import { factory } from '../../../utils/factory.js'; import { csEreach } from './csEreach.js'; import { createCsSymperm } from './csSymperm.js'; var name = 'csChol'; var dependencies = ['divideScalar', 'sqrt', 'subtract', 'multiply', 'im', 're', 'conj', 'equal', 'smallerEq', 'SparseMatrix']; export var createCsChol = /* #__PURE__ */factory(name, dependencies, _ref => { var { divideScalar, sqrt, subtract, multiply, im, re, conj, equal, smallerEq, SparseMatrix } = _ref; var csSymperm = createCsSymperm({ conj, SparseMatrix }); /** * Computes the Cholesky factorization of matrix A. It computes L and P so * L * L' = P * A * P' * * @param {Matrix} m The A Matrix to factorize, only upper triangular part used * @param {Object} s The symbolic analysis from cs_schol() * * @return {Number} The numeric Cholesky factorization of A or null * * Reference: http://faculty.cse.tamu.edu/davis/publications.html */ return function csChol(m, s) { // validate input if (!m) { return null; } // m arrays var size = m._size; // columns var n = size[1]; // symbolic analysis result var parent = s.parent; var cp = s.cp; var pinv = s.pinv; // L arrays var lvalues = []; var lindex = []; var lptr = []; // L var L = new SparseMatrix({ values: lvalues, index: lindex, ptr: lptr, size: [n, n] }); // vars var c = []; // (2 * n) var x = []; // (n) // compute C = P * A * P' var cm = pinv ? csSymperm(m, pinv, 1) : m; // C matrix arrays var cvalues = cm._values; var cindex = cm._index; var cptr = cm._ptr; // vars var k, p; // initialize variables for (k = 0; k < n; k++) { lptr[k] = c[k] = cp[k]; } // compute L(k,:) for L*L' = C for (k = 0; k < n; k++) { // nonzero pattern of L(k,:) var top = csEreach(cm, k, parent, c); // x (0:k) is now zero x[k] = 0; // x = full(triu(C(:,k))) for (p = cptr[k]; p < cptr[k + 1]; p++) { if (cindex[p] <= k) { x[cindex[p]] = cvalues[p]; } } // d = C(k,k) var d = x[k]; // clear x for k+1st iteration x[k] = 0; // solve L(0:k-1,0:k-1) * x = C(:,k) for (; top < n; top++) { // s[top..n-1] is pattern of L(k,:) var i = s[top]; // L(k,i) = x (i) / L(i,i) var lki = divideScalar(x[i], lvalues[lptr[i]]); // clear x for k+1st iteration x[i] = 0; for (p = lptr[i] + 1; p < c[i]; p++) { // row var r = lindex[p]; // update x[r] x[r] = subtract(x[r], multiply(lvalues[p], lki)); } // d = d - L(k,i)*L(k,i) d = subtract(d, multiply(lki, conj(lki))); p = c[i]++; // store L(k,i) in column i lindex[p] = k; lvalues[p] = conj(lki); } // compute L(k,k) if (smallerEq(re(d), 0) || !equal(im(d), 0)) { // not pos def return null; } p = c[k]++; // store L(k,k) = sqrt(d) in column k lindex[p] = k; lvalues[p] = sqrt(d); } // finalize L lptr[n] = cp[n]; // P matrix var P; // check we need to calculate P if (pinv) { // P arrays var pvalues = []; var pindex = []; var pptr = []; // create P matrix for (p = 0; p < n; p++) { // initialize ptr (one value per column) pptr[p] = p; // index (apply permutation vector) pindex.push(pinv[p]); // value 1 pvalues.push(1); } // update ptr pptr[n] = n; // P P = new SparseMatrix({ values: pvalues, index: pindex, ptr: pptr, size: [n, n] }); } // return L & P return { L: L, P: P }; }; });