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/*!
* \file func2d.c
*
* \author
* Lubos Mitas (original program and various modifications)
*
* \author
* H. Mitasova,
* I. Kosinovsky, D. Gerdes,
* D. McCauley
* (GRASS4.1 version of the program and GRASS4.2 modifications)
*
* \author
* L. Mitas ,
* H. Mitasova ,
* I. Kosinovsky,
* D.Gerdes
* D. McCauley (1993, 1995)
*
* \author modified by McCauley in August 1995
* \author modified by Mitasova in August 1995, Nov. 1996
*
* \copyright
* (C) 1993-1999 by Lubos Mitas and the GRASS Development Team
*
* \copyright
* This program is free software under the
* GNU General Public License (>=v2).
* Read the file COPYING that comes with GRASS
* for details.
*/
#include <stdio.h>
#include <math.h>
#include <grass/gis.h>
#include <grass/interpf.h>
/* parameter description from DESCRIPTION.INTERP */
/*!
* Radial basis function
*
* Radial basis function - completely regularized spline with tension (d=2)
*
*/
double IL_crst(double r, /**< distance squared */
double fi /**< tension */
)
{
double rfsta2 = fi * fi * r / 4.;
static double c[4] = {8.5733287401, 18.0590169730, 8.6347608925,
0.2677737343};
static double b[4] = {9.5733223454, 25.6329561486, 21.0996530827,
3.9584969228};
double ce = 0.57721566;
static double u[10] = {
1.e+00,
-.25e+00,
.055555555555556e+00,
-.010416666666667e+00, /*fixed bug 415.. repl. by 416.. */
.166666666666667e-02,
-2.31481481481482e-04,
2.83446712018141e-05,
-3.10019841269841e-06,
3.06192435822065e-07,
-2.75573192239859e-08};
double x = rfsta2;
double res;
double e1, ea, eb;
if (x < 1.e+00) {
res = x *
(u[0] +
x * (u[1] +
x * (u[2] +
x * (u[3] +
x * (u[4] +
x * (u[5] +
x * (u[6] +
x * (u[7] +
x * (u[8] + x * u[9])))))))));
return (res);
}
if (x > 25.e+00)
e1 = 0.00;
else {
ea = c[3] + x * (c[2] + x * (c[1] + x * (c[0] + x)));
eb = b[3] + x * (b[2] + x * (b[1] + x * (b[0] + x)));
e1 = (ea / eb) / (x * exp(x));
}
res = e1 + ce + log(x);
return (res);
}
/*!
* Function for calculating derivatives (d=2)
*
* Derivatives of radial basis function - regularized spline with tension(d=2)
*/
int IL_crstg(double r, /**< distance squared */
double fi, /**< tension */
double *gd1, /**< G1(r) */
double *gd2 /**< G2(r) */
)
{
double r2 = r;
double rfsta2 = fi * fi * r / 4.;
double x, exm, oneme, hold;
double fsta2 = fi * fi / 2.;
x = rfsta2;
if (x < 0.001) {
*gd1 = 1. - x / 2. + x * x / 6. - x * x * x / 24.;
*gd2 = fsta2 * (-.5 + x / 3. - x * x / 8. + x * x * x / 30.);
}
else {
if (x < 35.e+00) {
exm = exp(-x);
oneme = 1. - exm;
*gd1 = oneme / x;
hold = x * exm - oneme;
*gd2 = (hold + hold) / (r2 * x);
}
else {
*gd1 = 1. / x;
*gd2 = -2. / (x * r2);
}
}
return 1;
}
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