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/*
* DistLib : A C Library of Special Functions
* Copyright (C) 1998 R Core Team
*
* 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; 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.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
*
* data translated from C using perl script translate.pl
* script version 0.00
*/
package DistLib;
import org.apache.commons.logging.Log;
import org.apache.commons.logging.LogFactory;
/**
* Wrapper of functions for Wilcoxon distribution.
* <p>
* This actually the Mann-Whitney Ux statistic.
*/
public class wilcox {
private static Log log = LogFactory.getLog(wilcox.class);
public static final int WILCOX_MMAX = 50;
public static final int WILCOX_NMAX = 50;
/**
* check values for too large and log complaint
*/
private static boolean checkSizesLarge(final double m, final double n) {
if (m >= WILCOX_MMAX) {
log.info("m should be less than %d\n"+ WILCOX_MMAX);
return false;
}
if (n >= WILCOX_NMAX) {
log.info("n should be less than %d\n"+ WILCOX_NMAX);
return false;
}
return true;
}
/**
* round sizes to integer
*/
private static void roundSizes(double m, double n) {
m = Math.floor(m + 0.5);
n = Math.floor(n + 0.5);
}
// table of exact cumulative probabilities
static private double w[][][] = new double[WILCOX_MMAX][WILCOX_NMAX][];
/**
* The density of the Wilcoxon distribution.
*/
static private double cwilcox(int k, int m, int n) {
int u = m * n;
int c = (int)(u / 2);
if ((k < 0) || (k > u)) return(0);
if (k > c) k = u - k;
int i = m;
int j = n;
if (m >= n) {
i = n;
j = m;
}
if (w[i][j] == null) {
w[i][j] = new double[c + 1];
for (int l = 0; l <= c; l++)
w[i][j][l] = -1;
}
if (w[i][j][k] < 0) {
if ((i == 0) || (j == 0))
w[i][j][k] = (k == 0)?1.0:0.0;
else
w[i][j][k] = cwilcox(k - n, m - 1, n) + cwilcox(k, m, n - 1);
}
return(w[i][j][k]);
}
/**
* density function
* @param x
* @param m
* @param n
* @return density
*/
public static double density(double x, double m, double n) {
/*!* #ifdef IEEE_754 /*4!*/
/* NaNs propagated correctly */
if (Double.isNaN(x) || Double.isNaN(m) || Double.isNaN(n)) return x + m + n;
/*!* #endif /*4!*/
roundSizes(m,n);
if (m <= 0 || n <= 0) {
throw new java.lang.ArithmeticException("Math Error: DOMAIN");
// return Double.NaN;
}
if (!checkSizesLarge(m,n)) return Double.NaN;
/*!* x = floor(x + 0.5); *!*/
x = java.lang.Math.floor(x + 0.5);
if ((x < 0) || (x > m * n))
return 0;
/*!* return(cwilcox(x, m, n) / choose(m + n, n)); *!*/
return(cwilcox((int) x, (int) m, (int) n) / misc.choose(m + n, n));
}
/**
* Cumulative distribution function of the Wilcoxon distribution.
*/
public static double cumulative(double x, double m, double n) {
/*!* #ifdef IEEE_754 /*4!*/
if (Double.isNaN(x) || Double.isNaN(m) || Double.isNaN(n))
return x + m + n;
if (Double.isInfinite(m) || Double.isInfinite(n)) {
throw new java.lang.ArithmeticException("Math Error: DOMAIN");
// return Double.NaN;
}
/*!* #endif /*4!*/
roundSizes(m,n);
if (m <= 0 || n <= 0) {
throw new java.lang.ArithmeticException("Math Error: DOMAIN");
// return Double.NaN;
}
if (!checkSizesLarge(m,n)) return Double.NaN;
/*!* x = floor(x + 0.5); *!*/
x = java.lang.Math.floor(x + 0.5);
if (x < 0.0) return 0;
if (x >= m * n) return 1;
double p = 0.0;
for (int i = 0; i <= x; i++)
p += density(i, m, n);
return(p);
}
/**
* The quantile function of the Wilcoxon distribution.
*/
public static double quantile(double x, double m, double n) {
/*!* #ifdef IEEE_754 /*4!*/
if (Double.isNaN(x) || Double.isNaN(m) || Double.isNaN(n))
return x + m + n;
if(Double.isInfinite(x) || Double.isInfinite(m) || Double.isInfinite(n)) {
throw new java.lang.ArithmeticException("Math Error: DOMAIN");
// return Double.NaN;
}
/*!* #endif /*4!*/
roundSizes(m,n);
if (x < 0 || x > 1 || m <= 0 || n <= 0) {
throw new java.lang.ArithmeticException("Math Error: DOMAIN");
// return Double.NaN;
};
if (!checkSizesLarge(m,n)) return Double.NaN;
if (x == 0) return(0.0);
if (x == 1) return(m * n);
double p = 0.0;
double q = 0.0;
for (;;) {
/* Don't call cumulative() for efficiency */
p += density(q, m, n);
if (p >= x)
return(q);
q++;
}
}
/**
* Random variates from the Wilcoxon distribution.
*/
public static double random(double m, double n) {
/*!* #ifdef IEEE_754 /*4!*/
/* NaNs propagated correctly */
if (Double.isNaN(m) || Double.isNaN(n)) return(m + n);
/*!* #endif /*4!*/
roundSizes(m,n);
if ((m < 0) || (n < 0)) {
throw new java.lang.ArithmeticException("Math Error: DOMAIN");
// return Double.NaN;
}
if ((m == 0) || (n == 0))
return(0);
double r = 0.0;
int k = (int) (m + n);
int[] x = new int[k];
for (int i = 0; i < k; i++)
x[i] = i;
for (int i = 0; i < n; i++) {
/*!* j = floor(k * sunif()); *!*/
int j = (int) java.lang.Math.floor(k * uniform.random());
r += x[j];
x[j] = x[--k];
}
return(r - n * (n - 1) / 2);
}
}
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