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fasttransforms.cs
executable file
·3452 lines (2979 loc) · 116 KB
/
fasttransforms.cs
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/*************************************************************************
ALGLIB 4.00.0 (source code generated 2023-05-21)
Copyright (c) Sergey Bochkanov (ALGLIB project).
>>> SOURCE LICENSE >>>
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation (www.fsf.org); either version 2 of the
License, or (at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
A copy of the GNU General Public License is available at
http://www.fsf.org/licensing/licenses
>>> END OF LICENSE >>>
*************************************************************************/
#pragma warning disable 1691
#pragma warning disable 162
#pragma warning disable 164
#pragma warning disable 219
#pragma warning disable 8981
using System;
public partial class alglib
{
/*************************************************************************
1-dimensional complex FFT.
Array size N may be arbitrary number (composite or prime). Composite N's
are handled with cache-oblivious variation of a Cooley-Tukey algorithm.
Small prime-factors are transformed using hard coded codelets (similar to
FFTW codelets, but without low-level optimization), large prime-factors
are handled with Bluestein's algorithm.
Fastests transforms are for smooth N's (prime factors are 2, 3, 5 only),
most fast for powers of 2. When N have prime factors larger than these,
but orders of magnitude smaller than N, computations will be about 4 times
slower than for nearby highly composite N's. When N itself is prime, speed
will be 6 times lower.
Algorithm has O(N*logN) complexity for any N (composite or prime).
INPUT PARAMETERS
A - array[0..N-1] - complex function to be transformed
N - problem size
OUTPUT PARAMETERS
A - DFT of a input array, array[0..N-1]
A_out[j] = SUM(A_in[k]*exp(-2*pi*sqrt(-1)*j*k/N), k = 0..N-1)
-- ALGLIB --
Copyright 29.05.2009 by Bochkanov Sergey
*************************************************************************/
public static void fftc1d(complex[] a, int n)
{
fft.fftc1d(a, n, null);
}
public static void fftc1d(complex[] a, int n, alglib.xparams _params)
{
fft.fftc1d(a, n, _params);
}
public static void fftc1d(complex[] a)
{
int n;
n = ap.len(a);
fft.fftc1d(a, n, null);
return;
}
public static void fftc1d(complex[] a, alglib.xparams _params)
{
int n;
n = ap.len(a);
fft.fftc1d(a, n, _params);
return;
}
/*************************************************************************
1-dimensional complex inverse FFT.
Array size N may be arbitrary number (composite or prime). Algorithm has
O(N*logN) complexity for any N (composite or prime).
See FFTC1D() description for more information about algorithm performance.
INPUT PARAMETERS
A - array[0..N-1] - complex array to be transformed
N - problem size
OUTPUT PARAMETERS
A - inverse DFT of a input array, array[0..N-1]
A_out[j] = SUM(A_in[k]/N*exp(+2*pi*sqrt(-1)*j*k/N), k = 0..N-1)
-- ALGLIB --
Copyright 29.05.2009 by Bochkanov Sergey
*************************************************************************/
public static void fftc1dinv(complex[] a, int n)
{
fft.fftc1dinv(a, n, null);
}
public static void fftc1dinv(complex[] a, int n, alglib.xparams _params)
{
fft.fftc1dinv(a, n, _params);
}
public static void fftc1dinv(complex[] a)
{
int n;
n = ap.len(a);
fft.fftc1dinv(a, n, null);
return;
}
public static void fftc1dinv(complex[] a, alglib.xparams _params)
{
int n;
n = ap.len(a);
fft.fftc1dinv(a, n, _params);
return;
}
/*************************************************************************
1-dimensional real FFT.
Algorithm has O(N*logN) complexity for any N (composite or prime).
INPUT PARAMETERS
A - array[0..N-1] - real function to be transformed
N - problem size
OUTPUT PARAMETERS
F - DFT of a input array, array[0..N-1]
F[j] = SUM(A[k]*exp(-2*pi*sqrt(-1)*j*k/N), k = 0..N-1)
NOTE:
F[] satisfies symmetry property F[k] = conj(F[N-k]), so just one half
of array is usually needed. But for convinience subroutine returns full
complex array (with frequencies above N/2), so its result may be used by
other FFT-related subroutines.
-- ALGLIB --
Copyright 01.06.2009 by Bochkanov Sergey
*************************************************************************/
public static void fftr1d(double[] a, int n, out complex[] f)
{
f = new complex[0];
fft.fftr1d(a, n, ref f, null);
}
public static void fftr1d(double[] a, int n, out complex[] f, alglib.xparams _params)
{
f = new complex[0];
fft.fftr1d(a, n, ref f, _params);
}
public static void fftr1d(double[] a, out complex[] f)
{
int n;
f = new complex[0];
n = ap.len(a);
fft.fftr1d(a, n, ref f, null);
return;
}
public static void fftr1d(double[] a, out complex[] f, alglib.xparams _params)
{
int n;
f = new complex[0];
n = ap.len(a);
fft.fftr1d(a, n, ref f, _params);
return;
}
/*************************************************************************
1-dimensional real inverse FFT.
Algorithm has O(N*logN) complexity for any N (composite or prime).
INPUT PARAMETERS
F - array[0..floor(N/2)] - frequencies from forward real FFT
N - problem size
OUTPUT PARAMETERS
A - inverse DFT of a input array, array[0..N-1]
NOTE:
F[] should satisfy symmetry property F[k] = conj(F[N-k]), so just one
half of frequencies array is needed - elements from 0 to floor(N/2). F[0]
is ALWAYS real. If N is even F[floor(N/2)] is real too. If N is odd, then
F[floor(N/2)] has no special properties.
Relying on properties noted above, FFTR1DInv subroutine uses only elements
from 0th to floor(N/2)-th. It ignores imaginary part of F[0], and in case
N is even it ignores imaginary part of F[floor(N/2)] too.
When you call this function using full arguments list - "FFTR1DInv(F,N,A)"
- you can pass either either frequencies array with N elements or reduced
array with roughly N/2 elements - subroutine will successfully transform
both.
If you call this function using reduced arguments list - "FFTR1DInv(F,A)"
- you must pass FULL array with N elements (although higher N/2 are still
not used) because array size is used to automatically determine FFT length
-- ALGLIB --
Copyright 01.06.2009 by Bochkanov Sergey
*************************************************************************/
public static void fftr1dinv(complex[] f, int n, out double[] a)
{
a = new double[0];
fft.fftr1dinv(f, n, ref a, null);
}
public static void fftr1dinv(complex[] f, int n, out double[] a, alglib.xparams _params)
{
a = new double[0];
fft.fftr1dinv(f, n, ref a, _params);
}
public static void fftr1dinv(complex[] f, out double[] a)
{
int n;
a = new double[0];
n = ap.len(f);
fft.fftr1dinv(f, n, ref a, null);
return;
}
public static void fftr1dinv(complex[] f, out double[] a, alglib.xparams _params)
{
int n;
a = new double[0];
n = ap.len(f);
fft.fftr1dinv(f, n, ref a, _params);
return;
}
}
public partial class alglib
{
/*************************************************************************
1-dimensional Fast Hartley Transform.
Algorithm has O(N*logN) complexity for any N (composite or prime).
INPUT PARAMETERS
A - array[0..N-1] - real function to be transformed
N - problem size
OUTPUT PARAMETERS
A - FHT of a input array, array[0..N-1],
A_out[k] = sum(A_in[j]*(cos(2*pi*j*k/N)+sin(2*pi*j*k/N)), j=0..N-1)
-- ALGLIB --
Copyright 04.06.2009 by Bochkanov Sergey
*************************************************************************/
public static void fhtr1d(double[] a, int n)
{
fht.fhtr1d(a, n, null);
}
public static void fhtr1d(double[] a, int n, alglib.xparams _params)
{
fht.fhtr1d(a, n, _params);
}
/*************************************************************************
1-dimensional inverse FHT.
Algorithm has O(N*logN) complexity for any N (composite or prime).
INPUT PARAMETERS
A - array[0..N-1] - complex array to be transformed
N - problem size
OUTPUT PARAMETERS
A - inverse FHT of a input array, array[0..N-1]
-- ALGLIB --
Copyright 29.05.2009 by Bochkanov Sergey
*************************************************************************/
public static void fhtr1dinv(double[] a, int n)
{
fht.fhtr1dinv(a, n, null);
}
public static void fhtr1dinv(double[] a, int n, alglib.xparams _params)
{
fht.fhtr1dinv(a, n, _params);
}
}
public partial class alglib
{
/*************************************************************************
1-dimensional complex convolution.
For given A/B returns conv(A,B) (non-circular). Subroutine can automatically
choose between three implementations: straightforward O(M*N) formula for
very small N (or M), overlap-add algorithm for cases where max(M,N) is
significantly larger than min(M,N), but O(M*N) algorithm is too slow, and
general FFT-based formula for cases where two previois algorithms are too
slow.
Algorithm has max(M,N)*log(max(M,N)) complexity for any M/N.
INPUT PARAMETERS
A - array[0..M-1] - complex function to be transformed
M - problem size
B - array[0..N-1] - complex function to be transformed
N - problem size
OUTPUT PARAMETERS
R - convolution: A*B. array[0..N+M-2].
NOTE:
It is assumed that A is zero at T<0, B is zero too. If one or both
functions have non-zero values at negative T's, you can still use this
subroutine - just shift its result correspondingly.
-- ALGLIB --
Copyright 21.07.2009 by Bochkanov Sergey
*************************************************************************/
public static void convc1d(complex[] a, int m, complex[] b, int n, out complex[] r)
{
r = new complex[0];
conv.convc1d(a, m, b, n, ref r, null);
}
public static void convc1d(complex[] a, int m, complex[] b, int n, out complex[] r, alglib.xparams _params)
{
r = new complex[0];
conv.convc1d(a, m, b, n, ref r, _params);
}
/*************************************************************************
1-dimensional complex non-circular deconvolution (inverse of ConvC1D()).
Algorithm has M*log(M)) complexity for any M (composite or prime).
INPUT PARAMETERS
A - array[0..M-1] - convolved signal, A = conv(R, B)
M - convolved signal length
B - array[0..N-1] - response
N - response length, N<=M
OUTPUT PARAMETERS
R - deconvolved signal. array[0..M-N].
NOTE:
deconvolution is unstable process and may result in division by zero
(if your response function is degenerate, i.e. has zero Fourier coefficient).
NOTE:
It is assumed that A is zero at T<0, B is zero too. If one or both
functions have non-zero values at negative T's, you can still use this
subroutine - just shift its result correspondingly.
-- ALGLIB --
Copyright 21.07.2009 by Bochkanov Sergey
*************************************************************************/
public static void convc1dinv(complex[] a, int m, complex[] b, int n, out complex[] r)
{
r = new complex[0];
conv.convc1dinv(a, m, b, n, ref r, null);
}
public static void convc1dinv(complex[] a, int m, complex[] b, int n, out complex[] r, alglib.xparams _params)
{
r = new complex[0];
conv.convc1dinv(a, m, b, n, ref r, _params);
}
/*************************************************************************
1-dimensional circular complex convolution.
For given S/R returns conv(S,R) (circular). Algorithm has linearithmic
complexity for any M/N.
IMPORTANT: normal convolution is commutative, i.e. it is symmetric -
conv(A,B)=conv(B,A). Cyclic convolution IS NOT. One function - S - is a
signal, periodic function, and another - R - is a response, non-periodic
function with limited length.
INPUT PARAMETERS
S - array[0..M-1] - complex periodic signal
M - problem size
B - array[0..N-1] - complex non-periodic response
N - problem size
OUTPUT PARAMETERS
R - convolution: A*B. array[0..M-1].
NOTE:
It is assumed that B is zero at T<0. If it has non-zero values at
negative T's, you can still use this subroutine - just shift its result
correspondingly.
-- ALGLIB --
Copyright 21.07.2009 by Bochkanov Sergey
*************************************************************************/
public static void convc1dcircular(complex[] s, int m, complex[] r, int n, out complex[] c)
{
c = new complex[0];
conv.convc1dcircular(s, m, r, n, ref c, null);
}
public static void convc1dcircular(complex[] s, int m, complex[] r, int n, out complex[] c, alglib.xparams _params)
{
c = new complex[0];
conv.convc1dcircular(s, m, r, n, ref c, _params);
}
/*************************************************************************
1-dimensional circular complex deconvolution (inverse of ConvC1DCircular()).
Algorithm has M*log(M)) complexity for any M (composite or prime).
INPUT PARAMETERS
A - array[0..M-1] - convolved periodic signal, A = conv(R, B)
M - convolved signal length
B - array[0..N-1] - non-periodic response
N - response length
OUTPUT PARAMETERS
R - deconvolved signal. array[0..M-1].
NOTE:
deconvolution is unstable process and may result in division by zero
(if your response function is degenerate, i.e. has zero Fourier coefficient).
NOTE:
It is assumed that B is zero at T<0. If it has non-zero values at
negative T's, you can still use this subroutine - just shift its result
correspondingly.
-- ALGLIB --
Copyright 21.07.2009 by Bochkanov Sergey
*************************************************************************/
public static void convc1dcircularinv(complex[] a, int m, complex[] b, int n, out complex[] r)
{
r = new complex[0];
conv.convc1dcircularinv(a, m, b, n, ref r, null);
}
public static void convc1dcircularinv(complex[] a, int m, complex[] b, int n, out complex[] r, alglib.xparams _params)
{
r = new complex[0];
conv.convc1dcircularinv(a, m, b, n, ref r, _params);
}
/*************************************************************************
1-dimensional real convolution.
Analogous to ConvC1D(), see ConvC1D() comments for more details.
INPUT PARAMETERS
A - array[0..M-1] - real function to be transformed
M - problem size
B - array[0..N-1] - real function to be transformed
N - problem size
OUTPUT PARAMETERS
R - convolution: A*B. array[0..N+M-2].
NOTE:
It is assumed that A is zero at T<0, B is zero too. If one or both
functions have non-zero values at negative T's, you can still use this
subroutine - just shift its result correspondingly.
-- ALGLIB --
Copyright 21.07.2009 by Bochkanov Sergey
*************************************************************************/
public static void convr1d(double[] a, int m, double[] b, int n, out double[] r)
{
r = new double[0];
conv.convr1d(a, m, b, n, ref r, null);
}
public static void convr1d(double[] a, int m, double[] b, int n, out double[] r, alglib.xparams _params)
{
r = new double[0];
conv.convr1d(a, m, b, n, ref r, _params);
}
/*************************************************************************
1-dimensional real deconvolution (inverse of ConvC1D()).
Algorithm has M*log(M)) complexity for any M (composite or prime).
INPUT PARAMETERS
A - array[0..M-1] - convolved signal, A = conv(R, B)
M - convolved signal length
B - array[0..N-1] - response
N - response length, N<=M
OUTPUT PARAMETERS
R - deconvolved signal. array[0..M-N].
NOTE:
deconvolution is unstable process and may result in division by zero
(if your response function is degenerate, i.e. has zero Fourier coefficient).
NOTE:
It is assumed that A is zero at T<0, B is zero too. If one or both
functions have non-zero values at negative T's, you can still use this
subroutine - just shift its result correspondingly.
-- ALGLIB --
Copyright 21.07.2009 by Bochkanov Sergey
*************************************************************************/
public static void convr1dinv(double[] a, int m, double[] b, int n, out double[] r)
{
r = new double[0];
conv.convr1dinv(a, m, b, n, ref r, null);
}
public static void convr1dinv(double[] a, int m, double[] b, int n, out double[] r, alglib.xparams _params)
{
r = new double[0];
conv.convr1dinv(a, m, b, n, ref r, _params);
}
/*************************************************************************
1-dimensional circular real convolution.
Analogous to ConvC1DCircular(), see ConvC1DCircular() comments for more details.
INPUT PARAMETERS
S - array[0..M-1] - real signal
M - problem size
B - array[0..N-1] - real response
N - problem size
OUTPUT PARAMETERS
R - convolution: A*B. array[0..M-1].
NOTE:
It is assumed that B is zero at T<0. If it has non-zero values at
negative T's, you can still use this subroutine - just shift its result
correspondingly.
-- ALGLIB --
Copyright 21.07.2009 by Bochkanov Sergey
*************************************************************************/
public static void convr1dcircular(double[] s, int m, double[] r, int n, out double[] c)
{
c = new double[0];
conv.convr1dcircular(s, m, r, n, ref c, null);
}
public static void convr1dcircular(double[] s, int m, double[] r, int n, out double[] c, alglib.xparams _params)
{
c = new double[0];
conv.convr1dcircular(s, m, r, n, ref c, _params);
}
/*************************************************************************
1-dimensional complex deconvolution (inverse of ConvC1D()).
Algorithm has M*log(M)) complexity for any M (composite or prime).
INPUT PARAMETERS
A - array[0..M-1] - convolved signal, A = conv(R, B)
M - convolved signal length
B - array[0..N-1] - response
N - response length
OUTPUT PARAMETERS
R - deconvolved signal. array[0..M-N].
NOTE:
deconvolution is unstable process and may result in division by zero
(if your response function is degenerate, i.e. has zero Fourier coefficient).
NOTE:
It is assumed that B is zero at T<0. If it has non-zero values at
negative T's, you can still use this subroutine - just shift its result
correspondingly.
-- ALGLIB --
Copyright 21.07.2009 by Bochkanov Sergey
*************************************************************************/
public static void convr1dcircularinv(double[] a, int m, double[] b, int n, out double[] r)
{
r = new double[0];
conv.convr1dcircularinv(a, m, b, n, ref r, null);
}
public static void convr1dcircularinv(double[] a, int m, double[] b, int n, out double[] r, alglib.xparams _params)
{
r = new double[0];
conv.convr1dcircularinv(a, m, b, n, ref r, _params);
}
}
public partial class alglib
{
/*************************************************************************
1-dimensional complex cross-correlation.
For given Pattern/Signal returns corr(Pattern,Signal) (non-circular).
Correlation is calculated using reduction to convolution. Algorithm with
max(N,N)*log(max(N,N)) complexity is used (see ConvC1D() for more info
about performance).
IMPORTANT:
for historical reasons subroutine accepts its parameters in reversed
order: CorrC1D(Signal, Pattern) = Pattern x Signal (using traditional
definition of cross-correlation, denoting cross-correlation as "x").
INPUT PARAMETERS
Signal - array[0..N-1] - complex function to be transformed,
signal containing pattern
N - problem size
Pattern - array[0..M-1] - complex function to be transformed,
pattern to search withing signal
M - problem size
OUTPUT PARAMETERS
R - cross-correlation, array[0..N+M-2]:
* positive lags are stored in R[0..N-1],
R[i] = sum(conj(pattern[j])*signal[i+j]
* negative lags are stored in R[N..N+M-2],
R[N+M-1-i] = sum(conj(pattern[j])*signal[-i+j]
NOTE:
It is assumed that pattern domain is [0..M-1]. If Pattern is non-zero
on [-K..M-1], you can still use this subroutine, just shift result by K.
-- ALGLIB --
Copyright 21.07.2009 by Bochkanov Sergey
*************************************************************************/
public static void corrc1d(complex[] signal, int n, complex[] pattern, int m, out complex[] r)
{
r = new complex[0];
corr.corrc1d(signal, n, pattern, m, ref r, null);
}
public static void corrc1d(complex[] signal, int n, complex[] pattern, int m, out complex[] r, alglib.xparams _params)
{
r = new complex[0];
corr.corrc1d(signal, n, pattern, m, ref r, _params);
}
/*************************************************************************
1-dimensional circular complex cross-correlation.
For given Pattern/Signal returns corr(Pattern,Signal) (circular).
Algorithm has linearithmic complexity for any M/N.
IMPORTANT:
for historical reasons subroutine accepts its parameters in reversed
order: CorrC1DCircular(Signal, Pattern) = Pattern x Signal (using
traditional definition of cross-correlation, denoting cross-correlation
as "x").
INPUT PARAMETERS
Signal - array[0..N-1] - complex function to be transformed,
periodic signal containing pattern
N - problem size
Pattern - array[0..M-1] - complex function to be transformed,
non-periodic pattern to search withing signal
M - problem size
OUTPUT PARAMETERS
R - convolution: A*B. array[0..M-1].
-- ALGLIB --
Copyright 21.07.2009 by Bochkanov Sergey
*************************************************************************/
public static void corrc1dcircular(complex[] signal, int m, complex[] pattern, int n, out complex[] c)
{
c = new complex[0];
corr.corrc1dcircular(signal, m, pattern, n, ref c, null);
}
public static void corrc1dcircular(complex[] signal, int m, complex[] pattern, int n, out complex[] c, alglib.xparams _params)
{
c = new complex[0];
corr.corrc1dcircular(signal, m, pattern, n, ref c, _params);
}
/*************************************************************************
1-dimensional real cross-correlation.
For given Pattern/Signal returns corr(Pattern,Signal) (non-circular).
Correlation is calculated using reduction to convolution. Algorithm with
max(N,N)*log(max(N,N)) complexity is used (see ConvC1D() for more info
about performance).
IMPORTANT:
for historical reasons subroutine accepts its parameters in reversed
order: CorrR1D(Signal, Pattern) = Pattern x Signal (using traditional
definition of cross-correlation, denoting cross-correlation as "x").
INPUT PARAMETERS
Signal - array[0..N-1] - real function to be transformed,
signal containing pattern
N - problem size
Pattern - array[0..M-1] - real function to be transformed,
pattern to search withing signal
M - problem size
OUTPUT PARAMETERS
R - cross-correlation, array[0..N+M-2]:
* positive lags are stored in R[0..N-1],
R[i] = sum(pattern[j]*signal[i+j]
* negative lags are stored in R[N..N+M-2],
R[N+M-1-i] = sum(pattern[j]*signal[-i+j]
NOTE:
It is assumed that pattern domain is [0..M-1]. If Pattern is non-zero
on [-K..M-1], you can still use this subroutine, just shift result by K.
-- ALGLIB --
Copyright 21.07.2009 by Bochkanov Sergey
*************************************************************************/
public static void corrr1d(double[] signal, int n, double[] pattern, int m, out double[] r)
{
r = new double[0];
corr.corrr1d(signal, n, pattern, m, ref r, null);
}
public static void corrr1d(double[] signal, int n, double[] pattern, int m, out double[] r, alglib.xparams _params)
{
r = new double[0];
corr.corrr1d(signal, n, pattern, m, ref r, _params);
}
/*************************************************************************
1-dimensional circular real cross-correlation.
For given Pattern/Signal returns corr(Pattern,Signal) (circular).
Algorithm has linearithmic complexity for any M/N.
IMPORTANT:
for historical reasons subroutine accepts its parameters in reversed
order: CorrR1DCircular(Signal, Pattern) = Pattern x Signal (using
traditional definition of cross-correlation, denoting cross-correlation
as "x").
INPUT PARAMETERS
Signal - array[0..N-1] - real function to be transformed,
periodic signal containing pattern
N - problem size
Pattern - array[0..M-1] - real function to be transformed,
non-periodic pattern to search withing signal
M - problem size
OUTPUT PARAMETERS
R - convolution: A*B. array[0..M-1].
-- ALGLIB --
Copyright 21.07.2009 by Bochkanov Sergey
*************************************************************************/
public static void corrr1dcircular(double[] signal, int m, double[] pattern, int n, out double[] c)
{
c = new double[0];
corr.corrr1dcircular(signal, m, pattern, n, ref c, null);
}
public static void corrr1dcircular(double[] signal, int m, double[] pattern, int n, out double[] c, alglib.xparams _params)
{
c = new double[0];
corr.corrr1dcircular(signal, m, pattern, n, ref c, _params);
}
}
public partial class alglib
{
public class fft
{
/*************************************************************************
1-dimensional complex FFT.
Array size N may be arbitrary number (composite or prime). Composite N's
are handled with cache-oblivious variation of a Cooley-Tukey algorithm.
Small prime-factors are transformed using hard coded codelets (similar to
FFTW codelets, but without low-level optimization), large prime-factors
are handled with Bluestein's algorithm.
Fastests transforms are for smooth N's (prime factors are 2, 3, 5 only),
most fast for powers of 2. When N have prime factors larger than these,
but orders of magnitude smaller than N, computations will be about 4 times
slower than for nearby highly composite N's. When N itself is prime, speed
will be 6 times lower.
Algorithm has O(N*logN) complexity for any N (composite or prime).
INPUT PARAMETERS
A - array[0..N-1] - complex function to be transformed
N - problem size
OUTPUT PARAMETERS
A - DFT of a input array, array[0..N-1]
A_out[j] = SUM(A_in[k]*exp(-2*pi*sqrt(-1)*j*k/N), k = 0..N-1)
-- ALGLIB --
Copyright 29.05.2009 by Bochkanov Sergey
*************************************************************************/
public static void fftc1d(complex[] a,
int n,
alglib.xparams _params)
{
ftbase.fasttransformplan plan = new ftbase.fasttransformplan();
int i = 0;
double[] buf = new double[0];
alglib.ap.assert(n>0, "FFTC1D: incorrect N!");
alglib.ap.assert(alglib.ap.len(a)>=n, "FFTC1D: Length(A)<N!");
alglib.ap.assert(apserv.isfinitecvector(a, n, _params), "FFTC1D: A contains infinite or NAN values!");
//
// Special case: N=1, FFT is just identity transform.
// After this block we assume that N is strictly greater than 1.
//
if( n==1 )
{
return;
}
//
// convert input array to the more convinient format
//
buf = new double[2*n];
for(i=0; i<=n-1; i++)
{
buf[2*i+0] = a[i].x;
buf[2*i+1] = a[i].y;
}
//
// Generate plan and execute it.
//
// Plan is a combination of a successive factorizations of N and
// precomputed data. It is much like a FFTW plan, but is not stored
// between subroutine calls and is much simpler.
//
ftbase.ftcomplexfftplan(n, 1, plan, _params);
ftbase.ftapplyplan(plan, buf, 0, 1, _params);
//
// result
//
for(i=0; i<=n-1; i++)
{
a[i].x = buf[2*i+0];
a[i].y = buf[2*i+1];
}
}
/*************************************************************************
1-dimensional complex inverse FFT.
Array size N may be arbitrary number (composite or prime). Algorithm has
O(N*logN) complexity for any N (composite or prime).
See FFTC1D() description for more information about algorithm performance.
INPUT PARAMETERS
A - array[0..N-1] - complex array to be transformed
N - problem size
OUTPUT PARAMETERS
A - inverse DFT of a input array, array[0..N-1]
A_out[j] = SUM(A_in[k]/N*exp(+2*pi*sqrt(-1)*j*k/N), k = 0..N-1)
-- ALGLIB --
Copyright 29.05.2009 by Bochkanov Sergey
*************************************************************************/
public static void fftc1dinv(complex[] a,
int n,
alglib.xparams _params)
{
int i = 0;
alglib.ap.assert(n>0, "FFTC1DInv: incorrect N!");
alglib.ap.assert(alglib.ap.len(a)>=n, "FFTC1DInv: Length(A)<N!");
alglib.ap.assert(apserv.isfinitecvector(a, n, _params), "FFTC1DInv: A contains infinite or NAN values!");
//
// Inverse DFT can be expressed in terms of the DFT as
//
// invfft(x) = fft(x')'/N
//
// here x' means conj(x).
//
for(i=0; i<=n-1; i++)
{
a[i].y = -a[i].y;
}
fftc1d(a, n, _params);
for(i=0; i<=n-1; i++)
{
a[i].x = a[i].x/n;
a[i].y = -(a[i].y/n);
}
}
/*************************************************************************
1-dimensional real FFT.
Algorithm has O(N*logN) complexity for any N (composite or prime).
INPUT PARAMETERS
A - array[0..N-1] - real function to be transformed
N - problem size
OUTPUT PARAMETERS
F - DFT of a input array, array[0..N-1]
F[j] = SUM(A[k]*exp(-2*pi*sqrt(-1)*j*k/N), k = 0..N-1)
NOTE:
F[] satisfies symmetry property F[k] = conj(F[N-k]), so just one half
of array is usually needed. But for convinience subroutine returns full
complex array (with frequencies above N/2), so its result may be used by
other FFT-related subroutines.
-- ALGLIB --
Copyright 01.06.2009 by Bochkanov Sergey
*************************************************************************/
public static void fftr1d(double[] a,
int n,
ref complex[] f,
alglib.xparams _params)
{
int i = 0;
int n2 = 0;
int idx = 0;
complex hn = 0;
complex hmnc = 0;
complex v = 0;
double[] buf = new double[0];
ftbase.fasttransformplan plan = new ftbase.fasttransformplan();
int i_ = 0;
f = new complex[0];
alglib.ap.assert(n>0, "FFTR1D: incorrect N!");
alglib.ap.assert(alglib.ap.len(a)>=n, "FFTR1D: Length(A)<N!");
alglib.ap.assert(apserv.isfinitevector(a, n, _params), "FFTR1D: A contains infinite or NAN values!");