simple-squiggle/node_modules/mathjs/lib/esm/function/algebra/sparse/csSqr.js

import { csPermute } from './csPermute.js';
import { csPost } from './csPost.js';
import { csEtree } from './csEtree.js';
import { createCsAmd } from './csAmd.js';
import { createCsCounts } from './csCounts.js';
import { factory } from '../../../utils/factory.js';
var name = 'csSqr';
var dependencies = ['add', 'multiply', 'transpose'];
export var createCsSqr = /* #__PURE__ */factory(name, dependencies, _ref => {
  var {
    add,
    multiply,
    transpose
  } = _ref;
  var csAmd = createCsAmd({
    add,
    multiply,
    transpose
  });
  var csCounts = createCsCounts({
    transpose
  });
  /**
   * Symbolic ordering and analysis for QR and LU decompositions.
   *
   * @param {Number}  order           The ordering strategy (see csAmd for more details)
   * @param {Matrix}  a               The A matrix
   * @param {boolean} qr              Symbolic ordering and analysis for QR decomposition (true) or
   *                                  symbolic ordering and analysis for LU decomposition (false)
   *
   * @return {Object}                 The Symbolic ordering and analysis for matrix A
   *
   * Reference: http://faculty.cse.tamu.edu/davis/publications.html
   */

  return function csSqr(order, a, qr) {
    // a arrays
    var aptr = a._ptr;
    var asize = a._size; // columns

    var n = asize[1]; // vars

    var k; // symbolic analysis result

    var s = {}; // fill-reducing ordering

    s.q = csAmd(order, a); // validate results

    if (order && !s.q) {
      return null;
    } // QR symbolic analysis


    if (qr) {
      // apply permutations if needed
      var c = order ? csPermute(a, null, s.q, 0) : a; // etree of C'*C, where C=A(:,q)

      s.parent = csEtree(c, 1); // post order elimination tree

      var post = csPost(s.parent, n); // col counts chol(C'*C)

      s.cp = csCounts(c, s.parent, post, 1); // check we have everything needed to calculate number of nonzero elements

      if (c && s.parent && s.cp && _vcount(c, s)) {
        // calculate number of nonzero elements
        for (s.unz = 0, k = 0; k < n; k++) {
          s.unz += s.cp[k];
        }
      }
    } else {
      // for LU factorization only, guess nnz(L) and nnz(U)
      s.unz = 4 * aptr[n] + n;
      s.lnz = s.unz;
    } // return result S


    return s;
  };
  /**
   * Compute nnz(V) = s.lnz, s.pinv, s.leftmost, s.m2 from A and s.parent
   */

  function _vcount(a, s) {
    // a arrays
    var aptr = a._ptr;
    var aindex = a._index;
    var asize = a._size; // rows & columns

    var m = asize[0];
    var n = asize[1]; // initialize s arrays

    s.pinv = []; // (m + n)

    s.leftmost = []; // (m)
    // vars

    var parent = s.parent;
    var pinv = s.pinv;
    var leftmost = s.leftmost; // workspace, next: first m entries, head: next n entries, tail: next n entries, nque: next n entries

    var w = []; // (m + 3 * n)

    var next = 0;
    var head = m;
    var tail = m + n;
    var nque = m + 2 * n; // vars

    var i, k, p, p0, p1; // initialize w

    for (k = 0; k < n; k++) {
      // queue k is empty
      w[head + k] = -1;
      w[tail + k] = -1;
      w[nque + k] = 0;
    } // initialize row arrays


    for (i = 0; i < m; i++) {
      leftmost[i] = -1;
    } // loop columns backwards


    for (k = n - 1; k >= 0; k--) {
      // values & index for column k
      for (p0 = aptr[k], p1 = aptr[k + 1], p = p0; p < p1; p++) {
        // leftmost[i] = min(find(A(i,:)))
        leftmost[aindex[p]] = k;
      }
    } // scan rows in reverse order


    for (i = m - 1; i >= 0; i--) {
      // row i is not yet ordered
      pinv[i] = -1;
      k = leftmost[i]; // check row i is empty

      if (k === -1) {
        continue;
      } // first row in queue k


      if (w[nque + k]++ === 0) {
        w[tail + k] = i;
      } // put i at head of queue k


      w[next + i] = w[head + k];
      w[head + k] = i;
    }

    s.lnz = 0;
    s.m2 = m; // find row permutation and nnz(V)

    for (k = 0; k < n; k++) {
      // remove row i from queue k
      i = w[head + k]; // count V(k,k) as nonzero

      s.lnz++; // add a fictitious row

      if (i < 0) {
        i = s.m2++;
      } // associate row i with V(:,k)


      pinv[i] = k; // skip if V(k+1:m,k) is empty

      if (--nque[k] <= 0) {
        continue;
      } // nque[k] is nnz (V(k+1:m,k))


      s.lnz += w[nque + k]; // move all rows to parent of k

      var pa = parent[k];

      if (pa !== -1) {
        if (w[nque + pa] === 0) {
          w[tail + pa] = w[tail + k];
        }

        w[next + w[tail + k]] = w[head + pa];
        w[head + pa] = w[next + i];
        w[nque + pa] += w[nque + k];
      }
    }

    for (i = 0; i < m; i++) {
      if (pinv[i] < 0) {
        pinv[i] = k++;
      }
    }

    return true;
  }
});