## #2 Functions: FFT, IFFT, IWT, IWT2,...

open
None
5
2003-10-23
2002-10-17
No

: Anyways, since i needed to implement those for
my own ATPG project, i decided to write those
functions for blitz since i will be doing math
using
blitz.

There could be bugs.

Anyways, i have implemented
1-d vectorized FFT/IFFT (tested)
Shuffle, BitReverse, FFT, IFFT

1-d vectorized FWT/IFWT (wavelet) (tested)
Uphi, DownHi, UpLo, DownLo, FWT_PO,
IWT_PO

2-d FWT/IFWT (wavelet) (tested, but not
completely)
FWT2_PO, IWT2_PO

1-d vectorized FWT( walsh transform) (tested)
FWT, IFWT

&quot;vectorized&quot; matrix inverse (tested)
Inv
matrix svd (tested)
SVD , conditional SVD
matrix pesudo inverse (tested)
PInv

matrix LU decomposition (tested)
LU, LUBSB, LUInverse

matrix Cholesky decompostion (untested)
LL, LLBSB

HighPrecision Arthimetic( uncompiled)

and have applied a TEMPORARY patch to Range
just to
get the range to be divisible by the stride.
[Not Included]

And added a dummy Array::ascending(int) const to
get
tensor multiplication to compile for version 0.6.
[Not Included]

thanks, hopefully u will like it.
-suresh

## Discussion

• Suresh kumar - 2002-10-17

functions

• Julian Cummings - 2003-10-23
• assigned_to: nobody --> julianc

• Shakes - 2006-06-30

Logged In: YES
user_id=1335435

Re-Post:
The following is the code for getting FFT's on Blitz Arrays
using the mature and highly recognised FFTW C Library.

template <typename type, int size>
void
FourierTransform<type,size>::FFTW(Array<complex<double>,2>
&field, Array<complex<double>,2> &fftOfField)
{
complex<double> *ptrField, *ptrFFT;
fftw_plan plan;

ptrField = field.data();
ptrFFT = fftOfField.data();
plan =
fftw_plan_dft_2d(field.rows(),field.cols(),reinterpret_cast<fftw_complex*>(ptrField),reinterpret_cast<fftw_complex*>(ptrFFT),FFTW_FORWARD,FFTW_ESTIMATE);

fftw_execute(plan);

fftw_destroy_plan(plan);
}

I have tested and its does work. Note that this works
because as FFTW points out:
"C++ has its own complex<T> template class, defined in the
Reportedly, the C++ standards committee has recently agreed
to mandate that the storage
format used for this type be binary-compatible with the C99
type, i.e. an array T[2] with
consecutive real [0] and imaginary [1] parts. (See report
WG21/N1388.) Although not
part of the official standard as of this writing, the
proposal stated that: “This solution has
been tested with all current major implementations of the
standard library and shown to
be working.” To the extent that this is true, if you have a
variable complex<double> *x,
you can pass it directly to FFTW via
reinterpret_cast<fftw_complex*>(x)."

Also data reordering has to be done if DC is wanted in the
centre (http://www.fftw.org/faq/section3.html#centerorigin).
I have done it in the following:
void
FourierTransform<type,size>::centerDC(Array<complex<double>,2>
&field, Array<complex<double>,2> &result)
{
Array<complex<double>,2> tmp(field.rows(),field.cols());

for(int k = 0; k < field.cols(); k ++)
for(int j = 0; j < field.rows(); j ++)
tmp((j+field.rows()/2)%field.rows(),(k+field.cols()/2)%field.cols())
= field(j,k);

result = tmp;
}

Code Excerpt is taken from the FourierTransform Class in the
up and coming Quantum Mechanics and Discrete Geometry
Toolkit based on Blitz++ and Qt - qC++
(qcplusplus.sourceforge.net). It currently supports BEC
simulations and the Fourier class can be found in the
Subversion area.

Keep up the good work guys, more work on the tiny stuff
would be appreciated :)

Cheers
Shakes