removed QWQNG, added stdin
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249
RandTest/KolmogorovSmirnov.cpp
Executable file
249
RandTest/KolmogorovSmirnov.cpp
Executable file
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//#include "StdAfx.h"
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#include "KolmogorovSmirnov.h"
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#include "memory.h"
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#include "stdlib.h"
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#include "math.h"
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#include <float.h>
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CKolmogorovSmirnov::CKolmogorovSmirnov()
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{
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}
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///////////////////////////////////////////////////////////////////////////////
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// double CKolmogorovSmirnov::ZtoP
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//
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// Returns: cumulative normal distribution value based on input z-score
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// Accuracy better than 1% for zscore<=±7.5; better than 0.05% for zscore=±4
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double CKolmogorovSmirnov::ZtoP( double zscore )
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{
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double retval;
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// calculation variables
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double w;
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double y;
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double t;
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double num;
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double denom;
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// calculation constants
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double c[8];
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c[1] = 2.506628275; c[2] = 0.31938153; c[3] = -0.356563782; c[4] = 1.781477937;
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c[5] = -1.821255978; c[6] = 1.330274429; c[7] = 0.2316419;
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w = (zscore>=0)? 1 : -1;
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y = 1./( 1. + (c[7]*w*zscore) );
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t = 1. + (c[7]*w*zscore);
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num = w * ( 0.5 - c[2] + ((c[6] + (c[5]*t) + (c[4]*t*t) + (c[3]*t*t*t))/(t*t*t*t)) );
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denom = c[1] * pow( 10, pow(0.5*zscore, 2) );
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retval = 0.5 + (num/denom);
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return retval;
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}
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///////////////////////////////////////////////////////////////////////////////
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// double CKolmogorovSmirnov::PtoZ
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//
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// Returns: z-score based on input cumulative normal distribution value
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// Accuracy better than 0.1% for zscore<=±7.5; 6 digits for zscore=±6
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double CKolmogorovSmirnov::PtoZ( double p )
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{
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double retval = -8.2;
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if (p <= DBL_EPSILON)
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return retval;
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// calculation variables
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double pp;
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double y;
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double num;
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double denom;
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// calculation constants
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double P[5];
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P[0] = -0.322232431088; P[1] = -1.0; P[2] = -0.342242088547;
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P[3] = -0.0204231210245; P[4] = -0.453642210148e-4;
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double q[5];
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q[0] = 0.099348462606; q[1] = 0.588581570495; q[2] = 0.531103462366;
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q[3] = 0.10353775285; q[4] = 0.38560700634e-2;
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pp = (p<0.5)? p : (1.-p);
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y = sqrt( log(1./(pp*pp)) );
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num = y*(y*(y*(y*P[4]+P[3]) + P[2]) + P[1]) + P[0];
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denom = y*(y*(y*(y*q[4]+q[3]) + q[2]) + q[1]) + q[0];
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retval = y + (num/denom);
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retval = (p<0.5)? -retval : retval;
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return retval;
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}
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void CKolmogorovSmirnov::KSUP( double* pKn_pos, double* pKn_neg, double* U, unsigned long n )
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{
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unsigned long i; // universal index
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double val; // calc value
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double* Us = new double[n];
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double Kn_pos;
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double Kn_neg;
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double* cump1 = new double[n+2];
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double* cump2 = new double[n+2];
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double* kn = new double[n+2];
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double max;
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double min;
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memcpy( (void*)Us, (void*)U, n * sizeof(double) );
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qsort( Us, n, sizeof(double), KSUPcompare );
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cump1[1] = Us[0];
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cump2[1] = 0.;
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for ( i=1; i<=n; i++ )
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{
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cump1[i+1] = Us[i-1];
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val = (double)i/n;
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cump2[i+1] = val;
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}
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min = cump2[2] - cump1[2];
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max = min;
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for ( i=2; i<=(n+1); i++ )
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{
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kn[i-1] = cump2[i] - cump1[i];
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if ( kn[i-1] > max )
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{
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max = kn[i-1];
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}
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if ( kn[i-1] < min )
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{
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min = kn[i-1];
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}
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}
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Kn_pos = sqrt((double)n) * (double)max;
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Kn_neg = (-sqrt((double)n)) * ((double)min - (1/(double)n));
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*pKn_pos = KSProb( n, Kn_pos );
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*pKn_neg = KSProb( n, Kn_neg );
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if (Us!=NULL)
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{
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delete Us;
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Us = NULL;
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}
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if (kn!=NULL)
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{
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delete kn;
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kn = NULL;
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}
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if (cump1!=NULL)
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{
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delete cump1;
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cump1 = NULL;
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}
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if (cump2!=NULL)
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{
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delete cump2;
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cump2 = NULL;
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}
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}
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double CKolmogorovSmirnov::KSProb( unsigned long n, double Kn )
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{
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double retval;
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double e;
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double las;
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unsigned long j;
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double cof[7];
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cof[1] = 76.18009172947146; cof[2] = -86.50532032941677; cof[3] = 24.01409824083091;
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cof[4] = -1.231739572450155; cof[5] = 1.208650973866179e-3; cof[6] = -5.395239384953e-6;
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if ( Kn<=0 )
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{
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retval = 0;
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}
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else if ( Kn>=sqrt((double)n) )
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{
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retval = 1;
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}
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else
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{
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e = Kn / sqrt((double)n);
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las = floor( (double)n - ((double)n*e) );
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retval = 0;
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for ( j=0; j<=las; j++ )
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{
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double ee = exp(lnbin(n, j));
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double p1 = pow((e+(double)j/(double)n),((double)j-1.));
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double p2 = pow((1.0-e-(double)j/(double)n),(double)(n-j));
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retval += ee * p1 * p2;
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}
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retval = 1.-e*retval;
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}
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return retval;
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}
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double CKolmogorovSmirnov::lnbin( double n, double k )
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{
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double retval = 0;
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if (k==0)
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retval = 0;
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else
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{
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retval = lnf(n) - lnf(k) - lnf(n-k);
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}
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return retval;
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}
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double CKolmogorovSmirnov::lnf( double xx )
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{
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double retval = 0;
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double x1 = xx + 1.;
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double cof[7];
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cof[1] = 76.18009172947146; cof[2] = -86.50532032941677; cof[3] = 24.01409824083091;
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cof[4] = -1.231739572450155; cof[5] = 1.208650973866179e-3; cof[6] = -5.395239384953e-6;
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if (x1<=1.)
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retval = 0;
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else
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{
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double x = x1;
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double y = x1;
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double tmp = x + 5.5 - (x+.5)*log(x+5.5);
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double ser = 1.000000000190015;
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for (int j=0; j<=5; j++)
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{
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y = y+1.;
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ser += cof[j+1]/y;
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}
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retval = log(2.506628274631 * ser/x) - tmp;
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}
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return retval;
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}
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int CKolmogorovSmirnov::KSUPcompare( const void* elem1, const void* elem2 )
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{
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if ((*(double*)elem1)==(*(double*)elem2))
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return 0;
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if ((*(double*)elem1)>(*(double*)elem2))
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return 1;
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else
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return -1;
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}
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