jama
Version:
JavaScript port of JAMA, the Java Matrix Library by NIST and MathWorks.
826 lines (825 loc) • 30 kB
JavaScript
"use strict";
/* Generated from Java with JSweet 2.0.0 - http://www.jsweet.org */
var Maths_1 = require("./util/Maths");
var Matrix_1 = require("./Matrix");
/**
* Check for symmetry, then construct the eigenvalue decomposition
* Structure to access D and V.
* @param {Matrix} Arg Square matrix
* @class
*/
var EigenvalueDecomposition = (function () {
function EigenvalueDecomposition(Arg) {
this.n = 0;
this.issymmetric = false;
this.d = null;
this.e = null;
this.V = null;
this.H = null;
this.ort = null;
this.cdivr = 0;
this.cdivi = 0;
var A = Arg.getArray();
this.n = Arg.getColumnDimension();
this.V = (function (dims) { var allocate = function (dims) { if (dims.length == 0) {
return 0;
}
else {
var array = [];
for (var i = 0; i < dims[0]; i++) {
array.push(allocate(dims.slice(1)));
}
return array;
} }; return allocate(dims); })([this.n, this.n]);
this.d = (function (s) { var a = []; while (s-- > 0)
a.push(0); return a; })(this.n);
this.e = (function (s) { var a = []; while (s-- > 0)
a.push(0); return a; })(this.n);
this.issymmetric = true;
for (var j = 0; (function (lhs, rhs) { return lhs && rhs; })((j < this.n), this.issymmetric); j++) {
for (var i = 0; (function (lhs, rhs) { return lhs && rhs; })((i < this.n), this.issymmetric); i++) {
this.issymmetric = (A[i][j] === A[j][i]);
}
;
}
;
if (this.issymmetric) {
for (var i = 0; i < this.n; i++) {
for (var j = 0; j < this.n; j++) {
this.V[i][j] = A[i][j];
}
;
}
;
this.tred2();
this.tql2();
}
else {
this.H = (function (dims) { var allocate = function (dims) { if (dims.length == 0) {
return 0;
}
else {
var array = [];
for (var i = 0; i < dims[0]; i++) {
array.push(allocate(dims.slice(1)));
}
return array;
} }; return allocate(dims); })([this.n, this.n]);
this.ort = (function (s) { var a = []; while (s-- > 0)
a.push(0); return a; })(this.n);
for (var j = 0; j < this.n; j++) {
for (var i = 0; i < this.n; i++) {
this.H[i][j] = A[i][j];
}
;
}
;
this.orthes();
this.hqr2();
}
}
/*private*/ EigenvalueDecomposition.prototype.tred2 = function () {
for (var j = 0; j < this.n; j++) {
this.d[j] = this.V[this.n - 1][j];
}
;
for (var i = this.n - 1; i > 0; i--) {
var scale = 0.0;
var h = 0.0;
for (var k = 0; k < i; k++) {
scale = scale + Math.abs(this.d[k]);
}
;
if (scale === 0.0) {
this.e[i] = this.d[i - 1];
for (var j = 0; j < i; j++) {
this.d[j] = this.V[i - 1][j];
this.V[i][j] = 0.0;
this.V[j][i] = 0.0;
}
;
}
else {
for (var k = 0; k < i; k++) {
this.d[k] /= scale;
h += this.d[k] * this.d[k];
}
;
var f = this.d[i - 1];
var g = Math.sqrt(h);
if (f > 0) {
g = -g;
}
this.e[i] = scale * g;
h = h - f * g;
this.d[i - 1] = f - g;
for (var j = 0; j < i; j++) {
this.e[j] = 0.0;
}
;
for (var j = 0; j < i; j++) {
f = this.d[j];
this.V[j][i] = f;
g = this.e[j] + this.V[j][j] * f;
for (var k = j + 1; k <= i - 1; k++) {
g += this.V[k][j] * this.d[k];
this.e[k] += this.V[k][j] * f;
}
;
this.e[j] = g;
}
;
f = 0.0;
for (var j = 0; j < i; j++) {
this.e[j] /= h;
f += this.e[j] * this.d[j];
}
;
var hh = f / (h + h);
for (var j = 0; j < i; j++) {
this.e[j] -= hh * this.d[j];
}
;
for (var j = 0; j < i; j++) {
f = this.d[j];
g = this.e[j];
for (var k = j; k <= i - 1; k++) {
this.V[k][j] -= (f * this.e[k] + g * this.d[k]);
}
;
this.d[j] = this.V[i - 1][j];
this.V[i][j] = 0.0;
}
;
}
this.d[i] = h;
}
;
for (var i = 0; i < this.n - 1; i++) {
this.V[this.n - 1][i] = this.V[i][i];
this.V[i][i] = 1.0;
var h = this.d[i + 1];
if (h !== 0.0) {
for (var k = 0; k <= i; k++) {
this.d[k] = this.V[k][i + 1] / h;
}
;
for (var j = 0; j <= i; j++) {
var g = 0.0;
for (var k = 0; k <= i; k++) {
g += this.V[k][i + 1] * this.V[k][j];
}
;
for (var k = 0; k <= i; k++) {
this.V[k][j] -= g * this.d[k];
}
;
}
;
}
for (var k = 0; k <= i; k++) {
this.V[k][i + 1] = 0.0;
}
;
}
;
for (var j = 0; j < this.n; j++) {
this.d[j] = this.V[this.n - 1][j];
this.V[this.n - 1][j] = 0.0;
}
;
this.V[this.n - 1][this.n - 1] = 1.0;
this.e[0] = 0.0;
};
/*private*/ EigenvalueDecomposition.prototype.tql2 = function () {
for (var i = 1; i < this.n; i++) {
this.e[i - 1] = this.e[i];
}
;
this.e[this.n - 1] = 0.0;
var f = 0.0;
var tst1 = 0.0;
var eps = Math.pow(2.0, -52.0);
for (var l = 0; l < this.n; l++) {
tst1 = Math.max(tst1, Math.abs(this.d[l]) + Math.abs(this.e[l]));
var m = l;
while ((m < this.n)) {
if (Math.abs(this.e[m]) <= eps * tst1) {
break;
}
m++;
}
;
if (m > l) {
var iter = 0;
do {
iter = iter + 1;
var g = this.d[l];
var p = (this.d[l + 1] - g) / (2.0 * this.e[l]);
var r = Maths_1.Maths.hypot(p, 1.0);
if (p < 0) {
r = -r;
}
this.d[l] = this.e[l] / (p + r);
this.d[l + 1] = this.e[l] * (p + r);
var dl1 = this.d[l + 1];
var h = g - this.d[l];
for (var i = l + 2; i < this.n; i++) {
this.d[i] -= h;
}
;
f = f + h;
p = this.d[m];
var c = 1.0;
var c2 = c;
var c3 = c;
var el1 = this.e[l + 1];
var s = 0.0;
var s2 = 0.0;
for (var i = m - 1; i >= l; i--) {
c3 = c2;
c2 = c;
s2 = s;
g = c * this.e[i];
h = c * p;
r = Maths_1.Maths.hypot(p, this.e[i]);
this.e[i + 1] = s * r;
s = this.e[i] / r;
c = p / r;
p = c * this.d[i] - s * g;
this.d[i + 1] = h + s * (c * g + s * this.d[i]);
for (var k = 0; k < this.n; k++) {
h = this.V[k][i + 1];
this.V[k][i + 1] = s * this.V[k][i] + c * h;
this.V[k][i] = c * this.V[k][i] - s * h;
}
;
}
;
p = -s * s2 * c3 * el1 * this.e[l] / dl1;
this.e[l] = s * p;
this.d[l] = c * p;
} while ((Math.abs(this.e[l]) > eps * tst1));
}
this.d[l] = this.d[l] + f;
this.e[l] = 0.0;
}
;
for (var i = 0; i < this.n - 1; i++) {
var k = i;
var p = this.d[i];
for (var j = i + 1; j < this.n; j++) {
if (this.d[j] < p) {
k = j;
p = this.d[j];
}
}
;
if (k !== i) {
this.d[k] = this.d[i];
this.d[i] = p;
for (var j = 0; j < this.n; j++) {
p = this.V[j][i];
this.V[j][i] = this.V[j][k];
this.V[j][k] = p;
}
;
}
}
;
};
/*private*/ EigenvalueDecomposition.prototype.orthes = function () {
var low = 0;
var high = this.n - 1;
for (var m = low + 1; m <= high - 1; m++) {
var scale = 0.0;
for (var i = m; i <= high; i++) {
scale = scale + Math.abs(this.H[i][m - 1]);
}
;
if (scale !== 0.0) {
var h = 0.0;
for (var i = high; i >= m; i--) {
this.ort[i] = this.H[i][m - 1] / scale;
h += this.ort[i] * this.ort[i];
}
;
var g = Math.sqrt(h);
if (this.ort[m] > 0) {
g = -g;
}
h = h - this.ort[m] * g;
this.ort[m] = this.ort[m] - g;
for (var j = m; j < this.n; j++) {
var f = 0.0;
for (var i = high; i >= m; i--) {
f += this.ort[i] * this.H[i][j];
}
;
f = f / h;
for (var i = m; i <= high; i++) {
this.H[i][j] -= f * this.ort[i];
}
;
}
;
for (var i = 0; i <= high; i++) {
var f = 0.0;
for (var j = high; j >= m; j--) {
f += this.ort[j] * this.H[i][j];
}
;
f = f / h;
for (var j = m; j <= high; j++) {
this.H[i][j] -= f * this.ort[j];
}
;
}
;
this.ort[m] = scale * this.ort[m];
this.H[m][m - 1] = scale * g;
}
}
;
for (var i = 0; i < this.n; i++) {
for (var j = 0; j < this.n; j++) {
this.V[i][j] = (i === j ? 1.0 : 0.0);
}
;
}
;
for (var m = high - 1; m >= low + 1; m--) {
if (this.H[m][m - 1] !== 0.0) {
for (var i = m + 1; i <= high; i++) {
this.ort[i] = this.H[i][m - 1];
}
;
for (var j = m; j <= high; j++) {
var g = 0.0;
for (var i = m; i <= high; i++) {
g += this.ort[i] * this.V[i][j];
}
;
g = (g / this.ort[m]) / this.H[m][m - 1];
for (var i = m; i <= high; i++) {
this.V[i][j] += g * this.ort[i];
}
;
}
;
}
}
;
};
/*private*/ EigenvalueDecomposition.prototype.cdiv = function (xr, xi, yr, yi) {
var r;
var d;
if (Math.abs(yr) > Math.abs(yi)) {
r = yi / yr;
d = yr + r * yi;
this.cdivr = (xr + r * xi) / d;
this.cdivi = (xi - r * xr) / d;
}
else {
r = yr / yi;
d = yi + r * yr;
this.cdivr = (r * xr + xi) / d;
this.cdivi = (r * xi - xr) / d;
}
};
/*private*/ EigenvalueDecomposition.prototype.hqr2 = function () {
var nn = this.n;
var n = nn - 1;
var low = 0;
var high = nn - 1;
var eps = Math.pow(2.0, -52.0);
var exshift = 0.0;
var p = 0;
var q = 0;
var r = 0;
var s = 0;
var z = 0;
var t;
var w;
var x;
var y;
var norm = 0.0;
for (var i = 0; i < nn; i++) {
if ((function (lhs, rhs) { return lhs || rhs; })(i < low, i > high)) {
this.d[i] = this.H[i][i];
this.e[i] = 0.0;
}
for (var j = Math.max(i - 1, 0); j < nn; j++) {
norm = norm + Math.abs(this.H[i][j]);
}
;
}
;
var iter = 0;
while ((n >= low)) {
var l = n;
while ((l > low)) {
s = Math.abs(this.H[l - 1][l - 1]) + Math.abs(this.H[l][l]);
if (s === 0.0) {
s = norm;
}
if (Math.abs(this.H[l][l - 1]) < eps * s) {
break;
}
l--;
}
;
if (l === n) {
this.H[n][n] = this.H[n][n] + exshift;
this.d[n] = this.H[n][n];
this.e[n] = 0.0;
n--;
iter = 0;
}
else if (l === n - 1) {
w = this.H[n][n - 1] * this.H[n - 1][n];
p = (this.H[n - 1][n - 1] - this.H[n][n]) / 2.0;
q = p * p + w;
z = Math.sqrt(Math.abs(q));
this.H[n][n] = this.H[n][n] + exshift;
this.H[n - 1][n - 1] = this.H[n - 1][n - 1] + exshift;
x = this.H[n][n];
if (q >= 0) {
if (p >= 0) {
z = p + z;
}
else {
z = p - z;
}
this.d[n - 1] = x + z;
this.d[n] = this.d[n - 1];
if (z !== 0.0) {
this.d[n] = x - w / z;
}
this.e[n - 1] = 0.0;
this.e[n] = 0.0;
x = this.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 = p / r;
q = q / r;
for (var j = n - 1; j < nn; j++) {
z = this.H[n - 1][j];
this.H[n - 1][j] = q * z + p * this.H[n][j];
this.H[n][j] = q * this.H[n][j] - p * z;
}
;
for (var i = 0; i <= n; i++) {
z = this.H[i][n - 1];
this.H[i][n - 1] = q * z + p * this.H[i][n];
this.H[i][n] = q * this.H[i][n] - p * z;
}
;
for (var i = low; i <= high; i++) {
z = this.V[i][n - 1];
this.V[i][n - 1] = q * z + p * this.V[i][n];
this.V[i][n] = q * this.V[i][n] - p * z;
}
;
}
else {
this.d[n - 1] = x + p;
this.d[n] = x + p;
this.e[n - 1] = z;
this.e[n] = -z;
}
n = n - 2;
iter = 0;
}
else {
x = this.H[n][n];
y = 0.0;
w = 0.0;
if (l < n) {
y = this.H[n - 1][n - 1];
w = this.H[n][n - 1] * this.H[n - 1][n];
}
if (iter === 10) {
exshift += x;
for (var i = low; i <= n; i++) {
this.H[i][i] -= x;
}
;
s = Math.abs(this.H[n][n - 1]) + Math.abs(this.H[n - 1][n - 2]);
x = y = 0.75 * s;
w = -0.4375 * s * s;
}
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++) {
this.H[i][i] -= s;
}
;
exshift += s;
x = y = w = 0.964;
}
}
iter = iter + 1;
var m = n - 2;
while ((m >= l)) {
z = this.H[m][m];
r = x - z;
s = y - z;
p = (r * s - w) / this.H[m + 1][m] + this.H[m][m + 1];
q = this.H[m + 1][m + 1] - z - r - s;
r = this.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(this.H[m][m - 1]) * (Math.abs(q) + Math.abs(r)) < eps * (Math.abs(p) * (Math.abs(this.H[m - 1][m - 1]) + Math.abs(z) + Math.abs(this.H[m + 1][m + 1])))) {
break;
}
m--;
}
;
for (var i = m + 2; i <= n; i++) {
this.H[i][i - 2] = 0.0;
if (i > m + 2) {
this.H[i][i - 3] = 0.0;
}
}
;
for (var k = m; k <= n - 1; k++) {
var notlast = (k !== n - 1);
if (k !== m) {
p = this.H[k][k - 1];
q = this.H[k + 1][k - 1];
r = (notlast ? this.H[k + 2][k - 1] : 0.0);
x = Math.abs(p) + Math.abs(q) + Math.abs(r);
if (x === 0.0) {
continue;
}
p = p / x;
q = q / x;
r = r / x;
}
s = Math.sqrt(p * p + q * q + r * r);
if (p < 0) {
s = -s;
}
if (s !== 0) {
if (k !== m) {
this.H[k][k - 1] = -s * x;
}
else if (l !== m) {
this.H[k][k - 1] = -this.H[k][k - 1];
}
p = p + s;
x = p / s;
y = q / s;
z = r / s;
q = q / p;
r = r / p;
for (var j = k; j < nn; j++) {
p = this.H[k][j] + q * this.H[k + 1][j];
if (notlast) {
p = p + r * this.H[k + 2][j];
this.H[k + 2][j] = this.H[k + 2][j] - p * z;
}
this.H[k][j] = this.H[k][j] - p * x;
this.H[k + 1][j] = this.H[k + 1][j] - p * y;
}
;
for (var i = 0; i <= Math.min(n, k + 3); i++) {
p = x * this.H[i][k] + y * this.H[i][k + 1];
if (notlast) {
p = p + z * this.H[i][k + 2];
this.H[i][k + 2] = this.H[i][k + 2] - p * r;
}
this.H[i][k] = this.H[i][k] - p;
this.H[i][k + 1] = this.H[i][k + 1] - p * q;
}
;
for (var i = low; i <= high; i++) {
p = x * this.V[i][k] + y * this.V[i][k + 1];
if (notlast) {
p = p + z * this.V[i][k + 2];
this.V[i][k + 2] = this.V[i][k + 2] - p * r;
}
this.V[i][k] = this.V[i][k] - p;
this.V[i][k + 1] = this.V[i][k + 1] - p * q;
}
;
}
}
;
}
}
;
if (norm === 0.0) {
return;
}
for (n = nn - 1; n >= 0; n--) {
p = this.d[n];
q = this.e[n];
if (q === 0) {
var l = n;
this.H[n][n] = 1.0;
for (var i = n - 1; i >= 0; i--) {
w = this.H[i][i] - p;
r = 0.0;
for (var j = l; j <= n; j++) {
r = r + this.H[i][j] * this.H[j][n];
}
;
if (this.e[i] < 0.0) {
z = w;
s = r;
}
else {
l = i;
if (this.e[i] === 0.0) {
if (w !== 0.0) {
this.H[i][n] = -r / w;
}
else {
this.H[i][n] = -r / (eps * norm);
}
}
else {
x = this.H[i][i + 1];
y = this.H[i + 1][i];
q = (this.d[i] - p) * (this.d[i] - p) + this.e[i] * this.e[i];
t = (x * s - z * r) / q;
this.H[i][n] = t;
if (Math.abs(x) > Math.abs(z)) {
this.H[i + 1][n] = (-r - w * t) / x;
}
else {
this.H[i + 1][n] = (-s - y * t) / z;
}
}
t = Math.abs(this.H[i][n]);
if ((eps * t) * t > 1) {
for (var j = i; j <= n; j++) {
this.H[j][n] = this.H[j][n] / t;
}
;
}
}
}
;
}
else if (q < 0) {
var l = n - 1;
if (Math.abs(this.H[n][n - 1]) > Math.abs(this.H[n - 1][n])) {
this.H[n - 1][n - 1] = q / this.H[n][n - 1];
this.H[n - 1][n] = -(this.H[n][n] - p) / this.H[n][n - 1];
}
else {
this.cdiv(0.0, -this.H[n - 1][n], this.H[n - 1][n - 1] - p, q);
this.H[n - 1][n - 1] = this.cdivr;
this.H[n - 1][n] = this.cdivi;
}
this.H[n][n - 1] = 0.0;
this.H[n][n] = 1.0;
for (var i = n - 2; i >= 0; i--) {
var ra = void 0;
var sa = void 0;
var vr = void 0;
var vi = void 0;
ra = 0.0;
sa = 0.0;
for (var j = l; j <= n; j++) {
ra = ra + this.H[i][j] * this.H[j][n - 1];
sa = sa + this.H[i][j] * this.H[j][n];
}
;
w = this.H[i][i] - p;
if (this.e[i] < 0.0) {
z = w;
r = ra;
s = sa;
}
else {
l = i;
if (this.e[i] === 0) {
this.cdiv(-ra, -sa, w, q);
this.H[i][n - 1] = this.cdivr;
this.H[i][n] = this.cdivi;
}
else {
x = this.H[i][i + 1];
y = this.H[i + 1][i];
vr = (this.d[i] - p) * (this.d[i] - p) + this.e[i] * this.e[i] - q * q;
vi = (this.d[i] - p) * 2.0 * q;
if ((function (lhs, rhs) { return lhs && rhs; })(vr === 0.0, vi === 0.0)) {
vr = eps * norm * (Math.abs(w) + Math.abs(q) + Math.abs(x) + Math.abs(y) + Math.abs(z));
}
this.cdiv(x * r - z * ra + q * sa, x * s - z * sa - q * ra, vr, vi);
this.H[i][n - 1] = this.cdivr;
this.H[i][n] = this.cdivi;
if (Math.abs(x) > (Math.abs(z) + Math.abs(q))) {
this.H[i + 1][n - 1] = (-ra - w * this.H[i][n - 1] + q * this.H[i][n]) / x;
this.H[i + 1][n] = (-sa - w * this.H[i][n] - q * this.H[i][n - 1]) / x;
}
else {
this.cdiv(-r - y * this.H[i][n - 1], -s - y * this.H[i][n], z, q);
this.H[i + 1][n - 1] = this.cdivr;
this.H[i + 1][n] = this.cdivi;
}
}
t = Math.max(Math.abs(this.H[i][n - 1]), Math.abs(this.H[i][n]));
if ((eps * t) * t > 1) {
for (var j = i; j <= n; j++) {
this.H[j][n - 1] = this.H[j][n - 1] / t;
this.H[j][n] = this.H[j][n] / t;
}
;
}
}
}
;
}
}
;
for (var i = 0; i < nn; i++) {
if ((function (lhs, rhs) { return lhs || rhs; })(i < low, i > high)) {
for (var j = i; j < nn; j++) {
this.V[i][j] = this.H[i][j];
}
;
}
}
;
for (var j = nn - 1; j >= low; j--) {
for (var i = low; i <= high; i++) {
z = 0.0;
for (var k = low; k <= Math.min(j, high); k++) {
z = z + this.V[i][k] * this.H[k][j];
}
;
this.V[i][j] = z;
}
;
}
;
};
/**
* Return the eigenvector matrix
* @return {Matrix} V
*/
EigenvalueDecomposition.prototype.getV = function () {
return new Matrix_1.Matrix(this.V, this.n, this.n);
};
/**
* Return the real parts of the eigenvalues
* @return {Array} real(diag(D))
*/
EigenvalueDecomposition.prototype.getRealEigenvalues = function () {
return this.d;
};
/**
* Return the imaginary parts of the eigenvalues
* @return {Array} imag(diag(D))
*/
EigenvalueDecomposition.prototype.getImagEigenvalues = function () {
return this.e;
};
/**
* Return the block diagonal eigenvalue matrix
* @return {Matrix} D
*/
EigenvalueDecomposition.prototype.getD = function () {
var X = new Matrix_1.Matrix(this.n, this.n);
var D = X.getArray();
for (var i = 0; i < this.n; i++) {
for (var j = 0; j < this.n; j++) {
D[i][j] = 0.0;
}
;
D[i][i] = this.d[i];
if (this.e[i] > 0) {
D[i][i + 1] = this.e[i];
}
else if (this.e[i] < 0) {
D[i][i - 1] = this.e[i];
}
}
;
return X;
};
return EigenvalueDecomposition;
}());
EigenvalueDecomposition.serialVersionUID = 1;
exports.EigenvalueDecomposition = EigenvalueDecomposition;
EigenvalueDecomposition["__class"] = "Jama.EigenvalueDecomposition";
EigenvalueDecomposition["__interfaces"] = ["java.io.Serializable"];