76 lines
1.7 KiB
JavaScript
76 lines
1.7 KiB
JavaScript
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"use strict";
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Object.defineProperty(exports, "__esModule", {
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value: true
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});
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exports.createSchur = void 0;
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var _factory = require("../../../utils/factory.js");
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const name = 'schur';
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const dependencies = ['typed', 'matrix', 'identity', 'multiply', 'qr', 'norm', 'subtract'];
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const createSchur = exports.createSchur = /* #__PURE__ */(0, _factory.factory)(name, dependencies, _ref => {
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let {
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typed,
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matrix,
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identity,
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multiply,
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qr,
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norm,
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subtract
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} = _ref;
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/**
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*
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* Performs a real Schur decomposition of the real matrix A = UTU' where U is orthogonal
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* and T is upper quasi-triangular.
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* https://en.wikipedia.org/wiki/Schur_decomposition
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*
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* Syntax:
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*
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* math.schur(A)
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*
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* Examples:
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*
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* const A = [[1, 0], [-4, 3]]
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* math.schur(A) // returns {T: [[3, 4], [0, 1]], R: [[0, 1], [-1, 0]]}
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*
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* See also:
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*
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* sylvester, lyap, qr
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*
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* @param {Array | Matrix} A Matrix A
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* @return {{U: Array | Matrix, T: Array | Matrix}} Object containing both matrix U and T of the Schur Decomposition A=UTU'
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*/
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return typed(name, {
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Array: function (X) {
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const r = _schur(matrix(X));
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return {
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U: r.U.valueOf(),
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T: r.T.valueOf()
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};
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},
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Matrix: function (X) {
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return _schur(X);
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}
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});
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function _schur(X) {
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const n = X.size()[0];
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let A = X;
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let U = identity(n);
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let k = 0;
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let A0;
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do {
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A0 = A;
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const QR = qr(A);
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const Q = QR.Q;
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const R = QR.R;
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A = multiply(R, Q);
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U = multiply(U, Q);
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if (k++ > 100) {
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break;
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}
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} while (norm(subtract(A, A0)) > 1e-4);
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return {
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U,
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T: A
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};
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}
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});
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