csCounts = function csCounts(a, parent, post, ata) {
    // check inputs
    if (!a || !parent || !post) {
      return null;
    } // a matrix arrays


    var asize = a._size; // rows and columns

    var m = asize[0];
    var n = asize[1]; // variables

    var i, j, k, J, p, p0, p1; // workspace size

    var s = 4 * n + (ata ? n + m + 1 : 0); // allocate workspace

    var w = []; // (s)

    var ancestor = 0; // first n entries

    var maxfirst = n; // next n entries

    var prevleaf = 2 * n; // next n entries

    var first = 3 * n; // next n entries

    var head = 4 * n; // next n + 1 entries (used when ata is true)

    var next = 5 * n + 1; // last entries in workspace
    // clear workspace w[0..s-1]

    for (k = 0; k < s; k++) {
      w[k] = -1;
    } // allocate result


    var colcount = []; // (n)
    // AT = A'

    var at = transpose(a); // at arrays

    var tindex = at._index;
    var tptr = at._ptr; // find w[first + j]

    for (k = 0; k < n; k++) {
      j = post[k]; // colcount[j]=1 if j is a leaf

      colcount[j] = w[first + j] === -1 ? 1 : 0;

      for (; j !== -1 && w[first + j] === -1; j = parent[j]) {
        w[first + j] = k;
      }
    } // initialize ata if needed


    if (ata) {
      // invert post
      for (k = 0; k < n; k++) {
        w[post[k]] = k;
      } // loop rows (columns in AT)


      for (i = 0; i < m; i++) {
        // values in column i of AT
        for (k = n, p0 = tptr[i], p1 = tptr[i + 1], p = p0; p < p1; p++) {
          k = Math.min(k, w[tindex[p]]);
        } // place row i in linked list k


        w[next + i] = w[head + k];
        w[head + k] = i;
      }
    } // each node in its own set


    for (i = 0; i < n; i++) {
      w[ancestor + i] = i;
    }

    for (k = 0; k < n; k++) {
      // j is the kth node in postordered etree
      j = post[k]; // check j is not a root

      if (parent[j] !== -1) {
        colcount[parent[j]]--;
      } // J=j for LL'=A case


      for (J = ata ? w[head + k] : j; J !== -1; J = ata ? w[next + J] : -1) {
        for (p = tptr[J]; p < tptr[J + 1]; p++) {
          i = tindex[p];
          var r = csLeaf(i, j, w, first, maxfirst, prevleaf, ancestor); // check A(i,j) is in skeleton

          if (r.jleaf >= 1) {
            colcount[j]++;
          } // check account for overlap in q


          if (r.jleaf === 2) {
            colcount[r.q]--;
          }
        }
      }

      if (parent[j] !== -1) {
        w[ancestor + j] = parent[j];
      }
    } // sum up colcount's of each child


    for (j = 0; j < n; j++) {
      if (parent[j] !== -1) {
        colcount[parent[j]] += colcount[j];
      }
    }

    return colcount;
  }
Computes the column counts using the upper triangular part of A.
It transposes A internally, none of the input parameters are modified.

@param {Matrix} a           The sparse matrix A

@param {Matrix} ata         Count the columns of A'A instead

@return                     An array of size n of the column counts or null on error

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