114 lines
3.7 KiB
JavaScript
114 lines
3.7 KiB
JavaScript
"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.createLusolve = void 0;
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var _is = require("../../../utils/is.js");
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var _factory = require("../../../utils/factory.js");
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var _solveValidation = require("./utils/solveValidation.js");
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var _csIpvec = require("../sparse/csIpvec.js");
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const name = 'lusolve';
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const dependencies = ['typed', 'matrix', 'lup', 'slu', 'usolve', 'lsolve', 'DenseMatrix'];
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const createLusolve = exports.createLusolve = /* #__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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lup,
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slu,
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usolve,
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lsolve,
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DenseMatrix
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} = _ref;
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const solveValidation = (0, _solveValidation.createSolveValidation)({
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DenseMatrix
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});
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/**
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* Solves the linear system `A * x = b` where `A` is an [n x n] matrix and `b` is a [n] column vector.
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*
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* Syntax:
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*
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* math.lusolve(A, b) // returns column vector with the solution to the linear system A * x = b
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* math.lusolve(lup, b) // returns column vector with the solution to the linear system A * x = b, lup = math.lup(A)
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*
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* Examples:
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*
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* const m = [[1, 0, 0, 0], [0, 2, 0, 0], [0, 0, 3, 0], [0, 0, 0, 4]]
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*
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* const x = math.lusolve(m, [-1, -1, -1, -1]) // x = [[-1], [-0.5], [-1/3], [-0.25]]
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*
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* const f = math.lup(m)
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* const x1 = math.lusolve(f, [-1, -1, -1, -1]) // x1 = [[-1], [-0.5], [-1/3], [-0.25]]
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* const x2 = math.lusolve(f, [1, 2, 1, -1]) // x2 = [[1], [1], [1/3], [-0.25]]
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*
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* const a = [[-2, 3], [2, 1]]
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* const b = [11, 9]
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* const x = math.lusolve(a, b) // [[2], [5]]
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*
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* See also:
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*
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* lup, slu, lsolve, usolve
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*
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* @param {Matrix | Array | Object} A Invertible Matrix or the Matrix LU decomposition
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* @param {Matrix | Array} b Column Vector
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* @param {number} [order] The Symbolic Ordering and Analysis order, see slu for details. Matrix must be a SparseMatrix
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* @param {Number} [threshold] Partial pivoting threshold (1 for partial pivoting), see slu for details. Matrix must be a SparseMatrix.
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*
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* @return {DenseMatrix | Array} Column vector with the solution to the linear system A * x = b
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*/
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return typed(name, {
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'Array, Array | Matrix': function (a, b) {
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a = matrix(a);
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const d = lup(a);
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const x = _lusolve(d.L, d.U, d.p, null, b);
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return x.valueOf();
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},
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'DenseMatrix, Array | Matrix': function (a, b) {
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const d = lup(a);
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return _lusolve(d.L, d.U, d.p, null, b);
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},
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'SparseMatrix, Array | Matrix': function (a, b) {
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const d = lup(a);
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return _lusolve(d.L, d.U, d.p, null, b);
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},
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'SparseMatrix, Array | Matrix, number, number': function (a, b, order, threshold) {
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const d = slu(a, order, threshold);
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return _lusolve(d.L, d.U, d.p, d.q, b);
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},
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'Object, Array | Matrix': function (d, b) {
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return _lusolve(d.L, d.U, d.p, d.q, b);
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}
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});
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function _toMatrix(a) {
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if ((0, _is.isMatrix)(a)) {
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return a;
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}
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if ((0, _is.isArray)(a)) {
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return matrix(a);
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}
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throw new TypeError('Invalid Matrix LU decomposition');
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}
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function _lusolve(l, u, p, q, b) {
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// verify decomposition
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l = _toMatrix(l);
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u = _toMatrix(u);
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// apply row permutations if needed (b is a DenseMatrix)
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if (p) {
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b = solveValidation(l, b, true);
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b._data = (0, _csIpvec.csIpvec)(p, b._data);
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}
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// use forward substitution to resolve L * y = b
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const y = lsolve(l, b);
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// use backward substitution to resolve U * x = y
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const x = usolve(u, y);
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// apply column permutations if needed (x is a DenseMatrix)
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if (q) {
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x._data = (0, _csIpvec.csIpvec)(q, x._data);
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}
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return x;
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}
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}); |