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vario.c
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vario.c
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/*
* vario.c: basic variogram model functions (init, print, update, etc.)
*/
#include <stdio.h>
#include <stdlib.h> /* getenv() */
#include <ctype.h> /* toupper() */
#include <float.h> /* DBL_MIN */
#include <math.h>
#include <string.h>
#include "R.h" /* Rprintf() */
#include "defs.h"
#include "mtrx.h"
#include "userio.h"
#include "data.h"
#include "utils.h"
#include "debug.h"
#include "vario.h"
#include "vario_fn.h"
#include "glvars.h"
#include "lm.h"
static int is_valid_cs(const VARIOGRAM *aa, const VARIOGRAM *bb,
const VARIOGRAM *ab);
static int is_posdef(MAT *m);
static ANIS_TM *get_tm(double anis[5]);
static void init_variogram_part(VGM_MODEL *v);
const V_MODEL v_models[] = { /* the variogram model catalogue: */
/* first one needs to be NOT_SP: */
{ NOT_SP, "Nsp", "Nsp (not specified)", NULL, NULL },
{ NUGGET, "Nug", "Nug (nugget)", fn_nugget, da_is_zero },
{ EXPONENTIAL, "Exp", "Exp (exponential)", fn_exponential, da_fn_exponential },
{ SPHERICAL, "Sph", "Sph (spherical)", fn_spherical, da_fn_spherical },
{ GAUSSIAN, "Gau", "Gau (gaussian)", fn_gaussian, da_fn_gaussian },
{ EXCLASS, "Exc", "Exclass (Exponential class/stable)", fn_exclass, NULL },
{ MATERN, "Mat", "Mat (Matern)", fn_matern, NULL },
{ STEIN, "Ste", "Mat (Matern, M. Stein's parameterization)", fn_matern2, NULL },
{ CIRCULAR, "Cir", "Cir (circular)", fn_circular, NULL },
{ LINEAR, "Lin", "Lin (linear)", fn_linear, da_fn_linear },
/* one-parameter (a = 0), or two-parameter with sill */
{ BESSEL, "Bes", "Bes (bessel)", fn_bessel, NULL },
{ PENTASPHERICAL, "Pen", "Pen (pentaspherical)", fn_pentaspherical, da_fn_pentaspherical },
{ PERIODIC, "Per", "Per (periodic)", fn_periodic, da_fn_periodic },
{ WAVE, "Wav", "Wav (wave)", fn_wave, da_fn_wave },
{ HOLE, "Hol", "Hol (hole)", fn_hole, da_fn_hole },
{ LOGARITHMIC, "Log", "Log (logarithmic)", fn_logarithmic, da_fn_logarithmic },
{ POWER, "Pow", "Pow (power)", fn_power, da_fn_power },
/* Wackernagel 2nd ed., p. 225 -- not working yet */
{ SPLINE, "Spl", "Spl (spline)", fn_spline, NULL },
{ LEGENDRE, "Leg", "Leg (Legendre)", fn_legendre, NULL },
{ MERROR, "Err", "Err (Measurement error)", fn_nugget, da_is_zero },
/* the folowing two should always be the last ``valid'' one: */
{ INTERCEPT, "Int", "Int (Intercept)", fn_intercept, da_is_zero },
{ NOT_SP, NULL, NULL, NULL, NULL } /* THIS SHOULD BE LAST */
};
const char *vgm_type_str[] = {
"not specified",
"semivariogram",
"cross variogram",
"covariogram",
"cross covariogram"
};
VARIOGRAM *init_variogram(VARIOGRAM *v) {
/*
* initializes one variogram structure
* if v is NULL, memory is allocated for the structure
*/
int i;
if (v == NULL)
v = (VARIOGRAM *) emalloc(sizeof(VARIOGRAM));
v->id = v->id1 = v->id2 = -1;
v->n_models = 0;
v->is_valid_covariance = 1;
v->isotropic = 1;
v->n_fit = 0;
v->fit_is_singular = 0;
v->max_range = (double) DBL_MIN;
v->sum_sills = 0.0;
v->measurement_error = 0.0;
v->max_val = 0.0;
v->min_val = 0.0;
vgm_init_block_values(v);
v->part = (VGM_MODEL *) emalloc(INIT_N_VGMM * sizeof(VGM_MODEL));
v->table = NULL;
for (i = 0; i < INIT_N_VGMM; i++)
init_variogram_part(&(v->part[i]));
v->max_n_models = INIT_N_VGMM;
v->SSErr = 0.0;
v->ev = init_ev();
return v;
}
void vgm_init_block_values(VARIOGRAM *v) {
v->block_semivariance_set = 0;
v->block_covariance_set = 0;
v->block_covariance = -999999.0;
v->block_semivariance = -999999.0;
}
static void init_variogram_part(VGM_MODEL *p) {
int i;
p->sill = 0.0;
for (i = 0; i < NRANGEPARS; i++) {
p->range[i] = 0.0; /* quiets valgrind? */
set_mv_double(&(p->range[i])); /* trigger errors if misused */
}
p->model = NOT_SP;
p->fit_sill = p->fit_range = 1;
p->fnct = p->da_fnct = NULL;
p->tm_range = NULL;
p->id = -1;
}
SAMPLE_VGM *init_ev(void) {
SAMPLE_VGM *ev = NULL;
ev = (SAMPLE_VGM *) emalloc(sizeof(SAMPLE_VGM));
set_mv_double(&(ev->cutoff));
set_mv_double(&(ev->iwidth));
ev->gamma = NULL;
ev->dist = NULL;
ev->nh = NULL;
ev->pairs = NULL;
ev->n_max = 0;
ev->n_est = 0;
ev->zero = ZERO_DEFAULT;
ev->plot_numbers = 1;
ev->is_directional = 0;
ev->evt = NOTSPECIFIED;
ev->fit = NO_FIT;
ev->recalc = 1;
ev->refit = 1;
ev->pseudo = 0;
ev->is_asym = -1;
ev->map = NULL;
ev->S_grid = NULL;
ev->direction.x = 1.0;
ev->direction.y = ev->direction.z = 0.0;
return ev;
}
void free_variogram(VARIOGRAM *v) {
int i;
assert(v != NULL);
if (v->ev) {
if (v->ev->n_max > 0) {
efree(v->ev->gamma);
efree(v->ev->dist);
efree(v->ev->nh);
if (v->ev->pairs)
efree(v->ev->pairs);
}
if (v->ev->map)
efree(v->ev->map);
efree(v->ev);
}
for (i = 0; i < v->max_n_models; i++)
if (v->part[i].tm_range != NULL)
efree(v->part[i].tm_range);
efree(v->part);
if (v->table) {
efree(v->table->values);
efree(v->table);
}
efree(v);
}
void logprint_variogram(const VARIOGRAM *v, int verbose) {
/* prints contents of VARIOGRAM v to R console */
if (v->id1 < 0 && v->id2 < 0)
return; /* never set */
if (v->id1 == v->id2)
Rprintf("variogram(%s):\n", name_identifier(v->id1));
else
Rprintf("variogram(%s,%s):\n", name_identifier(v->id1), name_identifier(v->id2));
for (int i = 0; i < v->n_models; i++) {
Rprintf("# model: %d type: %s sill: %g range: %g\n",
i, v_models[v->part[i].model].name_long, v->part[i].sill, v->part[i].range[0]);
if (v->part[i].tm_range != NULL) {
Rprintf("# range anisotropy, rotation matrix:\n");
for (int j = 0; j < 3; j++) {
for (int k = 0; k < 3; k++)
Rprintf("%s%8.4f", k == 0 ? "# " : " ", v->part[i].tm_range->tm[j][k]);
Rprintf("\n");
}
}
}
Rprintf( "# sum sills %g, max %g, min %g, flat at distance %g\n",
v->sum_sills, v->max_val, v->min_val, v->max_range);
return;
}
void update_variogram(VARIOGRAM *vp) {
/*
* update min/max, n_fit, descr
* assumes that models are not changed: they can only be changed through
* read_variogram();
*/
VGM_MODEL *p;
vp->sum_sills = vp->min_val = vp->max_val = 0.0;
vp->measurement_error = 0.0;
vp->n_fit = 0;
vp->max_range = DBL_MIN;
for (int i = 0; i < vp->n_models; i++) {
p = &(vp->part[i]);
vp->sum_sills += p->sill;
if (p->sill < 0.0)
vp->min_val += p->sill;
/* else */ /* up to gstat_1.1-1 else was there; see https://stat.ethz.ch/pipermail/r-sig-geo/2015-December/023814.html */
vp->max_val += p->sill;
vp->max_range = MAX(p->range[0], vp->max_range);
if (p->model == BESSEL || p->model == GAUSSIAN ||
p->model == EXPONENTIAL || p->model == LOGARITHMIC ||
p->model == POWER || p->model == PERIODIC ||
p->model == EXCLASS || p->model == LEGENDRE ||
p->model == HOLE || p->model == WAVE || /* more??? */
p->model == MATERN ||
p->model == STEIN ||
(p->model == LINEAR && p->range[0] == 0))
/* sill is reached asymptotically or oscillates */
vp->max_range = DBL_MAX;
else /* transitive model: */
vp->max_range = MAX(p->range[0], vp->max_range);
if ((p->model == LINEAR && p->range[0] == 0.0) || p->model == NUGGET
|| p->model == INTERCEPT)
p->fit_range = 0; /* 1 would lead to singularity */
if (p->model == LOGARITHMIC || p->model == POWER || p->model == INTERCEPT
|| (p->model == LINEAR && p->range[0] == 0))
vp->is_valid_covariance = 0;
if (p->fit_sill)
vp->n_fit++;
if (p->fit_range)
vp->n_fit++;
if (p->model == MERROR)
vp->measurement_error += p->sill;
}
if (vp->table != NULL) {
vp->sum_sills = vp->table->values[0];
vp->max_val = vp->table->values[0];
vp->min_val = vp->table->values[0];
for (int i = 1; i < vp->table->n; i++) {
vp->max_val = MAX(vp->max_val, vp->table->values[i]);
vp->min_val = MIN(vp->min_val, vp->table->values[i]);
}
}
return;
}
/*
double get_max_sill(int n) {
int i, j;
VARIOGRAM *vp;
static double max_sill;
vp = get_vgm(0);
max_sill = vp->max_val;
for (i = 0; i < n; i++) {
for (j = 0; j <= i; j++) {
vp = get_vgm(LTI(i,j));
max_sill = MAX(max_sill, vp->max_val);
}
}
return max_sill;
}
*/
double get_semivariance(const VARIOGRAM *vp, double dx, double dy, double dz) {
/* returns gamma(dx,dy,dz) for variogram v: gamma(h) = cov(0) - cov(h) */
int i;
double sv = 0.0, dist = 0.0;
if (vp->table != NULL)
return(SEM_TABLE_VALUE(vp->table,
transform_norm(vp->table->tm_range, dx, dy, dz)));
if (! vp->isotropic) {
for (i = 0; i < vp->n_models; i++)
sv += vp->part[i].sill * vp->part[i].fnct(
transform_norm(vp->part[i].tm_range, dx, dy, dz),
vp->part[i].range);
} else {
dist = transform_norm(NULL, dx, dy, dz);
if (dist > vp->max_range)
return vp->sum_sills;
for (i = 0; i < vp->n_models; i++)
sv += vp->part[i].sill * vp->part[i].fnct(dist, vp->part[i].range);
}
return sv;
}
double get_covariance(const VARIOGRAM *vp, double dx, double dy, double dz) {
/* returns cov(dx,dy,dz) for variogram v */
int i;
static int warning = 0;
double ctmp = 0.0, dist;
if (vp == NULL) {
warning = 0;
return 0.0;
}
if (! vp->is_valid_covariance && !warning) {
pr_warning("non-transitive variogram model not allowed as covariance function");
warning = 1;
}
if (!vp->is_valid_covariance && !DEBUG_FORCE)
ErrMsg(ER_IMPOSVAL, "covariance from non-transitive variogram not allowed ");
if (vp->table != NULL)
return(COV_TABLE_VALUE(vp->table,
transform_norm(vp->table->tm_range, dx, dy, dz)));
if (! vp->isotropic) {
for (i = 0; i < vp->n_models; i++)
ctmp += vp->part[i].sill * (1.0 - vp->part[i].fnct(
transform_norm(vp->part[i].tm_range, dx, dy, dz),
vp->part[i].range));
} else {
dist = transform_norm(NULL, dx, dy, dz);
for (i = 0; i < vp->n_models; i++)
ctmp += vp->part[i].sill * (1.0 - vp->part[i].fnct(dist,
vp->part[i].range));
}
return ctmp;
}
static int is_valid_cs(const VARIOGRAM *aa, const VARIOGRAM *bb,
const VARIOGRAM *ab)
/*
* Purpose : Check Cauchy-Schwartz inequality on cross/variograms
* Created by : Edzer J. Pebesma
* Date : may 6th 1992
* Prerequisites :
* Returns : return nonzero if |g_ab(h)| > sqrt(g_aa(h)g_bb(h))
* Side effects : none
*/
{
int i, check_failed = 0;
double maxrange = 0, dist, dx, dy, dz;
for (i = 0; i < aa->n_models; i++)
if (aa->part[i].range[0] > maxrange)
maxrange = aa->part[i].range[0];
for (i = 0; i < ab->n_models; i++)
if (ab->part[i].range[0] > maxrange)
maxrange = ab->part[i].range[0];
for (i = 0; i < bb->n_models; i++)
if (bb->part[i].range[0] > maxrange)
maxrange = bb->part[i].range[0];
for (i = 0; i < 101 && !check_failed; i++) {
dist = (i * maxrange)/100;
dx = dy = dz = 0.0;
if (i % 3 == 0) dx = dist;
if (i % 3 == 1) dy = dist;
if (i % 3 == 2) dz = dist;
if (fabs(get_semivariance(ab, dx, dy, dz)) >
sqrt(get_semivariance(aa, dx, dy, dz) *
get_semivariance(bb, dx, dy, dz))) {
check_failed = 1; /* yes, the check failed */
pr_warning("%s %d %s %d %s %d\n%s %g %g %g\n",
"Cauchy-Schwartz violation: variogram",
aa->id,",",bb->id, "and cross variogram", ab->id,
"first failure on dx, dy and dz:", dx, dy, dz);
}
} /* for */
if (check_failed)
return 0;
else
return 1;
}
void check_variography(const VARIOGRAM **v, int n_vars)
/*
* check for intrinsic correlation, linear model of coregionalisation
* or else (with warning) Cauchy Swartz
*/
{
int i, j, k, ic = 0, lmc, posdef = 1;
MAT **a = NULL;
double b;
char *reason = NULL;
if (n_vars <= 1)
return;
/*
* find out if lmc (linear model of coregionalization) hold:
* all models must have equal base models (sequence and range)
*/
for (i = 1, lmc = 1; lmc && i < get_n_vgms(); i++) {
if (v[0]->n_models != v[i]->n_models) {
reason = "number of models differ";
lmc = 0;
}
for (k = 0; lmc && k < v[0]->n_models; k++) {
if (v[0]->part[k].model != v[i]->part[k].model) {
reason = "model types differ";
lmc = 0;
}
if (v[0]->part[k].range[0] != v[i]->part[k].range[0]) {
reason = "ranges differ";
lmc = 0;
}
}
for (k = 0; lmc && k < v[0]->n_models; k++)
if (v[0]->part[k].tm_range != NULL) {
if (v[i]->part[k].tm_range == NULL) {
reason = "anisotropy for part of models";
lmc = 0;
} else if (
v[0]->part[k].tm_range->ratio[0] != v[i]->part[k].tm_range->ratio[0] ||
v[0]->part[k].tm_range->ratio[1] != v[i]->part[k].tm_range->ratio[1] ||
v[0]->part[k].tm_range->angle[0] != v[i]->part[k].tm_range->angle[0] ||
v[0]->part[k].tm_range->angle[1] != v[i]->part[k].tm_range->angle[1] ||
v[0]->part[k].tm_range->angle[2] != v[i]->part[k].tm_range->angle[2]
) {
reason = "anisotropy parameters are not equal";
lmc = 0;
}
} else if (v[i]->part[k].tm_range != NULL) {
reason = "anisotropy for part of models";
lmc = 0;
}
}
if (lmc) {
/*
* check for ic:
*/
a = (MAT **) emalloc(v[0]->n_models * sizeof(MAT *));
for (k = 0; k < v[0]->n_models; k++)
a[k] = m_get(n_vars, n_vars);
for (i = 0; i < n_vars; i++) {
for (j = 0; j < n_vars; j++) { /* for all variogram triplets: */
for (k = 0; k < v[0]->n_models; k++)
ME(a[k], i, j) = v[LTI(i,j)]->part[k].sill;
}
}
/* for ic: a's must be scaled versions of each other: */
ic = 1;
for (k = 1, ic = 1; ic && k < v[0]->n_models; k++) {
b = ME(a[0], 0, 0)/ME(a[k], 0, 0);
for (i = 0; ic && i < n_vars; i++)
for (j = 0; ic && j < n_vars; j++)
if (fabs(ME(a[0], i, j) / ME(a[k], i, j) - b) > EPSILON)
ic = 0;
}
/* check posdef matrices */
for (i = 0, lmc = 1, posdef = 1; i < v[0]->n_models; i++) {
posdef = is_posdef(a[i]);
if (posdef == 0) {
reason = "coefficient matrix not positive definite";
if (DEBUG_COV) {
printlog("non-positive definite coefficient matrix %d:\n",
i);
m_logoutput(a[i]);
}
ic = lmc = 0;
}
if (! posdef)
printlog(
"non-positive definite coefficient matrix in structure %d",
i+1);
}
for (k = 0; k < v[0]->n_models; k++)
m_free(a[k]);
efree(a);
if (ic) {
printlog("Intrinsic Correlation found. Good.\n");
return;
} else if (lmc) {
printlog("Linear Model of Coregionalization found. Good.\n");
return;
}
}
/*
* lmc does not hold: check on Cauchy Swartz
*/
pr_warning("No Intrinsic Correlation or Linear Model of Coregionalization found\nReason: %s", reason ? reason : "unknown");
if (gl_nocheck == 0) {
pr_warning("[add `set = list(nocheck = 1)' to the gstat() or krige() to ignore the following error]\n");
ErrMsg(ER_IMPOSVAL, "variograms do not satisfy a legal model");
}
printlog("Now checking for Cauchy-Schwartz inequalities:\n");
for (i = 0; i < n_vars; i++)
for (j = 0; j < i; j++)
if (is_valid_cs(v[LTI(i,i)], v[LTI(j,j)], v[LTI(i,j)])) {
printlog("variogram(%s,%s) passed Cauchy-Schwartz\n",
name_identifier(j), name_identifier(i));
} else
pr_warning("Cauchy-Schwartz inequality found for variogram(%s,%s)",
name_identifier(j), name_identifier(i) );
return;
}
static int is_posdef(MAT *A) {
MAT *b = m_copy(A, MNULL);
int info;
CHfactor(b, PNULL, &info);
m_free(b);
return (info == 0);
}
double transform_norm(const ANIS_TM *tm, double dx, double dy, double dz) {
/* returns variogram distance given dx, dy, dz and VARIOGRAM v */
double dist = 0.0, tmp;
int i;
if (dx == 0.0 && dy == 0.0 && dz == 0.0)
return 0.0;
if (tm != NULL) {
for (i = 0, tmp = 0.0; i < 3; i++) {
tmp = tm->tm[i][0] * dx + tm->tm[i][1] * dy + tm->tm[i][2] * dz;
dist += tmp * tmp;
}
return sqrt(dist);
}
return sqrt((dx * dx) + (dy * dy) + (dz * dz));
}
double da_general(VGM_MODEL *part, double h) {
/* numerical approximation of derivative: */
int i;
double low, high, range, r[NRANGEPARS];
for (i = 0; i < NRANGEPARS; i++) {
if (is_mv_double(&(part->range[i])))
set_mv_double(&(r[i]));
else
r[i] = part->range[i];
}
range = MAX(1e-20, part->range[0]);
r[0] = range * (1.0 + DA_DELTA);
low = part->fnct(h, r);
r[0] = range * (1.0 - DA_DELTA);
high = part->fnct(h, r);
return part->sill * (low - high) / (2.0 * range * DA_DELTA);
}
int push_variogram_model(VARIOGRAM *v, VGM_MODEL part) {
int i, max_id, where = -1;
/*
* add the part submodel to v (if part.id < 0) or else
* modify the appropriate part of v, having the id of part.id.
* do a lot of checks, and set .fn and .da_fn functions.
*/
if (v->n_models == v->max_n_models) {
v->part = (VGM_MODEL *) erealloc(v->part,
(v->max_n_models + INIT_N_VGMM) * sizeof(VGM_MODEL));
for (i = v->max_n_models; i < v->max_n_models + INIT_N_VGMM; i++)
init_variogram_part(&(v->part[i]));
v->max_n_models += INIT_N_VGMM;
}
/*
* check some things:
*/
if (part.model == NOT_SP)
ErrMsg(ER_IMPOSVAL, "model NSP not allowed in variogram structure");
if (part.range[0] < 0.0)
ErrMsg(ER_RANGE, "variogram range cannot be negative");
if (part.model == LINEAR) {
if (part.range[0] == 0.0)
part.fit_range = 0;
} else if (part.model == NUGGET || part.model == INTERCEPT ||
part.model == MERROR) {
part.fit_range = 0;
if (part.range[0] > 0.0)
ErrMsg(ER_RANGE, "range must be zero");
} else if (part.range[0] == 0.0)
ErrMsg(ER_RANGE, "range must be positive");
if (part.model == POWER && part.range[0] > 2.0)
ErrMsg(ER_RANGE, "power model range (parameter) cannot exceed 2.0");
if (part.model == EXCLASS && part.range[1] > 2.0)
ErrMsg(ER_RANGE, "exponentical class model shape parameter cannot exceed 2.0");
if (part.id < 0) {
where = v->n_models;
v->n_models++;
for (i = max_id = 0; i < v->n_models; i++)
max_id = MAX(v->part[i].id, max_id);
part.id = max_id + 1;
} else { /* search in list: */
for (i = 0; where < 0 && i < v->n_models; i++)
if (v->part[i].id == part.id)
where = i;
assert(where >= 0); /* i.e., it should really be in the list */
}
if (v->isotropic)
v->isotropic = (part.tm_range == NULL);
/*
* check that the .fn and .da_fn functions in v_models
* will indeed be the correct ones:
*/
assert(part.model == v_models[part.model].model);
v->part[where] = part;
v->part[where].fnct = v_models[part.model].fn;
v->part[where].da_fnct = v_models[part.model].da_fn;
return part.id;
}
VGM_MODEL_TYPE which_variogram_model(const char *m) {
char s[4];
strncpy(s, m, 3);
s[0] = toupper(s[0]);
s[1] = tolower(s[1]);
s[2] = tolower(s[2]);
s[3] = '\0';
for (int i = 1; v_models[i].name != NULL; i++)
if (strcmp(s, v_models[i].name) == 0)
return v_models[i].model;
return NOT_SP;
}
double relative_nugget(VARIOGRAM *v) {
int i;
double nug = 0.0, sill = 0.0;
assert(v->n_models != 0);
if (v->n_models == 1)
return (v->part[0].model == NUGGET ? 1.0 : 0.0);
for (i = 0; i < v->n_models; i++) {
if (v->part[i].model == NUGGET)
nug += v->part[i].sill;
else
sill += v->part[i].sill;
}
assert(nug + sill > 0.0);
return (nug/(nug+sill));
}
DO_AT_ZERO zero_int2enum(int zero) {
switch(zero) {
case 0: return ZERO_DEFAULT;
case 1: return ZERO_INCLUDE;
case 2: return ZERO_AVOID;
case 3: return ZERO_SPECIAL;
}
ErrMsg(ER_IMPOSVAL, "invalid value for zero");
return ZERO_DEFAULT; /* never reached */
}
void push_to_v(VARIOGRAM *v, const char *mod, double sill, double *range,
int nrangepars, double *d, int fit_sill, int fit_range) {
VGM_MODEL vm;
int i;
init_variogram_part(&vm);
vm.model = which_variogram_model(mod);
if (nrangepars > NRANGEPARS)
ErrMsg(ER_IMPOSVAL, "too many range parameters");
for (i = 0; i < nrangepars; i++)
vm.range[i] = range[i];
vm.sill = sill;
vm.fit_sill = fit_sill;
vm.fit_range = fit_range;
if (d != NULL && d[0] != -9999.0)
vm.tm_range = get_tm(d);
if (vm.model == STEIN && range[1] > 100.0) {
vm.model = GAUSSIAN;
vm.range[1] = 0.0;
pr_warning("kappa values over 100 overflow gammafn: taking Gaussian approximation");
}
push_variogram_model(v, vm);
}
void push_to_v_table(VARIOGRAM *v, double maxdist, int length, double *values,
double *anis) {
int i;
v->table = (COV_TABLE *) emalloc(sizeof(COV_TABLE));
v->table->n = length;
v->table->maxdist = maxdist;
v->table->values = (double *) emalloc(length * sizeof(double));
for (i = 0; i < length; i++)
v->table->values[i] = values[i];
if (anis != NULL)
v->table->tm_range = get_tm(anis);
else
v->table->tm_range = NULL;
}
static ANIS_TM *get_tm(double anis[5]) {
/* Part of this routine was inspired by FORTRAN code in GSLIB, first edition:
C%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
C %
C Copyright (C) 1992 Stanford Center for Reservoir Forecasting. All %
C rights reserved. Distributed with: C.V. Deutsch and A.G. Journel. %
C ``GSLIB: Geostatistical Software Library and User's Guide,'' Oxford %
C University Press, New York, 1992. %
C %
C The programs in GSLIB are distributed in the hope that they will be %
C useful, but WITHOUT ANY WARRANTY. No author or distributor accepts %
C responsibility to anyone for the consequences of using them or for %
C whether they serve any particular purpose or work at all, unless he %
C says so in writing. Everyone is granted permission to copy, modify %
C and redistribute the programs in GSLIB, but only under the condition %
C that this notice and the above copyright notice remain intact. %
C %
C%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
*/
int i;
double alpha, beta, theta, sina, sinb, sint, cosa, cosb, cost, afac1, afac2;
ANIS_TM *t = NULL;
/*
About naming convention:
gstat GSLIB
===============
anis[0] ang1 (first anis. par. for 2D)
anis[1] ang2
anis[2] ang3
anis[3] anis1 (second anis. par. for 2D)
anis[4] anis2
*/
#define ANIS_ERR(x) message("parsing anis. pars. %g,%g,%g,%g,%g -- error on %g\n", \
anis[0],anis[1],anis[2],anis[3],anis[4],x)
#define DEG2RAD (PI/180.0)
for (i = 0; i < 3; i++) {
if (anis[i] < 0 || anis[i] >= 360) {
ANIS_ERR(anis[i]);
ErrMsg(ER_RANGE, "this value should be in [0..360>");
}
}
for (i = 3; i < 5; i++) {
if (anis[i] <= 0.0 || anis[i] > 1.0) {
ANIS_ERR(anis[i]);
ErrMsg(ER_RANGE, "this value should be in <0..1]");
}
}
/* from GSLIB: */
if (anis[0] >= 0.0 && anis[0] < 270)
alpha = (double) (90.0 - anis[0]) * DEG2RAD;
else
alpha = (double) (450.0 - anis[0]) * DEG2RAD;
beta = -1.0 * (double) anis[1] * DEG2RAD;
theta = (double) anis[2] * DEG2RAD;
sina = sin(alpha);
sinb = sin(beta);
sint = sin(theta);
cosa = cos(alpha);
cosb = cos(beta);
cost = cos(theta);
afac1 = 1.0 / MAX((double) anis[3], (double) EPSILON);
afac2 = 1.0 / MAX((double) anis[4], (double) EPSILON);
t = emalloc(sizeof(ANIS_TM));
t->angle[0] = anis[0];
t->angle[1] = anis[1];
t->angle[2] = anis[2];
t->ratio[0] = anis[3];
t->ratio[1] = anis[4];
t->tm[0][0] = (cosb * cosa);
t->tm[0][1] = (cosb * sina);
t->tm[0][2] = (-sinb);
t->tm[1][0] = afac1*(-cost*sina + sint*sinb*cosa);
t->tm[1][1] = afac1*(cost*cosa + sint*sinb*sina);
t->tm[1][2] = afac1*( sint * cosb);
t->tm[2][0] = afac2*(sint*sina + cost*sinb*cosa);
t->tm[2][1] = afac2*(-sint*cosa + cost*sinb*sina);
t->tm[2][2] = afac2*(cost * cosb);
return t;
}