https://github.com/cran/RandomFields
Tip revision: fab3d29ef16569604858ee648b9e1f6f7d4a7c96 authored by Martin Schlather on 21 September 2014, 00:00:00 UTC
version 3.0.42
version 3.0.42
Tip revision: fab3d29
auxiliary.cc
//#define DEBUG 1
/*
Authors
Martin Schlather, schlather@math.uni-mannheim.de
Collection of auxiliary functions
Copyright (C) 2001 -- 2014 Martin Schlather,
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 PURSE. 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., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
#include <math.h>
#include <unistd.h>
#include "auxiliary.h"
//#include <curses.h>
#include "RandomFields.h"
#include <R_ext/Lapack.h>
#include <R_ext/Linpack.h>
#include "RF.h"
#include <Rdefines.h>
// important check !!
#ifndef LOCAL_MACHINE
#ifdef SHOW_ADDRESSES
SHOW_ADRESSES IS NOT ALLOWED
#endif
#ifdef RANDOMFIELDS_DEBUGGING
RANDOMFIELDS_DEBUGGING IS NOT ALLOWED
#endif
#endif
double intpow(double x, int p) {
double res = 1.0;
if (p < 0) {
p = -p;
x = 1.0 / x;
}
while (p != 0) {
if (p % 2 == 1) res *= x;
x *= x;
p /= 2;
}
return res;
}
void AtA(double *a, int nrow, int ncol, double *A) {
// A = a^T %*% a
int i, k, j, m,
dimSq = ncol * ncol;
for (k=i=0; i<dimSq; i+=ncol) {
for (j=0; j<dimSq; j+=ncol, k++) {
double dummy = 0.0;
for (m=0; m<nrow; m++) {
dummy += a[i+m] * a[j+m];
}
A[k] = dummy;
}
}
}
void xA(double *x, double*A, int nrow, int ncol, double *y) {
int i,j,k;
if (A == NULL) {
if (nrow != ncol || nrow <= 0) BUG;
MEMCOPY(y, x, sizeof(double) * nrow);
} else {
for (k=i=0; i<ncol; i++) {
y[i] =0.0;
for (j=0; j<nrow; j++) {
y[i] += A[k++] * x[j];
}
}
}
}
void Ax(double *A, double*x, int nrow, int ncol, double *y) {
int i,j,k;
if (A == NULL) {
if (nrow != ncol || nrow <= 0) BUG;
MEMCOPY(y, x, sizeof(double) * nrow);
} else {
for (i=0; i<nrow; i++) y[i]=0.0;
for (k=i=0; i<ncol; i++) {
for (j=0; j<nrow; j++) {
y[j] += A[k++] * x[i];
}
}
}
}
void AxResType(double *A, res_type *x, int nrow, int ncol, double *y) {
int i,j,k;
for (i=0; i<nrow; i++) y[i]=0.0;
for (k=i=0; i<ncol; i++) {
for (j=0; j<nrow; j++) {
y[j] += A[k++] * x[i];
}
}
}
double XkCXtl(double *X, double *C, int nrow, int dim, int k, int l) {
// (k-th row of X) * C * (l-th column of X)
double *pX, *pY, scalar, result;
int i,j,ci,
size = nrow * dim;
pX = X + k;
pY = X + l;
result = 0.0;
for (ci=0, j=0; j<size; j+=nrow) {
for (i=0, scalar = 0.0; i<size; i+=nrow) {
scalar += pX[i] * C[ci++];
}
result += scalar * pY[j];
}
return result;
}
void XCXt(double *X, double *C, double *V, int nrow, int dim /* dim of C */) {
double *pX, *endpX, *dummy, *pdummy, scalar;
int i, cd, rv, ci, cv,
size = nrow * dim;
dummy = (double*) MALLOC(sizeof(double) * nrow * dim);
if (dummy == NULL) ERR("XCXt: memory allocation error in XCXt");
// dummy = XC
for (pX = X, pdummy=dummy, endpX = pX + nrow;
pX < endpX; pX++, pdummy++) {
for (ci=0, cd=0; cd<size; cd+=nrow) {
for (i=0, scalar = 0.0; i<size; i+=nrow) {
scalar += pX[i] * C[ci++];
}
pdummy[cd] = scalar;
}
}
// V = dummy X^t
for (rv=0; rv<nrow; rv++) {
for (cv=rv; cv<nrow; cv++) {
for (scalar=0.0, i=0; i<size; i+=nrow) {
scalar += dummy[rv + i] * X[cv + i];
}
V[rv + cv * nrow] = V[cv + rv * nrow] = scalar;
}
}
free(dummy);
}
double xUy(double *x, double *U, double *y, int dim) {
double dummy,
xVy = 0.0;
int j, d, i,
dimM1 = dim - 1;
for (j=d=0; d<dim; d++) {
j = dim * d;
for (dummy = 0.0, i=0; i<=d; i++) {
dummy += x[i] * U[j++];
}
for (j += dimM1; i<dim; i++, j+=dim) {
dummy += x[i] * U[j];
}
xVy += dummy * y[d];
}
return xVy;
}
double xUxz(double *x, double *U, int dim, double *z) {
double dummy,
xVx = 0.0;
int j, d, i,
dimM1 = dim - 1;
for (j=d=0; d<dim; d++) {
j = dim * d;
for (dummy = 0.0, i=0; i<=d; i++) {
dummy += x[i] * U[j++];
}
for (j += dimM1; i<dim; i++, j+=dim) {
dummy += x[i] * U[j];
}
if (z != NULL) z[d] = dummy;
xVx += dummy * x[d];
}
return xVx;
}
double xUx(double *x, double *U, int dim) {
return xUxz(x, U, dim, NULL);
}
double x_UxPz(double *x, double *U, double *z, int dim) {
// x^t (Ux + z); U dreieckmatrix
double dummy,
xVx = 0.0;
int j, d, i,
dimM1 = dim - 1;
for (j=d=0; d<dim; d++) {
j = dim * d;
for (dummy = z[d], i=0; i<=d; i++) {
dummy += x[i] * U[j++];
}
for (j += dimM1; i<dim; i++, j+=dim) {
dummy += x[i] * U[j];
}
xVx += dummy * x[d];
}
return xVx;
}
double getMinimalAbsEigenValue(double *Aniso, int dim) {
double dummy,
min = RF_INF,
*SICH = NULL,
*D = NULL,
*work = NULL;
int dd, Err,
err = NOERROR,
*iwork = NULL,
dimSq = dim * dim,
optim_work = 12 * dim;
if ((D =(double *) MALLOC(sizeof(double) * dim))==NULL ||
(work = (double *) MALLOC(sizeof(double) * optim_work))==NULL ||
(iwork = (int *) MALLOC(sizeof(int) * 8 * dim))==NULL ||
(SICH =(double *) MALLOC(sizeof(double) * dimSq))==NULL) {
err=ERRORMEMORYALLOCATION; goto ErrorHandling;
}
MEMCOPY(SICH, Aniso, sizeof(double) * dimSq);
F77_CALL(dgesdd)("N", &dim, &dim, SICH, &dim, D, NULL, &dim, NULL,
&dim, work, &optim_work, iwork, &Err);
if (Err != 0) GERR("SVD for anisotropy matrix failed.");
for (dd = 0; dd < dim; dd++) {
dummy = fabs(D[dd]);
if (dummy < min) min = dummy;
}
ErrorHandling:
if (D != NULL) free(D);
if (SICH != NULL) free(SICH);
if (work != NULL) free(work);
if (iwork != NULL) free(iwork);
if (err != NOERROR) XERR(err);
return min;
}
double getDet(double *Aniso, int dim) {
double
det = 1.0,
*SICH = NULL,
*D = NULL,
*work = NULL;
int dd, Err,
err = NOERROR,
*iwork = NULL,
dimSq = dim * dim,
optim_work = 12 * dim;
if ((D =(double *) MALLOC(sizeof(double) * dim))==NULL ||
(work = (double *) MALLOC(sizeof(double) * optim_work))==NULL ||
(iwork = (int *) MALLOC(sizeof(int) * 8 * dim))==NULL ||
(SICH =(double *) MALLOC(sizeof(double) * dimSq))==NULL) {
err=ERRORMEMORYALLOCATION; goto ErrorHandling;
}
MEMCOPY(SICH, Aniso, sizeof(double) * dimSq);
F77_CALL(dgesdd)("N", &dim, &dim, SICH, &dim, D, NULL, &dim, NULL,
&dim, work, &optim_work, iwork, &Err);
if (Err != 0) GERR("SVD for anisotropy matrix failed.");
for (dd = 0; dd < dim; det *= D[dd++]);
ErrorHandling:
if (D != NULL) free(D);
if (SICH != NULL) free(SICH);
if (work != NULL) free(work);
if (iwork != NULL) free(iwork);
if (err != NOERROR) XERR(err);
return det;
}
double detU(double *C, int dim) {
/* ACHTUNG!! detU zerstoert !!! */
int i, info,
// job = 10,
dimP1 = dim + 1,
dimsq = dim * dim;
double det = 1.0;
F77_CALL(dpofa)(C, &dim, &dim, &info); // C i s now cholesky
if (info != 0) {
ERR("detU: matrix does not seem to be strictly positive definite");
}
for (i=0; i<dimsq; i+=dimP1) det *= C[i];
return det * det;
}
void det_UpperInv(double *C, double *det, int dim) {
int i, info,
job = 01,
dimP1 = dim + 1,
dimsq = dim * dim;
F77_CALL(dpofa)(C, &dim, &dim, &info); // C i s now cholesky
if (info != 0) {
//printf("C=%f %f %f %f\n", C[0], C[1], C[2], C[3]);
ERR("det_UpperInv: dpofa failed -- is matrix positive definite?");
}
double Det = 1.0;
for (i=0; i<dimsq; i+=dimP1) Det *= C[i];
*det = Det * Det;
F77_CALL(dpodi)(C, &dim, &dim, det, &job); // C is now Cinv
}
void matmult(double *A, double *B, double *C, int l, int m, int n) {
// multiplying an lxm- and an mxn-matrix, saving krigult in C
int i, j, k;
for(i=0; i<l; i++)
for(j=0; j<n; j++) {
C[j*l+i] = 0;
for(k=0; k<m; k++)
C[j*l+i] += A[k*l+i]*B[j*m+k];
}
}
void matmulttransposed(double *A, double *B, double *C, int m, int l, int n) {
// multiplying t(A) and B with dim(A)=(m,l) and dim(B)=(m,n),
// saving result in C
int i, j, k;
for(i=0; i<l; i++)
for(j=0; j<n; j++) {
C[j*l+i] = 0;
for(k=0; k<m; k++)
C[j*l+i] += A[i*m+k]*B[j*m+k];
}
}
void Xmatmult(double *A, double *B, double *C, int l, int m, int n) {
// multiplying an lxm- and an mxn-matrix, saving krigult in C
int i, j, k, jl, jm, kl, endfor;
double dummy;
for(i=0; i<l; i++) {
for(jl=i, jm=j=0; j<n; j++, jl+=l, jm+=m) {
dummy = 0.0;
endfor = jm + m;
for(kl=i, k=jm; k<endfor; k++, kl+=l) dummy += A[kl] * B[k];
C[jl] = dummy;
}
}
}
void Xmatmulttransposed(double *A, double *B, double *C, int m, int l, int n) {
// multiplying t(A) and B with dim(A)=(m,l) and dim(B)=(m,n),
// saving result in C
int i, j, k, jl, im, jm, endfor, jmk;
double dummy;
for(im=i=0; i<l; i++, im+=m) {
for(jl=i, jm=j=0; j<n; j++, jl+=l, jm+=m) {
dummy = 0.0;
endfor = im + m;
for(jmk=jm, k=im; k<endfor; k++) dummy += A[k] * B[jmk++];
C[jl] = dummy;
}
}
}
/*
void InvChol(double *C, int dim) {
int i, info, ii, endfor,
job = 01,
dimP1 = dim + 1,
dimsq = dim * dim;
long ve, ho;
double Det = 1.0;
F77_CALL(dpofa)(C, &dim, &dim, &info); // C is now cholesky
if (info != 0) ERR("InvChol: Inversion failed, bad functions\n");
for (i=0; i<dimsq; i+=dimP1) Det *= C[i];
Det = Det * Det;
F77_CALL(dpodi)(C, &dim, &dim, &Det, &job); // C is now Cinv
for (ii=dim, i=0; ii>0; i+=dimP1, ii--) { // filling lower half
endfor = i + ii;
for (ve = i + 1, ho = i + dim; ve < endfor;
ve++, ho += dim) {
C[ve] = C[ho];
}
}
}
*/
int invertMatrix(double *M, int size, int* Methods, int nMeth) {
// http://www.nag.com/numeric/fl/nagdoc_fl23/xhtml/F01/f01intro.xml
int err, m, i,
method = -1,
sizeSq = size * size;
long j;
double *SICH = NULL;
if (nMeth > 1) {
if ((SICH = (double*) MALLOC(sizeof(double) * sizeSq)) == NULL) {
return ERRORMEMORYALLOCATION;
}
memcpy(SICH, M, sizeSq);
}
for (m=0; m<nMeth; m++) {
method = Methods[m];
if (method<0) break;
if (m>0) {
memcpy(M, SICH, sizeSq);
}
switch(method) {
case Cholesky : // cholesky
F77_CALL(dpotrf)("Upper", &size, M, &size, &err);
if (err != 0) {
if (PL >= PL_COV_STRUCTURE)
PRINTF("cholesky decomposition failed; the matrix does not seem to be strictly positive definite\n");
continue;
}
F77_CALL(dpotri)("U", &size, M, &size, &err);
if (err != 0) {
if (PL >= PL_COV_STRUCTURE)
PRINTF("Cholesky decomposition failed; matrix does not seem to be strictly positive definite\n");
continue;
}
long i2, i3;
for (i2=i=0; i<size; i++, i2+=size + 1) {
for (i3 = i2 + 1, j = i2 + size; j<sizeSq; j+=size) M[i3++] = M[j];
}
break;
case 1 : {// QR returns transposed of the inverse !!
int
*inc = NULL;
double *aijmax = NULL,
*workspaceD = NULL,
*workspaceU = NULL,
*workspaceDU = NULL;
if (//(aijmax = (double*) MALLOC(sizeof(double) * size)) == NULL ||
//(inc = (int*) MALLOC(sizeof(int) * size)) == NULL ||
(workspaceD = (double*) MALLOC(sizeof(double) * size)) == NULL ||
(workspaceU = (double*) MALLOC(sizeof(double) * sizeSq)) == NULL
// || (workspaceDU = (double*) MALLOC(sizeof(double) * size)) == NULL
) {
err = ERRORMEMORYALLOCATION; goto ErrorHandling;
}
// PseudoInverse:
// F77_CALL(f01blf)(&size, &size, &(GLOBAL.general.matrixtolerance),
// M, &size, aijmax, &irank, inc, workspaceD,
// workspaceU, &size, workspaceDU, &err);
F77_CALL(dgeqrf)(&size, &size,
M, &size, // aijmax, &irank, inc, workspaceD,
workspaceU, workspaceD, &size, &err);
if (err != NOERROR) GERR("QR decomposition failed");
ErrorHandling:
if (aijmax != NULL) free(aijmax);
if (inc != NULL) free(inc);
if (workspaceD != NULL) free(workspaceD);
if (workspaceU != NULL) free(workspaceU);
if (workspaceDU != NULL) free(workspaceDU);
if (err == NOERROR) break;
break;
}
case 2 : {// SVD
double optim_lwork,
tol = GLOBAL.general.matrixtolerance,
*VT = NULL,
*work = NULL,
*U = NULL,
*D = NULL;
int k,
lwork = -1,
*iwork = NULL;
if ((VT =(double *) MALLOC(sizeof(double) * sizeSq))==NULL ||
(U =(double *) MALLOC(sizeof(double) * sizeSq))==NULL ||
(D =(double *) MALLOC(sizeof(double) * size))==NULL ||
(iwork = (int *) MALLOC(sizeof(int) * 8 * size))==NULL) {
err=ERRORMEMORYALLOCATION;
goto ErrorHandling2;
}
F77_CALL(dgesdd)("A", &size, &size, M, &size, D, M, &size, VT, &size,
&optim_lwork, &lwork, iwork, &err);
if (err != NOERROR) {
err=ERRORDECOMPOSITION;
goto ErrorHandling2;
}
lwork = (int) optim_lwork;
if ((work = (double *) MALLOC(sizeof(double) * lwork))==NULL) {
err=ERRORMEMORYALLOCATION;
goto ErrorHandling2;
}
F77_CALL(dgesdd)("A", &size, &size, M, &size, D, U, &size, VT, &size,
work, &lwork, iwork, &err);
if (err==NOERROR && ISNAN(D[0])) err=9999;
if (err!=NOERROR) {
if (PL>PL_ERRORS) PRINTF("Error code F77_CALL(dgesdd) = %d\n", err);
err=ERRORDECOMPOSITION;
goto ErrorHandling2;
}
/* calculate SQRT of covariance matrix */
for (k=0, j=0; j<size; j++) {
double dummy;
dummy = fabs(D[j]) < tol ? 0.0 : 1.0 / D[j];
for (i=0; i<size; i++) U[k++] *= dummy;
}
matmult(U, VT, M, size, size, size); // U * V
ErrorHandling2:
if (VT != NULL) free(VT);
if (U != NULL) free(U);
if (D != NULL) free(D);
if (iwork != NULL) free(iwork);
if (work != NULL) free(work);
break;
}
default : BUG;
} // switch
if (err==NOERROR) break;
}
if (SICH != NULL) free(SICH);
// printf("method %d %d %d\n", method, m, nMeth);
if (method<0 || m>=nMeth) SERR("matrix inversion failed");
return NOERROR; // -method;
}
int invertMatrix(double *M, int size) {
return invertMatrix(M, size, GLOBAL.general.matrix_inversion, MAXINVERSIONS);
}
//void solveMatrix(int method, double *M, double *v, double *res, int size) {
// // alles symmetrische matrizen!!
// // http://www.nag.com/numeric/fl/nagdoc_fl23/xhtml/F01/f01intro.xml
// int i,j, k // err,
// //sizeSq = size * size
// ;
// // double *U;
//
// for (i=k=0; i<size; i++) {
// double dummy = 0.0;
// for (j=0; j<size; j++) dummy += M[k++] * v[j];
// res[i] = dummy;
// }
/*
switch(method) {
case 0 : // cholesky
double dummy;
for (i=0; i<size; i++) res[i] = 0.0;
for (i=k=0; i<size; i++) {
dummy = v[i];
for (j=0; j<size; j++) res[j] += M[k++] * dummy;
}
break;
case 1 : // QR
double dummy;
for (i=k=0; i++; i<size) {
dummy = 0.0;
for (j=0; j++; j<size) dummy += M[k++] * v[j];
res[i] = dummy;
}
break;
case 2 : // SVD
double dummy;
for (i=0; i<size; i++) res[i] = 0.0;
for (i=k=0; i<size; i++) {
dummy = v[i];
for (j=0; j<size; j++) res[j] += M[k++] * dummy;
}
break;
default : BUG;
}
*/
//}
void memory_copy(void *dest, void *src, int bytes) {
int i,
len = bytes / sizeof(int),
*d = (int*) dest,
*s = (int *) src;
if ((len * (int) sizeof(int)) != bytes) {
//printf("%d %d\n", bytes, len);
ERR("size not a multiple of int");
}
for (i=0; i<len; i++) d[i] = s[i];
}
SEXP distInt(SEXP XX, SEXP N, SEXP Genes) {
int i,j, k, di, diff, *x, *y, ve, ho, endfor,
*X = INTEGER(XX),
n = INTEGER(N)[0],
nP1 = n + 1,
genes = INTEGER(Genes)[0];
SEXP Dist;
PROTECT(Dist = allocMatrix(REALSXP, n, n));
double *dist = REAL(Dist);
x = y = X;
for (j=0, i=0; j<n; i += nP1, j++, y += genes) {
dist[i] = 0.0;
endfor = i + (n - j);
for (ve = i + 1, ho = i + n, x = y + genes;
ve < endfor;
ve++, ho += n) {
for (di=0.0, k=0; k<genes; k++, x++) {
diff = *x - y[k];
di += diff * diff;
}
dist[ve] = dist[ho] = sqrt((double) di);
}
}
UNPROTECT(1);
return Dist;
}
/*
SEXP GetChar(SEXP N, SEXP Choice, SEXP Shorter, SEXP Beep, SEXP Show) {
int i, j,
start = NA_INTEGER,
milli = 500,
len = length(Choice),
n = INTEGER(N)[0],
nline = 100;
bool shorter = LOGICAL(Shorter)[0],
piep = LOGICAL(Beep)[0],
show = LOGICAL(Show)[0];
char choice[256], *zk,
backspace = 127,
eof = 'e'; // crl-D, ^D
SEXP Zk;
zk = (char*) MALLOC(sizeof(char) * (n+1));
if (len > 256) len = 256;
for (i=0; i<len; i++) {
choice[i] = CHAR(STRING_ELT(Choice, i))[0];
}
system("/bin/stty cbreak -echo iuclc"); // or "stty raw"
for (j=0; j<n; ) {
if (j % nline == 0) {
start = j;
if (show) {
if (j != 0) PRINTF("\n");
int m = n-j;
if (m > nline) m = nline;
for (i=0; i<m; i++) if (i % 20 == 19) PRINTF(":"); else PRINTF(".");
for (i=0; i<m; i++) PRINTF("\b");
}
}
zk[j] = getchar();
if (zk[j] == eof && shorter) break;
if (zk[j] == backspace && j>start) {
j--;
PRINTF("\b \b");
continue;
}
for (i=0; i<len; i++)
if (zk[j] == choice[i]) break;
if (i < len) {
if (show) PRINTF("%c", zk[j], n-1-j);
j++;
} else {
if (piep) PRINTF("beep does not work.\n"); // beep();
}
}
// beep();
if (show) {
PRINTF("\n");
sleepMilli(&milli);
}
system("/bin/stty -cbreak echo -iuclc");
zk[j] = '\0';
PROTECT(Zk = allocVector(STRSXP, 1));
SET_STRING_ELT(Zk, 0, mkChar(zk));
UNPROTECT(1);
return Zk;
}
*/
void strcopyN(char *dest, const char *src, int n) {
if (n > 1) {
n--;
strncpy(dest, src, n);
}
dest[n] = '\0';
}
void I0ML0(double *x, int *n) {
int i;
for (i=0; i<*n; i++) x[i] = I0mL0(x[i]);
}
double I0mL0(double x){
/* Bessel I_0 - Struve L_0 for non-negative arguments x */
/* see J. MacLeod, Chebyshev expansions for modified {S}truve and
related functions, Mathematics of Computation, 60, 735-747, 1993 */
static double g2[24] = {
0.52468736791485599138e0,
-0.35612460699650586196e0,
0.20487202864009927687e0,
-0.10418640520402693629e0,
0.4634211095548429228e-1,
-0.1790587192403498630e-1,
0.597968695481143177e-2,
-0.171777547693565429e-2,
0.42204654469171422e-3,
-0.8796178522094125e-4,
0.1535434234869223e-4,
-0.219780769584743e-5,
0.24820683936666e-6,
-0.2032706035607e-7,
0.90984198421e-9,
0.2561793929e-10,
-0.710609790e-11,
0.32716960e-12,
0.2300215e-13,
-0.292109e-14,
-0.3566e-16,
0.1832e-16,
-0.10e-18,
-0.11e-18
};
static double g3[24] = {
2.00326510241160643125e0,
0.195206851576492081e-2,
0.38239523569908328e-3,
0.7534280817054436e-4,
0.1495957655897078e-4,
0.299940531210557e-5,
0.60769604822459e-6,
0.12399495544506e-6,
0.2523262552649e-7,
0.504634857332e-8,
0.97913236230e-9,
0.18389115241e-9,
0.3376309278e-10,
0.611179703e-11,
0.108472972e-11,
0.18861271e-12,
0.3280345e-13,
0.565647e-14,
0.93300e-15,
0.15881e-15,
0.2791e-16,
0.389e-17,
0.70e-18,
0.16e-18
};
double r, x2, ac;
int i;
if (x < 0.0) {return RF_NA;}
if (x < 16.0) {
r = 0.5 * g2[0];
ac = acos((6.0 * x - 40.0) / (x + 40.0));
for (i=1; i<24; i++) {
r += g2[i] * cos(i * ac);
}
} else {
r = 0.5 * g3[0];
x2 = x * x;
ac = acos((800.0 - x2) / (288.0 + x2));
for (i=1; i<24; i++) {
r += g3[i] * cos(i * ac);
}
r *= T_PI /* 2/pi */ / x;
}
return r;
}
void StruveH(double *x, double *nu) {*x=struve(*x, *nu, -1.0, false);}
void StruveL(double *x, double *nu, int * expScaled)
{
*x=struve(*x, *nu, 1.0, (bool) *expScaled);
}
double struve(double x, double nu, double factor_sign, bool expscaled)
{
double sign, value, epsilon=1e-20;
double dummy, logx, x1, x2;
if ((x==0.0) && (nu>-1.0)) return 0.0;
if (x<=0) return RF_NA; // not programmed yet
logx = log(0.5 * x);
x1=1.5;
x2=nu+1.5;
sign=1.0;
if (x2 > 0.0) {
dummy = (nu + 1.0) * logx - lgammafn(x1) - lgammafn(x2);
if (expscaled) dummy -= x;
value = exp(dummy);
} else {
if ( (double) ((int) (x1-0.5)) != x1-0.5 ) return RF_NA;
value=pow(0.5 * x, nu + 1.0) / (gammafn(x1) * gammafn(x2));
if (expscaled) value *= exp(-x);
if ((dummy= value) <0) {
dummy = -dummy;
sign = -1.0;
}
dummy = log(dummy);
}
logx *= 2.0;
do {
if (x2<0) { sign = -sign; }
dummy += logx - log(x1) - log(fabs(x2));
value += sign * exp(dummy);
x1 += 1.0;
x2 += 1.0;
sign = factor_sign * sign;
} while (exp(dummy) > fabs(value) * epsilon);
return value;
}
SEXP vectordist(SEXP V, SEXP DIAG){
bool notdiag = !LOGICAL(DIAG)[0];
int
d, dr,
rows = nrows(V),
cols = ncols(V),
rescols = (int) (cols * (cols - 1 + 2 * (int) !notdiag) / 2);
double *v1, *v2, *end, *Dist,
*v = REAL(V);
end = v + cols * rows;
SEXP DIST;
PROTECT(DIST = allocMatrix(REALSXP, rows, rescols));
Dist = REAL(DIST);
for (dr=0, v1=v; v1<end; v1+=rows) { // loop is one to large??
v2 = v1;
if (notdiag) {
v2 += rows;
}
for (; v2<end; ) {
for (d=0; d<rows; v2++) {
Dist[dr++] = v1[d++] - *v2;
}
}
}
UNPROTECT(1);
return DIST;
}
static int ORDERDIM;
static double *ORDERD;
static int *ORDERDINT;
typedef bool (*vergleich)(int, int);
vergleich SMALLER=NULL, GREATER=NULL;
bool smaller(int i, int j)
{
double *x, *y;
int d;
x = ORDERD + i * ORDERDIM;
y = ORDERD + j * ORDERDIM;
for(d=0; d<ORDERDIM; d++)
if (x[d] != y[d]) return x[d] < y[d];
return false;
}
bool greater(int i, int j)
{
double *x, *y;
int d;
x = ORDERD + i * ORDERDIM;
y = ORDERD + j * ORDERDIM;
for(d=0; d<ORDERDIM; d++)
if (x[d] != y[d]) return x[d] > y[d];
return false;
}
bool smallerInt(int i, int j)
{
int *x, *y;
int d;
x = ORDERDINT + i * ORDERDIM;
y = ORDERDINT + j * ORDERDIM;
for(d=0; d<ORDERDIM; d++)
if (x[d] != y[d]) return x[d] < y[d];
return false;
}
bool greaterInt(int i, int j)
{
int *x, *y;
int d;
x = ORDERDINT + i * ORDERDIM;
y = ORDERDINT + j * ORDERDIM;
for(d=0; d<ORDERDIM; d++)
if (x[d] != y[d]) return x[d] > y[d];
return false;
}
int is_positive_definite(double *C, int dim) {
int err,
bytes = sizeof(double) * dim * dim;
double *test;
test = (double*) MALLOC(bytes);
MEMCOPY(test, C, bytes);
F77_CALL(dpofa)(test, &dim, &dim, &err);
free(test);
return(err == 0);
}
void order(int *pos, int start, int end) {
int randpos, pivot, left, right, pivotpos, swap;
if( start < end ) {
//Get RNGstate();randpos = start + (int) (UNIFORM_RANDOM * (end-start+1)); PutRNGstate(); // use Get/Put RNGstate with great care !!
randpos = (int) (0.5 * (start + end));
pivot = pos[randpos];
pos[randpos] = pos[start];
pos[start] = pivot;
pivotpos=start;
left = start;
right=end+1;
while (left < right) {
while (++left < right && SMALLER(pos[left], pivot)) pivotpos++;
while (--right > left && GREATER(pos[right], pivot));
if (left < right) {
swap=pos[left]; pos[left]=pos[right]; pos[right]=swap;
pivotpos++;
}
}
pos[start] = pos[pivotpos];
pos[pivotpos] = pivot;
order(pos, start, pivotpos-1 );
order(pos, pivotpos + 1, end );
}
}
void ordering(double *d, int len, int dim, int *pos)
{
/* quicksort algorithm, slightly modified:
does not sort the data, but d[pos] will be ordered
NOTE: pos must have the values 0,1,2,...,start-end !
(orderdouble is a kind of sorting pos according to
the variable d)
*/
int i;
for (i=0; i<len;i++) pos[i]=i;
ORDERD = d;
ORDERDIM = dim;
SMALLER = smaller;
GREATER = greater;
order(pos, 0, len-1);
}
void Ordering(double *d, int *len, int *dim, int *pos)
{
int i;
for (i=0; i<*len; i++) pos[i]=i;
ORDERD = d;
ORDERDIM = *dim;
SMALLER = smaller;
GREATER = greater;
//intf("%d %d %d \n", pos[0], pos[1], *len - 1);assert(false);
order(pos, 0, *len-1 );
}
void orderingInt(int *d, int len, int dim, int *pos)
{
/* quicksort algorithm, slightly modified:
does not sort the data, but d[pos] will be ordered
NOTE: pos must have the values 0,1,2,...,start-end !
(orderdouble is a kind of sorting pos according to
the variable d)
*/
int i;
for (i=0; i<len;i++) pos[i]=i;
ORDERDINT = d;
ORDERDIM = dim;
SMALLER = smallerInt;
GREATER = greaterInt;
order(pos, 0, len-1);
}
int xMatch(char *name, char **list, unsigned int llen) {
unsigned int ln, nr;
// == -1 if no matching function is found
// == -2 if multiple matching fctns are found, without one matching exactly
// if more than one match exactly, the last one is taken (enables overwriting
// standard functions)
// see also GetModelNr !
nr=0;
ln=(unsigned int) strlen(name);
while ((nr < llen) && strncmp(name, list[nr], ln)) nr++;
if (nr < llen) {
// a matching method is found. Are there other methods that match?
unsigned int j;
if (ln == (unsigned int) strlen(list[nr])) return nr; // exact matching
j = nr + 1; // if two or more methods have the same name the last one is
// taken; stupid here, but nice in GetCovNr
while (j < llen && strncmp(name, list[j], ln)) j++;
if (j < llen) {
if (ln == (unsigned int) strlen(list[j])) return j; //exact matching
else return -2; // multiple matching
}
return nr;
} else return -1; // unmatched
}
int CeilIndex(double x, double *cum, int size) {
// der kleinste index i so das cum[i] >= x --- sollte das gleiche sein
// wie searchFirstGreater
int mitte,
min = 0,
max = size - 1;
while (min < max) {
mitte = 0.5 * (min + max);
if (cum[mitte] >= x) max = mitte;
else min = mitte + 1;
}
// printf("%f < %f <= %f\n", cum[min-1], x, cum[min]);
assert((min==0) || x > cum[min-1]);
assert(x <= cum[min] && (min==0 || x > cum[min-1]));
return min;
}
/*
int searchFirstGreater(double *v, int len, double z) {
// assumes the list has non decreasing values
int
firsti = 0,
lasti = len - 1,
i = len / 2;
if (z > v[lasti]) {
BUG;
}
if (z <= v[firsti]) return firsti;
while (firsti < lasti) {
if (v[i] < z) {
firsti = i + 1;
i = i + (int) ((lasti - i + 1) / 2);
} else { // v[i] <= z
lasti = i;
i = i - (int) ((i - firsti + 1) / 2);
}
}
assert((i==0) || z > v[i-1]);
assert(z <= v[i]);
// printf("%f < %f <= %f\n", v[i-1], z, v[i]);//
}
*/
/*
double searchInverse(isofct fct, double start, double *value,
double releps) {
while (fct(start, cov) > value) start *= 2.0;
while (fct(start, cov) < value) start *= 0.5;
double x = start,
step = start;
releps *= start;
while (step > releps) {
step *= 0.5;
if (fct(step, cov) < value) x -= step; else x += step;
}
}
*/
double searchInverse(covfct fct, cov_model *cov,
double start, double value, double releps) {
double v;
fct(&start, cov, &v);
while (v > value) {start *= 2.0; fct(&start, cov, &v);}
while (v < value) {start *= 0.5; fct(&start, cov, &v);}
double x = start,
step = start;
releps *= step;
while (step > releps) {
step *= 0.5;
fct(&step, cov, &v);
if (v < value) x -= step; else x += step;
}
return x;
}
double searchInverse(covfct fct, cov_model *cov,
double start, double min, double value, double releps) {
double v;
assert(start > min);
fct(&start, cov, &v);
while (v > value) {start = 2.0 * (start - min) + min; fct(&start, cov, &v);}
while (v < value) {start = 0.5 * (start - min) + min; fct(&start, cov, &v);}
double x = start,
step = start - min;
releps *= step;
while (step > releps) {
step *= 0.5;
fct(&step, cov, &v);
if (v < value) x -= step; else x += step;
}
return x;
}
//double gamma(double x) { BUG; } // use gammafn instead
double incomplete_gamma(double start, double end, double s) {
// int_start^end t^{s-1} e^{-t} \D t
// print("incomplete IN s=%f e=%f s=%f\n", start, end, s);
double
v = 0.0,
w = 0.0;
if (s <= 1.0) {
if (start == 0.0) return RF_NA;
}
double
e_start = exp(-start),
e_end = exp(-end),
power_start = pow(start, s),
power_end = end < RF_INF ? pow(end, s) : 0,
factor = 1.0;
while (s < 0.0) {
factor /= s;
v += factor * (power_end * e_end - power_start * e_start);
power_start *= start;
if (end < RF_INF) power_end *= end;
s += 1.0;
}
w = pgamma(start, s, 1.0, false, false); // q, shape, scale, lower, log
if (R_FINITE(end)) w -= pgamma(end, s, 1.0, false, false);
// print("incomplete s=%f e=%f s=%f v=%f g=%f w=%f\n", start, end, s, v, gammafn(s), w);
return v + gammafn(s) * w * factor;
}
int addressbits(void VARIABLE_IS_NOT_USED *addr) {
#ifndef RANDOMFIELDS_DEBUGGING
return 0;
#else
double x = (intptr_t) addr,
cut = 1e9;
x = x - trunc(x / cut) * cut;
return (int) x;
#endif
}
