import { factory } from '../../../utils/factory.js'; import { createSolveValidation } from './utils/solveValidation.js'; var name = 'lsolve'; var dependencies = ['typed', 'matrix', 'divideScalar', 'multiplyScalar', 'subtract', 'equalScalar', 'DenseMatrix']; export var createLsolve = /* #__PURE__ */factory(name, dependencies, _ref => { var { typed, matrix, divideScalar, multiplyScalar, subtract, equalScalar, DenseMatrix } = _ref; var solveValidation = createSolveValidation({ DenseMatrix }); /** * Finds one solution of a linear equation system by forwards substitution. Matrix must be a lower triangular matrix. Throws an error if there's no solution. * * `L * x = b` * * Syntax: * * math.lsolve(L, b) * * Examples: * * const a = [[-2, 3], [2, 1]] * const b = [11, 9] * const x = lsolve(a, b) // [[-5.5], [20]] * * See also: * * lsolveAll, 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} A column vector with the linear system solution (x) */ return typed(name, { 'SparseMatrix, Array | Matrix': function SparseMatrixArrayMatrix(m, b) { return _sparseForwardSubstitution(m, b); }, 'DenseMatrix, Array | Matrix': function DenseMatrixArrayMatrix(m, b) { return _denseForwardSubstitution(m, b); }, 'Array, Array | Matrix': function ArrayArrayMatrix(a, b) { var m = matrix(a); var r = _denseForwardSubstitution(m, b); return r.valueOf(); } }); function _denseForwardSubstitution(m, b) { // validate matrix and vector, return copy of column vector b b = solveValidation(m, b, true); var bdata = b._data; var rows = m._size[0]; var columns = m._size[1]; // result var x = []; var mdata = m._data; // loop columns for (var j = 0; j < columns; j++) { var bj = bdata[j][0] || 0; var xj = void 0; if (!equalScalar(bj, 0)) { // non-degenerate row, find solution var vjj = mdata[j][j]; if (equalScalar(vjj, 0)) { throw new Error('Linear system cannot be solved since matrix is singular'); } xj = divideScalar(bj, vjj); // loop rows for (var i = j + 1; i < rows; i++) { bdata[i] = [subtract(bdata[i][0] || 0, multiplyScalar(xj, mdata[i][j]))]; } } else { // degenerate row, we can choose any value xj = 0; } x[j] = [xj]; } return new DenseMatrix({ data: x, size: [rows, 1] }); } function _sparseForwardSubstitution(m, b) { // validate matrix and vector, return copy of column vector b b = solveValidation(m, b, true); var bdata = b._data; var rows = m._size[0]; var columns = m._size[1]; var values = m._values; var index = m._index; var ptr = m._ptr; // result var x = []; // loop columns for (var j = 0; j < columns; j++) { var bj = bdata[j][0] || 0; if (!equalScalar(bj, 0)) { // non-degenerate row, find solution var vjj = 0; // matrix values & indices (column j) var jValues = []; var jIndices = []; // first and last index in the column var firstIndex = ptr[j]; var lastIndex = ptr[j + 1]; // values in column, find value at [j, j] for (var k = firstIndex; k < lastIndex; k++) { var i = index[k]; // check row (rows are not sorted!) if (i === j) { vjj = values[k]; } else if (i > j) { // store lower triangular jValues.push(values[k]); jIndices.push(i); } } // at this point we must have a value in vjj if (equalScalar(vjj, 0)) { throw new Error('Linear system cannot be solved since matrix is singular'); } var xj = divideScalar(bj, vjj); for (var _k = 0, l = jIndices.length; _k < l; _k++) { var _i = jIndices[_k]; bdata[_i] = [subtract(bdata[_i][0] || 0, multiplyScalar(xj, jValues[_k]))]; } x[j] = [xj]; } else { // degenerate row, we can choose any value x[j] = [0]; } } return new DenseMatrix({ data: x, size: [rows, 1] }); } });