csLu = function csLu(m, s, tol) {
    // validate input
    if (!m) {
      return null;
    } // m arrays


    var size = m._size; // columns

    var n = size[1]; // symbolic analysis result

    var q;
    var lnz = 100;
    var unz = 100; // update symbolic analysis parameters

    if (s) {
      q = s.q;
      lnz = s.lnz || lnz;
      unz = s.unz || unz;
    } // L arrays


    var lvalues = []; // (lnz)

    var lindex = []; // (lnz)

    var lptr = []; // (n + 1)
    // L

    var L = new SparseMatrix({
      values: lvalues,
      index: lindex,
      ptr: lptr,
      size: [n, n]
    }); // U arrays

    var uvalues = []; // (unz)

    var uindex = []; // (unz)

    var uptr = []; // (n + 1)
    // U

    var U = new SparseMatrix({
      values: uvalues,
      index: uindex,
      ptr: uptr,
      size: [n, n]
    }); // inverse of permutation vector

    var pinv = []; // (n)
    // vars

    var i, p; // allocate arrays

    var x = []; // (n)

    var xi = []; // (2 * n)
    // initialize variables

    for (i = 0; i < n; i++) {
      // clear workspace
      x[i] = 0; // no rows pivotal yet

      pinv[i] = -1; // no cols of L yet

      lptr[i + 1] = 0;
    } // reset number of nonzero elements in L and U


    lnz = 0;
    unz = 0; // compute L(:,k) and U(:,k)

    for (var k = 0; k < n; k++) {
      // update ptr
      lptr[k] = lnz;
      uptr[k] = unz; // apply column permutations if needed

      var col = q ? q[k] : k; // solve triangular system, x = L\A(:,col)

      var top = csSpsolve(L, m, col, xi, x, pinv, 1); // find pivot

      var ipiv = -1;
      var a = -1; // loop xi[] from top -> n

      for (p = top; p < n; p++) {
        // x[i] is nonzero
        i = xi[p]; // check row i is not yet pivotal

        if (pinv[i] < 0) {
          // absolute value of x[i]
          var xabs = abs(x[i]); // check absoulte value is greater than pivot value

          if (larger(xabs, a)) {
            // largest pivot candidate so far
            a = xabs;
            ipiv = i;
          }
        } else {
          // x(i) is the entry U(pinv[i],k)
          uindex[unz] = pinv[i];
          uvalues[unz++] = x[i];
        }
      } // validate we found a valid pivot


      if (ipiv === -1 || a <= 0) {
        return null;
      } // update actual pivot column, give preference to diagonal value


      if (pinv[col] < 0 && largerEq(abs(x[col]), multiply(a, tol))) {
        ipiv = col;
      } // the chosen pivot


      var pivot = x[ipiv]; // last entry in U(:,k) is U(k,k)

      uindex[unz] = k;
      uvalues[unz++] = pivot; // ipiv is the kth pivot row

      pinv[ipiv] = k; // first entry in L(:,k) is L(k,k) = 1

      lindex[lnz] = ipiv;
      lvalues[lnz++] = 1; // L(k+1:n,k) = x / pivot

      for (p = top; p < n; p++) {
        // row
        i = xi[p]; // check x(i) is an entry in L(:,k)

        if (pinv[i] < 0) {
          // save unpermuted row in L
          lindex[lnz] = i; // scale pivot column

          lvalues[lnz++] = divideScalar(x[i], pivot);
        } // x[0..n-1] = 0 for next k


        x[i] = 0;
      }
    } // update ptr


    lptr[n] = lnz;
    uptr[n] = unz; // fix row indices of L for final pinv

    for (p = 0; p < lnz; p++) {
      lindex[p] = pinv[lindex[p]];
    } // trim arrays


    lvalues.splice(lnz, lvalues.length - lnz);
    lindex.splice(lnz, lindex.length - lnz);
    uvalues.splice(unz, uvalues.length - unz);
    uindex.splice(unz, uindex.length - unz); // return LU factor

    return {
      L: L,
      U: U,
      pinv: pinv
    };
  }
Computes the numeric LU factorization of the sparse matrix A. Implements a Left-looking LU factorization
algorithm that computes L and U one column at a tume. At the kth step, it access columns 1 to k-1 of L
and column k of A. Given the fill-reducing column ordering q (see parameter s) computes L, U and pinv so
L * U = A(p, q), where p is the inverse of pinv.

@param {Matrix}  m               The A Matrix to factorize
@param {Object}  s               The symbolic analysis from csSqr(). Provides the fill-reducing
                                 column ordering q
@param {Number}  tol             Partial pivoting threshold (1 for partial pivoting)

@return {Number}                 The numeric LU factorization of A or null

Reference: http://faculty.cse.tamu.edu/davis/publications.html