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/* PSPP - a program for statistical analysis.
Copyright (C) 2011 Free Software Foundation, Inc.
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 3 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, see <http://www.gnu.org/licenses/>.
*/
/* This file is taken from the R project source code, and modified.
The original copyright notice is reproduced below: */
/*
* Mathlib : A C Library of Special Functions
* Copyright (C) 1998 Ross Ihaka
* Copyright (C) 2000--2005 The R Development Core Team
* based in part on AS70 (C) 1974 Royal Statistical Society
*
* 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, a copy is available at
* http://www.r-project.org/Licenses/
*
* SYNOPSIS
*
* #include <Rmath.h>
* double qtukey(p, rr, cc, df, lower_tail, log_p);
*
* DESCRIPTION
*
* Computes the quantiles of the maximum of rr studentized
* ranges, each based on cc means and with df degrees of freedom
* for the standard error, is less than q.
*
* The algorithm is based on that of the reference.
*
* REFERENCE
*
* Copenhaver, Margaret Diponzio & Holland, Burt S.
* Multiple comparisons of simple effects in
* the two-way analysis of variance with fixed effects.
* Journal of Statistical Computation and Simulation,
* Vol.30, pp.1-15, 1988.
*/
#include <config.h>
#include "tukey.h"
#include <assert.h>
#include <math.h>
#define TRUE (1)
#define FALSE (0)
#define ML_POSINF (1.0 / 0.0)
#define ML_NEGINF (-1.0 / 0.0)
#define R_D_Lval(p) (lower_tail ? (p) : (0.5 - (p) + 0.5)) /* p */
#define R_DT_qIv(p) (log_p ? (lower_tail ? exp(p) : - expm1(p)) \
: R_D_Lval(p))
static double fmax2(double x, double y)
{
if (isnan(x) || isnan(y))
return x + y;
return (x < y) ? y : x;
}
#define R_Q_P01_boundaries(p, _LEFT_, _RIGHT_) \
if (log_p) { \
assert (p <= 0); \
if(p == 0) /* upper bound*/ \
return lower_tail ? _RIGHT_ : _LEFT_; \
if(p == ML_NEGINF) \
return lower_tail ? _LEFT_ : _RIGHT_; \
} \
else { /* !log_p */ \
assert (p >= 0 && p <= 1); \
if(p == 0) \
return lower_tail ? _LEFT_ : _RIGHT_; \
if(p == 1) \
return lower_tail ? _RIGHT_ : _LEFT_; \
}
/* qinv() :
* this function finds percentage point of the studentized range
* which is used as initial estimate for the secant method.
* function is adapted from portion of algorithm as 70
* from applied statistics (1974) ,vol. 23, no. 1
* by odeh, r. e. and evans, j. o.
*
* p = percentage point
* c = no. of columns or treatments
* v = degrees of freedom
* qinv = returned initial estimate
*
* vmax is cutoff above which degrees of freedom
* is treated as infinity.
*/
static double qinv(double p, double c, double v)
{
static const double p0 = 0.322232421088;
static const double q0 = 0.993484626060e-01;
static const double p1 = -1.0;
static const double q1 = 0.588581570495;
static const double p2 = -0.342242088547;
static const double q2 = 0.531103462366;
static const double p3 = -0.204231210125;
static const double q3 = 0.103537752850;
static const double p4 = -0.453642210148e-04;
static const double q4 = 0.38560700634e-02;
static const double c1 = 0.8832;
static const double c2 = 0.2368;
static const double c3 = 1.214;
static const double c4 = 1.208;
static const double c5 = 1.4142;
static const double vmax = 120.0;
double ps, q, t, yi;
ps = 0.5 - 0.5 * p;
yi = sqrt (log (1.0 / (ps * ps)));
t = yi + ((((yi * p4 + p3) * yi + p2) * yi + p1) * yi + p0)
/ ((((yi * q4 + q3) * yi + q2) * yi + q1) * yi + q0);
if (v < vmax) t += (t * t * t + t) / v / 4.0;
q = c1 - c2 * t;
if (v < vmax) q += -c3 / v + c4 * t / v;
return t * (q * log (c - 1.0) + c5);
}
/*
* Copenhaver, Margaret Diponzio & Holland, Burt S.
* Multiple comparisons of simple effects in
* the two-way analysis of variance with fixed effects.
* Journal of Statistical Computation and Simulation,
* Vol.30, pp.1-15, 1988.
*
* Uses the secant method to find critical values.
*
* p = confidence level (1 - alpha)
* rr = no. of rows or groups
* cc = no. of columns or treatments
* df = degrees of freedom of error term
*
* ir(1) = error flag = 1 if wprob probability > 1
* ir(2) = error flag = 1 if ptukey probability > 1
* ir(3) = error flag = 1 if convergence not reached in 50 iterations
* = 2 if df < 2
*
* qtukey = returned critical value
*
* If the difference between successive iterates is less than eps,
* the search is terminated
*/
double qtukey(double p, double rr, double cc, double df,
int lower_tail, int log_p)
{
static const double eps = 0.0001;
const int maxiter = 50;
double ans = 0.0, valx0, valx1, x0, x1, xabs;
int iter;
if (isnan(p) || isnan(rr) || isnan(cc) || isnan(df)) {
/* ML_ERROR(ME_DOMAIN, "qtukey"); */
return p + rr + cc + df;
}
/* df must be > 1 ; there must be at least two values */
/* ^^
JMD: The comment says 1 but the code says 2.
Which is correct?
*/
assert (df >= 2);
assert (rr >= 1);
assert (cc >= 2);
R_Q_P01_boundaries (p, 0, ML_POSINF);
p = R_DT_qIv(p); /* lower_tail,non-log "p" */
/* Initial value */
x0 = qinv(p, cc, df);
/* Find prob(value < x0) */
valx0 = ptukey(x0, rr, cc, df, /*LOWER*/TRUE, /*LOG_P*/FALSE) - p;
/* Find the second iterate and prob(value < x1). */
/* If the first iterate has probability value */
/* exceeding p then second iterate is 1 less than */
/* first iterate; otherwise it is 1 greater. */
if (valx0 > 0.0)
x1 = fmax2(0.0, x0 - 1.0);
else
x1 = x0 + 1.0;
valx1 = ptukey(x1, rr, cc, df, /*LOWER*/TRUE, /*LOG_P*/FALSE) - p;
/* Find new iterate */
for(iter=1 ; iter < maxiter ; iter++) {
ans = x1 - ((valx1 * (x1 - x0)) / (valx1 - valx0));
valx0 = valx1;
/* New iterate must be >= 0 */
x0 = x1;
if (ans < 0.0) {
ans = 0.0;
valx1 = -p;
}
/* Find prob(value < new iterate) */
valx1 = ptukey(ans, rr, cc, df, /*LOWER*/TRUE, /*LOG_P*/FALSE) - p;
x1 = ans;
/* If the difference between two successive */
/* iterates is less than eps, stop */
xabs = fabs(x1 - x0);
if (xabs < eps)
return ans;
}
/* The process did not converge in 'maxiter' iterations */
assert (0);
return ans;
}
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