/** Computes the next step of the Power Method. */
  public void step() throws IOException {
    double[] oldRank = rank, newRank = previousRank;
    DoubleArrays.fill(newRank, 0.0);

    // for each node, calculate its outdegree and redistribute its rank among pointed nodes
    double accum = 0.0;

    progressLogger.expectedUpdates = numNodes;
    progressLogger.start("Iteration " + (++iterationNumber) + "...");

    final ArcLabelledNodeIterator nodeIterator = g.nodeIterator();
    int i, outdegree, j, n = numNodes;
    int[] succ;
    Label[] lab;

    while (n-- != 0) {
      i = nodeIterator.nextInt();
      outdegree = nodeIterator.outdegree();

      if (outdegree == 0 || buckets != null && buckets.get(i)) accum += oldRank[i];
      else {
        j = outdegree;
        succ = nodeIterator.successorArray();
        lab = nodeIterator.labelArray();
        while (j-- != 0) {
          newRank[succ[j]] += (oldRank[i] * lab[j].getFloat()) / sumoutweight[i];
        }
      }
      progressLogger.update();
    }
    progressLogger.done();

    final double accumOverNumNodes = accum / numNodes;

    final double oneOverNumNodes = 1.0 / numNodes;
    if (preference != null)
      if (preferentialAdjustment == null)
        for (i = numNodes; i-- != 0; )
          newRank[i] =
              alpha * newRank[i]
                  + (1 - alpha) * preference.getDouble(i)
                  + alpha * accumOverNumNodes;
      else
        for (i = numNodes; i-- != 0; )
          newRank[i] =
              alpha * newRank[i]
                  + (1 - alpha) * preference.getDouble(i)
                  + alpha * accum * preferentialAdjustment.getDouble(i);
    else if (preferentialAdjustment == null)
      for (i = numNodes; i-- != 0; )
        newRank[i] = alpha * newRank[i] + (1 - alpha) * oneOverNumNodes + alpha * accumOverNumNodes;
    else
      for (i = numNodes; i-- != 0; )
        newRank[i] =
            alpha * newRank[i]
                + (1 - alpha) * oneOverNumNodes
                + alpha * accum * preferentialAdjustment.getDouble(i);

    // make the rank just computed the new rank
    rank = newRank;
    previousRank = oldRank;

    // Compute derivatives.
    n = iterationNumber;

    if (subset == null) {
      for (i = 0; i < order.length; i++) {
        final int k = order[i];
        final double alphak = Math.pow(alpha, k);
        final double nFallingK = Util.falling(n, k);
        for (j = 0; j < numNodes; j++)
          derivative[i][j] += nFallingK * (rank[j] - previousRank[j]) / alphak;
      }
    } else {
      for (i = 0; i < order.length; i++) {
        final int k = order[i];
        final double alphak = Math.pow(alpha, k);
        final double nFallingK = Util.falling(n, k);

        for (int t : subset) derivative[i][t] += nFallingK * (rank[t] - previousRank[t]) / alphak;
      }
    }

    // Compute coefficients, if required.

    if (coeffBasename != null) {
      final DataOutputStream coefficients =
          new DataOutputStream(
              new FastBufferedOutputStream(
                  new FileOutputStream(coeffBasename + "-" + (iterationNumber))));
      final double alphaN = Math.pow(alpha, n);
      for (i = 0; i < numNodes; i++) coefficients.writeDouble((rank[i] - previousRank[i]) / alphaN);
      coefficients.close();
    }
  }