/* interpolation/akima.c
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman
*
* 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., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
/* Author: G. Jungman
*/
#include <config.h>
#include <stdlib.h>
#include <math.h>
#include <gsl/gsl_errno.h>
#include "integ_eval.h"
#include <gsl/gsl_interp.h>
typedef struct
{
double * b;
double * c;
double * d;
double * _m;
} akima_state_t;
/* common creation */
static void *
akima_alloc (size_t size)
{
akima_state_t *state = (akima_state_t *) malloc (sizeof (akima_state_t));
if (state == NULL)
{
GSL_ERROR_NULL("failed to allocate space for state", GSL_ENOMEM);
}
state->b = (double *) malloc (size * sizeof (double));
if (state->b == NULL)
{
free (state);
GSL_ERROR_NULL("failed to allocate space for b", GSL_ENOMEM);
}
state->c = (double *) malloc (size * sizeof (double));
if (state->c == NULL)
{
free (state->b);
free (state);
GSL_ERROR_NULL("failed to allocate space for c", GSL_ENOMEM);
}
state->d = (double *) malloc (size * sizeof (double));
if (state->d == NULL)
{
free (state->c);
free (state->b);
free (state);
GSL_ERROR_NULL("failed to allocate space for d", GSL_ENOMEM);
}
state->_m = (double *) malloc ((size + 4) * sizeof (double));
if (state->_m == NULL)
{
free (state->d);
free (state->c);
free (state->b);
free (state);
GSL_ERROR_NULL("failed to allocate space for _m", GSL_ENOMEM);
}
return state;
}
/* common calculation */
static void
akima_calc (const double x_array[], double b[], double c[], double d[], size_t size, double m[])
{
size_t i;
for (i = 0; i < (size - 1); i++)
{
const double NE = fabs (m[i + 1] - m[i]) + fabs (m[i - 1] - m[i - 2]);
if (NE == 0.0)
{
b[i] = m[i];
c[i] = 0.0;
d[i] = 0.0;
}
else
{
const double h_i = x_array[i + 1] - x_array[i];
const double NE_next = fabs (m[i + 2] - m[i + 1]) + fabs (m[i] - m[i - 1]);
const double alpha_i = fabs (m[i - 1] - m[i - 2]) / NE;
double alpha_ip1;
double tL_ip1;
if (NE_next == 0.0)
{
tL_ip1 = m[i];
}
else
{
alpha_ip1 = fabs (m[i] - m[i - 1]) / NE_next;
tL_ip1 = (1.0 - alpha_ip1) * m[i] + alpha_ip1 * m[i + 1];
}
b[i] = (1.0 - alpha_i) * m[i - 1] + alpha_i * m[i];
c[i] = (3.0 * m[i] - 2.0 * b[i] - tL_ip1) / h_i;
d[i] = (b[i] + tL_ip1 - 2.0 * m[i]) / (h_i * h_i);
}
}
}
static int
akima_init (void * vstate, const double x_array[], const double y_array[],
size_t size)
{
akima_state_t *state = (akima_state_t *) vstate;
double * m = state->_m + 2; /* offset so we can address the -1,-2
components */
size_t i;
for (i = 0; i <= size - 2; i++)
{
m[i] = (y_array[i + 1] - y_array[i]) / (x_array[i + 1] - x_array[i]);
}
/* non-periodic boundary conditions */
m[-2] = 3.0 * m[0] - 2.0 * m[1];
m[-1] = 2.0 * m[0] - m[1];
m[size - 1] = 2.0 * m[size - 2] - m[size - 3];
m[size] = 3.0 * m[size - 2] - 2.0 * m[size - 3];
akima_calc (x_array, state->b, state->c, state->d, size, m);
return GSL_SUCCESS;
}
static int
akima_init_periodic (void * vstate,
const double x_array[],
const double y_array[],
size_t size)
{
akima_state_t *state = (akima_state_t *) vstate;
double * m = state->_m + 2; /* offset so we can address the -1,-2
components */
size_t i;
for (i = 0; i <= size - 2; i++)
{
m[i] = (y_array[i + 1] - y_array[i]) / (x_array[i + 1] - x_array[i]);
}
/* periodic boundary conditions */
m[-2] = m[size - 1 - 2];
m[-1] = m[size - 1 - 1];
m[size - 1] = m[0];
m[size] = m[1];
akima_calc (x_array, state->b, state->c, state->d, size, m);
return GSL_SUCCESS;
}
static void
akima_free (void * vstate)
{
akima_state_t *state = (akima_state_t *) vstate;
free (state->b);
free (state->c);
free (state->d);
free (state->_m);
free (state);
}
static
int
akima_eval (const void * vstate,
const double x_array[], const double y_array[], size_t size,
double x,
gsl_interp_accel * a,
double *y)
{
const akima_state_t *state = (const akima_state_t *) vstate;
size_t index;
if (a != 0)
{
index = gsl_interp_accel_find (a, x_array, size, x);
}
else
{
index = gsl_interp_bsearch (x_array, x, 0, size - 1);
}
/* evaluate */
{
const double x_lo = x_array[index];
const double delx = x - x_lo;
const double b = state->b[index];
const double c = state->c[index];
const double d = state->d[index];
*y = y_array[index] + delx * (b + delx * (c + d * delx));
return GSL_SUCCESS;
}
}
static int
akima_eval_deriv (const void * vstate,
const double x_array[], const double y_array[], size_t size,
double x,
gsl_interp_accel * a,
double *dydx)
{
const akima_state_t *state = (const akima_state_t *) vstate;
size_t index;
DISCARD_POINTER(y_array); /* prevent warning about unused parameter */
if (a != 0)
{
index = gsl_interp_accel_find (a, x_array, size, x);
}
else
{
index = gsl_interp_bsearch (x_array, x, 0, size - 1);
}
/* evaluate */
{
double x_lo = x_array[index];
double delx = x - x_lo;
double b = state->b[index];
double c = state->c[index];
double d = state->d[index];
*dydx = b + delx * (2.0 * c + 3.0 * d * delx);
return GSL_SUCCESS;
}
}
static
int
akima_eval_deriv2 (const void * vstate,
const double x_array[], const double y_array[], size_t size,
double x,
gsl_interp_accel * a,
double *y_pp)
{
const akima_state_t *state = (const akima_state_t *) vstate;
size_t index;
DISCARD_POINTER(y_array); /* prevent warning about unused parameter */
if (a != 0)
{
index = gsl_interp_accel_find (a, x_array, size, x);
}
else
{
index = gsl_interp_bsearch (x_array, x, 0, size - 1);
}
/* evaluate */
{
const double x_lo = x_array[index];
const double delx = x - x_lo;
const double c = state->c[index];
const double d = state->d[index];
*y_pp = 2.0 * c + 6.0 * d * delx;
return GSL_SUCCESS;
}
}
static
int
akima_eval_integ (const void * vstate,
const double x_array[], const double y_array[], size_t size,
gsl_interp_accel * acc,
double a, double b,
double * result)
{
const akima_state_t *state = (const akima_state_t *) vstate;
size_t i, index_a, index_b;
if (acc != 0)
{
index_a = gsl_interp_accel_find (acc, x_array, size, a);
index_b = gsl_interp_accel_find (acc, x_array, size, b);
}
else
{
index_a = gsl_interp_bsearch (x_array, a, 0, size - 1);
index_b = gsl_interp_bsearch (x_array, b, 0, size - 1);
}
*result = 0.0;
/* interior intervals */
for(i=index_a; i<=index_b; i++) {
const double x_hi = x_array[i + 1];
const double x_lo = x_array[i];
const double y_lo = y_array[i];
const double dx = x_hi - x_lo;
if(dx != 0.0) {
if (i == index_a || i == index_b)
{
double x1 = (i == index_a) ? a : x_lo;
double x2 = (i == index_b) ? b : x_hi;
*result += integ_eval (y_lo, state->b[i], state->c[i], state->d[i],
x_lo, x1, x2);
}
else
{
*result += dx * (y_lo
+ dx*(0.5*state->b[i]
+ dx*(state->c[i]/3.0
+ 0.25*state->d[i]*dx)));
}
}
else {
*result = 0.0;
return GSL_EINVAL;
}
}
return GSL_SUCCESS;
}
static const gsl_interp_type akima_type =
{
"akima",
5,
&akima_alloc,
&akima_init,
&akima_eval,
&akima_eval_deriv,
&akima_eval_deriv2,
&akima_eval_integ,
&akima_free
};
const gsl_interp_type * gsl_interp_akima = &akima_type;
static const gsl_interp_type akima_periodic_type =
{
"akima-periodic",
5,
&akima_alloc,
&akima_init_periodic,
&akima_eval,
&akima_eval_deriv,
&akima_eval_deriv2,
&akima_eval_integ,
&akima_free
};
const gsl_interp_type * gsl_interp_akima_periodic = &akima_periodic_type;