113 lines
3.6 KiB
JavaScript
113 lines
3.6 KiB
JavaScript
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;
|
|
}
|
|
}); |