[7673] | 1 | /*************************************************************************
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| 2 | Copyright (c) Sergey Bochkanov (ALGLIB project).
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| 3 |
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| 4 | >>> SOURCE LICENSE >>>
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| 5 | This program is free software; you can redistribute it and/or modify
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| 6 | it under the terms of the GNU General Public License as published by
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| 7 | the Free Software Foundation (www.fsf.org); either version 2 of the
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| 8 | License, or (at your option) any later version.
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| 9 |
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| 10 | This program is distributed in the hope that it will be useful,
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| 11 | but WITHOUT ANY WARRANTY; without even the implied warranty of
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| 12 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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| 13 | GNU General Public License for more details.
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| 14 |
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| 15 | A copy of the GNU General Public License is available at
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| 16 | http://www.fsf.org/licensing/licenses
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| 17 | >>> END OF LICENSE >>>
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| 18 | *************************************************************************/
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| 19 | #pragma warning disable 162
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| 20 | #pragma warning disable 219
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| 21 | using System;
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| 22 |
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| 23 | public partial class alglib
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| 24 | {
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| 25 |
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| 26 |
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| 27 | /*************************************************************************
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| 28 | 1-dimensional complex FFT.
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| 29 |
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| 30 | Array size N may be arbitrary number (composite or prime). Composite N's
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| 31 | are handled with cache-oblivious variation of a Cooley-Tukey algorithm.
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| 32 | Small prime-factors are transformed using hard coded codelets (similar to
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| 33 | FFTW codelets, but without low-level optimization), large prime-factors
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| 34 | are handled with Bluestein's algorithm.
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| 35 |
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| 36 | Fastests transforms are for smooth N's (prime factors are 2, 3, 5 only),
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| 37 | most fast for powers of 2. When N have prime factors larger than these,
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| 38 | but orders of magnitude smaller than N, computations will be about 4 times
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| 39 | slower than for nearby highly composite N's. When N itself is prime, speed
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| 40 | will be 6 times lower.
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| 41 |
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| 42 | Algorithm has O(N*logN) complexity for any N (composite or prime).
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| 43 |
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| 44 | INPUT PARAMETERS
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| 45 | A - array[0..N-1] - complex function to be transformed
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| 46 | N - problem size
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| 47 |
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| 48 | OUTPUT PARAMETERS
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| 49 | A - DFT of a input array, array[0..N-1]
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| 50 | A_out[j] = SUM(A_in[k]*exp(-2*pi*sqrt(-1)*j*k/N), k = 0..N-1)
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| 51 |
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| 52 |
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| 53 | -- ALGLIB --
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| 54 | Copyright 29.05.2009 by Bochkanov Sergey
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| 55 | *************************************************************************/
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| 56 | public static void fftc1d(ref complex[] a, int n)
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| 57 | {
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| 58 |
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| 59 | fft.fftc1d(ref a, n);
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| 60 | return;
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| 61 | }
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| 62 | public static void fftc1d(ref complex[] a)
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| 63 | {
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| 64 | int n;
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| 65 |
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| 66 |
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| 67 | n = ap.len(a);
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| 68 | fft.fftc1d(ref a, n);
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| 69 |
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| 70 | return;
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| 71 | }
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| 72 |
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| 73 | /*************************************************************************
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| 74 | 1-dimensional complex inverse FFT.
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| 75 |
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| 76 | Array size N may be arbitrary number (composite or prime). Algorithm has
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| 77 | O(N*logN) complexity for any N (composite or prime).
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| 78 |
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| 79 | See FFTC1D() description for more information about algorithm performance.
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| 80 |
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| 81 | INPUT PARAMETERS
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| 82 | A - array[0..N-1] - complex array to be transformed
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| 83 | N - problem size
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| 84 |
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| 85 | OUTPUT PARAMETERS
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| 86 | A - inverse DFT of a input array, array[0..N-1]
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| 87 | A_out[j] = SUM(A_in[k]/N*exp(+2*pi*sqrt(-1)*j*k/N), k = 0..N-1)
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| 88 |
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| 89 |
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| 90 | -- ALGLIB --
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| 91 | Copyright 29.05.2009 by Bochkanov Sergey
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| 92 | *************************************************************************/
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| 93 | public static void fftc1dinv(ref complex[] a, int n)
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| 94 | {
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| 95 |
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| 96 | fft.fftc1dinv(ref a, n);
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| 97 | return;
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| 98 | }
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| 99 | public static void fftc1dinv(ref complex[] a)
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| 100 | {
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| 101 | int n;
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| 102 |
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| 103 |
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| 104 | n = ap.len(a);
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| 105 | fft.fftc1dinv(ref a, n);
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| 106 |
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| 107 | return;
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| 108 | }
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| 109 |
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| 110 | /*************************************************************************
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| 111 | 1-dimensional real FFT.
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| 112 |
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| 113 | Algorithm has O(N*logN) complexity for any N (composite or prime).
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| 114 |
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| 115 | INPUT PARAMETERS
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| 116 | A - array[0..N-1] - real function to be transformed
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| 117 | N - problem size
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| 118 |
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| 119 | OUTPUT PARAMETERS
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| 120 | F - DFT of a input array, array[0..N-1]
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| 121 | F[j] = SUM(A[k]*exp(-2*pi*sqrt(-1)*j*k/N), k = 0..N-1)
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| 122 |
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| 123 | NOTE:
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| 124 | F[] satisfies symmetry property F[k] = conj(F[N-k]), so just one half
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| 125 | of array is usually needed. But for convinience subroutine returns full
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| 126 | complex array (with frequencies above N/2), so its result may be used by
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| 127 | other FFT-related subroutines.
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| 128 |
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| 129 |
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| 130 | -- ALGLIB --
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| 131 | Copyright 01.06.2009 by Bochkanov Sergey
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| 132 | *************************************************************************/
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| 133 | public static void fftr1d(double[] a, int n, out complex[] f)
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| 134 | {
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| 135 | f = new complex[0];
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| 136 | fft.fftr1d(a, n, ref f);
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| 137 | return;
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| 138 | }
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| 139 | public static void fftr1d(double[] a, out complex[] f)
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| 140 | {
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| 141 | int n;
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| 142 |
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| 143 | f = new complex[0];
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| 144 | n = ap.len(a);
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| 145 | fft.fftr1d(a, n, ref f);
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| 146 |
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| 147 | return;
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| 148 | }
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| 149 |
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| 150 | /*************************************************************************
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| 151 | 1-dimensional real inverse FFT.
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| 152 |
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| 153 | Algorithm has O(N*logN) complexity for any N (composite or prime).
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| 154 |
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| 155 | INPUT PARAMETERS
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| 156 | F - array[0..floor(N/2)] - frequencies from forward real FFT
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| 157 | N - problem size
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| 158 |
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| 159 | OUTPUT PARAMETERS
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| 160 | A - inverse DFT of a input array, array[0..N-1]
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| 161 |
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| 162 | NOTE:
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| 163 | F[] should satisfy symmetry property F[k] = conj(F[N-k]), so just one
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| 164 | half of frequencies array is needed - elements from 0 to floor(N/2). F[0]
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| 165 | is ALWAYS real. If N is even F[floor(N/2)] is real too. If N is odd, then
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| 166 | F[floor(N/2)] has no special properties.
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| 167 |
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| 168 | Relying on properties noted above, FFTR1DInv subroutine uses only elements
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| 169 | from 0th to floor(N/2)-th. It ignores imaginary part of F[0], and in case
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| 170 | N is even it ignores imaginary part of F[floor(N/2)] too.
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| 171 |
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| 172 | When you call this function using full arguments list - "FFTR1DInv(F,N,A)"
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| 173 | - you can pass either either frequencies array with N elements or reduced
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| 174 | array with roughly N/2 elements - subroutine will successfully transform
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| 175 | both.
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| 176 |
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| 177 | If you call this function using reduced arguments list - "FFTR1DInv(F,A)"
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| 178 | - you must pass FULL array with N elements (although higher N/2 are still
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| 179 | not used) because array size is used to automatically determine FFT length
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| 180 |
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| 181 |
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| 182 | -- ALGLIB --
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| 183 | Copyright 01.06.2009 by Bochkanov Sergey
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| 184 | *************************************************************************/
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| 185 | public static void fftr1dinv(complex[] f, int n, out double[] a)
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| 186 | {
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| 187 | a = new double[0];
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| 188 | fft.fftr1dinv(f, n, ref a);
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| 189 | return;
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| 190 | }
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| 191 | public static void fftr1dinv(complex[] f, out double[] a)
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| 192 | {
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| 193 | int n;
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| 194 |
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| 195 | a = new double[0];
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| 196 | n = ap.len(f);
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| 197 | fft.fftr1dinv(f, n, ref a);
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| 198 |
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| 199 | return;
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| 200 | }
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| 201 |
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| 202 | }
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| 203 | public partial class alglib
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| 204 | {
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| 205 |
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| 206 |
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| 207 | /*************************************************************************
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| 208 | 1-dimensional complex convolution.
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| 209 |
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| 210 | For given A/B returns conv(A,B) (non-circular). Subroutine can automatically
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| 211 | choose between three implementations: straightforward O(M*N) formula for
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| 212 | very small N (or M), overlap-add algorithm for cases where max(M,N) is
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| 213 | significantly larger than min(M,N), but O(M*N) algorithm is too slow, and
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| 214 | general FFT-based formula for cases where two previois algorithms are too
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| 215 | slow.
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| 216 |
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| 217 | Algorithm has max(M,N)*log(max(M,N)) complexity for any M/N.
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| 218 |
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| 219 | INPUT PARAMETERS
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| 220 | A - array[0..M-1] - complex function to be transformed
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| 221 | M - problem size
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| 222 | B - array[0..N-1] - complex function to be transformed
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| 223 | N - problem size
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| 224 |
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| 225 | OUTPUT PARAMETERS
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| 226 | R - convolution: A*B. array[0..N+M-2].
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| 227 |
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| 228 | NOTE:
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| 229 | It is assumed that A is zero at T<0, B is zero too. If one or both
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| 230 | functions have non-zero values at negative T's, you can still use this
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| 231 | subroutine - just shift its result correspondingly.
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| 232 |
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| 233 | -- ALGLIB --
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| 234 | Copyright 21.07.2009 by Bochkanov Sergey
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| 235 | *************************************************************************/
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| 236 | public static void convc1d(complex[] a, int m, complex[] b, int n, out complex[] r)
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| 237 | {
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| 238 | r = new complex[0];
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| 239 | conv.convc1d(a, m, b, n, ref r);
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| 240 | return;
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| 241 | }
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| 242 |
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| 243 | /*************************************************************************
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| 244 | 1-dimensional complex non-circular deconvolution (inverse of ConvC1D()).
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| 245 |
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| 246 | Algorithm has M*log(M)) complexity for any M (composite or prime).
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| 247 |
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| 248 | INPUT PARAMETERS
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| 249 | A - array[0..M-1] - convolved signal, A = conv(R, B)
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| 250 | M - convolved signal length
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| 251 | B - array[0..N-1] - response
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| 252 | N - response length, N<=M
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| 253 |
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| 254 | OUTPUT PARAMETERS
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| 255 | R - deconvolved signal. array[0..M-N].
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| 256 |
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| 257 | NOTE:
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| 258 | deconvolution is unstable process and may result in division by zero
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| 259 | (if your response function is degenerate, i.e. has zero Fourier coefficient).
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| 260 |
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| 261 | NOTE:
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| 262 | It is assumed that A is zero at T<0, B is zero too. If one or both
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| 263 | functions have non-zero values at negative T's, you can still use this
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| 264 | subroutine - just shift its result correspondingly.
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| 265 |
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| 266 | -- ALGLIB --
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| 267 | Copyright 21.07.2009 by Bochkanov Sergey
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| 268 | *************************************************************************/
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| 269 | public static void convc1dinv(complex[] a, int m, complex[] b, int n, out complex[] r)
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| 270 | {
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| 271 | r = new complex[0];
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| 272 | conv.convc1dinv(a, m, b, n, ref r);
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| 273 | return;
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| 274 | }
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| 275 |
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| 276 | /*************************************************************************
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| 277 | 1-dimensional circular complex convolution.
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| 278 |
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| 279 | For given S/R returns conv(S,R) (circular). Algorithm has linearithmic
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| 280 | complexity for any M/N.
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| 281 |
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| 282 | IMPORTANT: normal convolution is commutative, i.e. it is symmetric -
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| 283 | conv(A,B)=conv(B,A). Cyclic convolution IS NOT. One function - S - is a
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| 284 | signal, periodic function, and another - R - is a response, non-periodic
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| 285 | function with limited length.
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| 286 |
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| 287 | INPUT PARAMETERS
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| 288 | S - array[0..M-1] - complex periodic signal
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| 289 | M - problem size
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| 290 | B - array[0..N-1] - complex non-periodic response
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| 291 | N - problem size
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| 292 |
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| 293 | OUTPUT PARAMETERS
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| 294 | R - convolution: A*B. array[0..M-1].
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| 295 |
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| 296 | NOTE:
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| 297 | It is assumed that B is zero at T<0. If it has non-zero values at
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| 298 | negative T's, you can still use this subroutine - just shift its result
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| 299 | correspondingly.
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| 300 |
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| 301 | -- ALGLIB --
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| 302 | Copyright 21.07.2009 by Bochkanov Sergey
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| 303 | *************************************************************************/
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| 304 | public static void convc1dcircular(complex[] s, int m, complex[] r, int n, out complex[] c)
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| 305 | {
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| 306 | c = new complex[0];
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| 307 | conv.convc1dcircular(s, m, r, n, ref c);
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| 308 | return;
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| 309 | }
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| 310 |
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| 311 | /*************************************************************************
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| 312 | 1-dimensional circular complex deconvolution (inverse of ConvC1DCircular()).
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| 313 |
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| 314 | Algorithm has M*log(M)) complexity for any M (composite or prime).
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| 315 |
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| 316 | INPUT PARAMETERS
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| 317 | A - array[0..M-1] - convolved periodic signal, A = conv(R, B)
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| 318 | M - convolved signal length
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| 319 | B - array[0..N-1] - non-periodic response
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| 320 | N - response length
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| 321 |
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| 322 | OUTPUT PARAMETERS
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| 323 | R - deconvolved signal. array[0..M-1].
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| 324 |
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| 325 | NOTE:
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| 326 | deconvolution is unstable process and may result in division by zero
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| 327 | (if your response function is degenerate, i.e. has zero Fourier coefficient).
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| 328 |
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| 329 | NOTE:
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| 330 | It is assumed that B is zero at T<0. If it has non-zero values at
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| 331 | negative T's, you can still use this subroutine - just shift its result
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| 332 | correspondingly.
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| 333 |
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| 334 | -- ALGLIB --
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| 335 | Copyright 21.07.2009 by Bochkanov Sergey
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| 336 | *************************************************************************/
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| 337 | public static void convc1dcircularinv(complex[] a, int m, complex[] b, int n, out complex[] r)
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| 338 | {
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| 339 | r = new complex[0];
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| 340 | conv.convc1dcircularinv(a, m, b, n, ref r);
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| 341 | return;
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| 342 | }
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| 343 |
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| 344 | /*************************************************************************
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| 345 | 1-dimensional real convolution.
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| 346 |
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| 347 | Analogous to ConvC1D(), see ConvC1D() comments for more details.
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| 348 |
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| 349 | INPUT PARAMETERS
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| 350 | A - array[0..M-1] - real function to be transformed
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| 351 | M - problem size
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| 352 | B - array[0..N-1] - real function to be transformed
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| 353 | N - problem size
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| 354 |
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| 355 | OUTPUT PARAMETERS
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| 356 | R - convolution: A*B. array[0..N+M-2].
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| 357 |
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| 358 | NOTE:
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| 359 | It is assumed that A is zero at T<0, B is zero too. If one or both
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| 360 | functions have non-zero values at negative T's, you can still use this
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| 361 | subroutine - just shift its result correspondingly.
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| 362 |
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| 363 | -- ALGLIB --
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| 364 | Copyright 21.07.2009 by Bochkanov Sergey
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| 365 | *************************************************************************/
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| 366 | public static void convr1d(double[] a, int m, double[] b, int n, out double[] r)
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| 367 | {
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| 368 | r = new double[0];
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| 369 | conv.convr1d(a, m, b, n, ref r);
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| 370 | return;
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| 371 | }
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| 372 |
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| 373 | /*************************************************************************
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| 374 | 1-dimensional real deconvolution (inverse of ConvC1D()).
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| 375 |
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| 376 | Algorithm has M*log(M)) complexity for any M (composite or prime).
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| 377 |
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| 378 | INPUT PARAMETERS
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| 379 | A - array[0..M-1] - convolved signal, A = conv(R, B)
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| 380 | M - convolved signal length
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| 381 | B - array[0..N-1] - response
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| 382 | N - response length, N<=M
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| 383 |
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| 384 | OUTPUT PARAMETERS
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| 385 | R - deconvolved signal. array[0..M-N].
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| 386 |
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| 387 | NOTE:
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| 388 | deconvolution is unstable process and may result in division by zero
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| 389 | (if your response function is degenerate, i.e. has zero Fourier coefficient).
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| 390 |
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| 391 | NOTE:
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| 392 | It is assumed that A is zero at T<0, B is zero too. If one or both
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| 393 | functions have non-zero values at negative T's, you can still use this
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| 394 | subroutine - just shift its result correspondingly.
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| 395 |
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| 396 | -- ALGLIB --
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| 397 | Copyright 21.07.2009 by Bochkanov Sergey
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| 398 | *************************************************************************/
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| 399 | public static void convr1dinv(double[] a, int m, double[] b, int n, out double[] r)
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| 400 | {
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| 401 | r = new double[0];
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| 402 | conv.convr1dinv(a, m, b, n, ref r);
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| 403 | return;
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| 404 | }
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| 405 |
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| 406 | /*************************************************************************
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| 407 | 1-dimensional circular real convolution.
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| 408 |
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| 409 | Analogous to ConvC1DCircular(), see ConvC1DCircular() comments for more details.
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| 410 |
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| 411 | INPUT PARAMETERS
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| 412 | S - array[0..M-1] - real signal
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| 413 | M - problem size
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| 414 | B - array[0..N-1] - real response
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| 415 | N - problem size
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| 416 |
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| 417 | OUTPUT PARAMETERS
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| 418 | R - convolution: A*B. array[0..M-1].
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| 419 |
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| 420 | NOTE:
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| 421 | It is assumed that B is zero at T<0. If it has non-zero values at
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| 422 | negative T's, you can still use this subroutine - just shift its result
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| 423 | correspondingly.
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| 424 |
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| 425 | -- ALGLIB --
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| 426 | Copyright 21.07.2009 by Bochkanov Sergey
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| 427 | *************************************************************************/
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| 428 | public static void convr1dcircular(double[] s, int m, double[] r, int n, out double[] c)
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| 429 | {
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| 430 | c = new double[0];
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| 431 | conv.convr1dcircular(s, m, r, n, ref c);
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| 432 | return;
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| 433 | }
|
---|
| 434 |
|
---|
| 435 | /*************************************************************************
|
---|
| 436 | 1-dimensional complex deconvolution (inverse of ConvC1D()).
|
---|
| 437 |
|
---|
| 438 | Algorithm has M*log(M)) complexity for any M (composite or prime).
|
---|
| 439 |
|
---|
| 440 | INPUT PARAMETERS
|
---|
| 441 | A - array[0..M-1] - convolved signal, A = conv(R, B)
|
---|
| 442 | M - convolved signal length
|
---|
| 443 | B - array[0..N-1] - response
|
---|
| 444 | N - response length
|
---|
| 445 |
|
---|
| 446 | OUTPUT PARAMETERS
|
---|
| 447 | R - deconvolved signal. array[0..M-N].
|
---|
| 448 |
|
---|
| 449 | NOTE:
|
---|
| 450 | deconvolution is unstable process and may result in division by zero
|
---|
| 451 | (if your response function is degenerate, i.e. has zero Fourier coefficient).
|
---|
| 452 |
|
---|
| 453 | NOTE:
|
---|
| 454 | It is assumed that B is zero at T<0. If it has non-zero values at
|
---|
| 455 | negative T's, you can still use this subroutine - just shift its result
|
---|
| 456 | correspondingly.
|
---|
| 457 |
|
---|
| 458 | -- ALGLIB --
|
---|
| 459 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
| 460 | *************************************************************************/
|
---|
| 461 | public static void convr1dcircularinv(double[] a, int m, double[] b, int n, out double[] r)
|
---|
| 462 | {
|
---|
| 463 | r = new double[0];
|
---|
| 464 | conv.convr1dcircularinv(a, m, b, n, ref r);
|
---|
| 465 | return;
|
---|
| 466 | }
|
---|
| 467 |
|
---|
| 468 | }
|
---|
| 469 | public partial class alglib
|
---|
| 470 | {
|
---|
| 471 |
|
---|
| 472 |
|
---|
| 473 | /*************************************************************************
|
---|
| 474 | 1-dimensional complex cross-correlation.
|
---|
| 475 |
|
---|
| 476 | For given Pattern/Signal returns corr(Pattern,Signal) (non-circular).
|
---|
| 477 |
|
---|
| 478 | Correlation is calculated using reduction to convolution. Algorithm with
|
---|
| 479 | max(N,N)*log(max(N,N)) complexity is used (see ConvC1D() for more info
|
---|
| 480 | about performance).
|
---|
| 481 |
|
---|
| 482 | IMPORTANT:
|
---|
| 483 | for historical reasons subroutine accepts its parameters in reversed
|
---|
| 484 | order: CorrC1D(Signal, Pattern) = Pattern x Signal (using traditional
|
---|
| 485 | definition of cross-correlation, denoting cross-correlation as "x").
|
---|
| 486 |
|
---|
| 487 | INPUT PARAMETERS
|
---|
| 488 | Signal - array[0..N-1] - complex function to be transformed,
|
---|
| 489 | signal containing pattern
|
---|
| 490 | N - problem size
|
---|
| 491 | Pattern - array[0..M-1] - complex function to be transformed,
|
---|
| 492 | pattern to search withing signal
|
---|
| 493 | M - problem size
|
---|
| 494 |
|
---|
| 495 | OUTPUT PARAMETERS
|
---|
| 496 | R - cross-correlation, array[0..N+M-2]:
|
---|
| 497 | * positive lags are stored in R[0..N-1],
|
---|
| 498 | R[i] = sum(conj(pattern[j])*signal[i+j]
|
---|
| 499 | * negative lags are stored in R[N..N+M-2],
|
---|
| 500 | R[N+M-1-i] = sum(conj(pattern[j])*signal[-i+j]
|
---|
| 501 |
|
---|
| 502 | NOTE:
|
---|
| 503 | It is assumed that pattern domain is [0..M-1]. If Pattern is non-zero
|
---|
| 504 | on [-K..M-1], you can still use this subroutine, just shift result by K.
|
---|
| 505 |
|
---|
| 506 | -- ALGLIB --
|
---|
| 507 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
| 508 | *************************************************************************/
|
---|
| 509 | public static void corrc1d(complex[] signal, int n, complex[] pattern, int m, out complex[] r)
|
---|
| 510 | {
|
---|
| 511 | r = new complex[0];
|
---|
| 512 | corr.corrc1d(signal, n, pattern, m, ref r);
|
---|
| 513 | return;
|
---|
| 514 | }
|
---|
| 515 |
|
---|
| 516 | /*************************************************************************
|
---|
| 517 | 1-dimensional circular complex cross-correlation.
|
---|
| 518 |
|
---|
| 519 | For given Pattern/Signal returns corr(Pattern,Signal) (circular).
|
---|
| 520 | Algorithm has linearithmic complexity for any M/N.
|
---|
| 521 |
|
---|
| 522 | IMPORTANT:
|
---|
| 523 | for historical reasons subroutine accepts its parameters in reversed
|
---|
| 524 | order: CorrC1DCircular(Signal, Pattern) = Pattern x Signal (using
|
---|
| 525 | traditional definition of cross-correlation, denoting cross-correlation
|
---|
| 526 | as "x").
|
---|
| 527 |
|
---|
| 528 | INPUT PARAMETERS
|
---|
| 529 | Signal - array[0..N-1] - complex function to be transformed,
|
---|
| 530 | periodic signal containing pattern
|
---|
| 531 | N - problem size
|
---|
| 532 | Pattern - array[0..M-1] - complex function to be transformed,
|
---|
| 533 | non-periodic pattern to search withing signal
|
---|
| 534 | M - problem size
|
---|
| 535 |
|
---|
| 536 | OUTPUT PARAMETERS
|
---|
| 537 | R - convolution: A*B. array[0..M-1].
|
---|
| 538 |
|
---|
| 539 |
|
---|
| 540 | -- ALGLIB --
|
---|
| 541 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
| 542 | *************************************************************************/
|
---|
| 543 | public static void corrc1dcircular(complex[] signal, int m, complex[] pattern, int n, out complex[] c)
|
---|
| 544 | {
|
---|
| 545 | c = new complex[0];
|
---|
| 546 | corr.corrc1dcircular(signal, m, pattern, n, ref c);
|
---|
| 547 | return;
|
---|
| 548 | }
|
---|
| 549 |
|
---|
| 550 | /*************************************************************************
|
---|
| 551 | 1-dimensional real cross-correlation.
|
---|
| 552 |
|
---|
| 553 | For given Pattern/Signal returns corr(Pattern,Signal) (non-circular).
|
---|
| 554 |
|
---|
| 555 | Correlation is calculated using reduction to convolution. Algorithm with
|
---|
| 556 | max(N,N)*log(max(N,N)) complexity is used (see ConvC1D() for more info
|
---|
| 557 | about performance).
|
---|
| 558 |
|
---|
| 559 | IMPORTANT:
|
---|
| 560 | for historical reasons subroutine accepts its parameters in reversed
|
---|
| 561 | order: CorrR1D(Signal, Pattern) = Pattern x Signal (using traditional
|
---|
| 562 | definition of cross-correlation, denoting cross-correlation as "x").
|
---|
| 563 |
|
---|
| 564 | INPUT PARAMETERS
|
---|
| 565 | Signal - array[0..N-1] - real function to be transformed,
|
---|
| 566 | signal containing pattern
|
---|
| 567 | N - problem size
|
---|
| 568 | Pattern - array[0..M-1] - real function to be transformed,
|
---|
| 569 | pattern to search withing signal
|
---|
| 570 | M - problem size
|
---|
| 571 |
|
---|
| 572 | OUTPUT PARAMETERS
|
---|
| 573 | R - cross-correlation, array[0..N+M-2]:
|
---|
| 574 | * positive lags are stored in R[0..N-1],
|
---|
| 575 | R[i] = sum(pattern[j]*signal[i+j]
|
---|
| 576 | * negative lags are stored in R[N..N+M-2],
|
---|
| 577 | R[N+M-1-i] = sum(pattern[j]*signal[-i+j]
|
---|
| 578 |
|
---|
| 579 | NOTE:
|
---|
| 580 | It is assumed that pattern domain is [0..M-1]. If Pattern is non-zero
|
---|
| 581 | on [-K..M-1], you can still use this subroutine, just shift result by K.
|
---|
| 582 |
|
---|
| 583 | -- ALGLIB --
|
---|
| 584 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
| 585 | *************************************************************************/
|
---|
| 586 | public static void corrr1d(double[] signal, int n, double[] pattern, int m, out double[] r)
|
---|
| 587 | {
|
---|
| 588 | r = new double[0];
|
---|
| 589 | corr.corrr1d(signal, n, pattern, m, ref r);
|
---|
| 590 | return;
|
---|
| 591 | }
|
---|
| 592 |
|
---|
| 593 | /*************************************************************************
|
---|
| 594 | 1-dimensional circular real cross-correlation.
|
---|
| 595 |
|
---|
| 596 | For given Pattern/Signal returns corr(Pattern,Signal) (circular).
|
---|
| 597 | Algorithm has linearithmic complexity for any M/N.
|
---|
| 598 |
|
---|
| 599 | IMPORTANT:
|
---|
| 600 | for historical reasons subroutine accepts its parameters in reversed
|
---|
| 601 | order: CorrR1DCircular(Signal, Pattern) = Pattern x Signal (using
|
---|
| 602 | traditional definition of cross-correlation, denoting cross-correlation
|
---|
| 603 | as "x").
|
---|
| 604 |
|
---|
| 605 | INPUT PARAMETERS
|
---|
| 606 | Signal - array[0..N-1] - real function to be transformed,
|
---|
| 607 | periodic signal containing pattern
|
---|
| 608 | N - problem size
|
---|
| 609 | Pattern - array[0..M-1] - real function to be transformed,
|
---|
| 610 | non-periodic pattern to search withing signal
|
---|
| 611 | M - problem size
|
---|
| 612 |
|
---|
| 613 | OUTPUT PARAMETERS
|
---|
| 614 | R - convolution: A*B. array[0..M-1].
|
---|
| 615 |
|
---|
| 616 |
|
---|
| 617 | -- ALGLIB --
|
---|
| 618 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
| 619 | *************************************************************************/
|
---|
| 620 | public static void corrr1dcircular(double[] signal, int m, double[] pattern, int n, out double[] c)
|
---|
| 621 | {
|
---|
| 622 | c = new double[0];
|
---|
| 623 | corr.corrr1dcircular(signal, m, pattern, n, ref c);
|
---|
| 624 | return;
|
---|
| 625 | }
|
---|
| 626 |
|
---|
| 627 | }
|
---|
| 628 | public partial class alglib
|
---|
| 629 | {
|
---|
| 630 |
|
---|
| 631 |
|
---|
| 632 | /*************************************************************************
|
---|
| 633 | 1-dimensional Fast Hartley Transform.
|
---|
| 634 |
|
---|
| 635 | Algorithm has O(N*logN) complexity for any N (composite or prime).
|
---|
| 636 |
|
---|
| 637 | INPUT PARAMETERS
|
---|
| 638 | A - array[0..N-1] - real function to be transformed
|
---|
| 639 | N - problem size
|
---|
| 640 |
|
---|
| 641 | OUTPUT PARAMETERS
|
---|
| 642 | A - FHT of a input array, array[0..N-1],
|
---|
| 643 | A_out[k] = sum(A_in[j]*(cos(2*pi*j*k/N)+sin(2*pi*j*k/N)), j=0..N-1)
|
---|
| 644 |
|
---|
| 645 |
|
---|
| 646 | -- ALGLIB --
|
---|
| 647 | Copyright 04.06.2009 by Bochkanov Sergey
|
---|
| 648 | *************************************************************************/
|
---|
| 649 | public static void fhtr1d(ref double[] a, int n)
|
---|
| 650 | {
|
---|
| 651 |
|
---|
| 652 | fht.fhtr1d(ref a, n);
|
---|
| 653 | return;
|
---|
| 654 | }
|
---|
| 655 |
|
---|
| 656 | /*************************************************************************
|
---|
| 657 | 1-dimensional inverse FHT.
|
---|
| 658 |
|
---|
| 659 | Algorithm has O(N*logN) complexity for any N (composite or prime).
|
---|
| 660 |
|
---|
| 661 | INPUT PARAMETERS
|
---|
| 662 | A - array[0..N-1] - complex array to be transformed
|
---|
| 663 | N - problem size
|
---|
| 664 |
|
---|
| 665 | OUTPUT PARAMETERS
|
---|
| 666 | A - inverse FHT of a input array, array[0..N-1]
|
---|
| 667 |
|
---|
| 668 |
|
---|
| 669 | -- ALGLIB --
|
---|
| 670 | Copyright 29.05.2009 by Bochkanov Sergey
|
---|
| 671 | *************************************************************************/
|
---|
| 672 | public static void fhtr1dinv(ref double[] a, int n)
|
---|
| 673 | {
|
---|
| 674 |
|
---|
| 675 | fht.fhtr1dinv(ref a, n);
|
---|
| 676 | return;
|
---|
| 677 | }
|
---|
| 678 |
|
---|
| 679 | }
|
---|
| 680 | public partial class alglib
|
---|
| 681 | {
|
---|
| 682 | public class fft
|
---|
| 683 | {
|
---|
| 684 | /*************************************************************************
|
---|
| 685 | 1-dimensional complex FFT.
|
---|
| 686 |
|
---|
| 687 | Array size N may be arbitrary number (composite or prime). Composite N's
|
---|
| 688 | are handled with cache-oblivious variation of a Cooley-Tukey algorithm.
|
---|
| 689 | Small prime-factors are transformed using hard coded codelets (similar to
|
---|
| 690 | FFTW codelets, but without low-level optimization), large prime-factors
|
---|
| 691 | are handled with Bluestein's algorithm.
|
---|
| 692 |
|
---|
| 693 | Fastests transforms are for smooth N's (prime factors are 2, 3, 5 only),
|
---|
| 694 | most fast for powers of 2. When N have prime factors larger than these,
|
---|
| 695 | but orders of magnitude smaller than N, computations will be about 4 times
|
---|
| 696 | slower than for nearby highly composite N's. When N itself is prime, speed
|
---|
| 697 | will be 6 times lower.
|
---|
| 698 |
|
---|
| 699 | Algorithm has O(N*logN) complexity for any N (composite or prime).
|
---|
| 700 |
|
---|
| 701 | INPUT PARAMETERS
|
---|
| 702 | A - array[0..N-1] - complex function to be transformed
|
---|
| 703 | N - problem size
|
---|
| 704 |
|
---|
| 705 | OUTPUT PARAMETERS
|
---|
| 706 | A - DFT of a input array, array[0..N-1]
|
---|
| 707 | A_out[j] = SUM(A_in[k]*exp(-2*pi*sqrt(-1)*j*k/N), k = 0..N-1)
|
---|
| 708 |
|
---|
| 709 |
|
---|
| 710 | -- ALGLIB --
|
---|
| 711 | Copyright 29.05.2009 by Bochkanov Sergey
|
---|
| 712 | *************************************************************************/
|
---|
| 713 | public static void fftc1d(ref complex[] a,
|
---|
| 714 | int n)
|
---|
| 715 | {
|
---|
| 716 | ftbase.ftplan plan = new ftbase.ftplan();
|
---|
| 717 | int i = 0;
|
---|
| 718 | double[] buf = new double[0];
|
---|
| 719 |
|
---|
| 720 | alglib.ap.assert(n>0, "FFTC1D: incorrect N!");
|
---|
| 721 | alglib.ap.assert(alglib.ap.len(a)>=n, "FFTC1D: Length(A)<N!");
|
---|
| 722 | alglib.ap.assert(apserv.isfinitecvector(a, n), "FFTC1D: A contains infinite or NAN values!");
|
---|
| 723 |
|
---|
| 724 | //
|
---|
| 725 | // Special case: N=1, FFT is just identity transform.
|
---|
| 726 | // After this block we assume that N is strictly greater than 1.
|
---|
| 727 | //
|
---|
| 728 | if( n==1 )
|
---|
| 729 | {
|
---|
| 730 | return;
|
---|
| 731 | }
|
---|
| 732 |
|
---|
| 733 | //
|
---|
| 734 | // convert input array to the more convinient format
|
---|
| 735 | //
|
---|
| 736 | buf = new double[2*n];
|
---|
| 737 | for(i=0; i<=n-1; i++)
|
---|
| 738 | {
|
---|
| 739 | buf[2*i+0] = a[i].x;
|
---|
| 740 | buf[2*i+1] = a[i].y;
|
---|
| 741 | }
|
---|
| 742 |
|
---|
| 743 | //
|
---|
| 744 | // Generate plan and execute it.
|
---|
| 745 | //
|
---|
| 746 | // Plan is a combination of a successive factorizations of N and
|
---|
| 747 | // precomputed data. It is much like a FFTW plan, but is not stored
|
---|
| 748 | // between subroutine calls and is much simpler.
|
---|
| 749 | //
|
---|
| 750 | ftbase.ftbasegeneratecomplexfftplan(n, plan);
|
---|
| 751 | ftbase.ftbaseexecuteplan(ref buf, 0, n, plan);
|
---|
| 752 |
|
---|
| 753 | //
|
---|
| 754 | // result
|
---|
| 755 | //
|
---|
| 756 | for(i=0; i<=n-1; i++)
|
---|
| 757 | {
|
---|
| 758 | a[i].x = buf[2*i+0];
|
---|
| 759 | a[i].y = buf[2*i+1];
|
---|
| 760 | }
|
---|
| 761 | }
|
---|
| 762 |
|
---|
| 763 |
|
---|
| 764 | /*************************************************************************
|
---|
| 765 | 1-dimensional complex inverse FFT.
|
---|
| 766 |
|
---|
| 767 | Array size N may be arbitrary number (composite or prime). Algorithm has
|
---|
| 768 | O(N*logN) complexity for any N (composite or prime).
|
---|
| 769 |
|
---|
| 770 | See FFTC1D() description for more information about algorithm performance.
|
---|
| 771 |
|
---|
| 772 | INPUT PARAMETERS
|
---|
| 773 | A - array[0..N-1] - complex array to be transformed
|
---|
| 774 | N - problem size
|
---|
| 775 |
|
---|
| 776 | OUTPUT PARAMETERS
|
---|
| 777 | A - inverse DFT of a input array, array[0..N-1]
|
---|
| 778 | A_out[j] = SUM(A_in[k]/N*exp(+2*pi*sqrt(-1)*j*k/N), k = 0..N-1)
|
---|
| 779 |
|
---|
| 780 |
|
---|
| 781 | -- ALGLIB --
|
---|
| 782 | Copyright 29.05.2009 by Bochkanov Sergey
|
---|
| 783 | *************************************************************************/
|
---|
| 784 | public static void fftc1dinv(ref complex[] a,
|
---|
| 785 | int n)
|
---|
| 786 | {
|
---|
| 787 | int i = 0;
|
---|
| 788 |
|
---|
| 789 | alglib.ap.assert(n>0, "FFTC1DInv: incorrect N!");
|
---|
| 790 | alglib.ap.assert(alglib.ap.len(a)>=n, "FFTC1DInv: Length(A)<N!");
|
---|
| 791 | alglib.ap.assert(apserv.isfinitecvector(a, n), "FFTC1DInv: A contains infinite or NAN values!");
|
---|
| 792 |
|
---|
| 793 | //
|
---|
| 794 | // Inverse DFT can be expressed in terms of the DFT as
|
---|
| 795 | //
|
---|
| 796 | // invfft(x) = fft(x')'/N
|
---|
| 797 | //
|
---|
| 798 | // here x' means conj(x).
|
---|
| 799 | //
|
---|
| 800 | for(i=0; i<=n-1; i++)
|
---|
| 801 | {
|
---|
| 802 | a[i].y = -a[i].y;
|
---|
| 803 | }
|
---|
| 804 | fftc1d(ref a, n);
|
---|
| 805 | for(i=0; i<=n-1; i++)
|
---|
| 806 | {
|
---|
| 807 | a[i].x = a[i].x/n;
|
---|
| 808 | a[i].y = -(a[i].y/n);
|
---|
| 809 | }
|
---|
| 810 | }
|
---|
| 811 |
|
---|
| 812 |
|
---|
| 813 | /*************************************************************************
|
---|
| 814 | 1-dimensional real FFT.
|
---|
| 815 |
|
---|
| 816 | Algorithm has O(N*logN) complexity for any N (composite or prime).
|
---|
| 817 |
|
---|
| 818 | INPUT PARAMETERS
|
---|
| 819 | A - array[0..N-1] - real function to be transformed
|
---|
| 820 | N - problem size
|
---|
| 821 |
|
---|
| 822 | OUTPUT PARAMETERS
|
---|
| 823 | F - DFT of a input array, array[0..N-1]
|
---|
| 824 | F[j] = SUM(A[k]*exp(-2*pi*sqrt(-1)*j*k/N), k = 0..N-1)
|
---|
| 825 |
|
---|
| 826 | NOTE:
|
---|
| 827 | F[] satisfies symmetry property F[k] = conj(F[N-k]), so just one half
|
---|
| 828 | of array is usually needed. But for convinience subroutine returns full
|
---|
| 829 | complex array (with frequencies above N/2), so its result may be used by
|
---|
| 830 | other FFT-related subroutines.
|
---|
| 831 |
|
---|
| 832 |
|
---|
| 833 | -- ALGLIB --
|
---|
| 834 | Copyright 01.06.2009 by Bochkanov Sergey
|
---|
| 835 | *************************************************************************/
|
---|
| 836 | public static void fftr1d(double[] a,
|
---|
| 837 | int n,
|
---|
| 838 | ref complex[] f)
|
---|
| 839 | {
|
---|
| 840 | int i = 0;
|
---|
| 841 | int n2 = 0;
|
---|
| 842 | int idx = 0;
|
---|
| 843 | complex hn = 0;
|
---|
| 844 | complex hmnc = 0;
|
---|
| 845 | complex v = 0;
|
---|
| 846 | double[] buf = new double[0];
|
---|
| 847 | ftbase.ftplan plan = new ftbase.ftplan();
|
---|
| 848 | int i_ = 0;
|
---|
| 849 |
|
---|
| 850 | f = new complex[0];
|
---|
| 851 |
|
---|
| 852 | alglib.ap.assert(n>0, "FFTR1D: incorrect N!");
|
---|
| 853 | alglib.ap.assert(alglib.ap.len(a)>=n, "FFTR1D: Length(A)<N!");
|
---|
| 854 | alglib.ap.assert(apserv.isfinitevector(a, n), "FFTR1D: A contains infinite or NAN values!");
|
---|
| 855 |
|
---|
| 856 | //
|
---|
| 857 | // Special cases:
|
---|
| 858 | // * N=1, FFT is just identity transform.
|
---|
| 859 | // * N=2, FFT is simple too
|
---|
| 860 | //
|
---|
| 861 | // After this block we assume that N is strictly greater than 2
|
---|
| 862 | //
|
---|
| 863 | if( n==1 )
|
---|
| 864 | {
|
---|
| 865 | f = new complex[1];
|
---|
| 866 | f[0] = a[0];
|
---|
| 867 | return;
|
---|
| 868 | }
|
---|
| 869 | if( n==2 )
|
---|
| 870 | {
|
---|
| 871 | f = new complex[2];
|
---|
| 872 | f[0].x = a[0]+a[1];
|
---|
| 873 | f[0].y = 0;
|
---|
| 874 | f[1].x = a[0]-a[1];
|
---|
| 875 | f[1].y = 0;
|
---|
| 876 | return;
|
---|
| 877 | }
|
---|
| 878 |
|
---|
| 879 | //
|
---|
| 880 | // Choose between odd-size and even-size FFTs
|
---|
| 881 | //
|
---|
| 882 | if( n%2==0 )
|
---|
| 883 | {
|
---|
| 884 |
|
---|
| 885 | //
|
---|
| 886 | // even-size real FFT, use reduction to the complex task
|
---|
| 887 | //
|
---|
| 888 | n2 = n/2;
|
---|
| 889 | buf = new double[n];
|
---|
| 890 | for(i_=0; i_<=n-1;i_++)
|
---|
| 891 | {
|
---|
| 892 | buf[i_] = a[i_];
|
---|
| 893 | }
|
---|
| 894 | ftbase.ftbasegeneratecomplexfftplan(n2, plan);
|
---|
| 895 | ftbase.ftbaseexecuteplan(ref buf, 0, n2, plan);
|
---|
| 896 | f = new complex[n];
|
---|
| 897 | for(i=0; i<=n2; i++)
|
---|
| 898 | {
|
---|
| 899 | idx = 2*(i%n2);
|
---|
| 900 | hn.x = buf[idx+0];
|
---|
| 901 | hn.y = buf[idx+1];
|
---|
| 902 | idx = 2*((n2-i)%n2);
|
---|
| 903 | hmnc.x = buf[idx+0];
|
---|
| 904 | hmnc.y = -buf[idx+1];
|
---|
| 905 | v.x = -Math.Sin(-(2*Math.PI*i/n));
|
---|
| 906 | v.y = Math.Cos(-(2*Math.PI*i/n));
|
---|
| 907 | f[i] = hn+hmnc-v*(hn-hmnc);
|
---|
| 908 | f[i].x = 0.5*f[i].x;
|
---|
| 909 | f[i].y = 0.5*f[i].y;
|
---|
| 910 | }
|
---|
| 911 | for(i=n2+1; i<=n-1; i++)
|
---|
| 912 | {
|
---|
| 913 | f[i] = math.conj(f[n-i]);
|
---|
| 914 | }
|
---|
| 915 | }
|
---|
| 916 | else
|
---|
| 917 | {
|
---|
| 918 |
|
---|
| 919 | //
|
---|
| 920 | // use complex FFT
|
---|
| 921 | //
|
---|
| 922 | f = new complex[n];
|
---|
| 923 | for(i=0; i<=n-1; i++)
|
---|
| 924 | {
|
---|
| 925 | f[i] = a[i];
|
---|
| 926 | }
|
---|
| 927 | fftc1d(ref f, n);
|
---|
| 928 | }
|
---|
| 929 | }
|
---|
| 930 |
|
---|
| 931 |
|
---|
| 932 | /*************************************************************************
|
---|
| 933 | 1-dimensional real inverse FFT.
|
---|
| 934 |
|
---|
| 935 | Algorithm has O(N*logN) complexity for any N (composite or prime).
|
---|
| 936 |
|
---|
| 937 | INPUT PARAMETERS
|
---|
| 938 | F - array[0..floor(N/2)] - frequencies from forward real FFT
|
---|
| 939 | N - problem size
|
---|
| 940 |
|
---|
| 941 | OUTPUT PARAMETERS
|
---|
| 942 | A - inverse DFT of a input array, array[0..N-1]
|
---|
| 943 |
|
---|
| 944 | NOTE:
|
---|
| 945 | F[] should satisfy symmetry property F[k] = conj(F[N-k]), so just one
|
---|
| 946 | half of frequencies array is needed - elements from 0 to floor(N/2). F[0]
|
---|
| 947 | is ALWAYS real. If N is even F[floor(N/2)] is real too. If N is odd, then
|
---|
| 948 | F[floor(N/2)] has no special properties.
|
---|
| 949 |
|
---|
| 950 | Relying on properties noted above, FFTR1DInv subroutine uses only elements
|
---|
| 951 | from 0th to floor(N/2)-th. It ignores imaginary part of F[0], and in case
|
---|
| 952 | N is even it ignores imaginary part of F[floor(N/2)] too.
|
---|
| 953 |
|
---|
| 954 | When you call this function using full arguments list - "FFTR1DInv(F,N,A)"
|
---|
| 955 | - you can pass either either frequencies array with N elements or reduced
|
---|
| 956 | array with roughly N/2 elements - subroutine will successfully transform
|
---|
| 957 | both.
|
---|
| 958 |
|
---|
| 959 | If you call this function using reduced arguments list - "FFTR1DInv(F,A)"
|
---|
| 960 | - you must pass FULL array with N elements (although higher N/2 are still
|
---|
| 961 | not used) because array size is used to automatically determine FFT length
|
---|
| 962 |
|
---|
| 963 |
|
---|
| 964 | -- ALGLIB --
|
---|
| 965 | Copyright 01.06.2009 by Bochkanov Sergey
|
---|
| 966 | *************************************************************************/
|
---|
| 967 | public static void fftr1dinv(complex[] f,
|
---|
| 968 | int n,
|
---|
| 969 | ref double[] a)
|
---|
| 970 | {
|
---|
| 971 | int i = 0;
|
---|
| 972 | double[] h = new double[0];
|
---|
| 973 | complex[] fh = new complex[0];
|
---|
| 974 |
|
---|
| 975 | a = new double[0];
|
---|
| 976 |
|
---|
| 977 | alglib.ap.assert(n>0, "FFTR1DInv: incorrect N!");
|
---|
| 978 | alglib.ap.assert(alglib.ap.len(f)>=(int)Math.Floor((double)n/(double)2)+1, "FFTR1DInv: Length(F)<Floor(N/2)+1!");
|
---|
| 979 | alglib.ap.assert(math.isfinite(f[0].x), "FFTR1DInv: F contains infinite or NAN values!");
|
---|
| 980 | for(i=1; i<=(int)Math.Floor((double)n/(double)2)-1; i++)
|
---|
| 981 | {
|
---|
| 982 | alglib.ap.assert(math.isfinite(f[i].x) && math.isfinite(f[i].y), "FFTR1DInv: F contains infinite or NAN values!");
|
---|
| 983 | }
|
---|
| 984 | alglib.ap.assert(math.isfinite(f[(int)Math.Floor((double)n/(double)2)].x), "FFTR1DInv: F contains infinite or NAN values!");
|
---|
| 985 | if( n%2!=0 )
|
---|
| 986 | {
|
---|
| 987 | alglib.ap.assert(math.isfinite(f[(int)Math.Floor((double)n/(double)2)].y), "FFTR1DInv: F contains infinite or NAN values!");
|
---|
| 988 | }
|
---|
| 989 |
|
---|
| 990 | //
|
---|
| 991 | // Special case: N=1, FFT is just identity transform.
|
---|
| 992 | // After this block we assume that N is strictly greater than 1.
|
---|
| 993 | //
|
---|
| 994 | if( n==1 )
|
---|
| 995 | {
|
---|
| 996 | a = new double[1];
|
---|
| 997 | a[0] = f[0].x;
|
---|
| 998 | return;
|
---|
| 999 | }
|
---|
| 1000 |
|
---|
| 1001 | //
|
---|
| 1002 | // inverse real FFT is reduced to the inverse real FHT,
|
---|
| 1003 | // which is reduced to the forward real FHT,
|
---|
| 1004 | // which is reduced to the forward real FFT.
|
---|
| 1005 | //
|
---|
| 1006 | // Don't worry, it is really compact and efficient reduction :)
|
---|
| 1007 | //
|
---|
| 1008 | h = new double[n];
|
---|
| 1009 | a = new double[n];
|
---|
| 1010 | h[0] = f[0].x;
|
---|
| 1011 | for(i=1; i<=(int)Math.Floor((double)n/(double)2)-1; i++)
|
---|
| 1012 | {
|
---|
| 1013 | h[i] = f[i].x-f[i].y;
|
---|
| 1014 | h[n-i] = f[i].x+f[i].y;
|
---|
| 1015 | }
|
---|
| 1016 | if( n%2==0 )
|
---|
| 1017 | {
|
---|
| 1018 | h[(int)Math.Floor((double)n/(double)2)] = f[(int)Math.Floor((double)n/(double)2)].x;
|
---|
| 1019 | }
|
---|
| 1020 | else
|
---|
| 1021 | {
|
---|
| 1022 | h[(int)Math.Floor((double)n/(double)2)] = f[(int)Math.Floor((double)n/(double)2)].x-f[(int)Math.Floor((double)n/(double)2)].y;
|
---|
| 1023 | h[(int)Math.Floor((double)n/(double)2)+1] = f[(int)Math.Floor((double)n/(double)2)].x+f[(int)Math.Floor((double)n/(double)2)].y;
|
---|
| 1024 | }
|
---|
| 1025 | fftr1d(h, n, ref fh);
|
---|
| 1026 | for(i=0; i<=n-1; i++)
|
---|
| 1027 | {
|
---|
| 1028 | a[i] = (fh[i].x-fh[i].y)/n;
|
---|
| 1029 | }
|
---|
| 1030 | }
|
---|
| 1031 |
|
---|
| 1032 |
|
---|
| 1033 | /*************************************************************************
|
---|
| 1034 | Internal subroutine. Never call it directly!
|
---|
| 1035 |
|
---|
| 1036 |
|
---|
| 1037 | -- ALGLIB --
|
---|
| 1038 | Copyright 01.06.2009 by Bochkanov Sergey
|
---|
| 1039 | *************************************************************************/
|
---|
| 1040 | public static void fftr1dinternaleven(ref double[] a,
|
---|
| 1041 | int n,
|
---|
| 1042 | ref double[] buf,
|
---|
| 1043 | ftbase.ftplan plan)
|
---|
| 1044 | {
|
---|
| 1045 | double x = 0;
|
---|
| 1046 | double y = 0;
|
---|
| 1047 | int i = 0;
|
---|
| 1048 | int n2 = 0;
|
---|
| 1049 | int idx = 0;
|
---|
| 1050 | complex hn = 0;
|
---|
| 1051 | complex hmnc = 0;
|
---|
| 1052 | complex v = 0;
|
---|
| 1053 | int i_ = 0;
|
---|
| 1054 |
|
---|
| 1055 | alglib.ap.assert(n>0 && n%2==0, "FFTR1DEvenInplace: incorrect N!");
|
---|
| 1056 |
|
---|
| 1057 | //
|
---|
| 1058 | // Special cases:
|
---|
| 1059 | // * N=2
|
---|
| 1060 | //
|
---|
| 1061 | // After this block we assume that N is strictly greater than 2
|
---|
| 1062 | //
|
---|
| 1063 | if( n==2 )
|
---|
| 1064 | {
|
---|
| 1065 | x = a[0]+a[1];
|
---|
| 1066 | y = a[0]-a[1];
|
---|
| 1067 | a[0] = x;
|
---|
| 1068 | a[1] = y;
|
---|
| 1069 | return;
|
---|
| 1070 | }
|
---|
| 1071 |
|
---|
| 1072 | //
|
---|
| 1073 | // even-size real FFT, use reduction to the complex task
|
---|
| 1074 | //
|
---|
| 1075 | n2 = n/2;
|
---|
| 1076 | for(i_=0; i_<=n-1;i_++)
|
---|
| 1077 | {
|
---|
| 1078 | buf[i_] = a[i_];
|
---|
| 1079 | }
|
---|
| 1080 | ftbase.ftbaseexecuteplan(ref buf, 0, n2, plan);
|
---|
| 1081 | a[0] = buf[0]+buf[1];
|
---|
| 1082 | for(i=1; i<=n2-1; i++)
|
---|
| 1083 | {
|
---|
| 1084 | idx = 2*(i%n2);
|
---|
| 1085 | hn.x = buf[idx+0];
|
---|
| 1086 | hn.y = buf[idx+1];
|
---|
| 1087 | idx = 2*(n2-i);
|
---|
| 1088 | hmnc.x = buf[idx+0];
|
---|
| 1089 | hmnc.y = -buf[idx+1];
|
---|
| 1090 | v.x = -Math.Sin(-(2*Math.PI*i/n));
|
---|
| 1091 | v.y = Math.Cos(-(2*Math.PI*i/n));
|
---|
| 1092 | v = hn+hmnc-v*(hn-hmnc);
|
---|
| 1093 | a[2*i+0] = 0.5*v.x;
|
---|
| 1094 | a[2*i+1] = 0.5*v.y;
|
---|
| 1095 | }
|
---|
| 1096 | a[1] = buf[0]-buf[1];
|
---|
| 1097 | }
|
---|
| 1098 |
|
---|
| 1099 |
|
---|
| 1100 | /*************************************************************************
|
---|
| 1101 | Internal subroutine. Never call it directly!
|
---|
| 1102 |
|
---|
| 1103 |
|
---|
| 1104 | -- ALGLIB --
|
---|
| 1105 | Copyright 01.06.2009 by Bochkanov Sergey
|
---|
| 1106 | *************************************************************************/
|
---|
| 1107 | public static void fftr1dinvinternaleven(ref double[] a,
|
---|
| 1108 | int n,
|
---|
| 1109 | ref double[] buf,
|
---|
| 1110 | ftbase.ftplan plan)
|
---|
| 1111 | {
|
---|
| 1112 | double x = 0;
|
---|
| 1113 | double y = 0;
|
---|
| 1114 | double t = 0;
|
---|
| 1115 | int i = 0;
|
---|
| 1116 | int n2 = 0;
|
---|
| 1117 |
|
---|
| 1118 | alglib.ap.assert(n>0 && n%2==0, "FFTR1DInvInternalEven: incorrect N!");
|
---|
| 1119 |
|
---|
| 1120 | //
|
---|
| 1121 | // Special cases:
|
---|
| 1122 | // * N=2
|
---|
| 1123 | //
|
---|
| 1124 | // After this block we assume that N is strictly greater than 2
|
---|
| 1125 | //
|
---|
| 1126 | if( n==2 )
|
---|
| 1127 | {
|
---|
| 1128 | x = 0.5*(a[0]+a[1]);
|
---|
| 1129 | y = 0.5*(a[0]-a[1]);
|
---|
| 1130 | a[0] = x;
|
---|
| 1131 | a[1] = y;
|
---|
| 1132 | return;
|
---|
| 1133 | }
|
---|
| 1134 |
|
---|
| 1135 | //
|
---|
| 1136 | // inverse real FFT is reduced to the inverse real FHT,
|
---|
| 1137 | // which is reduced to the forward real FHT,
|
---|
| 1138 | // which is reduced to the forward real FFT.
|
---|
| 1139 | //
|
---|
| 1140 | // Don't worry, it is really compact and efficient reduction :)
|
---|
| 1141 | //
|
---|
| 1142 | n2 = n/2;
|
---|
| 1143 | buf[0] = a[0];
|
---|
| 1144 | for(i=1; i<=n2-1; i++)
|
---|
| 1145 | {
|
---|
| 1146 | x = a[2*i+0];
|
---|
| 1147 | y = a[2*i+1];
|
---|
| 1148 | buf[i] = x-y;
|
---|
| 1149 | buf[n-i] = x+y;
|
---|
| 1150 | }
|
---|
| 1151 | buf[n2] = a[1];
|
---|
| 1152 | fftr1dinternaleven(ref buf, n, ref a, plan);
|
---|
| 1153 | a[0] = buf[0]/n;
|
---|
| 1154 | t = (double)1/(double)n;
|
---|
| 1155 | for(i=1; i<=n2-1; i++)
|
---|
| 1156 | {
|
---|
| 1157 | x = buf[2*i+0];
|
---|
| 1158 | y = buf[2*i+1];
|
---|
| 1159 | a[i] = t*(x-y);
|
---|
| 1160 | a[n-i] = t*(x+y);
|
---|
| 1161 | }
|
---|
| 1162 | a[n2] = buf[1]/n;
|
---|
| 1163 | }
|
---|
| 1164 |
|
---|
| 1165 |
|
---|
| 1166 | }
|
---|
| 1167 | public class conv
|
---|
| 1168 | {
|
---|
| 1169 | /*************************************************************************
|
---|
| 1170 | 1-dimensional complex convolution.
|
---|
| 1171 |
|
---|
| 1172 | For given A/B returns conv(A,B) (non-circular). Subroutine can automatically
|
---|
| 1173 | choose between three implementations: straightforward O(M*N) formula for
|
---|
| 1174 | very small N (or M), overlap-add algorithm for cases where max(M,N) is
|
---|
| 1175 | significantly larger than min(M,N), but O(M*N) algorithm is too slow, and
|
---|
| 1176 | general FFT-based formula for cases where two previois algorithms are too
|
---|
| 1177 | slow.
|
---|
| 1178 |
|
---|
| 1179 | Algorithm has max(M,N)*log(max(M,N)) complexity for any M/N.
|
---|
| 1180 |
|
---|
| 1181 | INPUT PARAMETERS
|
---|
| 1182 | A - array[0..M-1] - complex function to be transformed
|
---|
| 1183 | M - problem size
|
---|
| 1184 | B - array[0..N-1] - complex function to be transformed
|
---|
| 1185 | N - problem size
|
---|
| 1186 |
|
---|
| 1187 | OUTPUT PARAMETERS
|
---|
| 1188 | R - convolution: A*B. array[0..N+M-2].
|
---|
| 1189 |
|
---|
| 1190 | NOTE:
|
---|
| 1191 | It is assumed that A is zero at T<0, B is zero too. If one or both
|
---|
| 1192 | functions have non-zero values at negative T's, you can still use this
|
---|
| 1193 | subroutine - just shift its result correspondingly.
|
---|
| 1194 |
|
---|
| 1195 | -- ALGLIB --
|
---|
| 1196 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
| 1197 | *************************************************************************/
|
---|
| 1198 | public static void convc1d(complex[] a,
|
---|
| 1199 | int m,
|
---|
| 1200 | complex[] b,
|
---|
| 1201 | int n,
|
---|
| 1202 | ref complex[] r)
|
---|
| 1203 | {
|
---|
| 1204 | r = new complex[0];
|
---|
| 1205 |
|
---|
| 1206 | alglib.ap.assert(n>0 && m>0, "ConvC1D: incorrect N or M!");
|
---|
| 1207 |
|
---|
| 1208 | //
|
---|
| 1209 | // normalize task: make M>=N,
|
---|
| 1210 | // so A will be longer that B.
|
---|
| 1211 | //
|
---|
| 1212 | if( m<n )
|
---|
| 1213 | {
|
---|
| 1214 | convc1d(b, n, a, m, ref r);
|
---|
| 1215 | return;
|
---|
| 1216 | }
|
---|
| 1217 | convc1dx(a, m, b, n, false, -1, 0, ref r);
|
---|
| 1218 | }
|
---|
| 1219 |
|
---|
| 1220 |
|
---|
| 1221 | /*************************************************************************
|
---|
| 1222 | 1-dimensional complex non-circular deconvolution (inverse of ConvC1D()).
|
---|
| 1223 |
|
---|
| 1224 | Algorithm has M*log(M)) complexity for any M (composite or prime).
|
---|
| 1225 |
|
---|
| 1226 | INPUT PARAMETERS
|
---|
| 1227 | A - array[0..M-1] - convolved signal, A = conv(R, B)
|
---|
| 1228 | M - convolved signal length
|
---|
| 1229 | B - array[0..N-1] - response
|
---|
| 1230 | N - response length, N<=M
|
---|
| 1231 |
|
---|
| 1232 | OUTPUT PARAMETERS
|
---|
| 1233 | R - deconvolved signal. array[0..M-N].
|
---|
| 1234 |
|
---|
| 1235 | NOTE:
|
---|
| 1236 | deconvolution is unstable process and may result in division by zero
|
---|
| 1237 | (if your response function is degenerate, i.e. has zero Fourier coefficient).
|
---|
| 1238 |
|
---|
| 1239 | NOTE:
|
---|
| 1240 | It is assumed that A is zero at T<0, B is zero too. If one or both
|
---|
| 1241 | functions have non-zero values at negative T's, you can still use this
|
---|
| 1242 | subroutine - just shift its result correspondingly.
|
---|
| 1243 |
|
---|
| 1244 | -- ALGLIB --
|
---|
| 1245 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
| 1246 | *************************************************************************/
|
---|
| 1247 | public static void convc1dinv(complex[] a,
|
---|
| 1248 | int m,
|
---|
| 1249 | complex[] b,
|
---|
| 1250 | int n,
|
---|
| 1251 | ref complex[] r)
|
---|
| 1252 | {
|
---|
| 1253 | int i = 0;
|
---|
| 1254 | int p = 0;
|
---|
| 1255 | double[] buf = new double[0];
|
---|
| 1256 | double[] buf2 = new double[0];
|
---|
| 1257 | ftbase.ftplan plan = new ftbase.ftplan();
|
---|
| 1258 | complex c1 = 0;
|
---|
| 1259 | complex c2 = 0;
|
---|
| 1260 | complex c3 = 0;
|
---|
| 1261 | double t = 0;
|
---|
| 1262 |
|
---|
| 1263 | r = new complex[0];
|
---|
| 1264 |
|
---|
| 1265 | alglib.ap.assert((n>0 && m>0) && n<=m, "ConvC1DInv: incorrect N or M!");
|
---|
| 1266 | p = ftbase.ftbasefindsmooth(m);
|
---|
| 1267 | ftbase.ftbasegeneratecomplexfftplan(p, plan);
|
---|
| 1268 | buf = new double[2*p];
|
---|
| 1269 | for(i=0; i<=m-1; i++)
|
---|
| 1270 | {
|
---|
| 1271 | buf[2*i+0] = a[i].x;
|
---|
| 1272 | buf[2*i+1] = a[i].y;
|
---|
| 1273 | }
|
---|
| 1274 | for(i=m; i<=p-1; i++)
|
---|
| 1275 | {
|
---|
| 1276 | buf[2*i+0] = 0;
|
---|
| 1277 | buf[2*i+1] = 0;
|
---|
| 1278 | }
|
---|
| 1279 | buf2 = new double[2*p];
|
---|
| 1280 | for(i=0; i<=n-1; i++)
|
---|
| 1281 | {
|
---|
| 1282 | buf2[2*i+0] = b[i].x;
|
---|
| 1283 | buf2[2*i+1] = b[i].y;
|
---|
| 1284 | }
|
---|
| 1285 | for(i=n; i<=p-1; i++)
|
---|
| 1286 | {
|
---|
| 1287 | buf2[2*i+0] = 0;
|
---|
| 1288 | buf2[2*i+1] = 0;
|
---|
| 1289 | }
|
---|
| 1290 | ftbase.ftbaseexecuteplan(ref buf, 0, p, plan);
|
---|
| 1291 | ftbase.ftbaseexecuteplan(ref buf2, 0, p, plan);
|
---|
| 1292 | for(i=0; i<=p-1; i++)
|
---|
| 1293 | {
|
---|
| 1294 | c1.x = buf[2*i+0];
|
---|
| 1295 | c1.y = buf[2*i+1];
|
---|
| 1296 | c2.x = buf2[2*i+0];
|
---|
| 1297 | c2.y = buf2[2*i+1];
|
---|
| 1298 | c3 = c1/c2;
|
---|
| 1299 | buf[2*i+0] = c3.x;
|
---|
| 1300 | buf[2*i+1] = -c3.y;
|
---|
| 1301 | }
|
---|
| 1302 | ftbase.ftbaseexecuteplan(ref buf, 0, p, plan);
|
---|
| 1303 | t = (double)1/(double)p;
|
---|
| 1304 | r = new complex[m-n+1];
|
---|
| 1305 | for(i=0; i<=m-n; i++)
|
---|
| 1306 | {
|
---|
| 1307 | r[i].x = t*buf[2*i+0];
|
---|
| 1308 | r[i].y = -(t*buf[2*i+1]);
|
---|
| 1309 | }
|
---|
| 1310 | }
|
---|
| 1311 |
|
---|
| 1312 |
|
---|
| 1313 | /*************************************************************************
|
---|
| 1314 | 1-dimensional circular complex convolution.
|
---|
| 1315 |
|
---|
| 1316 | For given S/R returns conv(S,R) (circular). Algorithm has linearithmic
|
---|
| 1317 | complexity for any M/N.
|
---|
| 1318 |
|
---|
| 1319 | IMPORTANT: normal convolution is commutative, i.e. it is symmetric -
|
---|
| 1320 | conv(A,B)=conv(B,A). Cyclic convolution IS NOT. One function - S - is a
|
---|
| 1321 | signal, periodic function, and another - R - is a response, non-periodic
|
---|
| 1322 | function with limited length.
|
---|
| 1323 |
|
---|
| 1324 | INPUT PARAMETERS
|
---|
| 1325 | S - array[0..M-1] - complex periodic signal
|
---|
| 1326 | M - problem size
|
---|
| 1327 | B - array[0..N-1] - complex non-periodic response
|
---|
| 1328 | N - problem size
|
---|
| 1329 |
|
---|
| 1330 | OUTPUT PARAMETERS
|
---|
| 1331 | R - convolution: A*B. array[0..M-1].
|
---|
| 1332 |
|
---|
| 1333 | NOTE:
|
---|
| 1334 | It is assumed that B is zero at T<0. If it has non-zero values at
|
---|
| 1335 | negative T's, you can still use this subroutine - just shift its result
|
---|
| 1336 | correspondingly.
|
---|
| 1337 |
|
---|
| 1338 | -- ALGLIB --
|
---|
| 1339 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
| 1340 | *************************************************************************/
|
---|
| 1341 | public static void convc1dcircular(complex[] s,
|
---|
| 1342 | int m,
|
---|
| 1343 | complex[] r,
|
---|
| 1344 | int n,
|
---|
| 1345 | ref complex[] c)
|
---|
| 1346 | {
|
---|
| 1347 | complex[] buf = new complex[0];
|
---|
| 1348 | int i1 = 0;
|
---|
| 1349 | int i2 = 0;
|
---|
| 1350 | int j2 = 0;
|
---|
| 1351 | int i_ = 0;
|
---|
| 1352 | int i1_ = 0;
|
---|
| 1353 |
|
---|
| 1354 | c = new complex[0];
|
---|
| 1355 |
|
---|
| 1356 | alglib.ap.assert(n>0 && m>0, "ConvC1DCircular: incorrect N or M!");
|
---|
| 1357 |
|
---|
| 1358 | //
|
---|
| 1359 | // normalize task: make M>=N,
|
---|
| 1360 | // so A will be longer (at least - not shorter) that B.
|
---|
| 1361 | //
|
---|
| 1362 | if( m<n )
|
---|
| 1363 | {
|
---|
| 1364 | buf = new complex[m];
|
---|
| 1365 | for(i1=0; i1<=m-1; i1++)
|
---|
| 1366 | {
|
---|
| 1367 | buf[i1] = 0;
|
---|
| 1368 | }
|
---|
| 1369 | i1 = 0;
|
---|
| 1370 | while( i1<n )
|
---|
| 1371 | {
|
---|
| 1372 | i2 = Math.Min(i1+m-1, n-1);
|
---|
| 1373 | j2 = i2-i1;
|
---|
| 1374 | i1_ = (i1) - (0);
|
---|
| 1375 | for(i_=0; i_<=j2;i_++)
|
---|
| 1376 | {
|
---|
| 1377 | buf[i_] = buf[i_] + r[i_+i1_];
|
---|
| 1378 | }
|
---|
| 1379 | i1 = i1+m;
|
---|
| 1380 | }
|
---|
| 1381 | convc1dcircular(s, m, buf, m, ref c);
|
---|
| 1382 | return;
|
---|
| 1383 | }
|
---|
| 1384 | convc1dx(s, m, r, n, true, -1, 0, ref c);
|
---|
| 1385 | }
|
---|
| 1386 |
|
---|
| 1387 |
|
---|
| 1388 | /*************************************************************************
|
---|
| 1389 | 1-dimensional circular complex deconvolution (inverse of ConvC1DCircular()).
|
---|
| 1390 |
|
---|
| 1391 | Algorithm has M*log(M)) complexity for any M (composite or prime).
|
---|
| 1392 |
|
---|
| 1393 | INPUT PARAMETERS
|
---|
| 1394 | A - array[0..M-1] - convolved periodic signal, A = conv(R, B)
|
---|
| 1395 | M - convolved signal length
|
---|
| 1396 | B - array[0..N-1] - non-periodic response
|
---|
| 1397 | N - response length
|
---|
| 1398 |
|
---|
| 1399 | OUTPUT PARAMETERS
|
---|
| 1400 | R - deconvolved signal. array[0..M-1].
|
---|
| 1401 |
|
---|
| 1402 | NOTE:
|
---|
| 1403 | deconvolution is unstable process and may result in division by zero
|
---|
| 1404 | (if your response function is degenerate, i.e. has zero Fourier coefficient).
|
---|
| 1405 |
|
---|
| 1406 | NOTE:
|
---|
| 1407 | It is assumed that B is zero at T<0. If it has non-zero values at
|
---|
| 1408 | negative T's, you can still use this subroutine - just shift its result
|
---|
| 1409 | correspondingly.
|
---|
| 1410 |
|
---|
| 1411 | -- ALGLIB --
|
---|
| 1412 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
| 1413 | *************************************************************************/
|
---|
| 1414 | public static void convc1dcircularinv(complex[] a,
|
---|
| 1415 | int m,
|
---|
| 1416 | complex[] b,
|
---|
| 1417 | int n,
|
---|
| 1418 | ref complex[] r)
|
---|
| 1419 | {
|
---|
| 1420 | int i = 0;
|
---|
| 1421 | int i1 = 0;
|
---|
| 1422 | int i2 = 0;
|
---|
| 1423 | int j2 = 0;
|
---|
| 1424 | double[] buf = new double[0];
|
---|
| 1425 | double[] buf2 = new double[0];
|
---|
| 1426 | complex[] cbuf = new complex[0];
|
---|
| 1427 | ftbase.ftplan plan = new ftbase.ftplan();
|
---|
| 1428 | complex c1 = 0;
|
---|
| 1429 | complex c2 = 0;
|
---|
| 1430 | complex c3 = 0;
|
---|
| 1431 | double t = 0;
|
---|
| 1432 | int i_ = 0;
|
---|
| 1433 | int i1_ = 0;
|
---|
| 1434 |
|
---|
| 1435 | r = new complex[0];
|
---|
| 1436 |
|
---|
| 1437 | alglib.ap.assert(n>0 && m>0, "ConvC1DCircularInv: incorrect N or M!");
|
---|
| 1438 |
|
---|
| 1439 | //
|
---|
| 1440 | // normalize task: make M>=N,
|
---|
| 1441 | // so A will be longer (at least - not shorter) that B.
|
---|
| 1442 | //
|
---|
| 1443 | if( m<n )
|
---|
| 1444 | {
|
---|
| 1445 | cbuf = new complex[m];
|
---|
| 1446 | for(i=0; i<=m-1; i++)
|
---|
| 1447 | {
|
---|
| 1448 | cbuf[i] = 0;
|
---|
| 1449 | }
|
---|
| 1450 | i1 = 0;
|
---|
| 1451 | while( i1<n )
|
---|
| 1452 | {
|
---|
| 1453 | i2 = Math.Min(i1+m-1, n-1);
|
---|
| 1454 | j2 = i2-i1;
|
---|
| 1455 | i1_ = (i1) - (0);
|
---|
| 1456 | for(i_=0; i_<=j2;i_++)
|
---|
| 1457 | {
|
---|
| 1458 | cbuf[i_] = cbuf[i_] + b[i_+i1_];
|
---|
| 1459 | }
|
---|
| 1460 | i1 = i1+m;
|
---|
| 1461 | }
|
---|
| 1462 | convc1dcircularinv(a, m, cbuf, m, ref r);
|
---|
| 1463 | return;
|
---|
| 1464 | }
|
---|
| 1465 |
|
---|
| 1466 | //
|
---|
| 1467 | // Task is normalized
|
---|
| 1468 | //
|
---|
| 1469 | ftbase.ftbasegeneratecomplexfftplan(m, plan);
|
---|
| 1470 | buf = new double[2*m];
|
---|
| 1471 | for(i=0; i<=m-1; i++)
|
---|
| 1472 | {
|
---|
| 1473 | buf[2*i+0] = a[i].x;
|
---|
| 1474 | buf[2*i+1] = a[i].y;
|
---|
| 1475 | }
|
---|
| 1476 | buf2 = new double[2*m];
|
---|
| 1477 | for(i=0; i<=n-1; i++)
|
---|
| 1478 | {
|
---|
| 1479 | buf2[2*i+0] = b[i].x;
|
---|
| 1480 | buf2[2*i+1] = b[i].y;
|
---|
| 1481 | }
|
---|
| 1482 | for(i=n; i<=m-1; i++)
|
---|
| 1483 | {
|
---|
| 1484 | buf2[2*i+0] = 0;
|
---|
| 1485 | buf2[2*i+1] = 0;
|
---|
| 1486 | }
|
---|
| 1487 | ftbase.ftbaseexecuteplan(ref buf, 0, m, plan);
|
---|
| 1488 | ftbase.ftbaseexecuteplan(ref buf2, 0, m, plan);
|
---|
| 1489 | for(i=0; i<=m-1; i++)
|
---|
| 1490 | {
|
---|
| 1491 | c1.x = buf[2*i+0];
|
---|
| 1492 | c1.y = buf[2*i+1];
|
---|
| 1493 | c2.x = buf2[2*i+0];
|
---|
| 1494 | c2.y = buf2[2*i+1];
|
---|
| 1495 | c3 = c1/c2;
|
---|
| 1496 | buf[2*i+0] = c3.x;
|
---|
| 1497 | buf[2*i+1] = -c3.y;
|
---|
| 1498 | }
|
---|
| 1499 | ftbase.ftbaseexecuteplan(ref buf, 0, m, plan);
|
---|
| 1500 | t = (double)1/(double)m;
|
---|
| 1501 | r = new complex[m];
|
---|
| 1502 | for(i=0; i<=m-1; i++)
|
---|
| 1503 | {
|
---|
| 1504 | r[i].x = t*buf[2*i+0];
|
---|
| 1505 | r[i].y = -(t*buf[2*i+1]);
|
---|
| 1506 | }
|
---|
| 1507 | }
|
---|
| 1508 |
|
---|
| 1509 |
|
---|
| 1510 | /*************************************************************************
|
---|
| 1511 | 1-dimensional real convolution.
|
---|
| 1512 |
|
---|
| 1513 | Analogous to ConvC1D(), see ConvC1D() comments for more details.
|
---|
| 1514 |
|
---|
| 1515 | INPUT PARAMETERS
|
---|
| 1516 | A - array[0..M-1] - real function to be transformed
|
---|
| 1517 | M - problem size
|
---|
| 1518 | B - array[0..N-1] - real function to be transformed
|
---|
| 1519 | N - problem size
|
---|
| 1520 |
|
---|
| 1521 | OUTPUT PARAMETERS
|
---|
| 1522 | R - convolution: A*B. array[0..N+M-2].
|
---|
| 1523 |
|
---|
| 1524 | NOTE:
|
---|
| 1525 | It is assumed that A is zero at T<0, B is zero too. If one or both
|
---|
| 1526 | functions have non-zero values at negative T's, you can still use this
|
---|
| 1527 | subroutine - just shift its result correspondingly.
|
---|
| 1528 |
|
---|
| 1529 | -- ALGLIB --
|
---|
| 1530 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
| 1531 | *************************************************************************/
|
---|
| 1532 | public static void convr1d(double[] a,
|
---|
| 1533 | int m,
|
---|
| 1534 | double[] b,
|
---|
| 1535 | int n,
|
---|
| 1536 | ref double[] r)
|
---|
| 1537 | {
|
---|
| 1538 | r = new double[0];
|
---|
| 1539 |
|
---|
| 1540 | alglib.ap.assert(n>0 && m>0, "ConvR1D: incorrect N or M!");
|
---|
| 1541 |
|
---|
| 1542 | //
|
---|
| 1543 | // normalize task: make M>=N,
|
---|
| 1544 | // so A will be longer that B.
|
---|
| 1545 | //
|
---|
| 1546 | if( m<n )
|
---|
| 1547 | {
|
---|
| 1548 | convr1d(b, n, a, m, ref r);
|
---|
| 1549 | return;
|
---|
| 1550 | }
|
---|
| 1551 | convr1dx(a, m, b, n, false, -1, 0, ref r);
|
---|
| 1552 | }
|
---|
| 1553 |
|
---|
| 1554 |
|
---|
| 1555 | /*************************************************************************
|
---|
| 1556 | 1-dimensional real deconvolution (inverse of ConvC1D()).
|
---|
| 1557 |
|
---|
| 1558 | Algorithm has M*log(M)) complexity for any M (composite or prime).
|
---|
| 1559 |
|
---|
| 1560 | INPUT PARAMETERS
|
---|
| 1561 | A - array[0..M-1] - convolved signal, A = conv(R, B)
|
---|
| 1562 | M - convolved signal length
|
---|
| 1563 | B - array[0..N-1] - response
|
---|
| 1564 | N - response length, N<=M
|
---|
| 1565 |
|
---|
| 1566 | OUTPUT PARAMETERS
|
---|
| 1567 | R - deconvolved signal. array[0..M-N].
|
---|
| 1568 |
|
---|
| 1569 | NOTE:
|
---|
| 1570 | deconvolution is unstable process and may result in division by zero
|
---|
| 1571 | (if your response function is degenerate, i.e. has zero Fourier coefficient).
|
---|
| 1572 |
|
---|
| 1573 | NOTE:
|
---|
| 1574 | It is assumed that A is zero at T<0, B is zero too. If one or both
|
---|
| 1575 | functions have non-zero values at negative T's, you can still use this
|
---|
| 1576 | subroutine - just shift its result correspondingly.
|
---|
| 1577 |
|
---|
| 1578 | -- ALGLIB --
|
---|
| 1579 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
| 1580 | *************************************************************************/
|
---|
| 1581 | public static void convr1dinv(double[] a,
|
---|
| 1582 | int m,
|
---|
| 1583 | double[] b,
|
---|
| 1584 | int n,
|
---|
| 1585 | ref double[] r)
|
---|
| 1586 | {
|
---|
| 1587 | int i = 0;
|
---|
| 1588 | int p = 0;
|
---|
| 1589 | double[] buf = new double[0];
|
---|
| 1590 | double[] buf2 = new double[0];
|
---|
| 1591 | double[] buf3 = new double[0];
|
---|
| 1592 | ftbase.ftplan plan = new ftbase.ftplan();
|
---|
| 1593 | complex c1 = 0;
|
---|
| 1594 | complex c2 = 0;
|
---|
| 1595 | complex c3 = 0;
|
---|
| 1596 | int i_ = 0;
|
---|
| 1597 |
|
---|
| 1598 | r = new double[0];
|
---|
| 1599 |
|
---|
| 1600 | alglib.ap.assert((n>0 && m>0) && n<=m, "ConvR1DInv: incorrect N or M!");
|
---|
| 1601 | p = ftbase.ftbasefindsmootheven(m);
|
---|
| 1602 | buf = new double[p];
|
---|
| 1603 | for(i_=0; i_<=m-1;i_++)
|
---|
| 1604 | {
|
---|
| 1605 | buf[i_] = a[i_];
|
---|
| 1606 | }
|
---|
| 1607 | for(i=m; i<=p-1; i++)
|
---|
| 1608 | {
|
---|
| 1609 | buf[i] = 0;
|
---|
| 1610 | }
|
---|
| 1611 | buf2 = new double[p];
|
---|
| 1612 | for(i_=0; i_<=n-1;i_++)
|
---|
| 1613 | {
|
---|
| 1614 | buf2[i_] = b[i_];
|
---|
| 1615 | }
|
---|
| 1616 | for(i=n; i<=p-1; i++)
|
---|
| 1617 | {
|
---|
| 1618 | buf2[i] = 0;
|
---|
| 1619 | }
|
---|
| 1620 | buf3 = new double[p];
|
---|
| 1621 | ftbase.ftbasegeneratecomplexfftplan(p/2, plan);
|
---|
| 1622 | fft.fftr1dinternaleven(ref buf, p, ref buf3, plan);
|
---|
| 1623 | fft.fftr1dinternaleven(ref buf2, p, ref buf3, plan);
|
---|
| 1624 | buf[0] = buf[0]/buf2[0];
|
---|
| 1625 | buf[1] = buf[1]/buf2[1];
|
---|
| 1626 | for(i=1; i<=p/2-1; i++)
|
---|
| 1627 | {
|
---|
| 1628 | c1.x = buf[2*i+0];
|
---|
| 1629 | c1.y = buf[2*i+1];
|
---|
| 1630 | c2.x = buf2[2*i+0];
|
---|
| 1631 | c2.y = buf2[2*i+1];
|
---|
| 1632 | c3 = c1/c2;
|
---|
| 1633 | buf[2*i+0] = c3.x;
|
---|
| 1634 | buf[2*i+1] = c3.y;
|
---|
| 1635 | }
|
---|
| 1636 | fft.fftr1dinvinternaleven(ref buf, p, ref buf3, plan);
|
---|
| 1637 | r = new double[m-n+1];
|
---|
| 1638 | for(i_=0; i_<=m-n;i_++)
|
---|
| 1639 | {
|
---|
| 1640 | r[i_] = buf[i_];
|
---|
| 1641 | }
|
---|
| 1642 | }
|
---|
| 1643 |
|
---|
| 1644 |
|
---|
| 1645 | /*************************************************************************
|
---|
| 1646 | 1-dimensional circular real convolution.
|
---|
| 1647 |
|
---|
| 1648 | Analogous to ConvC1DCircular(), see ConvC1DCircular() comments for more details.
|
---|
| 1649 |
|
---|
| 1650 | INPUT PARAMETERS
|
---|
| 1651 | S - array[0..M-1] - real signal
|
---|
| 1652 | M - problem size
|
---|
| 1653 | B - array[0..N-1] - real response
|
---|
| 1654 | N - problem size
|
---|
| 1655 |
|
---|
| 1656 | OUTPUT PARAMETERS
|
---|
| 1657 | R - convolution: A*B. array[0..M-1].
|
---|
| 1658 |
|
---|
| 1659 | NOTE:
|
---|
| 1660 | It is assumed that B is zero at T<0. If it has non-zero values at
|
---|
| 1661 | negative T's, you can still use this subroutine - just shift its result
|
---|
| 1662 | correspondingly.
|
---|
| 1663 |
|
---|
| 1664 | -- ALGLIB --
|
---|
| 1665 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
| 1666 | *************************************************************************/
|
---|
| 1667 | public static void convr1dcircular(double[] s,
|
---|
| 1668 | int m,
|
---|
| 1669 | double[] r,
|
---|
| 1670 | int n,
|
---|
| 1671 | ref double[] c)
|
---|
| 1672 | {
|
---|
| 1673 | double[] buf = new double[0];
|
---|
| 1674 | int i1 = 0;
|
---|
| 1675 | int i2 = 0;
|
---|
| 1676 | int j2 = 0;
|
---|
| 1677 | int i_ = 0;
|
---|
| 1678 | int i1_ = 0;
|
---|
| 1679 |
|
---|
| 1680 | c = new double[0];
|
---|
| 1681 |
|
---|
| 1682 | alglib.ap.assert(n>0 && m>0, "ConvC1DCircular: incorrect N or M!");
|
---|
| 1683 |
|
---|
| 1684 | //
|
---|
| 1685 | // normalize task: make M>=N,
|
---|
| 1686 | // so A will be longer (at least - not shorter) that B.
|
---|
| 1687 | //
|
---|
| 1688 | if( m<n )
|
---|
| 1689 | {
|
---|
| 1690 | buf = new double[m];
|
---|
| 1691 | for(i1=0; i1<=m-1; i1++)
|
---|
| 1692 | {
|
---|
| 1693 | buf[i1] = 0;
|
---|
| 1694 | }
|
---|
| 1695 | i1 = 0;
|
---|
| 1696 | while( i1<n )
|
---|
| 1697 | {
|
---|
| 1698 | i2 = Math.Min(i1+m-1, n-1);
|
---|
| 1699 | j2 = i2-i1;
|
---|
| 1700 | i1_ = (i1) - (0);
|
---|
| 1701 | for(i_=0; i_<=j2;i_++)
|
---|
| 1702 | {
|
---|
| 1703 | buf[i_] = buf[i_] + r[i_+i1_];
|
---|
| 1704 | }
|
---|
| 1705 | i1 = i1+m;
|
---|
| 1706 | }
|
---|
| 1707 | convr1dcircular(s, m, buf, m, ref c);
|
---|
| 1708 | return;
|
---|
| 1709 | }
|
---|
| 1710 |
|
---|
| 1711 | //
|
---|
| 1712 | // reduce to usual convolution
|
---|
| 1713 | //
|
---|
| 1714 | convr1dx(s, m, r, n, true, -1, 0, ref c);
|
---|
| 1715 | }
|
---|
| 1716 |
|
---|
| 1717 |
|
---|
| 1718 | /*************************************************************************
|
---|
| 1719 | 1-dimensional complex deconvolution (inverse of ConvC1D()).
|
---|
| 1720 |
|
---|
| 1721 | Algorithm has M*log(M)) complexity for any M (composite or prime).
|
---|
| 1722 |
|
---|
| 1723 | INPUT PARAMETERS
|
---|
| 1724 | A - array[0..M-1] - convolved signal, A = conv(R, B)
|
---|
| 1725 | M - convolved signal length
|
---|
| 1726 | B - array[0..N-1] - response
|
---|
| 1727 | N - response length
|
---|
| 1728 |
|
---|
| 1729 | OUTPUT PARAMETERS
|
---|
| 1730 | R - deconvolved signal. array[0..M-N].
|
---|
| 1731 |
|
---|
| 1732 | NOTE:
|
---|
| 1733 | deconvolution is unstable process and may result in division by zero
|
---|
| 1734 | (if your response function is degenerate, i.e. has zero Fourier coefficient).
|
---|
| 1735 |
|
---|
| 1736 | NOTE:
|
---|
| 1737 | It is assumed that B is zero at T<0. If it has non-zero values at
|
---|
| 1738 | negative T's, you can still use this subroutine - just shift its result
|
---|
| 1739 | correspondingly.
|
---|
| 1740 |
|
---|
| 1741 | -- ALGLIB --
|
---|
| 1742 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
| 1743 | *************************************************************************/
|
---|
| 1744 | public static void convr1dcircularinv(double[] a,
|
---|
| 1745 | int m,
|
---|
| 1746 | double[] b,
|
---|
| 1747 | int n,
|
---|
| 1748 | ref double[] r)
|
---|
| 1749 | {
|
---|
| 1750 | int i = 0;
|
---|
| 1751 | int i1 = 0;
|
---|
| 1752 | int i2 = 0;
|
---|
| 1753 | int j2 = 0;
|
---|
| 1754 | double[] buf = new double[0];
|
---|
| 1755 | double[] buf2 = new double[0];
|
---|
| 1756 | double[] buf3 = new double[0];
|
---|
| 1757 | complex[] cbuf = new complex[0];
|
---|
| 1758 | complex[] cbuf2 = new complex[0];
|
---|
| 1759 | ftbase.ftplan plan = new ftbase.ftplan();
|
---|
| 1760 | complex c1 = 0;
|
---|
| 1761 | complex c2 = 0;
|
---|
| 1762 | complex c3 = 0;
|
---|
| 1763 | int i_ = 0;
|
---|
| 1764 | int i1_ = 0;
|
---|
| 1765 |
|
---|
| 1766 | r = new double[0];
|
---|
| 1767 |
|
---|
| 1768 | alglib.ap.assert(n>0 && m>0, "ConvR1DCircularInv: incorrect N or M!");
|
---|
| 1769 |
|
---|
| 1770 | //
|
---|
| 1771 | // normalize task: make M>=N,
|
---|
| 1772 | // so A will be longer (at least - not shorter) that B.
|
---|
| 1773 | //
|
---|
| 1774 | if( m<n )
|
---|
| 1775 | {
|
---|
| 1776 | buf = new double[m];
|
---|
| 1777 | for(i=0; i<=m-1; i++)
|
---|
| 1778 | {
|
---|
| 1779 | buf[i] = 0;
|
---|
| 1780 | }
|
---|
| 1781 | i1 = 0;
|
---|
| 1782 | while( i1<n )
|
---|
| 1783 | {
|
---|
| 1784 | i2 = Math.Min(i1+m-1, n-1);
|
---|
| 1785 | j2 = i2-i1;
|
---|
| 1786 | i1_ = (i1) - (0);
|
---|
| 1787 | for(i_=0; i_<=j2;i_++)
|
---|
| 1788 | {
|
---|
| 1789 | buf[i_] = buf[i_] + b[i_+i1_];
|
---|
| 1790 | }
|
---|
| 1791 | i1 = i1+m;
|
---|
| 1792 | }
|
---|
| 1793 | convr1dcircularinv(a, m, buf, m, ref r);
|
---|
| 1794 | return;
|
---|
| 1795 | }
|
---|
| 1796 |
|
---|
| 1797 | //
|
---|
| 1798 | // Task is normalized
|
---|
| 1799 | //
|
---|
| 1800 | if( m%2==0 )
|
---|
| 1801 | {
|
---|
| 1802 |
|
---|
| 1803 | //
|
---|
| 1804 | // size is even, use fast even-size FFT
|
---|
| 1805 | //
|
---|
| 1806 | buf = new double[m];
|
---|
| 1807 | for(i_=0; i_<=m-1;i_++)
|
---|
| 1808 | {
|
---|
| 1809 | buf[i_] = a[i_];
|
---|
| 1810 | }
|
---|
| 1811 | buf2 = new double[m];
|
---|
| 1812 | for(i_=0; i_<=n-1;i_++)
|
---|
| 1813 | {
|
---|
| 1814 | buf2[i_] = b[i_];
|
---|
| 1815 | }
|
---|
| 1816 | for(i=n; i<=m-1; i++)
|
---|
| 1817 | {
|
---|
| 1818 | buf2[i] = 0;
|
---|
| 1819 | }
|
---|
| 1820 | buf3 = new double[m];
|
---|
| 1821 | ftbase.ftbasegeneratecomplexfftplan(m/2, plan);
|
---|
| 1822 | fft.fftr1dinternaleven(ref buf, m, ref buf3, plan);
|
---|
| 1823 | fft.fftr1dinternaleven(ref buf2, m, ref buf3, plan);
|
---|
| 1824 | buf[0] = buf[0]/buf2[0];
|
---|
| 1825 | buf[1] = buf[1]/buf2[1];
|
---|
| 1826 | for(i=1; i<=m/2-1; i++)
|
---|
| 1827 | {
|
---|
| 1828 | c1.x = buf[2*i+0];
|
---|
| 1829 | c1.y = buf[2*i+1];
|
---|
| 1830 | c2.x = buf2[2*i+0];
|
---|
| 1831 | c2.y = buf2[2*i+1];
|
---|
| 1832 | c3 = c1/c2;
|
---|
| 1833 | buf[2*i+0] = c3.x;
|
---|
| 1834 | buf[2*i+1] = c3.y;
|
---|
| 1835 | }
|
---|
| 1836 | fft.fftr1dinvinternaleven(ref buf, m, ref buf3, plan);
|
---|
| 1837 | r = new double[m];
|
---|
| 1838 | for(i_=0; i_<=m-1;i_++)
|
---|
| 1839 | {
|
---|
| 1840 | r[i_] = buf[i_];
|
---|
| 1841 | }
|
---|
| 1842 | }
|
---|
| 1843 | else
|
---|
| 1844 | {
|
---|
| 1845 |
|
---|
| 1846 | //
|
---|
| 1847 | // odd-size, use general real FFT
|
---|
| 1848 | //
|
---|
| 1849 | fft.fftr1d(a, m, ref cbuf);
|
---|
| 1850 | buf2 = new double[m];
|
---|
| 1851 | for(i_=0; i_<=n-1;i_++)
|
---|
| 1852 | {
|
---|
| 1853 | buf2[i_] = b[i_];
|
---|
| 1854 | }
|
---|
| 1855 | for(i=n; i<=m-1; i++)
|
---|
| 1856 | {
|
---|
| 1857 | buf2[i] = 0;
|
---|
| 1858 | }
|
---|
| 1859 | fft.fftr1d(buf2, m, ref cbuf2);
|
---|
| 1860 | for(i=0; i<=(int)Math.Floor((double)m/(double)2); i++)
|
---|
| 1861 | {
|
---|
| 1862 | cbuf[i] = cbuf[i]/cbuf2[i];
|
---|
| 1863 | }
|
---|
| 1864 | fft.fftr1dinv(cbuf, m, ref r);
|
---|
| 1865 | }
|
---|
| 1866 | }
|
---|
| 1867 |
|
---|
| 1868 |
|
---|
| 1869 | /*************************************************************************
|
---|
| 1870 | 1-dimensional complex convolution.
|
---|
| 1871 |
|
---|
| 1872 | Extended subroutine which allows to choose convolution algorithm.
|
---|
| 1873 | Intended for internal use, ALGLIB users should call ConvC1D()/ConvC1DCircular().
|
---|
| 1874 |
|
---|
| 1875 | INPUT PARAMETERS
|
---|
| 1876 | A - array[0..M-1] - complex function to be transformed
|
---|
| 1877 | M - problem size
|
---|
| 1878 | B - array[0..N-1] - complex function to be transformed
|
---|
| 1879 | N - problem size, N<=M
|
---|
| 1880 | Alg - algorithm type:
|
---|
| 1881 | *-2 auto-select Q for overlap-add
|
---|
| 1882 | *-1 auto-select algorithm and parameters
|
---|
| 1883 | * 0 straightforward formula for small N's
|
---|
| 1884 | * 1 general FFT-based code
|
---|
| 1885 | * 2 overlap-add with length Q
|
---|
| 1886 | Q - length for overlap-add
|
---|
| 1887 |
|
---|
| 1888 | OUTPUT PARAMETERS
|
---|
| 1889 | R - convolution: A*B. array[0..N+M-1].
|
---|
| 1890 |
|
---|
| 1891 | -- ALGLIB --
|
---|
| 1892 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
| 1893 | *************************************************************************/
|
---|
| 1894 | public static void convc1dx(complex[] a,
|
---|
| 1895 | int m,
|
---|
| 1896 | complex[] b,
|
---|
| 1897 | int n,
|
---|
| 1898 | bool circular,
|
---|
| 1899 | int alg,
|
---|
| 1900 | int q,
|
---|
| 1901 | ref complex[] r)
|
---|
| 1902 | {
|
---|
| 1903 | int i = 0;
|
---|
| 1904 | int j = 0;
|
---|
| 1905 | int p = 0;
|
---|
| 1906 | int ptotal = 0;
|
---|
| 1907 | int i1 = 0;
|
---|
| 1908 | int i2 = 0;
|
---|
| 1909 | int j1 = 0;
|
---|
| 1910 | int j2 = 0;
|
---|
| 1911 | complex[] bbuf = new complex[0];
|
---|
| 1912 | complex v = 0;
|
---|
| 1913 | double ax = 0;
|
---|
| 1914 | double ay = 0;
|
---|
| 1915 | double bx = 0;
|
---|
| 1916 | double by = 0;
|
---|
| 1917 | double t = 0;
|
---|
| 1918 | double tx = 0;
|
---|
| 1919 | double ty = 0;
|
---|
| 1920 | double flopcand = 0;
|
---|
| 1921 | double flopbest = 0;
|
---|
| 1922 | int algbest = 0;
|
---|
| 1923 | ftbase.ftplan plan = new ftbase.ftplan();
|
---|
| 1924 | double[] buf = new double[0];
|
---|
| 1925 | double[] buf2 = new double[0];
|
---|
| 1926 | int i_ = 0;
|
---|
| 1927 | int i1_ = 0;
|
---|
| 1928 |
|
---|
| 1929 | r = new complex[0];
|
---|
| 1930 |
|
---|
| 1931 | alglib.ap.assert(n>0 && m>0, "ConvC1DX: incorrect N or M!");
|
---|
| 1932 | alglib.ap.assert(n<=m, "ConvC1DX: N<M assumption is false!");
|
---|
| 1933 |
|
---|
| 1934 | //
|
---|
| 1935 | // Auto-select
|
---|
| 1936 | //
|
---|
| 1937 | if( alg==-1 || alg==-2 )
|
---|
| 1938 | {
|
---|
| 1939 |
|
---|
| 1940 | //
|
---|
| 1941 | // Initial candidate: straightforward implementation.
|
---|
| 1942 | //
|
---|
| 1943 | // If we want to use auto-fitted overlap-add,
|
---|
| 1944 | // flop count is initialized by large real number - to force
|
---|
| 1945 | // another algorithm selection
|
---|
| 1946 | //
|
---|
| 1947 | algbest = 0;
|
---|
| 1948 | if( alg==-1 )
|
---|
| 1949 | {
|
---|
| 1950 | flopbest = 2*m*n;
|
---|
| 1951 | }
|
---|
| 1952 | else
|
---|
| 1953 | {
|
---|
| 1954 | flopbest = math.maxrealnumber;
|
---|
| 1955 | }
|
---|
| 1956 |
|
---|
| 1957 | //
|
---|
| 1958 | // Another candidate - generic FFT code
|
---|
| 1959 | //
|
---|
| 1960 | if( alg==-1 )
|
---|
| 1961 | {
|
---|
| 1962 | if( circular && ftbase.ftbaseissmooth(m) )
|
---|
| 1963 | {
|
---|
| 1964 |
|
---|
| 1965 | //
|
---|
| 1966 | // special code for circular convolution of a sequence with a smooth length
|
---|
| 1967 | //
|
---|
| 1968 | flopcand = 3*ftbase.ftbasegetflopestimate(m)+6*m;
|
---|
| 1969 | if( (double)(flopcand)<(double)(flopbest) )
|
---|
| 1970 | {
|
---|
| 1971 | algbest = 1;
|
---|
| 1972 | flopbest = flopcand;
|
---|
| 1973 | }
|
---|
| 1974 | }
|
---|
| 1975 | else
|
---|
| 1976 | {
|
---|
| 1977 |
|
---|
| 1978 | //
|
---|
| 1979 | // general cyclic/non-cyclic convolution
|
---|
| 1980 | //
|
---|
| 1981 | p = ftbase.ftbasefindsmooth(m+n-1);
|
---|
| 1982 | flopcand = 3*ftbase.ftbasegetflopestimate(p)+6*p;
|
---|
| 1983 | if( (double)(flopcand)<(double)(flopbest) )
|
---|
| 1984 | {
|
---|
| 1985 | algbest = 1;
|
---|
| 1986 | flopbest = flopcand;
|
---|
| 1987 | }
|
---|
| 1988 | }
|
---|
| 1989 | }
|
---|
| 1990 |
|
---|
| 1991 | //
|
---|
| 1992 | // Another candidate - overlap-add
|
---|
| 1993 | //
|
---|
| 1994 | q = 1;
|
---|
| 1995 | ptotal = 1;
|
---|
| 1996 | while( ptotal<n )
|
---|
| 1997 | {
|
---|
| 1998 | ptotal = ptotal*2;
|
---|
| 1999 | }
|
---|
| 2000 | while( ptotal<=m+n-1 )
|
---|
| 2001 | {
|
---|
| 2002 | p = ptotal-n+1;
|
---|
| 2003 | flopcand = (int)Math.Ceiling((double)m/(double)p)*(2*ftbase.ftbasegetflopestimate(ptotal)+8*ptotal);
|
---|
| 2004 | if( (double)(flopcand)<(double)(flopbest) )
|
---|
| 2005 | {
|
---|
| 2006 | flopbest = flopcand;
|
---|
| 2007 | algbest = 2;
|
---|
| 2008 | q = p;
|
---|
| 2009 | }
|
---|
| 2010 | ptotal = ptotal*2;
|
---|
| 2011 | }
|
---|
| 2012 | alg = algbest;
|
---|
| 2013 | convc1dx(a, m, b, n, circular, alg, q, ref r);
|
---|
| 2014 | return;
|
---|
| 2015 | }
|
---|
| 2016 |
|
---|
| 2017 | //
|
---|
| 2018 | // straightforward formula for
|
---|
| 2019 | // circular and non-circular convolutions.
|
---|
| 2020 | //
|
---|
| 2021 | // Very simple code, no further comments needed.
|
---|
| 2022 | //
|
---|
| 2023 | if( alg==0 )
|
---|
| 2024 | {
|
---|
| 2025 |
|
---|
| 2026 | //
|
---|
| 2027 | // Special case: N=1
|
---|
| 2028 | //
|
---|
| 2029 | if( n==1 )
|
---|
| 2030 | {
|
---|
| 2031 | r = new complex[m];
|
---|
| 2032 | v = b[0];
|
---|
| 2033 | for(i_=0; i_<=m-1;i_++)
|
---|
| 2034 | {
|
---|
| 2035 | r[i_] = v*a[i_];
|
---|
| 2036 | }
|
---|
| 2037 | return;
|
---|
| 2038 | }
|
---|
| 2039 |
|
---|
| 2040 | //
|
---|
| 2041 | // use straightforward formula
|
---|
| 2042 | //
|
---|
| 2043 | if( circular )
|
---|
| 2044 | {
|
---|
| 2045 |
|
---|
| 2046 | //
|
---|
| 2047 | // circular convolution
|
---|
| 2048 | //
|
---|
| 2049 | r = new complex[m];
|
---|
| 2050 | v = b[0];
|
---|
| 2051 | for(i_=0; i_<=m-1;i_++)
|
---|
| 2052 | {
|
---|
| 2053 | r[i_] = v*a[i_];
|
---|
| 2054 | }
|
---|
| 2055 | for(i=1; i<=n-1; i++)
|
---|
| 2056 | {
|
---|
| 2057 | v = b[i];
|
---|
| 2058 | i1 = 0;
|
---|
| 2059 | i2 = i-1;
|
---|
| 2060 | j1 = m-i;
|
---|
| 2061 | j2 = m-1;
|
---|
| 2062 | i1_ = (j1) - (i1);
|
---|
| 2063 | for(i_=i1; i_<=i2;i_++)
|
---|
| 2064 | {
|
---|
| 2065 | r[i_] = r[i_] + v*a[i_+i1_];
|
---|
| 2066 | }
|
---|
| 2067 | i1 = i;
|
---|
| 2068 | i2 = m-1;
|
---|
| 2069 | j1 = 0;
|
---|
| 2070 | j2 = m-i-1;
|
---|
| 2071 | i1_ = (j1) - (i1);
|
---|
| 2072 | for(i_=i1; i_<=i2;i_++)
|
---|
| 2073 | {
|
---|
| 2074 | r[i_] = r[i_] + v*a[i_+i1_];
|
---|
| 2075 | }
|
---|
| 2076 | }
|
---|
| 2077 | }
|
---|
| 2078 | else
|
---|
| 2079 | {
|
---|
| 2080 |
|
---|
| 2081 | //
|
---|
| 2082 | // non-circular convolution
|
---|
| 2083 | //
|
---|
| 2084 | r = new complex[m+n-1];
|
---|
| 2085 | for(i=0; i<=m+n-2; i++)
|
---|
| 2086 | {
|
---|
| 2087 | r[i] = 0;
|
---|
| 2088 | }
|
---|
| 2089 | for(i=0; i<=n-1; i++)
|
---|
| 2090 | {
|
---|
| 2091 | v = b[i];
|
---|
| 2092 | i1_ = (0) - (i);
|
---|
| 2093 | for(i_=i; i_<=i+m-1;i_++)
|
---|
| 2094 | {
|
---|
| 2095 | r[i_] = r[i_] + v*a[i_+i1_];
|
---|
| 2096 | }
|
---|
| 2097 | }
|
---|
| 2098 | }
|
---|
| 2099 | return;
|
---|
| 2100 | }
|
---|
| 2101 |
|
---|
| 2102 | //
|
---|
| 2103 | // general FFT-based code for
|
---|
| 2104 | // circular and non-circular convolutions.
|
---|
| 2105 | //
|
---|
| 2106 | // First, if convolution is circular, we test whether M is smooth or not.
|
---|
| 2107 | // If it is smooth, we just use M-length FFT to calculate convolution.
|
---|
| 2108 | // If it is not, we calculate non-circular convolution and wrap it arount.
|
---|
| 2109 | //
|
---|
| 2110 | // IF convolution is non-circular, we use zero-padding + FFT.
|
---|
| 2111 | //
|
---|
| 2112 | if( alg==1 )
|
---|
| 2113 | {
|
---|
| 2114 | if( circular && ftbase.ftbaseissmooth(m) )
|
---|
| 2115 | {
|
---|
| 2116 |
|
---|
| 2117 | //
|
---|
| 2118 | // special code for circular convolution with smooth M
|
---|
| 2119 | //
|
---|
| 2120 | ftbase.ftbasegeneratecomplexfftplan(m, plan);
|
---|
| 2121 | buf = new double[2*m];
|
---|
| 2122 | for(i=0; i<=m-1; i++)
|
---|
| 2123 | {
|
---|
| 2124 | buf[2*i+0] = a[i].x;
|
---|
| 2125 | buf[2*i+1] = a[i].y;
|
---|
| 2126 | }
|
---|
| 2127 | buf2 = new double[2*m];
|
---|
| 2128 | for(i=0; i<=n-1; i++)
|
---|
| 2129 | {
|
---|
| 2130 | buf2[2*i+0] = b[i].x;
|
---|
| 2131 | buf2[2*i+1] = b[i].y;
|
---|
| 2132 | }
|
---|
| 2133 | for(i=n; i<=m-1; i++)
|
---|
| 2134 | {
|
---|
| 2135 | buf2[2*i+0] = 0;
|
---|
| 2136 | buf2[2*i+1] = 0;
|
---|
| 2137 | }
|
---|
| 2138 | ftbase.ftbaseexecuteplan(ref buf, 0, m, plan);
|
---|
| 2139 | ftbase.ftbaseexecuteplan(ref buf2, 0, m, plan);
|
---|
| 2140 | for(i=0; i<=m-1; i++)
|
---|
| 2141 | {
|
---|
| 2142 | ax = buf[2*i+0];
|
---|
| 2143 | ay = buf[2*i+1];
|
---|
| 2144 | bx = buf2[2*i+0];
|
---|
| 2145 | by = buf2[2*i+1];
|
---|
| 2146 | tx = ax*bx-ay*by;
|
---|
| 2147 | ty = ax*by+ay*bx;
|
---|
| 2148 | buf[2*i+0] = tx;
|
---|
| 2149 | buf[2*i+1] = -ty;
|
---|
| 2150 | }
|
---|
| 2151 | ftbase.ftbaseexecuteplan(ref buf, 0, m, plan);
|
---|
| 2152 | t = (double)1/(double)m;
|
---|
| 2153 | r = new complex[m];
|
---|
| 2154 | for(i=0; i<=m-1; i++)
|
---|
| 2155 | {
|
---|
| 2156 | r[i].x = t*buf[2*i+0];
|
---|
| 2157 | r[i].y = -(t*buf[2*i+1]);
|
---|
| 2158 | }
|
---|
| 2159 | }
|
---|
| 2160 | else
|
---|
| 2161 | {
|
---|
| 2162 |
|
---|
| 2163 | //
|
---|
| 2164 | // M is non-smooth, general code (circular/non-circular):
|
---|
| 2165 | // * first part is the same for circular and non-circular
|
---|
| 2166 | // convolutions. zero padding, FFTs, inverse FFTs
|
---|
| 2167 | // * second part differs:
|
---|
| 2168 | // * for non-circular convolution we just copy array
|
---|
| 2169 | // * for circular convolution we add array tail to its head
|
---|
| 2170 | //
|
---|
| 2171 | p = ftbase.ftbasefindsmooth(m+n-1);
|
---|
| 2172 | ftbase.ftbasegeneratecomplexfftplan(p, plan);
|
---|
| 2173 | buf = new double[2*p];
|
---|
| 2174 | for(i=0; i<=m-1; i++)
|
---|
| 2175 | {
|
---|
| 2176 | buf[2*i+0] = a[i].x;
|
---|
| 2177 | buf[2*i+1] = a[i].y;
|
---|
| 2178 | }
|
---|
| 2179 | for(i=m; i<=p-1; i++)
|
---|
| 2180 | {
|
---|
| 2181 | buf[2*i+0] = 0;
|
---|
| 2182 | buf[2*i+1] = 0;
|
---|
| 2183 | }
|
---|
| 2184 | buf2 = new double[2*p];
|
---|
| 2185 | for(i=0; i<=n-1; i++)
|
---|
| 2186 | {
|
---|
| 2187 | buf2[2*i+0] = b[i].x;
|
---|
| 2188 | buf2[2*i+1] = b[i].y;
|
---|
| 2189 | }
|
---|
| 2190 | for(i=n; i<=p-1; i++)
|
---|
| 2191 | {
|
---|
| 2192 | buf2[2*i+0] = 0;
|
---|
| 2193 | buf2[2*i+1] = 0;
|
---|
| 2194 | }
|
---|
| 2195 | ftbase.ftbaseexecuteplan(ref buf, 0, p, plan);
|
---|
| 2196 | ftbase.ftbaseexecuteplan(ref buf2, 0, p, plan);
|
---|
| 2197 | for(i=0; i<=p-1; i++)
|
---|
| 2198 | {
|
---|
| 2199 | ax = buf[2*i+0];
|
---|
| 2200 | ay = buf[2*i+1];
|
---|
| 2201 | bx = buf2[2*i+0];
|
---|
| 2202 | by = buf2[2*i+1];
|
---|
| 2203 | tx = ax*bx-ay*by;
|
---|
| 2204 | ty = ax*by+ay*bx;
|
---|
| 2205 | buf[2*i+0] = tx;
|
---|
| 2206 | buf[2*i+1] = -ty;
|
---|
| 2207 | }
|
---|
| 2208 | ftbase.ftbaseexecuteplan(ref buf, 0, p, plan);
|
---|
| 2209 | t = (double)1/(double)p;
|
---|
| 2210 | if( circular )
|
---|
| 2211 | {
|
---|
| 2212 |
|
---|
| 2213 | //
|
---|
| 2214 | // circular, add tail to head
|
---|
| 2215 | //
|
---|
| 2216 | r = new complex[m];
|
---|
| 2217 | for(i=0; i<=m-1; i++)
|
---|
| 2218 | {
|
---|
| 2219 | r[i].x = t*buf[2*i+0];
|
---|
| 2220 | r[i].y = -(t*buf[2*i+1]);
|
---|
| 2221 | }
|
---|
| 2222 | for(i=m; i<=m+n-2; i++)
|
---|
| 2223 | {
|
---|
| 2224 | r[i-m].x = r[i-m].x+t*buf[2*i+0];
|
---|
| 2225 | r[i-m].y = r[i-m].y-t*buf[2*i+1];
|
---|
| 2226 | }
|
---|
| 2227 | }
|
---|
| 2228 | else
|
---|
| 2229 | {
|
---|
| 2230 |
|
---|
| 2231 | //
|
---|
| 2232 | // non-circular, just copy
|
---|
| 2233 | //
|
---|
| 2234 | r = new complex[m+n-1];
|
---|
| 2235 | for(i=0; i<=m+n-2; i++)
|
---|
| 2236 | {
|
---|
| 2237 | r[i].x = t*buf[2*i+0];
|
---|
| 2238 | r[i].y = -(t*buf[2*i+1]);
|
---|
| 2239 | }
|
---|
| 2240 | }
|
---|
| 2241 | }
|
---|
| 2242 | return;
|
---|
| 2243 | }
|
---|
| 2244 |
|
---|
| 2245 | //
|
---|
| 2246 | // overlap-add method for
|
---|
| 2247 | // circular and non-circular convolutions.
|
---|
| 2248 | //
|
---|
| 2249 | // First part of code (separate FFTs of input blocks) is the same
|
---|
| 2250 | // for all types of convolution. Second part (overlapping outputs)
|
---|
| 2251 | // differs for different types of convolution. We just copy output
|
---|
| 2252 | // when convolution is non-circular. We wrap it around, if it is
|
---|
| 2253 | // circular.
|
---|
| 2254 | //
|
---|
| 2255 | if( alg==2 )
|
---|
| 2256 | {
|
---|
| 2257 | buf = new double[2*(q+n-1)];
|
---|
| 2258 |
|
---|
| 2259 | //
|
---|
| 2260 | // prepare R
|
---|
| 2261 | //
|
---|
| 2262 | if( circular )
|
---|
| 2263 | {
|
---|
| 2264 | r = new complex[m];
|
---|
| 2265 | for(i=0; i<=m-1; i++)
|
---|
| 2266 | {
|
---|
| 2267 | r[i] = 0;
|
---|
| 2268 | }
|
---|
| 2269 | }
|
---|
| 2270 | else
|
---|
| 2271 | {
|
---|
| 2272 | r = new complex[m+n-1];
|
---|
| 2273 | for(i=0; i<=m+n-2; i++)
|
---|
| 2274 | {
|
---|
| 2275 | r[i] = 0;
|
---|
| 2276 | }
|
---|
| 2277 | }
|
---|
| 2278 |
|
---|
| 2279 | //
|
---|
| 2280 | // pre-calculated FFT(B)
|
---|
| 2281 | //
|
---|
| 2282 | bbuf = new complex[q+n-1];
|
---|
| 2283 | for(i_=0; i_<=n-1;i_++)
|
---|
| 2284 | {
|
---|
| 2285 | bbuf[i_] = b[i_];
|
---|
| 2286 | }
|
---|
| 2287 | for(j=n; j<=q+n-2; j++)
|
---|
| 2288 | {
|
---|
| 2289 | bbuf[j] = 0;
|
---|
| 2290 | }
|
---|
| 2291 | fft.fftc1d(ref bbuf, q+n-1);
|
---|
| 2292 |
|
---|
| 2293 | //
|
---|
| 2294 | // prepare FFT plan for chunks of A
|
---|
| 2295 | //
|
---|
| 2296 | ftbase.ftbasegeneratecomplexfftplan(q+n-1, plan);
|
---|
| 2297 |
|
---|
| 2298 | //
|
---|
| 2299 | // main overlap-add cycle
|
---|
| 2300 | //
|
---|
| 2301 | i = 0;
|
---|
| 2302 | while( i<=m-1 )
|
---|
| 2303 | {
|
---|
| 2304 | p = Math.Min(q, m-i);
|
---|
| 2305 | for(j=0; j<=p-1; j++)
|
---|
| 2306 | {
|
---|
| 2307 | buf[2*j+0] = a[i+j].x;
|
---|
| 2308 | buf[2*j+1] = a[i+j].y;
|
---|
| 2309 | }
|
---|
| 2310 | for(j=p; j<=q+n-2; j++)
|
---|
| 2311 | {
|
---|
| 2312 | buf[2*j+0] = 0;
|
---|
| 2313 | buf[2*j+1] = 0;
|
---|
| 2314 | }
|
---|
| 2315 | ftbase.ftbaseexecuteplan(ref buf, 0, q+n-1, plan);
|
---|
| 2316 | for(j=0; j<=q+n-2; j++)
|
---|
| 2317 | {
|
---|
| 2318 | ax = buf[2*j+0];
|
---|
| 2319 | ay = buf[2*j+1];
|
---|
| 2320 | bx = bbuf[j].x;
|
---|
| 2321 | by = bbuf[j].y;
|
---|
| 2322 | tx = ax*bx-ay*by;
|
---|
| 2323 | ty = ax*by+ay*bx;
|
---|
| 2324 | buf[2*j+0] = tx;
|
---|
| 2325 | buf[2*j+1] = -ty;
|
---|
| 2326 | }
|
---|
| 2327 | ftbase.ftbaseexecuteplan(ref buf, 0, q+n-1, plan);
|
---|
| 2328 | t = (double)1/(double)(q+n-1);
|
---|
| 2329 | if( circular )
|
---|
| 2330 | {
|
---|
| 2331 | j1 = Math.Min(i+p+n-2, m-1)-i;
|
---|
| 2332 | j2 = j1+1;
|
---|
| 2333 | }
|
---|
| 2334 | else
|
---|
| 2335 | {
|
---|
| 2336 | j1 = p+n-2;
|
---|
| 2337 | j2 = j1+1;
|
---|
| 2338 | }
|
---|
| 2339 | for(j=0; j<=j1; j++)
|
---|
| 2340 | {
|
---|
| 2341 | r[i+j].x = r[i+j].x+buf[2*j+0]*t;
|
---|
| 2342 | r[i+j].y = r[i+j].y-buf[2*j+1]*t;
|
---|
| 2343 | }
|
---|
| 2344 | for(j=j2; j<=p+n-2; j++)
|
---|
| 2345 | {
|
---|
| 2346 | r[j-j2].x = r[j-j2].x+buf[2*j+0]*t;
|
---|
| 2347 | r[j-j2].y = r[j-j2].y-buf[2*j+1]*t;
|
---|
| 2348 | }
|
---|
| 2349 | i = i+p;
|
---|
| 2350 | }
|
---|
| 2351 | return;
|
---|
| 2352 | }
|
---|
| 2353 | }
|
---|
| 2354 |
|
---|
| 2355 |
|
---|
| 2356 | /*************************************************************************
|
---|
| 2357 | 1-dimensional real convolution.
|
---|
| 2358 |
|
---|
| 2359 | Extended subroutine which allows to choose convolution algorithm.
|
---|
| 2360 | Intended for internal use, ALGLIB users should call ConvR1D().
|
---|
| 2361 |
|
---|
| 2362 | INPUT PARAMETERS
|
---|
| 2363 | A - array[0..M-1] - complex function to be transformed
|
---|
| 2364 | M - problem size
|
---|
| 2365 | B - array[0..N-1] - complex function to be transformed
|
---|
| 2366 | N - problem size, N<=M
|
---|
| 2367 | Alg - algorithm type:
|
---|
| 2368 | *-2 auto-select Q for overlap-add
|
---|
| 2369 | *-1 auto-select algorithm and parameters
|
---|
| 2370 | * 0 straightforward formula for small N's
|
---|
| 2371 | * 1 general FFT-based code
|
---|
| 2372 | * 2 overlap-add with length Q
|
---|
| 2373 | Q - length for overlap-add
|
---|
| 2374 |
|
---|
| 2375 | OUTPUT PARAMETERS
|
---|
| 2376 | R - convolution: A*B. array[0..N+M-1].
|
---|
| 2377 |
|
---|
| 2378 | -- ALGLIB --
|
---|
| 2379 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
| 2380 | *************************************************************************/
|
---|
| 2381 | public static void convr1dx(double[] a,
|
---|
| 2382 | int m,
|
---|
| 2383 | double[] b,
|
---|
| 2384 | int n,
|
---|
| 2385 | bool circular,
|
---|
| 2386 | int alg,
|
---|
| 2387 | int q,
|
---|
| 2388 | ref double[] r)
|
---|
| 2389 | {
|
---|
| 2390 | double v = 0;
|
---|
| 2391 | int i = 0;
|
---|
| 2392 | int j = 0;
|
---|
| 2393 | int p = 0;
|
---|
| 2394 | int ptotal = 0;
|
---|
| 2395 | int i1 = 0;
|
---|
| 2396 | int i2 = 0;
|
---|
| 2397 | int j1 = 0;
|
---|
| 2398 | int j2 = 0;
|
---|
| 2399 | double ax = 0;
|
---|
| 2400 | double ay = 0;
|
---|
| 2401 | double bx = 0;
|
---|
| 2402 | double by = 0;
|
---|
| 2403 | double tx = 0;
|
---|
| 2404 | double ty = 0;
|
---|
| 2405 | double flopcand = 0;
|
---|
| 2406 | double flopbest = 0;
|
---|
| 2407 | int algbest = 0;
|
---|
| 2408 | ftbase.ftplan plan = new ftbase.ftplan();
|
---|
| 2409 | double[] buf = new double[0];
|
---|
| 2410 | double[] buf2 = new double[0];
|
---|
| 2411 | double[] buf3 = new double[0];
|
---|
| 2412 | int i_ = 0;
|
---|
| 2413 | int i1_ = 0;
|
---|
| 2414 |
|
---|
| 2415 | r = new double[0];
|
---|
| 2416 |
|
---|
| 2417 | alglib.ap.assert(n>0 && m>0, "ConvC1DX: incorrect N or M!");
|
---|
| 2418 | alglib.ap.assert(n<=m, "ConvC1DX: N<M assumption is false!");
|
---|
| 2419 |
|
---|
| 2420 | //
|
---|
| 2421 | // handle special cases
|
---|
| 2422 | //
|
---|
| 2423 | if( Math.Min(m, n)<=2 )
|
---|
| 2424 | {
|
---|
| 2425 | alg = 0;
|
---|
| 2426 | }
|
---|
| 2427 |
|
---|
| 2428 | //
|
---|
| 2429 | // Auto-select
|
---|
| 2430 | //
|
---|
| 2431 | if( alg<0 )
|
---|
| 2432 | {
|
---|
| 2433 |
|
---|
| 2434 | //
|
---|
| 2435 | // Initial candidate: straightforward implementation.
|
---|
| 2436 | //
|
---|
| 2437 | // If we want to use auto-fitted overlap-add,
|
---|
| 2438 | // flop count is initialized by large real number - to force
|
---|
| 2439 | // another algorithm selection
|
---|
| 2440 | //
|
---|
| 2441 | algbest = 0;
|
---|
| 2442 | if( alg==-1 )
|
---|
| 2443 | {
|
---|
| 2444 | flopbest = 0.15*m*n;
|
---|
| 2445 | }
|
---|
| 2446 | else
|
---|
| 2447 | {
|
---|
| 2448 | flopbest = math.maxrealnumber;
|
---|
| 2449 | }
|
---|
| 2450 |
|
---|
| 2451 | //
|
---|
| 2452 | // Another candidate - generic FFT code
|
---|
| 2453 | //
|
---|
| 2454 | if( alg==-1 )
|
---|
| 2455 | {
|
---|
| 2456 | if( (circular && ftbase.ftbaseissmooth(m)) && m%2==0 )
|
---|
| 2457 | {
|
---|
| 2458 |
|
---|
| 2459 | //
|
---|
| 2460 | // special code for circular convolution of a sequence with a smooth length
|
---|
| 2461 | //
|
---|
| 2462 | flopcand = 3*ftbase.ftbasegetflopestimate(m/2)+(double)(6*m)/(double)2;
|
---|
| 2463 | if( (double)(flopcand)<(double)(flopbest) )
|
---|
| 2464 | {
|
---|
| 2465 | algbest = 1;
|
---|
| 2466 | flopbest = flopcand;
|
---|
| 2467 | }
|
---|
| 2468 | }
|
---|
| 2469 | else
|
---|
| 2470 | {
|
---|
| 2471 |
|
---|
| 2472 | //
|
---|
| 2473 | // general cyclic/non-cyclic convolution
|
---|
| 2474 | //
|
---|
| 2475 | p = ftbase.ftbasefindsmootheven(m+n-1);
|
---|
| 2476 | flopcand = 3*ftbase.ftbasegetflopestimate(p/2)+(double)(6*p)/(double)2;
|
---|
| 2477 | if( (double)(flopcand)<(double)(flopbest) )
|
---|
| 2478 | {
|
---|
| 2479 | algbest = 1;
|
---|
| 2480 | flopbest = flopcand;
|
---|
| 2481 | }
|
---|
| 2482 | }
|
---|
| 2483 | }
|
---|
| 2484 |
|
---|
| 2485 | //
|
---|
| 2486 | // Another candidate - overlap-add
|
---|
| 2487 | //
|
---|
| 2488 | q = 1;
|
---|
| 2489 | ptotal = 1;
|
---|
| 2490 | while( ptotal<n )
|
---|
| 2491 | {
|
---|
| 2492 | ptotal = ptotal*2;
|
---|
| 2493 | }
|
---|
| 2494 | while( ptotal<=m+n-1 )
|
---|
| 2495 | {
|
---|
| 2496 | p = ptotal-n+1;
|
---|
| 2497 | flopcand = (int)Math.Ceiling((double)m/(double)p)*(2*ftbase.ftbasegetflopestimate(ptotal/2)+1*(ptotal/2));
|
---|
| 2498 | if( (double)(flopcand)<(double)(flopbest) )
|
---|
| 2499 | {
|
---|
| 2500 | flopbest = flopcand;
|
---|
| 2501 | algbest = 2;
|
---|
| 2502 | q = p;
|
---|
| 2503 | }
|
---|
| 2504 | ptotal = ptotal*2;
|
---|
| 2505 | }
|
---|
| 2506 | alg = algbest;
|
---|
| 2507 | convr1dx(a, m, b, n, circular, alg, q, ref r);
|
---|
| 2508 | return;
|
---|
| 2509 | }
|
---|
| 2510 |
|
---|
| 2511 | //
|
---|
| 2512 | // straightforward formula for
|
---|
| 2513 | // circular and non-circular convolutions.
|
---|
| 2514 | //
|
---|
| 2515 | // Very simple code, no further comments needed.
|
---|
| 2516 | //
|
---|
| 2517 | if( alg==0 )
|
---|
| 2518 | {
|
---|
| 2519 |
|
---|
| 2520 | //
|
---|
| 2521 | // Special case: N=1
|
---|
| 2522 | //
|
---|
| 2523 | if( n==1 )
|
---|
| 2524 | {
|
---|
| 2525 | r = new double[m];
|
---|
| 2526 | v = b[0];
|
---|
| 2527 | for(i_=0; i_<=m-1;i_++)
|
---|
| 2528 | {
|
---|
| 2529 | r[i_] = v*a[i_];
|
---|
| 2530 | }
|
---|
| 2531 | return;
|
---|
| 2532 | }
|
---|
| 2533 |
|
---|
| 2534 | //
|
---|
| 2535 | // use straightforward formula
|
---|
| 2536 | //
|
---|
| 2537 | if( circular )
|
---|
| 2538 | {
|
---|
| 2539 |
|
---|
| 2540 | //
|
---|
| 2541 | // circular convolution
|
---|
| 2542 | //
|
---|
| 2543 | r = new double[m];
|
---|
| 2544 | v = b[0];
|
---|
| 2545 | for(i_=0; i_<=m-1;i_++)
|
---|
| 2546 | {
|
---|
| 2547 | r[i_] = v*a[i_];
|
---|
| 2548 | }
|
---|
| 2549 | for(i=1; i<=n-1; i++)
|
---|
| 2550 | {
|
---|
| 2551 | v = b[i];
|
---|
| 2552 | i1 = 0;
|
---|
| 2553 | i2 = i-1;
|
---|
| 2554 | j1 = m-i;
|
---|
| 2555 | j2 = m-1;
|
---|
| 2556 | i1_ = (j1) - (i1);
|
---|
| 2557 | for(i_=i1; i_<=i2;i_++)
|
---|
| 2558 | {
|
---|
| 2559 | r[i_] = r[i_] + v*a[i_+i1_];
|
---|
| 2560 | }
|
---|
| 2561 | i1 = i;
|
---|
| 2562 | i2 = m-1;
|
---|
| 2563 | j1 = 0;
|
---|
| 2564 | j2 = m-i-1;
|
---|
| 2565 | i1_ = (j1) - (i1);
|
---|
| 2566 | for(i_=i1; i_<=i2;i_++)
|
---|
| 2567 | {
|
---|
| 2568 | r[i_] = r[i_] + v*a[i_+i1_];
|
---|
| 2569 | }
|
---|
| 2570 | }
|
---|
| 2571 | }
|
---|
| 2572 | else
|
---|
| 2573 | {
|
---|
| 2574 |
|
---|
| 2575 | //
|
---|
| 2576 | // non-circular convolution
|
---|
| 2577 | //
|
---|
| 2578 | r = new double[m+n-1];
|
---|
| 2579 | for(i=0; i<=m+n-2; i++)
|
---|
| 2580 | {
|
---|
| 2581 | r[i] = 0;
|
---|
| 2582 | }
|
---|
| 2583 | for(i=0; i<=n-1; i++)
|
---|
| 2584 | {
|
---|
| 2585 | v = b[i];
|
---|
| 2586 | i1_ = (0) - (i);
|
---|
| 2587 | for(i_=i; i_<=i+m-1;i_++)
|
---|
| 2588 | {
|
---|
| 2589 | r[i_] = r[i_] + v*a[i_+i1_];
|
---|
| 2590 | }
|
---|
| 2591 | }
|
---|
| 2592 | }
|
---|
| 2593 | return;
|
---|
| 2594 | }
|
---|
| 2595 |
|
---|
| 2596 | //
|
---|
| 2597 | // general FFT-based code for
|
---|
| 2598 | // circular and non-circular convolutions.
|
---|
| 2599 | //
|
---|
| 2600 | // First, if convolution is circular, we test whether M is smooth or not.
|
---|
| 2601 | // If it is smooth, we just use M-length FFT to calculate convolution.
|
---|
| 2602 | // If it is not, we calculate non-circular convolution and wrap it arount.
|
---|
| 2603 | //
|
---|
| 2604 | // If convolution is non-circular, we use zero-padding + FFT.
|
---|
| 2605 | //
|
---|
| 2606 | // We assume that M+N-1>2 - we should call small case code otherwise
|
---|
| 2607 | //
|
---|
| 2608 | if( alg==1 )
|
---|
| 2609 | {
|
---|
| 2610 | alglib.ap.assert(m+n-1>2, "ConvR1DX: internal error!");
|
---|
| 2611 | if( (circular && ftbase.ftbaseissmooth(m)) && m%2==0 )
|
---|
| 2612 | {
|
---|
| 2613 |
|
---|
| 2614 | //
|
---|
| 2615 | // special code for circular convolution with smooth even M
|
---|
| 2616 | //
|
---|
| 2617 | buf = new double[m];
|
---|
| 2618 | for(i_=0; i_<=m-1;i_++)
|
---|
| 2619 | {
|
---|
| 2620 | buf[i_] = a[i_];
|
---|
| 2621 | }
|
---|
| 2622 | buf2 = new double[m];
|
---|
| 2623 | for(i_=0; i_<=n-1;i_++)
|
---|
| 2624 | {
|
---|
| 2625 | buf2[i_] = b[i_];
|
---|
| 2626 | }
|
---|
| 2627 | for(i=n; i<=m-1; i++)
|
---|
| 2628 | {
|
---|
| 2629 | buf2[i] = 0;
|
---|
| 2630 | }
|
---|
| 2631 | buf3 = new double[m];
|
---|
| 2632 | ftbase.ftbasegeneratecomplexfftplan(m/2, plan);
|
---|
| 2633 | fft.fftr1dinternaleven(ref buf, m, ref buf3, plan);
|
---|
| 2634 | fft.fftr1dinternaleven(ref buf2, m, ref buf3, plan);
|
---|
| 2635 | buf[0] = buf[0]*buf2[0];
|
---|
| 2636 | buf[1] = buf[1]*buf2[1];
|
---|
| 2637 | for(i=1; i<=m/2-1; i++)
|
---|
| 2638 | {
|
---|
| 2639 | ax = buf[2*i+0];
|
---|
| 2640 | ay = buf[2*i+1];
|
---|
| 2641 | bx = buf2[2*i+0];
|
---|
| 2642 | by = buf2[2*i+1];
|
---|
| 2643 | tx = ax*bx-ay*by;
|
---|
| 2644 | ty = ax*by+ay*bx;
|
---|
| 2645 | buf[2*i+0] = tx;
|
---|
| 2646 | buf[2*i+1] = ty;
|
---|
| 2647 | }
|
---|
| 2648 | fft.fftr1dinvinternaleven(ref buf, m, ref buf3, plan);
|
---|
| 2649 | r = new double[m];
|
---|
| 2650 | for(i_=0; i_<=m-1;i_++)
|
---|
| 2651 | {
|
---|
| 2652 | r[i_] = buf[i_];
|
---|
| 2653 | }
|
---|
| 2654 | }
|
---|
| 2655 | else
|
---|
| 2656 | {
|
---|
| 2657 |
|
---|
| 2658 | //
|
---|
| 2659 | // M is non-smooth or non-even, general code (circular/non-circular):
|
---|
| 2660 | // * first part is the same for circular and non-circular
|
---|
| 2661 | // convolutions. zero padding, FFTs, inverse FFTs
|
---|
| 2662 | // * second part differs:
|
---|
| 2663 | // * for non-circular convolution we just copy array
|
---|
| 2664 | // * for circular convolution we add array tail to its head
|
---|
| 2665 | //
|
---|
| 2666 | p = ftbase.ftbasefindsmootheven(m+n-1);
|
---|
| 2667 | buf = new double[p];
|
---|
| 2668 | for(i_=0; i_<=m-1;i_++)
|
---|
| 2669 | {
|
---|
| 2670 | buf[i_] = a[i_];
|
---|
| 2671 | }
|
---|
| 2672 | for(i=m; i<=p-1; i++)
|
---|
| 2673 | {
|
---|
| 2674 | buf[i] = 0;
|
---|
| 2675 | }
|
---|
| 2676 | buf2 = new double[p];
|
---|
| 2677 | for(i_=0; i_<=n-1;i_++)
|
---|
| 2678 | {
|
---|
| 2679 | buf2[i_] = b[i_];
|
---|
| 2680 | }
|
---|
| 2681 | for(i=n; i<=p-1; i++)
|
---|
| 2682 | {
|
---|
| 2683 | buf2[i] = 0;
|
---|
| 2684 | }
|
---|
| 2685 | buf3 = new double[p];
|
---|
| 2686 | ftbase.ftbasegeneratecomplexfftplan(p/2, plan);
|
---|
| 2687 | fft.fftr1dinternaleven(ref buf, p, ref buf3, plan);
|
---|
| 2688 | fft.fftr1dinternaleven(ref buf2, p, ref buf3, plan);
|
---|
| 2689 | buf[0] = buf[0]*buf2[0];
|
---|
| 2690 | buf[1] = buf[1]*buf2[1];
|
---|
| 2691 | for(i=1; i<=p/2-1; i++)
|
---|
| 2692 | {
|
---|
| 2693 | ax = buf[2*i+0];
|
---|
| 2694 | ay = buf[2*i+1];
|
---|
| 2695 | bx = buf2[2*i+0];
|
---|
| 2696 | by = buf2[2*i+1];
|
---|
| 2697 | tx = ax*bx-ay*by;
|
---|
| 2698 | ty = ax*by+ay*bx;
|
---|
| 2699 | buf[2*i+0] = tx;
|
---|
| 2700 | buf[2*i+1] = ty;
|
---|
| 2701 | }
|
---|
| 2702 | fft.fftr1dinvinternaleven(ref buf, p, ref buf3, plan);
|
---|
| 2703 | if( circular )
|
---|
| 2704 | {
|
---|
| 2705 |
|
---|
| 2706 | //
|
---|
| 2707 | // circular, add tail to head
|
---|
| 2708 | //
|
---|
| 2709 | r = new double[m];
|
---|
| 2710 | for(i_=0; i_<=m-1;i_++)
|
---|
| 2711 | {
|
---|
| 2712 | r[i_] = buf[i_];
|
---|
| 2713 | }
|
---|
| 2714 | if( n>=2 )
|
---|
| 2715 | {
|
---|
| 2716 | i1_ = (m) - (0);
|
---|
| 2717 | for(i_=0; i_<=n-2;i_++)
|
---|
| 2718 | {
|
---|
| 2719 | r[i_] = r[i_] + buf[i_+i1_];
|
---|
| 2720 | }
|
---|
| 2721 | }
|
---|
| 2722 | }
|
---|
| 2723 | else
|
---|
| 2724 | {
|
---|
| 2725 |
|
---|
| 2726 | //
|
---|
| 2727 | // non-circular, just copy
|
---|
| 2728 | //
|
---|
| 2729 | r = new double[m+n-1];
|
---|
| 2730 | for(i_=0; i_<=m+n-2;i_++)
|
---|
| 2731 | {
|
---|
| 2732 | r[i_] = buf[i_];
|
---|
| 2733 | }
|
---|
| 2734 | }
|
---|
| 2735 | }
|
---|
| 2736 | return;
|
---|
| 2737 | }
|
---|
| 2738 |
|
---|
| 2739 | //
|
---|
| 2740 | // overlap-add method
|
---|
| 2741 | //
|
---|
| 2742 | if( alg==2 )
|
---|
| 2743 | {
|
---|
| 2744 | alglib.ap.assert((q+n-1)%2==0, "ConvR1DX: internal error!");
|
---|
| 2745 | buf = new double[q+n-1];
|
---|
| 2746 | buf2 = new double[q+n-1];
|
---|
| 2747 | buf3 = new double[q+n-1];
|
---|
| 2748 | ftbase.ftbasegeneratecomplexfftplan((q+n-1)/2, plan);
|
---|
| 2749 |
|
---|
| 2750 | //
|
---|
| 2751 | // prepare R
|
---|
| 2752 | //
|
---|
| 2753 | if( circular )
|
---|
| 2754 | {
|
---|
| 2755 | r = new double[m];
|
---|
| 2756 | for(i=0; i<=m-1; i++)
|
---|
| 2757 | {
|
---|
| 2758 | r[i] = 0;
|
---|
| 2759 | }
|
---|
| 2760 | }
|
---|
| 2761 | else
|
---|
| 2762 | {
|
---|
| 2763 | r = new double[m+n-1];
|
---|
| 2764 | for(i=0; i<=m+n-2; i++)
|
---|
| 2765 | {
|
---|
| 2766 | r[i] = 0;
|
---|
| 2767 | }
|
---|
| 2768 | }
|
---|
| 2769 |
|
---|
| 2770 | //
|
---|
| 2771 | // pre-calculated FFT(B)
|
---|
| 2772 | //
|
---|
| 2773 | for(i_=0; i_<=n-1;i_++)
|
---|
| 2774 | {
|
---|
| 2775 | buf2[i_] = b[i_];
|
---|
| 2776 | }
|
---|
| 2777 | for(j=n; j<=q+n-2; j++)
|
---|
| 2778 | {
|
---|
| 2779 | buf2[j] = 0;
|
---|
| 2780 | }
|
---|
| 2781 | fft.fftr1dinternaleven(ref buf2, q+n-1, ref buf3, plan);
|
---|
| 2782 |
|
---|
| 2783 | //
|
---|
| 2784 | // main overlap-add cycle
|
---|
| 2785 | //
|
---|
| 2786 | i = 0;
|
---|
| 2787 | while( i<=m-1 )
|
---|
| 2788 | {
|
---|
| 2789 | p = Math.Min(q, m-i);
|
---|
| 2790 | i1_ = (i) - (0);
|
---|
| 2791 | for(i_=0; i_<=p-1;i_++)
|
---|
| 2792 | {
|
---|
| 2793 | buf[i_] = a[i_+i1_];
|
---|
| 2794 | }
|
---|
| 2795 | for(j=p; j<=q+n-2; j++)
|
---|
| 2796 | {
|
---|
| 2797 | buf[j] = 0;
|
---|
| 2798 | }
|
---|
| 2799 | fft.fftr1dinternaleven(ref buf, q+n-1, ref buf3, plan);
|
---|
| 2800 | buf[0] = buf[0]*buf2[0];
|
---|
| 2801 | buf[1] = buf[1]*buf2[1];
|
---|
| 2802 | for(j=1; j<=(q+n-1)/2-1; j++)
|
---|
| 2803 | {
|
---|
| 2804 | ax = buf[2*j+0];
|
---|
| 2805 | ay = buf[2*j+1];
|
---|
| 2806 | bx = buf2[2*j+0];
|
---|
| 2807 | by = buf2[2*j+1];
|
---|
| 2808 | tx = ax*bx-ay*by;
|
---|
| 2809 | ty = ax*by+ay*bx;
|
---|
| 2810 | buf[2*j+0] = tx;
|
---|
| 2811 | buf[2*j+1] = ty;
|
---|
| 2812 | }
|
---|
| 2813 | fft.fftr1dinvinternaleven(ref buf, q+n-1, ref buf3, plan);
|
---|
| 2814 | if( circular )
|
---|
| 2815 | {
|
---|
| 2816 | j1 = Math.Min(i+p+n-2, m-1)-i;
|
---|
| 2817 | j2 = j1+1;
|
---|
| 2818 | }
|
---|
| 2819 | else
|
---|
| 2820 | {
|
---|
| 2821 | j1 = p+n-2;
|
---|
| 2822 | j2 = j1+1;
|
---|
| 2823 | }
|
---|
| 2824 | i1_ = (0) - (i);
|
---|
| 2825 | for(i_=i; i_<=i+j1;i_++)
|
---|
| 2826 | {
|
---|
| 2827 | r[i_] = r[i_] + buf[i_+i1_];
|
---|
| 2828 | }
|
---|
| 2829 | if( p+n-2>=j2 )
|
---|
| 2830 | {
|
---|
| 2831 | i1_ = (j2) - (0);
|
---|
| 2832 | for(i_=0; i_<=p+n-2-j2;i_++)
|
---|
| 2833 | {
|
---|
| 2834 | r[i_] = r[i_] + buf[i_+i1_];
|
---|
| 2835 | }
|
---|
| 2836 | }
|
---|
| 2837 | i = i+p;
|
---|
| 2838 | }
|
---|
| 2839 | return;
|
---|
| 2840 | }
|
---|
| 2841 | }
|
---|
| 2842 |
|
---|
| 2843 |
|
---|
| 2844 | }
|
---|
| 2845 | public class corr
|
---|
| 2846 | {
|
---|
| 2847 | /*************************************************************************
|
---|
| 2848 | 1-dimensional complex cross-correlation.
|
---|
| 2849 |
|
---|
| 2850 | For given Pattern/Signal returns corr(Pattern,Signal) (non-circular).
|
---|
| 2851 |
|
---|
| 2852 | Correlation is calculated using reduction to convolution. Algorithm with
|
---|
| 2853 | max(N,N)*log(max(N,N)) complexity is used (see ConvC1D() for more info
|
---|
| 2854 | about performance).
|
---|
| 2855 |
|
---|
| 2856 | IMPORTANT:
|
---|
| 2857 | for historical reasons subroutine accepts its parameters in reversed
|
---|
| 2858 | order: CorrC1D(Signal, Pattern) = Pattern x Signal (using traditional
|
---|
| 2859 | definition of cross-correlation, denoting cross-correlation as "x").
|
---|
| 2860 |
|
---|
| 2861 | INPUT PARAMETERS
|
---|
| 2862 | Signal - array[0..N-1] - complex function to be transformed,
|
---|
| 2863 | signal containing pattern
|
---|
| 2864 | N - problem size
|
---|
| 2865 | Pattern - array[0..M-1] - complex function to be transformed,
|
---|
| 2866 | pattern to search withing signal
|
---|
| 2867 | M - problem size
|
---|
| 2868 |
|
---|
| 2869 | OUTPUT PARAMETERS
|
---|
| 2870 | R - cross-correlation, array[0..N+M-2]:
|
---|
| 2871 | * positive lags are stored in R[0..N-1],
|
---|
| 2872 | R[i] = sum(conj(pattern[j])*signal[i+j]
|
---|
| 2873 | * negative lags are stored in R[N..N+M-2],
|
---|
| 2874 | R[N+M-1-i] = sum(conj(pattern[j])*signal[-i+j]
|
---|
| 2875 |
|
---|
| 2876 | NOTE:
|
---|
| 2877 | It is assumed that pattern domain is [0..M-1]. If Pattern is non-zero
|
---|
| 2878 | on [-K..M-1], you can still use this subroutine, just shift result by K.
|
---|
| 2879 |
|
---|
| 2880 | -- ALGLIB --
|
---|
| 2881 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
| 2882 | *************************************************************************/
|
---|
| 2883 | public static void corrc1d(complex[] signal,
|
---|
| 2884 | int n,
|
---|
| 2885 | complex[] pattern,
|
---|
| 2886 | int m,
|
---|
| 2887 | ref complex[] r)
|
---|
| 2888 | {
|
---|
| 2889 | complex[] p = new complex[0];
|
---|
| 2890 | complex[] b = new complex[0];
|
---|
| 2891 | int i = 0;
|
---|
| 2892 | int i_ = 0;
|
---|
| 2893 | int i1_ = 0;
|
---|
| 2894 |
|
---|
| 2895 | r = new complex[0];
|
---|
| 2896 |
|
---|
| 2897 | alglib.ap.assert(n>0 && m>0, "CorrC1D: incorrect N or M!");
|
---|
| 2898 | p = new complex[m];
|
---|
| 2899 | for(i=0; i<=m-1; i++)
|
---|
| 2900 | {
|
---|
| 2901 | p[m-1-i] = math.conj(pattern[i]);
|
---|
| 2902 | }
|
---|
| 2903 | conv.convc1d(p, m, signal, n, ref b);
|
---|
| 2904 | r = new complex[m+n-1];
|
---|
| 2905 | i1_ = (m-1) - (0);
|
---|
| 2906 | for(i_=0; i_<=n-1;i_++)
|
---|
| 2907 | {
|
---|
| 2908 | r[i_] = b[i_+i1_];
|
---|
| 2909 | }
|
---|
| 2910 | if( m+n-2>=n )
|
---|
| 2911 | {
|
---|
| 2912 | i1_ = (0) - (n);
|
---|
| 2913 | for(i_=n; i_<=m+n-2;i_++)
|
---|
| 2914 | {
|
---|
| 2915 | r[i_] = b[i_+i1_];
|
---|
| 2916 | }
|
---|
| 2917 | }
|
---|
| 2918 | }
|
---|
| 2919 |
|
---|
| 2920 |
|
---|
| 2921 | /*************************************************************************
|
---|
| 2922 | 1-dimensional circular complex cross-correlation.
|
---|
| 2923 |
|
---|
| 2924 | For given Pattern/Signal returns corr(Pattern,Signal) (circular).
|
---|
| 2925 | Algorithm has linearithmic complexity for any M/N.
|
---|
| 2926 |
|
---|
| 2927 | IMPORTANT:
|
---|
| 2928 | for historical reasons subroutine accepts its parameters in reversed
|
---|
| 2929 | order: CorrC1DCircular(Signal, Pattern) = Pattern x Signal (using
|
---|
| 2930 | traditional definition of cross-correlation, denoting cross-correlation
|
---|
| 2931 | as "x").
|
---|
| 2932 |
|
---|
| 2933 | INPUT PARAMETERS
|
---|
| 2934 | Signal - array[0..N-1] - complex function to be transformed,
|
---|
| 2935 | periodic signal containing pattern
|
---|
| 2936 | N - problem size
|
---|
| 2937 | Pattern - array[0..M-1] - complex function to be transformed,
|
---|
| 2938 | non-periodic pattern to search withing signal
|
---|
| 2939 | M - problem size
|
---|
| 2940 |
|
---|
| 2941 | OUTPUT PARAMETERS
|
---|
| 2942 | R - convolution: A*B. array[0..M-1].
|
---|
| 2943 |
|
---|
| 2944 |
|
---|
| 2945 | -- ALGLIB --
|
---|
| 2946 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
| 2947 | *************************************************************************/
|
---|
| 2948 | public static void corrc1dcircular(complex[] signal,
|
---|
| 2949 | int m,
|
---|
| 2950 | complex[] pattern,
|
---|
| 2951 | int n,
|
---|
| 2952 | ref complex[] c)
|
---|
| 2953 | {
|
---|
| 2954 | complex[] p = new complex[0];
|
---|
| 2955 | complex[] b = new complex[0];
|
---|
| 2956 | int i1 = 0;
|
---|
| 2957 | int i2 = 0;
|
---|
| 2958 | int i = 0;
|
---|
| 2959 | int j2 = 0;
|
---|
| 2960 | int i_ = 0;
|
---|
| 2961 | int i1_ = 0;
|
---|
| 2962 |
|
---|
| 2963 | c = new complex[0];
|
---|
| 2964 |
|
---|
| 2965 | alglib.ap.assert(n>0 && m>0, "ConvC1DCircular: incorrect N or M!");
|
---|
| 2966 |
|
---|
| 2967 | //
|
---|
| 2968 | // normalize task: make M>=N,
|
---|
| 2969 | // so A will be longer (at least - not shorter) that B.
|
---|
| 2970 | //
|
---|
| 2971 | if( m<n )
|
---|
| 2972 | {
|
---|
| 2973 | b = new complex[m];
|
---|
| 2974 | for(i1=0; i1<=m-1; i1++)
|
---|
| 2975 | {
|
---|
| 2976 | b[i1] = 0;
|
---|
| 2977 | }
|
---|
| 2978 | i1 = 0;
|
---|
| 2979 | while( i1<n )
|
---|
| 2980 | {
|
---|
| 2981 | i2 = Math.Min(i1+m-1, n-1);
|
---|
| 2982 | j2 = i2-i1;
|
---|
| 2983 | i1_ = (i1) - (0);
|
---|
| 2984 | for(i_=0; i_<=j2;i_++)
|
---|
| 2985 | {
|
---|
| 2986 | b[i_] = b[i_] + pattern[i_+i1_];
|
---|
| 2987 | }
|
---|
| 2988 | i1 = i1+m;
|
---|
| 2989 | }
|
---|
| 2990 | corrc1dcircular(signal, m, b, m, ref c);
|
---|
| 2991 | return;
|
---|
| 2992 | }
|
---|
| 2993 |
|
---|
| 2994 | //
|
---|
| 2995 | // Task is normalized
|
---|
| 2996 | //
|
---|
| 2997 | p = new complex[n];
|
---|
| 2998 | for(i=0; i<=n-1; i++)
|
---|
| 2999 | {
|
---|
| 3000 | p[n-1-i] = math.conj(pattern[i]);
|
---|
| 3001 | }
|
---|
| 3002 | conv.convc1dcircular(signal, m, p, n, ref b);
|
---|
| 3003 | c = new complex[m];
|
---|
| 3004 | i1_ = (n-1) - (0);
|
---|
| 3005 | for(i_=0; i_<=m-n;i_++)
|
---|
| 3006 | {
|
---|
| 3007 | c[i_] = b[i_+i1_];
|
---|
| 3008 | }
|
---|
| 3009 | if( m-n+1<=m-1 )
|
---|
| 3010 | {
|
---|
| 3011 | i1_ = (0) - (m-n+1);
|
---|
| 3012 | for(i_=m-n+1; i_<=m-1;i_++)
|
---|
| 3013 | {
|
---|
| 3014 | c[i_] = b[i_+i1_];
|
---|
| 3015 | }
|
---|
| 3016 | }
|
---|
| 3017 | }
|
---|
| 3018 |
|
---|
| 3019 |
|
---|
| 3020 | /*************************************************************************
|
---|
| 3021 | 1-dimensional real cross-correlation.
|
---|
| 3022 |
|
---|
| 3023 | For given Pattern/Signal returns corr(Pattern,Signal) (non-circular).
|
---|
| 3024 |
|
---|
| 3025 | Correlation is calculated using reduction to convolution. Algorithm with
|
---|
| 3026 | max(N,N)*log(max(N,N)) complexity is used (see ConvC1D() for more info
|
---|
| 3027 | about performance).
|
---|
| 3028 |
|
---|
| 3029 | IMPORTANT:
|
---|
| 3030 | for historical reasons subroutine accepts its parameters in reversed
|
---|
| 3031 | order: CorrR1D(Signal, Pattern) = Pattern x Signal (using traditional
|
---|
| 3032 | definition of cross-correlation, denoting cross-correlation as "x").
|
---|
| 3033 |
|
---|
| 3034 | INPUT PARAMETERS
|
---|
| 3035 | Signal - array[0..N-1] - real function to be transformed,
|
---|
| 3036 | signal containing pattern
|
---|
| 3037 | N - problem size
|
---|
| 3038 | Pattern - array[0..M-1] - real function to be transformed,
|
---|
| 3039 | pattern to search withing signal
|
---|
| 3040 | M - problem size
|
---|
| 3041 |
|
---|
| 3042 | OUTPUT PARAMETERS
|
---|
| 3043 | R - cross-correlation, array[0..N+M-2]:
|
---|
| 3044 | * positive lags are stored in R[0..N-1],
|
---|
| 3045 | R[i] = sum(pattern[j]*signal[i+j]
|
---|
| 3046 | * negative lags are stored in R[N..N+M-2],
|
---|
| 3047 | R[N+M-1-i] = sum(pattern[j]*signal[-i+j]
|
---|
| 3048 |
|
---|
| 3049 | NOTE:
|
---|
| 3050 | It is assumed that pattern domain is [0..M-1]. If Pattern is non-zero
|
---|
| 3051 | on [-K..M-1], you can still use this subroutine, just shift result by K.
|
---|
| 3052 |
|
---|
| 3053 | -- ALGLIB --
|
---|
| 3054 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
| 3055 | *************************************************************************/
|
---|
| 3056 | public static void corrr1d(double[] signal,
|
---|
| 3057 | int n,
|
---|
| 3058 | double[] pattern,
|
---|
| 3059 | int m,
|
---|
| 3060 | ref double[] r)
|
---|
| 3061 | {
|
---|
| 3062 | double[] p = new double[0];
|
---|
| 3063 | double[] b = new double[0];
|
---|
| 3064 | int i = 0;
|
---|
| 3065 | int i_ = 0;
|
---|
| 3066 | int i1_ = 0;
|
---|
| 3067 |
|
---|
| 3068 | r = new double[0];
|
---|
| 3069 |
|
---|
| 3070 | alglib.ap.assert(n>0 && m>0, "CorrR1D: incorrect N or M!");
|
---|
| 3071 | p = new double[m];
|
---|
| 3072 | for(i=0; i<=m-1; i++)
|
---|
| 3073 | {
|
---|
| 3074 | p[m-1-i] = pattern[i];
|
---|
| 3075 | }
|
---|
| 3076 | conv.convr1d(p, m, signal, n, ref b);
|
---|
| 3077 | r = new double[m+n-1];
|
---|
| 3078 | i1_ = (m-1) - (0);
|
---|
| 3079 | for(i_=0; i_<=n-1;i_++)
|
---|
| 3080 | {
|
---|
| 3081 | r[i_] = b[i_+i1_];
|
---|
| 3082 | }
|
---|
| 3083 | if( m+n-2>=n )
|
---|
| 3084 | {
|
---|
| 3085 | i1_ = (0) - (n);
|
---|
| 3086 | for(i_=n; i_<=m+n-2;i_++)
|
---|
| 3087 | {
|
---|
| 3088 | r[i_] = b[i_+i1_];
|
---|
| 3089 | }
|
---|
| 3090 | }
|
---|
| 3091 | }
|
---|
| 3092 |
|
---|
| 3093 |
|
---|
| 3094 | /*************************************************************************
|
---|
| 3095 | 1-dimensional circular real cross-correlation.
|
---|
| 3096 |
|
---|
| 3097 | For given Pattern/Signal returns corr(Pattern,Signal) (circular).
|
---|
| 3098 | Algorithm has linearithmic complexity for any M/N.
|
---|
| 3099 |
|
---|
| 3100 | IMPORTANT:
|
---|
| 3101 | for historical reasons subroutine accepts its parameters in reversed
|
---|
| 3102 | order: CorrR1DCircular(Signal, Pattern) = Pattern x Signal (using
|
---|
| 3103 | traditional definition of cross-correlation, denoting cross-correlation
|
---|
| 3104 | as "x").
|
---|
| 3105 |
|
---|
| 3106 | INPUT PARAMETERS
|
---|
| 3107 | Signal - array[0..N-1] - real function to be transformed,
|
---|
| 3108 | periodic signal containing pattern
|
---|
| 3109 | N - problem size
|
---|
| 3110 | Pattern - array[0..M-1] - real function to be transformed,
|
---|
| 3111 | non-periodic pattern to search withing signal
|
---|
| 3112 | M - problem size
|
---|
| 3113 |
|
---|
| 3114 | OUTPUT PARAMETERS
|
---|
| 3115 | R - convolution: A*B. array[0..M-1].
|
---|
| 3116 |
|
---|
| 3117 |
|
---|
| 3118 | -- ALGLIB --
|
---|
| 3119 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
| 3120 | *************************************************************************/
|
---|
| 3121 | public static void corrr1dcircular(double[] signal,
|
---|
| 3122 | int m,
|
---|
| 3123 | double[] pattern,
|
---|
| 3124 | int n,
|
---|
| 3125 | ref double[] c)
|
---|
| 3126 | {
|
---|
| 3127 | double[] p = new double[0];
|
---|
| 3128 | double[] b = new double[0];
|
---|
| 3129 | int i1 = 0;
|
---|
| 3130 | int i2 = 0;
|
---|
| 3131 | int i = 0;
|
---|
| 3132 | int j2 = 0;
|
---|
| 3133 | int i_ = 0;
|
---|
| 3134 | int i1_ = 0;
|
---|
| 3135 |
|
---|
| 3136 | c = new double[0];
|
---|
| 3137 |
|
---|
| 3138 | alglib.ap.assert(n>0 && m>0, "ConvC1DCircular: incorrect N or M!");
|
---|
| 3139 |
|
---|
| 3140 | //
|
---|
| 3141 | // normalize task: make M>=N,
|
---|
| 3142 | // so A will be longer (at least - not shorter) that B.
|
---|
| 3143 | //
|
---|
| 3144 | if( m<n )
|
---|
| 3145 | {
|
---|
| 3146 | b = new double[m];
|
---|
| 3147 | for(i1=0; i1<=m-1; i1++)
|
---|
| 3148 | {
|
---|
| 3149 | b[i1] = 0;
|
---|
| 3150 | }
|
---|
| 3151 | i1 = 0;
|
---|
| 3152 | while( i1<n )
|
---|
| 3153 | {
|
---|
| 3154 | i2 = Math.Min(i1+m-1, n-1);
|
---|
| 3155 | j2 = i2-i1;
|
---|
| 3156 | i1_ = (i1) - (0);
|
---|
| 3157 | for(i_=0; i_<=j2;i_++)
|
---|
| 3158 | {
|
---|
| 3159 | b[i_] = b[i_] + pattern[i_+i1_];
|
---|
| 3160 | }
|
---|
| 3161 | i1 = i1+m;
|
---|
| 3162 | }
|
---|
| 3163 | corrr1dcircular(signal, m, b, m, ref c);
|
---|
| 3164 | return;
|
---|
| 3165 | }
|
---|
| 3166 |
|
---|
| 3167 | //
|
---|
| 3168 | // Task is normalized
|
---|
| 3169 | //
|
---|
| 3170 | p = new double[n];
|
---|
| 3171 | for(i=0; i<=n-1; i++)
|
---|
| 3172 | {
|
---|
| 3173 | p[n-1-i] = pattern[i];
|
---|
| 3174 | }
|
---|
| 3175 | conv.convr1dcircular(signal, m, p, n, ref b);
|
---|
| 3176 | c = new double[m];
|
---|
| 3177 | i1_ = (n-1) - (0);
|
---|
| 3178 | for(i_=0; i_<=m-n;i_++)
|
---|
| 3179 | {
|
---|
| 3180 | c[i_] = b[i_+i1_];
|
---|
| 3181 | }
|
---|
| 3182 | if( m-n+1<=m-1 )
|
---|
| 3183 | {
|
---|
| 3184 | i1_ = (0) - (m-n+1);
|
---|
| 3185 | for(i_=m-n+1; i_<=m-1;i_++)
|
---|
| 3186 | {
|
---|
| 3187 | c[i_] = b[i_+i1_];
|
---|
| 3188 | }
|
---|
| 3189 | }
|
---|
| 3190 | }
|
---|
| 3191 |
|
---|
| 3192 |
|
---|
| 3193 | }
|
---|
| 3194 | public class fht
|
---|
| 3195 | {
|
---|
| 3196 | /*************************************************************************
|
---|
| 3197 | 1-dimensional Fast Hartley Transform.
|
---|
| 3198 |
|
---|
| 3199 | Algorithm has O(N*logN) complexity for any N (composite or prime).
|
---|
| 3200 |
|
---|
| 3201 | INPUT PARAMETERS
|
---|
| 3202 | A - array[0..N-1] - real function to be transformed
|
---|
| 3203 | N - problem size
|
---|
| 3204 |
|
---|
| 3205 | OUTPUT PARAMETERS
|
---|
| 3206 | A - FHT of a input array, array[0..N-1],
|
---|
| 3207 | A_out[k] = sum(A_in[j]*(cos(2*pi*j*k/N)+sin(2*pi*j*k/N)), j=0..N-1)
|
---|
| 3208 |
|
---|
| 3209 |
|
---|
| 3210 | -- ALGLIB --
|
---|
| 3211 | Copyright 04.06.2009 by Bochkanov Sergey
|
---|
| 3212 | *************************************************************************/
|
---|
| 3213 | public static void fhtr1d(ref double[] a,
|
---|
| 3214 | int n)
|
---|
| 3215 | {
|
---|
| 3216 | ftbase.ftplan plan = new ftbase.ftplan();
|
---|
| 3217 | int i = 0;
|
---|
| 3218 | complex[] fa = new complex[0];
|
---|
| 3219 |
|
---|
| 3220 | alglib.ap.assert(n>0, "FHTR1D: incorrect N!");
|
---|
| 3221 |
|
---|
| 3222 | //
|
---|
| 3223 | // Special case: N=1, FHT is just identity transform.
|
---|
| 3224 | // After this block we assume that N is strictly greater than 1.
|
---|
| 3225 | //
|
---|
| 3226 | if( n==1 )
|
---|
| 3227 | {
|
---|
| 3228 | return;
|
---|
| 3229 | }
|
---|
| 3230 |
|
---|
| 3231 | //
|
---|
| 3232 | // Reduce FHt to real FFT
|
---|
| 3233 | //
|
---|
| 3234 | fft.fftr1d(a, n, ref fa);
|
---|
| 3235 | for(i=0; i<=n-1; i++)
|
---|
| 3236 | {
|
---|
| 3237 | a[i] = fa[i].x-fa[i].y;
|
---|
| 3238 | }
|
---|
| 3239 | }
|
---|
| 3240 |
|
---|
| 3241 |
|
---|
| 3242 | /*************************************************************************
|
---|
| 3243 | 1-dimensional inverse FHT.
|
---|
| 3244 |
|
---|
| 3245 | Algorithm has O(N*logN) complexity for any N (composite or prime).
|
---|
| 3246 |
|
---|
| 3247 | INPUT PARAMETERS
|
---|
| 3248 | A - array[0..N-1] - complex array to be transformed
|
---|
| 3249 | N - problem size
|
---|
| 3250 |
|
---|
| 3251 | OUTPUT PARAMETERS
|
---|
| 3252 | A - inverse FHT of a input array, array[0..N-1]
|
---|
| 3253 |
|
---|
| 3254 |
|
---|
| 3255 | -- ALGLIB --
|
---|
| 3256 | Copyright 29.05.2009 by Bochkanov Sergey
|
---|
| 3257 | *************************************************************************/
|
---|
| 3258 | public static void fhtr1dinv(ref double[] a,
|
---|
| 3259 | int n)
|
---|
| 3260 | {
|
---|
| 3261 | int i = 0;
|
---|
| 3262 |
|
---|
| 3263 | alglib.ap.assert(n>0, "FHTR1DInv: incorrect N!");
|
---|
| 3264 |
|
---|
| 3265 | //
|
---|
| 3266 | // Special case: N=1, iFHT is just identity transform.
|
---|
| 3267 | // After this block we assume that N is strictly greater than 1.
|
---|
| 3268 | //
|
---|
| 3269 | if( n==1 )
|
---|
| 3270 | {
|
---|
| 3271 | return;
|
---|
| 3272 | }
|
---|
| 3273 |
|
---|
| 3274 | //
|
---|
| 3275 | // Inverse FHT can be expressed in terms of the FHT as
|
---|
| 3276 | //
|
---|
| 3277 | // invfht(x) = fht(x)/N
|
---|
| 3278 | //
|
---|
| 3279 | fhtr1d(ref a, n);
|
---|
| 3280 | for(i=0; i<=n-1; i++)
|
---|
| 3281 | {
|
---|
| 3282 | a[i] = a[i]/n;
|
---|
| 3283 | }
|
---|
| 3284 | }
|
---|
| 3285 |
|
---|
| 3286 |
|
---|
| 3287 | }
|
---|
| 3288 | }
|
---|
| 3289 |
|
---|