/************************************************************************* ALGLIB 3.16.0 (source code generated 2019-12-19) 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 >>> *************************************************************************/ #ifndef _fasttransforms_pkg_h #define _fasttransforms_pkg_h #include "ap.h" #include "alglibinternal.h" ///////////////////////////////////////////////////////////////////////// // // THIS SECTION CONTAINS COMPUTATIONAL CORE DECLARATIONS (DATATYPES) // ///////////////////////////////////////////////////////////////////////// namespace alglib_impl { #if defined(AE_COMPILE_FFT) || !defined(AE_PARTIAL_BUILD) #endif #if defined(AE_COMPILE_FHT) || !defined(AE_PARTIAL_BUILD) #endif #if defined(AE_COMPILE_CONV) || !defined(AE_PARTIAL_BUILD) #endif #if defined(AE_COMPILE_CORR) || !defined(AE_PARTIAL_BUILD) #endif } ///////////////////////////////////////////////////////////////////////// // // THIS SECTION CONTAINS C++ INTERFACE // ///////////////////////////////////////////////////////////////////////// namespace alglib { #if defined(AE_COMPILE_FFT) || !defined(AE_PARTIAL_BUILD) #endif #if defined(AE_COMPILE_FHT) || !defined(AE_PARTIAL_BUILD) #endif #if defined(AE_COMPILE_CONV) || !defined(AE_PARTIAL_BUILD) #endif #if defined(AE_COMPILE_CORR) || !defined(AE_PARTIAL_BUILD) #endif #if defined(AE_COMPILE_FFT) || !defined(AE_PARTIAL_BUILD) /************************************************************************* 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 *************************************************************************/ void fftc1d(complex_1d_array &a, const ae_int_t n, const xparams _xparams = alglib::xdefault); void fftc1d(complex_1d_array &a, const xparams _xparams = alglib::xdefault); /************************************************************************* 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 *************************************************************************/ void fftc1dinv(complex_1d_array &a, const ae_int_t n, const xparams _xparams = alglib::xdefault); void fftc1dinv(complex_1d_array &a, const xparams _xparams = alglib::xdefault); /************************************************************************* 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 *************************************************************************/ void fftr1d(const real_1d_array &a, const ae_int_t n, complex_1d_array &f, const xparams _xparams = alglib::xdefault); void fftr1d(const real_1d_array &a, complex_1d_array &f, const xparams _xparams = alglib::xdefault); /************************************************************************* 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 *************************************************************************/ void fftr1dinv(const complex_1d_array &f, const ae_int_t n, real_1d_array &a, const xparams _xparams = alglib::xdefault); void fftr1dinv(const complex_1d_array &f, real_1d_array &a, const xparams _xparams = alglib::xdefault); #endif #if defined(AE_COMPILE_FHT) || !defined(AE_PARTIAL_BUILD) /************************************************************************* 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 *************************************************************************/ void fhtr1d(real_1d_array &a, const ae_int_t n, const xparams _xparams = alglib::xdefault); /************************************************************************* 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 *************************************************************************/ void fhtr1dinv(real_1d_array &a, const ae_int_t n, const xparams _xparams = alglib::xdefault); #endif #if defined(AE_COMPILE_CONV) || !defined(AE_PARTIAL_BUILD) /************************************************************************* 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 *************************************************************************/ void convc1d(const complex_1d_array &a, const ae_int_t m, const complex_1d_array &b, const ae_int_t n, complex_1d_array &r, const xparams _xparams = alglib::xdefault); /************************************************************************* 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 *************************************************************************/ void convc1dinv(const complex_1d_array &a, const ae_int_t m, const complex_1d_array &b, const ae_int_t n, complex_1d_array &r, const xparams _xparams = alglib::xdefault); /************************************************************************* 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 *************************************************************************/ void convc1dcircular(const complex_1d_array &s, const ae_int_t m, const complex_1d_array &r, const ae_int_t n, complex_1d_array &c, const xparams _xparams = alglib::xdefault); /************************************************************************* 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 *************************************************************************/ void convc1dcircularinv(const complex_1d_array &a, const ae_int_t m, const complex_1d_array &b, const ae_int_t n, complex_1d_array &r, const xparams _xparams = alglib::xdefault); /************************************************************************* 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 *************************************************************************/ void convr1d(const real_1d_array &a, const ae_int_t m, const real_1d_array &b, const ae_int_t n, real_1d_array &r, const xparams _xparams = alglib::xdefault); /************************************************************************* 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 *************************************************************************/ void convr1dinv(const real_1d_array &a, const ae_int_t m, const real_1d_array &b, const ae_int_t n, real_1d_array &r, const xparams _xparams = alglib::xdefault); /************************************************************************* 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 *************************************************************************/ void convr1dcircular(const real_1d_array &s, const ae_int_t m, const real_1d_array &r, const ae_int_t n, real_1d_array &c, const xparams _xparams = alglib::xdefault); /************************************************************************* 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 *************************************************************************/ void convr1dcircularinv(const real_1d_array &a, const ae_int_t m, const real_1d_array &b, const ae_int_t n, real_1d_array &r, const xparams _xparams = alglib::xdefault); #endif #if defined(AE_COMPILE_CORR) || !defined(AE_PARTIAL_BUILD) /************************************************************************* 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 *************************************************************************/ void corrc1d(const complex_1d_array &signal, const ae_int_t n, const complex_1d_array &pattern, const ae_int_t m, complex_1d_array &r, const xparams _xparams = alglib::xdefault); /************************************************************************* 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 *************************************************************************/ void corrc1dcircular(const complex_1d_array &signal, const ae_int_t m, const complex_1d_array &pattern, const ae_int_t n, complex_1d_array &c, const xparams _xparams = alglib::xdefault); /************************************************************************* 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 *************************************************************************/ void corrr1d(const real_1d_array &signal, const ae_int_t n, const real_1d_array &pattern, const ae_int_t m, real_1d_array &r, const xparams _xparams = alglib::xdefault); /************************************************************************* 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 *************************************************************************/ void corrr1dcircular(const real_1d_array &signal, const ae_int_t m, const real_1d_array &pattern, const ae_int_t n, real_1d_array &c, const xparams _xparams = alglib::xdefault); #endif } ///////////////////////////////////////////////////////////////////////// // // THIS SECTION CONTAINS COMPUTATIONAL CORE DECLARATIONS (FUNCTIONS) // ///////////////////////////////////////////////////////////////////////// namespace alglib_impl { #if defined(AE_COMPILE_FFT) || !defined(AE_PARTIAL_BUILD) void fftc1d(/* Complex */ ae_vector* a, ae_int_t n, ae_state *_state); void fftc1dinv(/* Complex */ ae_vector* a, ae_int_t n, ae_state *_state); void fftr1d(/* Real */ ae_vector* a, ae_int_t n, /* Complex */ ae_vector* f, ae_state *_state); void fftr1dinv(/* Complex */ ae_vector* f, ae_int_t n, /* Real */ ae_vector* a, ae_state *_state); void fftr1dinternaleven(/* Real */ ae_vector* a, ae_int_t n, /* Real */ ae_vector* buf, fasttransformplan* plan, ae_state *_state); void fftr1dinvinternaleven(/* Real */ ae_vector* a, ae_int_t n, /* Real */ ae_vector* buf, fasttransformplan* plan, ae_state *_state); #endif #if defined(AE_COMPILE_FHT) || !defined(AE_PARTIAL_BUILD) void fhtr1d(/* Real */ ae_vector* a, ae_int_t n, ae_state *_state); void fhtr1dinv(/* Real */ ae_vector* a, ae_int_t n, ae_state *_state); #endif #if defined(AE_COMPILE_CONV) || !defined(AE_PARTIAL_BUILD) void convc1d(/* Complex */ ae_vector* a, ae_int_t m, /* Complex */ ae_vector* b, ae_int_t n, /* Complex */ ae_vector* r, ae_state *_state); void convc1dinv(/* Complex */ ae_vector* a, ae_int_t m, /* Complex */ ae_vector* b, ae_int_t n, /* Complex */ ae_vector* r, ae_state *_state); void convc1dcircular(/* Complex */ ae_vector* s, ae_int_t m, /* Complex */ ae_vector* r, ae_int_t n, /* Complex */ ae_vector* c, ae_state *_state); void convc1dcircularinv(/* Complex */ ae_vector* a, ae_int_t m, /* Complex */ ae_vector* b, ae_int_t n, /* Complex */ ae_vector* r, ae_state *_state); void convr1d(/* Real */ ae_vector* a, ae_int_t m, /* Real */ ae_vector* b, ae_int_t n, /* Real */ ae_vector* r, ae_state *_state); void convr1dinv(/* Real */ ae_vector* a, ae_int_t m, /* Real */ ae_vector* b, ae_int_t n, /* Real */ ae_vector* r, ae_state *_state); void convr1dcircular(/* Real */ ae_vector* s, ae_int_t m, /* Real */ ae_vector* r, ae_int_t n, /* Real */ ae_vector* c, ae_state *_state); void convr1dcircularinv(/* Real */ ae_vector* a, ae_int_t m, /* Real */ ae_vector* b, ae_int_t n, /* Real */ ae_vector* r, ae_state *_state); void convc1dx(/* Complex */ ae_vector* a, ae_int_t m, /* Complex */ ae_vector* b, ae_int_t n, ae_bool circular, ae_int_t alg, ae_int_t q, /* Complex */ ae_vector* r, ae_state *_state); void convr1dx(/* Real */ ae_vector* a, ae_int_t m, /* Real */ ae_vector* b, ae_int_t n, ae_bool circular, ae_int_t alg, ae_int_t q, /* Real */ ae_vector* r, ae_state *_state); #endif #if defined(AE_COMPILE_CORR) || !defined(AE_PARTIAL_BUILD) void corrc1d(/* Complex */ ae_vector* signal, ae_int_t n, /* Complex */ ae_vector* pattern, ae_int_t m, /* Complex */ ae_vector* r, ae_state *_state); void corrc1dcircular(/* Complex */ ae_vector* signal, ae_int_t m, /* Complex */ ae_vector* pattern, ae_int_t n, /* Complex */ ae_vector* c, ae_state *_state); void corrr1d(/* Real */ ae_vector* signal, ae_int_t n, /* Real */ ae_vector* pattern, ae_int_t m, /* Real */ ae_vector* r, ae_state *_state); void corrr1dcircular(/* Real */ ae_vector* signal, ae_int_t m, /* Real */ ae_vector* pattern, ae_int_t n, /* Real */ ae_vector* c, ae_state *_state); #endif } #endif