413 lines
10 KiB
JavaScript
413 lines
10 KiB
JavaScript
import { clone } from '../../../utils/object.js';
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import { factory } from '../../../utils/factory.js';
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var name = 'lup';
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var dependencies = ['typed', 'matrix', 'abs', 'addScalar', 'divideScalar', 'multiplyScalar', 'subtract', 'larger', 'equalScalar', 'unaryMinus', 'DenseMatrix', 'SparseMatrix', 'Spa'];
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export var createLup = /* #__PURE__ */factory(name, dependencies, _ref => {
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var {
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typed,
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matrix,
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abs,
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addScalar,
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divideScalar,
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multiplyScalar,
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subtract,
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larger,
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equalScalar,
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unaryMinus,
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DenseMatrix,
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SparseMatrix,
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Spa
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} = _ref;
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/**
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* Calculate the Matrix LU decomposition with partial pivoting. Matrix `A` is decomposed in two matrices (`L`, `U`) and a
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* row permutation vector `p` where `A[p,:] = L * U`
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*
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* Syntax:
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*
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* math.lup(A)
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*
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* Example:
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*
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* const m = [[2, 1], [1, 4]]
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* const r = math.lup(m)
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* // r = {
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* // L: [[1, 0], [0.5, 1]],
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* // U: [[2, 1], [0, 3.5]],
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* // P: [0, 1]
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* // }
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*
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* See also:
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*
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* slu, lsolve, lusolve, usolve
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*
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* @param {Matrix | Array} A A two dimensional matrix or array for which to get the LUP decomposition.
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*
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* @return {{L: Array | Matrix, U: Array | Matrix, P: Array.<number>}} The lower triangular matrix, the upper triangular matrix and the permutation matrix.
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*/
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return typed(name, {
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DenseMatrix: function DenseMatrix(m) {
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return _denseLUP(m);
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},
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SparseMatrix: function SparseMatrix(m) {
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return _sparseLUP(m);
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},
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Array: function Array(a) {
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// create dense matrix from array
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var m = matrix(a); // lup, use matrix implementation
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var r = _denseLUP(m); // result
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return {
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L: r.L.valueOf(),
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U: r.U.valueOf(),
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p: r.p
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};
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}
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});
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function _denseLUP(m) {
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// rows & columns
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var rows = m._size[0];
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var columns = m._size[1]; // minimum rows and columns
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var n = Math.min(rows, columns); // matrix array, clone original data
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var data = clone(m._data); // l matrix arrays
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var ldata = [];
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var lsize = [rows, n]; // u matrix arrays
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var udata = [];
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var usize = [n, columns]; // vars
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var i, j, k; // permutation vector
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var p = [];
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for (i = 0; i < rows; i++) {
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p[i] = i;
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} // loop columns
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for (j = 0; j < columns; j++) {
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// skip first column in upper triangular matrix
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if (j > 0) {
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// loop rows
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for (i = 0; i < rows; i++) {
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// min i,j
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var min = Math.min(i, j); // v[i, j]
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var s = 0; // loop up to min
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for (k = 0; k < min; k++) {
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// s = l[i, k] - data[k, j]
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s = addScalar(s, multiplyScalar(data[i][k], data[k][j]));
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}
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data[i][j] = subtract(data[i][j], s);
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}
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} // row with larger value in cvector, row >= j
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var pi = j;
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var pabsv = 0;
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var vjj = 0; // loop rows
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for (i = j; i < rows; i++) {
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// data @ i, j
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var v = data[i][j]; // absolute value
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var absv = abs(v); // value is greater than pivote value
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if (larger(absv, pabsv)) {
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// store row
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pi = i; // update max value
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pabsv = absv; // value @ [j, j]
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vjj = v;
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}
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} // swap rows (j <-> pi)
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if (j !== pi) {
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// swap values j <-> pi in p
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p[j] = [p[pi], p[pi] = p[j]][0]; // swap j <-> pi in data
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DenseMatrix._swapRows(j, pi, data);
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} // check column is in lower triangular matrix
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if (j < rows) {
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// loop rows (lower triangular matrix)
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for (i = j + 1; i < rows; i++) {
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// value @ i, j
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var vij = data[i][j];
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if (!equalScalar(vij, 0)) {
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// update data
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data[i][j] = divideScalar(data[i][j], vjj);
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}
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}
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}
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} // loop columns
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for (j = 0; j < columns; j++) {
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// loop rows
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for (i = 0; i < rows; i++) {
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// initialize row in arrays
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if (j === 0) {
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// check row exists in upper triangular matrix
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if (i < columns) {
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// U
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udata[i] = [];
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} // L
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ldata[i] = [];
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} // check we are in the upper triangular matrix
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if (i < j) {
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// check row exists in upper triangular matrix
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if (i < columns) {
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// U
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udata[i][j] = data[i][j];
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} // check column exists in lower triangular matrix
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if (j < rows) {
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// L
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ldata[i][j] = 0;
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}
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continue;
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} // diagonal value
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if (i === j) {
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// check row exists in upper triangular matrix
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if (i < columns) {
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// U
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udata[i][j] = data[i][j];
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} // check column exists in lower triangular matrix
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if (j < rows) {
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// L
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ldata[i][j] = 1;
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}
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continue;
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} // check row exists in upper triangular matrix
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if (i < columns) {
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// U
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udata[i][j] = 0;
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} // check column exists in lower triangular matrix
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if (j < rows) {
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// L
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ldata[i][j] = data[i][j];
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}
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}
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} // l matrix
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var l = new DenseMatrix({
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data: ldata,
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size: lsize
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}); // u matrix
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var u = new DenseMatrix({
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data: udata,
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size: usize
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}); // p vector
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var pv = [];
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for (i = 0, n = p.length; i < n; i++) {
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pv[p[i]] = i;
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} // return matrices
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return {
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L: l,
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U: u,
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p: pv,
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toString: function toString() {
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return 'L: ' + this.L.toString() + '\nU: ' + this.U.toString() + '\nP: ' + this.p;
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}
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};
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}
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function _sparseLUP(m) {
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// rows & columns
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var rows = m._size[0];
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var columns = m._size[1]; // minimum rows and columns
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var n = Math.min(rows, columns); // matrix arrays (will not be modified, thanks to permutation vector)
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var values = m._values;
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var index = m._index;
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var ptr = m._ptr; // l matrix arrays
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var lvalues = [];
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var lindex = [];
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var lptr = [];
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var lsize = [rows, n]; // u matrix arrays
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var uvalues = [];
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var uindex = [];
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var uptr = [];
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var usize = [n, columns]; // vars
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var i, j, k; // permutation vectors, (current index -> original index) and (original index -> current index)
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var pvCo = [];
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var pvOc = [];
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for (i = 0; i < rows; i++) {
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pvCo[i] = i;
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pvOc[i] = i;
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} // swap indices in permutation vectors (condition x < y)!
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var swapIndeces = function swapIndeces(x, y) {
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// find pv indeces getting data from x and y
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var kx = pvOc[x];
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var ky = pvOc[y]; // update permutation vector current -> original
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pvCo[kx] = y;
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pvCo[ky] = x; // update permutation vector original -> current
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pvOc[x] = ky;
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pvOc[y] = kx;
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}; // loop columns
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var _loop = function _loop() {
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// sparse accumulator
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var spa = new Spa(); // check lower triangular matrix has a value @ column j
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if (j < rows) {
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// update ptr
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lptr.push(lvalues.length); // first value in j column for lower triangular matrix
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lvalues.push(1);
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lindex.push(j);
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} // update ptr
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uptr.push(uvalues.length); // k0 <= k < k1 where k0 = _ptr[j] && k1 = _ptr[j+1]
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var k0 = ptr[j];
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var k1 = ptr[j + 1]; // copy column j into sparse accumulator
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for (k = k0; k < k1; k++) {
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// row
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i = index[k]; // copy column values into sparse accumulator (use permutation vector)
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spa.set(pvCo[i], values[k]);
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} // skip first column in upper triangular matrix
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if (j > 0) {
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// loop rows in column j (above diagonal)
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spa.forEach(0, j - 1, function (k, vkj) {
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// loop rows in column k (L)
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SparseMatrix._forEachRow(k, lvalues, lindex, lptr, function (i, vik) {
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// check row is below k
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if (i > k) {
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// update spa value
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spa.accumulate(i, unaryMinus(multiplyScalar(vik, vkj)));
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}
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});
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});
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} // row with larger value in spa, row >= j
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var pi = j;
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var vjj = spa.get(j);
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var pabsv = abs(vjj); // loop values in spa (order by row, below diagonal)
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spa.forEach(j + 1, rows - 1, function (x, v) {
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// absolute value
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var absv = abs(v); // value is greater than pivote value
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if (larger(absv, pabsv)) {
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// store row
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pi = x; // update max value
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pabsv = absv; // value @ [j, j]
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vjj = v;
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}
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}); // swap rows (j <-> pi)
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if (j !== pi) {
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// swap values j <-> pi in L
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SparseMatrix._swapRows(j, pi, lsize[1], lvalues, lindex, lptr); // swap values j <-> pi in U
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SparseMatrix._swapRows(j, pi, usize[1], uvalues, uindex, uptr); // swap values in spa
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spa.swap(j, pi); // update permutation vector (swap values @ j, pi)
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swapIndeces(j, pi);
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} // loop values in spa (order by row)
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spa.forEach(0, rows - 1, function (x, v) {
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// check we are above diagonal
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if (x <= j) {
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// update upper triangular matrix
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uvalues.push(v);
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uindex.push(x);
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} else {
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// update value
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v = divideScalar(v, vjj); // check value is non zero
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if (!equalScalar(v, 0)) {
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// update lower triangular matrix
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lvalues.push(v);
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lindex.push(x);
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}
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}
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});
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};
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for (j = 0; j < columns; j++) {
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_loop();
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} // update ptrs
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uptr.push(uvalues.length);
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lptr.push(lvalues.length); // return matrices
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return {
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L: new SparseMatrix({
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values: lvalues,
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index: lindex,
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ptr: lptr,
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size: lsize
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}),
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U: new SparseMatrix({
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values: uvalues,
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index: uindex,
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ptr: uptr,
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size: usize
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}),
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p: pvCo,
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toString: function toString() {
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return 'L: ' + this.L.toString() + '\nU: ' + this.U.toString() + '\nP: ' + this.p;
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}
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};
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}
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}); |