118 lines
4.1 KiB
JavaScript
118 lines
4.1 KiB
JavaScript
import { factory } from '../../utils/factory.js';
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var name = 'sylvester';
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var dependencies = ['typed', 'schur', 'matrixFromColumns', 'matrix', 'multiply', 'range', 'concat', 'transpose', 'index', 'subset', 'add', 'subtract', 'identity', 'lusolve', 'abs'];
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export var createSylvester = /* #__PURE__ */factory(name, dependencies, _ref => {
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var {
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typed,
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schur,
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matrixFromColumns,
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matrix,
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multiply,
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range,
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concat,
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transpose,
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index,
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subset,
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add,
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subtract,
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identity,
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lusolve,
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abs
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} = _ref;
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/**
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*
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* Solves the real-valued Sylvester equation AX+XB=C for X, where A, B and C are
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* matrices of appropriate dimensions, being A and B squared. Notice that other
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* equivalent definitions for the Sylvester equation exist and this function
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* assumes the one presented in the original publication of the the Bartels-
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* Stewart algorithm, which is implemented by this function.
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* https://en.wikipedia.org/wiki/Sylvester_equation
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*
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* Syntax:
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*
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* math.sylvester(A, B, C)
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*
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* Examples:
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*
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* const A = [[-1, -2], [1, 1]]
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* const B = [[2, -1], [1, -2]]
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* const C = [[-3, 2], [3, 0]]
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* math.sylvester(A, B, C) // returns DenseMatrix [[-0.25, 0.25], [1.5, -1.25]]
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*
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* See also:
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*
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* schur, lyap
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*
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* @param {Matrix | Array} A Matrix A
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* @param {Matrix | Array} B Matrix B
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* @param {Matrix | Array} C Matrix C
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* @return {Matrix | Array} Matrix X, solving the Sylvester equation
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*/
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return typed(name, {
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'Matrix, Matrix, Matrix': _sylvester,
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'Array, Matrix, Matrix': function Array_Matrix_Matrix(A, B, C) {
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return _sylvester(matrix(A), B, C);
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},
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'Array, Array, Matrix': function Array_Array_Matrix(A, B, C) {
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return _sylvester(matrix(A), matrix(B), C);
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},
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'Array, Matrix, Array': function Array_Matrix_Array(A, B, C) {
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return _sylvester(matrix(A), B, matrix(C));
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},
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'Matrix, Array, Matrix': function Matrix_Array_Matrix(A, B, C) {
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return _sylvester(A, matrix(B), C);
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},
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'Matrix, Array, Array': function Matrix_Array_Array(A, B, C) {
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return _sylvester(A, matrix(B), matrix(C));
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},
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'Matrix, Matrix, Array': function Matrix_Matrix_Array(A, B, C) {
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return _sylvester(A, B, matrix(C));
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},
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'Array, Array, Array': function Array_Array_Array(A, B, C) {
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return _sylvester(matrix(A), matrix(B), matrix(C)).toArray();
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}
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});
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function _sylvester(A, B, C) {
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var n = B.size()[0];
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var m = A.size()[0];
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var sA = schur(A);
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var F = sA.T;
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var U = sA.U;
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var sB = schur(multiply(-1, B));
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var G = sB.T;
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var V = sB.U;
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var D = multiply(multiply(transpose(U), C), V);
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var all = range(0, m);
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var y = [];
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var hc = (a, b) => concat(a, b, 1);
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var vc = (a, b) => concat(a, b, 0);
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for (var k = 0; k < n; k++) {
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if (k < n - 1 && abs(subset(G, index(k + 1, k))) > 1e-5) {
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var RHS = vc(subset(D, index(all, k)), subset(D, index(all, k + 1)));
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for (var j = 0; j < k; j++) {
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RHS = add(RHS, vc(multiply(y[j], subset(G, index(j, k))), multiply(y[j], subset(G, index(j, k + 1)))));
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}
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var gkk = multiply(identity(m), multiply(-1, subset(G, index(k, k))));
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var gmk = multiply(identity(m), multiply(-1, subset(G, index(k + 1, k))));
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var gkm = multiply(identity(m), multiply(-1, subset(G, index(k, k + 1))));
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var gmm = multiply(identity(m), multiply(-1, subset(G, index(k + 1, k + 1))));
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var LHS = vc(hc(add(F, gkk), gmk), hc(gkm, add(F, gmm)));
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var yAux = lusolve(LHS, RHS);
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y[k] = yAux.subset(index(range(0, m), 0));
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y[k + 1] = yAux.subset(index(range(m, 2 * m), 0));
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k++;
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} else {
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var _RHS = subset(D, index(all, k));
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for (var _j = 0; _j < k; _j++) {
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_RHS = add(_RHS, multiply(y[_j], subset(G, index(_j, k))));
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}
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var _gkk = subset(G, index(k, k));
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var _LHS = subtract(F, multiply(_gkk, identity(m)));
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y[k] = lusolve(_LHS, _RHS);
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}
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}
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var Y = matrix(matrixFromColumns(...y));
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var X = multiply(U, multiply(Y, transpose(V)));
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return X;
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}
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}); |