in benchmarks/JetStream2/ARES-6/ml/index.js [2030:2413]
function SingularValueDecomposition(value, options) {
if (!(this instanceof SingularValueDecomposition)) {
return new SingularValueDecomposition(value, options);
}
value = Matrix.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();
// eslint-disable-next-line no-console
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] = 0 - 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;
}
// no default
}
}
if (swapped) {
var tmp = V;
V = U;
U = tmp;
}
this.m = m;
this.n = n;
this.s = s;
this.U = U;
this.V = V;
}