/*
 * Copyright 2004 The Apache Software Foundation.
 * 
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 * 
 *      http://www.apache.org/licenses/LICENSE-2.0
 * 
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

package org.apache.commons.math.stat.mining;

import java.util.Arrays;
import org.apache.commons.math.linear.InvalidMatrixException;
import org.apache.commons.math.linear.RealMatrix;
import org.apache.commons.math.linear.RealMatrixImpl;

public class SpearmanRankCrossCorrelation {
    
    /*
     * http://en.wikipedia.org/wiki/Spearman%27s_rank_correlation_coefficient
     * and
     * http://mathworld.wolfram.com/SpearmanRankCorrelationCoefficient.html
     */
    
    /**
     * Local instance of the raw data
     */
    private RealMatrixImpl dataMatrix = null;
    
    /**
     * Constructor
     * 
     * @param dataMatrix Raw Data Matrix
     */    
    public SpearmanRankCrossCorrelation(final RealMatrixImpl dataMatrix) {
        this.dataMatrix = dataMatrix;
    }
    
    /**
     * Calculates the Spearman Rank Correlation Matrix 
     * 
     * @return Spearman Rank Correlation Matrix
     */
    public RealMatrix getCorrelationMatrix() {
        RealMatrixImpl correlationMatrix = new RealMatrixImpl(dataMatrix.getColumnDimension(), dataMatrix.getColumnDimension());
        for(int i=0; i<dataMatrix.getColumnDimension(); i++) {            
            double [] column1 = dataMatrix.getColumn(i);
            double [][] submatrix = new double[1][1];
            submatrix[0][0] = 1.0;
            correlationMatrix.setSubMatrix(submatrix, i, i);
            
            for(int j=i+1; j<dataMatrix.getColumnDimension(); j++) {
                double [] column2 = dataMatrix.getColumn(j);
                submatrix[0][0] = this.calculateRankCorrelation(column1, column2);
                correlationMatrix.setSubMatrix(submatrix, i, j);
                correlationMatrix.setSubMatrix(submatrix, j, i);
            }
        }
        return correlationMatrix;
    }
    
    /**
     * Calculates the Spearman Correlation Coefficient for the column vectors
     * 
     * @param columnVector1
     * @param columnVector2
     * @return Spearman Rank Correlation Coefficient for the column vectors
     */
    private double calculateRankCorrelation(final double [] columnVector1, final double [] columnVector2) throws InvalidMatrixException{
        if(columnVector1.length == columnVector2.length) {
            double [] sortedValues1 = new double[columnVector1.length];
            double [] sortedValues2 = new double[columnVector2.length];
            for(int i=0; i<columnVector1.length; i++) {
                sortedValues1[i] = columnVector1[i];
                sortedValues2[i] = columnVector2[i];
            }
            double rank1 = 0.0;
            double rank2 = 0.0;
            double rankDifference = 0.0;
            Arrays.sort(sortedValues1);
            Arrays.sort(sortedValues2);
            for(int i=0; i<sortedValues1.length; i++) {
                rank1 = Arrays.binarySearch(sortedValues1, columnVector1[i]);
                rank2 = Arrays.binarySearch(sortedValues2, columnVector2[i]);
                rankDifference += Math.pow(rank1 - rank2, 2.0);
            }
            return 1 - ((6 * rankDifference) / (Math.pow(sortedValues1.length,3) - sortedValues1.length)); 
        }
        else {
            throw new InvalidMatrixException("Column vectors need to be the same length.");
        }
    }
}