bicubic.c

/*
 * This file is part of interp2d, a GSL-compatible two-dimensional
 * interpolation library. <http://www.ellipsix.net/interp2d.html>
 *
 * Copyright 2012 Thomas Beutlich, David Zaslavsky
 * Portions based on alglib 3.6 interpolation code,
 *  copyright Sergey Bochkanov
 * Portions based on GNU GSL interpolation code,
 *  copyright 1996, 1997, 1998, 1999, 2000, 2004 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, see <http://www.gnu.org/licenses/>.
 */

#include <gsl/gsl_errno.h>
#include <gsl/gsl_interp.h>
#include <gsl/gsl_spline.h>
#include <gsl/gsl_vector.h>
#include <math.h>
#include "interp2d.h"

typedef struct
{
    double * zx;
    double * zy;
    double * zxy;
} bicubic_state_t;

static void* bicubic_alloc(size_t xsize, size_t ysize) {
    bicubic_state_t *state = (bicubic_state_t*) malloc(sizeof (bicubic_state_t));
    if (state == NULL)
    {
        GSL_ERROR_NULL("failed to allocate space for state", GSL_ENOMEM);
    }

    state->zx = (double *) malloc (xsize * ysize * sizeof (double));
    if (state->zx == NULL)
    {
        free (state);
        GSL_ERROR_NULL("failed to allocate space for zx", GSL_ENOMEM);
    }

    state->zy = (double *) malloc (xsize * ysize * sizeof (double));
    if (state->zy == NULL)
    {
        free (state->zx);
        free (state);
        GSL_ERROR_NULL("failed to allocate space for zy", GSL_ENOMEM);
    }

    state->zxy = (double *) malloc (xsize * ysize * sizeof (double));
    if (state->zxy == NULL)
    {
        free (state->zx);
        free (state->zy);
        free (state);
        GSL_ERROR_NULL("failed to allocate space for zxy", GSL_ENOMEM);
    }

  return state;
}

static int bicubic_init(void* vstate, const double xa[], const double ya[], const double za[], size_t xsize, size_t ysize) {
    bicubic_state_t *state = (bicubic_state_t *) vstate;

    gsl_interp_accel *acc = gsl_interp_accel_alloc();
    gsl_spline *spline;
    gsl_vector *x;
    gsl_vector *y;
    size_t i, j;

    x = gsl_vector_alloc(xsize);
    y = gsl_vector_alloc(xsize);
    spline = gsl_spline_alloc(gsl_interp_cspline, xsize);
    for (j = 0; j <= ysize - 1; j++)
    {
        for (i = 0; i <= xsize - 1; i++)
        {
            gsl_vector_set(x, i, xa[i]);
            gsl_vector_set(y, i, za[INDEX_2D(i, j, xsize, ysize)]);
        }
        gsl_spline_init(spline, x->data, y->data, xsize);
        for (i = 0; i <= xsize - 1; i++)
        {
            state->zx[INDEX_2D(i, j, xsize, ysize)] = gsl_spline_eval_deriv(spline, xa[i], acc);
        }
    }
    gsl_vector_free(x);
    gsl_vector_free(y);
    gsl_spline_free(spline);
	gsl_interp_accel_reset(acc);

    x = gsl_vector_alloc(ysize);
    y = gsl_vector_alloc(ysize);
    spline = gsl_spline_alloc(gsl_interp_cspline, ysize);
    for (i = 0; i <= xsize - 1; i++)
    {
        for (j = 0; j <= ysize - 1; j++)
        {
            gsl_vector_set(x, j, ya[j]);
            gsl_vector_set(y, j, za[INDEX_2D(i, j, xsize, ysize)]);
        }
        gsl_spline_init(spline, x->data, y->data, ysize);
        for (j = 0; j <= ysize - 1; j++)
        {
            state->zy[INDEX_2D(i, j, xsize, ysize)] = gsl_spline_eval_deriv(spline, ya[j], acc);
        }
    }
    gsl_vector_free(x);
    gsl_vector_free(y);
    gsl_spline_free(spline);
	gsl_interp_accel_reset(acc);

    x = gsl_vector_alloc(xsize);
    y = gsl_vector_alloc(xsize);
    spline = gsl_spline_alloc(gsl_interp_cspline, xsize);
    for (j = 0; j <= ysize - 1; j++)
    {
        for (i = 0; i <= xsize - 1; i++)
        {
            gsl_vector_set(x, i, xa[i]);
            gsl_vector_set(y, i, state->zy[INDEX_2D(i, j, xsize, ysize)]);
        }
        gsl_spline_init(spline, x->data, y->data, xsize);
        for (i = 0; i <= xsize - 1; i++)
        {
            state->zxy[INDEX_2D(i, j, xsize, ysize)] = gsl_spline_eval_deriv(spline, xa[i], acc);
        }
    }
    gsl_vector_free(x);
    gsl_vector_free(y);
    gsl_spline_free(spline);
    gsl_interp_accel_free(acc);
    return GSL_SUCCESS;
}

static void bicubic_free (void * vstate) {
    bicubic_state_t *state = (bicubic_state_t *) vstate;

    free (state->zx);
    free (state->zy);
    free (state->zxy);
    free (state);
}

static int bicubic_eval(const void* vstate, const double xarr[], const double yarr[], const double zarr[], size_t xsize, size_t ysize, double x, double y, gsl_interp_accel* xa, gsl_interp_accel* ya, double* z) {
    bicubic_state_t *state = (bicubic_state_t *) vstate;

    double xmin, xmax, ymin, ymax;
    double zminmin, zminmax, zmaxmin, zmaxmax;
    double zxminmin, zxminmax, zxmaxmin, zxmaxmax;
    double zyminmin, zyminmax, zymaxmin, zymaxmax;
    double zxyminmin, zxyminmax, zxymaxmin, zxymaxmax;
    // dx and dy are the size of the grid cell
    double dx, dy;
    double dt, du;
    // t and u are the positions within the grid cell at which we are computing
    // the interpolation, in units of grid cell size
    double t, u;
    double t0, t1, t2, t3, u0, u1, u2, u3;
    double v;
    size_t xi, yi;
    // First compute the indices into the data arrays where we are interpolating
    if (xa != NULL) {
        xi = gsl_interp_accel_find(xa, xarr, xsize, x);
    }
    else {
        xi = gsl_interp_bsearch(xarr, x, 0, xsize - 1);
    }
    if (ya != NULL) {
        yi = gsl_interp_accel_find(ya, yarr, ysize, y);
    }
    else {
        yi = gsl_interp_bsearch(yarr, y, 0, ysize - 1);
    }
    // Find the minimum and maximum values on the grid cell in each dimension
    xmin = xarr[xi];
    xmax = xarr[xi + 1];
    ymin = yarr[yi];
    ymax = yarr[yi + 1];
    zminmin = zarr[INDEX_2D(xi, yi, xsize, ysize)];
    zminmax = zarr[INDEX_2D(xi, yi + 1, xsize, ysize)];
    zmaxmin = zarr[INDEX_2D(xi + 1, yi, xsize, ysize)];
    zmaxmax = zarr[INDEX_2D(xi + 1, yi + 1, xsize, ysize)];
    // Get the width and height of the grid cell
    dx = xmax - xmin;
    dy = ymax - ymin;
    t = (x - xmin)/dx;
    u = (y - ymin)/dy;
    dt = 1./dx; // partial t / partial x
    du = 1./dy; // partial u / partial y
    zxminmin = state->zx[INDEX_2D(xi, yi, xsize, ysize)]/dt;
    zxminmax = state->zx[INDEX_2D(xi, yi + 1, xsize, ysize)]/dt;
    zxmaxmin = state->zx[INDEX_2D(xi + 1, yi, xsize, ysize)]/dt;
    zxmaxmax = state->zx[INDEX_2D(xi + 1, yi + 1, xsize, ysize)]/dt;
    zyminmin = state->zy[INDEX_2D(xi, yi, xsize, ysize)]/du;
    zyminmax = state->zy[INDEX_2D(xi, yi + 1, xsize, ysize)]/du;
    zymaxmin = state->zy[INDEX_2D(xi + 1, yi, xsize, ysize)]/du;
    zymaxmax = state->zy[INDEX_2D(xi + 1, yi + 1, xsize, ysize)]/du;
    zxyminmin = state->zxy[INDEX_2D(xi, yi, xsize, ysize)]/(dt*du);
    zxyminmax = state->zxy[INDEX_2D(xi, yi + 1, xsize, ysize)]/(dt*du);
    zxymaxmin = state->zxy[INDEX_2D(xi + 1, yi, xsize, ysize)]/(dt*du);
    zxymaxmax = state->zxy[INDEX_2D(xi + 1, yi + 1, xsize, ysize)]/(dt*du);
    t0 = 1;
    t1 = t;
    t2 = t*t;
    t3 = t*t2;
    u0 = 1;
    u1 = u;
    u2 = u*u;
    u3 = u*u2;

    *z = 0;
    v = zminmin;
    *z += v*t0*u0;
    v = zyminmin;
    *z += v*t0*u1;
    v = -3*zminmin + 3*zminmax - 2*zyminmin - zyminmax;
    *z += v*t0*u2;
    v = 2*zminmin - 2*zminmax + zyminmin + zyminmax;
    *z += v*t0*u3;
    v = zxminmin;
    *z += v*t1*u0;
    v = zxyminmin;
    *z += v*t1*u1;
    v = -3*zxminmin + 3*zxminmax - 2*zxyminmin - zxyminmax;
    *z += v*t1*u2;
    v = 2*zxminmin - 2*zxminmax + zxyminmin + zxyminmax;
    *z += v*t1*u3;
    v = -3*zminmin + 3*zmaxmin - 2*zxminmin - zxmaxmin;
    *z += v*t2*u0;
    v = -3*zyminmin + 3*zymaxmin - 2*zxyminmin - zxymaxmin;
    *z += v*t2*u1;
    v = 9*zminmin - 9*zmaxmin + 9*zmaxmax - 9*zminmax + 6*zxminmin + 3*zxmaxmin - 3*zxmaxmax - 6*zxminmax + 6*zyminmin - 6*zymaxmin - 3*zymaxmax + 3*zyminmax + 4*zxyminmin + 2*zxymaxmin + zxymaxmax + 2*zxyminmax;
    *z += v*t2*u2;
    v = -6*zminmin + 6*zmaxmin - 6*zmaxmax + 6*zminmax - 4*zxminmin - 2*zxmaxmin + 2*zxmaxmax + 4*zxminmax - 3*zyminmin + 3*zymaxmin + 3*zymaxmax - 3*zyminmax - 2*zxyminmin - zxymaxmin - zxymaxmax - 2*zxyminmax;
    *z += v*t2*u3;
    v = 2*zminmin - 2*zmaxmin + zxminmin + zxmaxmin;
    *z += v*t3*u0;
    v = 2*zyminmin - 2*zymaxmin + zxyminmin + zxymaxmin;
    *z += v*t3*u1;
    v = -6*zminmin + 6*zmaxmin - 6*zmaxmax + 6*zminmax - 3*zxminmin - 3*zxmaxmin + 3*zxmaxmax + 3*zxminmax - 4*zyminmin + 4*zymaxmin + 2*zymaxmax - 2*zyminmax - 2*zxyminmin - 2*zxymaxmin - zxymaxmax - zxyminmax;
    *z += v*t3*u2;
    v = 4*zminmin - 4*zmaxmin + 4*zmaxmax - 4*zminmax + 2*zxminmin + 2*zxmaxmin - 2*zxmaxmax - 2*zxminmax + 2*zyminmin - 2*zymaxmin - 2*zymaxmax + 2*zyminmax + zxyminmin + zxymaxmin + zxymaxmax + zxyminmax;
    *z += v*t3*u3;
    return GSL_SUCCESS;
}

static int bicubic_deriv_x(const void* vstate, const double xarr[], const double yarr[], const double zarr[], size_t xsize, size_t ysize, double x, double y, gsl_interp_accel* xa, gsl_interp_accel* ya, double* z_p) {
    bicubic_state_t *state = (bicubic_state_t *) vstate;

    double xmin, xmax, ymin, ymax;
    double zminmin, zminmax, zmaxmin, zmaxmax;
    double zxminmin, zxminmax, zxmaxmin, zxmaxmax;
    double zyminmin, zyminmax, zymaxmin, zymaxmax;
    double zxyminmin, zxyminmax, zxymaxmin, zxymaxmax;
    // dx and dy are the size of the grid cell
    double dx, dy;
    double dt, du;
    // t and u are the positions within the grid cell at which we are computing
    // the interpolation, in units of grid cell size
    double t, u;
    double t0, t1, t2, u0, u1, u2, u3;
    double v;
    size_t xi, yi;
    // First compute the indices into the data arrays where we are interpolating
    if (xa != NULL) {
        xi = gsl_interp_accel_find(xa, xarr, xsize, x);
    }
    else {
        xi = gsl_interp_bsearch(xarr, x, 0, xsize - 1);
    }
    if (ya != NULL) {
        yi = gsl_interp_accel_find(ya, yarr, ysize, y);
    }
    else {
        yi = gsl_interp_bsearch(yarr, y, 0, ysize - 1);
    }
    // Find the minimum and maximum values on the grid cell in each dimension
    xmin = xarr[xi];
    xmax = xarr[xi + 1];
    ymin = yarr[yi];
    ymax = yarr[yi + 1];
    zminmin = zarr[INDEX_2D(xi, yi, xsize, ysize)];
    zminmax = zarr[INDEX_2D(xi, yi + 1, xsize, ysize)];
    zmaxmin = zarr[INDEX_2D(xi + 1, yi, xsize, ysize)];
    zmaxmax = zarr[INDEX_2D(xi + 1, yi + 1, xsize, ysize)];
    // Get the width and height of the grid cell
    dx = xmax - xmin;
    dy = ymax - ymin;
    t = (x - xmin)/dx;
    u = (y - ymin)/dy;
    dt = 1./dx; // partial t / partial x
    du = 1./dy; // partial u / partial y
    zxminmin = state->zx[INDEX_2D(xi, yi, xsize, ysize)]/dt;
    zxminmax = state->zx[INDEX_2D(xi, yi + 1, xsize, ysize)]/dt;
    zxmaxmin = state->zx[INDEX_2D(xi + 1, yi, xsize, ysize)]/dt;
    zxmaxmax = state->zx[INDEX_2D(xi + 1, yi + 1, xsize, ysize)]/dt;
    zyminmin = state->zy[INDEX_2D(xi, yi, xsize, ysize)]/du;
    zyminmax = state->zy[INDEX_2D(xi, yi + 1, xsize, ysize)]/du;
    zymaxmin = state->zy[INDEX_2D(xi + 1, yi, xsize, ysize)]/du;
    zymaxmax = state->zy[INDEX_2D(xi + 1, yi + 1, xsize, ysize)]/du;
    zxyminmin = state->zxy[INDEX_2D(xi, yi, xsize, ysize)]/(dt*du);
    zxyminmax = state->zxy[INDEX_2D(xi, yi + 1, xsize, ysize)]/(dt*du);
    zxymaxmin = state->zxy[INDEX_2D(xi + 1, yi, xsize, ysize)]/(dt*du);
    zxymaxmax = state->zxy[INDEX_2D(xi + 1, yi + 1, xsize, ysize)]/(dt*du);
    t0 = 1;
    t1 = t;
    t2 = t*t;
    u0 = 1;
    u1 = u;
    u2 = u*u;
    u3 = u*u2;

    *z_p = 0;
    v = zxminmin;
    *z_p += v*t0*u0;
    v = zxyminmin;
    *z_p += v*t0*u1;
    v = -3*zxminmin + 3*zxminmax - 2*zxyminmin - zxyminmax;
    *z_p += v*t0*u2;
    v = 2*zxminmin - 2*zxminmax + zxyminmin + zxyminmax;
    *z_p += v*t0*u3;
    v = -3*zminmin + 3*zmaxmin - 2*zxminmin - zxmaxmin;
    *z_p += 2*v*t1*u0;
    v = -3*zyminmin + 3*zymaxmin - 2*zxyminmin - zxymaxmin;
    *z_p += 2*v*t1*u1;
    v = 9*zminmin - 9*zmaxmin + 9*zmaxmax - 9*zminmax + 6*zxminmin + 3*zxmaxmin - 3*zxmaxmax - 6*zxminmax + 6*zyminmin - 6*zymaxmin - 3*zymaxmax + 3*zyminmax + 4*zxyminmin + 2*zxymaxmin + zxymaxmax + 2*zxyminmax;
    *z_p += 2*v*t1*u2;
    v = -6*zminmin + 6*zmaxmin - 6*zmaxmax + 6*zminmax - 4*zxminmin - 2*zxmaxmin + 2*zxmaxmax + 4*zxminmax - 3*zyminmin + 3*zymaxmin + 3*zymaxmax - 3*zyminmax - 2*zxyminmin - zxymaxmin - zxymaxmax - 2*zxyminmax;
    *z_p += 2*v*t1*u3;
    v = 2*zminmin - 2*zmaxmin + zxminmin + zxmaxmin;
    *z_p += 3*v*t2*u0;
    v = 2*zyminmin - 2*zymaxmin + zxyminmin + zxymaxmin;
    *z_p += 3*v*t2*u1;
    v = -6*zminmin + 6*zmaxmin - 6*zmaxmax + 6*zminmax - 3*zxminmin - 3*zxmaxmin + 3*zxmaxmax + 3*zxminmax - 4*zyminmin + 4*zymaxmin + 2*zymaxmax - 2*zyminmax - 2*zxyminmin - 2*zxymaxmin - zxymaxmax - zxyminmax;
    *z_p += 3*v*t2*u2;
    v = 4*zminmin - 4*zmaxmin + 4*zmaxmax - 4*zminmax + 2*zxminmin + 2*zxmaxmin - 2*zxmaxmax - 2*zxminmax + 2*zyminmin - 2*zymaxmin - 2*zymaxmax + 2*zyminmax + zxyminmin + zxymaxmin + zxymaxmax + zxyminmax;
    *z_p += 3*v*t2*u3;
    *z_p *= dt;
    return GSL_SUCCESS;
}

static int bicubic_deriv_y(const void* vstate, const double xarr[], const double yarr[], const double zarr[], size_t xsize, size_t ysize, double x, double y, gsl_interp_accel* xa, gsl_interp_accel* ya, double* z_p) {
    bicubic_state_t *state = (bicubic_state_t *) vstate;

    double xmin, xmax, ymin, ymax;
    double zminmin, zminmax, zmaxmin, zmaxmax;
    double zxminmin, zxminmax, zxmaxmin, zxmaxmax;
    double zyminmin, zyminmax, zymaxmin, zymaxmax;
    double zxyminmin, zxyminmax, zxymaxmin, zxymaxmax;
    // dx and dy are the size of the grid cell
    double dx, dy;
    double dt, du;
    // t and u are the positions within the grid cell at which we are computing
    // the interpolation, in units of grid cell size
    double t, u;
    double t0, t1, t2, t3, u0, u1, u2;
    double v;
    size_t xi, yi;
    // First compute the indices into the data arrays where we are interpolating
    if (xa != NULL) {
        xi = gsl_interp_accel_find(xa, xarr, xsize, x);
    }
    else {
        xi = gsl_interp_bsearch(xarr, x, 0, xsize - 1);
    }
    if (ya != NULL) {
        yi = gsl_interp_accel_find(ya, yarr, ysize, y);
    }
    else {
        yi = gsl_interp_bsearch(yarr, y, 0, ysize - 1);
    }
    // Find the minimum and maximum values on the grid cell in each dimension
    xmin = xarr[xi];
    xmax = xarr[xi + 1];
    ymin = yarr[yi];
    ymax = yarr[yi + 1];
    zminmin = zarr[INDEX_2D(xi, yi, xsize, ysize)];
    zminmax = zarr[INDEX_2D(xi, yi + 1, xsize, ysize)];
    zmaxmin = zarr[INDEX_2D(xi + 1, yi, xsize, ysize)];
    zmaxmax = zarr[INDEX_2D(xi + 1, yi + 1, xsize, ysize)];
    // Get the width and height of the grid cell
    dx = xmax - xmin;
    dy = ymax - ymin;
    t = (x - xmin)/dx;
    u = (y - ymin)/dy;
    dt = 1./dx; // partial t / partial x
    du = 1./dy; // partial u / partial y
    zxminmin = state->zx[INDEX_2D(xi, yi, xsize, ysize)]/dt;
    zxminmax = state->zx[INDEX_2D(xi, yi + 1, xsize, ysize)]/dt;
    zxmaxmin = state->zx[INDEX_2D(xi + 1, yi, xsize, ysize)]/dt;
    zxmaxmax = state->zx[INDEX_2D(xi + 1, yi + 1, xsize, ysize)]/dt;
    zyminmin = state->zy[INDEX_2D(xi, yi, xsize, ysize)]/du;
    zyminmax = state->zy[INDEX_2D(xi, yi + 1, xsize, ysize)]/du;
    zymaxmin = state->zy[INDEX_2D(xi + 1, yi, xsize, ysize)]/du;
    zymaxmax = state->zy[INDEX_2D(xi + 1, yi + 1, xsize, ysize)]/du;
    zxyminmin = state->zxy[INDEX_2D(xi, yi, xsize, ysize)]/(dt*du);
    zxyminmax = state->zxy[INDEX_2D(xi, yi + 1, xsize, ysize)]/(dt*du);
    zxymaxmin = state->zxy[INDEX_2D(xi + 1, yi, xsize, ysize)]/(dt*du);
    zxymaxmax = state->zxy[INDEX_2D(xi + 1, yi + 1, xsize, ysize)]/(dt*du);
    t0 = 1;
    t1 = t;
    t2 = t*t;
    t3 = t*t2;
    u0 = 1;
    u1 = u;
    u2 = u*u;

    *z_p = 0;
    v = zyminmin;
    *z_p += v*t0*u0;
    v = -3*zminmin + 3*zminmax - 2*zyminmin - zyminmax;
    *z_p += 2*v*t0*u1;
    v = 2*zminmin-2*zminmax + zyminmin + zyminmax;
    *z_p += 3*v*t0*u2;
    v = zxyminmin;
    *z_p += v*t1*u0;
    v = -3*zxminmin + 3*zxminmax - 2*zxyminmin - zxyminmax;
    *z_p += 2*v*t1*u1;
    v = 2*zxminmin - 2*zxminmax + zxyminmin + zxyminmax;
    *z_p += 3*v*t1*u2;
    v = -3*zyminmin + 3*zymaxmin - 2*zxyminmin - zxymaxmin;
    *z_p += v*t2*u0;
    v = 9*zminmin - 9*zmaxmin + 9*zmaxmax - 9*zminmax + 6*zxminmin + 3*zxmaxmin - 3*zxmaxmax - 6*zxminmax + 6*zyminmin - 6*zymaxmin - 3*zymaxmax + 3*zyminmax + 4*zxyminmin + 2*zxymaxmin + zxymaxmax + 2*zxyminmax;
    *z_p += 2*v*t2*u1;
    v = -6*zminmin + 6*zmaxmin - 6*zmaxmax + 6*zminmax - 4*zxminmin - 2*zxmaxmin + 2*zxmaxmax + 4*zxminmax - 3*zyminmin + 3*zymaxmin + 3*zymaxmax - 3*zyminmax - 2*zxyminmin - zxymaxmin - zxymaxmax - 2*zxyminmax;
    *z_p += 3*v*t2*u2;
    v = 2*zyminmin - 2*zymaxmin + zxyminmin + zxymaxmin;
    *z_p += v*t3*u0;
    v = -6*zminmin + 6*zmaxmin - 6*zmaxmax + 6*zminmax - 3*zxminmin - 3*zxmaxmin + 3*zxmaxmax + 3*zxminmax - 4*zyminmin + 4*zymaxmin + 2*zymaxmax - 2*zyminmax - 2*zxyminmin - 2*zxymaxmin - zxymaxmax - zxyminmax;
    *z_p += 2*v*t3*u1;
    v = 4*zminmin - 4*zmaxmin + 4*zmaxmax - 4*zminmax + 2*zxminmin + 2*zxmaxmin - 2*zxmaxmax - 2*zxminmax + 2*zyminmin - 2*zymaxmin - 2*zymaxmax + 2*zyminmax + zxyminmin + zxymaxmin + zxymaxmax + zxyminmax;
    *z_p += 3*v*t3*u2;
    *z_p *= du;
    return GSL_SUCCESS;
}

static int bicubic_deriv_xx(const void* vstate, const double xarr[], const double yarr[], const double zarr[], size_t xsize, size_t ysize, double x, double y, gsl_interp_accel* xa, gsl_interp_accel* ya, double* z_pp) {
    bicubic_state_t *state = (bicubic_state_t *) vstate;

    double xmin, xmax, ymin, ymax;
    double zminmin, zminmax, zmaxmin, zmaxmax;
    double zxminmin, zxminmax, zxmaxmin, zxmaxmax;
    double zyminmin, zyminmax, zymaxmin, zymaxmax;
    double zxyminmin, zxyminmax, zxymaxmin, zxymaxmax;
    // dx and dy are the size of the grid cell
    double dx, dy;
    double dt, du;
    // t and u are the positions within the grid cell at which we are computing
    // the interpolation, in units of grid cell size
    double t, u;
    double t0, t1, u0, u1, u2, u3;
    double v;
    size_t xi, yi;
    // First compute the indices into the data arrays where we are interpolating
    if (xa != NULL) {
        xi = gsl_interp_accel_find(xa, xarr, xsize, x);
    }
    else {
        xi = gsl_interp_bsearch(xarr, x, 0, xsize - 1);
    }
    if (ya != NULL) {
        yi = gsl_interp_accel_find(ya, yarr, ysize, y);
    }
    else {
        yi = gsl_interp_bsearch(yarr, y, 0, ysize - 1);
    }
    // Find the minimum and maximum values on the grid cell in each dimension
    xmin = xarr[xi];
    xmax = xarr[xi + 1];
    ymin = yarr[yi];
    ymax = yarr[yi + 1];
    zminmin = zarr[INDEX_2D(xi, yi, xsize, ysize)];
    zminmax = zarr[INDEX_2D(xi, yi + 1, xsize, ysize)];
    zmaxmin = zarr[INDEX_2D(xi + 1, yi, xsize, ysize)];
    zmaxmax = zarr[INDEX_2D(xi + 1, yi + 1, xsize, ysize)];
    // Get the width and height of the grid cell
    dx = xmax - xmin;
    dy = ymax - ymin;
    t = (x - xmin)/dx;
    u = (y - ymin)/dy;
    dt = 1./dx; // partial t / partial x
    du = 1./dy; // partial u / partial y
    zxminmin = state->zx[INDEX_2D(xi, yi, xsize, ysize)]/dt;
    zxminmax = state->zx[INDEX_2D(xi, yi + 1, xsize, ysize)]/dt;
    zxmaxmin = state->zx[INDEX_2D(xi + 1, yi, xsize, ysize)]/dt;
    zxmaxmax = state->zx[INDEX_2D(xi + 1, yi + 1, xsize, ysize)]/dt;
    zyminmin = state->zy[INDEX_2D(xi, yi, xsize, ysize)]/du;
    zyminmax = state->zy[INDEX_2D(xi, yi + 1, xsize, ysize)]/du;
    zymaxmin = state->zy[INDEX_2D(xi + 1, yi, xsize, ysize)]/du;
    zymaxmax = state->zy[INDEX_2D(xi + 1, yi + 1, xsize, ysize)]/du;
    zxyminmin = state->zxy[INDEX_2D(xi, yi, xsize, ysize)]/(dt*du);
    zxyminmax = state->zxy[INDEX_2D(xi, yi + 1, xsize, ysize)]/(dt*du);
    zxymaxmin = state->zxy[INDEX_2D(xi + 1, yi, xsize, ysize)]/(dt*du);
    zxymaxmax = state->zxy[INDEX_2D(xi + 1, yi + 1, xsize, ysize)]/(dt*du);
    t0 = 1;
    t1 = t;
    u0 = 1;
    u1 = u;
    u2 = u*u;
    u3 = u*u2;

    *z_pp = 0;
    v = -3*zminmin + 3*zmaxmin - 2*zxminmin - zxmaxmin;
    *z_pp += 2*v*t0*u0;
    v = -3*zyminmin + 3*zymaxmin - 2*zxyminmin - zxymaxmin;
    *z_pp += 2*v*t0*u1;
    v = 9*zminmin - 9*zmaxmin + 9*zmaxmax - 9*zminmax + 6*zxminmin + 3*zxmaxmin - 3*zxmaxmax - 6*zxminmax + 6*zyminmin - 6*zymaxmin - 3*zymaxmax + 3*zyminmax + 4*zxyminmin + 2*zxymaxmin + zxymaxmax + 2*zxyminmax;
    *z_pp += 2*v*t0*u2;
    v = -6*zminmin + 6*zmaxmin - 6*zmaxmax + 6*zminmax - 4*zxminmin - 2*zxmaxmin + 2*zxmaxmax + 4*zxminmax - 3*zyminmin + 3*zymaxmin + 3*zymaxmax - 3*zyminmax - 2*zxyminmin - zxymaxmin - zxymaxmax - 2*zxyminmax;
    *z_pp += 2*v*t0*u3;
    v = 2*zminmin - 2*zmaxmin + zxminmin + zxmaxmin;
    *z_pp += 6*v*t1*u0;
    v = 2*zyminmin - 2*zymaxmin + zxyminmin + zxymaxmin;
    *z_pp += 6*v*t1*u1;
    v = -6*zminmin + 6*zmaxmin - 6*zmaxmax + 6*zminmax - 3*zxminmin - 3*zxmaxmin + 3*zxmaxmax + 3*zxminmax - 4*zyminmin + 4*zymaxmin + 2*zymaxmax - 2*zyminmax - 2*zxyminmin - 2*zxymaxmin - zxymaxmax - zxyminmax;
    *z_pp += 6*v*t1*u2;
    v = 4*zminmin - 4*zmaxmin + 4*zmaxmax - 4*zminmax + 2*zxminmin + 2*zxmaxmin - 2*zxmaxmax - 2*zxminmax + 2*zyminmin - 2*zymaxmin - 2*zymaxmax + 2*zyminmax + zxyminmin + zxymaxmin + zxymaxmax + zxyminmax;
    *z_pp += 6*v*t1*u3;
    *z_pp *= dt*dt;
    return GSL_SUCCESS;
}

static int bicubic_deriv_xy(const void* vstate, const double xarr[], const double yarr[], const double zarr[], size_t xsize, size_t ysize, double x, double y, gsl_interp_accel* xa, gsl_interp_accel* ya, double* z_pp) {
    bicubic_state_t *state = (bicubic_state_t *) vstate;

    double xmin, xmax, ymin, ymax;
    double zminmin, zminmax, zmaxmin, zmaxmax;
    double zxminmin, zxminmax, zxmaxmin, zxmaxmax;
    double zyminmin, zyminmax, zymaxmin, zymaxmax;
    double zxyminmin, zxyminmax, zxymaxmin, zxymaxmax;
    // dx and dy are the size of the grid cell
    double dx, dy;
    double dt, du;
    // t and u are the positions within the grid cell at which we are computing
    // the interpolation, in units of grid cell size
    double t, u;
    double t0, t1, t2, u0, u1, u2;
    double v;
    size_t xi, yi;
    // First compute the indices into the data arrays where we are interpolating
    if (xa != NULL) {
        xi = gsl_interp_accel_find(xa, xarr, xsize, x);
    }
    else {
        xi = gsl_interp_bsearch(xarr, x, 0, xsize - 1);
    }
    if (ya != NULL) {
        yi = gsl_interp_accel_find(ya, yarr, ysize, y);
    }
    else {
        yi = gsl_interp_bsearch(yarr, y, 0, ysize - 1);
    }
    // Find the minimum and maximum values on the grid cell in each dimension
    xmin = xarr[xi];
    xmax = xarr[xi + 1];
    ymin = yarr[yi];
    ymax = yarr[yi + 1];
    zminmin = zarr[INDEX_2D(xi, yi, xsize, ysize)];
    zminmax = zarr[INDEX_2D(xi, yi + 1, xsize, ysize)];
    zmaxmin = zarr[INDEX_2D(xi + 1, yi, xsize, ysize)];
    zmaxmax = zarr[INDEX_2D(xi + 1, yi + 1, xsize, ysize)];
    // Get the width and height of the grid cell
    dx = xmax - xmin;
    dy = ymax - ymin;
    t = (x - xmin)/dx;
    u = (y - ymin)/dy;
    dt = 1./dx; // partial t / partial x
    du = 1./dy; // partial u / partial y
    zxminmin = state->zx[INDEX_2D(xi, yi, xsize, ysize)]/dt;
    zxminmax = state->zx[INDEX_2D(xi, yi + 1, xsize, ysize)]/dt;
    zxmaxmin = state->zx[INDEX_2D(xi + 1, yi, xsize, ysize)]/dt;
    zxmaxmax = state->zx[INDEX_2D(xi + 1, yi + 1, xsize, ysize)]/dt;
    zyminmin = state->zy[INDEX_2D(xi, yi, xsize, ysize)]/du;
    zyminmax = state->zy[INDEX_2D(xi, yi + 1, xsize, ysize)]/du;
    zymaxmin = state->zy[INDEX_2D(xi + 1, yi, xsize, ysize)]/du;
    zymaxmax = state->zy[INDEX_2D(xi + 1, yi + 1, xsize, ysize)]/du;
    zxyminmin = state->zxy[INDEX_2D(xi, yi, xsize, ysize)]/(dt*du);
    zxyminmax = state->zxy[INDEX_2D(xi, yi + 1, xsize, ysize)]/(dt*du);
    zxymaxmin = state->zxy[INDEX_2D(xi + 1, yi, xsize, ysize)]/(dt*du);
    zxymaxmax = state->zxy[INDEX_2D(xi + 1, yi + 1, xsize, ysize)]/(dt*du);
    t0 = 1;
    t1 = t;
    t2 = t*t;
    u0 = 1;
    u1 = u;
    u2 = u*u;

    *z_pp = 0;
    v = zxyminmin;
    *z_pp += v*t0*u0;
    v = -3*zxminmin + 3*zxminmax - 2*zxyminmin - zxyminmax;
    *z_pp += 2*v*t0*u1;
    v = 2*zxminmin - 2*zxminmax + zxyminmin + zxyminmax;
    *z_pp += 3*v*t0*u2;
    v = -3*zyminmin + 3*zymaxmin - 2*zxyminmin - zxymaxmin;
    *z_pp += 2*v*t1*u0;
    v = 9*zminmin - 9*zmaxmin + 9*zmaxmax - 9*zminmax + 6*zxminmin + 3*zxmaxmin - 3*zxmaxmax - 6*zxminmax + 6*zyminmin - 6*zymaxmin - 3*zymaxmax + 3*zyminmax + 4*zxyminmin + 2*zxymaxmin + zxymaxmax + 2*zxyminmax;
    *z_pp += 4*v*t1*u1;
    v = -6*zminmin + 6*zmaxmin - 6*zmaxmax + 6*zminmax - 4*zxminmin - 2*zxmaxmin + 2*zxmaxmax + 4*zxminmax - 3*zyminmin + 3*zymaxmin + 3*zymaxmax - 3*zyminmax - 2*zxyminmin - zxymaxmin - zxymaxmax - 2*zxyminmax;
    *z_pp += 6*v*t1*u2;
    v = 2*zyminmin - 2*zymaxmin + zxyminmin + zxymaxmin;
    *z_pp += 3*v*t2*u0;
    v = -6*zminmin + 6*zmaxmin - 6*zmaxmax + 6*zminmax - 3*zxminmin - 3*zxmaxmin + 3*zxmaxmax + 3*zxminmax - 4*zyminmin + 4*zymaxmin + 2*zymaxmax - 2*zyminmax - 2*zxyminmin - 2*zxymaxmin - zxymaxmax - zxyminmax;
    *z_pp += 6*v*t2*u1;
    v = 4*zminmin - 4*zmaxmin + 4*zmaxmax - 4*zminmax + 2*zxminmin + 2*zxmaxmin - 2*zxmaxmax - 2*zxminmax + 2*zyminmin - 2*zymaxmin - 2*zymaxmax + 2*zyminmax + zxyminmin + zxymaxmin + zxymaxmax + zxyminmax;
    *z_pp += 9*v*t2*u2;
    *z_pp *= dt*du;
    return GSL_SUCCESS;
}

static int bicubic_deriv_yy(const void* vstate, const double xarr[], const double yarr[], const double zarr[], size_t xsize, size_t ysize, double x, double y, gsl_interp_accel* xa, gsl_interp_accel* ya, double* z_pp) {
    bicubic_state_t *state = (bicubic_state_t *) vstate;

    double xmin, xmax, ymin, ymax;
    double zminmin, zminmax, zmaxmin, zmaxmax;
    double zxminmin, zxminmax, zxmaxmin, zxmaxmax;
    double zyminmin, zyminmax, zymaxmin, zymaxmax;
    double zxyminmin, zxyminmax, zxymaxmin, zxymaxmax;
    // dx and dy are the size of the grid cell
    double dx, dy;
    double dt, du;
    // t and u are the positions within the grid cell at which we are computing
    // the interpolation, in units of grid cell size
    double t, u;
    double t0, t1, t2, t3, u0, u1;
    double v;
    size_t xi, yi;
    // First compute the indices into the data arrays where we are interpolating
    if (xa != NULL) {
        xi = gsl_interp_accel_find(xa, xarr, xsize, x);
    }
    else {
        xi = gsl_interp_bsearch(xarr, x, 0, xsize - 1);
    }
    if (ya != NULL) {
        yi = gsl_interp_accel_find(ya, yarr, ysize, y);
    }
    else {
        yi = gsl_interp_bsearch(yarr, y, 0, ysize - 1);
    }
    // Find the minimum and maximum values on the grid cell in each dimension
    xmin = xarr[xi];
    xmax = xarr[xi + 1];
    ymin = yarr[yi];
    ymax = yarr[yi + 1];
    zminmin = zarr[INDEX_2D(xi, yi, xsize, ysize)];
    zminmax = zarr[INDEX_2D(xi, yi + 1, xsize, ysize)];
    zmaxmin = zarr[INDEX_2D(xi + 1, yi, xsize, ysize)];
    zmaxmax = zarr[INDEX_2D(xi + 1, yi + 1, xsize, ysize)];
    // Get the width and height of the grid cell
    dx = xmax - xmin;
    dy = ymax - ymin;
    t = (x - xmin)/dx;
    u = (y - ymin)/dy;
    dt = 1./dx; // partial t / partial x
    du = 1./dy; // partial u / partial y
    zxminmin = state->zx[INDEX_2D(xi, yi, xsize, ysize)]/dt;
    zxminmax = state->zx[INDEX_2D(xi, yi + 1, xsize, ysize)]/dt;
    zxmaxmin = state->zx[INDEX_2D(xi + 1, yi, xsize, ysize)]/dt;
    zxmaxmax = state->zx[INDEX_2D(xi + 1, yi + 1, xsize, ysize)]/dt;
    zyminmin = state->zy[INDEX_2D(xi, yi, xsize, ysize)]/du;
    zyminmax = state->zy[INDEX_2D(xi, yi + 1, xsize, ysize)]/du;
    zymaxmin = state->zy[INDEX_2D(xi + 1, yi, xsize, ysize)]/du;
    zymaxmax = state->zy[INDEX_2D(xi + 1, yi + 1, xsize, ysize)]/du;
    zxyminmin = state->zxy[INDEX_2D(xi, yi, xsize, ysize)]/(dt*du);
    zxyminmax = state->zxy[INDEX_2D(xi, yi + 1, xsize, ysize)]/(dt*du);
    zxymaxmin = state->zxy[INDEX_2D(xi + 1, yi, xsize, ysize)]/(dt*du);
    zxymaxmax = state->zxy[INDEX_2D(xi + 1, yi + 1, xsize, ysize)]/(dt*du);
    t0 = 1;
    t1 = t;
    t2 = t*t;
    t3 = t*t2;
    u0 = 1;
    u1 = u;

    *z_pp = 0;
    v = -3*zminmin + 3*zminmax - 2*zyminmin - zyminmax;
    *z_pp += 2*v*t0*u0;
    v = 2*zminmin-2*zminmax + zyminmin + zyminmax;
    *z_pp += 6*v*t0*u1;
    v = -3*zxminmin + 3*zxminmax - 2*zxyminmin - zxyminmax;
    *z_pp += 2*v*t1*u0;
    v = 2*zxminmin - 2*zxminmax + zxyminmin + zxyminmax;
    *z_pp += 6*v*t1*u1;
    v = 9*zminmin - 9*zmaxmin + 9*zmaxmax - 9*zminmax + 6*zxminmin + 3*zxmaxmin - 3*zxmaxmax - 6*zxminmax + 6*zyminmin - 6*zymaxmin - 3*zymaxmax + 3*zyminmax + 4*zxyminmin + 2*zxymaxmin + zxymaxmax + 2*zxyminmax;
    *z_pp += 2*v*t2*u0;
    v = -6*zminmin + 6*zmaxmin - 6*zmaxmax + 6*zminmax - 4*zxminmin - 2*zxmaxmin + 2*zxmaxmax + 4*zxminmax - 3*zyminmin + 3*zymaxmin + 3*zymaxmax - 3*zyminmax - 2*zxyminmin - zxymaxmin - zxymaxmax - 2*zxyminmax;
    *z_pp += 6*v*t2*u1;
    v = -6*zminmin + 6*zmaxmin - 6*zmaxmax + 6*zminmax - 3*zxminmin - 3*zxmaxmin + 3*zxmaxmax + 3*zxminmax - 4*zyminmin + 4*zymaxmin + 2*zymaxmax - 2*zyminmax - 2*zxyminmin - 2*zxymaxmin - zxymaxmax - zxyminmax;
    *z_pp += 2*v*t3*u0;
    v = 4*zminmin - 4*zmaxmin + 4*zmaxmax - 4*zminmax + 2*zxminmin + 2*zxmaxmin - 2*zxmaxmax - 2*zxminmax + 2*zyminmin - 2*zymaxmin - 2*zymaxmax + 2*zyminmax + zxyminmin + zxymaxmin + zxymaxmax + zxyminmax;
    *z_pp += 6*v*t3*u1;
    *z_pp *= du*du;
    return GSL_SUCCESS;
}

static const interp2d_type bicubic_type = {
    "bicubic",
    4,
    bicubic_alloc,
    bicubic_init,
    bicubic_eval,
    bicubic_deriv_x,
    bicubic_deriv_y,
    bicubic_deriv_xx,
    bicubic_deriv_xy,
    bicubic_deriv_yy,
    bicubic_free
};

const interp2d_type* interp2d_bicubic = &bicubic_type;