ml-matrix
Version:
Matrix manipulation and computation library
514 lines (479 loc) • 15.2 kB
JavaScript
'use strict';
var Matrix = require('../matrix');
var util = require('./util');
var hypotenuse = util.hypotenuse;
var getFilled2DArray = util.getFilled2DArray;
// https://github.com/lutzroeder/Mapack/blob/master/Source/SingularValueDecomposition.cs
function SingularValueDecomposition(value, options) {
if (!(this instanceof SingularValueDecomposition)) {
return new SingularValueDecomposition(value, options);
}
value = Matrix.checkMatrix(value);
options = options || {};
var m = value.rows,
n = value.columns,
nu = Math.min(m, n);
var wantu = true, wantv = true;
if (options.computeLeftSingularVectors === false)
wantu = false;
if (options.computeRightSingularVectors === false)
wantv = false;
var autoTranspose = options.autoTranspose === true;
var swapped = false;
var a;
if (m < n) {
if (!autoTranspose) {
a = value.clone();
console.warn('Computing SVD on a matrix with more columns than rows. Consider enabling autoTranspose');
} else {
a = value.transpose();
m = a.rows;
n = a.columns;
swapped = true;
var aux = wantu;
wantu = wantv;
wantv = aux;
}
} else {
a = value.clone();
}
var s = new Array(Math.min(m + 1, n)),
U = getFilled2DArray(m, nu, 0),
V = getFilled2DArray(n, n, 0),
e = new Array(n),
work = new Array(m);
var nct = Math.min(m - 1, n);
var nrt = Math.max(0, Math.min(n - 2, m));
var i, j, k, p, t, ks, f, cs, sn, max, kase,
scale, sp, spm1, epm1, sk, ek, b, c, shift, g;
for (k = 0, max = Math.max(nct, nrt); k < max; k++) {
if (k < nct) {
s[k] = 0;
for (i = k; i < m; i++) {
s[k] = hypotenuse(s[k], a[i][k]);
}
if (s[k] !== 0) {
if (a[k][k] < 0) {
s[k] = -s[k];
}
for (i = k; i < m; i++) {
a[i][k] /= s[k];
}
a[k][k] += 1;
}
s[k] = -s[k];
}
for (j = k + 1; j < n; j++) {
if ((k < nct) && (s[k] !== 0)) {
t = 0;
for (i = k; i < m; i++) {
t += a[i][k] * a[i][j];
}
t = -t / a[k][k];
for (i = k; i < m; i++) {
a[i][j] += t * a[i][k];
}
}
e[j] = a[k][j];
}
if (wantu && (k < nct)) {
for (i = k; i < m; i++) {
U[i][k] = a[i][k];
}
}
if (k < nrt) {
e[k] = 0;
for (i = k + 1; i < n; i++) {
e[k] = hypotenuse(e[k], e[i]);
}
if (e[k] !== 0) {
if (e[k + 1] < 0)
e[k] = -e[k];
for (i = k + 1; i < n; i++) {
e[i] /= e[k];
}
e[k + 1] += 1;
}
e[k] = -e[k];
if ((k + 1 < m) && (e[k] !== 0)) {
for (i = k + 1; i < m; i++) {
work[i] = 0;
}
for (j = k + 1; j < n; j++) {
for (i = k + 1; i < m; i++) {
work[i] += e[j] * a[i][j];
}
}
for (j = k + 1; j < n; j++) {
t = -e[j] / e[k + 1];
for (i = k + 1; i < m; i++) {
a[i][j] += t * work[i];
}
}
}
if (wantv) {
for (i = k + 1; i < n; i++) {
V[i][k] = e[i];
}
}
}
}
p = Math.min(n, m + 1);
if (nct < n) {
s[nct] = a[nct][nct];
}
if (m < p) {
s[p - 1] = 0;
}
if (nrt + 1 < p) {
e[nrt] = a[nrt][p - 1];
}
e[p - 1] = 0;
if (wantu) {
for (j = nct; j < nu; j++) {
for (i = 0; i < m; i++) {
U[i][j] = 0;
}
U[j][j] = 1;
}
for (k = nct - 1; k >= 0; k--) {
if (s[k] !== 0) {
for (j = k + 1; j < nu; j++) {
t = 0;
for (i = k; i < m; i++) {
t += U[i][k] * U[i][j];
}
t = -t / U[k][k];
for (i = k; i < m; i++) {
U[i][j] += t * U[i][k];
}
}
for (i = k; i < m; i++) {
U[i][k] = -U[i][k];
}
U[k][k] = 1 + U[k][k];
for (i = 0; i < k - 1; i++) {
U[i][k] = 0;
}
} else {
for (i = 0; i < m; i++) {
U[i][k] = 0;
}
U[k][k] = 1;
}
}
}
if (wantv) {
for (k = n - 1; k >= 0; k--) {
if ((k < nrt) && (e[k] !== 0)) {
for (j = k + 1; j < n; j++) {
t = 0;
for (i = k + 1; i < n; i++) {
t += V[i][k] * V[i][j];
}
t = -t / V[k + 1][k];
for (i = k + 1; i < n; i++) {
V[i][j] += t * V[i][k];
}
}
}
for (i = 0; i < n; i++) {
V[i][k] = 0;
}
V[k][k] = 1;
}
}
var pp = p - 1,
iter = 0,
eps = Math.pow(2, -52);
while (p > 0) {
for (k = p - 2; k >= -1; k--) {
if (k === -1) {
break;
}
if (Math.abs(e[k]) <= eps * (Math.abs(s[k]) + Math.abs(s[k + 1]))) {
e[k] = 0;
break;
}
}
if (k === p - 2) {
kase = 4;
} else {
for (ks = p - 1; ks >= k; ks--) {
if (ks === k) {
break;
}
t = (ks !== p ? Math.abs(e[ks]) : 0) + (ks !== k + 1 ? Math.abs(e[ks - 1]) : 0);
if (Math.abs(s[ks]) <= eps * t) {
s[ks] = 0;
break;
}
}
if (ks === k) {
kase = 3;
} else if (ks === p - 1) {
kase = 1;
} else {
kase = 2;
k = ks;
}
}
k++;
switch (kase) {
case 1: {
f = e[p - 2];
e[p - 2] = 0;
for (j = p - 2; j >= k; j--) {
t = hypotenuse(s[j], f);
cs = s[j] / t;
sn = f / t;
s[j] = t;
if (j !== k) {
f = -sn * e[j - 1];
e[j - 1] = cs * e[j - 1];
}
if (wantv) {
for (i = 0; i < n; i++) {
t = cs * V[i][j] + sn * V[i][p - 1];
V[i][p - 1] = -sn * V[i][j] + cs * V[i][p - 1];
V[i][j] = t;
}
}
}
break;
}
case 2 : {
f = e[k - 1];
e[k - 1] = 0;
for (j = k; j < p; j++) {
t = hypotenuse(s[j], f);
cs = s[j] / t;
sn = f / t;
s[j] = t;
f = -sn * e[j];
e[j] = cs * e[j];
if (wantu) {
for (i = 0; i < m; i++) {
t = cs * U[i][j] + sn * U[i][k - 1];
U[i][k - 1] = -sn * U[i][j] + cs * U[i][k - 1];
U[i][j] = t;
}
}
}
break;
}
case 3 : {
scale = Math.max(Math.max(Math.max(Math.max(Math.abs(s[p - 1]), Math.abs(s[p - 2])), Math.abs(e[p - 2])), Math.abs(s[k])), Math.abs(e[k]));
sp = s[p - 1] / scale;
spm1 = s[p - 2] / scale;
epm1 = e[p - 2] / scale;
sk = s[k] / scale;
ek = e[k] / scale;
b = ((spm1 + sp) * (spm1 - sp) + epm1 * epm1) / 2;
c = (sp * epm1) * (sp * epm1);
shift = 0;
if ((b !== 0) || (c !== 0)) {
shift = Math.sqrt(b * b + c);
if (b < 0) {
shift = -shift;
}
shift = c / (b + shift);
}
f = (sk + sp) * (sk - sp) + shift;
g = sk * ek;
for (j = k; j < p - 1; j++) {
t = hypotenuse(f, g);
cs = f / t;
sn = g / t;
if (j !== k) {
e[j - 1] = t;
}
f = cs * s[j] + sn * e[j];
e[j] = cs * e[j] - sn * s[j];
g = sn * s[j + 1];
s[j + 1] = cs * s[j + 1];
if (wantv) {
for (i = 0; i < n; i++) {
t = cs * V[i][j] + sn * V[i][j + 1];
V[i][j + 1] = -sn * V[i][j] + cs * V[i][j + 1];
V[i][j] = t;
}
}
t = hypotenuse(f, g);
cs = f / t;
sn = g / t;
s[j] = t;
f = cs * e[j] + sn * s[j + 1];
s[j + 1] = -sn * e[j] + cs * s[j + 1];
g = sn * e[j + 1];
e[j + 1] = cs * e[j + 1];
if (wantu && (j < m - 1)) {
for (i = 0; i < m; i++) {
t = cs * U[i][j] + sn * U[i][j + 1];
U[i][j + 1] = -sn * U[i][j] + cs * U[i][j + 1];
U[i][j] = t;
}
}
}
e[p - 2] = f;
iter = iter + 1;
break;
}
case 4: {
if (s[k] <= 0) {
s[k] = (s[k] < 0 ? -s[k] : 0);
if (wantv) {
for (i = 0; i <= pp; i++) {
V[i][k] = -V[i][k];
}
}
}
while (k < pp) {
if (s[k] >= s[k + 1]) {
break;
}
t = s[k];
s[k] = s[k + 1];
s[k + 1] = t;
if (wantv && (k < n - 1)) {
for (i = 0; i < n; i++) {
t = V[i][k + 1];
V[i][k + 1] = V[i][k];
V[i][k] = t;
}
}
if (wantu && (k < m - 1)) {
for (i = 0; i < m; i++) {
t = U[i][k + 1];
U[i][k + 1] = U[i][k];
U[i][k] = t;
}
}
k++;
}
iter = 0;
p--;
break;
}
}
}
if (swapped) {
var tmp = V;
V = U;
U = tmp;
}
this.m = m;
this.n = n;
this.s = s;
this.U = U;
this.V = V;
}
SingularValueDecomposition.prototype = {
get condition() {
return this.s[0] / this.s[Math.min(this.m, this.n) - 1];
},
get norm2() {
return this.s[0];
},
get rank() {
var eps = Math.pow(2, -52),
tol = Math.max(this.m, this.n) * this.s[0] * eps,
r = 0,
s = this.s;
for (var i = 0, ii = s.length; i < ii; i++) {
if (s[i] > tol) {
r++;
}
}
return r;
},
get diagonal() {
return this.s;
},
// https://github.com/accord-net/framework/blob/development/Sources/Accord.Math/Decompositions/SingularValueDecomposition.cs
get threshold() {
return (Math.pow(2, -52) / 2) * Math.max(this.m, this.n) * this.s[0];
},
get leftSingularVectors() {
if (!Matrix.isMatrix(this.U)) {
this.U = new Matrix(this.U);
}
return this.U;
},
get rightSingularVectors() {
if (!Matrix.isMatrix(this.V)) {
this.V = new Matrix(this.V);
}
return this.V;
},
get diagonalMatrix() {
return Matrix.diag(this.s);
},
solve: function (value) {
var Y = value,
e = this.threshold,
scols = this.s.length,
Ls = Matrix.zeros(scols, scols),
i;
for (i = 0; i < scols; i++) {
if (Math.abs(this.s[i]) <= e) {
Ls[i][i] = 0;
} else {
Ls[i][i] = 1 / this.s[i];
}
}
var U = this.U;
var V = this.rightSingularVectors;
var VL = V.mmul(Ls),
vrows = V.rows,
urows = U.length,
VLU = Matrix.zeros(vrows, urows),
j, k, sum;
for (i = 0; i < vrows; i++) {
for (j = 0; j < urows; j++) {
sum = 0;
for (k = 0; k < scols; k++) {
sum += VL[i][k] * U[j][k];
}
VLU[i][j] = sum;
}
}
return VLU.mmul(Y);
},
solveForDiagonal: function (value) {
return this.solve(Matrix.diag(value));
},
inverse: function () {
var V = this.V;
var e = this.threshold,
vrows = V.length,
vcols = V[0].length,
X = new Matrix(vrows, this.s.length),
i, j;
for (i = 0; i < vrows; i++) {
for (j = 0; j < vcols; j++) {
if (Math.abs(this.s[j]) > e) {
X[i][j] = V[i][j] / this.s[j];
} else {
X[i][j] = 0;
}
}
}
var U = this.U;
var urows = U.length,
ucols = U[0].length,
Y = new Matrix(vrows, urows),
k, sum;
for (i = 0; i < vrows; i++) {
for (j = 0; j < urows; j++) {
sum = 0;
for (k = 0; k < ucols; k++) {
sum += X[i][k] * U[j][k];
}
Y[i][j] = sum;
}
}
return Y;
}
};
module.exports = SingularValueDecomposition;