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fisher.cpp
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fisher.cpp
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//////////////////////////////////////////////////////////////////
// //
// PLINK (c) 2005-2009 Shaun Purcell //
// //
// This file is distributed under the GNU General Public //
// License, Version 2. Please see the file COPYING for more //
// details //
// //
//////////////////////////////////////////////////////////////////
#include <climits>
#include "fisher.h"
#include "plink.h"
#include "helper.h"
double fisher(table_t t)
{
int nrow = t.size();
if ( nrow == 0 )
return -9;
int ncol = t[0].size();
if ( ncol == 0 )
return -9;
double table[200];
int c=0;
for (int j=0; j<ncol; j++)
for (int i=0; i<nrow; i++)
{
table[c++] = t[i][j];
}
double expect = -1.0;
double percnt = 100.0;
double emin = 0;
double pre = 0, prt = 0;
int ws = 300000;
fexact(&nrow, &ncol, table, &nrow, &expect, &percnt, &emin, &prt, &pre, &ws);
return pre;
}
/* fisher2.c: this is fexact.c, part of the R
(http://cran.r-project.org) distribution
(package ctest).
Minor edits by az-Uriarte (rdiaz@cnio.es). May 2003.
*/
/* [Notice from the original fexact.c]
Fisher's exact test for contingency tables -- usage see below
fexact.f -- translated by f2c (version 19971204).
Run through a slightly modified version of MM's f2c-clean.
Heavily hand-edited by KH and MM.
*/
#include <cstdlib>
#include <cstdio>
#include <cmath>
#include <limits>
#define SINT_MAX INT_MAX
#undef min
#undef max
#define max(a, b)((a) < (b) ? (b) : (a))
#define min(a, b)((a) > (b) ? (b) : (a))
static void f2xact(int *nrow, int *ncol, double *table, int *ldtabl,
double *expect, double *percnt, double *emin, double
*prt, double *pre, double *fact, int *ico, int
*iro, int *kyy, int *idif, int *irn, int *key,
int *ldkey, int *ipoin, double *stp, int *ldstp,
int *ifrq, double *dlp, double *dsp, double *tm,
int *key2, int *iwk, double *rwk);
static void f3xact(int *nrow, int *irow, int *ncol,int *icol,
double *dlp, int *mm, double *fact, int *ico, int
*iro, int *it, int *lb, int *nr, int *nt, int
*nu, int *itc, int *ist, double *stv, double *alen,
const double *tol);
static void f4xact(int *nrow, int *irow, int *ncol, int *icol,
double *dsp, double *fact, int *icstk, int *ncstk,
int *lstk, int *mstk, int *nstk, int *nrstk, int
*irstk, double *ystk, const double *tol);
static void f5xact(double *pastp, const double *tol, int *kval, int *key,
int *ldkey, int *ipoin, double *stp, int *ldstp,
int *ifrq, int *npoin, int *nr, int *nl, int
*ifreq, int *itop, int *ipsh);
static void f6xact(int *nrow, int *irow, int *iflag, int *kyy,
int *key, int *ldkey, int *last, int *ipn);
static void f7xact(int *nrow, int *imax, int *idif, int *k, int *ks,
int *iflag);
static void f8xact(int *irow, int *is, int *i1, int *izero, int *knew);
static double f9xact(int *n, int *mm, int *ir, double *fact);
static void f10act(int *nrow, int *irow, int *ncol, int *icol,
double *val, int *xmin, double *fact, int *nd,
int *ne, int *m);
static void f11act(int *irow, int *i1, int *i2, int *knew);
static void prterr(int icode, char *mes);
static int iwork(int iwkmax, int *iwkpt, int number, int itype);
#ifdef USING_R
# define isort(n, ix)R_isort(ix, *n)
# include <Rmath.h>/* -> pgamma() */
#else
static void isort(int *n, int *ix);
static double gammds(double *y, double *p, int *ifault);
static double alogam(double *x, int *ifault);
#endif
/* The only public function : */
void
fexact(int *nrow, int *ncol, double *table, int *ldtabl,
double *expect, double *percnt, double *emin, double *prt,
double *pre, int *workspace)
{
/*
ALGORITHM 643, COLLECTED ALGORITHMS FROM ACM.
THIS WORK PUBLISHED IN TRANSACTIONS ON MATHEMATICAL SOFTWARE,
VOL. 19, NO. 4, DECEMBER, 1993, PP. 484-488.
-----------------------------------------------------------------------
Name: FEXACT
Purpose: Computes Fisher's exact test probabilities and a hybrid
approximation to Fisher exact test probabilities for a
contingency table using the network algorithm.
Usage: CALL FEXACT (NROW, NCOL, TABLE, LDTABL, EXPECT, PERCNT,
EMIN, PRT, PRE)
Arguments:
NROW - The number of rows in the table.(Input)
NCOL - The number of columns in the table.(Input)
TABLE - NROW by NCOL matrix containing the contingency
table.(Input)
LDTABL - Leading dimension of TABLE exactly as specified
in the dimension statement in the calling
program.(Input)
EXPECT - Expected value used in the hybrid algorithm for
deciding when to use asymptotic theory
probabilities.(Input)
If EXPECT <= 0.0 then asymptotic theory probabilities
are not used and Fisher exact test probabilities are
computed. Otherwise, if PERCNT or more of the cells in
the remaining table have estimated expected values of
EXPECT or more, with no remaining cell having expected
value less than EMIN, then asymptotic chi-squared
probabilities are used. See the algorithm section of the
manual document for details.
Use EXPECT = 5.0 to obtain the 'Cochran' condition.
PERCNT - Percentage of remaining cells that must have
estimated expected values greater than EXPECT
before asymptotic probabilities can be used.(Input)
See argument EXPECT for details.
Use PERCNT = 80.0 to obtain the 'Cochran' condition.
EMIN - Minimum cell estimated expected value allowed for
asymptotic chi-squared probabilities to be used.(Input)
See argument EXPECT for details.
Use EMIN = 1.0 to obtain the 'Cochran' condition.
PRT - Probability of the observed table for fixed
marginal totals.(Output)
PRE - Table p-value.(Output)
PRE is the probability of a more extreme table,
where `extreme' is in a probabilistic sense.
If EXPECT < 0 then the Fisher exact probability
is returned. Otherwise, an approximation to the
Fisher exact probability is computed based upon
asymptotic chi-squared probabilities for ``large''
table expected values. The user defines ``large''
through the arguments EXPECT, PERCNT, and EMIN.
Remarks:
1. For many problems one megabyte or more of workspace can be
required.If the environment supports it, the user should begin
by increasing the workspace used to 200,000 units.
2. In FEXACT, LDSTP = 30*LDKEY. The proportion of table space used
by STP may be changed by changing the line MULT = 30 below to
another value.
3. FEXACT may be converted to single precision by setting IREAL = 3,
and converting all DOUBLE PRECISION specifications (except the
specifications for RWRK, IWRK, and DWRK) to REAL.This will
require changing the names and specifications of the intrinsic
functions ALOG, AMAX1, AMIN1, EXP, and REAL. In addition, the
machine specific constants will need to be changed, and the name
DWRK will need to be changed to RWRK in the call to F2XACT.
4. Machine specific constants are specified and documented in F2XACT.
A missing value code is specified in both FEXACT and F2XACT.
5. Although not a restriction, is is not generally practical to call
this routine with large tables which are not sparse and in
which the 'hybrid' algorithm has little effect. For example,
although it is feasible to compute exact probabilities for the
table
1 8 5 4 4 2 2
5 3 3 4 3 1 0
10 1 4 0 0 0 0,
computing exact probabilities for a similar table which has been
enlarged by the addition of an extra row (or column) may not be
feasible.
-----------------------------------------------------------------------
*/
/* CONSTANT Parameters : */
/* To increase the length of the table of paste path lengths relative
to the length of the hash table, increase MULT.
*/
const int mult = 30;
/* AMISS is a missing value indicator which is returned when the
probability is not defined.
*/
const double amiss = -12345.;
/*
Set IREAL = 4 for DOUBLE PRECISION
Set IREAL = 3 for SINGLE PRECISION
*/
#define i_real 4
#define i_int 2
/* System generated locals */
int ikh;
/* Local variables */
int nco, nro, ntot, numb, iiwk, irwk;
int i, j, k, kk, ldkey, ldstp, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10;
int i3a, i3b, i3c, i9a, iwkmax, iwkpt;
/* Workspace Allocation (freed at end) */
double *equiv;
iwkmax = 2 * (int) (*workspace / 2);
// equiv = (double *) R_alloc(iwkmax / 2, sizeof(double));
equiv = (double *) calloc(iwkmax / 2, sizeof(double));
/* The check could never happen with Calloc!
equiv = Calloc(iwkmax / 2, double);
if (!equiv) {
prterr(0, "Can not allocate specified workspace");
} */
#define dwrk (equiv)
#define iwrk ((int *)equiv)
#define rwrk ((float *)equiv)
/* Parameter adjustments */
table -= *ldtabl + 1;
/* Function Body */
iwkpt = 0;
if (*nrow > *ldtabl)
prterr(1, "NROW must be less than or equal to LDTABL.");
ntot = 0;
for (i = 1; i <= *nrow; ++i) {
for (j = 1; j <= *ncol; ++j) {
if (table[i + j * *ldtabl] < 0.)
prterr(2, "All elements of TABLE must be positive.");
ntot = (int) (ntot + table[i + j * *ldtabl]);
}
}
if (ntot == 0) {
prterr(3, "All elements of TABLE are zero.\n"
"PRT and PRE are set to missing values.");
*prt = amiss;
*pre = amiss;
goto L_End;
}
nco = max(*nrow, *ncol);
nro = *nrow + *ncol - nco;/* = min(*nrow, *ncol) */
k = *nrow + *ncol + 1;
kk = k * nco;
ikh = ntot + 1;
i1 = iwork(iwkmax, &iwkpt, ikh, i_real);
i2 = iwork(iwkmax, &iwkpt, nco, i_int);
i3 = iwork(iwkmax, &iwkpt, nco, i_int);
i3a = iwork(iwkmax, &iwkpt, nco, i_int);
i3b = iwork(iwkmax, &iwkpt, nro, i_int);
i3c = iwork(iwkmax, &iwkpt, nro, i_int);
ikh = max(k * 5 + (kk << 1), nco * 7 + 800);
iiwk= iwork(iwkmax, &iwkpt, ikh, i_int);
ikh = max(nco + 401, k);
irwk= iwork(iwkmax, &iwkpt, ikh, i_real);
/* NOTE:
What follows below splits the remaining amount iwkmax - iwkpt of
(int) workspace into hash tables as follows.
type size index
INT 2 * ldkey i4 i5 i11
REAL 2 * ldkey i8 i9 i10
REAL 2 * ldstp i6
INT 6 * ldstp i7
Hence, we need ldkey times
3 * 2 + 3 * 2 * s + 2 * mult * s + 6 * mult
chunks of integer memory, where s = sizeof(REAL) / sizeof(INT).
If doubles are used and are twice as long as ints, this gives
18 + 10 * mult
so that the value of ldkey can be obtained by dividing available
(int) workspace by this number.
In fact, because iwork() can actually s * n + s - 1 int chunks
when allocating a REAL, we use ldkey = available / numb - 1.
FIXME:
Can we always assume that sizeof(double) / sizeof(int) is 2?
*/
if (i_real == 4) {/* Double precision reals */
numb = 18 + 10 * mult;
} else {/* Single precision reals */
numb = (mult << 3) + 12;
}
ldkey = (iwkmax - iwkpt) / numb - 1;
ldstp = mult * ldkey;
ikh = ldkey << 1;i4 = iwork(iwkmax, &iwkpt, ikh, i_int);
ikh = ldkey << 1;i5 = iwork(iwkmax, &iwkpt, ikh, i_int);
ikh = ldstp << 1;i6 = iwork(iwkmax, &iwkpt, ikh, i_real);
ikh = ldstp * 6;i7 = iwork(iwkmax, &iwkpt, ikh, i_int);
ikh = ldkey << 1;i8 = iwork(iwkmax, &iwkpt, ikh, i_real);
ikh = ldkey << 1;i9 = iwork(iwkmax, &iwkpt, ikh, i_real);
ikh = ldkey << 1;i9a = iwork(iwkmax, &iwkpt, ikh, i_real);
ikh = ldkey << 1;i10 = iwork(iwkmax, &iwkpt, ikh, i_int);
/* To convert to double precision, change RWRK to DWRK in the next CALL.
*/
f2xact(nrow,
ncol,
&table[*ldtabl + 1],
ldtabl,
expect,
percnt,
emin,
prt,
pre,
dwrk + i1,
iwrk + i2,
iwrk + i3,
iwrk + i3a,
iwrk + i3b,
iwrk + i3c,
iwrk + i4,
&ldkey,
iwrk + i5,
dwrk + i6,
&ldstp,
iwrk + i7,
dwrk + i8,
dwrk + i9,
dwrk + i9a,
iwrk + i10,
iwrk + iiwk,
dwrk + irwk);
L_End:
/* Free(equiv); */
free(equiv);
return;
}
#undef rwrk
#undef iwrk
#undef dwrk
/*
-----------------------------------------------------------------------
Name:F2XACT
Purpose:Computes Fisher's exact test for a contingency table,
routine with workspace variables specified.
Usage:F2XACT (NROW, NCOL, TABLE, LDTABL, EXPECT, PERCNT,
EMIN, PRT, PRE, FACT, ICO, IRO, KYY, IDIF,
IRN, KEY, LDKEY, IPOIN, STP, LDSTP, IFRQ,
DLP, DSP, TM, KEY2, IWK, RWK)
-----------------------------------------------------------------------
*/
void
f2xact(int *nrow, int *ncol, double *table, int *ldtabl,
double *expect, double *percnt, double *emin, double *prt,
double *pre, double *fact, int *ico, int *iro, int *kyy,
int *idif, int *irn, int *key, int *ldkey, int *ipoin,
double *stp, int *ldstp, int *ifrq, double *dlp, double *dsp,
double *tm, int *key2, int *iwk, double *rwk)
{
/* IMAX is the largest representable int on the machine. */
const int imax = SINT_MAX;
/* AMISS is a missing value indicator which is returned when the
probability is not defined. */
const double amiss = -12345.;
/* TOL is chosen as the square root of the smallest relative spacing. */
#ifndef Macintosh
const static double tol = 3.45254e-7;
#else
static double tol = 3.45254e-7;
#endif
/* EMX is a large positive value used in comparing expected values. */
const static double emx = 1e30;
/* Local variables {{any really need to be static ???}} */
static int kval, kmax, jkey, last, ipsh, itmp, itop, jstp, ntot,
jstp2, jstp3, jstp4, i, ii, j, k, n, iflag, ncell, ifreq, chisq,
ikkey, ikstp, ikstp2, k1, kb, kd, ks,
i31, i32, i33, i34, i35, i36, i37, i38, i39,
i41, i42, i43, i44, i45, i46, i47, i48, i310, i311,
nco, nrb, ipn, ipo, itp, nro, nro2;
static double dspt, dd, df,ddf, drn,dro, emn, obs, obs2, obs3,
pastp, pv, tmp;
double d1;
#ifndef USING_R
double d2;
static int ifault;
#endif
bool nr_gt_nc;
/* Parameter adjustments */
table -= *ldtabl + 1;
--ico;
--iro;
--kyy;
--idif;
--irn;
--key;
--ipoin;
--stp;
--ifrq;
--dlp;
--dsp;
--tm;
--key2;
--iwk;
--rwk;
/* Check table dimensions */
if (*nrow > *ldtabl)
prterr(1, "NROW must be less than or equal to LDTABL.");
if (*ncol <= 1)
prterr(4, "NCOL must be at least 2");
/* Initialize KEY array */
for (i = 1; i <= *ldkey << 1; ++i) {
key[i] = -9999;
key2[i] = -9999;
}
/* Initialize parameters */
*pre = 0.;
itop = 0;
if (*expect > 0.)
emn = *emin;
else
emn = emx;
nr_gt_nc = *nrow > *ncol;
/* nco := max(nrow, ncol) : */
if(nr_gt_nc)
nco = *nrow;
else
nco = *ncol;
/* Initialize pointers for workspace */
/* f3xact */
i31 = 1;
i32 = i31 + nco;
i33 = i32 + nco;
i34 = i33 + nco;
i35 = i34 + nco;
i36 = i35 + nco;
i37 = i36 + nco;
i38 = i37 + nco;
i39 = i38 + 400;
i310 = 1;
i311 = 401;
/* f4xact */
k = *nrow + *ncol + 1;
i41 = 1;
i42 = i41 + k;
i43 = i42 + k;
i44 = i43 + k;
i45 = i44 + k;
i46 = i45 + k;
i47 = i46 + k * nco;
i48 = 1;
/* Compute row marginals and total */
ntot = 0;
for (i = 1; i <= *nrow; ++i) {
iro[i] = 0;
for (j = 1; j <= *ncol; ++j) {
if (table[i + j * *ldtabl] < -1e-4)
prterr(2, "All elements of TABLE must be positive.");
iro[i] += (int) table[i + j * *ldtabl];
}
ntot += iro[i];
}
if (ntot == 0) {
prterr(3, "All elements of TABLE are zero.\n"
"PRT and PRE are set to missing values.");
*pre = *prt = amiss;
return;
}
/* Column marginals */
for (i = 1; i <= *ncol; ++i) {
ico[i] = 0;
for (j = 1; j <= *nrow; ++j)
ico[i] += (int) table[j + i * *ldtabl];
}
/* sort marginals */
isort(nrow, &iro[1]);
isort(ncol, &ico[1]);
/*Determine row and column marginals.
Define max(nrow,ncol) =: nco >= nro := min(nrow,ncol)
nco is defined above
Swap marginals if necessary toico[1:nco] & iro[1:nro]
*/
if (nr_gt_nc) {
nro = *ncol;
/* Swap marginals */
for (i = 1; i <= nco; ++i) {
itmp = iro[i];
if (i <= nro)
iro[i] = ico[i];
ico[i] = itmp;
}
} else
nro = *nrow;
/* Get multiplers for stack */
kyy[1] = 1;
for (i = 2; i <= nro; ++i) {
/* Hash table multipliers */
if (iro[i - 1] + 1 <= imax / kyy[i - 1]) {
kyy[i] = kyy[i - 1] * (iro[i - 1] + 1);
j /= kyy[i - 1];
} else
goto L_ERR_5;
}
/* Maximum product */
if (iro[nro - 1] + 1 <= imax / kyy[nro - 1]) {
kmax = (iro[nro] + 1) * kyy[nro - 1];
} else {
L_ERR_5:
prterr(5, "The hash table key cannot be computed because "
"the largest key\n"
"is larger than the largest representable int.\n"
"The algorithm cannot proceed.\n"
"Reduce the workspace size, or use `exact = FALSE'.");
return;
}
/* Compute log factorials */
fact[0] = 0.;
fact[1] = 0.;
if(ntot >= 2) fact[2] = log(2.);
/* MM: old code assuming log() to be SLOW */
for (i = 3; i <= ntot; i += 2) {
fact[i] = fact[i - 1] + log((double) i);
j = i + 1;
if (j <= ntot)
fact[j] = fact[i] + fact[2] + fact[j / 2] - fact[j / 2 - 1];
}
/* Compute obs := observed path length */
obs = tol;
ntot = 0;
for (j = 1; j <= nco; ++j) {
dd = 0.;
for (i = 1; i <= nro; ++i) {
if (nr_gt_nc) {
dd += fact[(int) table[j + i * *ldtabl]];
ntot += (int) table[j + i * *ldtabl];
} else {
dd += fact[(int) table[i + j * *ldtabl]];
ntot += (int) table[i + j * *ldtabl];
}
}
obs += fact[ico[j]] - dd;
}
/* Denominator of observed table: DRO */
dro = f9xact(&nro, &ntot, &iro[1], fact);
*prt = exp(obs - dro);
/* Initialize pointers */
k = nco;
last = *ldkey + 1;
jkey = *ldkey + 1;
jstp = *ldstp + 1;
jstp2 = *ldstp * 3 + 1;
jstp3 = (*ldstp << 2) + 1;
jstp4 = *ldstp * 5 + 1;
ikkey = 0;
ikstp = 0;
ikstp2 = *ldstp << 1;
ipo = 1;
ipoin[1] = 1;
stp[1] = 0.;
ifrq[1] = 1;
ifrq[ikstp2 + 1] = -1;
Outer_Loop:
kb = nco - k + 1;
ks = 0;
n = ico[kb];
kd = nro + 1;
kmax = nro;
/* IDIF is the difference in going to the daughter */
for (i = 1; i <= nro; ++i)
idif[i] = 0;
/* Generate the first daughter */
do {
--kd;
ntot = min(n, iro[kd]);
idif[kd] = ntot;
if (idif[kmax] == 0)
--kmax;
n -= ntot;
}
while (n > 0 && kd != 1);
if (n != 0) {
goto L310;
}
k1 = k - 1;
n = ico[kb];
ntot = 0;
for (i = kb + 1; i <= nco; ++i)
ntot += ico[i];
L150:
/* Arc to daughter length=ICO(KB) */
for (i = 1; i <= nro; ++i)
irn[i] = iro[i] - idif[i];
/* Sort irn */
if (k1 > 1) {
if (nro == 2) {
if (irn[1] > irn[2]) {
ii = irn[1];
irn[1] = irn[2];
irn[2] = ii;
}
} else if (nro == 3) {
ii = irn[1];
if (ii > irn[3]) {
if (ii > irn[2]) {
if (irn[2] > irn[3]) {
irn[1] = irn[3];
irn[3] = ii;
} else {
irn[1] = irn[2];
irn[2] = irn[3];
irn[3] = ii;
}
} else {
irn[1] = irn[3];
irn[3] = irn[2];
irn[2] = ii;
}
} else if (ii > irn[2]) {
irn[1] = irn[2];
irn[2] = ii;
} else if (irn[2] > irn[3]) {
ii = irn[2];
irn[2] = irn[3];
irn[3] = ii;
}
} else {
for (j = 2; j <= nro; ++j) {
i = j - 1;
ii = irn[j];
while (ii < irn[i]) {
irn[i + 1] = irn[i];
--i;
if (i == 0)
break;
}
irn[i + 1] = ii;
}
}
/* Adjust start for zero */
for (i = 1; i <= nro; ++i) {
if (irn[i] != 0)
break;
}
nrb = i;
nro2 = nro - i + 1;
} else {
nrb = 1;
nro2 = nro;
}
/* Some table values */
ddf = f9xact(&nro, &n, &idif[1], fact);
drn = f9xact(&nro2, &ntot, &irn[nrb], fact) - dro + ddf;
/* Get hash value */
if (k1 > 1) {
kval = irn[1] + irn[2] * kyy[2];
for (i = 3; i <= nro; ++i) {
kval += irn[i] * kyy[i];
}
/* Get hash table entry */
i = kval % (*ldkey << 1) + 1;
/* Search for unused location */
for (itp = i; itp <= *ldkey << 1; ++itp) {
ii = key2[itp];
if (ii == kval) {
goto L240;
} else if (ii < 0) {
key2[itp] = kval;
dlp[itp] = 1.;
dsp[itp] = 1.;
goto L240;
}
}
for (itp = 1; itp <= i - 1; ++itp) {
ii = key2[itp];
if (ii == kval) {
goto L240;
} else if (ii < 0) {
key2[itp] = kval;
dlp[itp] = 1.;
goto L240;
}
}
/* KH
prterr(6, "LDKEY is too small.\n"
"It is not possible to give the value of LDKEY required,\n"
"but you could try doubling LDKEY (and possibly LDSTP).");
*/
prterr(6, "LDKEY is too small for this problem.\n"
"Try increasing the size of the workspace.");
}
L240:
ipsh = (1);
/* Recover pastp */
ipn = ipoin[ipo + ikkey];
pastp = stp[ipn + ikstp];
ifreq = ifrq[ipn + ikstp];
/* Compute shortest and longest path */
if (k1 > 1) {
obs2 = obs - fact[ico[kb + 1]] - fact[ico[kb + 2]] - ddf;
for (i = 3; i <= k1; ++i) {
obs2 -= fact[ico[kb + i]];
}
if (dlp[itp] > 0.) {
dspt = obs - obs2 - ddf;
/* Compute longest path */
dlp[itp] = 0.;
f3xact(&nro2, &irn[nrb], &k1, &ico[kb + 1], &dlp[itp],
&ntot, fact, &iwk[i31], &iwk[i32], &iwk[i33],
&iwk[i34], &iwk[i35], &iwk[i36], &iwk[i37],
&iwk[i38], &iwk[i39], &rwk[i310], &rwk[i311], &tol);
dlp[itp] = min(0., dlp[itp]);
/* Compute shortest path */
dsp[itp] = dspt;
f4xact(&nro2, &irn[nrb], &k1, &ico[kb + 1], &dsp[itp], fact,
&iwk[i47], &iwk[i41], &iwk[i42], &iwk[i43],
&iwk[i44], &iwk[i45], &iwk[i46], &rwk[i48], &tol);
dsp[itp] = min(0., dsp[itp] - dspt);
/* Use chi-squared approximation? */
if ((irn[nrb] * ico[kb + 1]) > ntot * emn) {
ncell = 0;
for (i = 0; i < nro2; ++i)
for (j = 1; j <= k1; ++j)
if (irn[nrb + i] * ico[kb + j] >= ntot * *expect)
ncell++;
if (ncell * 100 >= k1 * nro2 * *percnt) {
tmp = 0.;
for (i = 0; i < nro2; ++i)
tmp += (fact[irn[nrb + i]] -
fact[irn[nrb + i] - 1]);
tmp *= k1 - 1;
for (j = 1; j <= k1; ++j)
tmp += (nro2 - 1) * (fact[ico[kb + j]] -
fact[ico[kb + j] - 1]);
df = (double) ((nro2 - 1) * (k1 - 1));
tmp += df * 1.83787706640934548356065947281;
tmp -= (nro2 * k1 - 1) * (fact[ntot] - fact[ntot - 1]);
tm[itp] = (obs - dro) * -2. - tmp;
} else {
/* tm(itp) set to a flag value */
tm[itp] = -9876.;
}
} else {
tm[itp] = -9876.;
}
}
obs3 = obs2 - dlp[itp];
obs2 -= dsp[itp];
if (tm[itp] == -9876.) {
chisq = (0);
} else {
chisq = (1);
tmp = tm[itp];
}
} else {
obs2 = obs - drn - dro;
obs3 = obs2;
}
L300:
/* Process node with new PASTP */
if (pastp <= obs3) {
/* Update pre */
*pre += (double) ifreq * exp(pastp + drn);
} else if (pastp < obs2) {
if (chisq) {
df = (double) ((nro2 - 1) * (k1 - 1));
#ifdef USING_R
pv = pgamma(fmax2(0., tmp + (pastp + drn) * 2.) / 2.,
df / 2., /*scale = */ 1.,
/*lower_tail = */FALSE, /*log_p = */ FALSE);
#else
d1 = max(0., tmp + (pastp + drn) * 2.) / 2.;
d2 = df / 2.;
pv = 1. - gammds(&d1, &d2, &ifault);
#endif
*pre += (double) ifreq * exp(pastp + drn) * pv;
} else {
/* Put daughter on queue */
d1 = pastp + ddf;
f5xact(&d1, &tol, &kval, &key[jkey], ldkey, &ipoin[jkey],
&stp[jstp], ldstp, &ifrq[jstp], &ifrq[jstp2],
&ifrq[jstp3], &ifrq[jstp4], &ifreq, &itop, &ipsh);
ipsh = (0);
}
}
/* Get next PASTP on chain */
ipn = ifrq[ipn + ikstp2];
if (ipn > 0) {
pastp = stp[ipn + ikstp];
ifreq = ifrq[ipn + ikstp];
goto L300;
}
/* Generate a new daughter node */
f7xact(&kmax, &iro[1], &idif[1], &kd, &ks, &iflag);
if (iflag != 1) {
goto L150;
}
L310:
/* Go get a new mother from stage K */
do {
iflag = 1;
f6xact(&nro, &iro[1], &iflag, &kyy[1], &key[ikkey + 1], ldkey,
&last, &ipo);
/* Update pointers */
if (iflag != 3)
goto Outer_Loop;
/* else iflag == 3 : no additional nodes to process */
--k;
itop = 0;
ikkey = jkey - 1;
ikstp = jstp - 1;
ikstp2 = jstp2 - 1;
jkey = *ldkey - jkey + 2;
jstp = *ldstp - jstp + 2;
jstp2 = (*ldstp << 1) + jstp;
for (i = 1; i <= *ldkey << 1; ++i)
key2[i] = -9999;
} while (k >= 2);
}
/*
-----------------------------------------------------------------------
Name: F3XACT
Purpose: Computes the shortest path length for a given table.
Usage: F3XACT (NROW, IROW, NCOL, ICOL, DLP, MM, FACT, ICO, IRO,
IT, LB, NR, NT, NU, ITC, IST, STV, ALEN, TOL)
Arguments:
NROW - The number of rows in the table.(Input)
IROW - Vector of length NROW containing the row sums
for the table.(Input)
NCOL - The number of columns in the table.(Input)
ICOL - Vector of length K containing the column sums
for the table.(Input)
DLP - The longest path for the table.(Output)
MM - The total count in the table.(Output)
FACT - Vector containing the logarithms of factorials.(Input)
ICO - Work vector of length MAX(NROW,NCOL).
IRO - Work vector of length MAX(NROW,NCOL).
IT - Work vector of length MAX(NROW,NCOL).
LB - Work vector of length MAX(NROW,NCOL).
NR - Work vector of length MAX(NROW,NCOL).
NT - Work vector of length MAX(NROW,NCOL).
NU - Work vector of length MAX(NROW,NCOL).
ITC - Work vector of length 400.
IST - Work vector of length 400.
STV - Work vector of length 400.
ALEN - Work vector of length MAX(NROW,NCOL).
TOL - Tolerance.(Input)
-----------------------------------------------------------------------
*/
void
f3xact(int *nrow, int *irow, int *ncol, int *icol, double *dlp,
int *mm, double *fact, int *ico, int *iro, int *it,
int *lb, int *nr, int *nt, int *nu, int *itc, int *ist,
double *stv, double *alen, const double *tol)
{
/* Initialized data */
static int ldst = 200;
static int nst = 0;
static int nitc = 0;
/* Local variables */
static int xmin;
static int i, k;
static double v;
static int n11, n12, ii, nn, ks, ic1, ic2, nc1, nn1;
static int nr1, nco;
static double val;
static int nct, ipn, irl, key, lev, itp, nro;
static double vmn;
static int nrt, kyy, nc1s;
/* Parameter adjustments */
--stv;
--ist;
--itc;
--nu;
--nt;
--nr;
--lb;
--it;
--iro;
--ico;
--icol;
--irow;
/* Function Body */
for (i = 0; i <= *ncol; ++i) {
alen[i] = 0.;
}
for (i = 1; i <= 400; ++i) {
ist[i] = -1;
}
/* nrow is 1 */
if (*nrow <= 1) {
if (*nrow > 0) {
*dlp -= fact[icol[1]];
for (i = 2; i <= *ncol; ++i) {
*dlp -= fact[icol[i]];
}
}
return;
}
/* ncol is 1 */
if (*ncol <= 1) {
if (*ncol > 0) {
*dlp = *dlp - fact[irow[1]] - fact[irow[2]];
for (i = 3; i <= *nrow; ++i) {
*dlp -= fact[irow[i]];
}
}
return;
}
/* 2 by 2 table */
if (*nrow * *ncol == 4) {
n11 = (irow[1] + 1) * (icol[1] + 1) / (*mm + 2);
n12 = irow[1] - n11;
*dlp = *dlp - fact[n11] - fact[n12] - fact[icol[1] - n11]
- fact[icol[2] - n12];
return;
}
/* Test for optimal table */
val = 0.;
xmin = (0);
if (irow[*nrow] <= irow[1] + *ncol) {
f10act(nrow, &irow[1], ncol, &icol[1], &val, &xmin, fact,
&lb[1], &nu[1], &nr[1]);
}
if (! xmin) {
if (icol[*ncol] <= icol[1] + *nrow) {
f10act(ncol, &icol[1], nrow, &irow[1], &val, &xmin, fact,
&lb[1], &nu[1], &nr[1]);
}