问题
I'm working with batched 2D FFTs using the FFTW advanced data layout API.
According to the FFTW Advanced Complex DFT documentation:
Passing NULL for an nembed parameter is equivalent to passing n.
However, I'm getting different results when using inembed = onembed = NULL
vs. inembed = onembed = n
. What could be causing the results not to match?
Let's do an example...
Setup
int howMany = 2;
int nRows = 4;
int nCols = 4;
int n[2] = {nRows, nCols};
float* h_in = (float*)malloc(sizeof(float) * nRows*nCols*howMany);
for(int i=0; i<(nRows*nCols*howMany); i++){ //initialize h_in to [0 1 2 3 4 ...]
h_in[i] = (float)i;
printf("h_in[%d] = %f \n", i, h_in[i]);
}
FFTW Plan using inembed == onembed == NULL
fftwf_plan forwardPlan = fftwf_plan_many_dft_r2c(2, //rank
n, //dimensions = {nRows, nCols}
howMany, //howmany
h_in, //in
NULL, //inembed
howMany, //istride
1, //idist
h_freq, //out
NULL, //onembed
howMany, //ostride
1, //odist
FFTW_PATIENT /*flags*/);
I also ran a version of this with inembed = onembed = n = {nRows, nCols}
.
Results
Notice that using NULL
or n
gives the same numerical results, but in a different order in memory:
Version 1: inembed == onembed == NULL
result[0][0,1] = 240, 0
result[1][0,1] = 256, 0
result[2][0,1] = -16, 16
result[3][0,1] = -16, 16
result[4][0,1] = -16, 0
result[5][0,1] = -16, 0 //this line and above match the other version
result[6][0,1] = -64, 64 //this line and below don't match (data is in a different order)
result[7][0,1] = -64, 64
result[8][0,1] = 0, 0
result[9][0,1] = 0, 0
result[10][0,1] = 0, 0
result[11][0,1] = 0, 0
result[12][0,1] = -64, 0
result[13][0,1] = -64, 0
result[14][0,1] = 0, 0
result[15][0,1] = 0, 0
result[16][0,1] = 0, 0
result[17][0,1] = 0, 0
result[18][0,1] = -64, -64
result[19][0,1] = -64, -64
result[20][0,1] = 0, 0
result[21][0,1] = 0, 0
result[22][0,1] = 0, 0
result[23][0,1] = 0, 0
result[24][0,1] = 0, 0
result[25][0,1] = 0, 0
result[26][0,1] = 0, 0
result[27][0,1] = 0, 0
result[28][0,1] = 0, 0
result[29][0,1] = 0, 0
result[30][0,1] = 0, 0
result[31][0,1] = 0, 0
Version 2: inembed = onembed = n = {nRows, nCols}
result[0][0,1] = 240, 0
result[1][0,1] = 256, 0
result[2][0,1] = -16, 16
result[3][0,1] = -16, 16
result[4][0,1] = -16, 0
result[5][0,1] = -16, 0
result[6][0,1] = 0, 0
result[7][0,1] = 0, 0
result[8][0,1] = -64, 64
result[9][0,1] = -64, 64
result[10][0,1] = 0, 0
result[11][0,1] = 0, 0
result[12][0,1] = 0, 0
result[13][0,1] = 0, 0
result[14][0,1] = 0, 0
result[15][0,1] = 0, 0
result[16][0,1] = -64, 0
result[17][0,1] = -64, 0
result[18][0,1] = 0, 0
result[19][0,1] = 0, 0
result[20][0,1] = 0, 0
result[21][0,1] = 0, 0
result[22][0,1] = 0, 0
result[23][0,1] = 0, 0
result[24][0,1] = -64, -64
result[25][0,1] = -64, -64
result[26][0,1] = 0, 0
result[27][0,1] = 0, 0
result[28][0,1] = 0, 0
result[29][0,1] = 0, 0
result[30][0,1] = 0, 0
result[31][0,1] = 0, 0
Here's a working implementation of this experiment.
回答1:
Solution:
The out-of-place example with embed != NULL
in the above example is solved by setting inembed = {nRows, nCols}
and onembed = {nRows, (nCols/2 + 1)}
.
Details:
I resolved this after very carefully reading the FFTW documentation and getting some help from Matteo Frigo. You can retrace my steps here:
According to 4.4.2 Advanced Real-data DFTs in the FFTW manual: If an nembed parameter is NULL, it is interpreted as what it would be in the basic interface.
Let's assume our input real data is of dimension nx * ny
.
For the FFTW basic interface, 2.4 Multi-Dimensional DFTs of Real Data explains the following inembed
and onembed
conventions for 2D real-to-complex FFTs:
if out-of-place:
inembed = [ny, nx]
onembed = [ny, (nx/2 + 1)]
if in-place:
inembed = [ny, 2(nx/2 + 1)]
onembed = [ny, (nx/2 + 1)]
So, when we use the simple FFTW r2c
interface or use the advanced interface with embed=NULL
, FFTW defaults to the above embed
parameters. We can reproduce the numerical results from embed=NULL
by using the above embed
parameters.
It turns out that the statement Passing NULL for an nembed parameter is equivalent to passing n
comes from the FFTW complex-to-complex manual page. But, we're doing real-to-complex transforms in the examples above. Real-to-complex transforms have a different convention than complex-to-complex transforms for inembed
and onembed
.
来源:https://stackoverflow.com/questions/16905944/fftw-advanced-layout-inembed-n-and-inembed-null-give-different-results