/**

   * @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;

  }