100 lines
3.5 KiB
JavaScript
100 lines
3.5 KiB
JavaScript
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import { isInteger } from '../../../utils/number.js';
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import { factory } from '../../../utils/factory.js';
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import { createCsSqr } from '../sparse/csSqr.js';
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import { createCsLu } from '../sparse/csLu.js';
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var name = 'slu';
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var dependencies = ['typed', 'abs', 'add', 'multiply', 'transpose', 'divideScalar', 'subtract', 'larger', 'largerEq', 'SparseMatrix'];
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export var createSlu = /* #__PURE__ */factory(name, dependencies, _ref => {
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var {
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typed,
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abs,
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add,
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multiply,
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transpose,
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divideScalar,
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subtract,
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larger,
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largerEq,
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SparseMatrix
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} = _ref;
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var csSqr = createCsSqr({
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add,
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multiply,
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transpose
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});
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var csLu = createCsLu({
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abs,
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divideScalar,
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multiply,
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subtract,
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larger,
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largerEq,
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SparseMatrix
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});
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/**
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* Calculate the Sparse Matrix LU decomposition with full pivoting. Sparse Matrix `A` is decomposed in two matrices (`L`, `U`) and two permutation vectors (`pinv`, `q`) where
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*
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* `P * A * Q = L * U`
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*
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* Syntax:
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*
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* math.slu(A, order, threshold)
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*
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* Examples:
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*
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* const A = math.sparse([[4,3], [6, 3]])
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* math.slu(A, 1, 0.001)
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* // returns:
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* // {
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* // L: [[1, 0], [1.5, 1]]
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* // U: [[4, 3], [0, -1.5]]
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* // p: [0, 1]
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* // q: [0, 1]
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* // }
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*
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* See also:
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*
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* lup, lsolve, usolve, lusolve
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*
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* @param {SparseMatrix} A A two dimensional sparse matrix for which to get the LU decomposition.
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* @param {Number} order The Symbolic Ordering and Analysis order:
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* 0 - Natural ordering, no permutation vector q is returned
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* 1 - Matrix must be square, symbolic ordering and analisis is performed on M = A + A'
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* 2 - Symbolic ordering and analisis is performed on M = A' * A. Dense columns from A' are dropped, A recreated from A'.
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* This is appropriatefor LU factorization of unsymmetric matrices.
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* 3 - Symbolic ordering and analisis is performed on M = A' * A. This is best used for LU factorization is matrix M has no dense rows.
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* A dense row is a row with more than 10*sqr(columns) entries.
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* @param {Number} threshold Partial pivoting threshold (1 for partial pivoting)
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*
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* @return {Object} The lower triangular matrix, the upper triangular matrix and the permutation vectors.
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*/
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return typed(name, {
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'SparseMatrix, number, number': function SparseMatrixNumberNumber(a, order, threshold) {
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// verify order
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if (!isInteger(order) || order < 0 || order > 3) {
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throw new Error('Symbolic Ordering and Analysis order must be an integer number in the interval [0, 3]');
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} // verify threshold
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if (threshold < 0 || threshold > 1) {
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throw new Error('Partial pivoting threshold must be a number from 0 to 1');
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} // perform symbolic ordering and analysis
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var s = csSqr(order, a, false); // perform lu decomposition
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var f = csLu(a, s, threshold); // return decomposition
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return {
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L: f.L,
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U: f.U,
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p: f.pinv,
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q: s.q,
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toString: function toString() {
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return 'L: ' + this.L.toString() + '\nU: ' + this.U.toString() + '\np: ' + this.p.toString() + (this.q ? '\nq: ' + this.q.toString() : '') + '\n';
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}
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};
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}
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});
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});
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