https://github.com/cran/RandomFields
Tip revision: e10243fbd4eb0cbeaf518e67fbc5b8ad44889954 authored by Martin Schlather on 12 December 2019, 13:40:13 UTC
version 3.3.7
version 3.3.7
Tip revision: e10243f
primitive.cov.cc
/*
Authors
Martin Schlather, schlather@math.uni-mannheim.de
Definition of correlation functions and derivatives (spectral measures,
tbm operators)
Copyright (C) 2001 -- 2003 Martin Schlather
Copyright (C) 2004 -- 2004 Yindeng Jiang & Martin Schlather
Copyright (C) 2005 -- 2017 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 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., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
#include <Rmath.h>
#include <R_ext/Lapack.h>
#include <R_ext/Linpack.h>
#include "questions.h"
#include "primitive.h"
#include "operator.h"
#include "AutoRandomFields.h"
#include "shape.h"
#include "Processes.h"
//#define LOG2 M_LN2
#define i11 0
#define i21 1
#define i22 2
#define epsilon 1e-15
#define GOLDENR 0.61803399
#define GOLDENC (1.0 -GOLDENR)
#define GOLDENTOL 1e-8
#define GOLDENSHIFT2(a, b, c) (a) = (b); (b) = (c);
#define GOLDENSHIFT3(a, b, c, d) (a) = (b); (b) = (c); (c) = (d);
double BesselUpperB[Nothing + 1] =
{80, 80, 80, // circulant
80, RF_INF, // TBM
80, 80, // direct & sequ
RF_NA, RF_NA, RF_NA, // GMRF, ave, nugget
RF_NA, RF_NA, RF_NA, // exotic
RF_INF // Nothing
};
double interpolate(double y, double *stuetz, int nstuetz, int origin,
double lambda, int delta)
{
int index,minindex,maxindex,i;
double weights,sum,diff,a;
index = origin + (int) y;
minindex = index - delta; if (minindex<0) minindex=0;
maxindex = index + 1 + delta; if (maxindex>nstuetz) maxindex=nstuetz;
weights = sum = 0.0;
for (i=minindex;i<maxindex;i++) {
diff = y + (double) (index-i);
a = EXP( -lambda * diff * diff);
weights += a;
sum += a * stuetz[i]; // or a/stuetz[i]
}
return (double) (weights/sum); // and then sum/weights
}
/* BCW */
#define BCW_ALPHA 0
#define BCW_BETA 1
#define BCW_C 2
#define BCW_EPS 1e-7
#define BCW_TAYLOR_ZETA \
(- LOG2 * (1.0 + 0.5 * zetalog2 * (1.0 + ONETHIRD * zetalog2)))
#define BCW_CAUCHY (POW(1.0 + POW(*x, alpha), zeta) - 1.0)
void bcw(double *x, model *cov, double *v){
double alpha = P0(BCW_ALPHA), beta=P0(BCW_BETA),
zeta = beta / alpha,
absZeta = FABS(zeta);
if (absZeta > BCW_EPS)
*v = BCW_CAUCHY / (1.0 - POW(2.0, zeta));
else {
double dewijs = LOG(1.0 + POW(*x, alpha)),
zetadewijs = zeta * dewijs,
zetalog2 = zeta * LOG2
;
if (FABS(zetadewijs) > BCW_EPS)
*v = BCW_CAUCHY / (zeta * BCW_TAYLOR_ZETA);
else {
*v = dewijs * (1.0 + 0.5 * zetadewijs * (1.0 + ONETHIRD *zetadewijs))
/ BCW_TAYLOR_ZETA;
}
}
if (!PisNULL(BCW_C)) *v += P0(BCW_C);
}
void Dbcw(double *x, model *cov, double *v){
double ha,
alpha = P0(BCW_ALPHA),
beta=P0(BCW_BETA),
zeta=beta / alpha,
y=*x;
if (y ==0.0) {
*v = (alpha > 1.0) ? 0.0 : (alpha < 1.0) ? RF_INF : alpha;
} else {
ha = POW(y, alpha - 1.0);
*v = alpha * ha * POW(1.0 + ha * y, zeta - 1.0);
}
if (FABS(zeta) > BCW_EPS) *v *= zeta / (1.0 - POW(2.0, zeta));
else {
double zetalog2 = zeta * LOG2;
*v /= BCW_TAYLOR_ZETA;
}
}
void DDbcw(double *x, model *cov, double *v){
double
alpha = P0(BCW_ALPHA),
beta = P0(BCW_BETA),
zeta = beta / alpha,
y=*x;
if (y == 0.0) {
*v = alpha==2.0 ? alpha * (alpha - 1.0) :
alpha==1.0 ? beta - 1.0 :
alpha > 1.0 ? RF_INF : RF_NEGINF;
} else {
double ha2 = POW(y, alpha - 2),
ha = ha2 * y * y;
*v = alpha * ha2 * (alpha - 1.0 + (beta - 1.0) * ha) *
POW(1.0 + ha, zeta- 2.0);
}
if (FABS(zeta) > BCW_EPS) *v *= zeta / (1.0 - POW(2.0, zeta));
else {
double zetalog2 = zeta * LOG2;
*v /= BCW_TAYLOR_ZETA;
}
}
void D3bcw(double *x, model *cov, double *v){
double
alpha = P0(BCW_ALPHA),
beta=P0(BCW_BETA),
zeta = beta / alpha,
absZeta = FABS(zeta),
y=*x;
if (y == 0.0) {
*v = RF_INF;
} else {
double
ha3 = POW(y, alpha - 3),
ha = ha3 * y * y * y;
*v = alpha * POW(1.0 + ha, zeta - 3.0) * ha3 *
( (beta - 1.0) * (beta - 2.0) * ha * ha +
(alpha -1.0) * (3.0 * beta - alpha - 4.0) * ha +
(alpha - 2.0) * (alpha - 1.0) );
}
if (absZeta > BCW_EPS) *v *= zeta / (1.0 - POW(2.0, zeta));
else {
double zetalog2 = zeta * LOG2;
*v /= BCW_TAYLOR_ZETA;
}
}
void D4bcw(double *x, model *cov, double *v){
double
alpha = P0(BCW_ALPHA),
beta=P0(BCW_BETA),
zeta = beta / alpha,
absZeta = FABS(zeta),
y = *x;
if (y == 0.0) {
*v = RF_INF;
} else {
// olga please counter check, also for cauchy
double
ha4 = POW(y, alpha - 4),
y2q = y * y,
//alphaSq = alpha * alpha,
a123 = (alpha - 1.0) * (alpha - 2.0) * (alpha - 3.0),
a1 = alpha - 1,
coefha = -a1* (alpha * (4*alpha - 7*beta + 4) + 11 * beta - 18 ),
coefha2 = a1 * (-4*alpha*beta + alpha*(alpha + 7) + 6*beta*beta
-22*beta +18),
b1b2b3 = (beta - 1.0) * (beta - 2.0) * (beta - 3.0),
ha = ha4 * y2q * y2q;
*v = alpha * ha4 *
( a123 +
coefha * ha +
coefha2 * ha * ha +
b1b2b3 * ha * ha * ha
);
// *v = alpha * ha / (y * y * y * y) * (alpha*alpha*alpha*(ha*ha - 4*ha +1)
// +alpha*alpha*(-4*beta*ha*ha + 7*beta*ha + 6*ha*ha -6 )
// -2*(3*beta*beta - 11*beta +9)*ha*ha
// +alpha*((6*beta*beta -18*beta + 11)*ha*ha + (22-18*beta)*ha +11 )
// +(beta*beta*beta - 6*beta*beta +11*beta - 6)*ha*ha*ha
// + (11*beta - 18)*ha - 6)
// * POW(1.0 + ha, beta / alpha - 4.0);
}
if (absZeta > BCW_EPS) *v *= zeta / (1.0 - POW(2.0, zeta));
else {
double zetalog2 = zeta * LOG2;
*v /= BCW_TAYLOR_ZETA;
}
}
void Inversebcw(double *x, model *cov, double *v) {
double
alpha = P0(BCW_ALPHA),
beta=P0(BCW_BETA),
zeta = beta / alpha,
y = *x;
if (y == 0.0) {
*v = beta < 0.0 ? RF_INF : 0.0;
return;
}
if (!PisNULL(BCW_C)) y = P0(BCW_C) - y;
if (zeta != 0.0)
*v = POW(POW(y * (POW(2.0, zeta) - 1.0) + 1.0, 1.0/zeta) - 1.0,
1.0/alpha);
else
*v = POW(EXP(y * LOG2) - 1.0, 1.0 / alpha);
}
int checkbcw(model *cov) {
double
alpha = P0(BCW_ALPHA),
beta=P0(BCW_BETA);
if (OWNLOGDIM(0) > 2)
cov->pref[CircEmbedCutoff] = cov->pref[CircEmbedIntrinsic] = PREF_NONE;
cov->logspeed = beta > 0 ? RF_INF : beta < 0.0 ? 0 : alpha * INVLOG2;
RETURN_NOERROR;
}
void rangebcw(model *cov, range_type *range) {
bool tcf = isnowTcf(cov) || equalsSphericalIsotropic(OWNISO(0));
bool posdef = isnowPosDef(cov) && PisNULL(BCW_C); // tricky programming
range->min[BCW_ALPHA] = 0.0;
range->max[BCW_ALPHA] = tcf ? 1.0 : 2.0;
range->pmin[BCW_ALPHA] = 0.05;
range->pmax[BCW_ALPHA] = range->max[BCW_ALPHA];
range->openmin[BCW_ALPHA] = true;
range->openmax[BCW_ALPHA] = false;
range->min[BCW_BETA] = RF_NEGINF;
range->max[BCW_BETA] = posdef ? 0.0 : 2.0;
range->pmin[BCW_BETA] = - 10.0;
range->pmax[BCW_BETA] = 2.0;
range->openmin[BCW_BETA] = true;
range->openmax[BCW_BETA] = posdef;
range->min[BCW_C] = 0;
range->max[BCW_C] = RF_INF;
range->pmin[BCW_C] = 0;
range->pmax[BCW_C] = 1000;
range->openmin[BCW_C] = false;
range->openmax[BCW_C] = true;
}
void coinitbcw(model *cov, localinfotype *li) {
double
beta=P0(BCW_BETA);
if (beta < 0) coinitgenCauchy(cov, li);
else {
if (beta == 0) coinitdewijsian(cov, li);
else {
double thres[2] = {0.5, 1.0},
thresBeta[2] = {0.5, 1.0},
alpha=P0(BCW_ALPHA);
if (beta <= thresBeta[0] && alpha <= thres[0]) {
li->instances = 2;
li->value[0] = 0.5;
li->value[1] = 1.0;
li->msg[0] = li->msg[1] = MSGLOCAL_OK;
} else {
if (beta <= thresBeta[0] && alpha > thres[0] && alpha <= thres[1]) {
li->instances = 1;
li->value[0] = 1.0;
li->msg[0] = MSGLOCAL_OK;
} else {
if (beta>thresBeta[0] && beta <= thresBeta[1] && alpha <= thres[1]) {
li->instances = 1;
li->value[0] = 1.0;
li->msg[0] = MSGLOCAL_OK;
} else {
if (beta > thresBeta[1] && alpha <= thres[0] ) {
li->instances = 1;
li->instances = 1;
li->value[0] = CUTOFF_THIRD_CONDITION ;
li->msg[0] = MSGLOCAL_JUSTTRY;
} else {
li->instances = 0;
}
}
}
}
}
}
}
//void coinitbcw(model *cov, localinfotype *li) {
// double
// beta=P0(BCW_BETA);
// if (beta < 0) coinitgenCauchy(cov, li);
// else {
// li->instances = 0;
// }
//}
void ieinitbcw(model *cov, localinfotype *li) {
if (P0(BCW_BETA) < 0) ieinitgenCauchy(cov, li);
else {
ieinitBrownian(cov, li); // to do: can nicht passen!!
// todo: nachrechnen, dass OK!
}
}
#define LOW_BESSELJ 1e-20
#define LOW_BESSELK 1e-20
#define BESSEL_NU 0
void Bessel(double *x, model *cov, double *v){
// printf("bessel chec \n");
/*
GR 8.402: Bessel(2 x SQRT(nu), nu) -> e^(-x^2)
Differenz des k-ten koeffizienten in Taylor zu Gauss(ohne gemeinsame Faktoren):
1 - 1 / [ (1+k/nu)(1+(k-1)/nu) ... (1 + 1/nu) ] \approx 0.5 k(k+1) / nu.
Also ist der Abstand zu ungefaehr
e^(-x^2) - Bessel(2 x SQRT(nu), nu) \approx F / nu
fuer irgendein F > 0.
Also
e^(-x^2) - Bessel(2 x SQRT(nu), nu) \approx
nu0 nu^{-1} [ e^(-x^2) - Bessel(2 x SQRT(nu0), nu0) ]
*/
double nu = P0(BESSEL_NU),
nuThres = nu <= BESSEL_NU_THRES ? nu : BESSEL_NU_THRES,
y=*x,
bk[BESSEL_NU_THRES + 1L];
if (y <= LOW_BESSELJ) {*v = 1.0; return;}
if (y == RF_INF) {*v = 0.0; return;} // also for cosine i.e. nu=-1/2
assert(cov->qlen != 0 && cov->q != NULL);
//PMI(cov);
// printf("%10g %10g\n", nu, QVALUE);
*v = QVALUE * POW(2.0 / y, nuThres) * bessel_j_ex(y, nuThres, bk);
if (nu > BESSEL_NU_THRES) { // factor!=0.0 &&
// printf("UU \n");
double w,
g = BESSEL_NU_THRES / nu;
y = 0.5 * *x / SQRT(nuThres);
Gauss(&y, NULL, &w);
*v = *v * g + (1.0 - g) * w;
}
}
int initBessel(model *cov, gen_storage
VARIABLE_IS_NOT_USED *s) {
// printf("init chec \n");
assert(cov->q != NULL);
double nu = P0(BESSEL_NU),
nuThres = nu <= BESSEL_NU_THRES ? nu : BESSEL_NU_THRES;
QVALUE = gammafn(nuThres+1.0);
// printf("intit end chec \n");
ASSERT_GAUSS_METHOD(SpectralTBM);
RETURN_NOERROR;
}
int checkBessel(model *cov) {
// printf("chec \n");
// Whenever TBM3Bessel exists, add further check against too small nu!
double nu = P0(BESSEL_NU);
int i;
double dim = (2.0 * P0(BESSEL_NU) + 2.0);
for (i=0; i<= Nothing; i++)
cov->pref[i] *= ((bool) ISNAN(nu)) || nu < BesselUpperB[i];
if (OWNLOGDIM(0)>2) cov->pref[SpectralTBM] = PREF_NONE; // do to d > 2 !
set_maxdim(OWN, 0, ISNAN(dim) || dim >= INFDIM ? INFDIM : (int) dim);
if (cov->q == NULL) {
EXTRA_Q;
initBessel(cov, NULL);
}
// printf("chec e\n");
RETURN_NOERROR;
}
void spectralBessel(model *cov, gen_storage *S, double *e) {
spectral_storage *s = &(S->Sspectral);
double
nu = P0(BESSEL_NU);
/* see Yaglom ! */
// nu==0.0 ? 1.0 : // not allowed anymore;
// other wise densityBessel (to define) will not work
if (nu >= 0.0) {
E12(s, OWNLOGDIM(0), nu > 0 ? SQRT(1.0 - POW(UNIFORM_RANDOM, 1/nu)) : 1, e);
} else {
double A;
assert(OWNLOGDIM(0) == 1);
if (nu == -0.5) A = 1.0;
else { // siehe private/bessel.pdf, p. 6, Remarks
// http://homepage.tudelft.nl/11r49/documents/wi4006/bessel.pdf
while (true) {
A = 1.0 - POW(UNIFORM_RANDOM, 1.0 / ( P0(BESSEL_NU) + 0.5));
if (UNIFORM_RANDOM <= POW(1 + A, nu - 0.5)) break;
}
}
E1(s, A, e);
}
}
void rangeBessel(model *cov, range_type *range){
range->min[BESSEL_NU] = 0.5 * ((double) OWNLOGDIM(0) - 2.0);
range->max[BESSEL_NU] = RF_INF;
range->pmin[BESSEL_NU] = 0.0001 + range->min[BESSEL_NU];
range->pmax[BESSEL_NU] = range->pmin[BESSEL_NU] + 10.0;
range->openmin[BESSEL_NU] = false;
range->openmax[BESSEL_NU] = true;
}
/* circular model */
void circular(double *x, model VARIABLE_IS_NOT_USED *cov, double *v) {
double y = *x;
*v = 0.0;
if (y < 1.0) *v = 1.0 - (2.0 * (y * SQRT(1.0 - y * y) + ASIN(y))) * INVPI;
}
void Dcircular(double *x, model VARIABLE_IS_NOT_USED *cov, double *v){
double y = *x * *x;
*v = 0.0;
if (y < 1.0) *v =-4 * INVPI * SQRT(1.0 - y);
}
int structCircSph(model *cov, model **newmodel, int dim) {
ASSERT_NEWMODEL_NOT_NULL;
switch (cov->frame) {
case PoissonGaussType :
{
addModel(newmodel, BALL, cov);
addModel(newmodel, DOLLAR);
addModelKappa(*newmodel, DSCALE, SCALESPHERICAL);
kdefault((*newmodel)->kappasub[DSCALE], SPHERIC_SPACEDIM,
(double) OWNLOGDIM(0));
kdefault((*newmodel)->kappasub[DSCALE], SPHERIC_BALLDIM, (double) dim);
}
break;
case PoissonType : return addUnifModel(cov, 1.0, newmodel); // to do: felix
case SmithType : return addUnifModel(cov, 1.0, newmodel);
default:
BUG;
}
RETURN_NOERROR;
}
int structcircular(model *cov, model **newmodel) {
return structCircSph(cov, newmodel, 2);
}
/* coxgauss, cmp with nsst1 !! */
// see Gneiting.cc
/* cubic */
void cubic(double *x, model VARIABLE_IS_NOT_USED *cov, double *v) {
double y=*x, y2=y * y;
*v = 0.0;
if (y < 1.0) *v = (1.0 + (((0.75 * y2 - 3.5) * y2 + 8.75) * y - 7) * y2);
}
void Dcubic(double *x, model VARIABLE_IS_NOT_USED *cov, double *v) {
double y=*x, y2=y * y;
*v = 0.0;
if (y < 1.0) *v = y * (-14.0 + y * (26.25 + y2 * (-17.5 + 5.25 * y2)));
}
/* cutoff */
// see operator.cc
/* dagum */
#define DAGUM_BETA 0
#define DAGUM_GAMMA 1
#define DAGUM_BETAGAMMA 2
#define FIRST_INIT(init) \
int xerr; \
gen_storage s; \
gen_NULL(&s); \
s.check = true; \
if ((xerr=init(cov, &s)) != NOERROR) RETURN_ERR(xerr);
void dagum(double *x, model *cov, double *v){
double gamma = P0(DAGUM_GAMMA),
beta=P0(DAGUM_BETA);
*v = 1.0 - POW((1 + POW(*x, -beta)), -gamma/beta);
}
void Inversedagum(double *x, model *cov, double *v){
double gamma = P0(DAGUM_GAMMA),
beta=P0(DAGUM_BETA);
*v = RF_INF;
if (*x != 0.0) *v = POW(POW(1.0 - *x, - beta / gamma ) - 1.0, 1.0 / beta);
}
void Ddagum(double *x, model *cov, double *v){
double y=*x, xd,
gamma = P0(DAGUM_GAMMA),
beta=P0(DAGUM_BETA);
xd = POW(y, -beta);
*v = -gamma * xd / y * POW(1 + xd, -gamma/ beta -1);
}
int checkdagum(model *cov){
if (PisNULL(DAGUM_GAMMA) || PisNULL(DAGUM_BETA))
SERR("parameters are not given all");
double
gamma = P0(DAGUM_GAMMA),
beta = P0(DAGUM_BETA);
kdefault(cov, DAGUM_BETAGAMMA, beta/gamma);
FIRST_INIT(initdagum);
cov->monotone = beta >= gamma ? MONOTONE
: gamma <= 1.0 ? COMPLETELY_MON
: gamma <= 2.0 ? NORMAL_MIXTURE : MON_MISMATCH;
RETURN_NOERROR;
}
int initdagum(model *cov, gen_storage *s) {
double
gamma = P0(DAGUM_GAMMA),
beta = P0(DAGUM_BETA),
betagamma = P0(DAGUM_BETAGAMMA);
if (s->check) {
bool tcf = isnowTcf(cov) || equalsSphericalIsotropic(OWNISO(0));
bool isna_gamma = tcf && ISNA(gamma);
if (isna_gamma) {
if (cov->q == NULL) QALLOC(1); // just as a flag
} else {
P(DAGUM_BETAGAMMA)[0] = 1.0;
// dummy value just to be in the range !
}
} else {
bool isna_gamma = cov->q != NULL;
if (isna_gamma) P(DAGUM_GAMMA)[0] = beta / betagamma;
}
RETURN_NOERROR;
}
void rangedagum(model *cov, range_type *range){
bool tcf = isnowTcf(cov) || equalsSphericalIsotropic(OWNISO(0));
range->min[DAGUM_BETA] = 0.0;
range->max[DAGUM_BETA] = 1.0;
range->pmin[DAGUM_BETA] = 0.01;
range->pmax[DAGUM_BETA] = 1.0;
range->openmin[DAGUM_BETA] = true;
range->openmax[DAGUM_BETA] = false;
range->min[DAGUM_GAMMA] = 0.0;
range->max[DAGUM_GAMMA] = tcf ? 1.0 : 2.0;
range->pmin[DAGUM_GAMMA] = 0.01;
range->pmax[DAGUM_GAMMA] = range->max[DAGUM_GAMMA];
range->openmin[DAGUM_GAMMA] = true;
range->openmax[DAGUM_GAMMA] = tcf;
range->min[DAGUM_BETAGAMMA] = 0.0;
range->max[DAGUM_BETAGAMMA] = tcf ? 1.0 : RF_INF;
range->pmin[DAGUM_BETAGAMMA] = 0.01;
range->pmax[DAGUM_BETAGAMMA] = tcf ? 1.0 : 20.0;
range->openmin[DAGUM_BETAGAMMA] = true;
range->openmax[DAGUM_BETAGAMMA] = true;
}
/* damped cosine -- derivative of e xponential:*/
#define DC_LAMBDA 0
void dampedcosine(double *x, model *cov, double *v){
double y = *x, lambda = P0(DC_LAMBDA);
*v = (y == RF_INF) ? 0.0 : EXP(-y * lambda) * COS(y);
}
void logdampedcosine(double *x, model *cov, double *v, double *Sign){
double
y = *x,
lambda = P0(DC_LAMBDA);
if (y==RF_INF) {
*v = RF_NEGINF;
*Sign = 0.0;
} else {
double cosy=COS(y);
*v = -y * lambda + LOG(FABS(cosy));
*Sign = cosy > 0.0 ? 1.0 : cosy < 0.0 ? -1.0 : 0.0;
}
}
void Inversedampedcosine(double *x, model *cov, double *v){
Inverseexponential(x, cov, v);
}
void Ddampedcosine(double *x, model *cov, double *v){
double y = *x, lambda = P0(DC_LAMBDA);
*v = - EXP(-lambda*y) * (lambda * COS(y) + SIN(y));
}
int checkdampedcosine(model *cov){
int dim = INFDIM;
if (!ISNAN(P0(DC_LAMBDA))) dim = (int) (PIHALF / ATAN(1.0 / P0(DC_LAMBDA)));
set_maxdim(OWN, 0, dim);
RETURN_NOERROR;
}
void rangedampedcosine(model *cov, range_type *range){
int dim = OWNLOGDIM(0);
if (dim <= 3)
range->min[DC_LAMBDA] = dim==1 ? 0 : dim==2 ? 1 : 1.7320508075688771932;
else range->min[DC_LAMBDA] = 1.0 / TAN(PIHALF / dim);
range->max[DC_LAMBDA] = RF_INF;
range->pmin[DC_LAMBDA] = range->min[DC_LAMBDA] + 1e-10;
range->pmax[DC_LAMBDA] = 10;
range->openmin[DC_LAMBDA] = false;
range->openmax[DC_LAMBDA] = true;
}
/* De Wijsian */
#define DEW_ALPHA 0 // for both dewijsian models
#define DEW_D 1
void dewijsian(double *x, model *cov, double *v){
double alpha = P0(DEW_ALPHA);
*v = -LOG(1.0 + POW(*x, alpha));
}
void Ddewijsian(double *x, model *cov, double *v){
double alpha = P0(DEW_ALPHA),
p = POW(*x, alpha - 1.0) ;
*v = - alpha * p / (1.0 + *x * p);
}
void DDdewijsian(double *x, model *cov, double *v){
double alpha = P0(DEW_ALPHA),
p = POW(*x, alpha - 2.0),
ha = p * *x * *x,
haP1 = ha + 1.0;
*v = alpha * p * (1.0 - alpha + ha) / (haP1 * haP1);
}
void D3dewijsian(double *x, model *cov, double *v){
double alpha = P0(DEW_ALPHA),
p = POW(*x, alpha - 3.0),
ha = p * *x * *x * *x,
haP1 = ha + 1.0,
haP12 = haP1*haP1;
*v = alpha * p * (alpha*alpha*(ha - 1) +3*alpha*haP1 -2*haP12 )
/ (haP1 * haP12);
}
void D4dewijsian(double *x, model *cov, double *v){
double alpha = P0(DEW_ALPHA),
alpha2 = alpha*alpha,
p = POW(*x, alpha - 4.0),
ha = p * *x * *x * *x* *x,
haSq = ha * ha,
haP1 = ha + 1.0,
haP12 = haP1*haP1;
*v = -alpha * p * (alpha2*alpha*(haSq - 4*ha + 1) +
6*alpha2*(haSq - 1) + 11*alpha*haP12 -
6*haP1*haP12 ) / (haP12*haP12);
}
void Inversedewijsian(double *x, model *cov, double *v){
double alpha = P0(DEW_ALPHA);
*v = POW(EXP(*x) - 1.0, 1.0 / alpha);
}
int checkdewijsian(model *cov){
double alpha = P0(DEW_ALPHA);
cov->logspeed = alpha;
RETURN_NOERROR;
}
void rangedewijsian(model VARIABLE_IS_NOT_USED *cov, range_type *range){
range->min[DEW_ALPHA] = 0.0;
range->max[DEW_ALPHA] = 2.0;
range->pmin[DEW_ALPHA] = UNIT_EPSILON;
range->pmax[DEW_ALPHA] = 2.0;
range->openmin[DEW_ALPHA] = true;
range->openmax[DEW_ALPHA] = false;
}
void coinitdewijsian(model *cov, localinfotype *li) {
double
thres[3] = {0.5, 1.0, 1.8},
alpha=P0(DEW_ALPHA);
if (alpha <= thres[0]) {
li->instances = 2;
li->value[0] = 0.5;
li->value[1] = 1.0;
li->msg[0] = li->msg[1] = MSGLOCAL_OK;
} else {
if (alpha <= thres[1]) {
li->instances = 1;
li->value[0] = 1.0; // q[CUTOFF_A]
li->msg[0] =MSGLOCAL_OK;
} else {
if (alpha <= thres[2]) {
li->instances = 1;
li->value[0] = CUTOFF_THIRD_CONDITION ; // q[CUTOFF_A]
li->msg[0] = MSGLOCAL_OK;
}
else {
//TO DO: this is copied from Cauchy model and must be understood and changed
li->instances = 1;
li->value[0] = CUTOFF_THIRD_CONDITION ; // q[CUTOFF_A]
li->msg[0] = MSGLOCAL_JUSTTRY;
}
}
}
}
/* De Wijsian B */
#define DEW_RANGE 1
void DeWijsian(double *x, model *cov, double *v){
double alpha = P0(DEW_ALPHA),
range = P0(DEW_RANGE);
*v = 0.0;
if (*x < range) *v = 1.0-LOG(1.0 + POW(*x, alpha)) / LOG(1.0 + POW(range, alpha));
}
void InverseDeWijsian(double *x, model *cov, double *v){
double alpha = P0(DEW_ALPHA),
range = P0(DEW_RANGE);
*v = 0.0;
if (*x < 1.0)
*v = POW(POW(1.0 + POW(range, alpha), 1.0 - *x) - 1.0, 1.0 / alpha);
}
void rangeDeWijsian(model VARIABLE_IS_NOT_USED *cov, range_type *range){
range->min[DEW_ALPHA] = 0.0;
range->max[DEW_ALPHA] = 1.0;
range->pmin[DEW_ALPHA] = UNIT_EPSILON;
range->pmax[DEW_ALPHA] = 1.0;
range->openmin[DEW_ALPHA] = true;
range->openmax[DEW_ALPHA] = false;
range->min[DEW_RANGE] = 0.0;
range->max[DEW_RANGE] = RF_INF;
range->pmin[DEW_RANGE] = UNIT_EPSILON;
range->pmax[DEW_RANGE] = 1000;
range->openmin[DEW_RANGE] = true;
range->openmax[DEW_RANGE] = true;
}
// Brownian motion
int initlsfbm(model *cov, gen_storage VARIABLE_IS_NOT_USED *s) {
int d = OWNLOGDIM(0);
double alpha = P0(LOCALLY_BROWN_ALPHA),
a2 = 0.5 * alpha,
d2 = 0.5 * d;
if (PisNULL(LOCALLY_BROWN_C)) {
QVALUE = EXP(-alpha * LOG2 + lgammafn(a2 + d2) + lgammafn(1.0 - a2)
- lgammafn(d2));
if (PL >= PL_DETAILSUSER) {
PRINTF("'%.50s' in '%.50s' equals %10g for '%.50s'=%10g\n", KNAME(LOCALLY_BROWN_C),
NICK(cov), QVALUE, KNAME(LOCALLY_BROWN_ALPHA), alpha);
}
} else {
QVALUE = P0(LOCALLY_BROWN_C);
}
cov->taylor[0][TaylorPow] = cov->tail[0][TaylorPow] = alpha;
RETURN_NOERROR;
}
int checklsfbm(model *cov){
int err;
if (P(BROWN_ALPHA) == NULL) ERR("alpha must be given");
if ((err = checkkappas(cov, false)) != NOERROR) RETURN_ERR(err);
double alpha = P0(BROWN_ALPHA);
cov->logspeed = RF_INF;
cov->full_derivs = alpha <= 1.0 ? 0 : alpha < 2.0 ? 1 : cov->rese_derivs;
if (cov->q == NULL) {
EXTRA_Q;
if ((err = initlsfbm(cov, NULL)) != NOERROR) RETURN_ERR(err);
}
RETURN_NOERROR;
}
void rangelsfbm(model VARIABLE_IS_NOT_USED *cov, range_type *range){
range->min[LOCALLY_BROWN_ALPHA] = 0.0;
range->max[LOCALLY_BROWN_ALPHA] = 2.0;
range->pmin[LOCALLY_BROWN_ALPHA] = UNIT_EPSILON;
range->pmax[LOCALLY_BROWN_ALPHA] = 2.0;
range->openmin[LOCALLY_BROWN_ALPHA] = true;
range->openmax[LOCALLY_BROWN_ALPHA] = false;
range->min[LOCALLY_BROWN_C] = 0.5;
range->max[LOCALLY_BROWN_C] = RF_INF;
range->pmin[LOCALLY_BROWN_C] = 1.0;
range->pmax[LOCALLY_BROWN_C] = 1000;
range->openmin[LOCALLY_BROWN_C] = true;
range->openmax[LOCALLY_BROWN_C] = P(LOCALLY_BROWN_ALPHA)==NULL;
}
void lsfbm(double *x, model *cov, double *v) {
if (*x > 1.0)
ERR1("the coordinate distance in '%.50s' must be at most 1.", NICK(cov));
double alpha = P0(LOCALLY_BROWN_ALPHA);
*v = QVALUE - POW(*x, alpha);
}
/* lsfbm: first derivative at t=1 */
void Dlsfbm(double *x, model *cov, double *v)
{// FALSE VALUE FOR *x==0 and alpha < 1
if (*x > 1.0)
ERR1("the coordinate distance in '%.50s' must be at most 1.", NICK(cov));
double alpha = P0(LOCALLY_BROWN_ALPHA);
*v = (*x != 0.0) ? -alpha * POW(*x, alpha - 1.0)
: alpha > 1.0 ? 0.0
: alpha < 1.0 ? RF_NEGINF
: -1.0;
}
/* lsfbm: second derivative at t=1 */
void DDlsfbm(double *x, model *cov, double *v)
{// FALSE VALUE FOR *x==0 and alpha < 2
if (*x > 1.0)
ERR1("the coordinate distance in '%.50s' must be at most 1.", NICK(cov));
double alpha = P0(LOCALLY_BROWN_ALPHA);
*v = (alpha == 1.0) ? 0.0
: (*x != 0.0) ? -alpha * (alpha - 1.0) * POW(*x, alpha - 2.0)
: alpha < 1.0 ? RF_INF
: alpha < 2.0 ? RF_NEGINF
: -2.0;
}
void D3lsfbm(double *x, model *cov, double *v)
{// FALSE VALUE FOR *x==0 and alpha < 2
if (*x > 1.0)
ERR1("the coordinate distance in '%.50s' must be at most 1.", NICK(cov));
double alpha = P0(LOCALLY_BROWN_ALPHA);
*v = alpha == 1.0 || alpha == 2.0 ? 0.0
: (*x != 0.0) ? -alpha * (alpha - 1.0) * (alpha - 2.0) * POW(*x, alpha-3.0)
: alpha < 1.0 ? RF_NEGINF
: RF_INF;
}
void D4lsfbm(double *x, model *cov, double *v)
{// FALSE VALUE FOR *x==0 and alpha < 2
if (*x > 1.0)
ERR1("the coordinate distance in '%.50s' must be at most 1.", NICK(cov));
double alpha = P0(LOCALLY_BROWN_ALPHA);
*v = alpha == 1.0 || alpha == 2.0 ? 0.0
: (*x != 0.0)
? -alpha * (alpha - 1.0) * (alpha - 2.0) * (alpha - 3.0) * POW(*x,alpha-4.0)
: alpha < 1.0 ? RF_INF
: RF_NEGINF;
}
void Inverselsfbm(double *x, model *cov, double *v) {
if (*x > 1.0)
ERR1("the coordinate distance in '%.50s' must be at most 1.", NICK(cov));
double alpha = P0(LOCALLY_BROWN_ALPHA);
*v = POW(QVALUE - *x, 1.0 / alpha);
}
// Brownian motion
void fractalBrownian(double *x, model *cov, double *v) {
double alpha = P0(BROWN_ALPHA);
*v = - POW(*x, alpha);//this is an invalid covariance function!
// keep definition such that the value at the origin is 0
}
void logfractalBrownian(double *x, model *cov, double *v, double *Sign) {
double alpha = P0(BROWN_ALPHA);
*v = LOG(*x) * alpha;//this is an invalid covariance function!
*Sign = - 1.0;
// keep definition such that the value at the origin is 0
}
/* fractalBrownian: first derivative at t=1 */
void DfractalBrownian(double *x, model *cov, double *v)
{// FALSE VALUE FOR *x==0 and alpha < 1
double alpha = P0(BROWN_ALPHA);
*v = (*x != 0.0) ? -alpha * POW(*x, alpha - 1.0)
: alpha > 1.0 ? 0.0
: alpha < 1.0 ? RF_NEGINF
: -1.0;
}
/* fractalBrownian: second derivative at t=1 */
void DDfractalBrownian(double *x, model *cov, double *v)
{// FALSE VALUE FOR *x==0 and alpha < 2
double alpha = P0(BROWN_ALPHA);
*v = (alpha == 1.0) ? 0.0
: (*x != 0.0) ? -alpha * (alpha - 1.0) * POW(*x, alpha - 2.0)
: alpha < 1.0 ? RF_INF
: alpha < 2.0 ? RF_NEGINF
: -2.0;
}
void D3fractalBrownian(double *x, model *cov, double *v)
{// FALSE VALUE FOR *x==0 and alpha < 2
double alpha = P0(BROWN_ALPHA);
*v = alpha == 1.0 || alpha == 2.0 ? 0.0
: (*x != 0.0) ? -alpha * (alpha - 1.0) * (alpha - 2.0) * POW(*x, alpha-3.0)
: alpha < 1.0 ? RF_NEGINF
: RF_INF;
}
void D4fractalBrownian(double *x, model *cov, double *v)
{// FALSE VALUE FOR *x==0 and alpha < 2
double alpha = P0(BROWN_ALPHA);
*v = alpha == 1.0 || alpha == 2.0 ? 0.0
: (*x != 0.0) ? -alpha * (alpha - 1.0) * (alpha - 2.0) * (alpha - 3.0) *
POW(*x, alpha-4.0)
: alpha < 1.0 ? RF_INF
: RF_NEGINF;
}
int initfractalBrownian(model *cov, gen_storage VARIABLE_IS_NOT_USED *s) {
double alpha = P0(BROWN_ALPHA);
cov->taylor[0][TaylorPow] = cov->tail[0][TaylorPow]=alpha;
//PMI(cov);
RETURN_NOERROR;
}
int checkfractalBrownian(model *cov){
int err;
double alpha = P0(BROWN_ALPHA);
cov->logspeed = RF_INF;
cov->full_derivs = alpha <= 1.0 ? 0 : alpha < 2.0 ? 1 : cov->rese_derivs;
if ((err = initfractalBrownian(cov, NULL)) != NOERROR) RETURN_ERR(err);
RETURN_NOERROR;
}
void InversefractalBrownian(double *x, model *cov, double *v) {
double alpha = P0(BROWN_ALPHA);
*v = POW(*x, 1.0 / alpha);
}
void rangefractalBrownian(model VARIABLE_IS_NOT_USED *cov, range_type *range){
range->min[BROWN_ALPHA] = 0.0;
range->max[BROWN_ALPHA] = 2.0;
range->pmin[BROWN_ALPHA] = UNIT_EPSILON;
range->pmax[BROWN_ALPHA] = 2.0;
range->openmin[BROWN_ALPHA] = true;
range->openmax[BROWN_ALPHA] = false;
}
void ieinitBrownian(model *cov, localinfotype *li) {
li->instances = 1;
li->value[0] = (OWNLOGDIM(0) <= 2)
? ((P0(BROWN_ALPHA) <= 1.5) ? 1.0 : 2.0)
: ((P0(BROWN_ALPHA) <= 1.0) ? 1.0 : 2.0);
li->msg[0] = OWNLOGDIM(0) <= 3 ? MSGLOCAL_OK : MSGLOCAL_JUSTTRY;
}
/* FD model */
#define FD_ALPHA 0
void FD(double *x, model *cov, double *v){
double
alpha = P0(FD_ALPHA),
d = alpha * 0.5,
y = *x;
if (y == RF_INF) {*v = 0.0; return;}
double
k = TRUNC(y);
#ifdef DO_PARALLEL
double sk = 1.0,
kold = 0.0;
#else
static double kold = RF_INF, // only if not parallel
sk = RF_INF,
dold=RF_INF;
if (dold!=d || kold > k) {
sk = 1;
kold = 0.0;
}
#endif
// Sign (-1)^k is (kold+d), 16.11.03, checked.
for (; kold<k; kold += 1.0) sk = sk * (kold + d) / (kold + 1.0 - d);
#ifndef DO_PARALLEL
dold = d;
kold = k;
#endif
if (k == y) {
*v = sk;
} else {
double skP1 = sk * (kold + d) / (kold + 1.0 - d);
*v = sk + (y - k) * (skP1 - sk);
}
}
void rangeFD(model VARIABLE_IS_NOT_USED *cov, range_type *range){
range->min[FD_ALPHA] = - 1.0;
range->max[FD_ALPHA] = 1.0;
range->pmin[FD_ALPHA] = range->min[FD_ALPHA] + UNIT_EPSILON;
range->pmax[FD_ALPHA] = range->max[FD_ALPHA] - UNIT_EPSILON;
range->openmin[FD_ALPHA] = false;
range->openmax[FD_ALPHA] = true;
}
/* fractgauss */
#define FG_ALPHA 0
void fractGauss(double *x, model *cov, double *v){
double y = *x, alpha = P0(FG_ALPHA);
*v = (y == 0.0) ? 1.0 : (y==RF_INF) ? 0.0 :
0.5 *(POW(y + 1.0, alpha) - 2.0 * POW(y, alpha) + POW(FABS(y - 1.0),alpha));
}
void rangefractGauss(model VARIABLE_IS_NOT_USED *cov, range_type *range){
range->min[FG_ALPHA] = 0.0;
range->max[FG_ALPHA] = 2.0;
range->pmin[FG_ALPHA] = UNIT_EPSILON;
range->pmax[FG_ALPHA] = 2.0;
range->openmin[FG_ALPHA] = true;
range->openmax[FG_ALPHA] = false;
}
/* generalised fractal Brownian motion */
void genBrownian(double *x, model *cov, double *v) {
double
alpha = P0(BROWN_ALPHA),
beta = P0(BROWN_GEN_BETA),
delta = beta / alpha;
*v = 1.0 - POW(POW(*x, alpha) + 1.0, delta);
//this is an invalid covariance function!
// keep definition such that the value at the origin is 0
}
void loggenBrownian(double *x, model *cov, double *v, double *Sign) {
genBrownian(x, cov, v);
*v = LOG(-*v);
*Sign = - 1.0;
}
void InversegenBrownian(double *x, model *cov, double *v) {
double
alpha = P0(BROWN_ALPHA),
beta = P0(BROWN_GEN_BETA),
delta = beta / alpha;
*v = POW(POW(*x + 1.0, 1.0/delta) - 1.0, 1.0/alpha);
}
int checkgenBrownian(model *cov){
cov->logspeed = RF_INF;
RETURN_NOERROR;
}
void rangegenBrownian(model VARIABLE_IS_NOT_USED *cov, range_type *range){
range->min[BROWN_ALPHA] = 0.0;
range->max[BROWN_ALPHA] = 2.0;
range->pmin[BROWN_ALPHA] = UNIT_EPSILON;
range->pmax[BROWN_ALPHA] = 2.0 - UNIT_EPSILON;
range->openmin[BROWN_ALPHA] = true;
range->openmax[BROWN_ALPHA] = false;
range->min[BROWN_GEN_BETA] = 0.0;
range->max[BROWN_GEN_BETA] = 2.0;
range->pmin[BROWN_GEN_BETA] = UNIT_EPSILON;
range->pmax[BROWN_GEN_BETA] = 2.0 - UNIT_EPSILON;
range->openmin[BROWN_GEN_BETA] = true;
range->openmax[BROWN_GEN_BETA] = false;
}
/* gengneiting */
void genGneiting(double *x, model *cov, double *v)
{
int kk = P0INT(GENGNEITING_K);
double s,
mu=P0(GENGNEITING_MU),
y=*x;
if (y >= 1.0) {
*v = 0.0;
return;
}
s = mu + 2.0 * (double) kk + 0.5;
switch (kk) {
case 0:
*v = 1.0;
break;
case 1:
*v = 1.0 + s*y ;
break;
case 2:
*v = 1.0 + y * (s + y * (s*s-1.0) * ONETHIRD);
break;
case 3:
*v = 1 + y * (s + y * (0.2 * (2.0*s*s - 3 + y * (s*s-4) * s * ONETHIRD)));
break;
default : BUG;
}
*v *= POW(1.0 - y, s);
}
// control thanks to http://calc101.com/webMathematica/derivatives.jsp#topdoit
void DgenGneiting(double *x, model *cov, double *v)
{
int kk = P0INT(GENGNEITING_K);
double s,
mu=P0(GENGNEITING_MU),
y=*x;
if (y >= 1.0) {
*v = 0.0;
return;
}
s = mu + 2.0 * (double) kk + 0.5;
switch (kk) {
case 0:
*v = s;
break;
case 1:
*v = y * s * (s + 1.0);
break;
case 2:
*v = ONETHIRD * (s * s + 3.0 * s + 2.0) * y * ((s - 1.0) * y + 1.0);
break;
case 3:
*v = y * (s * (s + 5) + 6) * (y * (s * (s-2) * y + 3 * s - 3) + 3) / 15.0;
break;
default : BUG;
}
*v *= -POW(1.0 - y, s - 1.0);
}
void DDgenGneiting(double *x, model *cov, double *v){
int kk = P0INT(GENGNEITING_K);
double s,
mu=P0(GENGNEITING_MU),
y=*x;
if (y >= 1.0) {
*v = 0.0;
return;
}
s = mu + 2.0 * (double) kk + 0.5;
switch (kk) {
case 0:
*v = s * (s-1);
break;
case 1:
*v = s * (s + 1.0) * (s * y - 1) ;
break;
case 2: {
double s2;
s2 = s * s;
*v = ONETHIRD * (s2 + 3.0 * s + 2.0) * ( y * ((s2 - 1) * y - s + 2) - 1);
}
break;
case 3:
double s2;
s2 = s * s;
*v = (s2 + 5 * s + 6) / 15.0 *
(y * (y * ((s2 - 4) * s * y + 6 * s - 3) -3 * s + 6) - 3);
break;
default : BUG;
}
*v *= POW(1.0 - y, s - 2.0);
}
int checkgenGneiting(model *cov){
double mu=P0(GENGNEITING_MU),
dim = 2.0 * mu;
set_maxdim(OWN, 0, ISNAN(dim) || dim >= INFDIM ? INFDIM : (int) dim);
RETURN_NOERROR;
}
void rangegenGneiting(model *cov, range_type *range){
range->min[GENGNEITING_K] = range->pmin[GENGNEITING_K] = 0;
range->max[GENGNEITING_K] = range->pmax[GENGNEITING_K] = 3;
range->openmin[GENGNEITING_K] = false;
range->openmax[GENGNEITING_K] = false;
range->min[GENGNEITING_MU] = 0.5 * (double) OWNLOGDIM(0);
range->max[GENGNEITING_MU] = RF_INF;
range->pmin[GENGNEITING_MU] = range->min[GENGNEITING_MU];
range->pmax[GENGNEITING_MU] = range->pmin[GENGNEITING_MU] + 10.0;
range->openmin[GENGNEITING_MU] = false;
range->openmax[GENGNEITING_MU] = true;
}
/*
double porcusG(double t, double nu, double mu, double gamma) {
double t0 = FABS(t);
if (t0 > mu) return 0.0;
return POW(t0, nu) * POW(1.0 - t0 / mu, gamma);
}
*/
double biGneitQuot(double t, double* scale, double *gamma) {
double t0 = FABS(t);
return POW(1.0 - t0 / scale[0], gamma[0]) *
POW(1.0 - t0 / scale[3], gamma[3]) * POW(1.0 - t0 / scale[1], -2 * gamma[1]);
}
void biGneitingbasic(model *cov,
double *scale,
double *gamma,
double *cc
){
double
Sign, x12, min, det, a, b, c, sum,
k = (double) (P0INT(GNEITING_K)),
kP1 = k + (k >= 1),
Mu = P0(GNEITING_MU),
nu = Mu + 0.5,
*sdiag = P(GNEITING_S), // >= 0
s12red = P0(GNEITING_SRED), // in [0,1]
s12 = s12red * (sdiag[0] <= sdiag[1] ? sdiag[0] : sdiag[1]),
*tildegamma = P(GNEITING_GAMMA), // 11,22,12
*Cdiag = P(GNEITING_CDIAG),
*C = P(GNEITING_C),
rho = P0(GNEITING_RHORED);
scale[0] = sdiag[0];
scale[1] = scale[2] = s12; // = scale[2]
scale[3] = sdiag[1];
gamma[0] = tildegamma[0];
gamma[1] = gamma[2] = tildegamma[1]; //gamma[2]
gamma[3] = tildegamma[2];
sum = 0.0;
if (scale[0] == scale[1]) sum += gamma[0];
if (scale[0] == scale[3]) sum += gamma[3];
if (sum > 2.0 * gamma[1]) ERR("values of gamma not valid.");
min = 1.0;
a = 2 * gamma[1] - gamma[0] - gamma[3];
b = - 2 * gamma[1] * (scale[0] + scale[3]) + gamma[0] * (scale[1] + scale[3])
+ gamma[3] * (scale[1] + scale[0]);
c = 2 * gamma[1] * scale[0] * scale[3] - gamma[0] * scale[1] * scale[3]
- gamma[3] * scale[1] * scale[0];
det = b * b - 4 * a * c;
if (det >= 0) {
det = SQRT(det);
for (Sign=-1.0; Sign<=1.0; Sign+=2.0) {
x12 = 0.5 / a * (-b + Sign * det);
if (x12>0 && x12<scale[1]) {
double dummy = biGneitQuot(x12, scale, gamma);
if (dummy < min) min = dummy;
}
}
}
cc[0] = C[0] = Cdiag[0];
cc[3] = C[2] = Cdiag[1];
cc[1] = cc[2] = C[1] = rho * SQRT(C[0] * C[2] * min) *
POW(scale[1] * scale[1] / (scale[0] * scale[3]), 0.5 * (nu + 1 + 2.0 * k)) *
EXP(lgammafn(1.0 + gamma[1]) - lgammafn(2.0 + nu + gamma[1] + kP1)
+ 0.5 * ( lgammafn(2 + nu + gamma[0] + kP1) - lgammafn(1 + gamma[0])
+ lgammafn(2 + nu + gamma[3] + kP1) - lgammafn(1 + gamma[3]))
);
}
int initbiGneiting(model *cov, gen_storage *stor) {
double
*rho = P(GNEITING_RHORED),
*scale = P(GNEITING_S),
*sred = P(GNEITING_SRED),
*p_gamma = P(GNEITING_GAMMA),
*c = P(GNEITING_C),
*cdiag = P(GNEITING_CDIAG);
bool check = stor->check;
biwm_storage *S = cov->Sbiwm;
assert(S != NULL);
if (scale == NULL) {
PALLOC(GNEITING_S, 2, 1);
scale = P(GNEITING_S);
scale[0] = scale[1] = 1.0;
}
if (sred == NULL) {
PALLOC(GNEITING_SRED, 1, 1);
sred = P(GNEITING_SRED);
sred[0] = 1.0;
}
if (sred[0] == 1.0) {
double sum =0.0;
if (scale[0] <= scale[1]) sum += p_gamma[0];
if (scale[1] <= scale[0]) sum += p_gamma[2];
if (sum > 2.0 * p_gamma[1]) {
SERR7("if '%.50s'=1, then %.50s[2] must be greater than min(%.50s[1], %.50s[3]) / 2 if%.50s[1] and %.50s[3] differ and %.50s[1] otherwise.", KNAME(GNEITING_SRED),
KNAME(GNEITING_GAMMA), KNAME(GNEITING_GAMMA),
KNAME(GNEITING_GAMMA), KNAME(GNEITING_GAMMA),
KNAME(GNEITING_GAMMA), KNAME(GNEITING_GAMMA));
}
}
if (S->cdiag_given) { // cdiag or rho given
if (cdiag == NULL) {
PALLOC(GNEITING_CDIAG, 2, 1);
cdiag = P(GNEITING_CDIAG);
cdiag[0] = cdiag[1] = 1.0;
}
if (rho == NULL)
QERRC2(GNEITING_RHORED,
"'%.50s' and '%.50s' must be set at the same time ", GNEITING_CDIAG,
GNEITING_RHORED);
if (check && c != NULL) {
if (cov->nrow[GNEITING_C] != 3 || cov->ncol[GNEITING_C] != 1)
QERRC(GNEITING_C, "must be a 3 x 1 vector");
if (FABS(c[i11] - cdiag[0]) > c[i11] * epsilon ||
FABS(c[i22] - cdiag[1]) > c[i22] * epsilon ) {
QERRC1(GNEITING_C, "does not match '%.50s'.", GNEITING_CDIAG);
}
double savec12 = c[i21];
biGneitingbasic(cov, S->scale, S->gamma, S->c);
if (FABS(c[i21] - savec12) > FABS(c[i21]) * epsilon)
QERRC1(GNEITING_C, "does not match '%.50s'.", GNEITING_RHORED);
} else {
if (PisNULL(GNEITING_C)) PALLOC(GNEITING_C, 3, 1);
c = P(GNEITING_C);
biGneitingbasic(cov, S->scale, S->gamma, S->c);
}
} else {
if (c == NULL)
QERRC2(GNEITING_C, "either '%.50s' or '%.50s' must be set",
GNEITING_C, GNEITING_RHORED);
if (!ISNAN(c[i11]) && !ISNAN(c[i22]) && (c[i11] < 0.0 || c[i22] < 0.0))
QERRC2(GNEITING_C, "variance parameter %.50s[0], %.50s[2] must be non-negative",
GNEITING_C, GNEITING_C);
if (PisNULL(GNEITING_CDIAG)) PALLOC(GNEITING_CDIAG, 2, 1);
if (PisNULL(GNEITING_RHORED)) PALLOC(GNEITING_RHORED, 1, 1);
cdiag = P(GNEITING_CDIAG);
rho = P(GNEITING_RHORED);
cdiag[0] = c[i11];
cdiag[1] = c[i22];
double savec1 = c[i21];
if (savec1 == 0.0) rho[0] = 0.0; // wichtig falls c[0] oder c[2]=NA
else {
rho[0] = 1.0;
biGneitingbasic(cov, S->scale, S->gamma, S->c);
rho[0] = savec1 / c[i21];
}
}
biGneitingbasic(cov, S->scale, S->gamma, S->c);
cov->initialised = true;
RETURN_NOERROR;
}
void kappa_biGneiting(int i, model *cov, int *nr, int *nc){
*nc = *nr = i < DefList[COVNR].kappas? 1 : -1;
if (i==GNEITING_S || i==GNEITING_CDIAG) *nr=2; else
if (i==GNEITING_GAMMA || i==GNEITING_C) *nr=3 ;
}
void biGneiting(double *x, model *cov, double *v) {
double z,
mu = P0(GNEITING_MU);
int i;
biwm_storage *S = cov->Sbiwm;
assert(S != NULL);
// wegen ML aufruf immer neu berechnet
assert(cov->initialised);
for (i=0; i<4; i++) {
if (i==2) {
v[2] = v[1];
continue;
}
z = FABS(*x / S->scale[i]);
P(GENGNEITING_MU)[0] = mu + S->gamma[i] + 1.0;
genGneiting(&z, cov, v + i);
v[i] *= S->c[i];
}
P(GENGNEITING_MU)[0] = mu;
}
void DbiGneiting(double *x, model *cov, double *v){
double z,
mu = P0(GENGNEITING_MU);
int i;
biwm_storage *S = cov->Sbiwm;
assert(S != NULL);
assert(cov->initialised);
for (i=0; i<4; i++) {
if (i==2) {
v[2] = v[1];
continue;
}
z = FABS(*x / S->scale[i]);
P(GENGNEITING_MU)[0] = mu + S->gamma[i] + 1.0;
DgenGneiting(&z, cov, v + i);
v[i] *= S->c[i] / S->scale[i];
}
P(GENGNEITING_MU)[0] = mu;
}
void DDbiGneiting(double *x, model *cov, double *v){
double z,
mu = P0(GENGNEITING_MU);
int i;
biwm_storage *S = cov->Sbiwm;
assert(S != NULL);
assert(cov->initialised);
for (i=0; i<4; i++) {
if (i==2) {
v[2] = v[1];
continue;
}
z = FABS(*x / S->scale[i]);
P(GENGNEITING_MU)[0] = mu + S->gamma[i] + 1.0;
DDgenGneiting(&z, cov, v + i);
v[i] *= S->c[i] / (S->scale[i] * S->scale[i]);
}
P(GENGNEITING_MU)[0] = mu;
}
int checkbiGneiting(model *cov) {
int err;
gen_storage s;
gen_NULL(&s);
s.check = true;
if ((err = checkkappas(cov, false)) != NOERROR) RETURN_ERR(err);
if (PisNULL(GNEITING_K)) QERRC(GNEITING_K, "must be given.");
if (PisNULL(GNEITING_MU)) QERRC(GNEITING_MU, "must be given.");
if (PisNULL(GNEITING_GAMMA)) QERRC(GNEITING_GAMMA,"must be given.");
if (cov->Sbiwm == NULL) {
NEW_STORAGE(biwm);
biwm_storage *S = cov->Sbiwm;
S->cdiag_given = !PisNULL(GNEITING_CDIAG) || !PisNULL(GNEITING_RHORED);
}
if ((err=initbiGneiting(cov, &s)) != NOERROR) RETURN_ERR(err);
int dim = 2.0 * P0(GENGNEITING_MU);
set_maxdim(OWN, 0, ISNAN(dim) || dim >= INFDIM ? INFDIM : (int) dim);
RETURN_NOERROR;
}
sortsofparam sortof_biGneiting(model *cov, int k, int VARIABLE_IS_NOT_USED row,
int VARIABLE_IS_NOT_USED col,
sort_origin origin){
biwm_storage *S = cov->Sbiwm;
if (S == NULL) return UNKNOWNPARAM;
switch(k) {
case GNEITING_K : return ONLYRETURN;
case GNEITING_MU : return CRITICALPARAM;
case GNEITING_S : return SCALEPARAM;
case GNEITING_SRED : return ANYPARAM;
case GNEITING_GAMMA : return ANYPARAM;
case GNEITING_CDIAG :
// printf("xxxxxx %d\n", S ==NULL);
// printf("%d\n", S->cdiag_given);
//printf("%d\n", origin != original);
return S->cdiag_given || origin != original ? VARPARAM : IGNOREPARAM;
case GNEITING_RHORED :
return S->cdiag_given || origin != original ? ANYPARAM : IGNOREPARAM;
case GNEITING_C:
return S->cdiag_given || origin == mle_conform ? IGNOREPARAM : ONLYRETURN;
default : BUG;
}
}
sortsofparam sortof_biGneiting_INisOUT(model *cov, int k, int VARIABLE_IS_NOT_USED row,
int VARIABLE_IS_NOT_USED col){
biwm_storage *S = cov->Sbiwm;
if (S == NULL) return UNKNOWNPARAM;
switch(k) {
case GNEITING_K : return ONLYRETURN;
case GNEITING_MU : return CRITICALPARAM;
case GNEITING_S : return SCALEPARAM;
case GNEITING_SRED : return ANYPARAM;
case GNEITING_GAMMA : return ANYPARAM;
case GNEITING_CDIAG : return S->cdiag_given ? VARPARAM : VARONLYMLE;
case GNEITING_RHORED :return S->cdiag_given ? ANYPARAM : ONLYMLE;
case GNEITING_C: return S->cdiag_given ? IGNOREPARAM : ONLYRETURN;
default : BUG;
}
}
void rangebiGneiting(model *cov, range_type *range){
// *n = P0(GNEITING_K],
range->min[GNEITING_K] = range->pmin[GNEITING_K] = 0;
range->max[GNEITING_K] = range->pmax[GNEITING_K] = 3;
range->openmin[GNEITING_K] = false;
range->openmax[GNEITING_K] = false;
// *mu = P0(GNEITING_MU],
range->min[GNEITING_MU] = 0.5 * (double) OWNLOGDIM(0);
range->max[GNEITING_MU] = RF_INF;
range->pmin[GNEITING_MU] = range->min[GNEITING_MU];
range->pmax[GNEITING_MU] = range->pmin[GNEITING_MU] + 10.0;
range->openmin[GNEITING_MU] = false;
range->openmax[GNEITING_MU] = true;
// *scalediag = P0(GNEITING_S],
range->min[GNEITING_S] = 0.0;
range->max[GNEITING_S] = RF_INF;
range->pmin[GNEITING_S] = 1e-2;
range->pmax[GNEITING_S] = 6.0;
range->openmin[GNEITING_S] = true;
range->openmax[GNEITING_S] = true;
// *scalered12 = P0(GNEITING_SRED],
range->min[GNEITING_SRED] = 0;
range->max[GNEITING_SRED] = 1;
range->pmin[GNEITING_SRED] = 0.01;
range->pmax[GNEITING_SRED] = 1;
range->openmin[GNEITING_SRED] = true;
range->openmax[GNEITING_SRED] = false;
// *gamma = P0(GNEITING_GAMMA],
range->min[GNEITING_GAMMA] = 0.0;
range->max[GNEITING_GAMMA] = RF_INF;
range->pmin[GNEITING_GAMMA] = 1e-5;
range->pmax[GNEITING_GAMMA] = 100.0;
range->openmin[GNEITING_GAMMA] = false;
range->openmax[GNEITING_GAMMA] = true;
// *c diag = P0(GNEITING_CDIAG];
range->min[GNEITING_CDIAG] = 0;
range->max[GNEITING_CDIAG] = RF_INF;
range->pmin[GNEITING_CDIAG] = 1e-05;
range->pmax[GNEITING_CDIAG] = 1000;
range->openmin[GNEITING_CDIAG] = true;
range->openmax[GNEITING_CDIAG] = true;
// *rho = P0(GNEITING_RHORED];
range->min[GNEITING_RHORED] = - 1.0;
range->max[GNEITING_RHORED] = 1;
range->pmin[GNEITING_RHORED] = -0.95;
range->pmax[GNEITING_RHORED] = 0.95;
range->openmin[GNEITING_RHORED] = false;
range->openmax[GNEITING_RHORED] = false;
// *rho = P0(GNEITING_C];
range->min[GNEITING_C] = RF_NEGINF;
range->max[GNEITING_C] = RF_INF;
range->pmin[GNEITING_C] = - 1000;
range->pmax[GNEITING_C] = 1000;
range->openmin[GNEITING_C] = true;
range->openmax[GNEITING_C] = true;
}
/* Gneiting's functions -- alternative to Gaussian */
// #define Sqrt2TenD47 0.30089650263257344820 /* approcx 0.3 ?? */
#define GNEITING_ORIG 0
#define gneiting_origmu 1.5
#define NumericalScale 0.301187465825
#define kk_gneiting 3
#define mu_gneiting 2.683509
#define s_gneiting 0.2745640815
void Gneiting(double *x, model VARIABLE_IS_NOT_USED *cov, double *v){
double y = *x * cov->q[0];
genGneiting(&y, cov, v);
}
void DGneiting(double *x, model VARIABLE_IS_NOT_USED *cov, double *v){
double y = *x * cov->q[0];
DgenGneiting(&y, cov, v);
*v *= cov->q[0];
}
void DDGneiting(double *x, model VARIABLE_IS_NOT_USED *cov, double *v){
double y = *x * cov->q[0];
DgenGneiting(&y, cov, v);
*v *= cov->q[0] * cov->q[0];
}
int checkGneiting(model *cov) {
int err;
kdefault(cov, GNEITING_ORIG, 1);
if ((err = checkkappas(cov)) != NOERROR) RETURN_ERR(err);
bool orig = P0INT(GNEITING_ORIG);
PFREE(GNEITING_ORIG);
assert(cov->q == NULL);
set_nr(OWN, GNEITING_INTERN);
QALLOC(1);
if (orig) {
cov->q[0] = NumericalScale;
kdefault(cov, GENGNEITING_MU, gneiting_origmu);
kdefault(cov, GENGNEITING_K, kk_gneiting);
} else {
cov->q[0] = s_gneiting;
kdefault(cov, GENGNEITING_MU, mu_gneiting);
kdefault(cov, GENGNEITING_K, kk_gneiting);
}
return checkgenGneiting(cov);
}
void rangeGneiting(model VARIABLE_IS_NOT_USED *cov, range_type *range){
booleanRange(GNEITING_ORIG);
}
/* iaco cesare model */
#define CES_NU 0
#define CES_LAMBDA 1
#define CES_DELTA 2
void IacoCesare(double *x, model *cov, double *v){
double
nu = P0(CES_NU),
lambda=P0(CES_LAMBDA),
delta=P0(CES_DELTA);
*v = POW(1.0 + POW(x[0], nu) + POW(x[1], lambda), - delta);
// printf("x=%10g %10g nu=%10g %10g %10g 1-v=%10g\n", x[0], x[1], nu, lambda, delta, 1-*v);
// APMI(cov);
}
void rangeIacoCesare(model VARIABLE_IS_NOT_USED *cov, range_type *range){
range->min[CES_NU] = 0.0;
range->max[CES_NU] = 2.0;
range->pmin[CES_NU] = 1e-3;
range->pmax[CES_NU] = 2.0;
range->openmin[CES_NU] = true;
range->openmax[CES_NU] = false;
range->min[CES_LAMBDA] = 0.0;
range->max[CES_LAMBDA] = 2.0;
range->pmin[CES_LAMBDA] = 1e-3;
range->pmax[CES_LAMBDA] = 2.0;
range->openmin[CES_LAMBDA] = true;
range->openmax[CES_LAMBDA] = false;
range->min[CES_DELTA] = 0.0;
range->max[CES_DELTA] = RF_INF;
range->pmin[CES_DELTA] = 1e-3;
range->pmax[CES_DELTA] = 10.0;
range->openmin[CES_DELTA] = true;
range->openmax[CES_DELTA] = true;
}
/* Kolmogorov model */
void Kolmogorov(double *x, model *cov, double *v){
#define fourthird 1.33333333333333333333333333333333333
#define onethird 0.333333333333333333333333333333333
int d, i, j,
dim = OWNLOGDIM(0),
dimP1 = dim + 1,
dimsq = dim * dim;
double
rM23, r23,
r2 =0.0;
assert(dim == VDIM0 && dim == VDIM1);
for (d=0; d<dimsq; v[d++] = 0.0);
for (d=0; d<dim; d++) r2 += x[d] * x[d];
if (r2 == 0.0) return;
rM23 = onethird / r2; // r^-2 /3
for (d=0; d<dimsq; d+=dimP1) v[d] = fourthird;
for (d=i= 0; i<dim ; i++) {
for(j=0; j<dim; j++) {
v[d++] -= rM23 * x[i] * x[j];
}
}
r23 = -POW(r2, onethird); // ! -
for (d=0; d<dimsq; v[d++] *= r23);
}
int checkKolmogorov(model *cov) {
if (ANYDIM != 3) SERR1("dim (%d) != 3", ANYDIM);
RETURN_NOERROR;
}
/* local-global distinguisher */
#define LGD_ALPHA 0
#define LGD_BETA 1
void lgd1(double *x, model *cov, double *v) {
double y = *x, alpha = P0(LGD_ALPHA), beta=P0(LGD_BETA);
*v = 1.0;
if (y != 0.0) {
if (y < 1.0) *v = 1.0 - beta / (alpha + beta) * POW(y, alpha);
else *v = alpha / (alpha + beta) * POW(y, -beta);
}
}
void Inverselgd1(double *x, model *cov, double *v) {
double alpha = P0(LGD_ALPHA), beta=P0(LGD_BETA);
ERR("scle of lgd1 not programmed yet");
// 19 next line?!
// 1.0 / .... fehlt auch
if (19*alpha < beta) *v = EXP(LOG(1.0 - *x * (alpha + beta) / beta) / alpha);
else *v = EXP(LOG(*x * (alpha + beta) / alpha) / beta);
}
void Dlgd1(double *x, model *cov, double *v){
double y=*x, pp, alpha = P0(LGD_ALPHA), beta=P0(LGD_BETA);
if (y == 0.0) {
*v = 0.0;// falscher Wert, aber sonst NAN-Fehler#
return;
}
pp = ( (y < 1.0) ? alpha : -beta ) - 1.0;
*v = - alpha * beta / (alpha + beta) * EXP(pp * y);
}
int checklgd1(model *cov){
double dim = 2.0 * (1.5 - P0(LGD_ALPHA));
set_maxdim(OWN, 0, ISNAN(dim) || dim >= 2.0 ? 2 : (int) dim);
RETURN_NOERROR;
}
void rangelgd1(model *cov, range_type *range) {
range->min[LGD_ALPHA] = 0.0;
range->max[LGD_ALPHA] = (OWNLOGDIM(0)==2) ? 0.5 : 1.0;
range->pmin[LGD_ALPHA] = 0.01;
range->pmax[LGD_ALPHA] = range->max[LGD_ALPHA];
range->openmin[LGD_ALPHA] = true;
range->openmax[LGD_ALPHA] = false;
range->min[LGD_BETA] = 0.0;
range->max[LGD_BETA] = RF_INF;
range->pmin[LGD_BETA] = 0.01;
range->pmax[LGD_BETA] = 20.0;
range->openmin[LGD_BETA] = true;
range->openmax[LGD_BETA] = true;
}
#define MULTIQUAD_DELTA 0
#define MULTIQUAD_TAU 1
#define MULTIQUAD_EPS 1e-7
void multiquad(double *x, model *cov, double *v){
double delta = P0(MULTIQUAD_DELTA), // Auslesen der Parameter aus cov
deltaM1 = delta - 1.0,
tau = P0(MULTIQUAD_TAU);
double y = *x;
if (y < 0.0 || y >= PI) BUG;
*v = POW( deltaM1 * deltaM1 / (1.0 + delta * (delta - 2.0 * COS(y))), tau);
return;
}
/* range der Parameter delta & tau */
void rangemultiquad(model VARIABLE_IS_NOT_USED *cov, range_type *range){
range->min[MULTIQUAD_DELTA] = 0.0; // true range
range->max[MULTIQUAD_DELTA] = 1.0;
range->pmin[MULTIQUAD_DELTA] = MULTIQUAD_EPS; // practical range (assumed)
range->pmax[MULTIQUAD_DELTA] = 1.0 - MULTIQUAD_EPS;
range->openmin[MULTIQUAD_DELTA] = true; // lower endpoint included
range->openmax[MULTIQUAD_DELTA] = true; // upper endpoint excluded
range->min[MULTIQUAD_TAU] = 0; // true range
range->max[MULTIQUAD_TAU] = RF_INF;
range->pmin[MULTIQUAD_TAU] = 0.0001; // practical range (assumed)
range->pmax[MULTIQUAD_TAU] = 500;
range->openmin[MULTIQUAD_TAU] = true; // lower endpoint included
range->openmax[MULTIQUAD_TAU] = true; // upper endpoint excluded
}
// Brownian motion
#define OESTING_BETA 0
void oesting(double *x, model *cov, double *v) {
// klein beta interagiert mit 'define beta Rf_beta' in Rmath
double Beta = P0(OESTING_BETA),
x2 = *x * *x;
*v = - x2 * POW(1 + x2, -Beta);//this is an invalid covariance function!
// keep definition such that the value at the origin is 0
}
/* oesting: first derivative at t=1 */
void Doesting(double *x, model *cov, double *v)
{// FALSE VALUE FOR *x==0 and Beta < 1
double Beta = P0(OESTING_BETA),
x2 = *x * *x;
*v = 2 * *x * (1 + (1-Beta) * x2) * POW(1 + x2, -Beta-1);
}
/* oesting: second derivative at t=1 */
void DDoesting(double *x, model *cov, double *v)
{// FALSE VALUE FOR *x==0 and beta < 2
double Beta = P0(OESTING_BETA),
x2 = *x * *x;
*v = 2 * (1 + (2 - 5 * Beta) * x2 + (1 - 3 * Beta + 2 * Beta * Beta) *
x2 *x2) * POW(1 + x2, -Beta-2);
}
int initoesting(model *cov, gen_storage VARIABLE_IS_NOT_USED *s) {
double Beta = P0(OESTING_BETA);
cov->taylor[1][TaylorConst] = + Beta;
cov->taylor[2][TaylorConst] = - 0.5 * Beta * (Beta + 1);
cov->tail[0][TaylorPow] = 2 - 2 * Beta;
RETURN_NOERROR;
}
int checkoesting(model *cov){
int err;
cov->logspeed = RF_INF;
cov->full_derivs = cov->rese_derivs;
if ((err = initoesting(cov, NULL)) != NOERROR) RETURN_ERR(err);
RETURN_NOERROR;
}
void rangeoesting(model VARIABLE_IS_NOT_USED *cov, range_type *range){
range->min[OESTING_BETA] = 0.0;
range->max[OESTING_BETA] = 1.0;
range->pmin[OESTING_BETA] = UNIT_EPSILON;
range->pmax[OESTING_BETA] = 1.0;
range->openmin[OESTING_BETA] = true;
range->openmax[OESTING_BETA] = false;
}
/* penta */
void penta(double *x, model VARIABLE_IS_NOT_USED *cov, double *v)
{ ///
double y=*x, y2 = y * y;
*v = 0.0;
if (y < 1.0)
*v = (1.0 + y2 * (-7.333333333333333
+ y2 * (33.0 +
y * (-38.5 +
y2 * (16.5 +
y2 * (-5.5 +
y2 * 0.833333333333333))))));
}
void Dpenta(double *x, model VARIABLE_IS_NOT_USED *cov, double *v)
{
double y=*x, y2 = y * y;
*v = 0.0;
if (y < 1.0)
*v = y * (-14.66666666666666667 +
y2 * (132.0 +
y * (-192.5 +
y2 * (115.5 +
y2 * (-49.5 +
y2 * 9.16666666666666667)))));
}
void Inversepenta(double *x, model VARIABLE_IS_NOT_USED *cov, double *v) {
*v = (*x==0.05) ? 1.0 / 1.6552838957365 : RF_NA;
}
/* power model */
#define POW_ALPHA 0
void power(double *x, model *cov, double *v){
double alpha = P0(POW_ALPHA), y = *x;
*v = 0.0;
if (y < 1.0) *v = POW(1.0 - y, alpha);
}
void TBM2power(double *x, model *cov, double *v){
// only alpha=2 up to now !
double y = *x;
if (P0(POW_ALPHA) != 2.0)
ERR("TBM2 of power only allowed for alpha=2");
if (y > 1.0) *v = (1.0 - 2.0 * y *(ASIN(1.0 / y) - y + SQRT(y * y - 1.0) ));
else *v = 1.0 - y * (PI - 2.0 * y);
}
void Dpower(double *x, model *cov, double *v){
double alpha = P0(POW_ALPHA), y = *x;
*v = 0.0;
if (y < 1.0) *v = - alpha * POW(1.0 - y, alpha - 1.0);
}
int checkpower(model *cov) {
double alpha = P0(POW_ALPHA);
double dim = 2.0 * alpha - 1.0;
set_maxdim(OWN, 0, ISNAN(dim) || dim >= INFDIM ? INFDIM-1 : (int) dim);
cov->monotone = alpha >= (double) ((OWNLOGDIM(0) / 2) + 1)
? COMPLETELY_MON : NORMAL_MIXTURE;
RETURN_NOERROR;
}
// range definition:
// 0: min, theory, 1:max, theory
// 2: min, practically 3:max, practically
void rangepower(model *cov, range_type *range){
bool tcf = isnowTcf(cov) || equalsSphericalIsotropic(OWNISO(0));
int dim = OWNLOGDIM(0);
range->min[POW_ALPHA] = tcf
? (double) ((dim / 2) + 1) // Formel stimmt so! Nicht aendern!
: 0.5 * (double) (dim + 1);
range->max[POW_ALPHA] = RF_INF;
range->pmin[POW_ALPHA] = range->min[POW_ALPHA];
range->pmax[POW_ALPHA] = 20.0;
range->openmin[POW_ALPHA] = false;
range->openmax[POW_ALPHA] = true;
}
/* qexponential -- derivative of exponential */
#define QEXP_ALPHA 0
void qexponential(double *x, model *cov, double *v){
double
alpha = P0(QEXP_ALPHA),
y = EXP(-*x);
*v = y * (2.0 - alpha * y) / (2.0 - alpha);
}
void Inverseqexponential(double *x, model *cov, double *v){
double alpha = P0(QEXP_ALPHA);
*v = -LOG( (1.0 - SQRT(1.0 - alpha * (2.0 - alpha) * *x)) / alpha);
}
void Dqexponential(double *x, model *cov, double *v) {
double
alpha = P0(QEXP_ALPHA),
y = EXP(-*x);
*v = y * (alpha * y - 1.0) * 2.0 / (2.0 - alpha);
}
void rangeqexponential(model VARIABLE_IS_NOT_USED *cov, range_type *range){
range->min[QEXP_ALPHA] = 0.0;
range->max[QEXP_ALPHA] = 1.0;
range->pmin[QEXP_ALPHA] = 0.0;
range->pmax[QEXP_ALPHA] = 1.0;
range->openmin[QEXP_ALPHA] = false;
range->openmax[QEXP_ALPHA] = false;
}
#define SINEPOWER_ALPHA 0
void sinepower(double *x, model *cov, double *v){
double alpha = P0(SINEPOWER_ALPHA); // Auslesen des Parameters aus cov
double y = *x;
if (y < 0.0 || y >= PI) BUG;
*v = 1.0 - POW(SIN(y * 0.5), alpha);
return;
}
/* range des Parameters alpha */
void rangesinepower(model VARIABLE_IS_NOT_USED *cov, range_type *range){
range->min[SINEPOWER_ALPHA] = 0.0; // true range
range->max[SINEPOWER_ALPHA] = 2.0;
range->pmin[SINEPOWER_ALPHA] = 0.001; // practical range (assumed)
range->pmax[SINEPOWER_ALPHA] = 2.0;
range->openmin[SINEPOWER_ALPHA] = true; // lower endpoint included
range->openmax[SINEPOWER_ALPHA] = false; // upper endpoint excluded
}
/* spherical model */
void spherical(double *x, model VARIABLE_IS_NOT_USED *cov, double *v){
double y = *x;
*v = 0.0;
if (y < 1.0) *v = 1.0 + y * 0.5 * (y * y - 3.0);
}
// void Inversespherical(model *cov){ return 1.23243208931941;}
void TBM2spherical(double *x, model VARIABLE_IS_NOT_USED *cov, double *v){
double y = *x , y2 = y * y;
if (y>1.0) *v = (1.0- 0.75 * y * ((2.0 - y2) * ASIN(1.0/y) + SQRT(y2 -1.0)));
else *v = (1.0 - 0.375 * PI * y * (2.0 - y2));
}
void Dspherical(double *x, model VARIABLE_IS_NOT_USED *cov, double *v){
double y = *x;
*v = (y >= 1.0) ? 0.0 : 1.5 * (y * y - 1.0);
}
void DDspherical(double *x, model VARIABLE_IS_NOT_USED *cov, double *v){
*v = (*x >= 1.0) ? 0.0 : 3 * *x;
}
int structspherical(model *cov, model **newmodel) {
return structCircSph( cov, newmodel, 3);
}
void dospherical(model VARIABLE_IS_NOT_USED *cov, gen_storage VARIABLE_IS_NOT_USED *s) {
// todo diese void do... in Primitive necessary??
// mppinfotype *info = &(s->mppinfo);
//info->radius = cov->mpp.refradius;
}
double alphaIntSpherical(int a) {
// int r^a C(r) \D r
double A = (double) a;
return 1.0 / (A + 1.0) - 1.5 / (A + 2.0) + 0.5 / (A + 4.0);
}
int initspherical(model *cov, gen_storage VARIABLE_IS_NOT_USED *s) {
int dim = OWNLOGDIM(0);
if (hasAnyEvaluationFrame(cov)) {
if (cov->mpp.moments >= 1) SERR("too high moments required");
}
else if (hasSmithFrame(cov)) {
assert(cov->mpp.maxheights[0] == 1.0);
if (cov->mpp.moments >= 1) {
cov->mpp.mM[1] = cov->mpp.mMplus[1] =
SurfaceSphere(dim - 1, 1) * alphaIntSpherical(dim - 1);
}
}
else if (hasRandomFrame(cov)) { RETURN_NOERROR; }
else ILLEGAL_FRAME;
RETURN_NOERROR;
}
/* stein space-time model */
#define STEIN_NU 0
#define STEIN_Z 1
void kappaSteinST1(int i, model *cov, int *nr, int *nc){
*nc = 1;
*nr = (i == STEIN_NU) ? 1 : (i==STEIN_Z) ? OWNLOGDIM(0) - 1 : -1;
}
void SteinST1(double *x, model *cov, double *v){
/* 2^(1-nu)/Gamma(nu) [ h^nu K_nu(h) - 2 * tau (x T z) t h^{nu-1} K_{nu-1}(h) /
(2 nu + d + 1) ]
\|tau z \|<=1 hence \tau z replaced by z !!
*/
int d,
dim = OWNLOGDIM(0),
time = dim - 1;
double logconst, hz, y,
nu = P0(STEIN_NU),
*z=P(STEIN_Z);
hz = 0.0;
y = x[time] * x[time];
for (d=0; d<time; d++) {
y += x[d] * x[d];
hz += x[d] * z[d];
}
if ( y==0.0 ) *v = 1.0;
else {
double bk[MATERN_NU_THRES];
y = SQRT(y);
logconst = (nu - 1.0) * LOG(0.5 * y) - QVALUE;
*v = y * EXP(logconst + LOG(bessel_k_ex(y, nu, 2.0, bk)) - y)
- 2.0 * hz * x[time] * EXP(logconst +
LOG(bessel_k_ex(y, nu - 1.0, 2.0, bk)) - y)
/ (2.0 * nu + dim);
}
}
int checkSteinST1(model *cov) {
double nu = P0(STEIN_NU), *z= P(STEIN_Z), absz;
int d,
spatialdim=OWNLOGDIM(0) - 1;
for (d=0; d<= Nothing; d++) cov->pref[d] *= (nu < BesselUpperB[d]);
if (nu >= 2.5) cov->pref[CircEmbed] = 2;
if (spatialdim < 1)
SERR("dimension of coordinates, including time, must be at least 2");
if (nu > MATERN_NU_THRES) SERR1("'nu'>%d is too large for precise returns",
MATERN_NU_THRES)
for (absz=0.0, d=0; d<spatialdim; d++) absz += z[d] * z[d];
if (ISNAN(absz))
SERR("currently, components of z cannot be estimated by MLE, so NA's are not allowed");
if (absz > 1.0 + UNIT_EPSILON && !GLOBAL_UTILS->basic.skipchecks) {
SERR("||z|| must be less than or equal to 1");
}
if (cov->q == NULL) {
EXTRA_Q;
initSteinST1(cov, NULL);
}
RETURN_NOERROR;
}
double densitySteinST1(double *x, model *cov) {
double x2, wz, dWM, nu = P0(STEIN_NU),
*z=P(STEIN_Z);
int d,
dim = PREVLOGDIM(0),
spatialdim = dim - 1;
x2 = x[spatialdim] * x[spatialdim]; // v^2
wz = 0.0;
for (d=0; d<spatialdim; d++) {
x2 += x[d] * x[d]; // w^2 + v^2
wz += x[d] * z[d];
}
dWM = EXP(QVALUE2 - QVALUE3 * LOG(x2 + 1.0));
return (1.0 + 2.0 * wz * x[spatialdim] + x2) * dWM
/ (2.0 * nu + (double) dim + 1.0);
}
int initSteinST1(model *cov, gen_storage *s) {
int dim = PREVLOGDIM(0);
double nu = P0(STEIN_NU);
QVALUE = lgammafn(nu);
QVALUE2 = QVALUE - lgammafn(nu + 0.5 * dim) - dim * M_LN_SQRT_PI;
QVALUE3 = nu + dim; // factor
if (HAS_SPECTRAL_FRAME(cov)) {
spec_properties *cs = &(s->spec);
cs->density = densitySteinST1;
return search_metropolis(cov, s);
}
RETURN_NOERROR;
}
void spectralSteinST1(model *cov, gen_storage *S, double *e){
metropolis(cov, S, e);
}
void rangeSteinST1(model VARIABLE_IS_NOT_USED *cov, range_type *range){
range->min[STEIN_NU] = 1.0;
range->max[STEIN_NU] = RF_INF;
range->pmin[STEIN_NU] = 1e-10;
range->pmax[STEIN_NU] = 10.0;
range->openmin[STEIN_NU] = true;
range->openmax[STEIN_NU] = true;
range->min[STEIN_Z] = RF_NEGINF;
range->max[STEIN_Z] = RF_INF;
range->pmin[STEIN_Z] = - 10.0;
range->pmax[STEIN_Z] = 10.0;
range->openmin[STEIN_Z] = true;
range->openmax[STEIN_Z] = true;
}
/* wave */
void wave(double *x, model VARIABLE_IS_NOT_USED *cov, double *v) {
double y = *x;
*v = (y==0.0) ? 1.0 : (y==RF_INF) ? 0 : SIN(y) / y;
}
void Inversewave(double *x, model VARIABLE_IS_NOT_USED *cov, double *v) {
*v = (*x==0.05) ? 1.0/0.302320850755833 : RF_NA;
}
int initwave(model *cov, gen_storage VARIABLE_IS_NOT_USED *s) {
if (HAS_SPECTRAL_FRAME(cov)) {
return (OWNLOGDIM(0) <= 2) ? NOERROR : ERRORFAILED;
}
else if (hasRandomFrame(cov)) { RETURN_NOERROR; }
else ILLEGAL_FRAME;
}
void spectralwave(model *cov, gen_storage *S, double *e) {
spectral_storage *s = &(S->Sspectral);
/* see Yaglom ! */
double x;
x = UNIFORM_RANDOM;
E12(s, PREVLOGDIM(0), SQRT(1.0 - x * x), e);
}
#define USER_TYPE 0
#define USER_DOM 1
#define USER_ISO 2
#define USER_VDIM 3
#define USER_BETA 4
#define USER_COORD 5
#define USER_FCTN 6
#define USER_FST 7
#define USER_SND 8
#define USER_ENV 9
#define USER_LAST USER_ENV
void evaluateUser(double *x, double *y, bool Time, model *cov,
sexp_type *which, double *Res) {
SEXP res,
env = PENV(USER_ENV)->sexp;
int i,
vdim = VDIM0 * VDIM1,
ncol = cov->ncol[USER_BETA],
n = OWNXDIM(0);
double *beta = P(USER_BETA);
assert(which != NULL);
if (cov->nrow[USER_COORD] >= 2 && PINT(USER_COORD)[1] != -2) {
if (Time) {
addVariable( (char *) "T", x + (--n), 1, 1, env);
}
switch (n) {
case 3 : addVariable( (char *) "z", x+2, 1, 1, env);
FALLTHROUGH_OK;
case 2 : addVariable( (char *) "y", x+1, 1, 1, env);
FALLTHROUGH_OK;
case 1 : addVariable( (char *) "x", x+0, 1, 1, env);
break;
default:
BUG;
}
} else {
addVariable( (char *) "x", x, n, 1, env);
if (y != NULL) addVariable( (char *) "y", y, n, 1, env);
}
res = eval(which->sexp, env);
if (beta == NULL) {
for (i=0; i<vdim; i++) {
Res[i] = REAL(res)[i];
}
} else {
Ax(beta, REAL(res), vdim, ncol, Res);
}
}
void kappaUser(int i, model *cov, int *nr, int *nc){
*nc = *nr = i < DefList[COVNR].kappas ? 1 : -1;
if (i == USER_VDIM) *nr = SIZE_NOT_DETERMINED;
if (i == USER_COORD) *nr=SIZE_NOT_DETERMINED;
if (i == USER_BETA) *nr=*nc=SIZE_NOT_DETERMINED;
}
void User(double *x, model *cov, double *v){
evaluateUser(x, NULL, Loc(cov)->Time, cov, PLANG(USER_FCTN), v);
}
void UserNonStat(double *x, double *y, model *cov, double *v){
evaluateUser(x, y, false, cov, PLANG(USER_FCTN), v);
}
void DUser(double *x, model *cov, double *v){
evaluateUser(x, NULL, Loc(cov)->Time, cov, PLANG(USER_FST), v);
}
void DDUser(double *x, model *cov, double *v){
evaluateUser(x, NULL, Loc(cov)->Time, cov, PLANG(USER_SND), v);
}
int checkUser(model *cov){
defn *C = DefList + COVNR;
kdefault(cov, USER_DOM, XONLY);
if (PisNULL(USER_ISO)) {
Types type = (Types) P0INT(USER_TYPE);
if (isVariogram(type)) kdefault(cov, USER_ISO, ISOTROPIC);
else if (isProcess(type) || isShape(type))
kdefault(cov, USER_ISO, CARTESIAN_COORD);
else SERR1("type='%.50s' not allowed", TYPE_NAMES[type]);
}
int
*dom = PINT(USER_DOM),
*iso = PINT(USER_ISO),
*vdim =PINT(USER_VDIM);
bool
Time,
fctn = !PisNULL(USER_FCTN),
fst = !PisNULL(USER_FST),
snd = !PisNULL(USER_SND);
int err,
*nrow = cov->nrow,
*variab = PINT(USER_COORD), //codierung variab=1:x, 2:y 3:z, 4:T
nvar = cov->nrow[USER_COORD],
*pref = cov->pref;
if (nvar < 1) SERR("variables not of the required form ('x', 'y', 'z', 'T')");
if (OWNDOM(0) != (domain_type) *dom)
SERR2("wrong domain (requ='%.50s'; provided='%.50s')",
DOMAIN_NAMES[OWNDOM(0)], DOMAIN_NAMES[*dom]);
if (OWNISO(0) != (isotropy_type) *iso)
SERR2("wrong isotropy assumption (requ='%.50s'; provided='%.50s')",
ISO_NAMES[OWNISO(0)], ISO_NAMES[*iso]);
if (PENV(USER_ENV) == NULL) BUG;
if (!PisNULL(USER_BETA)) {
if (vdim == NULL) kdefault(cov, USER_VDIM, nrow[USER_BETA]);
else if (*vdim != nrow[USER_BETA])
SERR4("number of columns of '%.50s' (=%d) does not equal '%.50s' (=%d)",
KNAME(USER_BETA), nrow[USER_BETA], KNAME(USER_VDIM), *vdim);
VDIM0 = nrow[USER_BETA];
VDIM1 = 1;
} else {
if (PisNULL(USER_VDIM)) kdefault(cov, USER_VDIM, 1);
VDIM0 = P0INT(USER_VDIM);
VDIM1 = cov->nrow[USER_VDIM] == 1 ? 1 : PINT(USER_VDIM)[1];
}
if (cov->nrow[USER_VDIM] > 2) SERR1("'%.50s' must be a scalar or a vector of length 2", KNAME(USER_VDIM));
if ((err = checkkappas(cov, false)) != NOERROR) RETURN_ERR(err);
if (variab[0] != 1 && (variab[0] != 4 || nvar > 1)) SERR("'x' not given");
if (nvar > 1) {
variab[1] = std::abs(variab[1]); // integer ABS!
// it is set to its negativ value
// below, when a kernel is defined
if (variab[1] == 3) SERR("'z' given but not 'y'");
}
Time = variab[nvar-1] == 4;
if (((nvar >= 3 || variab[nvar-1] == 4) && GLOBAL.coords.xyz_notation==False)
// ||
// (nrow[USER_COORD] == 1 && !ISNA_INT(GLOBAL.coords.xyz_notation)
// && GLOBAL.coords.xyz_notation)
)
SERR("mismatch of indicated xyz-notation");
if (Time xor Loc(cov)->Time)
SERR("If 'T' is given, it must be given both as coordinates and as variable 'T' in the function 'fctn'");
if ((nvar > 2 || (nvar == 2 && variab[1] != 2)) && isKernel(OWN))
SERR1("'%.50s' not valid for anisotropic models", coords[COORDS_XYZNOTATION]);
if (nvar == 2 && variab[1] == 2) {
// sowohl nonstat also auch x, y Schreibweise moeglich
if (GLOBAL.coords.xyz_notation == Nan)
SERR1("'%.50s' equals 'NA', but should be a logical value.",
coords[COORDS_XYZNOTATION]);
//if (isKernel(OWN) && GLOBAL.coords.xyz_notation==2) // RFcov
// SERR1("'%.50s' is not valid for anisotropic models",
// coords[COORDS_XYZNOTATION]);
}
if (nvar > 1) {
if (isXonly(OWN)) {
if (equalsIsotropic(OWNISO(0))) {
SERR("two many variables given for motion invariant function");
} else if (isSpaceIsotropic(OWN) && nvar != 2)
SERR("number of variables does not match a space-isotropic model");
} else {
if (nvar == 2 && variab[1] == 2) variab[1] = -2;//i.e. non domain (kernel)
}
}
if (GLOBAL.coords.xyz_notation != Nan) {
if (//(GLOBAL.coords.xyz_notation == 2 && isKernel(OWN)) ||
((nvar > 2 || (nvar == 2 && isXonly(OWN))) && variab[1] == -2)) {
SERR("domain assumption, model and coordinates do not match.");
}
}
if ((OWNXDIM(0) == 4 && !Loc(cov)->Time) || OWNXDIM(0) > 4)
SERR("Notation using 'x', 'y', 'z' and 'T' allows only for 3 spatial dimensions and an additional time component.");
if (fctn) {
C->F_derivs = C->RS_derivs = 0;
pref[Direct] = pref[Sequential] = pref[CircEmbed] = pref[Nothing] = 5;
if (fst) {
C->F_derivs = C->RS_derivs = 1;
pref[TBM] = 5;
if (snd) {
C->F_derivs = C->RS_derivs = 2;
}
} else { // !fst
if (snd) SERR2("'%.50s' given but not '%.50s'",
KNAME(USER_SND), KNAME(USER_FST));
}
} else { // !fctn
if (fst || snd)
SERR3("'%.50s' or '%.50s' given but not '%.50s'",
KNAME(USER_SND), KNAME(USER_FST), KNAME(USER_FCTN));
}
RETURN_NOERROR;
}
Types TypeUser(Types required, model *cov,
isotropy_type VARIABLE_IS_NOT_USED i) {
if (PisNULL(USER_TYPE)) return BadType;
Types type = (Types) P0INT(USER_TYPE);
if (! (isShape(type) || equalsRandom(type)) ) return BadType;
return TypeConsistency(required, type);
}
bool setUser(model *cov){
// A PMI0(cov);
Types
type = PisNULL(USER_TYPE) ? BadType : (Types) P0INT(USER_TYPE);
domain_type
dom = PisNULL(USER_DOM) ? DOMAIN_MISMATCH : (domain_type) P0INT(USER_DOM);
isotropy_type
iso = PisNULL(USER_ISO) ? ISO_MISMATCH : (isotropy_type) P0INT(USER_ISO);
int
xdim = cov->nrow[USER_COORD];
// vdim = PisNULL(USER_VDIM) ? 0 : P0INT(USER_VDIM);
//printf("isset = %d %d\n", PREV_INITIALISEDXX, PREV_INITIALISED);
isotropy_type previso = CONDPREVISO(0);
set_system(OWN, 0, isFixed(previso) ? PREVLOGDIM(0) : xdim /* xdim only dummy! */,
xdim, xdim, type, dom, iso);
return true;
}
bool allowedDuser(model *cov) {
if (PisNULL(USER_DOM)) return allowedDtrue(cov);
bool *D = cov->allowedD;
for (int i=FIRST_DOMAIN; i<LAST_DOMAINUSER; D[i++]=false);
D[(domain_type) P0INT(USER_DOM)] = true;
return false;
}
bool allowedIuser(model *cov) {
if (PisNULL(USER_ISO)) return allowedDtrue(cov);
bool *I = cov->allowedI;
for (int i=(int) FIRST_ISOUSER; i<=(int) LAST_ISOUSER; I[i++] = false);
I[(domain_type) P0INT(USER_ISO)] = true;
return false;
}
void rangeUser(model VARIABLE_IS_NOT_USED *cov, range_type *range){
range->min[USER_TYPE] = TcfType;
range->max[USER_TYPE] = TrendType;
range->pmin[USER_TYPE] = TcfType;
range->pmax[USER_TYPE] = TrendType;
range->openmin[USER_TYPE] = false;
range->openmax[USER_TYPE] = false;
range->min[USER_DOM] = FIRST_DOMAIN;
range->max[USER_DOM] = LAST_DOMAINUSER;
range->pmin[USER_DOM] = FIRST_DOMAIN;
range->pmax[USER_DOM] = LAST_DOMAINUSER;
range->openmin[USER_DOM] = false;
range->openmax[USER_DOM] = false;
range->min[USER_ISO] = FIRST_CARTESIAN;
range->max[USER_ISO] = LAST_CARTESIAN;
range->pmin[USER_ISO] = FIRST_CARTESIAN;
range->pmax[USER_ISO] = LAST_CARTESIAN;
range->openmin[USER_ISO] = false;
range->openmax[USER_ISO] = false;
range->min[USER_VDIM] = 1;
range->max[USER_VDIM] = INFDIM;
range->pmin[USER_VDIM] = 1;
range->pmax[USER_VDIM] = 10;
range->openmin[USER_VDIM] = false;
range->openmax[USER_VDIM] = true;
range->min[USER_BETA] = RF_NEGINF;
range->max[USER_BETA] = RF_INF;
range->pmin[USER_BETA] = - 1e5;
range->pmax[USER_BETA] = 1e5;
range->openmin[USER_BETA] = true;
range->openmax[USER_BETA] = true;
range->min[USER_COORD] = -2;
range->max[USER_COORD] = 4;
range->pmin[USER_COORD] = 1;
range->pmax[USER_COORD] = 4;
range->openmin[USER_COORD] = false;
range->openmax[USER_COORD] = false;
#define user_n 4
int idx[user_n] = {USER_FCTN, USER_FST, USER_SND, USER_ENV};
for (int i=0; i<user_n; i++) {
int j = idx[i];
range->min[j] = RF_NAN;
range->max[j] = RF_NAN;
range->pmin[j] = RF_NAN;
range->pmax[j] = RF_NAN;
range->openmin[j] = false;
range->openmax[j] = false;
}
int kappas = DefList[COVNR].kappas;
for (int i=USER_LAST + 1; i<kappas; i++) {
range->min[i] = RF_NEGINF;
range->max[i] = RF_INF;
range->pmin[i] = 1e10;
range->pmax[i] = - 1e10;
range->openmin[i] = true;
range->openmax[i] = true;
}
}
