mathjs/lib/function/algebra/sparse/csReach.js

Math.js is an extensive math library for JavaScript and Node.js. It features a flexible expression parser with support for symbolic computation, comes with a large set of built-in functions and constants, and offers an integrated solution to work with dif

'use strict';

function factory(type, config, load) {
  var csDfs = load(require('./csDfs'));
  var csMarked = load(require('./csMarked'));
  var csMark = load(require('./csMark'));
  /**
   * The csReach function computes X = Reach(B), where B is the nonzero pattern of the n-by-1
   * sparse column of vector b. The function returns the set of nodes reachable from any node in B. The
   * nonzero pattern xi of the solution x to the sparse linear system Lx=b is given by X=Reach(B).
   *
   * @param {Matrix}  g               The G matrix
   * @param {Matrix}  b               The B matrix
   * @param {Number}  k               The kth column in B
   * @param {Array}   xi              The nonzero pattern xi[top] .. xi[n - 1], an array of size = 2 * n
   *                                  The first n entries is the nonzero pattern, the last n entries is the stack
   * @param {Array}   pinv            The inverse row permutation vector
   *
   * @return {Number}                 The index for the nonzero pattern
   *
   * Reference: http://faculty.cse.tamu.edu/davis/publications.html
   */

  var csReach = function csReach(g, b, k, xi, pinv) {
    // g arrays
    var gptr = g._ptr;
    var gsize = g._size; // b arrays

    var bindex = b._index;
    var bptr = b._ptr; // columns

    var n = gsize[1]; // vars

    var p, p0, p1; // initialize top

    var top = n; // loop column indeces in B

    for (p0 = bptr[k], p1 = bptr[k + 1], p = p0; p < p1; p++) {
      // node i
      var i = bindex[p]; // check node i is marked

      if (!csMarked(gptr, i)) {
        // start a dfs at unmarked node i
        top = csDfs(i, g, top, xi, pinv);
      }
    } // loop columns from top -> n - 1


    for (p = top; p < n; p++) {
      // restore G
      csMark(gptr, xi[p]);
    }

    return top;
  };

  return csReach;
}

exports.name = 'csReach';
exports.path = 'algebra.sparse';
exports.factory = factory;