// Fourier transform from x back to (complex) k:
kTable*
xTable::Transform() const {
kTable *kt = new kTable( N, 2*PI/(N*dx) );
fftw_plan plan =
fftw_plan_dft_r2c_2d(N,N,
array, reinterpret_cast<fftw_complex*> (kt->array),
FFTW_ESTIMATE);
if (plan==NULL) throw FFTInvalid();
fftw_execute(plan);
fftw_destroy_plan(plan);
// Now scale the k spectrum and flip signs for x=0 in middle.
double fac = scaleby * dx * dx;
size_t ind=0;
for (int i=0; i<N; i++)
for (int j=0; j<=N/2; j++) {
if ( (i+j)%2==0) kt->array[ind] *= fac;
else kt->array[ind] *= -fac;
ind++;
}
return kt;
}
// Fourier transform from x back to (complex) k:
void XTable::transform(KTable& kt) const
{
check_array();
// Make a new copy of data array since measurement will overwrite:
FFTW_Array<double> t_array = _array;
fftw_plan plan = fftw_plan_dft_r2c_2d(
_N,_N, t_array.get_fftw(), kt._array.get_fftw(), FFTW_ESTIMATE);
#ifdef FFT_DEBUG
if (plan==NULL) throw FFTInvalid();
#endif
fftw_execute(plan);
fftw_destroy_plan(plan);
// Now scale the k spectrum and flip signs for x=0 in middle.
double fac = _dx * _dx;
size_t ind=0;
for (int iy=0; iy<_N; iy++) {
for (int ix=0; ix<=_N/2; ix++) {
if ( (ix+iy)%2==0) kt._array[ind] *= fac;
else kt._array[ind] *= -fac;
ind++;
}
}
kt._dk = 2*M_PI/(_N*_dx);
}
// Fourier transform from (complex) k to x:
xTable*
kTable::Transform() const {
// We'll need a new k array because FFTW kills the k array in this
// operation. Also, to put x=0 in center of array, we need to flop
// every other sign of k array, and need to scale.
DComplex* t_array =
(DComplex*) fftw_malloc(sizeof(DComplex)*N*(N/2+1));
double fac = scaleby * dk * dk / (4*PI*PI);
long int ind=0;
for (int i=0; i<N; i++)
for (int j=0; j<=N/2; j++) {
if ( (i+j)%2==0) t_array[ind]=fac * array[ind];
else t_array[ind] = -fac* array[ind];
ind++;
}
xTable *xt = new xTable( N, 2*PI/(N*dk) );
fftw_plan plan =
fftw_plan_dft_c2r_2d(N, N,
reinterpret_cast<fftw_complex*> (t_array), xt->array,
FFTW_ESTIMATE);
if (plan==NULL) throw FFTInvalid();
// Run the transform:
fftw_execute(plan);
fftw_destroy_plan(plan);
fftw_free(t_array);
return xt;
}
void XTable::fftwMeasure() const
{
// Make a new copy of data array since measurement will overwrite:
// Copy data into new array to avoid NaN's, etc., but not bothering
// with scaling, etc.
FFTW_Array<double> t_array = _array;
KTable kt( _N, 2*M_PI/(_N*_dx) );
fftw_plan plan = fftw_plan_dft_r2c_2d(
_N,_N, t_array.get_fftw(), kt._array.get_fftw(), FFTW_MEASURE);
#ifdef FFT_DEBUG
if (plan==NULL) throw FFTInvalid();
#endif
fftw_destroy_plan(plan);
}
// Have FFTW develop "wisdom" on doing this kind of transform
void KTable::fftwMeasure() const
{
// Copy data into new array to avoid NaN's, etc., but not bothering
// with scaling, etc.
FFTW_Array<std::complex<double> > t_array = _array;
XTable xt( _N, 2*M_PI/(_N*_dk) );
// Note: The fftw_execute function is the only thread-safe FFTW routine.
// So if we decide to go with some kind of multi-threading (rather than multi-process
// parallelism) all of the plan creation and destruction calls in this file
// will need to be placed in critical blocks or the equivalent (mutex locks, etc.).
fftw_plan plan = fftw_plan_dft_c2r_2d(
_N, _N, t_array.get_fftw(), xt._array.get_fftw(), FFTW_MEASURE);
#ifdef FFT_DEBUG
if (plan==NULL) throw FFTInvalid();
#endif
fftw_destroy_plan(plan);
}
// Fourier transform from (complex) k to x:
// This version takes XTable reference as argument
void KTable::transform(XTable& xt) const
{
check_array();
// check proper dimensions for xt
assert(_N==xt.getN());
// We'll need a new k array because FFTW kills the k array in this
// operation. Also, to put x=0 in center of array, we need to flop
// every other sign of k array, and need to scale.
dbg<<"Before make t_array"<<std::endl;
FFTW_Array<std::complex<double> > t_array(_N);
dbg<<"After make t_array"<<std::endl;
double fac = _dk * _dk / (4*M_PI*M_PI);
long int ind=0;
dbg<<"t_array.size = "<<t_array.size()<<std::endl;
for (int iy=0; iy<_N; iy++) {
dbg<<"ind = "<<ind<<std::endl;
for (int ix=0; ix<=_N/2; ix++) {
if ( (ix+iy)%2==0) t_array[ind]=fac * _array[ind];
else t_array[ind] = -fac* _array[ind];
ind++;
}
}
dbg<<"After fill t_array"<<std::endl;
fftw_plan plan = fftw_plan_dft_c2r_2d(
_N, _N, t_array.get_fftw(), xt._array.get_fftw(), FFTW_ESTIMATE);
dbg<<"After make plan"<<std::endl;
#ifdef FFT_DEBUG
if (plan==NULL) throw FFTInvalid();
#endif
// Run the transform:
fftw_execute(plan);
dbg<<"After exec plan"<<std::endl;
fftw_destroy_plan(plan);
dbg<<"After destroy plan"<<std::endl;
xt._dx = 2*M_PI/(_N*_dk);
dbg<<"Done transform"<<std::endl;
}
// Have FFTW develop "wisdom" on doing this kind of transform
void
kTable::fftwMeasure() const {
DComplex* t_array =
(DComplex*) fftw_malloc(sizeof(DComplex)*N*(N/2+1));
// Copy data into new array to avoid NaN's, etc., but not bothering
// with scaling, etc.
for (int i=0; i<N*(N/2+1); i++)
t_array[i] = array[i];
xTable *xt = new xTable( N, 2*PI/(N*dk) );
fftw_plan plan =
fftw_plan_dft_c2r_2d(N, N,
reinterpret_cast<fftw_complex*> (t_array), xt->array,
FFTW_MEASURE);
if (plan==NULL) throw FFTInvalid();
delete xt;
fftw_free(t_array);
fftw_destroy_plan(plan);
}
void
xTable::fftwMeasure() const {
// Make a new copy of data array since measurement will overwrite:
double* t_array =
(double*) fftw_malloc(sizeof(double)*N*N);
// Copy data into new array to avoid NaN's, etc., but not bothering
// with scaling, etc.
for (int i=0; i<N*N; i++)
t_array[i] = array[i];
kTable *kt = new kTable( N, 2*PI/(N*dx) );
fftw_plan plan =
fftw_plan_dft_r2c_2d(N,N,
t_array, reinterpret_cast<fftw_complex*> (kt->array),
FFTW_MEASURE);
if (plan==NULL) throw FFTInvalid();
delete kt;
fftw_free(t_array);
fftw_destroy_plan(plan);
}
// same function, takes xTable reference as agrument
void
kTable::Transform(xTable& xt) const {
// ??? check proper dimensions for xt ?
Assert(N==xt.getN());
// We'll need a new k array because FFTW kills the k array in this
// operation. Also, to put x=0 in center of array, we need to flop
// every other sign of k array, and need to scale.
DComplex* t_array =
(DComplex*) fftw_malloc(sizeof(DComplex)*N*(N/2+1));
double fac = scaleby * dk * dk / (4*PI*PI);
long int ind=0;
for (int i=0; i<N; i++)
for (int j=0; j<=N/2; j++) {
if ( (i+j)%2==0) t_array[ind]=fac * array[ind];
else t_array[ind] = -fac* array[ind];
ind++;
}
fftw_plan plan =
fftw_plan_dft_c2r_2d(N, N,
reinterpret_cast<fftw_complex*> (t_array), xt.array,
FFTW_ESTIMATE);
if (plan==NULL) throw FFTInvalid();
// Run the transform:
fftw_execute(plan);
fftw_destroy_plan(plan);
fftw_free(t_array);
xt.dx = 2*PI/(N*dk);
xt.scaleby = 1.;
xt.valid = true;
}
