inline void computeNumMatchesWithFFT(double *t, double *p,int n, int m,
int transformSize,int *matches, fftw_plan *forward, fftw_plan *inverse){
printf("USING FFT\n");
printf("n: %d m: %d\n",n, m);
//TODO: Should probably move these out of the function. No point allocating
//and de-allocating the memory over and over for each character
double *textSubString = (double *) fftw_malloc(sizeof(double) * transformSize);
double *DFTofPattern = (double *) fftw_malloc(sizeof(double) * transformSize);
double *DFTofText = (double *) fftw_malloc(sizeof(double) * transformSize);
double *pTimesT = (double *) fftw_malloc(sizeof(double) * transformSize);
double *pTimesT_PR = (double *) fftw_malloc(sizeof(double) * transformSize);
int i;
if(*forward==NULL){
*forward = fftw_plan_r2r_1d(transformSize,p,DFTofPattern,FFTW_R2HC,FFTW_ESTIMATE);
fftw_execute(*forward);
}else{
fftw_execute_r2r(*forward,p,DFTofPattern);
}
int start = 0;
//Perform transforms on sub-strings of the text values
while(start <= n-m){
memcpy(textSubString,t+start,sizeof(double)*transformSize);
fftw_execute_r2r(*forward,textSubString,DFTofText);
/* Multiply the point representations*/
pTimesT_PR[0] = DFTofPattern[0] * DFTofText[0];
THE_COUNT++;
if(transformSize % 2==0){
for(i=1;i<transformSize/2;i++){
pTimesT_PR[i] = DFTofPattern[i] * DFTofText[i] - DFTofPattern[transformSize-i] * DFTofText[transformSize-i];
pTimesT_PR[transformSize-i] = DFTofPattern[transformSize-i] * DFTofText[i] + DFTofPattern[i] * DFTofText[transformSize-i];
}
pTimesT_PR[i] = DFTofPattern[i] * DFTofText[i];
}else{
for(i=1;i<=transformSize/2;i++){
pTimesT_PR[i] = DFTofPattern[i] * DFTofText[i] - DFTofPattern[transformSize-i] * DFTofText[transformSize-i];
pTimesT_PR[transformSize-i] = DFTofPattern[transformSize-i] * DFTofText[i] + DFTofPattern[i] * DFTofText[transformSize-i];
}
}
/* Convert back to a coefficient representation */
//On first iteration, need to create the inverse plan
if(*inverse==NULL){
*inverse = fftw_plan_r2r_1d(transformSize,pTimesT_PR,pTimesT,FFTW_HC2R,FFTW_ESTIMATE);
fftw_execute(*inverse);
}else{
fftw_execute_r2r(*inverse,pTimesT_PR,pTimesT);
}
for(i=0;i<=transformSize-m && (i+start)<=n-m;i++){
//printf("i+start: %d+%d=%d, value=%d\n",i,start,i+start,(int) ((pTimesT[m+i-1]/transformSize)+0.5));
//plus 0.5 to allow rounding via truncation
matches[i+start] += (int)((pTimesT[m+i-1]/transformSize)+0.5);
}
start +=transformSize-m +1;
}
fftw_free(textSubString);
fftw_free(DFTofPattern);
fftw_free(DFTofText);
fftw_free(pTimesT);
fftw_free(pTimesT_PR);
}
I8 mzi_fft(U32 X, U32 Y, U32 mzi_length, I8 hann_flag, I8 dB_flag,
U32 *mzi_indexes, T1 *in, DBL *intensity, DBL *phase, DBL *Re,
DBL *Im) {
DBL *hann_win = static_cast<DBL *>(fftw_malloc(sizeof(DBL) * mzi_length));
// create FFTW plan
fftw_plan fft_p = fftw_plan_r2r_1d(mzi_length, Re, Im, FFTW_R2HC,
FFTW_ESTIMATE);
U32 width = static_cast<U32>(mzi_length/2);
I32 j;
// prepare Hanning window
for (U32 i = 0; i < mzi_length; i++) {
if (hann_flag)
hann_win[i] = 0.5 * (1 - cos(kTwoPi * i / mzi_length));
else
hann_win[i] = 1.0;
}
// parallel run by A-lines
#pragma omp parallel for default(shared) private(j)
for (j = 0; j < static_cast<I32>(Y); j++) {
DBL *tmp_fft_in = static_cast<DBL *>(fftw_malloc(sizeof(DBL) * mzi_length));
DBL *tmp_fft_out =static_cast<DBL *>(fftw_malloc(sizeof(DBL) * mzi_length));
I32 pos = j * width;
// MZI filter: pick up RAW A-line values for corresponding MZI indexes
for (U32 i = 0; i < mzi_length; i++)
tmp_fft_in[i] = in[j * X + mzi_indexes[i]];
// apply hanning window or just make data cast
transform(tmp_fft_in, tmp_fft_in + mzi_length, hann_win, tmp_fft_in,
multiplies<DBL>());
// perform FFT using FFTW3 library
fftw_execute_r2r(fft_p, tmp_fft_in, tmp_fft_out);
// ZERO components
if (dB_flag)
intensity[pos] = 20 * log10(abs(tmp_fft_out[0]));
else
intensity[pos] = tmp_fft_out[0];
Re[pos] = tmp_fft_out[0];
phase[pos] = Im[pos] = 0.0;
// construct intensity and phase information, Re and Im parts
for (U32 pos1 = 1, pos2 = mzi_length - 1; pos1 < width; pos1++, pos2--) {
// intensity
if (dB_flag)
intensity[pos + pos1] = 20 * log10(sqrt(tmp_fft_out[pos1] * \
tmp_fft_out[pos1] + tmp_fft_out[pos2] * \
tmp_fft_out[pos2]));
else
intensity[pos + pos1] = sqrt(tmp_fft_out[pos1] * tmp_fft_out[pos1] + \
tmp_fft_out[pos2] * tmp_fft_out[pos2]);
// phase
phase[pos + pos1] = atan2(tmp_fft_out[pos2], tmp_fft_out[pos1]);
// Re part
Re[pos + pos1] = tmp_fft_out[pos1];
// Im part
Im[pos + pos1] = tmp_fft_out[pos2];
}
fftw_free(tmp_fft_in);
fftw_free(tmp_fft_out);
} // end of parallel code
fftw_destroy_plan(fft_p);
fftw_free(hann_win);
return EXIT_SUCCESS;
}
void SemiNaiveReduced(double *data,
int bw,
int m,
double *result,
double *workspace,
double *cos_pml_table,
double *weights,
fftw_plan *fplan )
{
int i, j, n;
double result0, result1, result2, result3;
double fudge ;
double d_bw;
int toggle ;
double *pml_ptr, *weighted_data, *cos_data ;
n = 2*bw;
d_bw = (double) bw;
weighted_data = workspace ;
cos_data = weighted_data + (2*bw) ;
/* for paranoia, zero out the result array */
memset( result, 0, sizeof(double)*(bw-m));
/*
need to apply quadrature weights to the data and compute
the cosine transform
*/
if ( m % 2 )
for ( i = 0; i < n ; ++i )
weighted_data[i] = data[ i ] * weights[ 2*bw + i ];
else
for ( i = 0; i < n ; ++i )
weighted_data[i] = data[ i ] * weights[ i ];
/*
smooth the weighted signal
*/
fftw_execute_r2r( *fplan,
weighted_data,
cos_data );
/* need to normalize */
cos_data[0] *= 0.707106781186547 ;
fudge = 1./sqrt(2. * ((double) n ) );
for ( j = 0 ; j < n ; j ++ )
cos_data[j] *= fudge ;
/*
do the projections; Note that the cos_pml_table has
had all the zeroes stripped out so the indexing is
complicated somewhat
*/
/******** this is the original loop
toggle = 0 ;
for (i=m; i<bw; i++)
{
pml_ptr = cos_pml_table + NewTableOffset(m,i);
if ((m % 2) == 0)
{
for (j=0; j<(i/2)+1; j++)
result[i-m] += cos_data[(2*j)+toggle] * pml_ptr[j];
}
else
{
if (((i-m) % 2) == 0)
{
for (j=0; j<(i/2)+1; j++)
result[i-m] += cos_data[(2*j)+toggle] * pml_ptr[j];
}
else
{
for (j=0; j<(i/2); j++)
result[i-m] += cos_data[(2*j)+toggle] * pml_ptr[j];
}
}
toggle = (toggle+1) % 2;
}
*****/
/******** this is the new loop *********/
toggle = 0 ;
for ( i=m; i<bw; i++ )
{
pml_ptr = cos_pml_table + NewTableOffset(m,i);
result0 = 0.0 ; result1 = 0.0 ;
result2 = 0.0 ; result3 = 0.0 ;
for ( j = 0 ; j < ( (i/2) % 4 ) ; ++j )
result0 += cos_data[(2*j)+toggle] * pml_ptr[j];
for ( ; j < (i/2) ; j += 4 )
{
result0 += cos_data[(2*j)+toggle] * pml_ptr[j];
result1 += cos_data[(2*(j+1))+toggle] * pml_ptr[j+1];
result2 += cos_data[(2*(j+2))+toggle] * pml_ptr[j+2];
result3 += cos_data[(2*(j+3))+toggle] * pml_ptr[j+3];
}
if ((((i-m) % 2) == 0 ) || ( (m % 2) == 0 ))
result0 += cos_data[(2*(i/2))+toggle] * pml_ptr[(i/2)];
result[i-m] = result0 + result1 + result2 + result3 ;
toggle = (toggle + 1)%2 ;
}
}
/* easy spline interpolation + FFT main function
PURPOSE:
calculate FFT (using fftw_plan_r2r_1d() function call from FFTW library) for
RAW B-scan [1] converted into linear wavenumber space (k-space) from linear
wavelength space using spline interpolation [2].
NOTE! For spectral domain optical coherence tomography (SD-OCT) the spectrum
can be less RAW A-line, thus, define the range to select only spectrum part
of each RAW A-line within start_index and end_index parameters.
INPUTS:
X - number of elements in each row (RAW A-line size)
Y - number of rows (# of RAW A-lines)
start_index - first index for spectrum (left RAW A-line cut-off)
end_index - last index for spectrum (right RAW A-line cut-off)
start_wavelength - start of wavelength range for laser
end_wavelength - end of wavelength range for laser
hann_flag - flag for Hanning window [3]
dB_flag - flag for scale: linear or dB (20log())
in - pointer to buffer with RAW B-scan before FFT (size: X * Y)
OUTPUTS:
intensity - pointer to buffer contained intensities, structural B-scan
(size: ((end_index - start_index) / 2) * Y)
phase - pointer to buffer contained phases, phase B-scan
(size: ((end_index - start_index) / 2) * Y)
Re - pointer to buffer contained real part of FFT
(size: ((end_index - start_index) / 2) * Y)
Im - pointer to buffer contained imaginary part of FFT
(size: ((end_index - start_index) / 2) * Y)
REMARKS:
this function is experimental to test the spline interpolation + FFT for
spectrum linear in wavelengths. Use spline_FFT.cpp file to perform spline
interpolation + FFT for any kind of spectrum.
REFERENCES:
[1] http://www.fftw.org/fftw3_doc/Real_002dto_002dReal-Transforms.html
[2] http://en.wikipedia.org/wiki/Spline_interpolation#Cubic_spline_interpolation
[3] http://en.wikipedia.org/wiki/Hann_function
*/
I8 OL_easy_spline_fft(U32 X, U32 Y, U32 start_index, U32 end_index,
DBL start_wavelength, DBL end_wavelength, I8 hann_flag,
I8 dB_flag, DBL *in, DBL *intensity, DBL *phase, DBL *Re,
DBL *Im) {
U32 size = end_index - start_index;
DBL *hann_win = static_cast<DBL *>(fftw_malloc(sizeof(DBL) * size));
DBL *XX = static_cast<DBL *>(fftw_malloc(sizeof(DBL) * size));
DBL *XXX = static_cast<DBL *>(fftw_malloc(sizeof(DBL) * size));
// create FFTW plan
fftw_plan fft_p = fftw_plan_r2r_1d(size, Re, Im, FFTW_R2HC, FFTW_ESTIMATE);
U32 width = static_cast<U32>(size/2);
// linear wavelength step
DBL wavelength_step = (end_wavelength - start_wavelength) / (size - 1);
DBL start_wavenumber = 1 / start_wavelength;
// linear wavenumber step
DBL wavenumber_step = (start_wavenumber - (1 / end_wavelength)) / (size - 1);
I32 j;
// prepare Hanning window and linear and non-linear wavelength vectors
for (U32 i = 0; i < size; i++) {
if (hann_flag)
hann_win[i] = 0.5 * (1 - cos(kTwoPi * i / size));
else
hann_win[i] = 1.0;
// linear in wavelength
XX[i] = wavelength_step * i + start_wavelength;
// non-linear in wavelength
XXX[i] = 1 /(start_wavenumber - wavenumber_step * i);
}
// parallel run by A-lines
#pragma omp parallel for default(shared) private(j)
for (j = 0; j < static_cast<I32>(Y); j++) {
DBL *tmp_fft_in = static_cast<DBL *>(fftw_malloc(sizeof(DBL) * size));
DBL *tmp_fft_out = static_cast<DBL *>(fftw_malloc(sizeof(DBL) * size));
DBL *b = static_cast<DBL *>(fftw_malloc(sizeof(DBL) * size));
DBL *c = static_cast<DBL *>(fftw_malloc(sizeof(DBL) * size));
DBL *d = static_cast<DBL *>(fftw_malloc(sizeof(DBL) * size));
U32 pos = j * width;
// spline interpolation
copy(in + j * X + start_index, in + j * X + end_index, tmp_fft_out);
cubic_nak(size, XX, tmp_fft_out, b, c, d);
// apply hanning window or just get values
for (U32 i = 0; i < size; i++) tmp_fft_in[i] =
hann_win[i] * spline_eval(size, XX, tmp_fft_out, b, c, d, XXX[i]);
// perform FFT using FFTW3 library
fftw_execute_r2r(fft_p, tmp_fft_in, tmp_fft_out);
// ZERO components
if (dB_flag)
intensity[pos] = 20 * log10(abs(tmp_fft_out[0]));
else
intensity[pos] = tmp_fft_out[0];
Re[pos] = tmp_fft_out[0];
phase[pos] = Im[pos] = 0.0;
// construct intensity and phase information, Re and Im parts
for (U32 pos1 = 1, pos2 = size - 1; pos1 < width; pos1++, pos2--) {
// intensity
if (dB_flag)
intensity[pos + pos1] = 20 * log10(sqrt(tmp_fft_out[pos1] * \
tmp_fft_out[pos1] + tmp_fft_out[pos2] * \
tmp_fft_out[pos2]));
else
intensity[pos + pos1] = sqrt(tmp_fft_out[pos1] * tmp_fft_out[pos1] + \
tmp_fft_out[pos2] * tmp_fft_out[pos2]);
// phase
phase[pos + pos1] = atan2(tmp_fft_out[pos2], tmp_fft_out[pos1]);
// Re part
Re[pos + pos1] = tmp_fft_out[pos1];
// Im part
Im[pos + pos1] = tmp_fft_out[pos2];
}
fftw_free(tmp_fft_in);
fftw_free(tmp_fft_out);
fftw_free(b);
fftw_free(c);
fftw_free(d);
} // end of parallel code
fftw_destroy_plan(fft_p);
fftw_free(hann_win);
fftw_free(XX);
fftw_free(XXX);
return EXIT_SUCCESS;
}
void InvSemiNaiveReduced(double *coeffs,
int bw,
int m,
double *result,
double *trans_cos_pml_table,
double *sin_values,
double *workspace,
fftw_plan *fplan )
{
double *trans_tableptr;
double *assoc_offset;
int i, j, rowsize;
double *p;
double *fcos, fcos0, fcos1, fcos2, fcos3;
double fudge ;
fcos = workspace ;
/* for paranoia, zero out arrays */
memset( fcos, 0, sizeof(double) * 2 * bw );
memset( result, 0, sizeof(double) * 2 * bw );
trans_tableptr = trans_cos_pml_table;
p = trans_cos_pml_table;
/* main loop - compute each value of fcos
Note that all zeroes have been stripped out of the
trans_cos_pml_table, so indexing is somewhat complicated.
*/
for (i=0; i<bw; i++)
{
if (i == (bw-1))
{
if ( m % 2 )
{
fcos[bw-1] = 0.0;
break;
}
}
rowsize = Transpose_RowSize(i, m, bw);
if (i > m)
assoc_offset = coeffs + (i - m) + (m % 2);
else
assoc_offset = coeffs + (i % 2);
fcos0 = 0.0 ; fcos1 = 0.0; fcos2 = 0.0; fcos3 = 0.0;
for (j = 0; j < rowsize % 4; ++j)
fcos0 += assoc_offset[2*j] * trans_tableptr[j];
for ( ; j < rowsize; j += 4){
fcos0 += assoc_offset[2*j] * trans_tableptr[j];
fcos1 += assoc_offset[2*(j+1)] * trans_tableptr[j+1];
fcos2 += assoc_offset[2*(j+2)] * trans_tableptr[j+2];
fcos3 += assoc_offset[2*(j+3)] * trans_tableptr[j+3];
}
fcos[i] = fcos0 + fcos1 + fcos2 + fcos3 ;
trans_tableptr += rowsize;
}
/*
now we have the cosine series for the result,
so now evaluate the cosine series at 2*bw Chebyshev nodes
*/
/* scale coefficients prior to taking inverse DCT */
fudge = 0.5 / sqrt((double) bw) ;
for ( j = 1 ; j < 2*bw ; j ++ )
fcos[j] *= fudge ;
fcos[0] /= sqrt(2. * ((double) bw));
/* now take the inverse dct */
/* NOTE that I am using the guru interface */
fftw_execute_r2r( *fplan,
fcos, result );
/* if m is odd, then need to multiply by sin(x) at Chebyshev nodes */
if ( m % 2 )
{
for (j=0; j<(2*bw); j++)
result[j] *= sin_values[j];
}
trans_tableptr = p;
/* amscray */
}