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04/09/14
5288
ФТИ им. Иоффе СПб
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А если нет, то попрошу у вас Не откладывая и на всякий случай (меня может не быть завтра).
/*
CONVNC.CPP .MEX file
Implements full N-D convolution.
Inputs must be real, numeric, and float.
Only one syntax is supported:
C = CONVNC(A,B)
Copyright 1984-2004 The MathWorks, Inc.
*/
#include "mex.h"
static char rcsid[] = "$Revision $";
/* Input and output arguments */
#define A (prhs[0])
#define B (prhs[1])
#define C (plhs[0])
/* Increment subscripts */
/* Increment subscript vector by one element */
/* in the direction of linear indexing. */
/* The subscript vector is assumed to be zero-based. */
inline void INCREMENT_SUBSCRIPTS(int *subs, const int*size, int ndims) {
subs[0] += 1;
for (int p = 0; p < (ndims-1); p++) {
if (subs[p] > (size[p]-1)) {
subs[p] = 0;
subs[p+1] += 1;
}
}
}
/* Convert a zero-based subscript vector to a linear index. */
inline void SUBSCRIPTS_TO_LINEAR(const int *subs, int ndims, const int *pdims,
int *index)
{
int i = ndims;
int factor = 1;
*index = 0;
while (i--) {
*index += *subs++ * factor;
factor *= *pdims++;
}
}
template <class Tout, class Tin1, class Tin2>
void convolve(Tout *c, const Tin1 *a, const Tin2 *b,
const int *sizeA, const int *sizeB, const int *sizeC,
int ndimsA, int ndimsB, int ndimsC)
{
/* Input sanity checking */
/* Any of the following error messages indicates that */
/* something went seriously wrong in mexFunction(). */
/* I would use utAssert() if the API had it. -sle */
if (a==NULL || b==NULL || c==NULL) {
mexErrMsgIdAndTxt("MATLAB:convnc:InternalError1",
"Internal consistency error in convolve().");
}
if (sizeA==NULL || sizeB==NULL || sizeC==NULL) {
mexErrMsgIdAndTxt("MATLAB:convnc:InternalError1",
"Internal consistency error in convolve().");
}
if ((ndimsA != ndimsB) || (ndimsA != ndimsC)) {
mexErrMsgIdAndTxt("MATLAB:convnc:InternalError1",
"Internal consistency error in convolve().");
}
/* Compute the number of elements in inputs a and b */
int lengthA = 1; /* length of input A */
for (int p = 0; p < ndimsA; p++) {
lengthA *= sizeA[p];
}
int lengthB = 1; /* length of input B */
for (int p = 0; p < ndimsB; p++) {
lengthB *= sizeB[p];
}
/* Initialize subscript vectors */
int *subsA = (int *) mxCalloc(ndimsA, sizeof(int)); /* subscript vector for A */
int *subsB = (int *) mxCalloc(ndimsB, sizeof(int)); /* subscript vector for B */
int *subsC = (int *) mxCalloc(ndimsC, sizeof(int)); /* subscript vector for C */
if (subsA==NULL || subsB==NULL || subsC==NULL) {
if (subsA != NULL) {
mxFree(subsA);
}
if (subsB != NULL) {
mxFree(subsB);
}
if (subsC != NULL) {
mxFree(subsC);
}
mexErrMsgIdAndTxt("MATLAB:convnc:InternalError2",
"Memory allocation failure.");
}
/* Initialize subscript array for a to be a(-1,0,0,...,0) */
/* This is ok since subscripts will be incremented once before use. */
subsA[0] = -1;
for (int p = 1; p < ndimsA; p++) {
subsA[p] = 0;
}
/* Core computation loops */
int linearIndexC=0; /* linear index into output array */
for (int p = 0; p < lengthA; p++) {
/* Increment subscript vector for A */
INCREMENT_SUBSCRIPTS(subsA, sizeA, ndimsA);
/* Initialize subscript array for a to be b(-1,0,0,...,0) */
/* This is ok since subscripts will be incremented once before use. */
subsB[0] = -1;
for (int r = 1; r < ndimsA; r++) {
subsB[r] = 0;
}
for (int q = 0; q < lengthB; q++) {
/* Increment subscript vector for B */
INCREMENT_SUBSCRIPTS(subsB, sizeB, ndimsB);
/* Where should the next partial product go in the output array? */
/* Answer: subsC = subsA + subsB */
for (int r = 0; r < ndimsA; r++) {
subsC[r] = subsA[r] + subsB[r];
}
/* But we need the answer as a linear index rather than a */
/* subscript array */
SUBSCRIPTS_TO_LINEAR(subsC, ndimsC, sizeC, &linearIndexC);
/* Accumulate partial product */
c[linearIndexC] += a[p] * b[q];
}
}
/* Clean up and go home */
mxFree(subsA);
mxFree(subsB);
mxFree(subsC);
}
void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[])
{
const int NumInputs = 2;
/* Sanity check input */
if (nrhs != NumInputs) mexErrMsgIdAndTxt("MATLAB:convnc:WrongNumInputs",
"Two input arguments required.");
bool singleA = mxIsSingle(A);
bool singleB = mxIsSingle(B);
if ((!mxIsDouble(A) && !singleA) || mxIsComplex(A) ||
(!mxIsDouble(B) && !singleB) || mxIsComplex(B)) {
mexErrMsgIdAndTxt("MATLAB:convnc:UnsupportedDataType",
"Inputs must be real and float (double or single).");
}
mxClassID outputClass = (singleA || singleB ? mxSINGLE_CLASS : mxDOUBLE_CLASS);
/* If either A or B is empty, return an empty matrix and go home. */
if (mxIsEmpty(A) || mxIsEmpty(B)) {
C = mxCreateNumericMatrix(0,0, outputClass, mxREAL);
return;
}
int ndimsA = mxGetNumberOfDimensions(A); /* Dimensionality of first input */
int ndimsB = mxGetNumberOfDimensions(B); /* Dimensionality of second input */
const int *sizeA = mxGetDimensions(A); /* Size of first input */
const int *sizeB = mxGetDimensions(B); /* Size of second input */
/* Make dimensionality of A and B conform */
int *adjustedSizeA=NULL; /* Adjusted size of first input */
int *adjustedSizeB=NULL; /* Adjusted size of second input */
int adjustedNDimsA=0; /* Adjusted dimensionality of first input */
int adjustedNDimsB=0; /* Adjusted dimensionality of second input */
if (ndimsA != ndimsB) {
if (ndimsA > ndimsB) {
adjustedNDimsA = ndimsA;
adjustedNDimsB = ndimsA;
adjustedSizeB = (int *) mxCalloc(adjustedNDimsB, sizeof(int));
adjustedSizeA = (int *) mxCalloc(adjustedNDimsA, sizeof(int));
if (adjustedSizeB == NULL || adjustedSizeA == NULL) {
if (adjustedSizeB != NULL) mxFree((void *) adjustedSizeB);
if (adjustedSizeA != NULL) mxFree((void *) adjustedSizeA);
mexErrMsgIdAndTxt("MATLAB:convnc:InternalError2",
"Memory allocation failure.");
}
for (int p = 0; p < ndimsB; p++) {
adjustedSizeB[p] = sizeB[p];
adjustedSizeA[p] = sizeA[p];
}
for (int p = ndimsB; p < adjustedNDimsB; p++) {
adjustedSizeB[p] = 1;
adjustedSizeA[p] = sizeA[p];
}
} else {
adjustedNDimsA = ndimsB;
adjustedNDimsB = ndimsB;
adjustedSizeA = (int *) mxCalloc(adjustedNDimsA, sizeof(int));
adjustedSizeB = (int *) mxCalloc(adjustedNDimsB, sizeof(int));
if (adjustedSizeA == NULL || adjustedSizeB == NULL) {
if (adjustedSizeA != NULL) mxFree((void *) adjustedSizeA);
if (adjustedSizeB != NULL) mxFree((void *) adjustedSizeB);
mexErrMsgIdAndTxt("MATLAB:convnc:InternalError2",
"Memory allocation failure.");
}
for (int p = 0; p < ndimsA; p++) {
adjustedSizeA[p] = sizeA[p];
adjustedSizeB[p] = sizeB[p];
}
for (int p = ndimsA; p < adjustedNDimsA; p++) {
adjustedSizeA[p] = 1;
adjustedSizeB[p] = sizeB[p];
}
}
} else {
adjustedNDimsA = ndimsA;
adjustedNDimsB = ndimsB;
adjustedSizeA = (int *) mxCalloc(adjustedNDimsA, sizeof(int));
adjustedSizeB = (int *) mxCalloc(adjustedNDimsB, sizeof(int));
if (adjustedSizeA == NULL || adjustedSizeB == NULL) {
if (adjustedSizeA != NULL) mxFree((void *) adjustedSizeA);
if (adjustedSizeB != NULL) mxFree((void *) adjustedSizeB);
mexErrMsgIdAndTxt("MATLAB:convnc:InternalError2",
"Memory allocation failure.");
}
for (int p = 0; p < adjustedNDimsA; p++) {
adjustedSizeA[p] = sizeA[p];
adjustedSizeB[p] = sizeB[p];
}
}
/* Initialize output */
int *sizeC = (int *) mxCalloc(adjustedNDimsA, sizeof(int));
if (sizeC == NULL) {
mxFree((void *) adjustedSizeA);
mxFree((void *) adjustedSizeB);
mexErrMsgIdAndTxt("MATLAB:convnc:InternalError2",
"Memory allocation failure.");
}
for (int p = 0; p < adjustedNDimsA; p++) {
sizeC[p] = adjustedSizeA[p] + adjustedSizeB[p] - 1;
}
C = mxCreateNumericArray(adjustedNDimsA, sizeC, outputClass, mxREAL);
if (C == NULL) {
mxFree((void *) adjustedSizeA);
mxFree((void *) adjustedSizeB);
mxFree((void *) sizeC);
mexErrMsgIdAndTxt("MATLAB:convnc:InternalError2",
"Memory allocation failure.");
}
if (singleA && singleB) {
real32_T *sA = (real32_T *) mxGetData(A);
real32_T *sB = (real32_T *) mxGetData(B);
real32_T *sC = (real32_T *) mxGetData(C);
convolve(sC, sA, sB,
adjustedSizeA, adjustedSizeB, sizeC,
adjustedNDimsA, adjustedNDimsB, adjustedNDimsB);
} else if (singleA && !singleB) {
real32_T *sA = (real32_T *) mxGetData(A);
double *dB = (double *) mxGetData(B);
real32_T *sC = (real32_T *) mxGetData(C);
convolve(sC, sA, dB,
adjustedSizeA, adjustedSizeB, sizeC,
adjustedNDimsA, adjustedNDimsB, adjustedNDimsB);
} else if (!singleA && singleB) {
double *dA = (double *) mxGetData(A);
real32_T *sB = (real32_T *) mxGetData(B);
real32_T *sC = (real32_T *) mxGetData(C);
convolve(sC, dA, sB,
adjustedSizeA, adjustedSizeB, sizeC,
adjustedNDimsA, adjustedNDimsB, adjustedNDimsB);
} else { /* both inputs are double */
double *dA = (double *) mxGetData(A);
double *dB = (double *) mxGetData(B);
double *dC = (double *) mxGetData(C);
convolve(dC, dA, dB,
adjustedSizeA, adjustedSizeB, sizeC,
adjustedNDimsA, adjustedNDimsB, adjustedNDimsB);
}
}
А это - код conv
function C = convn(A,B,shape)
%CONVN N-dimensional convolution.
% C = CONVN(A, B) performs the N-dimensional convolution of
% matrices A and B.
% C = CONVN(A, B, 'shape') controls the size of the answer C:
% 'full' - (default) returns the full N-D convolution
% 'same' - returns the central part of the convolution that
% is the same size as A.
% 'valid' - returns only the part of the result that can be
% computed without assuming zero-padded arrays. The
% size of the result is max(size(A)-size(B)+1,0).
%
% Class support for inputs A,B:
% float: double, single
%
% See also CONV, CONV2.
% Copyright 1984-2004 The MathWorks, Inc.
% $Revision: 1.10.4.3 $ $Date: 2004/03/09 16:16:09 $
error(nargchk(2,3,nargin));
if (nargin < 3)
shape = 'full';
end
if (issparse(A) || issparse(B))
error('MATLAB:convn:SparseInput', 'Input arguments must be full.')
end
if ~isfloat(A)
A = double(A);
end
if ~isfloat(B)
B = double(B);
end
Aisreal = isreal(A);
Bisreal = isreal(B);
if (Aisreal && Bisreal)
C = convnc(A,B);
elseif (Aisreal && ~Bisreal)
C = convnc(A,real(B)) + j*convnc(A,imag(B));
elseif (~Aisreal && Bisreal)
C = convnc(real(A),B) + j*convnc(imag(A),B);
else
Ar = real(A);
Ai = imag(A);
Br = real(B);
Bi = imag(B);
C = convnc(Ar,Br) - convnc(Ai,Bi) + j*(convnc(Ai,Br) + convnc(Ar,Bi));
end
if (strcmp(shape,'same'))
sizeA = [size(A) ones(1,ndims(C)-ndims(A))];
sizeB = [size(B) ones(1,ndims(C)-ndims(B))];
flippedKernelCenter = ceil((1 + sizeB)/2);
subs = cell(1,ndims(C));
for p = 1:length(subs)
subs{p} = (1:sizeA(p)) + flippedKernelCenter(p) - 1;
end
C = C(subs{:});
elseif (strcmp(shape,'valid'))
sizeB = [size(B) ones(1,ndims(C)-ndims(B))];
outSize = max([size(A) ones(1,ndims(C)-ndims(A))] - sizeB + 1, 0);
subs = cell(1,ndims(C));
for p = 1:length(subs)
subs{p} = (1:outSize(p)) + sizeB(p) - 1;
end
C = C(subs{:});
end
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на случай 
измерений. Сделать это нетрудно даже без пространственного воображения, надо только аккуратно писать формулы. Единственную трудность я вижу в точном понимании того, что именно подразумевается под "центральной частью" результата, в случае, когда соответствующие размерности массивов чётные или нечётные, и поэтому не делятся точно на 2.
размера 
и 
размера 
свертка 
размера 
(где 
) будет такой:
, 
не совпадет, просто выбрать какое-то предпочтительное направление от центра и округлить либо в меньшую, либо в большую сторону положение центра.