simple-squiggle/node_modules/mathjs/lib/cjs/function/algebra/sparse/csChol.js

"use strict";

Object.defineProperty(exports, "__esModule", {
  value: true
});
exports.createCsChol = void 0;

var _factory = require("../../../utils/factory.js");

var _csEreach = require("./csEreach.js");

var _csSymperm = require("./csSymperm.js");

var name = 'csChol';
var dependencies = ['divideScalar', 'sqrt', 'subtract', 'multiply', 'im', 're', 'conj', 'equal', 'smallerEq', 'SparseMatrix'];
var createCsChol = /* #__PURE__ */(0, _factory.factory)(name, dependencies, function (_ref) {
  var divideScalar = _ref.divideScalar,
      sqrt = _ref.sqrt,
      subtract = _ref.subtract,
      multiply = _ref.multiply,
      im = _ref.im,
      re = _ref.re,
      conj = _ref.conj,
      equal = _ref.equal,
      smallerEq = _ref.smallerEq,
      SparseMatrix = _ref.SparseMatrix;
  var csSymperm = (0, _csSymperm.createCsSymperm)({
    conj: conj,
    SparseMatrix: 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 = (0, _csEreach.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
    };
  };
});
exports.createCsChol = createCsChol;