/**
   * @throws IllegalArgumentException if {@link DataModel} does not have preference values
   */
  public PearsonCorrelationSimilarity(DataModel dataModel, Weighting weighting) throws TasteException {
    //这里CenterData传的时true
    /* pearson其实做的事情就是先把两个向量都减去他们的平均值，然后再计算cosine值。
     * 在 AbstractSimilarity里的实现代码如下：
     *  double result;
        if (centerData) {
          double meanX = sumX / count;
          double meanY = sumY / count;
          // double centeredSumXY = sumXY - meanY * sumX - meanX * sumY + n * meanX * meanY;
          double centeredSumXY = sumXY - meanY * sumX;
          // double centeredSumX2 = sumX2 - 2.0 * meanX * sumX + n * meanX * meanX;
          double centeredSumX2 = sumX2 - meanX * sumX;
          // double centeredSumY2 = sumY2 - 2.0 * meanY * sumY + n * meanY * meanY;
          double centeredSumY2 = sumY2 - meanY * sumY;
          result = computeResult(count, centeredSumXY, centeredSumX2, centeredSumY2, sumXYdiff2);
        } else {
          result = computeResult(count, sumXY, sumX2, sumY2, sumXYdiff2);
        }
     */
    super(dataModel, weighting, true);
    Preconditions.checkArgument(dataModel.hasPreferenceValues(), "DataModel doesn't have preference values");
  }
  
  @Override
  double computeResult(int n, double sumXY, double sumX2, double sumY2, double sumXYdiff2) {
    if (n == 0) {
      return Double.NaN;
    }
    // Note that sum of X and sum of Y don't appear here since they are assumed to be 0;
    // the data is assumed to be centered.
    double denominator = Math.sqrt(sumX2) * Math.sqrt(sumY2);
    if (denominator == 0.0) {
      // One or both parties has -all- the same ratings;
      // can't really say much similarity under this measure
      return Double.NaN;
    }
    return sumXY / denominator;
  }

@Override
  public double userSimilarity(long userID1, long userID2) throws TasteException {
    DataModel dataModel = getDataModel();
　　//获取用户偏好
    PreferenceArray xPrefs = dataModel.getPreferencesFromUser(userID1);
    PreferenceArray yPrefs = dataModel.getPreferencesFromUser(userID2);
    int xLength = xPrefs.length();
    int yLength = yPrefs.length();
    
    if (xLength == 0 || yLength == 0) {
      return Double.NaN;
    }
    
    long xIndex = xPrefs.getItemID(0);
    long yIndex = yPrefs.getItemID(0);
    int xPrefIndex = 0;
    int yPrefIndex = 0;
    
    double sumX = 0.0;
    double sumX2 = 0.0;
    double sumY = 0.0;
    double sumY2 = 0.0;
    double sumXY = 0.0;
    double sumXYdiff2 = 0.0;
    int count = 0;
    
    boolean hasInferrer = inferrer != null;
    
    while (true) {
      int compare = xIndex < yIndex ? -1 : xIndex > yIndex ? 1 : 0;
      if (hasInferrer || compare == 0) {
        double x;
        double y;
        if (xIndex == yIndex) {
          // Both users expressed a preference for the item
          x = xPrefs.getValue(xPrefIndex);
          y = yPrefs.getValue(yPrefIndex);
        } else {
            //如果不存在对应的分数,则进行推断...
          // Only one user expressed a preference, but infer the other one's preference and tally
          // as if the other user expressed that preference
          if (compare < 0) {
            // X has a value; infer Y's
            x = xPrefs.getValue(xPrefIndex);
            y = inferrer.inferPreference(userID2, xIndex);
          } else {
            // compare > 0
            // Y has a value; infer X's
            x = inferrer.inferPreference(userID1, yIndex);
            y = yPrefs.getValue(yPrefIndex);
          }
        }
        sumXY += x * y;
        sumX += x;
        sumX2 += x * x;
        sumY += y;
        sumY2 += y * y;
        double diff = x - y;
        sumXYdiff2 += diff * diff;
        count++;
      }
      if (compare <= 0) {
        if (++xPrefIndex >= xLength) {
          if (hasInferrer) {
            // Must count other Ys; pretend next X is far away
            if (yIndex == Long.MAX_VALUE) {
              // ... but stop if both are done!
              break;
            }
            xIndex = Long.MAX_VALUE;
          } else {
            break;
          }
        } else {
          xIndex = xPrefs.getItemID(xPrefIndex);
        }
      }
      if (compare >= 0) {
        if (++yPrefIndex >= yLength) {
          if (hasInferrer) {
            // Must count other Xs; pretend next Y is far away
            if (xIndex == Long.MAX_VALUE) {
              // ... but stop if both are done!
              break;
            }
            yIndex = Long.MAX_VALUE;
          } else {
            break;
          }
        } else {
          yIndex = yPrefs.getItemID(yPrefIndex);
        }
      }
    }
    
    // "Center" the data. If my math is correct, this'll do it.
    double result;
    if (centerData) {
      double meanX = sumX / count;
      double meanY = sumY / count;
      // double centeredSumXY = sumXY - meanY * sumX - meanX * sumY + n * meanX * meanY;
      double centeredSumXY = sumXY - meanY * sumX;
      // double centeredSumX2 = sumX2 - 2.0 * meanX * sumX + n * meanX * meanX;
      double centeredSumX2 = sumX2 - meanX * sumX;
      // double centeredSumY2 = sumY2 - 2.0 * meanY * sumY + n * meanY * meanY;
      double centeredSumY2 = sumY2 - meanY * sumY;
      result = computeResult(count, centeredSumXY, centeredSumX2, centeredSumY2, sumXYdiff2);
    } else {
      result = computeResult(count, sumXY, sumX2, sumY2, sumXYdiff2);
    }
    
    if (!Double.isNaN(result)) {
      result = normalizeWeightResult(result, count, cachedNumItems);
    }
    return result;
  }