"use strict"; Object.defineProperty(exports, "__esModule", { value: true }); exports.createLsolveAll = void 0; var _factory = require("../../../utils/factory.js"); var _solveValidation = require("./utils/solveValidation.js"); const name = 'lsolveAll'; const dependencies = ['typed', 'matrix', 'divideScalar', 'multiplyScalar', 'subtractScalar', 'equalScalar', 'DenseMatrix']; const createLsolveAll = exports.createLsolveAll = /* #__PURE__ */(0, _factory.factory)(name, dependencies, _ref => { let { typed, matrix, divideScalar, multiplyScalar, subtractScalar, equalScalar, DenseMatrix } = _ref; const solveValidation = (0, _solveValidation.createSolveValidation)({ DenseMatrix }); /** * Finds all solutions of a linear equation system by forwards substitution. Matrix must be a lower triangular matrix. * * `L * x = b` * * Syntax: * * math.lsolveAll(L, b) * * Examples: * * const a = [[-2, 3], [2, 1]] * const b = [11, 9] * const x = lsolveAll(a, b) // [ [[-5.5], [20]] ] * * See also: * * lsolve, lup, slu, usolve, lusolve * * @param {Matrix, Array} L A N x N matrix or array (L) * @param {Matrix, Array} b A column vector with the b values * * @return {DenseMatrix[] | Array[]} An array of affine-independent column vectors (x) that solve the linear system */ return typed(name, { 'SparseMatrix, Array | Matrix': function (m, b) { return _sparseForwardSubstitution(m, b); }, 'DenseMatrix, Array | Matrix': function (m, b) { return _denseForwardSubstitution(m, b); }, 'Array, Array | Matrix': function (a, b) { const m = matrix(a); const R = _denseForwardSubstitution(m, b); return R.map(r => r.valueOf()); } }); function _denseForwardSubstitution(m, b_) { // the algorithm is derived from // https://www.overleaf.com/read/csvgqdxggyjv // array of right-hand sides const B = [solveValidation(m, b_, true)._data.map(e => e[0])]; const M = m._data; const rows = m._size[0]; const columns = m._size[1]; // loop columns for (let i = 0; i < columns; i++) { let L = B.length; // loop right-hand sides for (let k = 0; k < L; k++) { const b = B[k]; if (!equalScalar(M[i][i], 0)) { // non-singular row b[i] = divideScalar(b[i], M[i][i]); for (let j = i + 1; j < columns; j++) { // b[j] -= b[i] * M[j,i] b[j] = subtractScalar(b[j], multiplyScalar(b[i], M[j][i])); } } else if (!equalScalar(b[i], 0)) { // singular row, nonzero RHS if (k === 0) { // There is no valid solution return []; } else { // This RHS is invalid but other solutions may still exist B.splice(k, 1); k -= 1; L -= 1; } } else if (k === 0) { // singular row, RHS is zero const bNew = [...b]; bNew[i] = 1; for (let j = i + 1; j < columns; j++) { bNew[j] = subtractScalar(bNew[j], M[j][i]); } B.push(bNew); } } } return B.map(x => new DenseMatrix({ data: x.map(e => [e]), size: [rows, 1] })); } function _sparseForwardSubstitution(m, b_) { // array of right-hand sides const B = [solveValidation(m, b_, true)._data.map(e => e[0])]; const rows = m._size[0]; const columns = m._size[1]; const values = m._values; const index = m._index; const ptr = m._ptr; // loop columns for (let i = 0; i < columns; i++) { let L = B.length; // loop right-hand sides for (let k = 0; k < L; k++) { const b = B[k]; // values & indices (column i) const iValues = []; const iIndices = []; // first & last indeces in column const firstIndex = ptr[i]; const lastIndex = ptr[i + 1]; // find the value at [i, i] let Mii = 0; for (let j = firstIndex; j < lastIndex; j++) { const J = index[j]; // check row if (J === i) { Mii = values[j]; } else if (J > i) { // store lower triangular iValues.push(values[j]); iIndices.push(J); } } if (!equalScalar(Mii, 0)) { // non-singular row b[i] = divideScalar(b[i], Mii); for (let j = 0, lastIndex = iIndices.length; j < lastIndex; j++) { const J = iIndices[j]; b[J] = subtractScalar(b[J], multiplyScalar(b[i], iValues[j])); } } else if (!equalScalar(b[i], 0)) { // singular row, nonzero RHS if (k === 0) { // There is no valid solution return []; } else { // This RHS is invalid but other solutions may still exist B.splice(k, 1); k -= 1; L -= 1; } } else if (k === 0) { // singular row, RHS is zero const bNew = [...b]; bNew[i] = 1; for (let j = 0, lastIndex = iIndices.length; j < lastIndex; j++) { const J = iIndices[j]; bNew[J] = subtractScalar(bNew[J], iValues[j]); } B.push(bNew); } } } return B.map(x => new DenseMatrix({ data: x.map(e => [e]), size: [rows, 1] })); } });