0.0</span><span class="p">]</span></span>

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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -203,15 +270,17 @@ class TestPCoABiplot(TestCase):</td>

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<pre style="margin: 0;"> <span id="LC270" class="line" lang="python">        <span class="bp" style="color: #999;">self</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">descriptors</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">index</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">pd</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">Index</span><span class="p">(</span><span class="n" style="color: #333;">new_index</span><span class="p">)</span></span>

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<pre style="margin: 0;"> <span id="LC271" class="line" lang="python"></span>

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<pre style="margin: 0;"> <span id="LC272" class="line" lang="python">        <span class="k" style="font-weight: 600;">with</span> <span class="bp" style="color: #999;">self</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">assertRaisesRegex</span><span class="p">(</span><span class="nb" style="color: #0086b3;">ValueError</span><span class="p">,</span> <span class="s" style="color: #d14;">'The eigenvectors and the '</span></span>

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<td class="diff-line-num new_line old" data-linenumber="273" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<pre style="margin: 0;">-<span id="LC206" class="line" lang="python">                                    <span class="s" style="color: #d14;">'descriptors must describe the same '</span></span>

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<pre style="margin: 0;">-<span id="LC207" class="line" lang="python">                                    <span class="s" style="color: #d14;">'samples.'</span><span class="p">):</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="208" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="273" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC273" class="line" lang="python">                                                <span class="s" style="color: #d14;">'descriptors must describe '</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="208" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="274" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC274" class="line" lang="python">                                                <span class="s" style="color: #d14;">'the same '</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC275" class="line" lang="python">                                                <span class="s" style="color: #d14;">'samples.'</span><span class="p">):</span></span>

</pre>

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<pre style="margin: 0;"> <span id="LC276" class="line" lang="python">            <span class="n" style="color: #333;">pcoa_biplot</span><span class="p">(</span><span class="bp" style="color: #999;">self</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">ordination</span><span class="p">,</span> <span class="bp" style="color: #999;">self</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">descriptors</span><span class="p">)</span></span>

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<pre style="margin: 0;"> <span id="LC277" class="line" lang="python"></span>

</pre>

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<pre style="margin: 0;"> <span id="LC278" class="line" lang="python">    <span class="k" style="font-weight: 600;">def</span> <span class="nf" style="color: #900; font-weight: 600;">test_not_a_pcoa</span><span class="p">(</span><span class="bp" style="color: #999;">self</span><span class="p">):</span></span>

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<td class="diff-line-num new_line" data-linenumber="279" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<pre style="margin: 0;"> <span id="LC279" class="line" lang="python">        <span class="bp" style="color: #999;">self</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">ordination</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">short_method_name</span> <span class="o" style="font-weight: 600;">=</span> <span class="s" style="color: #d14;">'RDA'</span></span>

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<pre style="margin: 0;"> <span id="LC280" class="line" lang="python">        <span class="bp" style="color: #999;">self</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">ordination</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">long_method_name</span> <span class="o" style="font-weight: 600;">=</span> <span class="s" style="color: #d14;">'Redundancy Analysis'</span></span>

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<td class="diff-line-num new_line" data-linenumber="281" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<pre style="margin: 0;"> <span id="LC281" class="line" lang="python">        <span class="k" style="font-weight: 600;">with</span> <span class="bp" style="color: #999;">self</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">assertRaisesRegex</span><span class="p">(</span><span class="nb" style="color: #0086b3;">ValueError</span><span class="p">,</span> <span class="s" style="color: #d14;">'This biplot computation can'</span></span>

</pre>

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<pre style="margin: 0;">-<span id="LC214" class="line" lang="python">                                    <span class="s" style="color: #d14;">' only be performed in a PCoA matrix.'</span><span class="p">):</span></span>

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<pre style="margin: 0;">+<span id="LC282" class="line" lang="python">                                                <span class="s" style="color: #d14;">' only be performed in a '</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC283" class="line" lang="python">                                                <span class="s" style="color: #d14;">'PCoA matrix.'</span><span class="p">):</span></span>

</pre>

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<pre style="margin: 0;"> <span id="LC284" class="line" lang="python">            <span class="n" style="color: #333;">pcoa_biplot</span><span class="p">(</span><span class="bp" style="color: #999;">self</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">ordination</span><span class="p">,</span> <span class="bp" style="color: #999;">self</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">descriptors</span><span class="p">)</span></span>

</pre>

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<pre style="margin: 0;"> <span id="LC285" class="line" lang="python"></span>

</pre>

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<pre style="margin: 0;"> <span id="LC286" class="line" lang="python">    <span class="k" style="font-weight: 600;">def</span> <span class="nf" style="color: #900; font-weight: 600;">test_from_seralized_results</span><span class="p">(</span><span class="bp" style="color: #999;">self</span><span class="p">):</span></span>

</pre>

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<br>

</li>

<li id="941ac564379c7746c712dca1c7187329b868b6cc">

<a href="https://salsa.debian.org/med-team/python-skbio/compare/3d3c45f3254533f7a7055537dba85e12078e2138...59737a89a9cfea9e36f5487d037b6dc5e014ee74#941ac564379c7746c712dca1c7187329b868b6cc"><strong>skbio/stats/ordination/tests/test_util.py</strong></a>

<hr>

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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -6,12 +6,16 @@</td>

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<pre style="margin: 0;"> <span id="LC6" class="line" lang="python"><span class="c" style="color: #998; font-style: italic;"># The full license is in the file COPYING.txt, distributed with this software.</span></span>

</pre>

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7

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<td class="diff-line-num new_line" data-linenumber="7" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

7

</td>

<td class="line_content noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;">

<pre style="margin: 0;"> <span id="LC7" class="line" lang="python"><span class="c" style="color: #998; font-style: italic;"># ----------------------------------------------------------------------------</span></span>

</pre>

</td>

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<tr class="line_holder" id="" style="line-height: 1.6;">

<td class="diff-line-num old_line" data-linenumber="8" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

8

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<td class="diff-line-num new_line" data-linenumber="8" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

8

</td>

<td class="line_content noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;">

<pre style="margin: 0;"> <span id="LC8" class="line" lang="python"></span>

</pre>

</td>

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<tr class="line_holder new" id="" style="line-height: 1.6;">

<td class="diff-line-num new old_line" data-linenumber="9" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

</td>

<td class="diff-line-num new new_line" data-linenumber="9" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

9

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC9" class="line" lang="python"><span class="kn" style="font-weight: 600;">from</span> <span class="nn" style="color: #555;">unittest</span> <span class="kn" style="font-weight: 600;">import</span> <span class="n" style="color: #333;">TestCase</span><span class="p">,</span> <span class="n" style="color: #333;">main</span></span>

</pre>

</td>

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<tr class="line_holder new" id="" style="line-height: 1.6;">

<td class="diff-line-num new old_line" data-linenumber="9" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

</td>

<td class="diff-line-num new new_line" data-linenumber="10" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

10

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC10" class="line" lang="python"><span class="kn" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">copy</span></span>

</pre>

</td>

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<td class="diff-line-num new old_line" data-linenumber="9" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

</td>

<td class="diff-line-num new new_line" data-linenumber="11" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

11

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC11" class="line" lang="python"></span>

</pre>

</td>

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<td class="diff-line-num old_line" data-linenumber="9" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

9

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<td class="diff-line-num new_line" data-linenumber="12" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

12

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<td class="line_content noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;">

<pre style="margin: 0;"> <span id="LC12" class="line" lang="python"><span class="kn" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">numpy</span> <span class="k" style="font-weight: 600;">as</span> <span class="n" style="color: #333;">np</span></span>

</pre>

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<td class="diff-line-num old_line" data-linenumber="10" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

10

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<td class="diff-line-num new_line" data-linenumber="13" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

13

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<td class="line_content noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;">

<pre style="margin: 0;"> <span id="LC13" class="line" lang="python"><span class="kn" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">numpy.testing</span> <span class="k" style="font-weight: 600;">as</span> <span class="n" style="color: #333;">npt</span></span>

</pre>

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<td class="diff-line-num old_line" data-linenumber="11" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

11

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<td class="diff-line-num new_line" data-linenumber="14" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

14

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<td class="line_content noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;">

<pre style="margin: 0;"> <span id="LC14" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num old old_line" data-linenumber="12" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

12

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<td class="diff-line-num new_line old" data-linenumber="15" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

</td>

<td class="line_content noteable_line old" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#fbe9eb">

<pre style="margin: 0;">-<span id="LC12" class="line" lang="python"><span class="kn" style="font-weight: 600;">from</span> <span class="nn" style="color: #555;">unittest</span> <span class="kn" style="font-weight: 600;">import</span> <span class="n" style="color: #333;">TestCase</span><span class="p">,</span> <span class="n" style="color: #333;">main</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="13" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

</td>

<td class="diff-line-num new new_line" data-linenumber="15" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

15

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC15" class="line" lang="python"><span class="kn" style="font-weight: 600;">from</span> <span class="nn" style="color: #555;">skbio.stats.ordination</span> <span class="kn" style="font-weight: 600;">import</span> <span class="n" style="color: #333;">corr</span><span class="p">,</span> <span class="n" style="color: #333;">mean_and_std</span><span class="p">,</span> <span class="n" style="color: #333;">e_matrix</span><span class="p">,</span> <span class="n" style="color: #333;">f_matrix</span><span class="p">,</span> \</span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="13" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

</td>

<td class="diff-line-num new new_line" data-linenumber="16" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

16

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC16" class="line" lang="python">    <span class="n" style="color: #333;">center_distance_matrix</span></span>

</pre>

</td>

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<td class="diff-line-num old_line" data-linenumber="13" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

13

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<td class="diff-line-num new_line" data-linenumber="17" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

17

</td>

<td class="line_content noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;">

<pre style="margin: 0;"> <span id="LC17" class="line" lang="python"></span>

</pre>

</td>

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<tr class="line_holder old" id="" style="line-height: 1.6;">

<td class="diff-line-num old old_line" data-linenumber="14" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

14

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<td class="diff-line-num new_line old" data-linenumber="18" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

</td>

<td class="line_content noteable_line old" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#fbe9eb">

<pre style="margin: 0;">-<span id="LC14" class="line" lang="python"><span class="kn" style="font-weight: 600;">from</span> <span class="nn" style="color: #555;">skbio.stats.ordination</span><span class="idiff left"> </span><span class="kn" style="font-weight: 600;"><span class="idiff">import</span></span><span class="idiff"> </span><span class="n" style="color: #333;"><span class="idiff">corr</span></span><span class="p"><span class="idiff">,</span></span><span class="idiff"> </span><span class="n" style="color: #333;"><span class="idiff">mean_and_std</span></span><span class="p"><span class="idiff">,</span></span><span class="idiff"> </span><span class="n" style="color: #333;"><span class="idiff">e_matrix</span></span><span class="p"><span class="idiff">,</span></span><span class="idiff"> </span><span class="n" style="color: #333;"><span class="idiff right">f_matrix</span></span></span>

</pre>

</td>

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<td class="diff-line-num new old_line" data-linenumber="15" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

</td>

<td class="diff-line-num new new_line" data-linenumber="18" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

18

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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">

<pre style="margin: 0;">+<span id="LC18" class="line" lang="python"><span class="kn" style="font-weight: 600;">from</span> <span class="nn" style="color: #555;">skbio.stats.ordination<span class="idiff left">._utils</span></span><span class="idiff"> </span><span class="kn" style="font-weight: 600;"><span class="idiff">import</span></span><span class="idiff"> </span><span class="n" style="color: #333;"><span class="idiff">_e_matrix_inplace</span></span><span class="p"><span class="idiff">,</span></span><span class="idiff"> </span><span class="n" style="color: #333;"><span class="idiff right">_f_matrix_inplace</span></span></span>

</pre>

</td>

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<td class="diff-line-num old_line" data-linenumber="15" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

15

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<td class="diff-line-num new_line" data-linenumber="19" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

19

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<td class="line_content noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;">

<pre style="margin: 0;"> <span id="LC19" class="line" lang="python"></span>

</pre>

</td>

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<td class="diff-line-num old_line" data-linenumber="16" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<td class="diff-line-num new_line" data-linenumber="20" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<td class="line_content noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;">

<pre style="margin: 0;"> <span id="LC20" class="line" lang="python"></span>

</pre>

</td>

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<td class="diff-line-num old_line" data-linenumber="17" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<td class="diff-line-num new_line" data-linenumber="21" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<td class="line_content noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;">

<pre style="margin: 0;"> <span id="LC21" class="line" lang="python"><span class="k" style="font-weight: 600;">class</span> <span class="nc" style="color: #458; font-weight: 600;">TestUtils</span><span class="p">(</span><span class="n" style="color: #333;">TestCase</span><span class="p">):</span></span>

</pre>

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<td class="diff-line-num unfold js-unfold old_line" data-linenumber="51" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">...</td>

<td class="diff-line-num unfold js-unfold new_line" data-linenumber="55" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">...</td>

<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -51,7 +55,7 @@ class TestUtils(TestCase):</td>

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<td class="diff-line-num old_line" data-linenumber="51" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<td class="diff-line-num new_line" data-linenumber="55" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<td class="line_content noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;">

<pre style="margin: 0;"> <span id="LC55" class="line" lang="python"></span>

</pre>

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<pre style="margin: 0;"> <span id="LC56" class="line" lang="python">    <span class="k" style="font-weight: 600;">def</span> <span class="nf" style="color: #900; font-weight: 600;">test_e_matrix</span><span class="p">(</span><span class="bp" style="color: #999;">self</span><span class="p">):</span></span>

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<pre style="margin: 0;"> <span id="LC57" class="line" lang="python">        <span class="n" style="color: #333;">E</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">e_matrix</span><span class="p">(</span><span class="bp" style="color: #999;">self</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">matrix</span><span class="p">)</span></span>

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<pre style="margin: 0;">-<span id="LC54" class="line" lang="python">        <span class="n" style="color: #333;">expected_E</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">np</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">array</span><span class="p">([[</span><span class="o" style="font-weight: 600;">-</span><span class="mf" style="color: #099;">0.5</span><span class="p">,</span> <span class="idiff left"> </span><span class="o" style="font-weight: 600;"><span class="idiff">-</span></span><span class="mf" style="color: #099;"><span class="idiff">2.</span></span><span class="p"><span class="idiff">,</span></span><span class="idiff right"> </span> <span class="o" style="font-weight: 600;">-</span><span class="mf" style="color: #099;">4.5</span><span class="p">],</span></span>

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<pre style="margin: 0;">+<span id="LC58" class="line" lang="python">        <span class="n" style="color: #333;">expected_E</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">np</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">array</span><span class="p">([[</span><span class="o" style="font-weight: 600;">-</span><span class="mf" style="color: #099;">0.5</span><span class="p">,</span> <span class="o" style="font-weight: 600;"><span class="idiff left">-</span></span><span class="mf" style="color: #099;"><span class="idiff">2.</span></span><span class="p"><span class="idiff right">,</span></span> <span class="o" style="font-weight: 600;">-</span><span class="mf" style="color: #099;">4.5</span><span class="p">],</span></span>

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<pre style="margin: 0;"> <span id="LC59" class="line" lang="python">                               <span class="p">[</span><span class="o" style="font-weight: 600;">-</span><span class="mf" style="color: #099;">8.</span><span class="p">,</span> <span class="o" style="font-weight: 600;">-</span><span class="mf" style="color: #099;">12.5</span><span class="p">,</span> <span class="o" style="font-weight: 600;">-</span><span class="mf" style="color: #099;">18.</span><span class="p">]])</span></span>

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<pre style="margin: 0;"> <span id="LC60" class="line" lang="python">        <span class="n" style="color: #333;">npt</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">assert_almost_equal</span><span class="p">(</span><span class="n" style="color: #333;">E</span><span class="p">,</span> <span class="n" style="color: #333;">expected_E</span><span class="p">)</span></span>

</pre>

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<pre style="margin: 0;"> <span id="LC61" class="line" lang="python"></span>

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<td class="diff-line-num unfold js-unfold old_line" data-linenumber="61" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">...</td>

<td class="diff-line-num unfold js-unfold new_line" data-linenumber="65" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">...</td>

<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -61,6 +65,37 @@ class TestUtils(TestCase):</td>

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<pre style="margin: 0;"> <span id="LC65" class="line" lang="python">        <span class="c" style="color: #998; font-style: italic;"># Note that `test_make_F_matrix` in cogent is wrong</span></span>

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<pre style="margin: 0;"> <span id="LC66" class="line" lang="python">        <span class="n" style="color: #333;">npt</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">assert_almost_equal</span><span class="p">(</span><span class="n" style="color: #333;">F</span><span class="p">,</span> <span class="n" style="color: #333;">expected_F</span><span class="p">)</span></span>

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<pre style="margin: 0;"> <span id="LC67" class="line" lang="python"></span>

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<pre style="margin: 0;">+<span id="LC68" class="line" lang="python">    <span class="k" style="font-weight: 600;">def</span> <span class="nf" style="color: #900; font-weight: 600;">test_e_matrix_inplace</span><span class="p">(</span><span class="bp" style="color: #999;">self</span><span class="p">):</span></span>

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<pre style="margin: 0;">+<span id="LC69" class="line" lang="python">        <span class="n" style="color: #333;">E</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">_e_matrix_inplace</span><span class="p">(</span><span class="bp" style="color: #999;">self</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">matrix</span><span class="p">)</span></span>

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<pre style="margin: 0;">+<span id="LC70" class="line" lang="python">        <span class="n" style="color: #333;">expected_E</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">np</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">array</span><span class="p">([[</span><span class="o" style="font-weight: 600;">-</span><span class="mf" style="color: #099;">0.5</span><span class="p">,</span> <span class="o" style="font-weight: 600;">-</span><span class="mf" style="color: #099;">2.</span><span class="p">,</span> <span class="o" style="font-weight: 600;">-</span><span class="mf" style="color: #099;">4.5</span><span class="p">],</span></span>

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<pre style="margin: 0;">+<span id="LC71" class="line" lang="python">                               <span class="p">[</span><span class="o" style="font-weight: 600;">-</span><span class="mf" style="color: #099;">8.</span><span class="p">,</span> <span class="o" style="font-weight: 600;">-</span><span class="mf" style="color: #099;">12.5</span><span class="p">,</span> <span class="o" style="font-weight: 600;">-</span><span class="mf" style="color: #099;">18.</span><span class="p">]])</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC72" class="line" lang="python">        <span class="n" style="color: #333;">npt</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">assert_almost_equal</span><span class="p">(</span><span class="n" style="color: #333;">E</span><span class="p">,</span> <span class="n" style="color: #333;">expected_E</span><span class="p">)</span></span>

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<pre style="margin: 0;">+<span id="LC73" class="line" lang="python"></span>

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<td class="diff-line-num new new_line" data-linenumber="74" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC74" class="line" lang="python">    <span class="k" style="font-weight: 600;">def</span> <span class="nf" style="color: #900; font-weight: 600;">test_f_matrix_inplace</span><span class="p">(</span><span class="bp" style="color: #999;">self</span><span class="p">):</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="75" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC75" class="line" lang="python">        <span class="n" style="color: #333;">F</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">_f_matrix_inplace</span><span class="p">(</span><span class="bp" style="color: #999;">self</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">matrix2</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="76" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC76" class="line" lang="python">        <span class="n" style="color: #333;">expected_F</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">np</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">zeros</span><span class="p">((</span><span class="mi" style="color: #099;">3</span><span class="p">,</span> <span class="mi" style="color: #099;">3</span><span class="p">))</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="77" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC77" class="line" lang="python">        <span class="n" style="color: #333;">npt</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">assert_almost_equal</span><span class="p">(</span><span class="n" style="color: #333;">F</span><span class="p">,</span> <span class="n" style="color: #333;">expected_F</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="78" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC78" class="line" lang="python"></span>

</pre>

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<pre style="margin: 0;">+<span id="LC79" class="line" lang="python">    <span class="k" style="font-weight: 600;">def</span> <span class="nf" style="color: #900; font-weight: 600;">test_center_distance_matrix_inplace</span><span class="p">(</span><span class="bp" style="color: #999;">self</span><span class="p">):</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="80" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC80" class="line" lang="python">        <span class="n" style="color: #333;">dm_expected</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">f_matrix</span><span class="p">(</span><span class="n" style="color: #333;">e_matrix</span><span class="p">(</span><span class="bp" style="color: #999;">self</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">small_mat</span><span class="p">))</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="81" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

81

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<pre style="margin: 0;">+<span id="LC81" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="64" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="82" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC82" class="line" lang="python">        <span class="c" style="color: #998; font-style: italic;"># make copy of matrix to test inplace centering</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC83" class="line" lang="python">        <span class="n" style="color: #333;">matrix_copy</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">copy</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">deepcopy</span><span class="p">(</span><span class="bp" style="color: #999;">self</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">small_mat</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="84" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC84" class="line" lang="python">        <span class="n" style="color: #333;">dm_centered</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">center_distance_matrix</span><span class="p">(</span><span class="n" style="color: #333;">matrix_copy</span><span class="p">,</span> <span class="n" style="color: #333;">inplace</span><span class="o" style="font-weight: 600;">=</span><span class="bp" style="color: #999;">False</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="85" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC85" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="86" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC86" class="line" lang="python">        <span class="c" style="color: #998; font-style: italic;"># ensure that matrix_copy was NOT modified inplace</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="64" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="87" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC87" class="line" lang="python">        <span class="bp" style="color: #999;">self</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">assertTrue</span><span class="p">(</span><span class="n" style="color: #333;">np</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">array_equal</span><span class="p">(</span><span class="n" style="color: #333;">matrix_copy</span><span class="p">,</span> <span class="bp" style="color: #999;">self</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">small_mat</span><span class="p">))</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="64" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="88" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC88" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="64" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="89" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC89" class="line" lang="python">        <span class="c" style="color: #998; font-style: italic;"># and ensure that the result of centering was correct</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC90" class="line" lang="python">        <span class="n" style="color: #333;">npt</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">assert_almost_equal</span><span class="p">(</span><span class="n" style="color: #333;">dm_expected</span><span class="p">,</span> <span class="n" style="color: #333;">dm_centered</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="91" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

91

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<pre style="margin: 0;">+<span id="LC91" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="64" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="92" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC92" class="line" lang="python">        <span class="c" style="color: #998; font-style: italic;"># next, sort same matrix inplace</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="64" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="93" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC93" class="line" lang="python">        <span class="n" style="color: #333;">matrix_copy2</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">copy</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">deepcopy</span><span class="p">(</span><span class="bp" style="color: #999;">self</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">small_mat</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="64" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="94" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC94" class="line" lang="python">        <span class="n" style="color: #333;">dm_centered_inp</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">center_distance_matrix</span><span class="p">(</span><span class="n" style="color: #333;">matrix_copy2</span><span class="p">,</span> <span class="n" style="color: #333;">inplace</span><span class="o" style="font-weight: 600;">=</span><span class="bp" style="color: #999;">True</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="95" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC95" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num new old_line" data-linenumber="64" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<td class="diff-line-num new new_line" data-linenumber="96" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC96" class="line" lang="python">        <span class="c" style="color: #998; font-style: italic;"># and ensure that the result of inplace centering was correct</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="97" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC97" class="line" lang="python">        <span class="n" style="color: #333;">npt</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">assert_almost_equal</span><span class="p">(</span><span class="n" style="color: #333;">dm_expected</span><span class="p">,</span> <span class="n" style="color: #333;">dm_centered_inp</span><span class="p">)</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="98" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC98" class="line" lang="python"></span>

</pre>

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64

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<td class="diff-line-num new_line" data-linenumber="99" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<pre style="margin: 0;"> <span id="LC99" class="line" lang="python"></span>

</pre>

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<pre style="margin: 0;"> <span id="LC100" class="line" lang="python"><span class="k" style="font-weight: 600;">if</span> <span class="n" style="color: #333;">__name__</span> <span class="o" style="font-weight: 600;">==</span> <span class="s" style="color: #d14;">'__main__'</span><span class="p">:</span></span>

</pre>

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<td class="diff-line-num old_line" data-linenumber="66" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<pre style="margin: 0;"> <span id="LC101" class="line" lang="python">    <span class="n" style="color: #333;">main</span><span class="p">()</span></span></pre>

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<br>

</li>

<li id="21f22f46349a2970cbaac9ddeaee97358aee79b5">

<a href="https://salsa.debian.org/med-team/python-skbio/compare/3d3c45f3254533f7a7055537dba85e12078e2138...59737a89a9cfea9e36f5487d037b6dc5e014ee74#21f22f46349a2970cbaac9ddeaee97358aee79b5"><strong>skbio/util/_testing.py</strong></a>

<hr>

<table class="code white" style="font-family: monospace; font-size: 90%;" bgcolor="#fff" width="100%" cellpadding="0" cellspacing="0">

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<td class="diff-line-num unfold js-unfold old_line" data-linenumber="6" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">...</td>

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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -6,9 +6,9 @@</td>

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<pre style="margin: 0;"> <span id="LC6" class="line" lang="python"><span class="c" style="color: #998; font-style: italic;"># The full license is in the file COPYING.txt, distributed with this software.</span></span>

</pre>

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<td class="diff-line-num new_line" data-linenumber="7" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">

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<pre style="margin: 0;"> <span id="LC7" class="line" lang="python"><span class="c" style="color: #998; font-style: italic;"># ----------------------------------------------------------------------------</span></span>

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<pre style="margin: 0;"> <span id="LC8" class="line" lang="python"></span>

</pre>

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<td class="diff-line-num old old_line" data-linenumber="9" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<td class="diff-line-num new_line old" data-linenumber="9" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<pre style="margin: 0;">-<span id="LC9" class="line" lang="python"><span class="kn" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">os</span></span>

</pre>

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<td class="diff-line-num new_line old" data-linenumber="9" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">

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<pre style="margin: 0;">-<span id="LC10" class="line" lang="python"><span class="kn" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">inspect</span></span>

</pre>

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<pre style="margin: 0;"> <span id="LC9" class="line" lang="python"><span class="kn" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">warnings</span></span>

</pre>

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<td class="diff-line-num new new_line" data-linenumber="10" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">

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<pre style="margin: 0;">+<span id="LC10" class="line" lang="python"><span class="kn" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">inspect</span></span>

</pre>

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<pre style="margin: 0;">+<span id="LC11" class="line" lang="python"><span class="kn" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">os</span></span>

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<pre style="margin: 0;"> <span id="LC12" class="line" lang="python"></span>

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<pre style="margin: 0;"> <span id="LC13" class="line" lang="python"><span class="kn" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">nose</span></span>

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<pre style="margin: 0;"> <span id="LC14" class="line" lang="python"><span class="kn" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">numpy</span> <span class="k" style="font-weight: 600;">as</span> <span class="n" style="color: #333;">np</span></span>

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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -80,6 +80,7 @@ class TestRunner:</td>

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<pre style="margin: 0;"> <span id="LC80" class="line" lang="python"><span class="s" style="color: #d14;">    and ugly. This class invokes nose with the required options.</span></span>

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<pre style="margin: 0;"> <span id="LC81" class="line" lang="python"></span>

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<pre style="margin: 0;"> <span id="LC82" class="line" lang="python"><span class="s" style="color: #d14;">    """</span></span>

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<pre style="margin: 0;">+<span id="LC83" class="line" lang="python"></span>

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<pre style="margin: 0;"> <span id="LC84" class="line" lang="python">    <span class="nd">@experimental</span><span class="p">(</span><span class="n" style="color: #333;">as_of</span><span class="o" style="font-weight: 600;">=</span><span class="s" style="color: #d14;">"0.4.0"</span><span class="p">)</span></span>

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<pre style="margin: 0;"> <span id="LC85" class="line" lang="python">    <span class="k" style="font-weight: 600;">def</span> <span class="nf" style="color: #900; font-weight: 600;">__init__</span><span class="p">(</span><span class="bp" style="color: #999;">self</span><span class="p">,</span> <span class="n" style="color: #333;">filename</span><span class="p">):</span></span>

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<pre style="margin: 0;"> <span id="LC86" class="line" lang="python">        <span class="bp" style="color: #999;">self</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">_filename</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">filename</span></span>

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<td class="diff-line-num unfold js-unfold new_line" data-linenumber="280" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">...</td>

<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -279,7 +280,7 @@ def _normalize_signs(arr1, arr2):</td>

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<pre style="margin: 0;"> <span id="LC280" class="line" lang="python">        <span class="k" style="font-weight: 600;">raise</span> <span class="nb" style="color: #0086b3;">ValueError</span><span class="p">(</span></span>

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<pre style="margin: 0;"> <span id="LC281" class="line" lang="python">            <span class="s" style="color: #d14;">"Arrays must have the same shape ({0} vs {1})."</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">format</span><span class="p">(</span><span class="n" style="color: #333;">arr1</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">shape</span><span class="p">,</span></span>

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<pre style="margin: 0;"> <span id="LC282" class="line" lang="python">                                                                   <span class="n" style="color: #333;">arr2</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">shape</span><span class="p">)</span></span>

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<pre style="margin: 0;">-<span id="LC282" class="line" lang="python">        <span class="idiff left right">    </span><span class="p">)</span></span>

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<pre style="margin: 0;">+<span id="LC283" class="line" lang="python">        <span class="p">)</span></span>

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<pre style="margin: 0;"> <span id="LC284" class="line" lang="python"></span>

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<pre style="margin: 0;"> <span id="LC285" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># To avoid issues around zero, we'll compare signs of the values</span></span>

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<pre style="margin: 0;"> <span id="LC286" class="line" lang="python">    <span class="c" style="color: #998; font-style: italic;"># with highest absolute value</span></span>

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