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

import { csMarked } from './csMarked'
import { csMark } from './csMark'
import { csDfs } from './csDfs'

/**
 * 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
 */
export function csReach (g, b, k, xi, pinv) {
  // g arrays
  const gptr = g._ptr
  const gsize = g._size
  // b arrays
  const bindex = b._index
  const bptr = b._ptr
  // columns
  const n = gsize[1]
  // vars
  let p, p0, p1
  // initialize top
  let top = n
  // loop column indeces in B
  for (p0 = bptr[k], p1 = bptr[k + 1], p = p0; p < p1; p++) {
    // node i
    const 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
}