// utils
void FFT_2d(int sizeX, int sizeY,
std::vector< std::complex<Real_t> > signal_in,
std::vector< std::complex<Real_t> > *signal_out){
std::vector< std::complex<Real_t> > out_tmp(sizeX*sizeY);
// x direction fft
for(int y=0; y<sizeY; y++){
std::vector< std::complex<Real_t> > x_tmp_in(sizeX);
std::vector< std::complex<Real_t> > x_tmp_out(sizeX);
for(int x=0; x<sizeX; x++){
x_tmp_in[x] =signal_in[x +sizeX*y];
}
FFT_1d(x_tmp_in, &x_tmp_out);
for(int x=0; x<sizeX; x++){
out_tmp[x +y*sizeX] =x_tmp_out[x];
}
}
// y direction fft
for(int x=0; x<sizeX; x++){
std::vector< std::complex<Real_t> > y_tmp_in(sizeY);
std::vector< std::complex<Real_t> > y_tmp_out(sizeY);
for(int y=0; y<sizeY; y++){
y_tmp_in[y] =out_tmp[x+sizeX*y];
}
FFT_1d(y_tmp_in, &y_tmp_out);
for(int y=0; y<sizeY; y++){
out_tmp[x +y*sizeX] =y_tmp_out[y];
}
}
auto& F = *signal_out;
for(int i =0; i<signal_in.size(); i++){
F[i] =out_tmp[i];
}
}
int main(int argc, char *argv[])
{ void *block;
(void) argc;
(void) argv;
if (GSIZE > DSIZE*DSIZE)
block = (void *) malloc(sizeof(double)*GSIZE*4);
else
block = (void *) malloc(sizeof(double)*DSIZE*DSIZE*4);
{ Complex_f *data = (Complex_f *) block;
int i, k;
printf("\n1-DIMENSIONAL FFT EXAMPLE:\n");
for (k = 0; k < 1; k++)
{ for (i = 0; i < QSIZE; i++)
{ data[i].real = (float) i;
data[i].imag = (float) (QSIZE-i);
}
Print_Complex_1f(QSIZE,data,"In");
FFT_1f(QSIZE,data,0);
Print_Complex_1f(QSIZE,data,"FFT");
FFT_1f(QSIZE,data,1);
Print_Complex_1f(QSIZE,data,"FFT_1(FFT)");
}
}
{ Complex_f *data = (Complex_f *) block;
int i, k;
printf("\n1-DIMENSIONAL FFT TEST:\n\n");
for (k = 1; k <= GSIZE; k *= 2)
{ for (i = 0; i < k; i++)
{ data[i].real = (float) ((i % 256) + 1);
data[i].imag = (float) (((k-i) % 256) + 1);
}
if (FFT_1f(k,data,0) == NULL) goto error;
if (FFT_1f(k,data,1) == NULL) goto error;
{ double avg, dev, mxdev, mxdiff;
avg = 0.;
mxdiff = 0.;
mxdev = 0.;
for (i = 0; i < k; i++)
{ dev = fabs(data[i].real - ((i%256)+1));
if (dev > mxdiff) mxdiff = dev;
dev /= ((i%256)+1.);
if (dev > mxdev) mxdev = dev;
avg += dev;
dev = fabs(data[i].imag - (((k-i) % 256) + 1));
if (dev > mxdiff) mxdiff = dev;
dev /= ((k-i) % 256) + 1.;
if (dev > mxdev) mxdev = dev;
avg += dev;
}
printf("For %8d: max diff = %.3e, max dev = %.3e, avg dev = %.3e\n",
k,mxdiff,mxdev,avg/(2.*k));
}
}
}
{ float *data = (float *) block;
int i, k;
Complex_f *fft;
printf("\n1-DIMENSIONAL *REAL* FFT EXAMPLE:\n");
for (k = 0; k < 1; k++)
{ for (i = 0; i < QSIZE; i++)
data[i] = (float) i;
Print_Real_1f(QSIZE,data,"Input");
fft = Real_FFT_1f(QSIZE,data);
Print_Complex_1f(QSIZE/2,fft,"Real_FFT");
Real_FFT_Inverse_1f(QSIZE,fft);
Print_Real_1f(QSIZE,data,"F_1(F(data))");
}
}
{ float *data = (float *) block;
int i, k;
Complex_f *fft;
printf("\n1-DIMENSIONAL *REAL* FFT TEST:\n\n");
for (k = 1; k <= 2*GSIZE; k *= 2)
{ for (i = 0; i < k; i++)
data[i] = (float) ((i%256)+1);
if ((fft = Real_FFT_1f(k,data)) == NULL) goto error;
if (Real_FFT_Inverse_1f(k,fft) == NULL) goto error;
{ double avg, dev, mxdev, mxdiff;
avg = 0.;
mxdiff = 0.;
mxdev = 0.;
for (i = 0; i < k; i++)
{ dev = fabs(data[i] - (i%256+1));
if (dev > mxdiff) mxdiff = dev;
dev /= (i%256+1);
if (dev > mxdev) mxdev = dev;
avg += dev;
}
printf("For %8d: max diff = %.3e, max dev = %.3e, avg dev = %.3e\n",
k,mxdiff,mxdev,avg/k);
}
}
}
{ float *rata = (float *) block;
float *fata = rata + QSIZE;
int i, k;
printf("\n1-DIMENSIONAL REAL CONVOLUTION EXAMPLE:\n");
for (k = 0; k < 1; k++)
{ for (i = 0; i < QSIZE; i++)
{ rata[i] = (float) (i%2+1);
fata[i] = (float) (i%2+1);
}
Print_Real_1f(QSIZE,fata,"Inputs 1 & 2");
Real_FFT_Inverse_1f(QSIZE,Real_Convolution_1f(QSIZE,Real_FFT_1f(QSIZE,fata),
Real_FFT_1f(QSIZE,rata)));
Print_Real_1f(QSIZE,fata,"Convolution");
}
}
{ float *rata = (float *) block;
float *fata = rata + QSIZE;
int i, k;
printf("\n1-DIMENSIONAL REAL CORRELATION EXAMPLE:\n");
for (k = 0; k < 1; k++)
{ for (i = 0; i < QSIZE; i++)
{ rata[i] = (float) (i%2+1);
fata[i] = (float) (i%2+1);
}
Print_Real_1f(QSIZE,fata,"Inputs 1 & 2");
Real_FFT_Inverse_1f(QSIZE,Real_Correlation_1f(QSIZE,Real_FFT_1f(QSIZE,fata),
Real_FFT_1f(QSIZE,rata)));
Print_Real_1f(QSIZE,fata,"Correlation");
}
}
{ float *data = (float *) block;
float *rata = data + 2*GSIZE;
int i, k;
printf("\n1-DIMENSIONAL REAL CONVOLUTION TEST:\n\n");
for (k = 1; k <= 2*GSIZE; k *= 2)
{ for (i = 0; i < k; i++)
data[i] = rata[i] = (float) (i%2+1);
if (Real_FFT_1f(k,data) == NULL) goto error;
if (Real_FFT_1f(k,rata) == NULL) goto error;
if (Real_Convolution_1f(k,(Complex_f *) data,(Complex_f *) rata) == NULL) goto error;
if (Real_FFT_Inverse_1f(k,(Complex_f *) data) == NULL) goto error;
{ double avg, dev, mxdev, mxdiff;
int x;
avg = 0.;
mxdiff = 0.;
mxdev = 0.;
for (i = 0; i < k; i++)
{ if (k == 1)
x = 1;
else
x = 2*k + ((i+1)%2)*(k/2);
dev = fabs(data[i] - x);
if (dev > mxdiff) mxdiff = dev;
dev /= x;
if (dev > mxdev) mxdev = dev;
avg += dev;
}
printf("For %8d: max diff = %.3e, max dev = %.3e, avg dev = %.3e\n",
k,mxdiff,mxdev,avg/k);
}
}
}
{ float *data = (float *) block;
float *rata = data + 2*GSIZE;
int i, k;
printf("\n1-DIMENSIONAL REAL CORRELATION TEST:\n\n");
for (k = 1; k <= 2*GSIZE; k *= 2)
{ for (i = 0; i < k; i++)
data[i] = rata[i] = (float) (i%2+1);
if (Real_FFT_1f(k,data) == NULL) goto error;
if (Real_FFT_1f(k,rata) == NULL) goto error;
if (Real_Correlation_1f(k,(Complex_f *) data,(Complex_f *) rata) == NULL) goto error;
if (Real_FFT_Inverse_1f(k,(Complex_f *) data) == NULL) goto error;
{ double avg, dev, mxdev, mxdiff;
int x;
avg = 0.;
mxdiff = 0.;
mxdev = 0.;
for (i = 0; i < k; i++)
{ if (k == 1)
x = 1;
else
x = 2*k + ((i+1)%2)*(k/2);
dev = fabs(data[i] - x);
if (dev > mxdiff) mxdiff = dev;
dev /= x;
if (dev > mxdev) mxdev = dev;
avg += dev;
}
printf("For %8d: max diff = %.3e, max dev = %.3e, avg dev = %.3e\n",
k,mxdiff,mxdev,avg/k);
}
}
}
{ Complex_f *data = (Complex_f *) block;
int dims[2];
int i, j, k, d;
dims[0] = HSIZE;
dims[1] = HSIZE;
printf("\nMULTI-DIMENSIONAL FFT EXAMPLE:\n");
for (k = 0; k < 1; k++)
{ int base1 = dims[0];
for (i = 0; i < dims[1]; i++)
for (j = 0; j < dims[0]; j++)
{ d = i*base1+j;
data[d].real = (float) d;
data[d].imag = (float) (base1-d);
}
Print_Complex_nf(2,dims,data,"Input");
FFT_nf(2,dims,data,0);
Print_Complex_nf(2,dims,data,"FFT");
FFT_nf(2,dims,data,1);
Print_Complex_nf(2,dims,data,"FFT_1(FFT)");
}
}
{ Complex_f *data = (Complex_f *) block;
int dims[2];
int h, k, i, j, d;
printf("\nMULTI-DIMENSIONAL FFT TEST:\n\n");
for (h = 1; h <= DSIZE; h *= 2)
for (k = 1; k <= DSIZE; k *= 2)
{ dims[0] = k;
dims[1] = h;
for (i = 0; i < dims[1]; i++)
for (j = 0; j < dims[0]; j++)
{ d = i*k+j;
data[d].real = (float) ((d % 256) + 1);
data[d].imag = (float) (abs((k-d) % 256) + 1);
}
if (FFT_nf(2,dims,data,0) == NULL) goto error;
if (FFT_nf(2,dims,data,1) == NULL) goto error;
{ double avg, dev, mxdev, mxdiff;
int x;
avg = 0.;
mxdiff = 0.;
mxdev = 0.;
for (i = 0; i < dims[1]; i++)
for (j = 0; j < dims[0]; j++)
{ d = i*k+j;
x = (d % 256) + 1;
dev = fabs(data[d].real - x);
if (dev > mxdiff) mxdiff = dev;
dev /= x;
if (dev > mxdev) mxdev = dev;
avg += dev;
x = abs((k-d) % 256) + 1;
dev = fabs(data[d].imag - x);
if (dev > mxdiff) mxdiff = dev;
dev /= x;
if (dev > mxdev) mxdev = dev;
avg += dev;
}
printf("For %4d,%4d: max diff = %.3e, max dev = %.3e, avg dev = %.3e\n",
h,k,mxdiff,mxdev,avg/(2.*k*h));
}
}
}
{ float *data = (float *) block;
int dims[2];
Complex_f *fft;
int k, i;
dims[0] = HSIZE;
dims[1] = HSIZE;
printf("\nMULTI-DIMENSIONAL *REAL* FFT EXAMPLE:\n");
for (k = 0; k < 1; k++)
{ for (i = 0; i < dims[0]*dims[1]; i++)
data[i] = (float) i;
Print_Real_nf(2,dims,data,"Input");
fft = Real_FFT_nf(2,dims,data);
dims[0] /= 2;
Print_Complex_nf(2,dims,fft,"Real_FFT");
dims[0] *= 2;
Real_FFT_Inverse_nf(2,dims,fft);
Print_Real_nf(2,dims,data,"F_1(F(data))");
}
}
{ float *data = (float *) block;
int dims[2];
Complex_f *fft;
int h, k, i;
printf("\nMULTI-DIMENSIONAL *REAL* FFT TEST:\n\n");
for (h = 1; h <= DSIZE; h *= 2)
for (k = 1; k <= 2*DSIZE; k *= 2)
{ dims[0] = k;
dims[1] = h;
for (i = 0; i < k*h; i++)
data[i] = (float) ((i % 256) + 1);
if ((fft = Real_FFT_nf(2,dims,data)) == NULL) goto error;
if (Real_FFT_Inverse_nf(2,dims,fft) == NULL) goto error;
{ double avg, dev, mxdev, mxdiff;
int x;
avg = 0.;
mxdiff = 0.;
mxdev = 0.;
for (i = 0; i < k*h; i++)
{ x = (i % 256) + 1;
dev = fabs(data[i] - x);
if (dev > mxdiff) mxdiff = dev;
dev /= x;
if (dev > mxdev) mxdev = dev;
avg += dev;
}
printf("For %4d,%4d: max diff = %.3e, max dev = %.3e, avg dev = %.3e\n",
h,k,mxdiff,mxdev,avg/(2.*k*h));
}
}
}
{ float *rata = (float *) block;
float *fata = rata + HSIZE*HSIZE;
int dims[2];
int i, j, k, d;
dims[0] = HSIZE;
dims[1] = HSIZE;
printf("\nMULTI-DIMENSIONAL REAL CONVOLUTION EXAMPLE:\n");
for (k = 0; k < 1; k++)
{ int base1 = dims[0];
for (i = 0; i < dims[1]; i++)
for (j = 0; j < dims[0]; j++)
{ d = i*base1+j;
rata[d] = (float) (d % 2 + 1);
fata[d] = (float) (d % 2 + 1);
}
Print_Real_nf(2,dims,fata,"Inputs 1 & 2");
Real_FFT_Inverse_nf(2,dims,
Real_Convolution_nf(2,dims,Real_FFT_nf(2,dims,fata),Real_FFT_nf(2,dims,rata)));
Print_Real_nf(2,dims,fata,"Convolution");
}
}
{ float *rata = (float *) block;
float *fata = rata + HSIZE*HSIZE;
int dims[2];
int i, j, k, d;
dims[0] = HSIZE;
dims[1] = HSIZE;
printf("\nMULTI-DIMENSIONAL REAL CORRELATION EXAMPLE:\n");
for (k = 0; k < 1; k++)
{ int base1 = dims[0];
for (i = 0; i < dims[1]; i++)
for (j = 0; j < dims[0]; j++)
{ d = i*base1+j;
rata[d] = (float) (d % 2 + 1);
fata[d] = (float) (d % 2 + 1);
}
Print_Real_nf(2,dims,fata,"Inputs 1 & 2");
Real_FFT_Inverse_nf(2,dims,
Real_Correlation_nf(2,dims,Real_FFT_nf(2,dims,fata),Real_FFT_nf(2,dims,rata)));
Print_Real_nf(2,dims,fata,"Correlation");
}
}
{ float *rata = (float *) block;
float *fata = rata + 2*DSIZE*DSIZE;
int dims[2];
int h, k, i;
printf("\nMULTI-DIMENSIONAL REAL CONVOLUTION TEST:\n\n");
for (h = 1; h <= DSIZE; h *= 2)
for (k = 1; k <= 2*DSIZE; k *= 2)
{ int size;
dims[0] = k;
dims[1] = h;
size = k*h;
for (i = 0; i < size; i++)
{ rata[i] = (float) ((i % 2) + 1);
fata[i] = (float) ((i % 2) + 1);
}
if (Real_FFT_nf(2,dims,fata) == NULL) goto error;
if (Real_FFT_nf(2,dims,rata) == NULL) goto error;
if (Real_Convolution_nf(2,dims,(Complex_f *) fata,(Complex_f *) rata) == NULL) goto error;
if (Real_FFT_Inverse_nf(2,dims,(Complex_f *) fata) == NULL) goto error;
{ double avg, dev, mxdev, mxdiff;
int x;
avg = 0.;
mxdiff = 0.;
mxdev = 0.;
for (i = 0; i < size; i++)
{ if (size == 1)
x = 1;
else
{ x = 4 + (i+1)%2;
x = x * k * h / 2;
}
dev = fabs(fata[i] - x);
if (dev > mxdiff) mxdiff = dev;
dev /= x;
if (dev > mxdev) mxdev = dev;
avg += dev;
}
printf("For %4d,%4d: max diff = %.3e, max dev = %.3e, avg dev = %.3e\n",
h,k,mxdiff,mxdev,avg/(2.*k*h));
}
}
}
{ float *rata = (float *) block;
float *fata = rata + 2*DSIZE*DSIZE;
int dims[2];
int h, k, i;
printf("\nMULTI-DIMENSIONAL REAL CORRELATION TEST:\n\n");
for (h = 1; h <= DSIZE; h *= 2)
for (k = 1; k <= 2*DSIZE; k *= 2)
{ int size;
dims[0] = k;
dims[1] = h;
size = k*h;
for (i = 0; i < size; i++)
{ rata[i] = (float) ((i % 2) + 1);
fata[i] = (float) ((i % 2) + 1);
}
if (Real_FFT_nf(2,dims,fata) == NULL) goto error;
if (Real_FFT_nf(2,dims,rata) == NULL) goto error;
if (Real_Correlation_nf(2,dims,(Complex_f *) fata,(Complex_f *) rata) == NULL) goto error;
if (Real_FFT_Inverse_nf(2,dims,(Complex_f *) fata) == NULL) goto error;
{ double avg, dev, mxdev, mxdiff;
int x;
avg = 0.;
mxdiff = 0.;
mxdev = 0.;
for (i = 0; i < size; i++)
{ if (size == 1)
x = 1;
else
{ x = 4 + (i+1)%2;
x = x * k * h / 2;
}
dev = fabs(fata[i] - x);
if (dev > mxdiff) mxdiff = dev;
dev /= x;
if (dev > mxdev) mxdev = dev;
avg += dev;
}
printf("For %4d,%4d: max diff = %.3e, max dev = %.3e, avg dev = %.3e\n",
h,k,mxdiff,mxdev,avg/(2.*k*h));
}
}
}
{ Complex_d *data = (Complex_d *) block;
int i, k;
printf("\n1-DIMENSIONAL FFT EXAMPLE:\n");
for (k = 0; k < 1; k++)
{ for (i = 0; i < QSIZE; i++)
{ data[i].real = i;
data[i].imag = QSIZE-i;
}
Print_Complex_1d(QSIZE,data,"In");
FFT_1d(QSIZE,data,0);
Print_Complex_1d(QSIZE,data,"FFT");
FFT_1d(QSIZE,data,1);
Print_Complex_1d(QSIZE,data,"FFT_1(FFT)");
}
}
{ Complex_d *data = (Complex_d *) block;
int i, k;
printf("\n1-DIMENSIONAL FFT TEST:\n\n");
for (k = 1; k <= GSIZE; k *= 2)
{ for (i = 0; i < k; i++)
{ data[i].real = (i % 256) + 1;
data[i].imag = ((k-i) % 256) + 1;
}
FFT_1d(k,data,0);
FFT_1d(k,data,1);
{ double avg, dev, mxdev, mxdiff;
avg = 0.;
mxdiff = 0.;
mxdev = 0.;
for (i = 0; i < k; i++)
{ dev = fabs(data[i].real - ((i%256)+1));
if (dev > mxdiff) mxdiff = dev;
dev /= ((i%256)+1.);
if (dev > mxdev) mxdev = dev;
avg += dev;
dev = fabs(data[i].imag - (((k-i) % 256) + 1));
if (dev > mxdiff) mxdiff = dev;
dev /= ((k-i) % 256) + 1.;
if (dev > mxdev) mxdev = dev;
avg += dev;
}
printf("For %8d: max diff = %.3e, max dev = %.3e, avg dev = %.3e\n",
k,mxdiff,mxdev,avg/(2.*k));
}
}
}
{ double *data = (double *) block;
int i, k;
Complex_d *fft;
printf("\n1-DIMENSIONAL *REAL* FFT EXAMPLE:\n");
for (k = 0; k < 1; k++)
{ for (i = 0; i < QSIZE; i++)
data[i] = i;
Print_Real_1d(QSIZE,data,"Input");
fft = Real_FFT_1d(QSIZE,data);
Print_Complex_1d(QSIZE/2,fft,"Real_FFT");
Real_FFT_Inverse_1d(QSIZE,fft);
Print_Real_1d(QSIZE,data,"F_1(F(data))");
}
}
{ double *data = (double *) block;
int i, k;
Complex_d *fft;
printf("\n1-DIMENSIONAL *REAL* FFT TEST:\n\n");
for (k = 1; k <= 2*GSIZE; k *= 2)
{ for (i = 0; i < k; i++)
data[i] = (i%256)+1;
fft = Real_FFT_1d(k,data);
Real_FFT_Inverse_1d(k,fft);
{ double avg, dev, mxdev, mxdiff;
avg = 0.;
mxdiff = 0.;
mxdev = 0.;
for (i = 0; i < k; i++)
{ dev = fabs(data[i] - (i%256+1));
if (dev > mxdiff) mxdiff = dev;
dev /= (i%256+1);
if (dev > mxdev) mxdev = dev;
avg += dev;
}
printf("For %8d: max diff = %.3e, max dev = %.3e, avg dev = %.3e\n",
k,mxdiff,mxdev,avg/k);
}
}
}
{ double *rata = (double *) block;
double *fata = rata + QSIZE;
int i, k;
printf("\n1-DIMENSIONAL REAL CONVOLUTION EXAMPLE:\n");
for (k = 0; k < 1; k++)
{ for (i = 0; i < QSIZE; i++)
{ rata[i] = i%2+1;
fata[i] = i%2+1;
}
Print_Real_1d(QSIZE,fata,"Inputs 1 & 2");
Real_FFT_Inverse_1d(QSIZE,
Real_Convolution_1d(QSIZE,Real_FFT_1d(QSIZE,fata),Real_FFT_1d(QSIZE,rata)));
Print_Real_1d(QSIZE,fata,"Convolution");
}
}
{ double *rata = (double *) block;
double *fata = rata + QSIZE;
int i, k;
printf("\n1-DIMENSIONAL REAL CORRELATION EXAMPLE:\n");
for (k = 0; k < 1; k++)
{ for (i = 0; i < QSIZE; i++)
{ rata[i] = i%2+1;
fata[i] = i%2+1;
}
Print_Real_1d(QSIZE,fata,"Inputs 1 & 2");
Real_FFT_Inverse_1d(QSIZE,
Real_Correlation_1d(QSIZE,Real_FFT_1d(QSIZE,fata),Real_FFT_1d(QSIZE,rata)));
Print_Real_1d(QSIZE,fata,"Correlation");
}
}
{ double *data = (double *) block;
double *rata = data + 2*GSIZE;
int i, k;
printf("\n1-DIMENSIONAL REAL CONVOLUTION TEST:\n\n");
for (k = 1; k <= 2*GSIZE; k *= 2)
{ for (i = 0; i < k; i++)
data[i] = rata[i] = i%2+1;
Real_FFT_Inverse_1d(k,Real_Convolution_1d(k,Real_FFT_1d(k,data),Real_FFT_1d(k,rata)));
{ double avg, dev, mxdev, mxdiff;
int x;
avg = 0.;
mxdiff = 0.;
mxdev = 0.;
for (i = 0; i < k; i++)
{ if (k == 1)
x = 1;
else
x = 2*k + ((i+1)%2)*(k/2);
dev = fabs(data[i] - x);
if (dev > mxdiff) mxdiff = dev;
dev /= x;
if (dev > mxdev) mxdev = dev;
avg += dev;
}
printf("For %8d: max diff = %.3e, max dev = %.3e, avg dev = %.3e\n",
k,mxdiff,mxdev,avg/k);
}
}
}
{ double *data = (double *) block;
double *rata = data + 2*GSIZE;
int i, k;
printf("\n1-DIMENSIONAL REAL CORRELATION TEST:\n\n");
for (k = 1; k <= 2*GSIZE; k *= 2)
{ for (i = 0; i < k; i++)
data[i] = rata[i] = i%2+1;
Real_FFT_Inverse_1d(k,Real_Correlation_1d(k,Real_FFT_1d(k,data),Real_FFT_1d(k,rata)));
{ double avg, dev, mxdev, mxdiff;
int x;
avg = 0.;
mxdiff = 0.;
mxdev = 0.;
for (i = 0; i < k; i++)
{ if (k == 1)
x = 1;
else
x = 2*k + ((i+1)%2)*(k/2);
dev = fabs(data[i] - x);
if (dev > mxdiff) mxdiff = dev;
dev /= x;
if (dev > mxdev) mxdev = dev;
avg += dev;
}
printf("For %8d: max diff = %.3e, max dev = %.3e, avg dev = %.3e\n",
k,mxdiff,mxdev,avg/k);
}
}
}
{ Complex_d *data = (Complex_d *) block;
int dims[2];
int i, j, k, d;
dims[0] = HSIZE;
dims[1] = HSIZE;
printf("\nMULTI-DIMENSIONAL FFT EXAMPLE:\n");
for (k = 0; k < 1; k++)
{ int base1 = dims[0];
for (i = 0; i < dims[1]; i++)
for (j = 0; j < dims[0]; j++)
{ d = i*base1+j;
data[d].real = d;
data[d].imag = base1-d;
}
Print_Complex_nd(2,dims,data,"Input");
FFT_nd(2,dims,data,0);
Print_Complex_nd(2,dims,data,"FFT");
FFT_nd(2,dims,data,1);
Print_Complex_nd(2,dims,data,"FFT_1(FFT)");
}
}
{ Complex_d *data = (Complex_d *) block;
int dims[2];
int h, k, i, j, d;
printf("\nMULTI-DIMENSIONAL FFT TEST:\n\n");
for (h = 1; h <= DSIZE; h *= 2)
for (k = 1; k <= DSIZE; k *= 2)
{ dims[0] = k;
dims[1] = h;
for (i = 0; i < dims[1]; i++)
for (j = 0; j < dims[0]; j++)
{ d = i*k+j;
data[d].real = (d % 256) + 1;
data[d].imag = abs((k-d) % 256) + 1;
}
FFT_nd(2,dims,data,0);
FFT_nd(2,dims,data,1);
{ double avg, dev, mxdev, mxdiff;
int x;
avg = 0.;
mxdiff = 0.;
mxdev = 0.;
for (i = 0; i < dims[1]; i++)
for (j = 0; j < dims[0]; j++)
{ d = i*k+j;
x = (d % 256) + 1;
dev = fabs(data[d].real - x);
if (dev > mxdiff) mxdiff = dev;
dev /= x;
if (dev > mxdev) mxdev = dev;
avg += dev;
x = abs((k-d) % 256) + 1;
dev = fabs(data[d].imag - x);
if (dev > mxdiff) mxdiff = dev;
dev /= x;
if (dev > mxdev) mxdev = dev;
avg += dev;
}
printf("For %4d,%4d: max diff = %.3e, max dev = %.3e, avg dev = %.3e\n",
h,k,mxdiff,mxdev,avg/(2.*k*h));
}
}
}
{ double *data = (double *) block;
int dims[2];
Complex_d *fft;
int k, i;
dims[0] = HSIZE;
dims[1] = HSIZE;
printf("\nMULTI-DIMENSIONAL *REAL* FFT EXAMPLE:\n");
for (k = 0; k < 1; k++)
{ for (i = 0; i < dims[0]*dims[1]; i++)
data[i] = i;
Print_Real_nd(2,dims,data,"Input");
fft = Real_FFT_nd(2,dims,data);
dims[0] /= 2;
Print_Complex_nd(2,dims,fft,"Real_FFT");
dims[0] *= 2;
Real_FFT_Inverse_nd(2,dims,fft);
Print_Real_nd(2,dims,data,"F_1(F(data))");
}
}
{ double *data = (double *) block;
int dims[2];
Complex_d *fft;
int h, k, i;
printf("\nMULTI-DIMENSIONAL *REAL* FFT TEST:\n\n");
for (h = 1; h <= DSIZE; h *= 2)
for (k = 1; k <= DSIZE; k *= 2)
{ dims[0] = k;
dims[1] = h;
for (i = 0; i < k*h; i++)
data[i] = (i % 256) + 1;
fft = Real_FFT_nd(2,dims,data);
Real_FFT_Inverse_nd(2,dims,fft);
{ double avg, dev, mxdev, mxdiff;
int x;
avg = 0.;
mxdiff = 0.;
mxdev = 0.;
for (i = 0; i < k*h; i++)
{ x = (i % 256) + 1;
dev = fabs(data[i] - x);
if (dev > mxdiff) mxdiff = dev;
dev /= x;
if (dev > mxdev) mxdev = dev;
avg += dev;
}
printf("For %4d,%4d: max diff = %.3e, max dev = %.3e, avg dev = %.3e\n",
h,k,mxdiff,mxdev,avg/(2.*k*h));
}
}
}
{ double *rata = (double *) block;
double *fata = rata + HSIZE*HSIZE;
int dims[2];
int i, j, k, d;
dims[0] = HSIZE;
dims[1] = HSIZE;
printf("\nMULTI-DIMENSIONAL REAL CONVOLUTION EXAMPLE:\n");
for (k = 0; k < 1; k++)
{ int base1 = dims[0];
for (i = 0; i < dims[1]; i++)
for (j = 0; j < dims[0]; j++)
{ d = i*base1+j;
rata[d] = d % 2 + 1;
fata[d] = d % 2 + 1;
}
Print_Real_nd(2,dims,fata,"Inputs 1 & 2");
Real_FFT_Inverse_nd(2,dims,
Real_Convolution_nd(2,dims,Real_FFT_nd(2,dims,fata),Real_FFT_nd(2,dims,rata)));
Print_Real_nd(2,dims,fata,"Convolution");
}
}
{ double *rata = (double *) block;
double *fata = rata + HSIZE*HSIZE;
int dims[2];
int i, j, k, d;
dims[0] = HSIZE;
dims[1] = HSIZE;
printf("\nMULTI-DIMENSIONAL REAL CORRELATION EXAMPLE:\n");
for (k = 0; k < 1; k++)
{ int base1 = dims[0];
for (i = 0; i < dims[1]; i++)
for (j = 0; j < dims[0]; j++)
{ d = i*base1+j;
rata[d] = d % 2 + 1;
fata[d] = d % 2 + 1;
}
Print_Real_nd(2,dims,fata,"Inputs 1 & 2");
Real_FFT_Inverse_nd(2,dims,
Real_Correlation_nd(2,dims,Real_FFT_nd(2,dims,fata),Real_FFT_nd(2,dims,rata)));
Print_Real_nd(2,dims,fata,"Correlation");
}
}
{ double *rata = (double *) block;
double *fata = rata + 2*DSIZE*DSIZE;
int dims[2];
int h, k, i;
printf("\nMULTI-DIMENSIONAL REAL CONVOLUTION TEST:\n\n");
for (h = 1; h <= DSIZE; h *= 2)
for (k = 1; k <= 2*DSIZE; k *= 2)
{ int size;
dims[0] = k;
dims[1] = h;
size = k*h;
for (i = 0; i < size; i++)
{ rata[i] = (i % 2) + 1;
fata[i] = (i % 2) + 1;
}
Real_FFT_Inverse_nd(2,dims,
Real_Convolution_nd(2,dims,Real_FFT_nd(2,dims,fata),Real_FFT_nd(2,dims,rata)));
{ double avg, dev, mxdev, mxdiff;
int x;
avg = 0.;
mxdiff = 0.;
mxdev = 0.;
for (i = 0; i < size; i++)
{ if (size == 1)
x = 1;
else
{ x = 4 + (i+1)%2;
x = x * k * h / 2;
}
dev = fabs(fata[i] - x);
if (dev > mxdiff) mxdiff = dev;
dev /= x;
if (dev > mxdev) mxdev = dev;
avg += dev;
}
printf("For %4d,%4d: max diff = %.3e, max dev = %.3e, avg dev = %.3e\n",
h,k,mxdiff,mxdev,avg/(2.*k*h));
}
}
}
{ double *rata = (double *) block;
double *fata = rata + 2*DSIZE*DSIZE;
int dims[2];
int h, k, i;
printf("\nMULTI-DIMENSIONAL REAL CORRELATION TEST:\n\n");
for (h = 1; h <= DSIZE; h *= 2)
for (k = 1; k <= 2*DSIZE; k *= 2)
{ int size;
dims[0] = k;
dims[1] = h;
size = k*h;
for (i = 0; i < size; i++)
{ rata[i] = (i % 2) + 1;
fata[i] = (i % 2) + 1;
}
Real_FFT_Inverse_nd(2,dims,
Real_Correlation_nd(2,dims,Real_FFT_nd(2,dims,fata),Real_FFT_nd(2,dims,rata)));
{ double avg, dev, mxdev, mxdiff;
int x;
avg = 0.;
mxdiff = 0.;
mxdev = 0.;
for (i = 0; i < size; i++)
{ if (size == 1)
x = 1;
else
{ x = 4 + (i+1)%2;
x = x * k * h / 2;
}
dev = fabs(fata[i] - x);
if (dev > mxdiff) mxdiff = dev;
dev /= x;
if (dev > mxdev) mxdev = dev;
avg += dev;
}
printf("For %4d,%4d: max diff = %.3e, max dev = %.3e, avg dev = %.3e\n",
h,k,mxdiff,mxdev,avg/(2.*k*h));
}
}
}
exit (0);
error:
printf("Encounted an error (%s) %s\n",FFT_Error_Source(),FFT_Error_String());
exit (0);
}
