[Pkg-javascript-commits] [science.js] 51/87: Rename science.vector to science.lin.
bhuvan krishna
bhuvan-guest at moszumanska.debian.org
Thu Dec 8 06:11:59 UTC 2016
This is an automated email from the git hooks/post-receive script.
bhuvan-guest pushed a commit to branch master
in repository science.js.
commit 48868457ac1d7c4462605b4ee3ee7c8b53203b73
Author: Jason Davies <jason at jasondavies.com>
Date: Thu Dec 15 13:03:54 2011 +0000
Rename science.vector to science.lin.
---
Makefile | 24 +-
science.js | 874 -------------------------------------
science.lin.js | 873 ++++++++++++++++++++++++++++++++++++
science.lin.min.js | 2 +-
science.min.js | 2 +-
src/{vector => lin}/cross.js | 2 +-
src/{vector => lin}/decompose.js | 28 +-
src/{vector => lin}/determinant.js | 2 +-
src/{vector => lin}/dot.js | 2 +-
src/{vector => lin}/gaussjordan.js | 2 +-
src/{vector => lin}/inverse.js | 4 +-
src/{vector => lin}/length.js | 2 +-
src/{vector => lin}/multiply.js | 2 +-
src/lin/normalize.js | 4 +
src/{vector => lin}/transpose.js | 2 +-
src/vector/normalize.js | 4 -
src/vector/vector.js | 1 -
test/lin/decompose-test.js | 24 +
test/lin/tridag-test.js | 2 +-
test/vector/decompose-test.js | 23 -
20 files changed, 937 insertions(+), 942 deletions(-)
diff --git a/Makefile b/Makefile
index 3c4eaa7..e686c2c 100644
--- a/Makefile
+++ b/Makefile
@@ -13,7 +13,6 @@ all: \
.INTERMEDIATE science.js: \
src/start.js \
science.core.js \
- science.vector.js \
src/end.js
science.core.js: \
@@ -26,22 +25,19 @@ science.core.js: \
src/core/quadratic.js \
src/core/zeroes.js
-science.vector.js: \
- src/vector/vector.js \
- src/vector/decompose.js \
- src/vector/cross.js \
- src/vector/dot.js \
- src/vector/length.js \
- src/vector/normalize.js \
- src/vector/determinant.js \
- src/vector/gaussjordan.js \
- src/vector/inverse.js \
- src/vector/multiply.js \
- src/vector/transpose.js
-
science.lin.js: \
src/start.js \
src/lin/lin.js \
+ src/lin/decompose.js \
+ src/lin/cross.js \
+ src/lin/dot.js \
+ src/lin/length.js \
+ src/lin/normalize.js \
+ src/lin/determinant.js \
+ src/lin/gaussjordan.js \
+ src/lin/inverse.js \
+ src/lin/multiply.js \
+ src/lin/transpose.js \
src/lin/tridag.js \
src/end.js
diff --git a/science.js b/science.js
index 0d0c91b..87293e9 100644
--- a/science.js
+++ b/science.js
@@ -69,878 +69,4 @@ science.zeroes = function(n) {
this, Array.prototype.slice.call(arguments, 1));
return a;
};
-science.vector = {};
-science.vector.decompose = function() {
-
- function decompose(A) {
- var n = A.length; // column dimension
- var V = [],
- d = [],
- e = [];
-
- for (var i = 0; i < n; i++) {
- V[i] = [];
- d[i] = [];
- e[i] = [];
- }
-
- var symmetric = true;
- for (var j = 0; j < n; j++) {
- for (var i = 0; i < n; i++) {
- if (A[i][j] !== A[j][i]) {
- symmetric = false;
- break;
- }
- }
- }
-
- if (symmetric) {
- for (var i = 0; i < n; i++) V[i] = A[i].slice();
-
- // Tridiagonalize.
- science_vector_decomposeTred2(d, e, V);
-
- // Diagonalize.
- science_vector_decomposeTql2(d, e, V);
- } else {
- var H = [];
- for (var i = 0; i < n; i++) H[i] = A[i].slice();
-
- // Reduce to Hessenberg form.
- science_vector_decomposeOrthes(H, V);
-
- // Reduce Hessenberg to real Schur form.
- science_vector_decomposeHqr2(d, e, H, V);
- }
-
- var D = [];
- for (var i=0; i<n; i++) {
- var row = D[i] = [];
- for (var j=0; j<n; j++) row[j] = i === j ? d[i] : 0;
- if (e[i] > 0) D[i][i+1] = e[i];
- else if (e[i] < 0) D[i][i-1] = e[i];
- }
- return {D: D, V: V};
- }
-
- return decompose;
-};
-
-// Symmetric Householder reduction to tridiagonal form.
-function science_vector_decomposeTred2(d, e, V) {
- // This is derived from the Algol procedures tred2 by
- // Bowdler, Martin, Reinsch, and Wilkinson, Handbook for
- // Auto. Comp., Vol.ii-Linear Algebra, and the corresponding
- // Fortran subroutine in EISPACK.
-
- var n = V.length;
-
- for (var j = 0; j < n; j++) d[j] = V[n - 1][j];
-
- // Householder reduction to tridiagonal form.
- for (var i = n - 1; i > 0; i--) {
- // Scale to avoid under/overflow.
-
- var scale = 0,
- h = 0;
- for (var k = 0; k < i; k++) { scale = scale + Math.abs(d[k]); }
- if (scale === 0) {
- e[i] = d[i-1];
- for (var j = 0; j < i; j++) {
- d[j] = V[i-1][j];
- V[i][j] = 0;
- V[j][i] = 0;
- }
- } else {
- // Generate Householder vector.
- for (var k = 0; k < i; k++) {
- d[k] /= scale;
- h += d[k] * d[k];
- }
- var f = d[i-1];
- var g = Math.sqrt(h);
- if (f > 0) g = -g;
- e[i] = scale * g;
- h = h - f * g;
- d[i-1] = f - g;
- for (var j = 0; j < i; j++) e[j] = 0;
-
- // Apply similarity transformation to remaining columns.
-
- for (var j = 0; j < i; j++) {
- f = d[j];
- V[j][i] = f;
- g = e[j] + V[j][j] * f;
- for (var k = j+1; k <= i-1; k++) {
- g += V[k][j] * d[k];
- e[k] += V[k][j] * f;
- }
- e[j] = g;
- }
- f = 0;
- for (var j = 0; j < i; j++) {
- e[j] /= h;
- f += e[j] * d[j];
- }
- var hh = f / (h + h);
- for (var j = 0; j < i; j++) { e[j] -= hh * d[j]; }
- for (var j = 0; j < i; j++) {
- f = d[j];
- g = e[j];
- for (var k = j; k <= i-1; k++) { V[k][j] -= (f * e[k] + g * d[k]); }
- d[j] = V[i-1][j];
- V[i][j] = 0;
- }
- }
- d[i] = h;
- }
-
- // Accumulate transformations.
- for (var i = 0; i < n - 1; i++) {
- V[n - 1][i] = V[i][i];
- V[i][i] = 1.0;
- var h = d[i+1];
- if (h != 0) {
- for (var k = 0; k <= i; k++) { d[k] = V[k][i+1] / h; }
- for (var j = 0; j <= i; j++) {
- var g = 0;
- for (var k = 0; k <= i; k++) { g += V[k][i+1] * V[k][j]; }
- for (var k = 0; k <= i; k++) { V[k][j] -= g * d[k]; }
- }
- }
- for (var k = 0; k <= i; k++) { V[k][i+1] = 0; }
- }
- for (var j = 0; j < n; j++) {
- d[j] = V[n - 1][j];
- V[n - 1][j] = 0;
- }
- V[n - 1][n - 1] = 1;
- e[0] = 0;
-}
-
-// Symmetric tridiagonal QL algorithm.
-function science_vector_decomposeTql2(d, e, V) {
- // This is derived from the Algol procedures tql2, by
- // Bowdler, Martin, Reinsch, and Wilkinson, Handbook for
- // Auto. Comp., Vol.ii-Linear Algebra, and the corresponding
- // Fortran subroutine in EISPACK.
-
- var n = V.length;
-
- for (var i = 1; i < n; i++) { e[i-1] = e[i]; }
- e[n - 1] = 0;
-
- var f = 0;
- var tst1 = 0;
- var eps = 1e-12;
- for (var l = 0; l < n; l++) {
- // Find small subdiagonal element
- tst1 = Math.max(tst1, Math.abs(d[l]) + Math.abs(e[l]));
- var m = l;
- while (m < n) {
- if (Math.abs(e[m]) <= eps*tst1) { break; }
- m++;
- }
-
- // If m == l, d[l] is an eigenvalue,
- // otherwise, iterate.
- if (m > l) {
- var iter = 0;
- do {
- iter++; // (Could check iteration count here.)
-
- // Compute implicit shift
- var g = d[l];
- var p = (d[l+1] - g) / (2.0 * e[l]);
- var r = science.hypot(p, 1);
- if (p < 0) {
- r = -r;
- }
- d[l] = e[l] / (p + r);
- d[l+1] = e[l] * (p + r);
- var dl1 = d[l+1];
- var h = g - d[l];
- for (var i = l+2; i < n; i++) {
- d[i] -= h;
- }
- f = f + h;
-
- // Implicit QL transformation.
- p = d[m];
- var c = 1.0;
- var c2 = c;
- var c3 = c;
- var el1 = e[l+1];
- var s = 0;
- var s2 = 0;
- for (var i = m-1; i >= l; i--) {
- c3 = c2;
- c2 = c;
- s2 = s;
- g = c * e[i];
- h = c * p;
- r = science.hypot(p,e[i]);
- e[i+1] = s * r;
- s = e[i] / r;
- c = p / r;
- p = c * d[i] - s * g;
- d[i+1] = h + s * (c * g + s * d[i]);
-
- // Accumulate transformation.
- for (var k = 0; k < n; k++) {
- h = V[k][i+1];
- V[k][i+1] = s * V[k][i] + c * h;
- V[k][i] = c * V[k][i] - s * h;
- }
- }
- p = -s * s2 * c3 * el1 * e[l] / dl1;
- e[l] = s * p;
- d[l] = c * p;
-
- // Check for convergence.
- } while (Math.abs(e[l]) > eps*tst1);
- }
- d[l] = d[l] + f;
- e[l] = 0;
- }
-
- // Sort eigenvalues and corresponding vectors.
- for (var i = 0; i < n - 1; i++) {
- var k = i;
- var p = d[i];
- for (var j = i+1; j < n; j++) {
- if (d[j] < p) {
- k = j;
- p = d[j];
- }
- }
- if (k != i) {
- d[k] = d[i];
- d[i] = p;
- for (var j = 0; j < n; j++) {
- p = V[j][i];
- V[j][i] = V[j][k];
- V[j][k] = p;
- }
- }
- }
-}
-
-// Nonsymmetric reduction to Hessenberg form.
-function science_vector_decomposeOrthes(H, V) {
- // This is derived from the Algol procedures orthes and ortran,
- // by Martin and Wilkinson, Handbook for Auto. Comp.,
- // Vol.ii-Linear Algebra, and the corresponding
- // Fortran subroutines in EISPACK.
-
- var n = H.length;
- var ort = [];
-
- var low = 0;
- var high = n - 1;
-
- for (var m = low + 1; m < high; m++) {
- // Scale column.
- var scale = 0;
- for (var i = m; i <= high; i++) scale += Math.abs(H[i][m - 1]);
-
- if (scale !== 0) {
- // Compute Householder transformation.
- var h = 0;
- for (var i = high; i >= m; i--) {
- ort[i] = H[i][m - 1] / scale;
- h += ort[i] * ort[i];
- }
- var g = Math.sqrt(h);
- if (ort[m] > 0) { g = -g; }
- h = h - ort[m] * g;
- ort[m] = ort[m] - g;
-
- // Apply Householder similarity transformation
- // H = (I-u*u'/h)*H*(I-u*u')/h)
- for (var j = m; j < n; j++) {
- var f = 0;
- for (var i = high; i >= m; i--) f += ort[i] * H[i][j];
- f /= h;
- for (var i = m; i <= high; i++) H[i][j] -= f * ort[i];
- }
-
- for (var i = 0; i <= high; i++) {
- var f = 0;
- for (var j = high; j >= m; j--) f += ort[j] * H[i][j];
- f /= h;
- for (var j = m; j <= high; j++) H[i][j] -= f * ort[j];
- }
- ort[m] = scale * ort[m];
- H[m][m - 1] = scale * g;
- }
- }
-
- // Accumulate transformations (Algol's ortran).
- for (var i = 0; i < n; i++) {
- for (var j = 0; j < n; j++) V[i][j] = i === j ? 1 : 0;
- }
-
- for (var m = high-1; m >= low+1; m--) {
- if (H[m][m - 1] !== 0) {
- for (var i = m + 1; i <= high; i++) { ort[i] = H[i][m-1]; }
- for (var j = m; j <= high; j++) {
- var g = 0;
- for (var i = m; i <= high; i++) { g += ort[i] * V[i][j]; }
- // Double division avoids possible underflow
- g = (g / ort[m]) / H[m][m-1];
- for (var i = m; i <= high; i++) { V[i][j] += g * ort[i]; }
- }
- }
- }
-}
-
-// Nonsymmetric reduction from Hessenberg to real Schur form.
-function science_vector_decomposeHqr2(d, e, H, V) {
- // This is derived from the Algol procedure hqr2,
- // by Martin and Wilkinson, Handbook for Auto. Comp.,
- // Vol.ii-Linear Algebra, and the corresponding
- // Fortran subroutine in EISPACK.
-
- var nn = H.length,
- n = nn - 1,
- low = 0,
- high = nn - 1,
- eps = 1e-12,
- exshift = 0,
- p = 0,
- q = 0,
- r = 0,
- s = 0,
- z = 0,
- t,
- w,
- x,
- y;
-
- // Store roots isolated by balanc and compute matrix norm
- var norm = 0;
- for (var i = 0; i < nn; i++) {
- if (i < low || i > high) {
- d[i] = H[i][i];
- e[i] = 0;
- }
- for (var j = Math.max(i - 1, 0); j < nn; j++) norm += Math.abs(H[i][j]);
- }
-
- // Outer loop over eigenvalue index
- var iter = 0;
- while (n >= low) {
- // Look for single small sub-diagonal element
- var l = n;
- while (l > low) {
- s = Math.abs(H[l - 1][l - 1]) + Math.abs(H[l][l]);
- if (s === 0) s = norm;
- if (Math.abs(H[l][l - 1]) < eps * s) break;
- l--;
- }
-
- // Check for convergence
- // One root found
- if (l === n) {
- H[n][n] = H[n][n] + exshift;
- d[n] = H[n][n];
- e[n] = 0;
- n--;
- iter = 0;
-
- // Two roots found
- } else if (l === n - 1) {
- w = H[n][n - 1] * H[n - 1][n];
- p = (H[n - 1][n - 1] - H[n][n]) / 2;
- q = p * p + w;
- z = Math.sqrt(Math.abs(q));
- H[n][n] = H[n][n] + exshift;
- H[n - 1][n - 1] = H[n - 1][n - 1] + exshift;
- x = H[n][n];
-
- // Real pair
- if (q >= 0) {
- z = p + (p >= 0 ? z : -z);
- d[n - 1] = x + z;
- d[n] = d[n - 1];
- if (z !== 0) d[n] = x - w / z;
- e[n - 1] = 0;
- e[n] = 0;
- x = H[n][n - 1];
- s = Math.abs(x) + Math.abs(z);
- p = x / s;
- q = z / s;
- r = Math.sqrt(p * p+q * q);
- p /= r;
- q /= r;
-
- // Row modification
- for (var j = n - 1; j < nn; j++) {
- z = H[n - 1][j];
- H[n - 1][j] = q * z + p * H[n][j];
- H[n][j] = q * H[n][j] - p * z;
- }
-
- // Column modification
- for (var i = 0; i <= n; i++) {
- z = H[i][n - 1];
- H[i][n - 1] = q * z + p * H[i][n];
- H[i][n] = q * H[i][n] - p * z;
- }
-
- // Accumulate transformations
- for (var i = low; i <= high; i++) {
- z = V[i][n - 1];
- V[i][n - 1] = q * z + p * V[i][n];
- V[i][n] = q * V[i][n] - p * z;
- }
-
- // Complex pair
- } else {
- d[n - 1] = x + p;
- d[n] = x + p;
- e[n - 1] = z;
- e[n] = -z;
- }
- n = n - 2;
- iter = 0;
-
- // No convergence yet
- } else {
-
- // Form shift
- x = H[n][n];
- y = 0;
- w = 0;
- if (l < n) {
- y = H[n - 1][n - 1];
- w = H[n][n - 1] * H[n - 1][n];
- }
-
- // Wilkinson's original ad hoc shift
- if (iter == 10) {
- exshift += x;
- for (var i = low; i <= n; i++) {
- H[i][i] -= x;
- }
- s = Math.abs(H[n][n - 1]) + Math.abs(H[n - 1][n-2]);
- x = y = 0.75 * s;
- w = -0.4375 * s * s;
- }
-
- // MATLAB's new ad hoc shift
- if (iter == 30) {
- s = (y - x) / 2.0;
- s = s * s + w;
- if (s > 0) {
- s = Math.sqrt(s);
- if (y < x) {
- s = -s;
- }
- s = x - w / ((y - x) / 2.0 + s);
- for (var i = low; i <= n; i++) {
- H[i][i] -= s;
- }
- exshift += s;
- x = y = w = 0.964;
- }
- }
-
- iter++; // (Could check iteration count here.)
-
- // Look for two consecutive small sub-diagonal elements
- var m = n-2;
- while (m >= l) {
- z = H[m][m];
- r = x - z;
- s = y - z;
- p = (r * s - w) / H[m+1][m] + H[m][m+1];
- q = H[m+1][m+1] - z - r - s;
- r = H[m+2][m+1];
- s = Math.abs(p) + Math.abs(q) + Math.abs(r);
- p = p / s;
- q = q / s;
- r = r / s;
- if (m == l) {
- break;
- }
- if (Math.abs(H[m][m-1]) * (Math.abs(q) + Math.abs(r)) <
- eps * (Math.abs(p) * (Math.abs(H[m-1][m-1]) + Math.abs(z) +
- Math.abs(H[m+1][m+1])))) {
- break;
- }
- m--;
- }
-
- for (var i = m+2; i <= n; i++) {
- H[i][i-2] = 0;
- if (i > m+2) { H[i][i-3] = 0; }
- }
-
- // Double QR step involving rows l:n and columns m:n
- for (var k = m; k <= n - 1; k++) {
- var notlast = (k != n - 1);
- if (k != m) {
- p = H[k][k-1];
- q = H[k+1][k-1];
- r = (notlast ? H[k+2][k-1] : 0);
- x = Math.abs(p) + Math.abs(q) + Math.abs(r);
- if (x != 0) {
- p /= x;
- q /= x;
- r /= x;
- }
- }
- if (x == 0) { break; }
- s = Math.sqrt(p * p + q * q + r * r);
- if (p < 0) { s = -s; }
- if (s != 0) {
- if (k != m) H[k][k-1] = -s * x;
- else if (l != m) H[k][k-1] = -H[k][k-1];
- p += s;
- x = p / s;
- y = q / s;
- z = r / s;
- q /= p;
- r /= p;
-
- // Row modification
- for (var j = k; j < nn; j++) {
- p = H[k][j] + q * H[k+1][j];
- if (notlast) {
- p = p + r * H[k+2][j];
- H[k+2][j] = H[k+2][j] - p * z;
- }
- H[k][j] = H[k][j] - p * x;
- H[k+1][j] = H[k+1][j] - p * y;
- }
-
- // Column modification
- for (var i = 0; i <= Math.min(n,k+3); i++) {
- p = x * H[i][k] + y * H[i][k+1];
- if (notlast) {
- p += z * H[i][k+2];
- H[i][k+2] = H[i][k+2] - p * r;
- }
- H[i][k] = H[i][k] - p;
- H[i][k+1] = H[i][k+1] - p * q;
- }
-
- // Accumulate transformations
- for (var i = low; i <= high; i++) {
- p = x * V[i][k] + y * V[i][k+1];
- if (notlast) {
- p = p + z * V[i][k+2];
- V[i][k+2] = V[i][k+2] - p * r;
- }
- V[i][k] = V[i][k] - p;
- V[i][k+1] = V[i][k+1] - p * q;
- }
- } // (s != 0)
- } // k loop
- } // check convergence
- } // while (n >= low)
-
- // Backsubstitute to find vectors of upper triangular form
- if (norm == 0) { return; }
-
- for (n = nn - 1; n >= 0; n--) {
- p = d[n];
- q = e[n];
-
- // Real vector
- if (q == 0) {
- var l = n;
- H[n][n] = 1.0;
- for (var i = n - 1; i >= 0; i--) {
- w = H[i][i] - p;
- r = 0;
- for (var j = l; j <= n; j++) { r = r + H[i][j] * H[j][n]; }
- if (e[i] < 0) {
- z = w;
- s = r;
- } else {
- l = i;
- if (e[i] == 0) {
- if (w != 0) {
- H[i][n] = -r / w;
- } else {
- H[i][n] = -r / (eps * norm);
- }
- } else {
- // Solve real equations
- x = H[i][i+1];
- y = H[i+1][i];
- q = (d[i] - p) * (d[i] - p) + e[i] * e[i];
- t = (x * s - z * r) / q;
- H[i][n] = t;
- if (Math.abs(x) > Math.abs(z)) {
- H[i+1][n] = (-r - w * t) / x;
- } else {
- H[i+1][n] = (-s - y * t) / z;
- }
- }
-
- // Overflow control
- t = Math.abs(H[i][n]);
- if ((eps * t) * t > 1) {
- for (var j = i; j <= n; j++) H[j][n] = H[j][n] / t;
- }
- }
- }
- // Complex vector
- } else if (q < 0) {
- var l = n - 1;
-
- // Last vector component imaginary so matrix is triangular
- if (Math.abs(H[n][n - 1]) > Math.abs(H[n - 1][n])) {
- H[n - 1][n - 1] = q / H[n][n - 1];
- H[n - 1][n] = -(H[n][n] - p) / H[n][n - 1];
- } else {
- var zz = science_vector_decomposeCdiv(0, -H[n - 1][n], H[n - 1][n - 1] - p, q);
- H[n - 1][n - 1] = zz[0];
- H[n - 1][n] = zz[1];
- }
- H[n][n - 1] = 0;
- H[n][n] = 1;
- for (var i = n-2; i >= 0; i--) {
- var ra = 0,
- sa = 0,
- vr,
- vi;
- for (var j = l; j <= n; j++) {
- ra = ra + H[i][j] * H[j][n - 1];
- sa = sa + H[i][j] * H[j][n];
- }
- w = H[i][i] - p;
-
- if (e[i] < 0) {
- z = w;
- r = ra;
- s = sa;
- } else {
- l = i;
- if (e[i] == 0) {
- var zz = science_vector_decomposeCdiv(-ra,-sa,w,q);
- H[i][n - 1] = zz[0];
- H[i][n] = zz[1];
- } else {
- // Solve complex equations
- x = H[i][i+1];
- y = H[i+1][i];
- vr = (d[i] - p) * (d[i] - p) + e[i] * e[i] - q * q;
- vi = (d[i] - p) * 2.0 * q;
- if (vr == 0 & vi == 0) {
- vr = eps * norm * (Math.abs(w) + Math.abs(q) +
- Math.abs(x) + Math.abs(y) + Math.abs(z));
- }
- var zz = science_vector_decomposeCdiv(x*r-z*ra+q*sa,x*s-z*sa-q*ra,vr,vi);
- H[i][n - 1] = zz[0];
- H[i][n] = zz[1];
- if (Math.abs(x) > (Math.abs(z) + Math.abs(q))) {
- H[i+1][n - 1] = (-ra - w * H[i][n - 1] + q * H[i][n]) / x;
- H[i+1][n] = (-sa - w * H[i][n] - q * H[i][n - 1]) / x;
- } else {
- var zz = science_vector_decomposeCdiv(-r-y*H[i][n - 1],-s-y*H[i][n],z,q);
- H[i+1][n - 1] = zz[0];
- H[i+1][n] = zz[1];
- }
- }
-
- // Overflow control
- t = Math.max(Math.abs(H[i][n - 1]),Math.abs(H[i][n]));
- if ((eps * t) * t > 1) {
- for (var j = i; j <= n; j++) {
- H[j][n - 1] = H[j][n - 1] / t;
- H[j][n] = H[j][n] / t;
- }
- }
- }
- }
- }
- }
-
- // Vectors of isolated roots
- for (var i = 0; i < nn; i++) {
- if (i < low || i > high) {
- for (var j = i; j < nn; j++) { V[i][j] = H[i][j]; }
- }
- }
-
- // Back transformation to get eigenvectors of original matrix
- for (var j = nn - 1; j >= low; j--) {
- for (var i = low; i <= high; i++) {
- z = 0;
- for (var k = low; k <= Math.min(j,high); k++) z += V[i][k] * H[k][j];
- V[i][j] = z;
- }
- }
-}
-
-// Complex scalar division.
-function science_vector_decomposeCdiv(xr, xi, yr, yi) {
- var r, d;
- if (Math.abs(yr) > Math.abs(yi)) {
- r = yi / yr;
- d = yr + r * yi;
- return [(xr + r * xi) / d, (xi - r * xr) / d];
- } else {
- r = yr / yi;
- d = yi + r * yr;
- return [(r * xr + xi) / d, (r * xi - xr) / d];
- }
-}
-science.vector.cross = function(a, b) {
- // TODO how to handle non-3D vectors?
- // TODO handle 7D vectors?
- return [
- a[1] * b[2] - a[2] * b[1],
- a[2] * b[0] - a[0] * b[2],
- a[0] * b[1] - a[1] * b[0]
- ];
-};
-science.vector.dot = function(a, b) {
- var s = 0,
- i = -1,
- n = Math.min(a.length, b.length);
- while (++i < n) s += a[i] * b[i];
- return s;
-};
-science.vector.length = function(p) {
- return Math.sqrt(science.vector.dot(p, p));
-};
-science.vector.normalize = function(p) {
- var length = science.vector.length(p);
- return p.map(function(d) { return d / length; });
-};
-// 4x4 matrix determinant.
-science.vector.determinant = function(matrix) {
- var m = matrix[0].concat(matrix[1]).concat(matrix[2]).concat(matrix[3]);
- return (
- m[12] * m[9] * m[6] * m[3] - m[8] * m[13] * m[6] * m[3] -
- m[12] * m[5] * m[10] * m[3] + m[4] * m[13] * m[10] * m[3] +
- m[8] * m[5] * m[14] * m[3] - m[4] * m[9] * m[14] * m[3] -
- m[12] * m[9] * m[2] * m[7] + m[8] * m[13] * m[2] * m[7] +
- m[12] * m[1] * m[10] * m[7] - m[0] * m[13] * m[10] * m[7] -
- m[8] * m[1] * m[14] * m[7] + m[0] * m[9] * m[14] * m[7] +
- m[12] * m[5] * m[2] * m[11] - m[4] * m[13] * m[2] * m[11] -
- m[12] * m[1] * m[6] * m[11] + m[0] * m[13] * m[6] * m[11] +
- m[4] * m[1] * m[14] * m[11] - m[0] * m[5] * m[14] * m[11] -
- m[8] * m[5] * m[2] * m[15] + m[4] * m[9] * m[2] * m[15] +
- m[8] * m[1] * m[6] * m[15] - m[0] * m[9] * m[6] * m[15] -
- m[4] * m[1] * m[10] * m[15] + m[0] * m[5] * m[10] * m[15]);
-};
-// Performs in-place Gauss-Jordan elimination.
-//
-// Based on Jarno Elonen's Python version (public domain):
-// http://elonen.iki.fi/code/misc-notes/python-gaussj/index.html
-science.vector.gaussjordan = function(m, eps) {
- if (!eps) eps = 1e-10;
-
- var h = m.length,
- w = m[0].length,
- y = -1,
- y2,
- x;
-
- while (++y < h) {
- var maxrow = y;
-
- // Find max pivot.
- y2 = y; while (++y2 < h) {
- if (Math.abs(m[y2][y]) > Math.abs(m[maxrow][y]))
- maxrow = y2;
- }
-
- // Swap.
- var tmp = m[y];
- m[y] = m[maxrow];
- m[maxrow] = tmp;
-
- // Singular?
- if (Math.abs(m[y][y]) <= eps) return false;
-
- // Eliminate column y.
- y2 = y; while (++y2 < h) {
- var c = m[y2][y] / m[y][y];
- x = y - 1; while (++x < w) {
- m[y2][x] -= m[y][x] * c;
- }
- }
- }
-
- // Backsubstitute.
- y = h; while (--y >= 0) {
- var c = m[y][y];
- y2 = -1; while (++y2 < y) {
- x = w; while (--x >= y) {
- m[y2][x] -= m[y][x] * m[y2][y] / c;
- }
- }
- m[y][y] /= c;
- // Normalize row y.
- x = h - 1; while (++x < w) {
- m[y][x] /= c;
- }
- }
- return true;
-};
-// Find matrix inverse using Gauss-Jordan.
-science.vector.inverse = function(m) {
- var n = m.length
- i = -1;
-
- // Check if the matrix is square.
- if (n !== m[0].length) return;
-
- // Augment with identity matrix I to get AI.
- m = m.map(function(row, i) {
- var identity = new Array(n),
- j = -1;
- while (++j < n) identity[j] = i === j ? 1 : 0;
- return row.concat(identity);
- });
-
- // Compute IA^-1.
- science.vector.gaussjordan(m);
-
- // Remove identity matrix I to get A^-1.
- while (++i < n) {
- m[i] = m[i].slice(n);
- }
-
- return m;
-};
-science.vector.multiply = function(a, b) {
- var m = a.length,
- n = b[0].length,
- p = b.length,
- i = -1,
- j,
- k;
- if (p !== a[0].length) throw {"error": "columns(a) != rows(b); " + a[0].length + " != " + p};
- var ab = new Array(m);
- while (++i < m) {
- ab[i] = new Array(n);
- j = -1; while(++j < n) {
- var s = 0;
- k = -1; while (++k < p) s += a[i][k] * b[k][j];
- ab[i][j] = s;
- }
- }
- return ab;
-};
-science.vector.transpose = function(a) {
- var m = a.length,
- n = a[0].length,
- i = -1,
- j,
- b = new Array(n);
- while (++i < n) {
- b[i] = new Array(m);
- j = -1; while (++j < m) b[i][j] = a[j][i];
- }
- return b;
-};
})()
\ No newline at end of file
diff --git a/science.lin.js b/science.lin.js
index cbdc2ac..4626e1b 100644
--- a/science.lin.js
+++ b/science.lin.js
@@ -1,4 +1,877 @@
(function(){science.lin = {};
+science.lin.decompose = function() {
+
+ function decompose(A) {
+ var n = A.length; // column dimension
+ var V = [],
+ d = [],
+ e = [];
+
+ for (var i = 0; i < n; i++) {
+ V[i] = [];
+ d[i] = [];
+ e[i] = [];
+ }
+
+ var symmetric = true;
+ for (var j = 0; j < n; j++) {
+ for (var i = 0; i < n; i++) {
+ if (A[i][j] !== A[j][i]) {
+ symmetric = false;
+ break;
+ }
+ }
+ }
+
+ if (symmetric) {
+ for (var i = 0; i < n; i++) V[i] = A[i].slice();
+
+ // Tridiagonalize.
+ science_lin_decomposeTred2(d, e, V);
+
+ // Diagonalize.
+ science_lin_decomposeTql2(d, e, V);
+ } else {
+ var H = [];
+ for (var i = 0; i < n; i++) H[i] = A[i].slice();
+
+ // Reduce to Hessenberg form.
+ science_lin_decomposeOrthes(H, V);
+
+ // Reduce Hessenberg to real Schur form.
+ science_lin_decomposeHqr2(d, e, H, V);
+ }
+
+ var D = [];
+ for (var i=0; i<n; i++) {
+ var row = D[i] = [];
+ for (var j=0; j<n; j++) row[j] = i === j ? d[i] : 0;
+ if (e[i] > 0) D[i][i+1] = e[i];
+ else if (e[i] < 0) D[i][i-1] = e[i];
+ }
+ return {D: D, V: V};
+ }
+
+ return decompose;
+};
+
+// Symmetric Householder reduction to tridiagonal form.
+function science_lin_decomposeTred2(d, e, V) {
+ // This is derived from the Algol procedures tred2 by
+ // Bowdler, Martin, Reinsch, and Wilkinson, Handbook for
+ // Auto. Comp., Vol.ii-Linear Algebra, and the corresponding
+ // Fortran subroutine in EISPACK.
+
+ var n = V.length;
+
+ for (var j = 0; j < n; j++) d[j] = V[n - 1][j];
+
+ // Householder reduction to tridiagonal form.
+ for (var i = n - 1; i > 0; i--) {
+ // Scale to avoid under/overflow.
+
+ var scale = 0,
+ h = 0;
+ for (var k = 0; k < i; k++) { scale = scale + Math.abs(d[k]); }
+ if (scale === 0) {
+ e[i] = d[i-1];
+ for (var j = 0; j < i; j++) {
+ d[j] = V[i-1][j];
+ V[i][j] = 0;
+ V[j][i] = 0;
+ }
+ } else {
+ // Generate Householder vector.
+ for (var k = 0; k < i; k++) {
+ d[k] /= scale;
+ h += d[k] * d[k];
+ }
+ var f = d[i-1];
+ var g = Math.sqrt(h);
+ if (f > 0) g = -g;
+ e[i] = scale * g;
+ h = h - f * g;
+ d[i-1] = f - g;
+ for (var j = 0; j < i; j++) e[j] = 0;
+
+ // Apply similarity transformation to remaining columns.
+
+ for (var j = 0; j < i; j++) {
+ f = d[j];
+ V[j][i] = f;
+ g = e[j] + V[j][j] * f;
+ for (var k = j+1; k <= i-1; k++) {
+ g += V[k][j] * d[k];
+ e[k] += V[k][j] * f;
+ }
+ e[j] = g;
+ }
+ f = 0;
+ for (var j = 0; j < i; j++) {
+ e[j] /= h;
+ f += e[j] * d[j];
+ }
+ var hh = f / (h + h);
+ for (var j = 0; j < i; j++) { e[j] -= hh * d[j]; }
+ for (var j = 0; j < i; j++) {
+ f = d[j];
+ g = e[j];
+ for (var k = j; k <= i-1; k++) { V[k][j] -= (f * e[k] + g * d[k]); }
+ d[j] = V[i-1][j];
+ V[i][j] = 0;
+ }
+ }
+ d[i] = h;
+ }
+
+ // Accumulate transformations.
+ for (var i = 0; i < n - 1; i++) {
+ V[n - 1][i] = V[i][i];
+ V[i][i] = 1.0;
+ var h = d[i+1];
+ if (h != 0) {
+ for (var k = 0; k <= i; k++) { d[k] = V[k][i+1] / h; }
+ for (var j = 0; j <= i; j++) {
+ var g = 0;
+ for (var k = 0; k <= i; k++) { g += V[k][i+1] * V[k][j]; }
+ for (var k = 0; k <= i; k++) { V[k][j] -= g * d[k]; }
+ }
+ }
+ for (var k = 0; k <= i; k++) { V[k][i+1] = 0; }
+ }
+ for (var j = 0; j < n; j++) {
+ d[j] = V[n - 1][j];
+ V[n - 1][j] = 0;
+ }
+ V[n - 1][n - 1] = 1;
+ e[0] = 0;
+}
+
+// Symmetric tridiagonal QL algorithm.
+function science_lin_decomposeTql2(d, e, V) {
+ // This is derived from the Algol procedures tql2, by
+ // Bowdler, Martin, Reinsch, and Wilkinson, Handbook for
+ // Auto. Comp., Vol.ii-Linear Algebra, and the corresponding
+ // Fortran subroutine in EISPACK.
+
+ var n = V.length;
+
+ for (var i = 1; i < n; i++) { e[i-1] = e[i]; }
+ e[n - 1] = 0;
+
+ var f = 0;
+ var tst1 = 0;
+ var eps = 1e-12;
+ for (var l = 0; l < n; l++) {
+ // Find small subdiagonal element
+ tst1 = Math.max(tst1, Math.abs(d[l]) + Math.abs(e[l]));
+ var m = l;
+ while (m < n) {
+ if (Math.abs(e[m]) <= eps*tst1) { break; }
+ m++;
+ }
+
+ // If m == l, d[l] is an eigenvalue,
+ // otherwise, iterate.
+ if (m > l) {
+ var iter = 0;
+ do {
+ iter++; // (Could check iteration count here.)
+
+ // Compute implicit shift
+ var g = d[l];
+ var p = (d[l+1] - g) / (2.0 * e[l]);
+ var r = science.hypot(p, 1);
+ if (p < 0) {
+ r = -r;
+ }
+ d[l] = e[l] / (p + r);
+ d[l+1] = e[l] * (p + r);
+ var dl1 = d[l+1];
+ var h = g - d[l];
+ for (var i = l+2; i < n; i++) {
+ d[i] -= h;
+ }
+ f = f + h;
+
+ // Implicit QL transformation.
+ p = d[m];
+ var c = 1.0;
+ var c2 = c;
+ var c3 = c;
+ var el1 = e[l+1];
+ var s = 0;
+ var s2 = 0;
+ for (var i = m-1; i >= l; i--) {
+ c3 = c2;
+ c2 = c;
+ s2 = s;
+ g = c * e[i];
+ h = c * p;
+ r = science.hypot(p,e[i]);
+ e[i+1] = s * r;
+ s = e[i] / r;
+ c = p / r;
+ p = c * d[i] - s * g;
+ d[i+1] = h + s * (c * g + s * d[i]);
+
+ // Accumulate transformation.
+ for (var k = 0; k < n; k++) {
+ h = V[k][i+1];
+ V[k][i+1] = s * V[k][i] + c * h;
+ V[k][i] = c * V[k][i] - s * h;
+ }
+ }
+ p = -s * s2 * c3 * el1 * e[l] / dl1;
+ e[l] = s * p;
+ d[l] = c * p;
+
+ // Check for convergence.
+ } while (Math.abs(e[l]) > eps*tst1);
+ }
+ d[l] = d[l] + f;
+ e[l] = 0;
+ }
+
+ // Sort eigenvalues and corresponding vectors.
+ for (var i = 0; i < n - 1; i++) {
+ var k = i;
+ var p = d[i];
+ for (var j = i+1; j < n; j++) {
+ if (d[j] < p) {
+ k = j;
+ p = d[j];
+ }
+ }
+ if (k != i) {
+ d[k] = d[i];
+ d[i] = p;
+ for (var j = 0; j < n; j++) {
+ p = V[j][i];
+ V[j][i] = V[j][k];
+ V[j][k] = p;
+ }
+ }
+ }
+}
+
+// Nonsymmetric reduction to Hessenberg form.
+function science_lin_decomposeOrthes(H, V) {
+ // This is derived from the Algol procedures orthes and ortran,
+ // by Martin and Wilkinson, Handbook for Auto. Comp.,
+ // Vol.ii-Linear Algebra, and the corresponding
+ // Fortran subroutines in EISPACK.
+
+ var n = H.length;
+ var ort = [];
+
+ var low = 0;
+ var high = n - 1;
+
+ for (var m = low + 1; m < high; m++) {
+ // Scale column.
+ var scale = 0;
+ for (var i = m; i <= high; i++) scale += Math.abs(H[i][m - 1]);
+
+ if (scale !== 0) {
+ // Compute Householder transformation.
+ var h = 0;
+ for (var i = high; i >= m; i--) {
+ ort[i] = H[i][m - 1] / scale;
+ h += ort[i] * ort[i];
+ }
+ var g = Math.sqrt(h);
+ if (ort[m] > 0) { g = -g; }
+ h = h - ort[m] * g;
+ ort[m] = ort[m] - g;
+
+ // Apply Householder similarity transformation
+ // H = (I-u*u'/h)*H*(I-u*u')/h)
+ for (var j = m; j < n; j++) {
+ var f = 0;
+ for (var i = high; i >= m; i--) f += ort[i] * H[i][j];
+ f /= h;
+ for (var i = m; i <= high; i++) H[i][j] -= f * ort[i];
+ }
+
+ for (var i = 0; i <= high; i++) {
+ var f = 0;
+ for (var j = high; j >= m; j--) f += ort[j] * H[i][j];
+ f /= h;
+ for (var j = m; j <= high; j++) H[i][j] -= f * ort[j];
+ }
+ ort[m] = scale * ort[m];
+ H[m][m - 1] = scale * g;
+ }
+ }
+
+ // Accumulate transformations (Algol's ortran).
+ for (var i = 0; i < n; i++) {
+ for (var j = 0; j < n; j++) V[i][j] = i === j ? 1 : 0;
+ }
+
+ for (var m = high-1; m >= low+1; m--) {
+ if (H[m][m - 1] !== 0) {
+ for (var i = m + 1; i <= high; i++) { ort[i] = H[i][m-1]; }
+ for (var j = m; j <= high; j++) {
+ var g = 0;
+ for (var i = m; i <= high; i++) { g += ort[i] * V[i][j]; }
+ // Double division avoids possible underflow
+ g = (g / ort[m]) / H[m][m-1];
+ for (var i = m; i <= high; i++) { V[i][j] += g * ort[i]; }
+ }
+ }
+ }
+}
+
+// Nonsymmetric reduction from Hessenberg to real Schur form.
+function science_lin_decomposeHqr2(d, e, H, V) {
+ // This is derived from the Algol procedure hqr2,
+ // by Martin and Wilkinson, Handbook for Auto. Comp.,
+ // Vol.ii-Linear Algebra, and the corresponding
+ // Fortran subroutine in EISPACK.
+
+ var nn = H.length,
+ n = nn - 1,
+ low = 0,
+ high = nn - 1,
+ eps = 1e-12,
+ exshift = 0,
+ p = 0,
+ q = 0,
+ r = 0,
+ s = 0,
+ z = 0,
+ t,
+ w,
+ x,
+ y;
+
+ // Store roots isolated by balanc and compute matrix norm
+ var norm = 0;
+ for (var i = 0; i < nn; i++) {
+ if (i < low || i > high) {
+ d[i] = H[i][i];
+ e[i] = 0;
+ }
+ for (var j = Math.max(i - 1, 0); j < nn; j++) norm += Math.abs(H[i][j]);
+ }
+
+ // Outer loop over eigenvalue index
+ var iter = 0;
+ while (n >= low) {
+ // Look for single small sub-diagonal element
+ var l = n;
+ while (l > low) {
+ s = Math.abs(H[l - 1][l - 1]) + Math.abs(H[l][l]);
+ if (s === 0) s = norm;
+ if (Math.abs(H[l][l - 1]) < eps * s) break;
+ l--;
+ }
+
+ // Check for convergence
+ // One root found
+ if (l === n) {
+ H[n][n] = H[n][n] + exshift;
+ d[n] = H[n][n];
+ e[n] = 0;
+ n--;
+ iter = 0;
+
+ // Two roots found
+ } else if (l === n - 1) {
+ w = H[n][n - 1] * H[n - 1][n];
+ p = (H[n - 1][n - 1] - H[n][n]) / 2;
+ q = p * p + w;
+ z = Math.sqrt(Math.abs(q));
+ H[n][n] = H[n][n] + exshift;
+ H[n - 1][n - 1] = H[n - 1][n - 1] + exshift;
+ x = H[n][n];
+
+ // Real pair
+ if (q >= 0) {
+ z = p + (p >= 0 ? z : -z);
+ d[n - 1] = x + z;
+ d[n] = d[n - 1];
+ if (z !== 0) d[n] = x - w / z;
+ e[n - 1] = 0;
+ e[n] = 0;
+ x = H[n][n - 1];
+ s = Math.abs(x) + Math.abs(z);
+ p = x / s;
+ q = z / s;
+ r = Math.sqrt(p * p+q * q);
+ p /= r;
+ q /= r;
+
+ // Row modification
+ for (var j = n - 1; j < nn; j++) {
+ z = H[n - 1][j];
+ H[n - 1][j] = q * z + p * H[n][j];
+ H[n][j] = q * H[n][j] - p * z;
+ }
+
+ // Column modification
+ for (var i = 0; i <= n; i++) {
+ z = H[i][n - 1];
+ H[i][n - 1] = q * z + p * H[i][n];
+ H[i][n] = q * H[i][n] - p * z;
+ }
+
+ // Accumulate transformations
+ for (var i = low; i <= high; i++) {
+ z = V[i][n - 1];
+ V[i][n - 1] = q * z + p * V[i][n];
+ V[i][n] = q * V[i][n] - p * z;
+ }
+
+ // Complex pair
+ } else {
+ d[n - 1] = x + p;
+ d[n] = x + p;
+ e[n - 1] = z;
+ e[n] = -z;
+ }
+ n = n - 2;
+ iter = 0;
+
+ // No convergence yet
+ } else {
+
+ // Form shift
+ x = H[n][n];
+ y = 0;
+ w = 0;
+ if (l < n) {
+ y = H[n - 1][n - 1];
+ w = H[n][n - 1] * H[n - 1][n];
+ }
+
+ // Wilkinson's original ad hoc shift
+ if (iter == 10) {
+ exshift += x;
+ for (var i = low; i <= n; i++) {
+ H[i][i] -= x;
+ }
+ s = Math.abs(H[n][n - 1]) + Math.abs(H[n - 1][n-2]);
+ x = y = 0.75 * s;
+ w = -0.4375 * s * s;
+ }
+
+ // MATLAB's new ad hoc shift
+ if (iter == 30) {
+ s = (y - x) / 2.0;
+ s = s * s + w;
+ if (s > 0) {
+ s = Math.sqrt(s);
+ if (y < x) {
+ s = -s;
+ }
+ s = x - w / ((y - x) / 2.0 + s);
+ for (var i = low; i <= n; i++) {
+ H[i][i] -= s;
+ }
+ exshift += s;
+ x = y = w = 0.964;
+ }
+ }
+
+ iter++; // (Could check iteration count here.)
+
+ // Look for two consecutive small sub-diagonal elements
+ var m = n-2;
+ while (m >= l) {
+ z = H[m][m];
+ r = x - z;
+ s = y - z;
+ p = (r * s - w) / H[m+1][m] + H[m][m+1];
+ q = H[m+1][m+1] - z - r - s;
+ r = H[m+2][m+1];
+ s = Math.abs(p) + Math.abs(q) + Math.abs(r);
+ p = p / s;
+ q = q / s;
+ r = r / s;
+ if (m == l) {
+ break;
+ }
+ if (Math.abs(H[m][m-1]) * (Math.abs(q) + Math.abs(r)) <
+ eps * (Math.abs(p) * (Math.abs(H[m-1][m-1]) + Math.abs(z) +
+ Math.abs(H[m+1][m+1])))) {
+ break;
+ }
+ m--;
+ }
+
+ for (var i = m+2; i <= n; i++) {
+ H[i][i-2] = 0;
+ if (i > m+2) { H[i][i-3] = 0; }
+ }
+
+ // Double QR step involving rows l:n and columns m:n
+ for (var k = m; k <= n - 1; k++) {
+ var notlast = (k != n - 1);
+ if (k != m) {
+ p = H[k][k-1];
+ q = H[k+1][k-1];
+ r = (notlast ? H[k+2][k-1] : 0);
+ x = Math.abs(p) + Math.abs(q) + Math.abs(r);
+ if (x != 0) {
+ p /= x;
+ q /= x;
+ r /= x;
+ }
+ }
+ if (x == 0) { break; }
+ s = Math.sqrt(p * p + q * q + r * r);
+ if (p < 0) { s = -s; }
+ if (s != 0) {
+ if (k != m) H[k][k-1] = -s * x;
+ else if (l != m) H[k][k-1] = -H[k][k-1];
+ p += s;
+ x = p / s;
+ y = q / s;
+ z = r / s;
+ q /= p;
+ r /= p;
+
+ // Row modification
+ for (var j = k; j < nn; j++) {
+ p = H[k][j] + q * H[k+1][j];
+ if (notlast) {
+ p = p + r * H[k+2][j];
+ H[k+2][j] = H[k+2][j] - p * z;
+ }
+ H[k][j] = H[k][j] - p * x;
+ H[k+1][j] = H[k+1][j] - p * y;
+ }
+
+ // Column modification
+ for (var i = 0; i <= Math.min(n,k+3); i++) {
+ p = x * H[i][k] + y * H[i][k+1];
+ if (notlast) {
+ p += z * H[i][k+2];
+ H[i][k+2] = H[i][k+2] - p * r;
+ }
+ H[i][k] = H[i][k] - p;
+ H[i][k+1] = H[i][k+1] - p * q;
+ }
+
+ // Accumulate transformations
+ for (var i = low; i <= high; i++) {
+ p = x * V[i][k] + y * V[i][k+1];
+ if (notlast) {
+ p = p + z * V[i][k+2];
+ V[i][k+2] = V[i][k+2] - p * r;
+ }
+ V[i][k] = V[i][k] - p;
+ V[i][k+1] = V[i][k+1] - p * q;
+ }
+ } // (s != 0)
+ } // k loop
+ } // check convergence
+ } // while (n >= low)
+
+ // Backsubstitute to find vectors of upper triangular form
+ if (norm == 0) { return; }
+
+ for (n = nn - 1; n >= 0; n--) {
+ p = d[n];
+ q = e[n];
+
+ // Real vector
+ if (q == 0) {
+ var l = n;
+ H[n][n] = 1.0;
+ for (var i = n - 1; i >= 0; i--) {
+ w = H[i][i] - p;
+ r = 0;
+ for (var j = l; j <= n; j++) { r = r + H[i][j] * H[j][n]; }
+ if (e[i] < 0) {
+ z = w;
+ s = r;
+ } else {
+ l = i;
+ if (e[i] == 0) {
+ if (w != 0) {
+ H[i][n] = -r / w;
+ } else {
+ H[i][n] = -r / (eps * norm);
+ }
+ } else {
+ // Solve real equations
+ x = H[i][i+1];
+ y = H[i+1][i];
+ q = (d[i] - p) * (d[i] - p) + e[i] * e[i];
+ t = (x * s - z * r) / q;
+ H[i][n] = t;
+ if (Math.abs(x) > Math.abs(z)) {
+ H[i+1][n] = (-r - w * t) / x;
+ } else {
+ H[i+1][n] = (-s - y * t) / z;
+ }
+ }
+
+ // Overflow control
+ t = Math.abs(H[i][n]);
+ if ((eps * t) * t > 1) {
+ for (var j = i; j <= n; j++) H[j][n] = H[j][n] / t;
+ }
+ }
+ }
+ // Complex vector
+ } else if (q < 0) {
+ var l = n - 1;
+
+ // Last vector component imaginary so matrix is triangular
+ if (Math.abs(H[n][n - 1]) > Math.abs(H[n - 1][n])) {
+ H[n - 1][n - 1] = q / H[n][n - 1];
+ H[n - 1][n] = -(H[n][n] - p) / H[n][n - 1];
+ } else {
+ var zz = science_lin_decomposeCdiv(0, -H[n - 1][n], H[n - 1][n - 1] - p, q);
+ H[n - 1][n - 1] = zz[0];
+ H[n - 1][n] = zz[1];
+ }
+ H[n][n - 1] = 0;
+ H[n][n] = 1;
+ for (var i = n-2; i >= 0; i--) {
+ var ra = 0,
+ sa = 0,
+ vr,
+ vi;
+ for (var j = l; j <= n; j++) {
+ ra = ra + H[i][j] * H[j][n - 1];
+ sa = sa + H[i][j] * H[j][n];
+ }
+ w = H[i][i] - p;
+
+ if (e[i] < 0) {
+ z = w;
+ r = ra;
+ s = sa;
+ } else {
+ l = i;
+ if (e[i] == 0) {
+ var zz = science_lin_decomposeCdiv(-ra,-sa,w,q);
+ H[i][n - 1] = zz[0];
+ H[i][n] = zz[1];
+ } else {
+ // Solve complex equations
+ x = H[i][i+1];
+ y = H[i+1][i];
+ vr = (d[i] - p) * (d[i] - p) + e[i] * e[i] - q * q;
+ vi = (d[i] - p) * 2.0 * q;
+ if (vr == 0 & vi == 0) {
+ vr = eps * norm * (Math.abs(w) + Math.abs(q) +
+ Math.abs(x) + Math.abs(y) + Math.abs(z));
+ }
+ var zz = science_lin_decomposeCdiv(x*r-z*ra+q*sa,x*s-z*sa-q*ra,vr,vi);
+ H[i][n - 1] = zz[0];
+ H[i][n] = zz[1];
+ if (Math.abs(x) > (Math.abs(z) + Math.abs(q))) {
+ H[i+1][n - 1] = (-ra - w * H[i][n - 1] + q * H[i][n]) / x;
+ H[i+1][n] = (-sa - w * H[i][n] - q * H[i][n - 1]) / x;
+ } else {
+ var zz = science_lin_decomposeCdiv(-r-y*H[i][n - 1],-s-y*H[i][n],z,q);
+ H[i+1][n - 1] = zz[0];
+ H[i+1][n] = zz[1];
+ }
+ }
+
+ // Overflow control
+ t = Math.max(Math.abs(H[i][n - 1]),Math.abs(H[i][n]));
+ if ((eps * t) * t > 1) {
+ for (var j = i; j <= n; j++) {
+ H[j][n - 1] = H[j][n - 1] / t;
+ H[j][n] = H[j][n] / t;
+ }
+ }
+ }
+ }
+ }
+ }
+
+ // Vectors of isolated roots
+ for (var i = 0; i < nn; i++) {
+ if (i < low || i > high) {
+ for (var j = i; j < nn; j++) { V[i][j] = H[i][j]; }
+ }
+ }
+
+ // Back transformation to get eigenvectors of original matrix
+ for (var j = nn - 1; j >= low; j--) {
+ for (var i = low; i <= high; i++) {
+ z = 0;
+ for (var k = low; k <= Math.min(j,high); k++) z += V[i][k] * H[k][j];
+ V[i][j] = z;
+ }
+ }
+}
+
+// Complex scalar division.
+function science_lin_decomposeCdiv(xr, xi, yr, yi) {
+ var r, d;
+ if (Math.abs(yr) > Math.abs(yi)) {
+ r = yi / yr;
+ d = yr + r * yi;
+ return [(xr + r * xi) / d, (xi - r * xr) / d];
+ } else {
+ r = yr / yi;
+ d = yi + r * yr;
+ return [(r * xr + xi) / d, (r * xi - xr) / d];
+ }
+}
+science.lin.cross = function(a, b) {
+ // TODO how to handle non-3D vectors?
+ // TODO handle 7D vectors?
+ return [
+ a[1] * b[2] - a[2] * b[1],
+ a[2] * b[0] - a[0] * b[2],
+ a[0] * b[1] - a[1] * b[0]
+ ];
+};
+science.lin.dot = function(a, b) {
+ var s = 0,
+ i = -1,
+ n = Math.min(a.length, b.length);
+ while (++i < n) s += a[i] * b[i];
+ return s;
+};
+science.lin.length = function(p) {
+ return Math.sqrt(science.vector.dot(p, p));
+};
+science.lin.normalize = function(p) {
+ var length = science.lin.length(p);
+ return p.map(function(d) { return d / length; });
+};
+// 4x4 matrix determinant.
+science.lin.determinant = function(matrix) {
+ var m = matrix[0].concat(matrix[1]).concat(matrix[2]).concat(matrix[3]);
+ return (
+ m[12] * m[9] * m[6] * m[3] - m[8] * m[13] * m[6] * m[3] -
+ m[12] * m[5] * m[10] * m[3] + m[4] * m[13] * m[10] * m[3] +
+ m[8] * m[5] * m[14] * m[3] - m[4] * m[9] * m[14] * m[3] -
+ m[12] * m[9] * m[2] * m[7] + m[8] * m[13] * m[2] * m[7] +
+ m[12] * m[1] * m[10] * m[7] - m[0] * m[13] * m[10] * m[7] -
+ m[8] * m[1] * m[14] * m[7] + m[0] * m[9] * m[14] * m[7] +
+ m[12] * m[5] * m[2] * m[11] - m[4] * m[13] * m[2] * m[11] -
+ m[12] * m[1] * m[6] * m[11] + m[0] * m[13] * m[6] * m[11] +
+ m[4] * m[1] * m[14] * m[11] - m[0] * m[5] * m[14] * m[11] -
+ m[8] * m[5] * m[2] * m[15] + m[4] * m[9] * m[2] * m[15] +
+ m[8] * m[1] * m[6] * m[15] - m[0] * m[9] * m[6] * m[15] -
+ m[4] * m[1] * m[10] * m[15] + m[0] * m[5] * m[10] * m[15]);
+};
+// Performs in-place Gauss-Jordan elimination.
+//
+// Based on Jarno Elonen's Python version (public domain):
+// http://elonen.iki.fi/code/misc-notes/python-gaussj/index.html
+science.lin.gaussjordan = function(m, eps) {
+ if (!eps) eps = 1e-10;
+
+ var h = m.length,
+ w = m[0].length,
+ y = -1,
+ y2,
+ x;
+
+ while (++y < h) {
+ var maxrow = y;
+
+ // Find max pivot.
+ y2 = y; while (++y2 < h) {
+ if (Math.abs(m[y2][y]) > Math.abs(m[maxrow][y]))
+ maxrow = y2;
+ }
+
+ // Swap.
+ var tmp = m[y];
+ m[y] = m[maxrow];
+ m[maxrow] = tmp;
+
+ // Singular?
+ if (Math.abs(m[y][y]) <= eps) return false;
+
+ // Eliminate column y.
+ y2 = y; while (++y2 < h) {
+ var c = m[y2][y] / m[y][y];
+ x = y - 1; while (++x < w) {
+ m[y2][x] -= m[y][x] * c;
+ }
+ }
+ }
+
+ // Backsubstitute.
+ y = h; while (--y >= 0) {
+ var c = m[y][y];
+ y2 = -1; while (++y2 < y) {
+ x = w; while (--x >= y) {
+ m[y2][x] -= m[y][x] * m[y2][y] / c;
+ }
+ }
+ m[y][y] /= c;
+ // Normalize row y.
+ x = h - 1; while (++x < w) {
+ m[y][x] /= c;
+ }
+ }
+ return true;
+};
+// Find matrix inverse using Gauss-Jordan.
+science.lin.inverse = function(m) {
+ var n = m.length
+ i = -1;
+
+ // Check if the matrix is square.
+ if (n !== m[0].length) return;
+
+ // Augment with identity matrix I to get AI.
+ m = m.map(function(row, i) {
+ var identity = new Array(n),
+ j = -1;
+ while (++j < n) identity[j] = i === j ? 1 : 0;
+ return row.concat(identity);
+ });
+
+ // Compute IA^-1.
+ science.lin.gaussjordan(m);
+
+ // Remove identity matrix I to get A^-1.
+ while (++i < n) {
+ m[i] = m[i].slice(n);
+ }
+
+ return m;
+};
+science.lin.multiply = function(a, b) {
+ var m = a.length,
+ n = b[0].length,
+ p = b.length,
+ i = -1,
+ j,
+ k;
+ if (p !== a[0].length) throw {"error": "columns(a) != rows(b); " + a[0].length + " != " + p};
+ var ab = new Array(m);
+ while (++i < m) {
+ ab[i] = new Array(n);
+ j = -1; while(++j < n) {
+ var s = 0;
+ k = -1; while (++k < p) s += a[i][k] * b[k][j];
+ ab[i][j] = s;
+ }
+ }
+ return ab;
+};
+science.lin.transpose = function(a) {
+ var m = a.length,
+ n = a[0].length,
+ i = -1,
+ j,
+ b = new Array(n);
+ while (++i < n) {
+ b[i] = new Array(m);
+ j = -1; while (++j < m) b[i][j] = a[j][i];
+ }
+ return b;
+};
/**
* Solves tridiagonal systems of linear equations.
*
diff --git a/science.lin.min.js b/science.lin.min.js
index 734bfa6..823c921 100644
--- a/science.lin.min.js
+++ b/science.lin.min.js
@@ -1 +1 @@
-(function(){science.lin={},science.lin.tridag=function(a,b,c,d,e,f){var g,h;for(g=1;g<f;g++)h=a[g]/b[g-1],b[g]-=h*c[g-1],d[g]-=h*d[g-1];e[f-1]=d[f-1]/b[f-1];for(g=f-2;g>=0;g--)e[g]=(d[g]-c[g]*e[g+1])/b[g]}})();
\ No newline at end of file
+(function(){function a(a,b,c){var d=c.length;for(var e=0;e<d;e++)a[e]=c[d-1][e];for(var f=d-1;f>0;f--){var g=0,h=0;for(var i=0;i<f;i++)g+=Math.abs(a[i]);if(g===0){b[f]=a[f-1];for(var e=0;e<f;e++)a[e]=c[f-1][e],c[f][e]=0,c[e][f]=0}else{for(var i=0;i<f;i++)a[i]/=g,h+=a[i]*a[i];var j=a[f-1],k=Math.sqrt(h);j>0&&(k=-k),b[f]=g*k,h-=j*k,a[f-1]=j-k;for(var e=0;e<f;e++)b[e]=0;for(var e=0;e<f;e++){j=a[e],c[e][f]=j,k=b[e]+c[e][e]*j;for(var i=e+1;i<=f-1;i++)k+=c[i][e]*a[i],b[i]+=c[i][e]*j;b[e]=k}j=0 [...]
\ No newline at end of file
diff --git a/science.min.js b/science.min.js
index b7defd6..a9473ba 100644
--- a/science.min.js
+++ b/science.min.js
@@ -1 +1 @@
-(function(){function a(a,b,c){var d=c.length;for(var e=0;e<d;e++)a[e]=c[d-1][e];for(var f=d-1;f>0;f--){var g=0,h=0;for(var i=0;i<f;i++)g+=Math.abs(a[i]);if(g===0){b[f]=a[f-1];for(var e=0;e<f;e++)a[e]=c[f-1][e],c[f][e]=0,c[e][f]=0}else{for(var i=0;i<f;i++)a[i]/=g,h+=a[i]*a[i];var j=a[f-1],k=Math.sqrt(h);j>0&&(k=-k),b[f]=g*k,h-=j*k,a[f-1]=j-k;for(var e=0;e<f;e++)b[e]=0;for(var e=0;e<f;e++){j=a[e],c[e][f]=j,k=b[e]+c[e][e]*j;for(var i=e+1;i<=f-1;i++)k+=c[i][e]*a[i],b[i]+=c[i][e]*j;b[e]=k}j=0 [...]
\ No newline at end of file
+(function(){science={version:"1.7.1"},science.ascending=function(a,b){return a-b},science.EULER=.5772156649015329,science.expm1=function(a){return a<1e-5&&a>-0.00001?a+.5*a*a:Math.exp(a)-1},science.functor=function(a){return typeof a=="function"?a:function(){return a}},science.hypot=function(a,b){a=Math.abs(a),b=Math.abs(b);var c,d;a>b?(c=a,d=b):(c=b,d=a);var e=d/c;return c*Math.sqrt(1+e*e)},science.quadratic=function(){function b(b,c,d){var e=c*c-4*b*d;return e>0?(e=Math.sqrt(e)/(2*b),a [...]
\ No newline at end of file
diff --git a/src/vector/cross.js b/src/lin/cross.js
similarity index 81%
rename from src/vector/cross.js
rename to src/lin/cross.js
index 97cd71f..7620260 100644
--- a/src/vector/cross.js
+++ b/src/lin/cross.js
@@ -1,4 +1,4 @@
-science.vector.cross = function(a, b) {
+science.lin.cross = function(a, b) {
// TODO how to handle non-3D vectors?
// TODO handle 7D vectors?
return [
diff --git a/src/vector/decompose.js b/src/lin/decompose.js
similarity index 95%
rename from src/vector/decompose.js
rename to src/lin/decompose.js
index 8e312b9..c2d7d3d 100644
--- a/src/vector/decompose.js
+++ b/src/lin/decompose.js
@@ -1,4 +1,4 @@
-science.vector.decompose = function() {
+science.lin.decompose = function() {
function decompose(A) {
var n = A.length; // column dimension
@@ -26,19 +26,19 @@ science.vector.decompose = function() {
for (var i = 0; i < n; i++) V[i] = A[i].slice();
// Tridiagonalize.
- science_vector_decomposeTred2(d, e, V);
+ science_lin_decomposeTred2(d, e, V);
// Diagonalize.
- science_vector_decomposeTql2(d, e, V);
+ science_lin_decomposeTql2(d, e, V);
} else {
var H = [];
for (var i = 0; i < n; i++) H[i] = A[i].slice();
// Reduce to Hessenberg form.
- science_vector_decomposeOrthes(H, V);
+ science_lin_decomposeOrthes(H, V);
// Reduce Hessenberg to real Schur form.
- science_vector_decomposeHqr2(d, e, H, V);
+ science_lin_decomposeHqr2(d, e, H, V);
}
var D = [];
@@ -55,7 +55,7 @@ science.vector.decompose = function() {
};
// Symmetric Householder reduction to tridiagonal form.
-function science_vector_decomposeTred2(d, e, V) {
+function science_lin_decomposeTred2(d, e, V) {
// This is derived from the Algol procedures tred2 by
// Bowdler, Martin, Reinsch, and Wilkinson, Handbook for
// Auto. Comp., Vol.ii-Linear Algebra, and the corresponding
@@ -147,7 +147,7 @@ function science_vector_decomposeTred2(d, e, V) {
}
// Symmetric tridiagonal QL algorithm.
-function science_vector_decomposeTql2(d, e, V) {
+function science_lin_decomposeTql2(d, e, V) {
// This is derived from the Algol procedures tql2, by
// Bowdler, Martin, Reinsch, and Wilkinson, Handbook for
// Auto. Comp., Vol.ii-Linear Algebra, and the corresponding
@@ -255,7 +255,7 @@ function science_vector_decomposeTql2(d, e, V) {
}
// Nonsymmetric reduction to Hessenberg form.
-function science_vector_decomposeOrthes(H, V) {
+function science_lin_decomposeOrthes(H, V) {
// This is derived from the Algol procedures orthes and ortran,
// by Martin and Wilkinson, Handbook for Auto. Comp.,
// Vol.ii-Linear Algebra, and the corresponding
@@ -324,7 +324,7 @@ function science_vector_decomposeOrthes(H, V) {
}
// Nonsymmetric reduction from Hessenberg to real Schur form.
-function science_vector_decomposeHqr2(d, e, H, V) {
+function science_lin_decomposeHqr2(d, e, H, V) {
// This is derived from the Algol procedure hqr2,
// by Martin and Wilkinson, Handbook for Auto. Comp.,
// Vol.ii-Linear Algebra, and the corresponding
@@ -626,7 +626,7 @@ function science_vector_decomposeHqr2(d, e, H, V) {
H[n - 1][n - 1] = q / H[n][n - 1];
H[n - 1][n] = -(H[n][n] - p) / H[n][n - 1];
} else {
- var zz = science_vector_decomposeCdiv(0, -H[n - 1][n], H[n - 1][n - 1] - p, q);
+ var zz = science_lin_decomposeCdiv(0, -H[n - 1][n], H[n - 1][n - 1] - p, q);
H[n - 1][n - 1] = zz[0];
H[n - 1][n] = zz[1];
}
@@ -650,7 +650,7 @@ function science_vector_decomposeHqr2(d, e, H, V) {
} else {
l = i;
if (e[i] == 0) {
- var zz = science_vector_decomposeCdiv(-ra,-sa,w,q);
+ var zz = science_lin_decomposeCdiv(-ra,-sa,w,q);
H[i][n - 1] = zz[0];
H[i][n] = zz[1];
} else {
@@ -663,14 +663,14 @@ function science_vector_decomposeHqr2(d, e, H, V) {
vr = eps * norm * (Math.abs(w) + Math.abs(q) +
Math.abs(x) + Math.abs(y) + Math.abs(z));
}
- var zz = science_vector_decomposeCdiv(x*r-z*ra+q*sa,x*s-z*sa-q*ra,vr,vi);
+ var zz = science_lin_decomposeCdiv(x*r-z*ra+q*sa,x*s-z*sa-q*ra,vr,vi);
H[i][n - 1] = zz[0];
H[i][n] = zz[1];
if (Math.abs(x) > (Math.abs(z) + Math.abs(q))) {
H[i+1][n - 1] = (-ra - w * H[i][n - 1] + q * H[i][n]) / x;
H[i+1][n] = (-sa - w * H[i][n] - q * H[i][n - 1]) / x;
} else {
- var zz = science_vector_decomposeCdiv(-r-y*H[i][n - 1],-s-y*H[i][n],z,q);
+ var zz = science_lin_decomposeCdiv(-r-y*H[i][n - 1],-s-y*H[i][n],z,q);
H[i+1][n - 1] = zz[0];
H[i+1][n] = zz[1];
}
@@ -707,7 +707,7 @@ function science_vector_decomposeHqr2(d, e, H, V) {
}
// Complex scalar division.
-function science_vector_decomposeCdiv(xr, xi, yr, yi) {
+function science_lin_decomposeCdiv(xr, xi, yr, yi) {
var r, d;
if (Math.abs(yr) > Math.abs(yi)) {
r = yi / yr;
diff --git a/src/vector/determinant.js b/src/lin/determinant.js
similarity index 95%
rename from src/vector/determinant.js
rename to src/lin/determinant.js
index b79e76a..3e72aa5 100644
--- a/src/vector/determinant.js
+++ b/src/lin/determinant.js
@@ -1,5 +1,5 @@
// 4x4 matrix determinant.
-science.vector.determinant = function(matrix) {
+science.lin.determinant = function(matrix) {
var m = matrix[0].concat(matrix[1]).concat(matrix[2]).concat(matrix[3]);
return (
m[12] * m[9] * m[6] * m[3] - m[8] * m[13] * m[6] * m[3] -
diff --git a/src/vector/dot.js b/src/lin/dot.js
similarity index 75%
rename from src/vector/dot.js
rename to src/lin/dot.js
index 74dfd00..81a6681 100644
--- a/src/vector/dot.js
+++ b/src/lin/dot.js
@@ -1,4 +1,4 @@
-science.vector.dot = function(a, b) {
+science.lin.dot = function(a, b) {
var s = 0,
i = -1,
n = Math.min(a.length, b.length);
diff --git a/src/vector/gaussjordan.js b/src/lin/gaussjordan.js
similarity index 95%
rename from src/vector/gaussjordan.js
rename to src/lin/gaussjordan.js
index 08a8ca1..a7ebd40 100644
--- a/src/vector/gaussjordan.js
+++ b/src/lin/gaussjordan.js
@@ -2,7 +2,7 @@
//
// Based on Jarno Elonen's Python version (public domain):
// http://elonen.iki.fi/code/misc-notes/python-gaussj/index.html
-science.vector.gaussjordan = function(m, eps) {
+science.lin.gaussjordan = function(m, eps) {
if (!eps) eps = 1e-10;
var h = m.length,
diff --git a/src/vector/inverse.js b/src/lin/inverse.js
similarity index 87%
rename from src/vector/inverse.js
rename to src/lin/inverse.js
index 0a8bb5e..6a87045 100644
--- a/src/vector/inverse.js
+++ b/src/lin/inverse.js
@@ -1,5 +1,5 @@
// Find matrix inverse using Gauss-Jordan.
-science.vector.inverse = function(m) {
+science.lin.inverse = function(m) {
var n = m.length
i = -1;
@@ -15,7 +15,7 @@ science.vector.inverse = function(m) {
});
// Compute IA^-1.
- science.vector.gaussjordan(m);
+ science.lin.gaussjordan(m);
// Remove identity matrix I to get A^-1.
while (++i < n) {
diff --git a/src/vector/length.js b/src/lin/length.js
similarity index 56%
rename from src/vector/length.js
rename to src/lin/length.js
index 49618f5..2ed5b56 100644
--- a/src/vector/length.js
+++ b/src/lin/length.js
@@ -1,3 +1,3 @@
-science.vector.length = function(p) {
+science.lin.length = function(p) {
return Math.sqrt(science.vector.dot(p, p));
};
diff --git a/src/vector/multiply.js b/src/lin/multiply.js
similarity index 90%
rename from src/vector/multiply.js
rename to src/lin/multiply.js
index dc29173..2917110 100644
--- a/src/vector/multiply.js
+++ b/src/lin/multiply.js
@@ -1,4 +1,4 @@
-science.vector.multiply = function(a, b) {
+science.lin.multiply = function(a, b) {
var m = a.length,
n = b[0].length,
p = b.length,
diff --git a/src/lin/normalize.js b/src/lin/normalize.js
new file mode 100644
index 0000000..3389aca
--- /dev/null
+++ b/src/lin/normalize.js
@@ -0,0 +1,4 @@
+science.lin.normalize = function(p) {
+ var length = science.lin.length(p);
+ return p.map(function(d) { return d / length; });
+};
diff --git a/src/vector/transpose.js b/src/lin/transpose.js
similarity index 83%
rename from src/vector/transpose.js
rename to src/lin/transpose.js
index 48a61db..fa7e47d 100644
--- a/src/vector/transpose.js
+++ b/src/lin/transpose.js
@@ -1,4 +1,4 @@
-science.vector.transpose = function(a) {
+science.lin.transpose = function(a) {
var m = a.length,
n = a[0].length,
i = -1,
diff --git a/src/vector/normalize.js b/src/vector/normalize.js
deleted file mode 100644
index 3f6bc36..0000000
--- a/src/vector/normalize.js
+++ /dev/null
@@ -1,4 +0,0 @@
-science.vector.normalize = function(p) {
- var length = science.vector.length(p);
- return p.map(function(d) { return d / length; });
-};
diff --git a/src/vector/vector.js b/src/vector/vector.js
deleted file mode 100644
index fe140eb..0000000
--- a/src/vector/vector.js
+++ /dev/null
@@ -1 +0,0 @@
-science.vector = {};
diff --git a/test/lin/decompose-test.js b/test/lin/decompose-test.js
new file mode 100644
index 0000000..cd8f965
--- /dev/null
+++ b/test/lin/decompose-test.js
@@ -0,0 +1,24 @@
+require("../../science");
+require("../../science.lin");
+
+var vows = require("vows"),
+ assert = require("assert");
+
+var suite = vows.describe("science.lin.decompose");
+
+suite.addBatch({
+ "decompose": {
+ topic: science.lin.decompose,
+ "symmetric": function(decompose) {
+ var A = [[1, 1, 1], [1, 2, 3], [1, 3, 6]],
+ result = decompose(A);
+ assert.inDelta(
+ science.lin.multiply(A, result.V),
+ science.lin.multiply(result.V, result.D),
+ 1e-6
+ );
+ }
+ }
+});
+
+suite.export(module);
diff --git a/test/lin/tridag-test.js b/test/lin/tridag-test.js
index ed04362..a2e43d2 100644
--- a/test/lin/tridag-test.js
+++ b/test/lin/tridag-test.js
@@ -28,7 +28,7 @@ suite.addBatch({
if (i > 0) matrix[i - 1][i] = a[i];
if (i < n - 1) matrix[i + 1][i] = c[i];
}
- var result = science.vector.multiply(matrix, x.map(function(d) { return [d]; }));
+ var result = science.lin.multiply(matrix, x.map(function(d) { return [d]; }));
var epsilon = 1e-12;
for (var i=0; i<n; i++) {
assert.isTrue(result[i] - d[i] < epsilon);
diff --git a/test/vector/decompose-test.js b/test/vector/decompose-test.js
deleted file mode 100644
index 334da3d..0000000
--- a/test/vector/decompose-test.js
+++ /dev/null
@@ -1,23 +0,0 @@
-require("../../science");
-
-var vows = require("vows"),
- assert = require("assert");
-
-var suite = vows.describe("science.vector.decompose");
-
-suite.addBatch({
- "decompose": {
- "symmetric": function() {
- var decompose = science.vector.decompose();
- var A = [[1, 1, 1], [1, 2, 3], [1, 3, 6]];
- var result = decompose(A);
- assert.inDelta(
- science.vector.multiply(A, result.V),
- science.vector.multiply(result.V, result.D),
- 1e-6
- );
- }
- }
-});
-
-suite.export(module);
--
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