mathjs/src/function/algebra/sparse/csEtree.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 () {
  /**
   * Computes the elimination tree of Matrix A (using triu(A)) or the
   * elimination tree of A'A without forming A'A.
   *
   * @param {Matrix}  a               The A Matrix
   * @param {boolean} ata             A value of true the function computes the etree of A'A
   *
   * Reference: http://faculty.cse.tamu.edu/davis/publications.html
   */
  const csEtree = function (a, ata) {
    // check inputs
    if (!a) { return null }
    // a arrays
    const aindex = a._index
    const aptr = a._ptr
    const asize = a._size
    // rows & columns
    const m = asize[0]
    const n = asize[1]

    // allocate result
    const parent = [] // (n)

    // allocate workspace
    const w = [] // (n + (ata ? m : 0))
    const ancestor = 0 // first n entries in w
    const prev = n // last m entries (ata = true)

    let i, inext

    // check we are calculating A'A
    if (ata) {
      // initialize workspace
      for (i = 0; i < m; i++) { w[prev + i] = -1 }
    }
    // loop columns
    for (let k = 0; k < n; k++) {
      // node k has no parent yet
      parent[k] = -1
      // nor does k have an ancestor
      w[ancestor + k] = -1
      // values in column k
      for (let p0 = aptr[k], p1 = aptr[k + 1], p = p0; p < p1; p++) {
        // row
        const r = aindex[p]
        // node
        i = ata ? (w[prev + r]) : r
        // traverse from i to k
        for (; i !== -1 && i < k; i = inext) {
          // inext = ancestor of i
          inext = w[ancestor + i]
          // path compression
          w[ancestor + i] = k
          // check no anc., parent is k
          if (inext === -1) { parent[i] = k }
        }
        if (ata) { w[prev + r] = k }
      }
    }
    return parent
  }

  return csEtree
}

exports.name = 'csEtree'
exports.path = 'algebra.sparse'
exports.factory = factory