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_FAILURE;
}
}
return GSL_SUCCESS;
}
static
int
cspline_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 cspline_state_t *state = (const cspline_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 y_hi = y_array[i + 1];
const double dx = x_hi - x_lo;
const double dy = y_hi - y_lo;
if(dx != 0.0) {
double b_i, c_i, d_i;
coeff_calc(state->c, dy, dx, i, &b_i, &c_i, &d_i);
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, b_i, c_i, d_i, x_lo, x1, x2);
}
else
{
*result += dx * (y_lo + dx*(0.5*b_i + dx*(c_i/3.0 + 0.25*d_i*dx)));
}
}
else {
*result = 0.0;
return GSL_EINVAL;
}
}
return GSL_SUCCESS;
}
static
int
linear_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)
{
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);
}
/* endpoints span more than one interval */
*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 y_hi = y_array[i + 1];
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;
const double D = (y_hi-y_lo)/dx;
*result += (x2-x1) * (y_lo + 0.5*D*((x2-x_lo)+(x1-x_lo)));
}
else
{
*result += 0.5 * dx * (y_lo + y_hi);
}
}
}
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 (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 VALUE rb_gsl_interp_bsearch(int argc, VALUE *argv, VALUE obj)
{
gsl_vector *v = NULL;
double x;
size_t indexl, indexh;
switch (TYPE(obj)) {
case T_MODULE: case T_CLASS: case T_OBJECT:
switch (argc) {
case 2:
CHECK_VECTOR(argv[0]);
Need_Float(argv[1]);
Data_Get_Struct(argv[0], gsl_vector, v);
x = NUM2DBL(argv[1]);
indexl = gsl_vector_get(v, 0);
indexh = gsl_vector_get(v, v->size-1);
break;
case 4:
CHECK_VECTOR(argv[0]);
Need_Float(argv[1]); Need_Float(argv[2]); Need_Float(argv[3]);
Data_Get_Struct(argv[0], gsl_vector, v);
x = NUM2DBL(argv[1]);
indexl = NUM2DBL(argv[2]);
indexh = NUM2DBL(argv[3]);
break;
default:
rb_raise(rb_eArgError, "wrong number of arguments (%d for 2 or 4)", argc);
break;
}
break;
default:
Data_Get_Struct(obj, gsl_vector, v);
switch (argc) {
case 1:
Need_Float(argv[0]);
x = NUM2DBL(argv[0]);
indexl = gsl_vector_get(v, 0);
indexh = gsl_vector_get(v, v->size-1);
break;
case 3:
Need_Float(argv[0]); Need_Float(argv[1]); Need_Float(argv[2]);
x = NUM2DBL(argv[0]);
indexl = NUM2DBL(argv[1]);
indexh = NUM2DBL(argv[2]);
break;
default:
rb_raise(rb_eArgError, "wrong number of arguments (%d for 1 or 3)", argc);
break;
}
break;
}
return INT2FIX(gsl_interp_bsearch(v->data, x, indexl, indexh));
}
int
gsl_interp_accel_find (gsl_interp_accel * a, const double xa[], int len, double x)
{
int x_index = a->cache;
if (x < xa[x_index])
{
a->miss_count++;
a->cache = gsl_interp_bsearch (xa, x, 0, x_index);
}
else if (x > xa[x_index + 1])
{
a->miss_count++;
a->cache = gsl_interp_bsearch (xa, x, x_index, len - 1);
}
else
{
a->hit_count++;
}
return a->cache;
}
static int
bilinear_deriv_x(const void * state, 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)
{
double xmin, xmax, ymin, ymax, zminmin, zminmax, zmaxmin, zmaxmax;
double dx, dy;
double dt, u;
size_t xi, yi;
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);
xmin = xarr[xi];
xmax = xarr[xi + 1];
ymin = yarr[yi];
ymax = yarr[yi + 1];
zminmin = zarr[IDX2D(xi, yi, xsize, ysize)];
zminmax = zarr[IDX2D(xi, yi + 1, xsize, ysize)];
zmaxmin = zarr[IDX2D(xi + 1, yi, xsize, ysize)];
zmaxmax = zarr[IDX2D(xi + 1, yi + 1, xsize, ysize)];
dx = xmax - xmin;
dy = ymax - ymin;
dt = 1./dx; /* partial t / partial x */
u = (y - ymin)/dy;
*z_p = dt*(-(1.-u)*zminmin + (1.-u)*zmaxmin - u*zminmax + u*zmaxmax);
return GSL_SUCCESS;
}
static int
bilinear_eval(const void * state, 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)
{
double xmin, xmax, ymin, ymax, zminmin, zminmax, zmaxmin, zmaxmax;
double dx, dy;
double t, u;
size_t xi, yi;
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);
xmin = xarr[xi];
xmax = xarr[xi + 1];
ymin = yarr[yi];
ymax = yarr[yi + 1];
zminmin = zarr[IDX2D(xi, yi, xsize, ysize)];
zminmax = zarr[IDX2D(xi, yi + 1, xsize, ysize)];
zmaxmin = zarr[IDX2D(xi + 1, yi, xsize, ysize)];
zmaxmax = zarr[IDX2D(xi + 1, yi + 1, xsize, ysize)];
dx = xmax - xmin;
dy = ymax - ymin;
t = (x - xmin)/dx;
u = (y - ymin)/dy;
*z = (1.-t)*(1.-u)*zminmin + t*(1.-u)*zmaxmin + (1.-t)*u*zminmax + t*u*zmaxmax;
return GSL_SUCCESS;
}
static
int
cspline_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 cspline_state_t *state = (const cspline_state_t *) vstate;
double x_lo, x_hi;
double dx;
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 */
x_hi = x_array[index + 1];
x_lo = x_array[index];
dx = x_hi - x_lo;
if (dx > 0.0)
{
const double y_lo = y_array[index];
const double y_hi = y_array[index + 1];
const double dy = y_hi - y_lo;
double delx = x - x_lo;
double b_i, c_i, d_i;
coeff_calc(state->c, dy, dx, index, &b_i, &c_i, &d_i);
*y_pp = 2.0 * c_i + 6.0 * d_i * delx;
return GSL_SUCCESS;
}
else
{
*y_pp = 0.0;
return GSL_EINVAL;
}
}
static
int
linear_eval_deriv (const void * vstate,
const double x_array[], const double y_array[], size_t size,
double x,
gsl_interp_accel * a,
double *dydx)
{
double x_lo, x_hi;
double y_lo, y_hi;
double dx;
double dy;
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 */
x_lo = x_array[index];
x_hi = x_array[index + 1];
y_lo = y_array[index];
y_hi = y_array[index + 1];
dx = x_hi - x_lo;
dy = y_hi - y_lo;
if (dx > 0.0)
{
*dydx = dy / dx;;
return GSL_SUCCESS;
}
else
{
*dydx = 0.0;
return GSL_EINVAL;
}
}
int
test_bsearch(void)
{
double x_array[5] = { 0.0, 1.0, 2.0, 3.0, 4.0 };
size_t index_result;
int status = 0;
int s;
/* check an interior point */
index_result = gsl_interp_bsearch(x_array, 1.5, 0, 4);
s = (index_result != 1);
status += s;
gsl_test (s, "simple bsearch");
/* check that we get the last interval if x == last value */
index_result = gsl_interp_bsearch(x_array, 4.0, 0, 4);
s = (index_result != 3);
status += s;
gsl_test (s, "upper endpoint bsearch");
/* check that we get the first interval if x == first value */
index_result = gsl_interp_bsearch(x_array, 0.0, 0, 4);
s = (index_result != 0);
status += s;
gsl_test (s, "lower endpoint bsearch");
/* check that we get correct interior boundary behaviour */
index_result = gsl_interp_bsearch(x_array, 2.0, 0, 4);
s = (index_result != 2);
status += s;
gsl_test (s, "degenerate bsearch");
/* check out of bounds above */
index_result = gsl_interp_bsearch(x_array, 10.0, 0, 4);
s = (index_result != 3);
status += s;
gsl_test (s, "out of bounds bsearch +");
/* check out of bounds below */
index_result = gsl_interp_bsearch(x_array, -10.0, 0, 4);
s = (index_result != 0);
status += s;
gsl_test (s, "out of bounds bsearch -");
return status;
}
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;
double dx, dy; /* size of the grid cell */
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[IDX2D(xi, yi, state)];
zminmax = zarr[IDX2D(xi, yi + 1, state)];
zmaxmin = zarr[IDX2D(xi + 1, yi, state)];
zmaxmax = zarr[IDX2D(xi + 1, yi + 1, state)];
/* 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[IDX2D(xi, yi, state)]/dt;
zxminmax = state->zx[IDX2D(xi, yi + 1, state)]/dt;
zxmaxmin = state->zx[IDX2D(xi + 1, yi, state)]/dt;
zxmaxmax = state->zx[IDX2D(xi + 1, yi + 1, state)]/dt;
zyminmin = state->zy[IDX2D(xi, yi, state)]/du;
zyminmax = state->zy[IDX2D(xi, yi + 1, state)]/du;
zymaxmin = state->zy[IDX2D(xi + 1, yi, state)]/du;
zymaxmax = state->zy[IDX2D(xi + 1, yi + 1, state)]/du;
zxyminmin = state->zxy[IDX2D(xi, yi, state)]/(dt*du);
zxyminmax = state->zxy[IDX2D(xi, yi + 1, state)]/(dt*du);
zxymaxmin = state->zxy[IDX2D(xi + 1, yi, state)]/(dt*du);
zxymaxmax = state->zxy[IDX2D(xi + 1, yi + 1, state)]/(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;
}
