source: trunk/sources/ALGLIB/correlation.cs @ 2546

/*************************************************************************
Copyright (c) 2007, Sergey Bochkanov (ALGLIB project).

>>> SOURCE LICENSE >>>
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation (www.fsf.org); either version 2 of the 
License, or (at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

A copy of the GNU General Public License is available at
http://www.fsf.org/licensing/licenses

>>> END OF LICENSE >>>
*************************************************************************/

using System;

namespace alglib
{
    public class correlation
    {
        /*************************************************************************
        Pearson product-moment correlation coefficient

        Input parameters:
            X       -   sample 1 (array indexes: [0..N-1])
            Y       -   sample 2 (array indexes: [0..N-1])
            N       -   sample size.

        Result:
            Pearson product-moment correlation coefficient

          -- ALGLIB --
             Copyright 09.04.2007 by Bochkanov Sergey
        *************************************************************************/
        public static double pearsoncorrelation(ref double[] x,
            ref double[] y,
            int n)
        {
            double result = 0;
            int i = 0;
            double xmean = 0;
            double ymean = 0;
            double s = 0;
            double xv = 0;
            double yv = 0;
            double t1 = 0;
            double t2 = 0;

            xv = 0;
            yv = 0;
            if( n<=1 )
            {
                result = 0;
                return result;
            }
            
            //
            // Mean
            //
            xmean = 0;
            ymean = 0;
            for(i=0; i<=n-1; i++)
            {
                xmean = xmean+x[i];
                ymean = ymean+y[i];
            }
            xmean = xmean/n;
            ymean = ymean/n;
            
            //
            // numerator and denominator
            //
            s = 0;
            xv = 0;
            yv = 0;
            for(i=0; i<=n-1; i++)
            {
                t1 = x[i]-xmean;
                t2 = y[i]-ymean;
                xv = xv+AP.Math.Sqr(t1);
                yv = yv+AP.Math.Sqr(t2);
                s = s+t1*t2;
            }
            if( xv==0 | yv==0 )
            {
                result = 0;
            }
            else
            {
                result = s/(Math.Sqrt(xv)*Math.Sqrt(yv));
            }
            return result;
        }


        /*************************************************************************
        Spearman's rank correlation coefficient

        Input parameters:
            X       -   sample 1 (array indexes: [0..N-1])
            Y       -   sample 2 (array indexes: [0..N-1])
            N       -   sample size.

        Result:
            Spearman's rank correlation coefficient

          -- ALGLIB --
             Copyright 09.04.2007 by Bochkanov Sergey
        *************************************************************************/
        public static double spearmanrankcorrelation(double[] x,
            double[] y,
            int n)
        {
            double result = 0;

            x = (double[])x.Clone();
            y = (double[])y.Clone();

            rankx(ref x, n);
            rankx(ref y, n);
            result = pearsoncorrelation(ref x, ref y, n);
            return result;
        }


        /*************************************************************************
        Internal ranking subroutine
        *************************************************************************/
        private static void rankx(ref double[] x,
            int n)
        {
            int i = 0;
            int j = 0;
            int k = 0;
            int t = 0;
            double tmp = 0;
            int tmpi = 0;
            double[] r = new double[0];
            int[] c = new int[0];

            
            //
            // Prepare
            //
            if( n<=1 )
            {
                x[0] = 1;
                return;
            }
            r = new double[n-1+1];
            c = new int[n-1+1];
            for(i=0; i<=n-1; i++)
            {
                r[i] = x[i];
                c[i] = i;
            }
            
            //
            // sort {R, C}
            //
            if( n!=1 )
            {
                i = 2;
                do
                {
                    t = i;
                    while( t!=1 )
                    {
                        k = t/2;
                        if( r[k-1]>=r[t-1] )
                        {
                            t = 1;
                        }
                        else
                        {
                            tmp = r[k-1];
                            r[k-1] = r[t-1];
                            r[t-1] = tmp;
                            tmpi = c[k-1];
                            c[k-1] = c[t-1];
                            c[t-1] = tmpi;
                            t = k;
                        }
                    }
                    i = i+1;
                }
                while( i<=n );
                i = n-1;
                do
                {
                    tmp = r[i];
                    r[i] = r[0];
                    r[0] = tmp;
                    tmpi = c[i];
                    c[i] = c[0];
                    c[0] = tmpi;
                    t = 1;
                    while( t!=0 )
                    {
                        k = 2*t;
                        if( k>i )
                        {
                            t = 0;
                        }
                        else
                        {
                            if( k<i )
                            {
                                if( r[k]>r[k-1] )
                                {
                                    k = k+1;
                                }
                            }
                            if( r[t-1]>=r[k-1] )
                            {
                                t = 0;
                            }
                            else
                            {
                                tmp = r[k-1];
                                r[k-1] = r[t-1];
                                r[t-1] = tmp;
                                tmpi = c[k-1];
                                c[k-1] = c[t-1];
                                c[t-1] = tmpi;
                                t = k;
                            }
                        }
                    }
                    i = i-1;
                }
                while( i>=1 );
            }
            
            //
            // compute tied ranks
            //
            i = 0;
            while( i<=n-1 )
            {
                j = i+1;
                while( j<=n-1 )
                {
                    if( r[j]!=r[i] )
                    {
                        break;
                    }
                    j = j+1;
                }
                for(k=i; k<=j-1; k++)
                {
                    r[k] = 1+((double)(i+j-1))/(double)(2);
                }
                i = j;
            }
            
            //
            // back to x
            //
            for(i=0; i<=n-1; i++)
            {
                x[c[i]] = r[i];
            }
        }
    }
}