'use strict';

function factory (type, config, load) {

  var divideScalar = load(require('../../arithmetic/divideScalar'));
  var multiply = load(require('../../arithmetic/multiply'));
  var subtract = load(require('../../arithmetic/subtract'));

  var cs_reach = load(require('./cs_reach'));

  /**
   * The function cs_spsolve() computes the solution to G * x = bk, where bk is the
   * kth column of B. When lo is true, the function assumes G = L is lower triangular with the
   * diagonal entry as the first entry in each column. When lo is true, the function assumes G = U 
   * is upper triangular with the diagonal entry as the last entry in each column.
   *
   * @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}   x               The soluton to the linear system G * x = b
   * @param {Array}   pinv            The inverse row permutation vector, must be null for L * x = b
   * @param {boolean} lo              The lower (true) upper triangular (false) flag
   *
   * @return {Number}                 The index for the nonzero pattern
   *
   * Reference: http://faculty.cse.tamu.edu/davis/publications.html
   */
  var cs_spsolve = function (g, b, k, xi, x, pinv, lo) {
    // g arrays
    var gvalues = g._values;
    var gindex = g._index;
    var gptr = g._ptr;
    var gsize = g._size;
    // columns
    var n = gsize[1];
    // b arrays
    var bvalues = b._values;
    var bindex = b._index;
    var bptr = b._ptr;
    // vars
    var p, p0, p1, q;
    // xi[top..n-1] = cs_reach(B(:,k))
    var top = cs_reach(g, b, k, xi, pinv);
    // clear x
    for (p = top; p < n; p++) 
      x[xi[p]] = 0;
    // scatter b
    for (p0 = bptr[k], p1 = bptr[k + 1], p = p0; p < p1; p++) 
      x[bindex[p]] = bvalues[p];
    // loop columns
    for (var px = top; px < n; px++) {
      // x array index for px
      var j = xi[px];
      // apply permutation vector (U x = b), j maps to column J of G
      var J = pinv ? pinv[j] : j;
      // check column J is empty
      if (J < 0)
        continue;
      // column value indeces in G, p0 <= p < p1
      p0 = gptr[J];
      p1 = gptr[J + 1];
      // x(j) /= G(j,j)
      x[j] = divideScalar(x[j], gvalues[lo ? p0 : (p1 - 1)]);
      // first entry L(j,j)
      p = lo ? (p0 + 1) : p0;
      q = lo ? (p1) : (p1 - 1);
      // loop
      for ( ; p < q ; p++) {
        // row
        var i = gindex[p];
        // x(i) -= G(i,j) * x(j)
        x[i] = subtract(x[i], multiply(gvalues[p], x[j]));
      }
    }
    // return top of stack
    return top;
  };
  
  return cs_spsolve;
}

exports.name = 'cs_spsolve';
exports.path = 'sparse';
exports.factory = factory;