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ni_interpolation.c
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ni_interpolation.c
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/* Copyright (C) 2003-2005 Peter J. Verveer
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above
* copyright notice, this list of conditions and the following
* disclaimer in the documentation and/or other materials provided
* with the distribution.
*
* 3. The name of the author may not be used to endorse or promote
* products derived from this software without specific prior
* written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS
* OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
* WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
* DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE
* GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
* WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
* NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#include "ni_support.h"
#include "ni_interpolation.h"
#include <stdlib.h>
#include <math.h>
/* calculate the B-spline interpolation coefficients for given x: */
static void
spline_coefficients(double x, int order, double *result)
{
int hh;
double y, start;
if (order & 1) {
start = (int)floor(x) - order / 2;
} else {
start = (int)floor(x + 0.5) - order / 2;
}
for(hh = 0; hh <= order; hh++) {
y = fabs(start - x + hh);
switch(order) {
case 1:
result[hh] = y > 1.0 ? 0.0 : 1.0 - y;
break;
case 2:
if (y < 0.5) {
result[hh] = 0.75 - y * y;
} else if (y < 1.5) {
y = 1.5 - y;
result[hh] = 0.5 * y * y;
} else {
result[hh] = 0.0;
}
break;
case 3:
if (y < 1.0) {
result[hh] =
(y * y * (y - 2.0) * 3.0 + 4.0) / 6.0;
} else if (y < 2.0) {
y = 2.0 - y;
result[hh] = y * y * y / 6.0;
} else {
result[hh] = 0.0;
}
break;
case 4:
if (y < 0.5) {
y *= y;
result[hh] = y * (y * 0.25 - 0.625) + 115.0 / 192.0;
} else if (y < 1.5) {
result[hh] = y * (y * (y * (5.0 / 6.0 - y / 6.0) - 1.25) +
5.0 / 24.0) + 55.0 / 96.0;
} else if (y < 2.5) {
y -= 2.5;
y *= y;
result[hh] = y * y / 24.0;
} else {
result[hh] = 0.0;
}
break;
case 5:
if (y < 1.0) {
double f = y * y;
result[hh] =
f * (f * (0.25 - y / 12.0) - 0.5) + 0.55;
} else if (y < 2.0) {
result[hh] = y * (y * (y * (y * (y / 24.0 - 0.375)
+ 1.25) - 1.75) + 0.625) + 0.425;
} else if (y < 3.0) {
double f = 3.0 - y;
y = f * f;
result[hh] = f * y * y / 120.0;
} else {
result[hh] = 0.0;
}
break;
}
}
}
/* map a coordinate outside the borders, according to the requested
boundary condition: */
static double
map_coordinate(double in, npy_intp len, int mode)
{
if (in < 0) {
switch (mode) {
case NI_EXTEND_MIRROR:
if (len <= 1) {
in = 0;
} else {
npy_intp sz2 = 2 * len - 2;
in = sz2 * (npy_intp)(-in / sz2) + in;
in = in <= 1 - len ? in + sz2 : -in;
}
break;
case NI_EXTEND_REFLECT:
if (len <= 1) {
in = 0;
} else {
npy_intp sz2 = 2 * len;
if (in < -sz2)
in = sz2 * (npy_intp)(-in / sz2) + in;
in = in < -len ? in + sz2 : -in - 1;
}
break;
case NI_EXTEND_WRAP:
if (len <= 1) {
in = 0;
} else {
npy_intp sz = len - 1;
// Integer division of -in/sz gives (-in mod sz)
// Note that 'in' is negative
in += sz * ((npy_intp)(-in / sz) + 1);
}
break;
case NI_EXTEND_NEAREST:
in = 0;
break;
case NI_EXTEND_CONSTANT:
in = -1;
break;
}
} else if (in > len-1) {
switch (mode) {
case NI_EXTEND_MIRROR:
if (len <= 1) {
in = 0;
} else {
npy_intp sz2 = 2 * len - 2;
in -= sz2 * (npy_intp)(in / sz2);
if (in >= len)
in = sz2 - in;
}
break;
case NI_EXTEND_REFLECT:
if (len <= 1) {
in = 0;
} else {
npy_intp sz2 = 2 * len;
in -= sz2 * (npy_intp)(in / sz2);
if (in >= len)
in = sz2 - in - 1;
}
break;
case NI_EXTEND_WRAP:
if (len <= 1) {
in = 0;
} else {
npy_intp sz = len - 1;
in -= sz * (npy_intp)(in / sz);
}
break;
case NI_EXTEND_NEAREST:
in = len - 1;
break;
case NI_EXTEND_CONSTANT:
in = -1;
break;
}
}
return in;
}
#define BUFFER_SIZE 256000
#define TOLERANCE 1e-15
/* one-dimensional spline filter: */
int NI_SplineFilter1D(PyArrayObject *input, int order, int axis,
PyArrayObject *output)
{
int hh, npoles = 0, more;
npy_intp kk, ll, lines, len;
double *buffer = NULL, weight, pole[2];
NI_LineBuffer iline_buffer, oline_buffer;
char errmsg[NI_MAX_ERR_MSG];
NPY_BEGIN_THREADS_DEF;
errmsg[0] = 0;
len = input->nd > 0 ? input->dimensions[axis] : 1;
if (len < 1)
goto exit;
/* these are used in the spline filter calculation below: */
switch (order) {
case 2:
npoles = 1;
pole[0] = sqrt(8.0) - 3.0;
break;
case 3:
npoles = 1;
pole[0] = sqrt(3.0) - 2.0;
break;
case 4:
npoles = 2;
pole[0] = sqrt(664.0 - sqrt(438976.0)) + sqrt(304.0) - 19.0;
pole[1] = sqrt(664.0 + sqrt(438976.0)) - sqrt(304.0) - 19.0;
break;
case 5:
npoles = 2;
pole[0] = sqrt(67.5 - sqrt(4436.25)) + sqrt(26.25) - 6.5;
pole[1] = sqrt(67.5 + sqrt(4436.25)) - sqrt(26.25) - 6.5;
break;
default:
break;
}
weight = 1.0;
for(hh = 0; hh < npoles; hh++)
weight *= (1.0 - pole[hh]) * (1.0 - 1.0 / pole[hh]);
/* allocate an initialize the line buffer, only a single one is used,
because the calculation is in-place: */
lines = -1;
if (!NI_AllocateLineBuffer(input, axis, 0, 0, &lines, BUFFER_SIZE,
&buffer))
goto exit;
if (!NI_InitLineBuffer(input, axis, 0, 0, lines, buffer,
NI_EXTEND_DEFAULT, 0.0, &iline_buffer))
goto exit;
if (!NI_InitLineBuffer(output, axis, 0, 0, lines, buffer,
NI_EXTEND_DEFAULT, 0.0, &oline_buffer))
goto exit;
NPY_BEGIN_THREADS;
/* iterate over all the array lines: */
do {
/* copy lines from array to buffer: */
if (!NI_ArrayToLineBuffer(&iline_buffer, &lines, &more, errmsg))
goto exit;
/* iterate over the lines in the buffer: */
for(kk = 0; kk < lines; kk++) {
/* get line: */
double *ln = NI_GET_LINE(iline_buffer, kk);
/* spline filter: */
if (len > 1) {
for(ll = 0; ll < len; ll++)
ln[ll] *= weight;
for(hh = 0; hh < npoles; hh++) {
double p = pole[hh];
int max = (int)ceil(log(TOLERANCE) / log(fabs(p)));
if (max < len) {
double zn = p;
double sum = ln[0];
for(ll = 1; ll < max; ll++) {
sum += zn * ln[ll];
zn *= p;
}
ln[0] = sum;
} else {
double zn = p;
double iz = 1.0 / p;
double z2n = pow(p, (double)(len - 1));
double sum = ln[0] + z2n * ln[len - 1];
z2n *= z2n * iz;
for(ll = 1; ll <= len - 2; ll++) {
sum += (zn + z2n) * ln[ll];
zn *= p;
z2n *= iz;
}
ln[0] = sum / (1.0 - zn * zn);
}
for(ll = 1; ll < len; ll++)
ln[ll] += p * ln[ll - 1];
ln[len-1] = (p / (p * p - 1.0)) * (ln[len-1] + p * ln[len-2]);
for(ll = len - 2; ll >= 0; ll--)
ln[ll] = p * (ln[ll + 1] - ln[ll]);
}
}
}
/* copy lines from buffer to array: */
if (!NI_LineBufferToArray(&oline_buffer, errmsg))
goto exit;
} while(more);
exit:
NPY_END_THREADS;
if (errmsg[0] != 0) {
PyErr_SetString(PyExc_RuntimeError, errmsg);
}
free(buffer);
return PyErr_Occurred() ? 0 : 1;
}
/* copy row of coordinate array from location at _p to _coor */
#define CASE_MAP_COORDINATES(_p, _coor, _rank, _stride, _type) \
case t ## _type: \
{ \
npy_intp _hh; \
for(_hh = 0; _hh < _rank; _hh++) { \
_coor[_hh] = *(_type*)_p; \
_p += _stride; \
} \
} \
break;
#define CASE_INTERP_COEFF(_coeff, _pi, _idx, _type) \
case t ## _type: \
_coeff = *(_type*)(_pi + _idx); \
break;
#define CASE_INTERP_OUT(_po, _t, _type) \
case t ## _type: \
*(_type*)_po = (_type)_t; \
break;
#define CASE_INTERP_OUT_UINT(_po, _t, _type, type_min, type_max) \
case t ## _type: \
_t = _t > 0 ? _t + 0.5 : 0; \
_t = _t > type_max ? type_max : t; \
_t = _t < type_min ? type_min : t; \
*(_type*)_po = (_type)_t; \
break;
#define CASE_INTERP_OUT_INT(_po, _t, _type, type_min, type_max) \
case t ## _type: \
_t = _t > 0 ? _t + 0.5 : _t - 0.5; \
_t = _t > type_max ? type_max : t; \
_t = _t < type_min ? type_min : t; \
*(_type*)_po = (_type)_t; \
break;
int
NI_GeometricTransform(PyArrayObject *input, int (*map)(npy_intp*, double*,
int, int, void*), void* map_data, PyArrayObject* matrix_ar,
PyArrayObject* shift_ar, PyArrayObject *coordinates,
PyArrayObject *output, int order, int mode, double cval)
{
char *po, *pi, *pc = NULL;
npy_intp **edge_offsets = NULL, **data_offsets = NULL, filter_size;
npy_intp ftmp[MAXDIM], *fcoordinates = NULL, *foffsets = NULL;
npy_intp cstride = 0, kk, hh, ll, jj;
npy_intp size;
double **splvals = NULL, icoor[MAXDIM];
npy_intp idimensions[MAXDIM], istrides[MAXDIM];
NI_Iterator io, ic;
Float64 *matrix = matrix_ar ? (Float64*)PyArray_DATA(matrix_ar) : NULL;
Float64 *shift = shift_ar ? (Float64*)PyArray_DATA(shift_ar) : NULL;
int irank = 0, orank, qq;
NPY_BEGIN_THREADS_DEF;
NPY_BEGIN_THREADS;
for(kk = 0; kk < input->nd; kk++) {
idimensions[kk] = input->dimensions[kk];
istrides[kk] = input->strides[kk];
}
irank = input->nd;
orank = output->nd;
/* if the mapping is from array coordinates: */
if (coordinates) {
/* initialze a line iterator along the first axis: */
if (!NI_InitPointIterator(coordinates, &ic))
goto exit;
cstride = ic.strides[0];
if (!NI_LineIterator(&ic, 0))
goto exit;
pc = (void *)(PyArray_DATA(coordinates));
}
/* offsets used at the borders: */
edge_offsets = malloc(irank * sizeof(npy_intp*));
data_offsets = malloc(irank * sizeof(npy_intp*));
if (NI_UNLIKELY(!edge_offsets || !data_offsets)) {
NPY_END_THREADS;
PyErr_NoMemory();
goto exit;
}
for(jj = 0; jj < irank; jj++)
data_offsets[jj] = NULL;
for(jj = 0; jj < irank; jj++) {
data_offsets[jj] = malloc((order + 1) * sizeof(npy_intp));
if (NI_UNLIKELY(!data_offsets[jj])) {
NPY_END_THREADS;
PyErr_NoMemory();
goto exit;
}
}
/* will hold the spline coefficients: */
splvals = malloc(irank * sizeof(double*));
if (NI_UNLIKELY(!splvals)) {
NPY_END_THREADS;
PyErr_NoMemory();
goto exit;
}
for(jj = 0; jj < irank; jj++)
splvals[jj] = NULL;
for(jj = 0; jj < irank; jj++) {
splvals[jj] = malloc((order + 1) * sizeof(double));
if (NI_UNLIKELY(!splvals[jj])) {
NPY_END_THREADS;
PyErr_NoMemory();
goto exit;
}
}
filter_size = 1;
for(jj = 0; jj < irank; jj++)
filter_size *= order + 1;
/* initialize output iterator: */
if (!NI_InitPointIterator(output, &io))
goto exit;
/* get data pointers: */
pi = (void *)PyArray_DATA(input);
po = (void *)PyArray_DATA(output);
/* make a table of all possible coordinates within the spline filter: */
fcoordinates = malloc(irank * filter_size * sizeof(npy_intp));
/* make a table of all offsets within the spline filter: */
foffsets = malloc(filter_size * sizeof(npy_intp));
if (NI_UNLIKELY(!fcoordinates || !foffsets)) {
NPY_END_THREADS;
PyErr_NoMemory();
goto exit;
}
for(jj = 0; jj < irank; jj++)
ftmp[jj] = 0;
kk = 0;
for(hh = 0; hh < filter_size; hh++) {
for(jj = 0; jj < irank; jj++)
fcoordinates[jj + hh * irank] = ftmp[jj];
foffsets[hh] = kk;
for(jj = irank - 1; jj >= 0; jj--) {
if (ftmp[jj] < order) {
ftmp[jj]++;
kk += istrides[jj];
break;
} else {
ftmp[jj] = 0;
kk -= istrides[jj] * order;
}
}
}
size = 1;
for(qq = 0; qq < output->nd; qq++)
size *= output->dimensions[qq];
for(kk = 0; kk < size; kk++) {
double t = 0.0;
int constant = 0, edge = 0;
npy_intp offset = 0;
if (map) {
NPY_END_THREADS;
/* call mappint functions: */
if (!map(io.coordinates, icoor, orank, irank, map_data)) {
if (!PyErr_Occurred())
PyErr_SetString(PyExc_RuntimeError,
"unknown error in mapping function");
goto exit;
}
NPY_BEGIN_THREADS;
} else if (matrix) {
/* do an affine transformation: */
Float64 *p = matrix;
for(hh = 0; hh < irank; hh++) {
icoor[hh] = 0.0;
for(ll = 0; ll < orank; ll++)
icoor[hh] += io.coordinates[ll] * *p++;
icoor[hh] += shift[hh];
}
} else if (coordinates) {
/* mapping is from an coordinates array: */
char *p = pc;
switch (NI_NormalizeType(coordinates->descr->type_num)) {
CASE_MAP_COORDINATES(p, icoor, irank, cstride, Bool);
CASE_MAP_COORDINATES(p, icoor, irank, cstride, UInt8);
CASE_MAP_COORDINATES(p, icoor, irank, cstride, UInt16);
CASE_MAP_COORDINATES(p, icoor, irank, cstride, UInt32);
#if HAS_UINT64
CASE_MAP_COORDINATES(p, icoor, irank, cstride, UInt64);
#endif
CASE_MAP_COORDINATES(p, icoor, irank, cstride, Int8);
CASE_MAP_COORDINATES(p, icoor, irank, cstride, Int16);
CASE_MAP_COORDINATES(p, icoor, irank, cstride, Int32);
CASE_MAP_COORDINATES(p, icoor, irank, cstride, Int64);
CASE_MAP_COORDINATES(p, icoor, irank, cstride, Float32);
CASE_MAP_COORDINATES(p, icoor, irank, cstride, Float64);
default:
NPY_END_THREADS;
PyErr_SetString(PyExc_RuntimeError,
"coordinate array data type not supported");
goto exit;
}
}
/* iterate over axes: */
for(hh = 0; hh < irank; hh++) {
/* if the input coordinate is outside the borders, map it: */
double cc = map_coordinate(icoor[hh], idimensions[hh], mode);
if (cc > -1.0) {
/* find the filter location along this axis: */
npy_intp start;
if (order & 1) {
start = (npy_intp)floor(cc) - order / 2;
} else {
start = (npy_intp)floor(cc + 0.5) - order / 2;
}
/* get the offset to the start of the filter: */
offset += istrides[hh] * start;
if (start < 0 || start + order >= idimensions[hh]) {
/* implement border mapping, if outside border: */
edge = 1;
edge_offsets[hh] = data_offsets[hh];
for(ll = 0; ll <= order; ll++) {
npy_intp idx = start + ll;
npy_intp len = idimensions[hh];
if (len <= 1) {
idx = 0;
} else {
npy_intp s2 = 2 * len - 2;
if (idx < 0) {
idx = s2 * (int)(-idx / s2) + idx;
idx = idx <= 1 - len ? idx + s2 : -idx;
} else if (idx >= len) {
idx -= s2 * (int)(idx / s2);
if (idx >= len)
idx = s2 - idx;
}
}
/* calculate and store the offests at this edge: */
edge_offsets[hh][ll] = istrides[hh] * (idx - start);
}
} else {
/* we are not at the border, use precalculated offsets: */
edge_offsets[hh] = NULL;
}
spline_coefficients(cc, order, splvals[hh]);
} else {
/* we use the constant border condition: */
constant = 1;
break;
}
}
if (!constant) {
npy_intp *ff = fcoordinates;
const int type_num = NI_NormalizeType(input->descr->type_num);
t = 0.0;
for(hh = 0; hh < filter_size; hh++) {
double coeff = 0.0;
npy_intp idx = 0;
if (NI_UNLIKELY(edge)) {
for(ll = 0; ll < irank; ll++) {
if (edge_offsets[ll])
idx += edge_offsets[ll][ff[ll]];
else
idx += ff[ll] * istrides[ll];
}
} else {
idx = foffsets[hh];
}
idx += offset;
switch (type_num) {
CASE_INTERP_COEFF(coeff, pi, idx, Bool);
CASE_INTERP_COEFF(coeff, pi, idx, UInt8);
CASE_INTERP_COEFF(coeff, pi, idx, UInt16);
CASE_INTERP_COEFF(coeff, pi, idx, UInt32);
#if HAS_UINT64
CASE_INTERP_COEFF(coeff, pi, idx, UInt64);
#endif
CASE_INTERP_COEFF(coeff, pi, idx, Int8);
CASE_INTERP_COEFF(coeff, pi, idx, Int16);
CASE_INTERP_COEFF(coeff, pi, idx, Int32);
CASE_INTERP_COEFF(coeff, pi, idx, Int64);
CASE_INTERP_COEFF(coeff, pi, idx, Float32);
CASE_INTERP_COEFF(coeff, pi, idx, Float64);
default:
NPY_END_THREADS;
PyErr_SetString(PyExc_RuntimeError,
"data type not supported");
goto exit;
}
/* calculate the interpolated value: */
for(ll = 0; ll < irank; ll++)
if (order > 0)
coeff *= splvals[ll][ff[ll]];
t += coeff;
ff += irank;
}
} else {
t = cval;
}
/* store output value: */
switch (NI_NormalizeType(output->descr->type_num)) {
CASE_INTERP_OUT(po, t, Bool);
CASE_INTERP_OUT_UINT(po, t, UInt8, 0, MAX_UINT8);
CASE_INTERP_OUT_UINT(po, t, UInt16, 0, MAX_UINT16);
CASE_INTERP_OUT_UINT(po, t, UInt32, 0, MAX_UINT32);
#if HAS_UINT64
/* There was a bug in numpy as of (at least) <= 1.6.1 such that
* MAX_UINT64 was incorrectly defined, leading to a compiler error.
* NPY_MAX_UINT64 is correctly defined
*/
CASE_INTERP_OUT_UINT(po, t, UInt64, 0, NPY_MAX_UINT64);
#endif
CASE_INTERP_OUT_INT(po, t, Int8, MIN_INT8, MAX_INT8);
CASE_INTERP_OUT_INT(po, t, Int16, MIN_INT16, MAX_INT16);
CASE_INTERP_OUT_INT(po, t, Int32, MIN_INT32, MAX_INT32);
CASE_INTERP_OUT_INT(po, t, Int64, MIN_INT64, MAX_INT64);
CASE_INTERP_OUT(po, t, Float32);
CASE_INTERP_OUT(po, t, Float64);
default:
NPY_END_THREADS;
PyErr_SetString(PyExc_RuntimeError, "data type not supported");
goto exit;
}
if (coordinates) {
NI_ITERATOR_NEXT2(io, ic, po, pc);
} else {
NI_ITERATOR_NEXT(io, po);
}
}
exit:
NPY_END_THREADS;
free(edge_offsets);
if (data_offsets) {
for(jj = 0; jj < irank; jj++)
free(data_offsets[jj]);
free(data_offsets);
}
if (splvals) {
for(jj = 0; jj < irank; jj++)
free(splvals[jj]);
free(splvals);
}
free(foffsets);
free(fcoordinates);
return PyErr_Occurred() ? 0 : 1;
}
int NI_ZoomShift(PyArrayObject *input, PyArrayObject* zoom_ar,
PyArrayObject* shift_ar, PyArrayObject *output,
int order, int mode, double cval)
{
char *po, *pi;
npy_intp **zeros = NULL, **offsets = NULL, ***edge_offsets = NULL;
npy_intp ftmp[MAXDIM], *fcoordinates = NULL, *foffsets = NULL;
npy_intp jj, hh, kk, filter_size, odimensions[MAXDIM];
npy_intp idimensions[MAXDIM], istrides[MAXDIM];
npy_intp size;
double ***splvals = NULL;
NI_Iterator io;
Float64 *zooms = zoom_ar ? (Float64*)PyArray_DATA(zoom_ar) : NULL;
Float64 *shifts = shift_ar ? (Float64*)PyArray_DATA(shift_ar) : NULL;
int rank = 0, qq;
NPY_BEGIN_THREADS_DEF;
NPY_BEGIN_THREADS;
for(kk = 0; kk < input->nd; kk++) {
idimensions[kk] = input->dimensions[kk];
istrides[kk] = input->strides[kk];
odimensions[kk] = output->dimensions[kk];
}
rank = input->nd;
/* if the mode is 'constant' we need some temps later: */
if (mode == NI_EXTEND_CONSTANT) {
zeros = malloc(rank * sizeof(npy_intp*));
if (NI_UNLIKELY(!zeros)) {
NPY_END_THREADS;
PyErr_NoMemory();
goto exit;
}
for(jj = 0; jj < rank; jj++)
zeros[jj] = NULL;
for(jj = 0; jj < rank; jj++) {
zeros[jj] = malloc(odimensions[jj] * sizeof(npy_intp));
if (NI_UNLIKELY(!zeros[jj])) {
NPY_END_THREADS;
PyErr_NoMemory();
goto exit;
}
}
}
/* store offsets, along each axis: */
offsets = malloc(rank * sizeof(npy_intp*));
/* store spline coefficients, along each axis: */
splvals = malloc(rank * sizeof(double**));
/* store offsets at all edges: */
edge_offsets = malloc(rank * sizeof(npy_intp**));
if (NI_UNLIKELY(!offsets || !splvals || !edge_offsets)) {
NPY_END_THREADS;
PyErr_NoMemory();
goto exit;
}
for(jj = 0; jj < rank; jj++) {
offsets[jj] = NULL;
splvals[jj] = NULL;
edge_offsets[jj] = NULL;
}
for(jj = 0; jj < rank; jj++) {
offsets[jj] = malloc(odimensions[jj] * sizeof(npy_intp));
splvals[jj] = malloc(odimensions[jj] * sizeof(double*));
edge_offsets[jj] = malloc(odimensions[jj] * sizeof(npy_intp*));
if (NI_UNLIKELY(!offsets[jj] || !splvals[jj] || !edge_offsets[jj])) {
NPY_END_THREADS;
PyErr_NoMemory();
goto exit;
}
for(hh = 0; hh < odimensions[jj]; hh++) {
splvals[jj][hh] = NULL;
edge_offsets[jj][hh] = NULL;
}
}
/* precalculate offsets, and offsets at the edge: */
for(jj = 0; jj < rank; jj++) {
double shift = 0.0, zoom = 0.0;
if (shifts)
shift = shifts[jj];
if (zooms)
zoom = zooms[jj];
for(kk = 0; kk < odimensions[jj]; kk++) {
double cc = (double)kk;
if (shifts)
cc += shift;
if (zooms)
cc *= zoom;
cc = map_coordinate(cc, idimensions[jj], mode);
if (cc > -1.0) {
npy_intp start;
if (zeros && zeros[jj])
zeros[jj][kk] = 0;
if (order & 1) {
start = (npy_intp)floor(cc) - order / 2;
} else {
start = (npy_intp)floor(cc + 0.5) - order / 2;
}
offsets[jj][kk] = istrides[jj] * start;
if (start < 0 || start + order >= idimensions[jj]) {
edge_offsets[jj][kk] = malloc((order + 1) * sizeof(npy_intp));
if (NI_UNLIKELY(!edge_offsets[jj][kk])) {
NPY_END_THREADS;
PyErr_NoMemory();
goto exit;
}
for(hh = 0; hh <= order; hh++) {
npy_intp idx = start + hh;
npy_intp len = idimensions[jj];
if (len <= 1) {
idx = 0;
} else {
npy_intp s2 = 2 * len - 2;
if (idx < 0) {
idx = s2 * (npy_intp)(-idx / s2) + idx;
idx = idx <= 1 - len ? idx + s2 : -idx;
} else if (idx >= len) {
idx -= s2 * (npy_intp)(idx / s2);
if (idx >= len)
idx = s2 - idx;
}
}
edge_offsets[jj][kk][hh] = istrides[jj] * (idx - start);
}
}
if (order > 0) {
splvals[jj][kk] = malloc((order + 1) * sizeof(double));
if (NI_UNLIKELY(!splvals[jj][kk])) {
NPY_END_THREADS;
PyErr_NoMemory();
goto exit;
}
spline_coefficients(cc, order, splvals[jj][kk]);
}
} else {
zeros[jj][kk] = 1;
}
}
}
filter_size = 1;
for(jj = 0; jj < rank; jj++)
filter_size *= order + 1;
if (!NI_InitPointIterator(output, &io))
goto exit;
pi = (void *)PyArray_DATA(input);
po = (void *)PyArray_DATA(output);
/* store all coordinates and offsets with filter: */
fcoordinates = malloc(rank * filter_size * sizeof(npy_intp));
foffsets = malloc(filter_size * sizeof(npy_intp));
if (NI_UNLIKELY(!fcoordinates || !foffsets)) {
NPY_END_THREADS;
PyErr_NoMemory();
goto exit;
}
for(jj = 0; jj < rank; jj++)
ftmp[jj] = 0;
kk = 0;
for(hh = 0; hh < filter_size; hh++) {
for(jj = 0; jj < rank; jj++)
fcoordinates[jj + hh * rank] = ftmp[jj];
foffsets[hh] = kk;
for(jj = rank - 1; jj >= 0; jj--) {
if (ftmp[jj] < order) {
ftmp[jj]++;
kk += istrides[jj];
break;
} else {
ftmp[jj] = 0;
kk -= istrides[jj] * order;
}
}
}
size = 1;
for(qq = 0; qq < output->nd; qq++)
size *= output->dimensions[qq];
for(kk = 0; kk < size; kk++) {
double t = 0.0;
npy_intp edge = 0, oo = 0, zero = 0;
for(hh = 0; hh < rank; hh++) {
if (zeros && zeros[hh][io.coordinates[hh]]) {
/* we use constant border condition */
zero = 1;
break;
}
oo += offsets[hh][io.coordinates[hh]];
if (edge_offsets[hh][io.coordinates[hh]])
edge = 1;
}
if (!zero) {
npy_intp *ff = fcoordinates;
const int type_num = NI_NormalizeType(input->descr->type_num);
t = 0.0;
for(hh = 0; hh < filter_size; hh++) {
npy_intp idx = 0;
double coeff = 0.0;
if (NI_UNLIKELY(edge)) {
/* use precalculated edge offsets: */
for(jj = 0; jj < rank; jj++) {
if (edge_offsets[jj][io.coordinates[jj]])
idx += edge_offsets[jj][io.coordinates[jj]][ff[jj]];
else
idx += ff[jj] * istrides[jj];
}
idx += oo;
} else {
/* use normal offsets: */
idx += oo + foffsets[hh];
}
switch (type_num) {
CASE_INTERP_COEFF(coeff, pi, idx, Bool);
CASE_INTERP_COEFF(coeff, pi, idx, UInt8);
CASE_INTERP_COEFF(coeff, pi, idx, UInt16);
CASE_INTERP_COEFF(coeff, pi, idx, UInt32);
#if HAS_UINT64
CASE_INTERP_COEFF(coeff, pi, idx, UInt64);
#endif
CASE_INTERP_COEFF(coeff, pi, idx, Int8);
CASE_INTERP_COEFF(coeff, pi, idx, Int16);
CASE_INTERP_COEFF(coeff, pi, idx, Int32);
CASE_INTERP_COEFF(coeff, pi, idx, Int64);
CASE_INTERP_COEFF(coeff, pi, idx, Float32);
CASE_INTERP_COEFF(coeff, pi, idx, Float64);
default:
NPY_END_THREADS;
PyErr_SetString(PyExc_RuntimeError,
"data type not supported");
goto exit;
}
/* calculate interpolated value: */
for(jj = 0; jj < rank; jj++)
if (order > 0)
coeff *= splvals[jj][io.coordinates[jj]][ff[jj]];
t += coeff;
ff += rank;
}
} else {
t = cval;
}
/* store output: */
switch (NI_NormalizeType(output->descr->type_num)) {
CASE_INTERP_OUT(po, t, Bool);
CASE_INTERP_OUT_UINT(po, t, UInt8, 0, MAX_UINT8);
CASE_INTERP_OUT_UINT(po, t, UInt16, 0, MAX_UINT16);
CASE_INTERP_OUT_UINT(po, t, UInt32, 0, MAX_UINT32);
#if HAS_UINT64
/* There was a bug in numpy as of (at least) <= 1.6.1 such that
* MAX_UINT64 was incorrectly defined, leading to a compiler error.
* NPY_MAX_UINT64 is correctly defined
*/
CASE_INTERP_OUT_UINT(po, t, UInt64, 0, NPY_MAX_UINT64);
#endif
CASE_INTERP_OUT_INT(po, t, Int8, MIN_INT8, MAX_INT8);
CASE_INTERP_OUT_INT(po, t, Int16, MIN_INT16, MAX_INT16);
CASE_INTERP_OUT_INT(po, t, Int32, MIN_INT32, MAX_INT32);
CASE_INTERP_OUT_INT(po, t, Int64, MIN_INT64, MAX_INT64);
CASE_INTERP_OUT(po, t, Float32);
CASE_INTERP_OUT(po, t, Float64);
default:
NPY_END_THREADS;
PyErr_SetString(PyExc_RuntimeError, "data type not supported");
goto exit;
}
NI_ITERATOR_NEXT(io, po);
}
exit:
NPY_END_THREADS;
if (zeros) {
for(jj = 0; jj < rank; jj++)
free(zeros[jj]);
free(zeros);
}
if (offsets) {
for(jj = 0; jj < rank; jj++)
free(offsets[jj]);
free(offsets);
}
if (splvals) {
for(jj = 0; jj < rank; jj++) {
if (splvals[jj]) {
for(hh = 0; hh < odimensions[jj]; hh++)
free(splvals[jj][hh]);
free(splvals[jj]);
}
}
free(splvals);
}
if (edge_offsets) {
for(jj = 0; jj < rank; jj++) {
if (edge_offsets[jj]) {
for(hh = 0; hh < odimensions[jj]; hh++)
free(edge_offsets[jj][hh]);
free(edge_offsets[jj]);
}
}
free(edge_offsets);
}
free(foffsets);
free(fcoordinates);
return PyErr_Occurred() ? 0 : 1;
}