ysjj-system/node_modules/mathjs/lib/esm/function/algebra/solver/lusolve.js

import { isArray, isMatrix } from '../../../utils/is.js';
import { factory } from '../../../utils/factory.js';
import { createSolveValidation } from './utils/solveValidation.js';
import { csIpvec } from '../sparse/csIpvec.js';
var name = 'lusolve';
var dependencies = ['typed', 'matrix', 'lup', 'slu', 'usolve', 'lsolve', 'DenseMatrix'];
export var createLusolve = /* #__PURE__ */factory(name, dependencies, _ref => {
  var {
    typed,
    matrix,
    lup,
    slu,
    usolve,
    lsolve,
    DenseMatrix
  } = _ref;
  var solveValidation = createSolveValidation({
    DenseMatrix
  });

  /**
   * Solves the linear system `A * x = b` where `A` is an [n x n] matrix and `b` is a [n] column vector.
   *
   * Syntax:
   *
   *    math.lusolve(A, b)     // returns column vector with the solution to the linear system A * x = b
   *    math.lusolve(lup, b)   // returns column vector with the solution to the linear system A * x = b, lup = math.lup(A)
   *
   * Examples:
   *
   *    const m = [[1, 0, 0, 0], [0, 2, 0, 0], [0, 0, 3, 0], [0, 0, 0, 4]]
   *
   *    const x = math.lusolve(m, [-1, -1, -1, -1])        // x = [[-1], [-0.5], [-1/3], [-0.25]]
   *
   *    const f = math.lup(m)
   *    const x1 = math.lusolve(f, [-1, -1, -1, -1])       // x1 = [[-1], [-0.5], [-1/3], [-0.25]]
   *    const x2 = math.lusolve(f, [1, 2, 1, -1])          // x2 = [[1], [1], [1/3], [-0.25]]
   *
   *    const a = [[-2, 3], [2, 1]]
   *    const b = [11, 9]
   *    const x = math.lusolve(a, b)  // [[2], [5]]
   *
   * See also:
   *
   *    lup, slu, lsolve, usolve
   *
   * @param {Matrix | Array | Object} A      Invertible Matrix or the Matrix LU decomposition
   * @param {Matrix | Array} b               Column Vector
   * @param {number} [order]                 The Symbolic Ordering and Analysis order, see slu for details. Matrix must be a SparseMatrix
   * @param {Number} [threshold]             Partial pivoting threshold (1 for partial pivoting), see slu for details. Matrix must be a SparseMatrix.
   *
   * @return {DenseMatrix | Array}           Column vector with the solution to the linear system A * x = b
   */
  return typed(name, {
    'Array, Array | Matrix': function ArrayArrayMatrix(a, b) {
      a = matrix(a);
      var d = lup(a);
      var x = _lusolve(d.L, d.U, d.p, null, b);
      return x.valueOf();
    },
    'DenseMatrix, Array | Matrix': function DenseMatrixArrayMatrix(a, b) {
      var d = lup(a);
      return _lusolve(d.L, d.U, d.p, null, b);
    },
    'SparseMatrix, Array | Matrix': function SparseMatrixArrayMatrix(a, b) {
      var d = lup(a);
      return _lusolve(d.L, d.U, d.p, null, b);
    },
    'SparseMatrix, Array | Matrix, number, number': function SparseMatrixArrayMatrixNumberNumber(a, b, order, threshold) {
      var d = slu(a, order, threshold);
      return _lusolve(d.L, d.U, d.p, d.q, b);
    },
    'Object, Array | Matrix': function ObjectArrayMatrix(d, b) {
      return _lusolve(d.L, d.U, d.p, d.q, b);
    }
  });
  function _toMatrix(a) {
    if (isMatrix(a)) {
      return a;
    }
    if (isArray(a)) {
      return matrix(a);
    }
    throw new TypeError('Invalid Matrix LU decomposition');
  }
  function _lusolve(l, u, p, q, b) {
    // verify decomposition
    l = _toMatrix(l);
    u = _toMatrix(u);

    // apply row permutations if needed (b is a DenseMatrix)
    if (p) {
      b = solveValidation(l, b, true);
      b._data = csIpvec(p, b._data);
    }

    // use forward substitution to resolve L * y = b
    var y = lsolve(l, b);
    // use backward substitution to resolve U * x = y
    var x = usolve(u, y);

    // apply column permutations if needed (x is a DenseMatrix)
    if (q) {
      x._data = csIpvec(q, x._data);
    }
    return x;
  }
});