[4977] | 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 convolution.
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| 29 |
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| 30 | For given A/B returns conv(A,B) (non-circular). Subroutine can automatically
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| 31 | choose between three implementations: straightforward O(M*N) formula for
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| 32 | very small N (or M), overlap-add algorithm for cases where max(M,N) is
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| 33 | significantly larger than min(M,N), but O(M*N) algorithm is too slow, and
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| 34 | general FFT-based formula for cases where two previois algorithms are too
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| 35 | slow.
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| 36 |
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| 37 | Algorithm has max(M,N)*log(max(M,N)) complexity for any M/N.
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| 38 |
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| 39 | INPUT PARAMETERS
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| 40 | A - array[0..M-1] - complex function to be transformed
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| 41 | M - problem size
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| 42 | B - array[0..N-1] - complex function to be transformed
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| 43 | N - problem size
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| 44 |
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| 45 | OUTPUT PARAMETERS
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| 46 | R - convolution: A*B. array[0..N+M-2].
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| 47 |
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| 48 | NOTE:
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| 49 | It is assumed that A is zero at T<0, B is zero too. If one or both
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| 50 | functions have non-zero values at negative T's, you can still use this
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| 51 | subroutine - just shift its result correspondingly.
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| 52 |
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| 53 | -- ALGLIB --
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| 54 | Copyright 21.07.2009 by Bochkanov Sergey
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| 55 | *************************************************************************/
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| 56 | public static void convc1d(complex[] a, int m, complex[] b, int n, out complex[] r)
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| 57 | {
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| 58 | r = new complex[0];
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| 59 | conv.convc1d(a, m, b, n, ref r);
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| 60 | return;
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| 61 | }
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| 62 |
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| 63 | /*************************************************************************
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| 64 | 1-dimensional complex non-circular deconvolution (inverse of ConvC1D()).
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| 65 |
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| 66 | Algorithm has M*log(M)) complexity for any M (composite or prime).
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| 67 |
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| 68 | INPUT PARAMETERS
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| 69 | A - array[0..M-1] - convolved signal, A = conv(R, B)
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| 70 | M - convolved signal length
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| 71 | B - array[0..N-1] - response
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| 72 | N - response length, N<=M
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| 73 |
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| 74 | OUTPUT PARAMETERS
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| 75 | R - deconvolved signal. array[0..M-N].
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| 76 |
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| 77 | NOTE:
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| 78 | deconvolution is unstable process and may result in division by zero
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| 79 | (if your response function is degenerate, i.e. has zero Fourier coefficient).
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| 80 |
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| 81 | NOTE:
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| 82 | It is assumed that A is zero at T<0, B is zero too. If one or both
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| 83 | functions have non-zero values at negative T's, you can still use this
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| 84 | subroutine - just shift its result correspondingly.
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| 85 |
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| 86 | -- ALGLIB --
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| 87 | Copyright 21.07.2009 by Bochkanov Sergey
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| 88 | *************************************************************************/
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| 89 | public static void convc1dinv(complex[] a, int m, complex[] b, int n, out complex[] r)
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| 90 | {
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| 91 | r = new complex[0];
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| 92 | conv.convc1dinv(a, m, b, n, ref r);
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| 93 | return;
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| 94 | }
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| 95 |
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| 96 | /*************************************************************************
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| 97 | 1-dimensional circular complex convolution.
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| 98 |
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| 99 | For given S/R returns conv(S,R) (circular). Algorithm has linearithmic
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| 100 | complexity for any M/N.
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| 101 |
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| 102 | IMPORTANT: normal convolution is commutative, i.e. it is symmetric -
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| 103 | conv(A,B)=conv(B,A). Cyclic convolution IS NOT. One function - S - is a
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| 104 | signal, periodic function, and another - R - is a response, non-periodic
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| 105 | function with limited length.
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| 106 |
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| 107 | INPUT PARAMETERS
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| 108 | S - array[0..M-1] - complex periodic signal
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| 109 | M - problem size
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| 110 | B - array[0..N-1] - complex non-periodic response
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| 111 | N - problem size
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| 112 |
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| 113 | OUTPUT PARAMETERS
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| 114 | R - convolution: A*B. array[0..M-1].
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| 115 |
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| 116 | NOTE:
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| 117 | It is assumed that B is zero at T<0. If it has non-zero values at
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| 118 | negative T's, you can still use this subroutine - just shift its result
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| 119 | correspondingly.
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| 120 |
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| 121 | -- ALGLIB --
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| 122 | Copyright 21.07.2009 by Bochkanov Sergey
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| 123 | *************************************************************************/
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| 124 | public static void convc1dcircular(complex[] s, int m, complex[] r, int n, out complex[] c)
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| 125 | {
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| 126 | c = new complex[0];
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| 127 | conv.convc1dcircular(s, m, r, n, ref c);
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| 128 | return;
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| 129 | }
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| 130 |
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| 131 | /*************************************************************************
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| 132 | 1-dimensional circular complex deconvolution (inverse of ConvC1DCircular()).
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| 133 |
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| 134 | Algorithm has M*log(M)) complexity for any M (composite or prime).
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| 135 |
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| 136 | INPUT PARAMETERS
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| 137 | A - array[0..M-1] - convolved periodic signal, A = conv(R, B)
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| 138 | M - convolved signal length
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| 139 | B - array[0..N-1] - non-periodic response
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| 140 | N - response length
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| 141 |
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| 142 | OUTPUT PARAMETERS
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| 143 | R - deconvolved signal. array[0..M-1].
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| 144 |
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| 145 | NOTE:
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| 146 | deconvolution is unstable process and may result in division by zero
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| 147 | (if your response function is degenerate, i.e. has zero Fourier coefficient).
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| 148 |
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| 149 | NOTE:
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| 150 | It is assumed that B is zero at T<0. If it has non-zero values at
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| 151 | negative T's, you can still use this subroutine - just shift its result
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| 152 | correspondingly.
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| 153 |
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| 154 | -- ALGLIB --
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| 155 | Copyright 21.07.2009 by Bochkanov Sergey
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| 156 | *************************************************************************/
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| 157 | public static void convc1dcircularinv(complex[] a, int m, complex[] b, int n, out complex[] r)
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| 158 | {
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| 159 | r = new complex[0];
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| 160 | conv.convc1dcircularinv(a, m, b, n, ref r);
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| 161 | return;
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| 162 | }
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| 163 |
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| 164 | /*************************************************************************
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| 165 | 1-dimensional real convolution.
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| 166 |
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| 167 | Analogous to ConvC1D(), see ConvC1D() comments for more details.
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| 168 |
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| 169 | INPUT PARAMETERS
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| 170 | A - array[0..M-1] - real function to be transformed
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| 171 | M - problem size
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| 172 | B - array[0..N-1] - real function to be transformed
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| 173 | N - problem size
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| 174 |
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| 175 | OUTPUT PARAMETERS
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| 176 | R - convolution: A*B. array[0..N+M-2].
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| 177 |
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| 178 | NOTE:
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| 179 | It is assumed that A is zero at T<0, B is zero too. If one or both
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| 180 | functions have non-zero values at negative T's, you can still use this
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| 181 | subroutine - just shift its result correspondingly.
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| 182 |
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| 183 | -- ALGLIB --
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| 184 | Copyright 21.07.2009 by Bochkanov Sergey
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| 185 | *************************************************************************/
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| 186 | public static void convr1d(double[] a, int m, double[] b, int n, out double[] r)
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| 187 | {
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| 188 | r = new double[0];
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| 189 | conv.convr1d(a, m, b, n, ref r);
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| 190 | return;
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| 191 | }
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| 192 |
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| 193 | /*************************************************************************
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| 194 | 1-dimensional real deconvolution (inverse of ConvC1D()).
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| 195 |
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| 196 | Algorithm has M*log(M)) complexity for any M (composite or prime).
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| 197 |
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| 198 | INPUT PARAMETERS
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| 199 | A - array[0..M-1] - convolved signal, A = conv(R, B)
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| 200 | M - convolved signal length
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| 201 | B - array[0..N-1] - response
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| 202 | N - response length, N<=M
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| 203 |
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| 204 | OUTPUT PARAMETERS
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| 205 | R - deconvolved signal. array[0..M-N].
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| 206 |
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| 207 | NOTE:
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| 208 | deconvolution is unstable process and may result in division by zero
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| 209 | (if your response function is degenerate, i.e. has zero Fourier coefficient).
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| 210 |
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| 211 | NOTE:
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| 212 | It is assumed that A is zero at T<0, B is zero too. If one or both
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| 213 | functions have non-zero values at negative T's, you can still use this
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| 214 | subroutine - just shift its result correspondingly.
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| 215 |
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| 216 | -- ALGLIB --
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| 217 | Copyright 21.07.2009 by Bochkanov Sergey
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| 218 | *************************************************************************/
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| 219 | public static void convr1dinv(double[] a, int m, double[] b, int n, out double[] r)
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| 220 | {
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| 221 | r = new double[0];
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| 222 | conv.convr1dinv(a, m, b, n, ref r);
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| 223 | return;
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| 224 | }
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| 225 |
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| 226 | /*************************************************************************
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| 227 | 1-dimensional circular real convolution.
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| 228 |
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| 229 | Analogous to ConvC1DCircular(), see ConvC1DCircular() comments for more details.
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| 230 |
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| 231 | INPUT PARAMETERS
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| 232 | S - array[0..M-1] - real signal
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| 233 | M - problem size
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| 234 | B - array[0..N-1] - real response
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| 235 | N - problem size
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| 236 |
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| 237 | OUTPUT PARAMETERS
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| 238 | R - convolution: A*B. array[0..M-1].
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| 239 |
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| 240 | NOTE:
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| 241 | It is assumed that B is zero at T<0. If it has non-zero values at
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| 242 | negative T's, you can still use this subroutine - just shift its result
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| 243 | correspondingly.
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| 244 |
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| 245 | -- ALGLIB --
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| 246 | Copyright 21.07.2009 by Bochkanov Sergey
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| 247 | *************************************************************************/
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| 248 | public static void convr1dcircular(double[] s, int m, double[] r, int n, out double[] c)
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| 249 | {
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| 250 | c = new double[0];
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| 251 | conv.convr1dcircular(s, m, r, n, ref c);
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| 252 | return;
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| 253 | }
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| 254 |
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| 255 | /*************************************************************************
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| 256 | 1-dimensional complex deconvolution (inverse of ConvC1D()).
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| 257 |
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| 258 | Algorithm has M*log(M)) complexity for any M (composite or prime).
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| 259 |
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| 260 | INPUT PARAMETERS
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| 261 | A - array[0..M-1] - convolved signal, A = conv(R, B)
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| 262 | M - convolved signal length
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| 263 | B - array[0..N-1] - response
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| 264 | N - response length
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| 265 |
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| 266 | OUTPUT PARAMETERS
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| 267 | R - deconvolved signal. array[0..M-N].
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| 268 |
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| 269 | NOTE:
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| 270 | deconvolution is unstable process and may result in division by zero
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| 271 | (if your response function is degenerate, i.e. has zero Fourier coefficient).
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| 272 |
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| 273 | NOTE:
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| 274 | It is assumed that B is zero at T<0. If it has non-zero values at
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| 275 | negative T's, you can still use this subroutine - just shift its result
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| 276 | correspondingly.
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| 277 |
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| 278 | -- ALGLIB --
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| 279 | Copyright 21.07.2009 by Bochkanov Sergey
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| 280 | *************************************************************************/
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| 281 | public static void convr1dcircularinv(double[] a, int m, double[] b, int n, out double[] r)
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| 282 | {
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| 283 | r = new double[0];
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| 284 | conv.convr1dcircularinv(a, m, b, n, ref r);
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| 285 | return;
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| 286 | }
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| 287 |
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| 288 | }
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| 289 | public partial class alglib
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| 290 | {
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| 291 |
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| 292 |
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| 293 | /*************************************************************************
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| 294 | 1-dimensional complex FFT.
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| 295 |
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| 296 | Array size N may be arbitrary number (composite or prime). Composite N's
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| 297 | are handled with cache-oblivious variation of a Cooley-Tukey algorithm.
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| 298 | Small prime-factors are transformed using hard coded codelets (similar to
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| 299 | FFTW codelets, but without low-level optimization), large prime-factors
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| 300 | are handled with Bluestein's algorithm.
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| 301 |
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| 302 | Fastests transforms are for smooth N's (prime factors are 2, 3, 5 only),
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| 303 | most fast for powers of 2. When N have prime factors larger than these,
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| 304 | but orders of magnitude smaller than N, computations will be about 4 times
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| 305 | slower than for nearby highly composite N's. When N itself is prime, speed
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| 306 | will be 6 times lower.
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| 307 |
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| 308 | Algorithm has O(N*logN) complexity for any N (composite or prime).
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| 309 |
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| 310 | INPUT PARAMETERS
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| 311 | A - array[0..N-1] - complex function to be transformed
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| 312 | N - problem size
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| 313 |
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| 314 | OUTPUT PARAMETERS
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| 315 | A - DFT of a input array, array[0..N-1]
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| 316 | A_out[j] = SUM(A_in[k]*exp(-2*pi*sqrt(-1)*j*k/N), k = 0..N-1)
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| 317 |
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| 318 |
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| 319 | -- ALGLIB --
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| 320 | Copyright 29.05.2009 by Bochkanov Sergey
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| 321 | *************************************************************************/
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| 322 | public static void fftc1d(ref complex[] a, int n)
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| 323 | {
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| 324 |
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| 325 | fft.fftc1d(ref a, n);
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| 326 | return;
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| 327 | }
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| 328 | public static void fftc1d(ref complex[] a)
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| 329 | {
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| 330 | int n;
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| 331 |
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| 332 |
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| 333 | n = ap.len(a);
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| 334 | fft.fftc1d(ref a, n);
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| 335 |
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| 336 | return;
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| 337 | }
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| 338 |
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| 339 | /*************************************************************************
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| 340 | 1-dimensional complex inverse FFT.
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| 341 |
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| 342 | Array size N may be arbitrary number (composite or prime). Algorithm has
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| 343 | O(N*logN) complexity for any N (composite or prime).
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| 344 |
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| 345 | See FFTC1D() description for more information about algorithm performance.
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| 346 |
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| 347 | INPUT PARAMETERS
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| 348 | A - array[0..N-1] - complex array to be transformed
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| 349 | N - problem size
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| 350 |
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| 351 | OUTPUT PARAMETERS
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| 352 | A - inverse DFT of a input array, array[0..N-1]
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| 353 | A_out[j] = SUM(A_in[k]/N*exp(+2*pi*sqrt(-1)*j*k/N), k = 0..N-1)
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| 354 |
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| 355 |
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| 356 | -- ALGLIB --
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| 357 | Copyright 29.05.2009 by Bochkanov Sergey
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| 358 | *************************************************************************/
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| 359 | public static void fftc1dinv(ref complex[] a, int n)
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| 360 | {
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| 361 |
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| 362 | fft.fftc1dinv(ref a, n);
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| 363 | return;
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| 364 | }
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| 365 | public static void fftc1dinv(ref complex[] a)
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| 366 | {
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| 367 | int n;
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| 368 |
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| 369 |
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| 370 | n = ap.len(a);
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| 371 | fft.fftc1dinv(ref a, n);
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| 372 |
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| 373 | return;
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| 374 | }
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| 375 |
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| 376 | /*************************************************************************
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| 377 | 1-dimensional real FFT.
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| 378 |
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| 379 | Algorithm has O(N*logN) complexity for any N (composite or prime).
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| 380 |
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| 381 | INPUT PARAMETERS
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| 382 | A - array[0..N-1] - real function to be transformed
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| 383 | N - problem size
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| 384 |
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| 385 | OUTPUT PARAMETERS
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| 386 | F - DFT of a input array, array[0..N-1]
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| 387 | F[j] = SUM(A[k]*exp(-2*pi*sqrt(-1)*j*k/N), k = 0..N-1)
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| 388 |
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| 389 | NOTE:
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| 390 | F[] satisfies symmetry property F[k] = conj(F[N-k]), so just one half
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| 391 | of array is usually needed. But for convinience subroutine returns full
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| 392 | complex array (with frequencies above N/2), so its result may be used by
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| 393 | other FFT-related subroutines.
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| 394 |
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| 395 |
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| 396 | -- ALGLIB --
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| 397 | Copyright 01.06.2009 by Bochkanov Sergey
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| 398 | *************************************************************************/
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| 399 | public static void fftr1d(double[] a, int n, out complex[] f)
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| 400 | {
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| 401 | f = new complex[0];
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| 402 | fft.fftr1d(a, n, ref f);
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| 403 | return;
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| 404 | }
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| 405 | public static void fftr1d(double[] a, out complex[] f)
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| 406 | {
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| 407 | int n;
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| 408 |
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| 409 | f = new complex[0];
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| 410 | n = ap.len(a);
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| 411 | fft.fftr1d(a, n, ref f);
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| 412 |
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| 413 | return;
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| 414 | }
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| 415 |
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| 416 | /*************************************************************************
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| 417 | 1-dimensional real inverse FFT.
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| 418 |
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| 419 | Algorithm has O(N*logN) complexity for any N (composite or prime).
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| 420 |
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| 421 | INPUT PARAMETERS
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| 422 | F - array[0..floor(N/2)] - frequencies from forward real FFT
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| 423 | N - problem size
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| 424 |
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| 425 | OUTPUT PARAMETERS
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| 426 | A - inverse DFT of a input array, array[0..N-1]
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| 427 |
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| 428 | NOTE:
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| 429 | F[] should satisfy symmetry property F[k] = conj(F[N-k]), so just one
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| 430 | half of frequencies array is needed - elements from 0 to floor(N/2). F[0]
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| 431 | is ALWAYS real. If N is even F[floor(N/2)] is real too. If N is odd, then
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| 432 | F[floor(N/2)] has no special properties.
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| 433 |
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| 434 | Relying on properties noted above, FFTR1DInv subroutine uses only elements
|
---|
| 435 | from 0th to floor(N/2)-th. It ignores imaginary part of F[0], and in case
|
---|
| 436 | N is even it ignores imaginary part of F[floor(N/2)] too.
|
---|
| 437 |
|
---|
| 438 | When you call this function using full arguments list - "FFTR1DInv(F,N,A)"
|
---|
| 439 | - you can pass either either frequencies array with N elements or reduced
|
---|
| 440 | array with roughly N/2 elements - subroutine will successfully transform
|
---|
| 441 | both.
|
---|
| 442 |
|
---|
| 443 | If you call this function using reduced arguments list - "FFTR1DInv(F,A)"
|
---|
| 444 | - you must pass FULL array with N elements (although higher N/2 are still
|
---|
| 445 | not used) because array size is used to automatically determine FFT length
|
---|
| 446 |
|
---|
| 447 |
|
---|
| 448 | -- ALGLIB --
|
---|
| 449 | Copyright 01.06.2009 by Bochkanov Sergey
|
---|
| 450 | *************************************************************************/
|
---|
| 451 | public static void fftr1dinv(complex[] f, int n, out double[] a)
|
---|
| 452 | {
|
---|
| 453 | a = new double[0];
|
---|
| 454 | fft.fftr1dinv(f, n, ref a);
|
---|
| 455 | return;
|
---|
| 456 | }
|
---|
| 457 | public static void fftr1dinv(complex[] f, out double[] a)
|
---|
| 458 | {
|
---|
| 459 | int n;
|
---|
| 460 |
|
---|
| 461 | a = new double[0];
|
---|
| 462 | n = ap.len(f);
|
---|
| 463 | fft.fftr1dinv(f, n, ref a);
|
---|
| 464 |
|
---|
| 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 conv
|
---|
| 683 | {
|
---|
| 684 | /*************************************************************************
|
---|
| 685 | 1-dimensional complex convolution.
|
---|
| 686 |
|
---|
| 687 | For given A/B returns conv(A,B) (non-circular). Subroutine can automatically
|
---|
| 688 | choose between three implementations: straightforward O(M*N) formula for
|
---|
| 689 | very small N (or M), overlap-add algorithm for cases where max(M,N) is
|
---|
| 690 | significantly larger than min(M,N), but O(M*N) algorithm is too slow, and
|
---|
| 691 | general FFT-based formula for cases where two previois algorithms are too
|
---|
| 692 | slow.
|
---|
| 693 |
|
---|
| 694 | Algorithm has max(M,N)*log(max(M,N)) complexity for any M/N.
|
---|
| 695 |
|
---|
| 696 | INPUT PARAMETERS
|
---|
| 697 | A - array[0..M-1] - complex function to be transformed
|
---|
| 698 | M - problem size
|
---|
| 699 | B - array[0..N-1] - complex function to be transformed
|
---|
| 700 | N - problem size
|
---|
| 701 |
|
---|
| 702 | OUTPUT PARAMETERS
|
---|
| 703 | R - convolution: A*B. array[0..N+M-2].
|
---|
| 704 |
|
---|
| 705 | NOTE:
|
---|
| 706 | It is assumed that A is zero at T<0, B is zero too. If one or both
|
---|
| 707 | functions have non-zero values at negative T's, you can still use this
|
---|
| 708 | subroutine - just shift its result correspondingly.
|
---|
| 709 |
|
---|
| 710 | -- ALGLIB --
|
---|
| 711 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
| 712 | *************************************************************************/
|
---|
| 713 | public static void convc1d(complex[] a,
|
---|
| 714 | int m,
|
---|
| 715 | complex[] b,
|
---|
| 716 | int n,
|
---|
| 717 | ref complex[] r)
|
---|
| 718 | {
|
---|
| 719 | r = new complex[0];
|
---|
| 720 |
|
---|
| 721 | ap.assert(n>0 & m>0, "ConvC1D: incorrect N or M!");
|
---|
| 722 |
|
---|
| 723 | //
|
---|
| 724 | // normalize task: make M>=N,
|
---|
| 725 | // so A will be longer that B.
|
---|
| 726 | //
|
---|
| 727 | if( m<n )
|
---|
| 728 | {
|
---|
| 729 | convc1d(b, n, a, m, ref r);
|
---|
| 730 | return;
|
---|
| 731 | }
|
---|
| 732 | convc1dx(a, m, b, n, false, -1, 0, ref r);
|
---|
| 733 | }
|
---|
| 734 |
|
---|
| 735 |
|
---|
| 736 | /*************************************************************************
|
---|
| 737 | 1-dimensional complex non-circular deconvolution (inverse of ConvC1D()).
|
---|
| 738 |
|
---|
| 739 | Algorithm has M*log(M)) complexity for any M (composite or prime).
|
---|
| 740 |
|
---|
| 741 | INPUT PARAMETERS
|
---|
| 742 | A - array[0..M-1] - convolved signal, A = conv(R, B)
|
---|
| 743 | M - convolved signal length
|
---|
| 744 | B - array[0..N-1] - response
|
---|
| 745 | N - response length, N<=M
|
---|
| 746 |
|
---|
| 747 | OUTPUT PARAMETERS
|
---|
| 748 | R - deconvolved signal. array[0..M-N].
|
---|
| 749 |
|
---|
| 750 | NOTE:
|
---|
| 751 | deconvolution is unstable process and may result in division by zero
|
---|
| 752 | (if your response function is degenerate, i.e. has zero Fourier coefficient).
|
---|
| 753 |
|
---|
| 754 | NOTE:
|
---|
| 755 | It is assumed that A is zero at T<0, B is zero too. If one or both
|
---|
| 756 | functions have non-zero values at negative T's, you can still use this
|
---|
| 757 | subroutine - just shift its result correspondingly.
|
---|
| 758 |
|
---|
| 759 | -- ALGLIB --
|
---|
| 760 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
| 761 | *************************************************************************/
|
---|
| 762 | public static void convc1dinv(complex[] a,
|
---|
| 763 | int m,
|
---|
| 764 | complex[] b,
|
---|
| 765 | int n,
|
---|
| 766 | ref complex[] r)
|
---|
| 767 | {
|
---|
| 768 | int i = 0;
|
---|
| 769 | int p = 0;
|
---|
| 770 | double[] buf = new double[0];
|
---|
| 771 | double[] buf2 = new double[0];
|
---|
| 772 | ftbase.ftplan plan = new ftbase.ftplan();
|
---|
| 773 | complex c1 = 0;
|
---|
| 774 | complex c2 = 0;
|
---|
| 775 | complex c3 = 0;
|
---|
| 776 | double t = 0;
|
---|
| 777 |
|
---|
| 778 | r = new complex[0];
|
---|
| 779 |
|
---|
| 780 | ap.assert((n>0 & m>0) & n<=m, "ConvC1DInv: incorrect N or M!");
|
---|
| 781 | p = ftbase.ftbasefindsmooth(m);
|
---|
| 782 | ftbase.ftbasegeneratecomplexfftplan(p, plan);
|
---|
| 783 | buf = new double[2*p];
|
---|
| 784 | for(i=0; i<=m-1; i++)
|
---|
| 785 | {
|
---|
| 786 | buf[2*i+0] = a[i].x;
|
---|
| 787 | buf[2*i+1] = a[i].y;
|
---|
| 788 | }
|
---|
| 789 | for(i=m; i<=p-1; i++)
|
---|
| 790 | {
|
---|
| 791 | buf[2*i+0] = 0;
|
---|
| 792 | buf[2*i+1] = 0;
|
---|
| 793 | }
|
---|
| 794 | buf2 = new double[2*p];
|
---|
| 795 | for(i=0; i<=n-1; i++)
|
---|
| 796 | {
|
---|
| 797 | buf2[2*i+0] = b[i].x;
|
---|
| 798 | buf2[2*i+1] = b[i].y;
|
---|
| 799 | }
|
---|
| 800 | for(i=n; i<=p-1; i++)
|
---|
| 801 | {
|
---|
| 802 | buf2[2*i+0] = 0;
|
---|
| 803 | buf2[2*i+1] = 0;
|
---|
| 804 | }
|
---|
| 805 | ftbase.ftbaseexecuteplan(ref buf, 0, p, plan);
|
---|
| 806 | ftbase.ftbaseexecuteplan(ref buf2, 0, p, plan);
|
---|
| 807 | for(i=0; i<=p-1; i++)
|
---|
| 808 | {
|
---|
| 809 | c1.x = buf[2*i+0];
|
---|
| 810 | c1.y = buf[2*i+1];
|
---|
| 811 | c2.x = buf2[2*i+0];
|
---|
| 812 | c2.y = buf2[2*i+1];
|
---|
| 813 | c3 = c1/c2;
|
---|
| 814 | buf[2*i+0] = c3.x;
|
---|
| 815 | buf[2*i+1] = -c3.y;
|
---|
| 816 | }
|
---|
| 817 | ftbase.ftbaseexecuteplan(ref buf, 0, p, plan);
|
---|
| 818 | t = (double)1/(double)p;
|
---|
| 819 | r = new complex[m-n+1];
|
---|
| 820 | for(i=0; i<=m-n; i++)
|
---|
| 821 | {
|
---|
| 822 | r[i].x = t*buf[2*i+0];
|
---|
| 823 | r[i].y = -(t*buf[2*i+1]);
|
---|
| 824 | }
|
---|
| 825 | }
|
---|
| 826 |
|
---|
| 827 |
|
---|
| 828 | /*************************************************************************
|
---|
| 829 | 1-dimensional circular complex convolution.
|
---|
| 830 |
|
---|
| 831 | For given S/R returns conv(S,R) (circular). Algorithm has linearithmic
|
---|
| 832 | complexity for any M/N.
|
---|
| 833 |
|
---|
| 834 | IMPORTANT: normal convolution is commutative, i.e. it is symmetric -
|
---|
| 835 | conv(A,B)=conv(B,A). Cyclic convolution IS NOT. One function - S - is a
|
---|
| 836 | signal, periodic function, and another - R - is a response, non-periodic
|
---|
| 837 | function with limited length.
|
---|
| 838 |
|
---|
| 839 | INPUT PARAMETERS
|
---|
| 840 | S - array[0..M-1] - complex periodic signal
|
---|
| 841 | M - problem size
|
---|
| 842 | B - array[0..N-1] - complex non-periodic response
|
---|
| 843 | N - problem size
|
---|
| 844 |
|
---|
| 845 | OUTPUT PARAMETERS
|
---|
| 846 | R - convolution: A*B. array[0..M-1].
|
---|
| 847 |
|
---|
| 848 | NOTE:
|
---|
| 849 | It is assumed that B is zero at T<0. If it has non-zero values at
|
---|
| 850 | negative T's, you can still use this subroutine - just shift its result
|
---|
| 851 | correspondingly.
|
---|
| 852 |
|
---|
| 853 | -- ALGLIB --
|
---|
| 854 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
| 855 | *************************************************************************/
|
---|
| 856 | public static void convc1dcircular(complex[] s,
|
---|
| 857 | int m,
|
---|
| 858 | complex[] r,
|
---|
| 859 | int n,
|
---|
| 860 | ref complex[] c)
|
---|
| 861 | {
|
---|
| 862 | complex[] buf = new complex[0];
|
---|
| 863 | int i1 = 0;
|
---|
| 864 | int i2 = 0;
|
---|
| 865 | int j2 = 0;
|
---|
| 866 | int i_ = 0;
|
---|
| 867 | int i1_ = 0;
|
---|
| 868 |
|
---|
| 869 | c = new complex[0];
|
---|
| 870 |
|
---|
| 871 | ap.assert(n>0 & m>0, "ConvC1DCircular: incorrect N or M!");
|
---|
| 872 |
|
---|
| 873 | //
|
---|
| 874 | // normalize task: make M>=N,
|
---|
| 875 | // so A will be longer (at least - not shorter) that B.
|
---|
| 876 | //
|
---|
| 877 | if( m<n )
|
---|
| 878 | {
|
---|
| 879 | buf = new complex[m];
|
---|
| 880 | for(i1=0; i1<=m-1; i1++)
|
---|
| 881 | {
|
---|
| 882 | buf[i1] = 0;
|
---|
| 883 | }
|
---|
| 884 | i1 = 0;
|
---|
| 885 | while( i1<n )
|
---|
| 886 | {
|
---|
| 887 | i2 = Math.Min(i1+m-1, n-1);
|
---|
| 888 | j2 = i2-i1;
|
---|
| 889 | i1_ = (i1) - (0);
|
---|
| 890 | for(i_=0; i_<=j2;i_++)
|
---|
| 891 | {
|
---|
| 892 | buf[i_] = buf[i_] + r[i_+i1_];
|
---|
| 893 | }
|
---|
| 894 | i1 = i1+m;
|
---|
| 895 | }
|
---|
| 896 | convc1dcircular(s, m, buf, m, ref c);
|
---|
| 897 | return;
|
---|
| 898 | }
|
---|
| 899 | convc1dx(s, m, r, n, true, -1, 0, ref c);
|
---|
| 900 | }
|
---|
| 901 |
|
---|
| 902 |
|
---|
| 903 | /*************************************************************************
|
---|
| 904 | 1-dimensional circular complex deconvolution (inverse of ConvC1DCircular()).
|
---|
| 905 |
|
---|
| 906 | Algorithm has M*log(M)) complexity for any M (composite or prime).
|
---|
| 907 |
|
---|
| 908 | INPUT PARAMETERS
|
---|
| 909 | A - array[0..M-1] - convolved periodic signal, A = conv(R, B)
|
---|
| 910 | M - convolved signal length
|
---|
| 911 | B - array[0..N-1] - non-periodic response
|
---|
| 912 | N - response length
|
---|
| 913 |
|
---|
| 914 | OUTPUT PARAMETERS
|
---|
| 915 | R - deconvolved signal. array[0..M-1].
|
---|
| 916 |
|
---|
| 917 | NOTE:
|
---|
| 918 | deconvolution is unstable process and may result in division by zero
|
---|
| 919 | (if your response function is degenerate, i.e. has zero Fourier coefficient).
|
---|
| 920 |
|
---|
| 921 | NOTE:
|
---|
| 922 | It is assumed that B is zero at T<0. If it has non-zero values at
|
---|
| 923 | negative T's, you can still use this subroutine - just shift its result
|
---|
| 924 | correspondingly.
|
---|
| 925 |
|
---|
| 926 | -- ALGLIB --
|
---|
| 927 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
| 928 | *************************************************************************/
|
---|
| 929 | public static void convc1dcircularinv(complex[] a,
|
---|
| 930 | int m,
|
---|
| 931 | complex[] b,
|
---|
| 932 | int n,
|
---|
| 933 | ref complex[] r)
|
---|
| 934 | {
|
---|
| 935 | int i = 0;
|
---|
| 936 | int i1 = 0;
|
---|
| 937 | int i2 = 0;
|
---|
| 938 | int j2 = 0;
|
---|
| 939 | double[] buf = new double[0];
|
---|
| 940 | double[] buf2 = new double[0];
|
---|
| 941 | complex[] cbuf = new complex[0];
|
---|
| 942 | ftbase.ftplan plan = new ftbase.ftplan();
|
---|
| 943 | complex c1 = 0;
|
---|
| 944 | complex c2 = 0;
|
---|
| 945 | complex c3 = 0;
|
---|
| 946 | double t = 0;
|
---|
| 947 | int i_ = 0;
|
---|
| 948 | int i1_ = 0;
|
---|
| 949 |
|
---|
| 950 | r = new complex[0];
|
---|
| 951 |
|
---|
| 952 | ap.assert(n>0 & m>0, "ConvC1DCircularInv: incorrect N or M!");
|
---|
| 953 |
|
---|
| 954 | //
|
---|
| 955 | // normalize task: make M>=N,
|
---|
| 956 | // so A will be longer (at least - not shorter) that B.
|
---|
| 957 | //
|
---|
| 958 | if( m<n )
|
---|
| 959 | {
|
---|
| 960 | cbuf = new complex[m];
|
---|
| 961 | for(i=0; i<=m-1; i++)
|
---|
| 962 | {
|
---|
| 963 | cbuf[i] = 0;
|
---|
| 964 | }
|
---|
| 965 | i1 = 0;
|
---|
| 966 | while( i1<n )
|
---|
| 967 | {
|
---|
| 968 | i2 = Math.Min(i1+m-1, n-1);
|
---|
| 969 | j2 = i2-i1;
|
---|
| 970 | i1_ = (i1) - (0);
|
---|
| 971 | for(i_=0; i_<=j2;i_++)
|
---|
| 972 | {
|
---|
| 973 | cbuf[i_] = cbuf[i_] + b[i_+i1_];
|
---|
| 974 | }
|
---|
| 975 | i1 = i1+m;
|
---|
| 976 | }
|
---|
| 977 | convc1dcircularinv(a, m, cbuf, m, ref r);
|
---|
| 978 | return;
|
---|
| 979 | }
|
---|
| 980 |
|
---|
| 981 | //
|
---|
| 982 | // Task is normalized
|
---|
| 983 | //
|
---|
| 984 | ftbase.ftbasegeneratecomplexfftplan(m, plan);
|
---|
| 985 | buf = new double[2*m];
|
---|
| 986 | for(i=0; i<=m-1; i++)
|
---|
| 987 | {
|
---|
| 988 | buf[2*i+0] = a[i].x;
|
---|
| 989 | buf[2*i+1] = a[i].y;
|
---|
| 990 | }
|
---|
| 991 | buf2 = new double[2*m];
|
---|
| 992 | for(i=0; i<=n-1; i++)
|
---|
| 993 | {
|
---|
| 994 | buf2[2*i+0] = b[i].x;
|
---|
| 995 | buf2[2*i+1] = b[i].y;
|
---|
| 996 | }
|
---|
| 997 | for(i=n; i<=m-1; i++)
|
---|
| 998 | {
|
---|
| 999 | buf2[2*i+0] = 0;
|
---|
| 1000 | buf2[2*i+1] = 0;
|
---|
| 1001 | }
|
---|
| 1002 | ftbase.ftbaseexecuteplan(ref buf, 0, m, plan);
|
---|
| 1003 | ftbase.ftbaseexecuteplan(ref buf2, 0, m, plan);
|
---|
| 1004 | for(i=0; i<=m-1; i++)
|
---|
| 1005 | {
|
---|
| 1006 | c1.x = buf[2*i+0];
|
---|
| 1007 | c1.y = buf[2*i+1];
|
---|
| 1008 | c2.x = buf2[2*i+0];
|
---|
| 1009 | c2.y = buf2[2*i+1];
|
---|
| 1010 | c3 = c1/c2;
|
---|
| 1011 | buf[2*i+0] = c3.x;
|
---|
| 1012 | buf[2*i+1] = -c3.y;
|
---|
| 1013 | }
|
---|
| 1014 | ftbase.ftbaseexecuteplan(ref buf, 0, m, plan);
|
---|
| 1015 | t = (double)1/(double)m;
|
---|
| 1016 | r = new complex[m];
|
---|
| 1017 | for(i=0; i<=m-1; i++)
|
---|
| 1018 | {
|
---|
| 1019 | r[i].x = t*buf[2*i+0];
|
---|
| 1020 | r[i].y = -(t*buf[2*i+1]);
|
---|
| 1021 | }
|
---|
| 1022 | }
|
---|
| 1023 |
|
---|
| 1024 |
|
---|
| 1025 | /*************************************************************************
|
---|
| 1026 | 1-dimensional real convolution.
|
---|
| 1027 |
|
---|
| 1028 | Analogous to ConvC1D(), see ConvC1D() comments for more details.
|
---|
| 1029 |
|
---|
| 1030 | INPUT PARAMETERS
|
---|
| 1031 | A - array[0..M-1] - real function to be transformed
|
---|
| 1032 | M - problem size
|
---|
| 1033 | B - array[0..N-1] - real function to be transformed
|
---|
| 1034 | N - problem size
|
---|
| 1035 |
|
---|
| 1036 | OUTPUT PARAMETERS
|
---|
| 1037 | R - convolution: A*B. array[0..N+M-2].
|
---|
| 1038 |
|
---|
| 1039 | NOTE:
|
---|
| 1040 | It is assumed that A is zero at T<0, B is zero too. If one or both
|
---|
| 1041 | functions have non-zero values at negative T's, you can still use this
|
---|
| 1042 | subroutine - just shift its result correspondingly.
|
---|
| 1043 |
|
---|
| 1044 | -- ALGLIB --
|
---|
| 1045 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
| 1046 | *************************************************************************/
|
---|
| 1047 | public static void convr1d(double[] a,
|
---|
| 1048 | int m,
|
---|
| 1049 | double[] b,
|
---|
| 1050 | int n,
|
---|
| 1051 | ref double[] r)
|
---|
| 1052 | {
|
---|
| 1053 | r = new double[0];
|
---|
| 1054 |
|
---|
| 1055 | ap.assert(n>0 & m>0, "ConvR1D: incorrect N or M!");
|
---|
| 1056 |
|
---|
| 1057 | //
|
---|
| 1058 | // normalize task: make M>=N,
|
---|
| 1059 | // so A will be longer that B.
|
---|
| 1060 | //
|
---|
| 1061 | if( m<n )
|
---|
| 1062 | {
|
---|
| 1063 | convr1d(b, n, a, m, ref r);
|
---|
| 1064 | return;
|
---|
| 1065 | }
|
---|
| 1066 | convr1dx(a, m, b, n, false, -1, 0, ref r);
|
---|
| 1067 | }
|
---|
| 1068 |
|
---|
| 1069 |
|
---|
| 1070 | /*************************************************************************
|
---|
| 1071 | 1-dimensional real deconvolution (inverse of ConvC1D()).
|
---|
| 1072 |
|
---|
| 1073 | Algorithm has M*log(M)) complexity for any M (composite or prime).
|
---|
| 1074 |
|
---|
| 1075 | INPUT PARAMETERS
|
---|
| 1076 | A - array[0..M-1] - convolved signal, A = conv(R, B)
|
---|
| 1077 | M - convolved signal length
|
---|
| 1078 | B - array[0..N-1] - response
|
---|
| 1079 | N - response length, N<=M
|
---|
| 1080 |
|
---|
| 1081 | OUTPUT PARAMETERS
|
---|
| 1082 | R - deconvolved signal. array[0..M-N].
|
---|
| 1083 |
|
---|
| 1084 | NOTE:
|
---|
| 1085 | deconvolution is unstable process and may result in division by zero
|
---|
| 1086 | (if your response function is degenerate, i.e. has zero Fourier coefficient).
|
---|
| 1087 |
|
---|
| 1088 | NOTE:
|
---|
| 1089 | It is assumed that A is zero at T<0, B is zero too. If one or both
|
---|
| 1090 | functions have non-zero values at negative T's, you can still use this
|
---|
| 1091 | subroutine - just shift its result correspondingly.
|
---|
| 1092 |
|
---|
| 1093 | -- ALGLIB --
|
---|
| 1094 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
| 1095 | *************************************************************************/
|
---|
| 1096 | public static void convr1dinv(double[] a,
|
---|
| 1097 | int m,
|
---|
| 1098 | double[] b,
|
---|
| 1099 | int n,
|
---|
| 1100 | ref double[] r)
|
---|
| 1101 | {
|
---|
| 1102 | int i = 0;
|
---|
| 1103 | int p = 0;
|
---|
| 1104 | double[] buf = new double[0];
|
---|
| 1105 | double[] buf2 = new double[0];
|
---|
| 1106 | double[] buf3 = new double[0];
|
---|
| 1107 | ftbase.ftplan plan = new ftbase.ftplan();
|
---|
| 1108 | complex c1 = 0;
|
---|
| 1109 | complex c2 = 0;
|
---|
| 1110 | complex c3 = 0;
|
---|
| 1111 | int i_ = 0;
|
---|
| 1112 |
|
---|
| 1113 | r = new double[0];
|
---|
| 1114 |
|
---|
| 1115 | ap.assert((n>0 & m>0) & n<=m, "ConvR1DInv: incorrect N or M!");
|
---|
| 1116 | p = ftbase.ftbasefindsmootheven(m);
|
---|
| 1117 | buf = new double[p];
|
---|
| 1118 | for(i_=0; i_<=m-1;i_++)
|
---|
| 1119 | {
|
---|
| 1120 | buf[i_] = a[i_];
|
---|
| 1121 | }
|
---|
| 1122 | for(i=m; i<=p-1; i++)
|
---|
| 1123 | {
|
---|
| 1124 | buf[i] = 0;
|
---|
| 1125 | }
|
---|
| 1126 | buf2 = new double[p];
|
---|
| 1127 | for(i_=0; i_<=n-1;i_++)
|
---|
| 1128 | {
|
---|
| 1129 | buf2[i_] = b[i_];
|
---|
| 1130 | }
|
---|
| 1131 | for(i=n; i<=p-1; i++)
|
---|
| 1132 | {
|
---|
| 1133 | buf2[i] = 0;
|
---|
| 1134 | }
|
---|
| 1135 | buf3 = new double[p];
|
---|
| 1136 | ftbase.ftbasegeneratecomplexfftplan(p/2, plan);
|
---|
| 1137 | fft.fftr1dinternaleven(ref buf, p, ref buf3, plan);
|
---|
| 1138 | fft.fftr1dinternaleven(ref buf2, p, ref buf3, plan);
|
---|
| 1139 | buf[0] = buf[0]/buf2[0];
|
---|
| 1140 | buf[1] = buf[1]/buf2[1];
|
---|
| 1141 | for(i=1; i<=p/2-1; i++)
|
---|
| 1142 | {
|
---|
| 1143 | c1.x = buf[2*i+0];
|
---|
| 1144 | c1.y = buf[2*i+1];
|
---|
| 1145 | c2.x = buf2[2*i+0];
|
---|
| 1146 | c2.y = buf2[2*i+1];
|
---|
| 1147 | c3 = c1/c2;
|
---|
| 1148 | buf[2*i+0] = c3.x;
|
---|
| 1149 | buf[2*i+1] = c3.y;
|
---|
| 1150 | }
|
---|
| 1151 | fft.fftr1dinvinternaleven(ref buf, p, ref buf3, plan);
|
---|
| 1152 | r = new double[m-n+1];
|
---|
| 1153 | for(i_=0; i_<=m-n;i_++)
|
---|
| 1154 | {
|
---|
| 1155 | r[i_] = buf[i_];
|
---|
| 1156 | }
|
---|
| 1157 | }
|
---|
| 1158 |
|
---|
| 1159 |
|
---|
| 1160 | /*************************************************************************
|
---|
| 1161 | 1-dimensional circular real convolution.
|
---|
| 1162 |
|
---|
| 1163 | Analogous to ConvC1DCircular(), see ConvC1DCircular() comments for more details.
|
---|
| 1164 |
|
---|
| 1165 | INPUT PARAMETERS
|
---|
| 1166 | S - array[0..M-1] - real signal
|
---|
| 1167 | M - problem size
|
---|
| 1168 | B - array[0..N-1] - real response
|
---|
| 1169 | N - problem size
|
---|
| 1170 |
|
---|
| 1171 | OUTPUT PARAMETERS
|
---|
| 1172 | R - convolution: A*B. array[0..M-1].
|
---|
| 1173 |
|
---|
| 1174 | NOTE:
|
---|
| 1175 | It is assumed that B is zero at T<0. If it has non-zero values at
|
---|
| 1176 | negative T's, you can still use this subroutine - just shift its result
|
---|
| 1177 | correspondingly.
|
---|
| 1178 |
|
---|
| 1179 | -- ALGLIB --
|
---|
| 1180 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
| 1181 | *************************************************************************/
|
---|
| 1182 | public static void convr1dcircular(double[] s,
|
---|
| 1183 | int m,
|
---|
| 1184 | double[] r,
|
---|
| 1185 | int n,
|
---|
| 1186 | ref double[] c)
|
---|
| 1187 | {
|
---|
| 1188 | double[] buf = new double[0];
|
---|
| 1189 | int i1 = 0;
|
---|
| 1190 | int i2 = 0;
|
---|
| 1191 | int j2 = 0;
|
---|
| 1192 | int i_ = 0;
|
---|
| 1193 | int i1_ = 0;
|
---|
| 1194 |
|
---|
| 1195 | c = new double[0];
|
---|
| 1196 |
|
---|
| 1197 | ap.assert(n>0 & m>0, "ConvC1DCircular: incorrect N or M!");
|
---|
| 1198 |
|
---|
| 1199 | //
|
---|
| 1200 | // normalize task: make M>=N,
|
---|
| 1201 | // so A will be longer (at least - not shorter) that B.
|
---|
| 1202 | //
|
---|
| 1203 | if( m<n )
|
---|
| 1204 | {
|
---|
| 1205 | buf = new double[m];
|
---|
| 1206 | for(i1=0; i1<=m-1; i1++)
|
---|
| 1207 | {
|
---|
| 1208 | buf[i1] = 0;
|
---|
| 1209 | }
|
---|
| 1210 | i1 = 0;
|
---|
| 1211 | while( i1<n )
|
---|
| 1212 | {
|
---|
| 1213 | i2 = Math.Min(i1+m-1, n-1);
|
---|
| 1214 | j2 = i2-i1;
|
---|
| 1215 | i1_ = (i1) - (0);
|
---|
| 1216 | for(i_=0; i_<=j2;i_++)
|
---|
| 1217 | {
|
---|
| 1218 | buf[i_] = buf[i_] + r[i_+i1_];
|
---|
| 1219 | }
|
---|
| 1220 | i1 = i1+m;
|
---|
| 1221 | }
|
---|
| 1222 | convr1dcircular(s, m, buf, m, ref c);
|
---|
| 1223 | return;
|
---|
| 1224 | }
|
---|
| 1225 |
|
---|
| 1226 | //
|
---|
| 1227 | // reduce to usual convolution
|
---|
| 1228 | //
|
---|
| 1229 | convr1dx(s, m, r, n, true, -1, 0, ref c);
|
---|
| 1230 | }
|
---|
| 1231 |
|
---|
| 1232 |
|
---|
| 1233 | /*************************************************************************
|
---|
| 1234 | 1-dimensional complex deconvolution (inverse of ConvC1D()).
|
---|
| 1235 |
|
---|
| 1236 | Algorithm has M*log(M)) complexity for any M (composite or prime).
|
---|
| 1237 |
|
---|
| 1238 | INPUT PARAMETERS
|
---|
| 1239 | A - array[0..M-1] - convolved signal, A = conv(R, B)
|
---|
| 1240 | M - convolved signal length
|
---|
| 1241 | B - array[0..N-1] - response
|
---|
| 1242 | N - response length
|
---|
| 1243 |
|
---|
| 1244 | OUTPUT PARAMETERS
|
---|
| 1245 | R - deconvolved signal. array[0..M-N].
|
---|
| 1246 |
|
---|
| 1247 | NOTE:
|
---|
| 1248 | deconvolution is unstable process and may result in division by zero
|
---|
| 1249 | (if your response function is degenerate, i.e. has zero Fourier coefficient).
|
---|
| 1250 |
|
---|
| 1251 | NOTE:
|
---|
| 1252 | It is assumed that B is zero at T<0. If it has non-zero values at
|
---|
| 1253 | negative T's, you can still use this subroutine - just shift its result
|
---|
| 1254 | correspondingly.
|
---|
| 1255 |
|
---|
| 1256 | -- ALGLIB --
|
---|
| 1257 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
| 1258 | *************************************************************************/
|
---|
| 1259 | public static void convr1dcircularinv(double[] a,
|
---|
| 1260 | int m,
|
---|
| 1261 | double[] b,
|
---|
| 1262 | int n,
|
---|
| 1263 | ref double[] r)
|
---|
| 1264 | {
|
---|
| 1265 | int i = 0;
|
---|
| 1266 | int i1 = 0;
|
---|
| 1267 | int i2 = 0;
|
---|
| 1268 | int j2 = 0;
|
---|
| 1269 | double[] buf = new double[0];
|
---|
| 1270 | double[] buf2 = new double[0];
|
---|
| 1271 | double[] buf3 = new double[0];
|
---|
| 1272 | complex[] cbuf = new complex[0];
|
---|
| 1273 | complex[] cbuf2 = new complex[0];
|
---|
| 1274 | ftbase.ftplan plan = new ftbase.ftplan();
|
---|
| 1275 | complex c1 = 0;
|
---|
| 1276 | complex c2 = 0;
|
---|
| 1277 | complex c3 = 0;
|
---|
| 1278 | int i_ = 0;
|
---|
| 1279 | int i1_ = 0;
|
---|
| 1280 |
|
---|
| 1281 | r = new double[0];
|
---|
| 1282 |
|
---|
| 1283 | ap.assert(n>0 & m>0, "ConvR1DCircularInv: incorrect N or M!");
|
---|
| 1284 |
|
---|
| 1285 | //
|
---|
| 1286 | // normalize task: make M>=N,
|
---|
| 1287 | // so A will be longer (at least - not shorter) that B.
|
---|
| 1288 | //
|
---|
| 1289 | if( m<n )
|
---|
| 1290 | {
|
---|
| 1291 | buf = new double[m];
|
---|
| 1292 | for(i=0; i<=m-1; i++)
|
---|
| 1293 | {
|
---|
| 1294 | buf[i] = 0;
|
---|
| 1295 | }
|
---|
| 1296 | i1 = 0;
|
---|
| 1297 | while( i1<n )
|
---|
| 1298 | {
|
---|
| 1299 | i2 = Math.Min(i1+m-1, n-1);
|
---|
| 1300 | j2 = i2-i1;
|
---|
| 1301 | i1_ = (i1) - (0);
|
---|
| 1302 | for(i_=0; i_<=j2;i_++)
|
---|
| 1303 | {
|
---|
| 1304 | buf[i_] = buf[i_] + b[i_+i1_];
|
---|
| 1305 | }
|
---|
| 1306 | i1 = i1+m;
|
---|
| 1307 | }
|
---|
| 1308 | convr1dcircularinv(a, m, buf, m, ref r);
|
---|
| 1309 | return;
|
---|
| 1310 | }
|
---|
| 1311 |
|
---|
| 1312 | //
|
---|
| 1313 | // Task is normalized
|
---|
| 1314 | //
|
---|
| 1315 | if( m%2==0 )
|
---|
| 1316 | {
|
---|
| 1317 |
|
---|
| 1318 | //
|
---|
| 1319 | // size is even, use fast even-size FFT
|
---|
| 1320 | //
|
---|
| 1321 | buf = new double[m];
|
---|
| 1322 | for(i_=0; i_<=m-1;i_++)
|
---|
| 1323 | {
|
---|
| 1324 | buf[i_] = a[i_];
|
---|
| 1325 | }
|
---|
| 1326 | buf2 = new double[m];
|
---|
| 1327 | for(i_=0; i_<=n-1;i_++)
|
---|
| 1328 | {
|
---|
| 1329 | buf2[i_] = b[i_];
|
---|
| 1330 | }
|
---|
| 1331 | for(i=n; i<=m-1; i++)
|
---|
| 1332 | {
|
---|
| 1333 | buf2[i] = 0;
|
---|
| 1334 | }
|
---|
| 1335 | buf3 = new double[m];
|
---|
| 1336 | ftbase.ftbasegeneratecomplexfftplan(m/2, plan);
|
---|
| 1337 | fft.fftr1dinternaleven(ref buf, m, ref buf3, plan);
|
---|
| 1338 | fft.fftr1dinternaleven(ref buf2, m, ref buf3, plan);
|
---|
| 1339 | buf[0] = buf[0]/buf2[0];
|
---|
| 1340 | buf[1] = buf[1]/buf2[1];
|
---|
| 1341 | for(i=1; i<=m/2-1; i++)
|
---|
| 1342 | {
|
---|
| 1343 | c1.x = buf[2*i+0];
|
---|
| 1344 | c1.y = buf[2*i+1];
|
---|
| 1345 | c2.x = buf2[2*i+0];
|
---|
| 1346 | c2.y = buf2[2*i+1];
|
---|
| 1347 | c3 = c1/c2;
|
---|
| 1348 | buf[2*i+0] = c3.x;
|
---|
| 1349 | buf[2*i+1] = c3.y;
|
---|
| 1350 | }
|
---|
| 1351 | fft.fftr1dinvinternaleven(ref buf, m, ref buf3, plan);
|
---|
| 1352 | r = new double[m];
|
---|
| 1353 | for(i_=0; i_<=m-1;i_++)
|
---|
| 1354 | {
|
---|
| 1355 | r[i_] = buf[i_];
|
---|
| 1356 | }
|
---|
| 1357 | }
|
---|
| 1358 | else
|
---|
| 1359 | {
|
---|
| 1360 |
|
---|
| 1361 | //
|
---|
| 1362 | // odd-size, use general real FFT
|
---|
| 1363 | //
|
---|
| 1364 | fft.fftr1d(a, m, ref cbuf);
|
---|
| 1365 | buf2 = new double[m];
|
---|
| 1366 | for(i_=0; i_<=n-1;i_++)
|
---|
| 1367 | {
|
---|
| 1368 | buf2[i_] = b[i_];
|
---|
| 1369 | }
|
---|
| 1370 | for(i=n; i<=m-1; i++)
|
---|
| 1371 | {
|
---|
| 1372 | buf2[i] = 0;
|
---|
| 1373 | }
|
---|
| 1374 | fft.fftr1d(buf2, m, ref cbuf2);
|
---|
| 1375 | for(i=0; i<=(int)Math.Floor((double)m/(double)2); i++)
|
---|
| 1376 | {
|
---|
| 1377 | cbuf[i] = cbuf[i]/cbuf2[i];
|
---|
| 1378 | }
|
---|
| 1379 | fft.fftr1dinv(cbuf, m, ref r);
|
---|
| 1380 | }
|
---|
| 1381 | }
|
---|
| 1382 |
|
---|
| 1383 |
|
---|
| 1384 | /*************************************************************************
|
---|
| 1385 | 1-dimensional complex convolution.
|
---|
| 1386 |
|
---|
| 1387 | Extended subroutine which allows to choose convolution algorithm.
|
---|
| 1388 | Intended for internal use, ALGLIB users should call ConvC1D()/ConvC1DCircular().
|
---|
| 1389 |
|
---|
| 1390 | INPUT PARAMETERS
|
---|
| 1391 | A - array[0..M-1] - complex function to be transformed
|
---|
| 1392 | M - problem size
|
---|
| 1393 | B - array[0..N-1] - complex function to be transformed
|
---|
| 1394 | N - problem size, N<=M
|
---|
| 1395 | Alg - algorithm type:
|
---|
| 1396 | *-2 auto-select Q for overlap-add
|
---|
| 1397 | *-1 auto-select algorithm and parameters
|
---|
| 1398 | * 0 straightforward formula for small N's
|
---|
| 1399 | * 1 general FFT-based code
|
---|
| 1400 | * 2 overlap-add with length Q
|
---|
| 1401 | Q - length for overlap-add
|
---|
| 1402 |
|
---|
| 1403 | OUTPUT PARAMETERS
|
---|
| 1404 | R - convolution: A*B. array[0..N+M-1].
|
---|
| 1405 |
|
---|
| 1406 | -- ALGLIB --
|
---|
| 1407 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
| 1408 | *************************************************************************/
|
---|
| 1409 | public static void convc1dx(complex[] a,
|
---|
| 1410 | int m,
|
---|
| 1411 | complex[] b,
|
---|
| 1412 | int n,
|
---|
| 1413 | bool circular,
|
---|
| 1414 | int alg,
|
---|
| 1415 | int q,
|
---|
| 1416 | ref complex[] r)
|
---|
| 1417 | {
|
---|
| 1418 | int i = 0;
|
---|
| 1419 | int j = 0;
|
---|
| 1420 | int p = 0;
|
---|
| 1421 | int ptotal = 0;
|
---|
| 1422 | int i1 = 0;
|
---|
| 1423 | int i2 = 0;
|
---|
| 1424 | int j1 = 0;
|
---|
| 1425 | int j2 = 0;
|
---|
| 1426 | complex[] bbuf = new complex[0];
|
---|
| 1427 | complex v = 0;
|
---|
| 1428 | double ax = 0;
|
---|
| 1429 | double ay = 0;
|
---|
| 1430 | double bx = 0;
|
---|
| 1431 | double by = 0;
|
---|
| 1432 | double t = 0;
|
---|
| 1433 | double tx = 0;
|
---|
| 1434 | double ty = 0;
|
---|
| 1435 | double flopcand = 0;
|
---|
| 1436 | double flopbest = 0;
|
---|
| 1437 | int algbest = 0;
|
---|
| 1438 | ftbase.ftplan plan = new ftbase.ftplan();
|
---|
| 1439 | double[] buf = new double[0];
|
---|
| 1440 | double[] buf2 = new double[0];
|
---|
| 1441 | int i_ = 0;
|
---|
| 1442 | int i1_ = 0;
|
---|
| 1443 |
|
---|
| 1444 | r = new complex[0];
|
---|
| 1445 |
|
---|
| 1446 | ap.assert(n>0 & m>0, "ConvC1DX: incorrect N or M!");
|
---|
| 1447 | ap.assert(n<=m, "ConvC1DX: N<M assumption is false!");
|
---|
| 1448 |
|
---|
| 1449 | //
|
---|
| 1450 | // Auto-select
|
---|
| 1451 | //
|
---|
| 1452 | if( alg==-1 | alg==-2 )
|
---|
| 1453 | {
|
---|
| 1454 |
|
---|
| 1455 | //
|
---|
| 1456 | // Initial candidate: straightforward implementation.
|
---|
| 1457 | //
|
---|
| 1458 | // If we want to use auto-fitted overlap-add,
|
---|
| 1459 | // flop count is initialized by large real number - to force
|
---|
| 1460 | // another algorithm selection
|
---|
| 1461 | //
|
---|
| 1462 | algbest = 0;
|
---|
| 1463 | if( alg==-1 )
|
---|
| 1464 | {
|
---|
| 1465 | flopbest = 2*m*n;
|
---|
| 1466 | }
|
---|
| 1467 | else
|
---|
| 1468 | {
|
---|
| 1469 | flopbest = math.maxrealnumber;
|
---|
| 1470 | }
|
---|
| 1471 |
|
---|
| 1472 | //
|
---|
| 1473 | // Another candidate - generic FFT code
|
---|
| 1474 | //
|
---|
| 1475 | if( alg==-1 )
|
---|
| 1476 | {
|
---|
| 1477 | if( circular & ftbase.ftbaseissmooth(m) )
|
---|
| 1478 | {
|
---|
| 1479 |
|
---|
| 1480 | //
|
---|
| 1481 | // special code for circular convolution of a sequence with a smooth length
|
---|
| 1482 | //
|
---|
| 1483 | flopcand = 3*ftbase.ftbasegetflopestimate(m)+6*m;
|
---|
| 1484 | if( (double)(flopcand)<(double)(flopbest) )
|
---|
| 1485 | {
|
---|
| 1486 | algbest = 1;
|
---|
| 1487 | flopbest = flopcand;
|
---|
| 1488 | }
|
---|
| 1489 | }
|
---|
| 1490 | else
|
---|
| 1491 | {
|
---|
| 1492 |
|
---|
| 1493 | //
|
---|
| 1494 | // general cyclic/non-cyclic convolution
|
---|
| 1495 | //
|
---|
| 1496 | p = ftbase.ftbasefindsmooth(m+n-1);
|
---|
| 1497 | flopcand = 3*ftbase.ftbasegetflopestimate(p)+6*p;
|
---|
| 1498 | if( (double)(flopcand)<(double)(flopbest) )
|
---|
| 1499 | {
|
---|
| 1500 | algbest = 1;
|
---|
| 1501 | flopbest = flopcand;
|
---|
| 1502 | }
|
---|
| 1503 | }
|
---|
| 1504 | }
|
---|
| 1505 |
|
---|
| 1506 | //
|
---|
| 1507 | // Another candidate - overlap-add
|
---|
| 1508 | //
|
---|
| 1509 | q = 1;
|
---|
| 1510 | ptotal = 1;
|
---|
| 1511 | while( ptotal<n )
|
---|
| 1512 | {
|
---|
| 1513 | ptotal = ptotal*2;
|
---|
| 1514 | }
|
---|
| 1515 | while( ptotal<=m+n-1 )
|
---|
| 1516 | {
|
---|
| 1517 | p = ptotal-n+1;
|
---|
| 1518 | flopcand = (int)Math.Ceiling((double)m/(double)p)*(2*ftbase.ftbasegetflopestimate(ptotal)+8*ptotal);
|
---|
| 1519 | if( (double)(flopcand)<(double)(flopbest) )
|
---|
| 1520 | {
|
---|
| 1521 | flopbest = flopcand;
|
---|
| 1522 | algbest = 2;
|
---|
| 1523 | q = p;
|
---|
| 1524 | }
|
---|
| 1525 | ptotal = ptotal*2;
|
---|
| 1526 | }
|
---|
| 1527 | alg = algbest;
|
---|
| 1528 | convc1dx(a, m, b, n, circular, alg, q, ref r);
|
---|
| 1529 | return;
|
---|
| 1530 | }
|
---|
| 1531 |
|
---|
| 1532 | //
|
---|
| 1533 | // straightforward formula for
|
---|
| 1534 | // circular and non-circular convolutions.
|
---|
| 1535 | //
|
---|
| 1536 | // Very simple code, no further comments needed.
|
---|
| 1537 | //
|
---|
| 1538 | if( alg==0 )
|
---|
| 1539 | {
|
---|
| 1540 |
|
---|
| 1541 | //
|
---|
| 1542 | // Special case: N=1
|
---|
| 1543 | //
|
---|
| 1544 | if( n==1 )
|
---|
| 1545 | {
|
---|
| 1546 | r = new complex[m];
|
---|
| 1547 | v = b[0];
|
---|
| 1548 | for(i_=0; i_<=m-1;i_++)
|
---|
| 1549 | {
|
---|
| 1550 | r[i_] = v*a[i_];
|
---|
| 1551 | }
|
---|
| 1552 | return;
|
---|
| 1553 | }
|
---|
| 1554 |
|
---|
| 1555 | //
|
---|
| 1556 | // use straightforward formula
|
---|
| 1557 | //
|
---|
| 1558 | if( circular )
|
---|
| 1559 | {
|
---|
| 1560 |
|
---|
| 1561 | //
|
---|
| 1562 | // circular convolution
|
---|
| 1563 | //
|
---|
| 1564 | r = new complex[m];
|
---|
| 1565 | v = b[0];
|
---|
| 1566 | for(i_=0; i_<=m-1;i_++)
|
---|
| 1567 | {
|
---|
| 1568 | r[i_] = v*a[i_];
|
---|
| 1569 | }
|
---|
| 1570 | for(i=1; i<=n-1; i++)
|
---|
| 1571 | {
|
---|
| 1572 | v = b[i];
|
---|
| 1573 | i1 = 0;
|
---|
| 1574 | i2 = i-1;
|
---|
| 1575 | j1 = m-i;
|
---|
| 1576 | j2 = m-1;
|
---|
| 1577 | i1_ = (j1) - (i1);
|
---|
| 1578 | for(i_=i1; i_<=i2;i_++)
|
---|
| 1579 | {
|
---|
| 1580 | r[i_] = r[i_] + v*a[i_+i1_];
|
---|
| 1581 | }
|
---|
| 1582 | i1 = i;
|
---|
| 1583 | i2 = m-1;
|
---|
| 1584 | j1 = 0;
|
---|
| 1585 | j2 = m-i-1;
|
---|
| 1586 | i1_ = (j1) - (i1);
|
---|
| 1587 | for(i_=i1; i_<=i2;i_++)
|
---|
| 1588 | {
|
---|
| 1589 | r[i_] = r[i_] + v*a[i_+i1_];
|
---|
| 1590 | }
|
---|
| 1591 | }
|
---|
| 1592 | }
|
---|
| 1593 | else
|
---|
| 1594 | {
|
---|
| 1595 |
|
---|
| 1596 | //
|
---|
| 1597 | // non-circular convolution
|
---|
| 1598 | //
|
---|
| 1599 | r = new complex[m+n-1];
|
---|
| 1600 | for(i=0; i<=m+n-2; i++)
|
---|
| 1601 | {
|
---|
| 1602 | r[i] = 0;
|
---|
| 1603 | }
|
---|
| 1604 | for(i=0; i<=n-1; i++)
|
---|
| 1605 | {
|
---|
| 1606 | v = b[i];
|
---|
| 1607 | i1_ = (0) - (i);
|
---|
| 1608 | for(i_=i; i_<=i+m-1;i_++)
|
---|
| 1609 | {
|
---|
| 1610 | r[i_] = r[i_] + v*a[i_+i1_];
|
---|
| 1611 | }
|
---|
| 1612 | }
|
---|
| 1613 | }
|
---|
| 1614 | return;
|
---|
| 1615 | }
|
---|
| 1616 |
|
---|
| 1617 | //
|
---|
| 1618 | // general FFT-based code for
|
---|
| 1619 | // circular and non-circular convolutions.
|
---|
| 1620 | //
|
---|
| 1621 | // First, if convolution is circular, we test whether M is smooth or not.
|
---|
| 1622 | // If it is smooth, we just use M-length FFT to calculate convolution.
|
---|
| 1623 | // If it is not, we calculate non-circular convolution and wrap it arount.
|
---|
| 1624 | //
|
---|
| 1625 | // IF convolution is non-circular, we use zero-padding + FFT.
|
---|
| 1626 | //
|
---|
| 1627 | if( alg==1 )
|
---|
| 1628 | {
|
---|
| 1629 | if( circular & ftbase.ftbaseissmooth(m) )
|
---|
| 1630 | {
|
---|
| 1631 |
|
---|
| 1632 | //
|
---|
| 1633 | // special code for circular convolution with smooth M
|
---|
| 1634 | //
|
---|
| 1635 | ftbase.ftbasegeneratecomplexfftplan(m, plan);
|
---|
| 1636 | buf = new double[2*m];
|
---|
| 1637 | for(i=0; i<=m-1; i++)
|
---|
| 1638 | {
|
---|
| 1639 | buf[2*i+0] = a[i].x;
|
---|
| 1640 | buf[2*i+1] = a[i].y;
|
---|
| 1641 | }
|
---|
| 1642 | buf2 = new double[2*m];
|
---|
| 1643 | for(i=0; i<=n-1; i++)
|
---|
| 1644 | {
|
---|
| 1645 | buf2[2*i+0] = b[i].x;
|
---|
| 1646 | buf2[2*i+1] = b[i].y;
|
---|
| 1647 | }
|
---|
| 1648 | for(i=n; i<=m-1; i++)
|
---|
| 1649 | {
|
---|
| 1650 | buf2[2*i+0] = 0;
|
---|
| 1651 | buf2[2*i+1] = 0;
|
---|
| 1652 | }
|
---|
| 1653 | ftbase.ftbaseexecuteplan(ref buf, 0, m, plan);
|
---|
| 1654 | ftbase.ftbaseexecuteplan(ref buf2, 0, m, plan);
|
---|
| 1655 | for(i=0; i<=m-1; i++)
|
---|
| 1656 | {
|
---|
| 1657 | ax = buf[2*i+0];
|
---|
| 1658 | ay = buf[2*i+1];
|
---|
| 1659 | bx = buf2[2*i+0];
|
---|
| 1660 | by = buf2[2*i+1];
|
---|
| 1661 | tx = ax*bx-ay*by;
|
---|
| 1662 | ty = ax*by+ay*bx;
|
---|
| 1663 | buf[2*i+0] = tx;
|
---|
| 1664 | buf[2*i+1] = -ty;
|
---|
| 1665 | }
|
---|
| 1666 | ftbase.ftbaseexecuteplan(ref buf, 0, m, plan);
|
---|
| 1667 | t = (double)1/(double)m;
|
---|
| 1668 | r = new complex[m];
|
---|
| 1669 | for(i=0; i<=m-1; i++)
|
---|
| 1670 | {
|
---|
| 1671 | r[i].x = t*buf[2*i+0];
|
---|
| 1672 | r[i].y = -(t*buf[2*i+1]);
|
---|
| 1673 | }
|
---|
| 1674 | }
|
---|
| 1675 | else
|
---|
| 1676 | {
|
---|
| 1677 |
|
---|
| 1678 | //
|
---|
| 1679 | // M is non-smooth, general code (circular/non-circular):
|
---|
| 1680 | // * first part is the same for circular and non-circular
|
---|
| 1681 | // convolutions. zero padding, FFTs, inverse FFTs
|
---|
| 1682 | // * second part differs:
|
---|
| 1683 | // * for non-circular convolution we just copy array
|
---|
| 1684 | // * for circular convolution we add array tail to its head
|
---|
| 1685 | //
|
---|
| 1686 | p = ftbase.ftbasefindsmooth(m+n-1);
|
---|
| 1687 | ftbase.ftbasegeneratecomplexfftplan(p, plan);
|
---|
| 1688 | buf = new double[2*p];
|
---|
| 1689 | for(i=0; i<=m-1; i++)
|
---|
| 1690 | {
|
---|
| 1691 | buf[2*i+0] = a[i].x;
|
---|
| 1692 | buf[2*i+1] = a[i].y;
|
---|
| 1693 | }
|
---|
| 1694 | for(i=m; i<=p-1; i++)
|
---|
| 1695 | {
|
---|
| 1696 | buf[2*i+0] = 0;
|
---|
| 1697 | buf[2*i+1] = 0;
|
---|
| 1698 | }
|
---|
| 1699 | buf2 = new double[2*p];
|
---|
| 1700 | for(i=0; i<=n-1; i++)
|
---|
| 1701 | {
|
---|
| 1702 | buf2[2*i+0] = b[i].x;
|
---|
| 1703 | buf2[2*i+1] = b[i].y;
|
---|
| 1704 | }
|
---|
| 1705 | for(i=n; i<=p-1; i++)
|
---|
| 1706 | {
|
---|
| 1707 | buf2[2*i+0] = 0;
|
---|
| 1708 | buf2[2*i+1] = 0;
|
---|
| 1709 | }
|
---|
| 1710 | ftbase.ftbaseexecuteplan(ref buf, 0, p, plan);
|
---|
| 1711 | ftbase.ftbaseexecuteplan(ref buf2, 0, p, plan);
|
---|
| 1712 | for(i=0; i<=p-1; i++)
|
---|
| 1713 | {
|
---|
| 1714 | ax = buf[2*i+0];
|
---|
| 1715 | ay = buf[2*i+1];
|
---|
| 1716 | bx = buf2[2*i+0];
|
---|
| 1717 | by = buf2[2*i+1];
|
---|
| 1718 | tx = ax*bx-ay*by;
|
---|
| 1719 | ty = ax*by+ay*bx;
|
---|
| 1720 | buf[2*i+0] = tx;
|
---|
| 1721 | buf[2*i+1] = -ty;
|
---|
| 1722 | }
|
---|
| 1723 | ftbase.ftbaseexecuteplan(ref buf, 0, p, plan);
|
---|
| 1724 | t = (double)1/(double)p;
|
---|
| 1725 | if( circular )
|
---|
| 1726 | {
|
---|
| 1727 |
|
---|
| 1728 | //
|
---|
| 1729 | // circular, add tail to head
|
---|
| 1730 | //
|
---|
| 1731 | r = new complex[m];
|
---|
| 1732 | for(i=0; i<=m-1; i++)
|
---|
| 1733 | {
|
---|
| 1734 | r[i].x = t*buf[2*i+0];
|
---|
| 1735 | r[i].y = -(t*buf[2*i+1]);
|
---|
| 1736 | }
|
---|
| 1737 | for(i=m; i<=m+n-2; i++)
|
---|
| 1738 | {
|
---|
| 1739 | r[i-m].x = r[i-m].x+t*buf[2*i+0];
|
---|
| 1740 | r[i-m].y = r[i-m].y-t*buf[2*i+1];
|
---|
| 1741 | }
|
---|
| 1742 | }
|
---|
| 1743 | else
|
---|
| 1744 | {
|
---|
| 1745 |
|
---|
| 1746 | //
|
---|
| 1747 | // non-circular, just copy
|
---|
| 1748 | //
|
---|
| 1749 | r = new complex[m+n-1];
|
---|
| 1750 | for(i=0; i<=m+n-2; i++)
|
---|
| 1751 | {
|
---|
| 1752 | r[i].x = t*buf[2*i+0];
|
---|
| 1753 | r[i].y = -(t*buf[2*i+1]);
|
---|
| 1754 | }
|
---|
| 1755 | }
|
---|
| 1756 | }
|
---|
| 1757 | return;
|
---|
| 1758 | }
|
---|
| 1759 |
|
---|
| 1760 | //
|
---|
| 1761 | // overlap-add method for
|
---|
| 1762 | // circular and non-circular convolutions.
|
---|
| 1763 | //
|
---|
| 1764 | // First part of code (separate FFTs of input blocks) is the same
|
---|
| 1765 | // for all types of convolution. Second part (overlapping outputs)
|
---|
| 1766 | // differs for different types of convolution. We just copy output
|
---|
| 1767 | // when convolution is non-circular. We wrap it around, if it is
|
---|
| 1768 | // circular.
|
---|
| 1769 | //
|
---|
| 1770 | if( alg==2 )
|
---|
| 1771 | {
|
---|
| 1772 | buf = new double[2*(q+n-1)];
|
---|
| 1773 |
|
---|
| 1774 | //
|
---|
| 1775 | // prepare R
|
---|
| 1776 | //
|
---|
| 1777 | if( circular )
|
---|
| 1778 | {
|
---|
| 1779 | r = new complex[m];
|
---|
| 1780 | for(i=0; i<=m-1; i++)
|
---|
| 1781 | {
|
---|
| 1782 | r[i] = 0;
|
---|
| 1783 | }
|
---|
| 1784 | }
|
---|
| 1785 | else
|
---|
| 1786 | {
|
---|
| 1787 | r = new complex[m+n-1];
|
---|
| 1788 | for(i=0; i<=m+n-2; i++)
|
---|
| 1789 | {
|
---|
| 1790 | r[i] = 0;
|
---|
| 1791 | }
|
---|
| 1792 | }
|
---|
| 1793 |
|
---|
| 1794 | //
|
---|
| 1795 | // pre-calculated FFT(B)
|
---|
| 1796 | //
|
---|
| 1797 | bbuf = new complex[q+n-1];
|
---|
| 1798 | for(i_=0; i_<=n-1;i_++)
|
---|
| 1799 | {
|
---|
| 1800 | bbuf[i_] = b[i_];
|
---|
| 1801 | }
|
---|
| 1802 | for(j=n; j<=q+n-2; j++)
|
---|
| 1803 | {
|
---|
| 1804 | bbuf[j] = 0;
|
---|
| 1805 | }
|
---|
| 1806 | fft.fftc1d(ref bbuf, q+n-1);
|
---|
| 1807 |
|
---|
| 1808 | //
|
---|
| 1809 | // prepare FFT plan for chunks of A
|
---|
| 1810 | //
|
---|
| 1811 | ftbase.ftbasegeneratecomplexfftplan(q+n-1, plan);
|
---|
| 1812 |
|
---|
| 1813 | //
|
---|
| 1814 | // main overlap-add cycle
|
---|
| 1815 | //
|
---|
| 1816 | i = 0;
|
---|
| 1817 | while( i<=m-1 )
|
---|
| 1818 | {
|
---|
| 1819 | p = Math.Min(q, m-i);
|
---|
| 1820 | for(j=0; j<=p-1; j++)
|
---|
| 1821 | {
|
---|
| 1822 | buf[2*j+0] = a[i+j].x;
|
---|
| 1823 | buf[2*j+1] = a[i+j].y;
|
---|
| 1824 | }
|
---|
| 1825 | for(j=p; j<=q+n-2; j++)
|
---|
| 1826 | {
|
---|
| 1827 | buf[2*j+0] = 0;
|
---|
| 1828 | buf[2*j+1] = 0;
|
---|
| 1829 | }
|
---|
| 1830 | ftbase.ftbaseexecuteplan(ref buf, 0, q+n-1, plan);
|
---|
| 1831 | for(j=0; j<=q+n-2; j++)
|
---|
| 1832 | {
|
---|
| 1833 | ax = buf[2*j+0];
|
---|
| 1834 | ay = buf[2*j+1];
|
---|
| 1835 | bx = bbuf[j].x;
|
---|
| 1836 | by = bbuf[j].y;
|
---|
| 1837 | tx = ax*bx-ay*by;
|
---|
| 1838 | ty = ax*by+ay*bx;
|
---|
| 1839 | buf[2*j+0] = tx;
|
---|
| 1840 | buf[2*j+1] = -ty;
|
---|
| 1841 | }
|
---|
| 1842 | ftbase.ftbaseexecuteplan(ref buf, 0, q+n-1, plan);
|
---|
| 1843 | t = (double)1/(double)(q+n-1);
|
---|
| 1844 | if( circular )
|
---|
| 1845 | {
|
---|
| 1846 | j1 = Math.Min(i+p+n-2, m-1)-i;
|
---|
| 1847 | j2 = j1+1;
|
---|
| 1848 | }
|
---|
| 1849 | else
|
---|
| 1850 | {
|
---|
| 1851 | j1 = p+n-2;
|
---|
| 1852 | j2 = j1+1;
|
---|
| 1853 | }
|
---|
| 1854 | for(j=0; j<=j1; j++)
|
---|
| 1855 | {
|
---|
| 1856 | r[i+j].x = r[i+j].x+buf[2*j+0]*t;
|
---|
| 1857 | r[i+j].y = r[i+j].y-buf[2*j+1]*t;
|
---|
| 1858 | }
|
---|
| 1859 | for(j=j2; j<=p+n-2; j++)
|
---|
| 1860 | {
|
---|
| 1861 | r[j-j2].x = r[j-j2].x+buf[2*j+0]*t;
|
---|
| 1862 | r[j-j2].y = r[j-j2].y-buf[2*j+1]*t;
|
---|
| 1863 | }
|
---|
| 1864 | i = i+p;
|
---|
| 1865 | }
|
---|
| 1866 | return;
|
---|
| 1867 | }
|
---|
| 1868 | }
|
---|
| 1869 |
|
---|
| 1870 |
|
---|
| 1871 | /*************************************************************************
|
---|
| 1872 | 1-dimensional real convolution.
|
---|
| 1873 |
|
---|
| 1874 | Extended subroutine which allows to choose convolution algorithm.
|
---|
| 1875 | Intended for internal use, ALGLIB users should call ConvR1D().
|
---|
| 1876 |
|
---|
| 1877 | INPUT PARAMETERS
|
---|
| 1878 | A - array[0..M-1] - complex function to be transformed
|
---|
| 1879 | M - problem size
|
---|
| 1880 | B - array[0..N-1] - complex function to be transformed
|
---|
| 1881 | N - problem size, N<=M
|
---|
| 1882 | Alg - algorithm type:
|
---|
| 1883 | *-2 auto-select Q for overlap-add
|
---|
| 1884 | *-1 auto-select algorithm and parameters
|
---|
| 1885 | * 0 straightforward formula for small N's
|
---|
| 1886 | * 1 general FFT-based code
|
---|
| 1887 | * 2 overlap-add with length Q
|
---|
| 1888 | Q - length for overlap-add
|
---|
| 1889 |
|
---|
| 1890 | OUTPUT PARAMETERS
|
---|
| 1891 | R - convolution: A*B. array[0..N+M-1].
|
---|
| 1892 |
|
---|
| 1893 | -- ALGLIB --
|
---|
| 1894 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
| 1895 | *************************************************************************/
|
---|
| 1896 | public static void convr1dx(double[] a,
|
---|
| 1897 | int m,
|
---|
| 1898 | double[] b,
|
---|
| 1899 | int n,
|
---|
| 1900 | bool circular,
|
---|
| 1901 | int alg,
|
---|
| 1902 | int q,
|
---|
| 1903 | ref double[] r)
|
---|
| 1904 | {
|
---|
| 1905 | double v = 0;
|
---|
| 1906 | int i = 0;
|
---|
| 1907 | int j = 0;
|
---|
| 1908 | int p = 0;
|
---|
| 1909 | int ptotal = 0;
|
---|
| 1910 | int i1 = 0;
|
---|
| 1911 | int i2 = 0;
|
---|
| 1912 | int j1 = 0;
|
---|
| 1913 | int j2 = 0;
|
---|
| 1914 | double ax = 0;
|
---|
| 1915 | double ay = 0;
|
---|
| 1916 | double bx = 0;
|
---|
| 1917 | double by = 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 | double[] buf3 = new double[0];
|
---|
| 1927 | int i_ = 0;
|
---|
| 1928 | int i1_ = 0;
|
---|
| 1929 |
|
---|
| 1930 | r = new double[0];
|
---|
| 1931 |
|
---|
| 1932 | ap.assert(n>0 & m>0, "ConvC1DX: incorrect N or M!");
|
---|
| 1933 | ap.assert(n<=m, "ConvC1DX: N<M assumption is false!");
|
---|
| 1934 |
|
---|
| 1935 | //
|
---|
| 1936 | // handle special cases
|
---|
| 1937 | //
|
---|
| 1938 | if( Math.Min(m, n)<=2 )
|
---|
| 1939 | {
|
---|
| 1940 | alg = 0;
|
---|
| 1941 | }
|
---|
| 1942 |
|
---|
| 1943 | //
|
---|
| 1944 | // Auto-select
|
---|
| 1945 | //
|
---|
| 1946 | if( alg<0 )
|
---|
| 1947 | {
|
---|
| 1948 |
|
---|
| 1949 | //
|
---|
| 1950 | // Initial candidate: straightforward implementation.
|
---|
| 1951 | //
|
---|
| 1952 | // If we want to use auto-fitted overlap-add,
|
---|
| 1953 | // flop count is initialized by large real number - to force
|
---|
| 1954 | // another algorithm selection
|
---|
| 1955 | //
|
---|
| 1956 | algbest = 0;
|
---|
| 1957 | if( alg==-1 )
|
---|
| 1958 | {
|
---|
| 1959 | flopbest = 0.15*m*n;
|
---|
| 1960 | }
|
---|
| 1961 | else
|
---|
| 1962 | {
|
---|
| 1963 | flopbest = math.maxrealnumber;
|
---|
| 1964 | }
|
---|
| 1965 |
|
---|
| 1966 | //
|
---|
| 1967 | // Another candidate - generic FFT code
|
---|
| 1968 | //
|
---|
| 1969 | if( alg==-1 )
|
---|
| 1970 | {
|
---|
| 1971 | if( (circular & ftbase.ftbaseissmooth(m)) & m%2==0 )
|
---|
| 1972 | {
|
---|
| 1973 |
|
---|
| 1974 | //
|
---|
| 1975 | // special code for circular convolution of a sequence with a smooth length
|
---|
| 1976 | //
|
---|
| 1977 | flopcand = 3*ftbase.ftbasegetflopestimate(m/2)+(double)(6*m)/(double)2;
|
---|
| 1978 | if( (double)(flopcand)<(double)(flopbest) )
|
---|
| 1979 | {
|
---|
| 1980 | algbest = 1;
|
---|
| 1981 | flopbest = flopcand;
|
---|
| 1982 | }
|
---|
| 1983 | }
|
---|
| 1984 | else
|
---|
| 1985 | {
|
---|
| 1986 |
|
---|
| 1987 | //
|
---|
| 1988 | // general cyclic/non-cyclic convolution
|
---|
| 1989 | //
|
---|
| 1990 | p = ftbase.ftbasefindsmootheven(m+n-1);
|
---|
| 1991 | flopcand = 3*ftbase.ftbasegetflopestimate(p/2)+(double)(6*p)/(double)2;
|
---|
| 1992 | if( (double)(flopcand)<(double)(flopbest) )
|
---|
| 1993 | {
|
---|
| 1994 | algbest = 1;
|
---|
| 1995 | flopbest = flopcand;
|
---|
| 1996 | }
|
---|
| 1997 | }
|
---|
| 1998 | }
|
---|
| 1999 |
|
---|
| 2000 | //
|
---|
| 2001 | // Another candidate - overlap-add
|
---|
| 2002 | //
|
---|
| 2003 | q = 1;
|
---|
| 2004 | ptotal = 1;
|
---|
| 2005 | while( ptotal<n )
|
---|
| 2006 | {
|
---|
| 2007 | ptotal = ptotal*2;
|
---|
| 2008 | }
|
---|
| 2009 | while( ptotal<=m+n-1 )
|
---|
| 2010 | {
|
---|
| 2011 | p = ptotal-n+1;
|
---|
| 2012 | flopcand = (int)Math.Ceiling((double)m/(double)p)*(2*ftbase.ftbasegetflopestimate(ptotal/2)+1*(ptotal/2));
|
---|
| 2013 | if( (double)(flopcand)<(double)(flopbest) )
|
---|
| 2014 | {
|
---|
| 2015 | flopbest = flopcand;
|
---|
| 2016 | algbest = 2;
|
---|
| 2017 | q = p;
|
---|
| 2018 | }
|
---|
| 2019 | ptotal = ptotal*2;
|
---|
| 2020 | }
|
---|
| 2021 | alg = algbest;
|
---|
| 2022 | convr1dx(a, m, b, n, circular, alg, q, ref r);
|
---|
| 2023 | return;
|
---|
| 2024 | }
|
---|
| 2025 |
|
---|
| 2026 | //
|
---|
| 2027 | // straightforward formula for
|
---|
| 2028 | // circular and non-circular convolutions.
|
---|
| 2029 | //
|
---|
| 2030 | // Very simple code, no further comments needed.
|
---|
| 2031 | //
|
---|
| 2032 | if( alg==0 )
|
---|
| 2033 | {
|
---|
| 2034 |
|
---|
| 2035 | //
|
---|
| 2036 | // Special case: N=1
|
---|
| 2037 | //
|
---|
| 2038 | if( n==1 )
|
---|
| 2039 | {
|
---|
| 2040 | r = new double[m];
|
---|
| 2041 | v = b[0];
|
---|
| 2042 | for(i_=0; i_<=m-1;i_++)
|
---|
| 2043 | {
|
---|
| 2044 | r[i_] = v*a[i_];
|
---|
| 2045 | }
|
---|
| 2046 | return;
|
---|
| 2047 | }
|
---|
| 2048 |
|
---|
| 2049 | //
|
---|
| 2050 | // use straightforward formula
|
---|
| 2051 | //
|
---|
| 2052 | if( circular )
|
---|
| 2053 | {
|
---|
| 2054 |
|
---|
| 2055 | //
|
---|
| 2056 | // circular convolution
|
---|
| 2057 | //
|
---|
| 2058 | r = new double[m];
|
---|
| 2059 | v = b[0];
|
---|
| 2060 | for(i_=0; i_<=m-1;i_++)
|
---|
| 2061 | {
|
---|
| 2062 | r[i_] = v*a[i_];
|
---|
| 2063 | }
|
---|
| 2064 | for(i=1; i<=n-1; i++)
|
---|
| 2065 | {
|
---|
| 2066 | v = b[i];
|
---|
| 2067 | i1 = 0;
|
---|
| 2068 | i2 = i-1;
|
---|
| 2069 | j1 = m-i;
|
---|
| 2070 | j2 = m-1;
|
---|
| 2071 | i1_ = (j1) - (i1);
|
---|
| 2072 | for(i_=i1; i_<=i2;i_++)
|
---|
| 2073 | {
|
---|
| 2074 | r[i_] = r[i_] + v*a[i_+i1_];
|
---|
| 2075 | }
|
---|
| 2076 | i1 = i;
|
---|
| 2077 | i2 = m-1;
|
---|
| 2078 | j1 = 0;
|
---|
| 2079 | j2 = m-i-1;
|
---|
| 2080 | i1_ = (j1) - (i1);
|
---|
| 2081 | for(i_=i1; i_<=i2;i_++)
|
---|
| 2082 | {
|
---|
| 2083 | r[i_] = r[i_] + v*a[i_+i1_];
|
---|
| 2084 | }
|
---|
| 2085 | }
|
---|
| 2086 | }
|
---|
| 2087 | else
|
---|
| 2088 | {
|
---|
| 2089 |
|
---|
| 2090 | //
|
---|
| 2091 | // non-circular convolution
|
---|
| 2092 | //
|
---|
| 2093 | r = new double[m+n-1];
|
---|
| 2094 | for(i=0; i<=m+n-2; i++)
|
---|
| 2095 | {
|
---|
| 2096 | r[i] = 0;
|
---|
| 2097 | }
|
---|
| 2098 | for(i=0; i<=n-1; i++)
|
---|
| 2099 | {
|
---|
| 2100 | v = b[i];
|
---|
| 2101 | i1_ = (0) - (i);
|
---|
| 2102 | for(i_=i; i_<=i+m-1;i_++)
|
---|
| 2103 | {
|
---|
| 2104 | r[i_] = r[i_] + v*a[i_+i1_];
|
---|
| 2105 | }
|
---|
| 2106 | }
|
---|
| 2107 | }
|
---|
| 2108 | return;
|
---|
| 2109 | }
|
---|
| 2110 |
|
---|
| 2111 | //
|
---|
| 2112 | // general FFT-based code for
|
---|
| 2113 | // circular and non-circular convolutions.
|
---|
| 2114 | //
|
---|
| 2115 | // First, if convolution is circular, we test whether M is smooth or not.
|
---|
| 2116 | // If it is smooth, we just use M-length FFT to calculate convolution.
|
---|
| 2117 | // If it is not, we calculate non-circular convolution and wrap it arount.
|
---|
| 2118 | //
|
---|
| 2119 | // If convolution is non-circular, we use zero-padding + FFT.
|
---|
| 2120 | //
|
---|
| 2121 | // We assume that M+N-1>2 - we should call small case code otherwise
|
---|
| 2122 | //
|
---|
| 2123 | if( alg==1 )
|
---|
| 2124 | {
|
---|
| 2125 | ap.assert(m+n-1>2, "ConvR1DX: internal error!");
|
---|
| 2126 | if( (circular & ftbase.ftbaseissmooth(m)) & m%2==0 )
|
---|
| 2127 | {
|
---|
| 2128 |
|
---|
| 2129 | //
|
---|
| 2130 | // special code for circular convolution with smooth even M
|
---|
| 2131 | //
|
---|
| 2132 | buf = new double[m];
|
---|
| 2133 | for(i_=0; i_<=m-1;i_++)
|
---|
| 2134 | {
|
---|
| 2135 | buf[i_] = a[i_];
|
---|
| 2136 | }
|
---|
| 2137 | buf2 = new double[m];
|
---|
| 2138 | for(i_=0; i_<=n-1;i_++)
|
---|
| 2139 | {
|
---|
| 2140 | buf2[i_] = b[i_];
|
---|
| 2141 | }
|
---|
| 2142 | for(i=n; i<=m-1; i++)
|
---|
| 2143 | {
|
---|
| 2144 | buf2[i] = 0;
|
---|
| 2145 | }
|
---|
| 2146 | buf3 = new double[m];
|
---|
| 2147 | ftbase.ftbasegeneratecomplexfftplan(m/2, plan);
|
---|
| 2148 | fft.fftr1dinternaleven(ref buf, m, ref buf3, plan);
|
---|
| 2149 | fft.fftr1dinternaleven(ref buf2, m, ref buf3, plan);
|
---|
| 2150 | buf[0] = buf[0]*buf2[0];
|
---|
| 2151 | buf[1] = buf[1]*buf2[1];
|
---|
| 2152 | for(i=1; i<=m/2-1; i++)
|
---|
| 2153 | {
|
---|
| 2154 | ax = buf[2*i+0];
|
---|
| 2155 | ay = buf[2*i+1];
|
---|
| 2156 | bx = buf2[2*i+0];
|
---|
| 2157 | by = buf2[2*i+1];
|
---|
| 2158 | tx = ax*bx-ay*by;
|
---|
| 2159 | ty = ax*by+ay*bx;
|
---|
| 2160 | buf[2*i+0] = tx;
|
---|
| 2161 | buf[2*i+1] = ty;
|
---|
| 2162 | }
|
---|
| 2163 | fft.fftr1dinvinternaleven(ref buf, m, ref buf3, plan);
|
---|
| 2164 | r = new double[m];
|
---|
| 2165 | for(i_=0; i_<=m-1;i_++)
|
---|
| 2166 | {
|
---|
| 2167 | r[i_] = buf[i_];
|
---|
| 2168 | }
|
---|
| 2169 | }
|
---|
| 2170 | else
|
---|
| 2171 | {
|
---|
| 2172 |
|
---|
| 2173 | //
|
---|
| 2174 | // M is non-smooth or non-even, general code (circular/non-circular):
|
---|
| 2175 | // * first part is the same for circular and non-circular
|
---|
| 2176 | // convolutions. zero padding, FFTs, inverse FFTs
|
---|
| 2177 | // * second part differs:
|
---|
| 2178 | // * for non-circular convolution we just copy array
|
---|
| 2179 | // * for circular convolution we add array tail to its head
|
---|
| 2180 | //
|
---|
| 2181 | p = ftbase.ftbasefindsmootheven(m+n-1);
|
---|
| 2182 | buf = new double[p];
|
---|
| 2183 | for(i_=0; i_<=m-1;i_++)
|
---|
| 2184 | {
|
---|
| 2185 | buf[i_] = a[i_];
|
---|
| 2186 | }
|
---|
| 2187 | for(i=m; i<=p-1; i++)
|
---|
| 2188 | {
|
---|
| 2189 | buf[i] = 0;
|
---|
| 2190 | }
|
---|
| 2191 | buf2 = new double[p];
|
---|
| 2192 | for(i_=0; i_<=n-1;i_++)
|
---|
| 2193 | {
|
---|
| 2194 | buf2[i_] = b[i_];
|
---|
| 2195 | }
|
---|
| 2196 | for(i=n; i<=p-1; i++)
|
---|
| 2197 | {
|
---|
| 2198 | buf2[i] = 0;
|
---|
| 2199 | }
|
---|
| 2200 | buf3 = new double[p];
|
---|
| 2201 | ftbase.ftbasegeneratecomplexfftplan(p/2, plan);
|
---|
| 2202 | fft.fftr1dinternaleven(ref buf, p, ref buf3, plan);
|
---|
| 2203 | fft.fftr1dinternaleven(ref buf2, p, ref buf3, plan);
|
---|
| 2204 | buf[0] = buf[0]*buf2[0];
|
---|
| 2205 | buf[1] = buf[1]*buf2[1];
|
---|
| 2206 | for(i=1; i<=p/2-1; i++)
|
---|
| 2207 | {
|
---|
| 2208 | ax = buf[2*i+0];
|
---|
| 2209 | ay = buf[2*i+1];
|
---|
| 2210 | bx = buf2[2*i+0];
|
---|
| 2211 | by = buf2[2*i+1];
|
---|
| 2212 | tx = ax*bx-ay*by;
|
---|
| 2213 | ty = ax*by+ay*bx;
|
---|
| 2214 | buf[2*i+0] = tx;
|
---|
| 2215 | buf[2*i+1] = ty;
|
---|
| 2216 | }
|
---|
| 2217 | fft.fftr1dinvinternaleven(ref buf, p, ref buf3, plan);
|
---|
| 2218 | if( circular )
|
---|
| 2219 | {
|
---|
| 2220 |
|
---|
| 2221 | //
|
---|
| 2222 | // circular, add tail to head
|
---|
| 2223 | //
|
---|
| 2224 | r = new double[m];
|
---|
| 2225 | for(i_=0; i_<=m-1;i_++)
|
---|
| 2226 | {
|
---|
| 2227 | r[i_] = buf[i_];
|
---|
| 2228 | }
|
---|
| 2229 | if( n>=2 )
|
---|
| 2230 | {
|
---|
| 2231 | i1_ = (m) - (0);
|
---|
| 2232 | for(i_=0; i_<=n-2;i_++)
|
---|
| 2233 | {
|
---|
| 2234 | r[i_] = r[i_] + buf[i_+i1_];
|
---|
| 2235 | }
|
---|
| 2236 | }
|
---|
| 2237 | }
|
---|
| 2238 | else
|
---|
| 2239 | {
|
---|
| 2240 |
|
---|
| 2241 | //
|
---|
| 2242 | // non-circular, just copy
|
---|
| 2243 | //
|
---|
| 2244 | r = new double[m+n-1];
|
---|
| 2245 | for(i_=0; i_<=m+n-2;i_++)
|
---|
| 2246 | {
|
---|
| 2247 | r[i_] = buf[i_];
|
---|
| 2248 | }
|
---|
| 2249 | }
|
---|
| 2250 | }
|
---|
| 2251 | return;
|
---|
| 2252 | }
|
---|
| 2253 |
|
---|
| 2254 | //
|
---|
| 2255 | // overlap-add method
|
---|
| 2256 | //
|
---|
| 2257 | if( alg==2 )
|
---|
| 2258 | {
|
---|
| 2259 | ap.assert((q+n-1)%2==0, "ConvR1DX: internal error!");
|
---|
| 2260 | buf = new double[q+n-1];
|
---|
| 2261 | buf2 = new double[q+n-1];
|
---|
| 2262 | buf3 = new double[q+n-1];
|
---|
| 2263 | ftbase.ftbasegeneratecomplexfftplan((q+n-1)/2, plan);
|
---|
| 2264 |
|
---|
| 2265 | //
|
---|
| 2266 | // prepare R
|
---|
| 2267 | //
|
---|
| 2268 | if( circular )
|
---|
| 2269 | {
|
---|
| 2270 | r = new double[m];
|
---|
| 2271 | for(i=0; i<=m-1; i++)
|
---|
| 2272 | {
|
---|
| 2273 | r[i] = 0;
|
---|
| 2274 | }
|
---|
| 2275 | }
|
---|
| 2276 | else
|
---|
| 2277 | {
|
---|
| 2278 | r = new double[m+n-1];
|
---|
| 2279 | for(i=0; i<=m+n-2; i++)
|
---|
| 2280 | {
|
---|
| 2281 | r[i] = 0;
|
---|
| 2282 | }
|
---|
| 2283 | }
|
---|
| 2284 |
|
---|
| 2285 | //
|
---|
| 2286 | // pre-calculated FFT(B)
|
---|
| 2287 | //
|
---|
| 2288 | for(i_=0; i_<=n-1;i_++)
|
---|
| 2289 | {
|
---|
| 2290 | buf2[i_] = b[i_];
|
---|
| 2291 | }
|
---|
| 2292 | for(j=n; j<=q+n-2; j++)
|
---|
| 2293 | {
|
---|
| 2294 | buf2[j] = 0;
|
---|
| 2295 | }
|
---|
| 2296 | fft.fftr1dinternaleven(ref buf2, q+n-1, ref buf3, 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 | i1_ = (i) - (0);
|
---|
| 2306 | for(i_=0; i_<=p-1;i_++)
|
---|
| 2307 | {
|
---|
| 2308 | buf[i_] = a[i_+i1_];
|
---|
| 2309 | }
|
---|
| 2310 | for(j=p; j<=q+n-2; j++)
|
---|
| 2311 | {
|
---|
| 2312 | buf[j] = 0;
|
---|
| 2313 | }
|
---|
| 2314 | fft.fftr1dinternaleven(ref buf, q+n-1, ref buf3, plan);
|
---|
| 2315 | buf[0] = buf[0]*buf2[0];
|
---|
| 2316 | buf[1] = buf[1]*buf2[1];
|
---|
| 2317 | for(j=1; j<=(q+n-1)/2-1; j++)
|
---|
| 2318 | {
|
---|
| 2319 | ax = buf[2*j+0];
|
---|
| 2320 | ay = buf[2*j+1];
|
---|
| 2321 | bx = buf2[2*j+0];
|
---|
| 2322 | by = buf2[2*j+1];
|
---|
| 2323 | tx = ax*bx-ay*by;
|
---|
| 2324 | ty = ax*by+ay*bx;
|
---|
| 2325 | buf[2*j+0] = tx;
|
---|
| 2326 | buf[2*j+1] = ty;
|
---|
| 2327 | }
|
---|
| 2328 | fft.fftr1dinvinternaleven(ref buf, q+n-1, ref buf3, plan);
|
---|
| 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 | i1_ = (0) - (i);
|
---|
| 2340 | for(i_=i; i_<=i+j1;i_++)
|
---|
| 2341 | {
|
---|
| 2342 | r[i_] = r[i_] + buf[i_+i1_];
|
---|
| 2343 | }
|
---|
| 2344 | if( p+n-2>=j2 )
|
---|
| 2345 | {
|
---|
| 2346 | i1_ = (j2) - (0);
|
---|
| 2347 | for(i_=0; i_<=p+n-2-j2;i_++)
|
---|
| 2348 | {
|
---|
| 2349 | r[i_] = r[i_] + buf[i_+i1_];
|
---|
| 2350 | }
|
---|
| 2351 | }
|
---|
| 2352 | i = i+p;
|
---|
| 2353 | }
|
---|
| 2354 | return;
|
---|
| 2355 | }
|
---|
| 2356 | }
|
---|
| 2357 |
|
---|
| 2358 |
|
---|
| 2359 | }
|
---|
| 2360 | public class fft
|
---|
| 2361 | {
|
---|
| 2362 | /*************************************************************************
|
---|
| 2363 | 1-dimensional complex FFT.
|
---|
| 2364 |
|
---|
| 2365 | Array size N may be arbitrary number (composite or prime). Composite N's
|
---|
| 2366 | are handled with cache-oblivious variation of a Cooley-Tukey algorithm.
|
---|
| 2367 | Small prime-factors are transformed using hard coded codelets (similar to
|
---|
| 2368 | FFTW codelets, but without low-level optimization), large prime-factors
|
---|
| 2369 | are handled with Bluestein's algorithm.
|
---|
| 2370 |
|
---|
| 2371 | Fastests transforms are for smooth N's (prime factors are 2, 3, 5 only),
|
---|
| 2372 | most fast for powers of 2. When N have prime factors larger than these,
|
---|
| 2373 | but orders of magnitude smaller than N, computations will be about 4 times
|
---|
| 2374 | slower than for nearby highly composite N's. When N itself is prime, speed
|
---|
| 2375 | will be 6 times lower.
|
---|
| 2376 |
|
---|
| 2377 | Algorithm has O(N*logN) complexity for any N (composite or prime).
|
---|
| 2378 |
|
---|
| 2379 | INPUT PARAMETERS
|
---|
| 2380 | A - array[0..N-1] - complex function to be transformed
|
---|
| 2381 | N - problem size
|
---|
| 2382 |
|
---|
| 2383 | OUTPUT PARAMETERS
|
---|
| 2384 | A - DFT of a input array, array[0..N-1]
|
---|
| 2385 | A_out[j] = SUM(A_in[k]*exp(-2*pi*sqrt(-1)*j*k/N), k = 0..N-1)
|
---|
| 2386 |
|
---|
| 2387 |
|
---|
| 2388 | -- ALGLIB --
|
---|
| 2389 | Copyright 29.05.2009 by Bochkanov Sergey
|
---|
| 2390 | *************************************************************************/
|
---|
| 2391 | public static void fftc1d(ref complex[] a,
|
---|
| 2392 | int n)
|
---|
| 2393 | {
|
---|
| 2394 | ftbase.ftplan plan = new ftbase.ftplan();
|
---|
| 2395 | int i = 0;
|
---|
| 2396 | double[] buf = new double[0];
|
---|
| 2397 |
|
---|
| 2398 | ap.assert(n>0, "FFTC1D: incorrect N!");
|
---|
| 2399 | ap.assert(ap.len(a)>=n, "FFTC1D: Length(A)<N!");
|
---|
| 2400 | ap.assert(apserv.isfinitecvector(a, n), "FFTC1D: A contains infinite or NAN values!");
|
---|
| 2401 |
|
---|
| 2402 | //
|
---|
| 2403 | // Special case: N=1, FFT is just identity transform.
|
---|
| 2404 | // After this block we assume that N is strictly greater than 1.
|
---|
| 2405 | //
|
---|
| 2406 | if( n==1 )
|
---|
| 2407 | {
|
---|
| 2408 | return;
|
---|
| 2409 | }
|
---|
| 2410 |
|
---|
| 2411 | //
|
---|
| 2412 | // convert input array to the more convinient format
|
---|
| 2413 | //
|
---|
| 2414 | buf = new double[2*n];
|
---|
| 2415 | for(i=0; i<=n-1; i++)
|
---|
| 2416 | {
|
---|
| 2417 | buf[2*i+0] = a[i].x;
|
---|
| 2418 | buf[2*i+1] = a[i].y;
|
---|
| 2419 | }
|
---|
| 2420 |
|
---|
| 2421 | //
|
---|
| 2422 | // Generate plan and execute it.
|
---|
| 2423 | //
|
---|
| 2424 | // Plan is a combination of a successive factorizations of N and
|
---|
| 2425 | // precomputed data. It is much like a FFTW plan, but is not stored
|
---|
| 2426 | // between subroutine calls and is much simpler.
|
---|
| 2427 | //
|
---|
| 2428 | ftbase.ftbasegeneratecomplexfftplan(n, plan);
|
---|
| 2429 | ftbase.ftbaseexecuteplan(ref buf, 0, n, plan);
|
---|
| 2430 |
|
---|
| 2431 | //
|
---|
| 2432 | // result
|
---|
| 2433 | //
|
---|
| 2434 | for(i=0; i<=n-1; i++)
|
---|
| 2435 | {
|
---|
| 2436 | a[i].x = buf[2*i+0];
|
---|
| 2437 | a[i].y = buf[2*i+1];
|
---|
| 2438 | }
|
---|
| 2439 | }
|
---|
| 2440 |
|
---|
| 2441 |
|
---|
| 2442 | /*************************************************************************
|
---|
| 2443 | 1-dimensional complex inverse FFT.
|
---|
| 2444 |
|
---|
| 2445 | Array size N may be arbitrary number (composite or prime). Algorithm has
|
---|
| 2446 | O(N*logN) complexity for any N (composite or prime).
|
---|
| 2447 |
|
---|
| 2448 | See FFTC1D() description for more information about algorithm performance.
|
---|
| 2449 |
|
---|
| 2450 | INPUT PARAMETERS
|
---|
| 2451 | A - array[0..N-1] - complex array to be transformed
|
---|
| 2452 | N - problem size
|
---|
| 2453 |
|
---|
| 2454 | OUTPUT PARAMETERS
|
---|
| 2455 | A - inverse DFT of a input array, array[0..N-1]
|
---|
| 2456 | A_out[j] = SUM(A_in[k]/N*exp(+2*pi*sqrt(-1)*j*k/N), k = 0..N-1)
|
---|
| 2457 |
|
---|
| 2458 |
|
---|
| 2459 | -- ALGLIB --
|
---|
| 2460 | Copyright 29.05.2009 by Bochkanov Sergey
|
---|
| 2461 | *************************************************************************/
|
---|
| 2462 | public static void fftc1dinv(ref complex[] a,
|
---|
| 2463 | int n)
|
---|
| 2464 | {
|
---|
| 2465 | int i = 0;
|
---|
| 2466 |
|
---|
| 2467 | ap.assert(n>0, "FFTC1DInv: incorrect N!");
|
---|
| 2468 | ap.assert(ap.len(a)>=n, "FFTC1DInv: Length(A)<N!");
|
---|
| 2469 | ap.assert(apserv.isfinitecvector(a, n), "FFTC1DInv: A contains infinite or NAN values!");
|
---|
| 2470 |
|
---|
| 2471 | //
|
---|
| 2472 | // Inverse DFT can be expressed in terms of the DFT as
|
---|
| 2473 | //
|
---|
| 2474 | // invfft(x) = fft(x')'/N
|
---|
| 2475 | //
|
---|
| 2476 | // here x' means conj(x).
|
---|
| 2477 | //
|
---|
| 2478 | for(i=0; i<=n-1; i++)
|
---|
| 2479 | {
|
---|
| 2480 | a[i].y = -a[i].y;
|
---|
| 2481 | }
|
---|
| 2482 | fftc1d(ref a, n);
|
---|
| 2483 | for(i=0; i<=n-1; i++)
|
---|
| 2484 | {
|
---|
| 2485 | a[i].x = a[i].x/n;
|
---|
| 2486 | a[i].y = -(a[i].y/n);
|
---|
| 2487 | }
|
---|
| 2488 | }
|
---|
| 2489 |
|
---|
| 2490 |
|
---|
| 2491 | /*************************************************************************
|
---|
| 2492 | 1-dimensional real FFT.
|
---|
| 2493 |
|
---|
| 2494 | Algorithm has O(N*logN) complexity for any N (composite or prime).
|
---|
| 2495 |
|
---|
| 2496 | INPUT PARAMETERS
|
---|
| 2497 | A - array[0..N-1] - real function to be transformed
|
---|
| 2498 | N - problem size
|
---|
| 2499 |
|
---|
| 2500 | OUTPUT PARAMETERS
|
---|
| 2501 | F - DFT of a input array, array[0..N-1]
|
---|
| 2502 | F[j] = SUM(A[k]*exp(-2*pi*sqrt(-1)*j*k/N), k = 0..N-1)
|
---|
| 2503 |
|
---|
| 2504 | NOTE:
|
---|
| 2505 | F[] satisfies symmetry property F[k] = conj(F[N-k]), so just one half
|
---|
| 2506 | of array is usually needed. But for convinience subroutine returns full
|
---|
| 2507 | complex array (with frequencies above N/2), so its result may be used by
|
---|
| 2508 | other FFT-related subroutines.
|
---|
| 2509 |
|
---|
| 2510 |
|
---|
| 2511 | -- ALGLIB --
|
---|
| 2512 | Copyright 01.06.2009 by Bochkanov Sergey
|
---|
| 2513 | *************************************************************************/
|
---|
| 2514 | public static void fftr1d(double[] a,
|
---|
| 2515 | int n,
|
---|
| 2516 | ref complex[] f)
|
---|
| 2517 | {
|
---|
| 2518 | int i = 0;
|
---|
| 2519 | int n2 = 0;
|
---|
| 2520 | int idx = 0;
|
---|
| 2521 | complex hn = 0;
|
---|
| 2522 | complex hmnc = 0;
|
---|
| 2523 | complex v = 0;
|
---|
| 2524 | double[] buf = new double[0];
|
---|
| 2525 | ftbase.ftplan plan = new ftbase.ftplan();
|
---|
| 2526 | int i_ = 0;
|
---|
| 2527 |
|
---|
| 2528 | f = new complex[0];
|
---|
| 2529 |
|
---|
| 2530 | ap.assert(n>0, "FFTR1D: incorrect N!");
|
---|
| 2531 | ap.assert(ap.len(a)>=n, "FFTR1D: Length(A)<N!");
|
---|
| 2532 | ap.assert(apserv.isfinitevector(a, n), "FFTR1D: A contains infinite or NAN values!");
|
---|
| 2533 |
|
---|
| 2534 | //
|
---|
| 2535 | // Special cases:
|
---|
| 2536 | // * N=1, FFT is just identity transform.
|
---|
| 2537 | // * N=2, FFT is simple too
|
---|
| 2538 | //
|
---|
| 2539 | // After this block we assume that N is strictly greater than 2
|
---|
| 2540 | //
|
---|
| 2541 | if( n==1 )
|
---|
| 2542 | {
|
---|
| 2543 | f = new complex[1];
|
---|
| 2544 | f[0] = a[0];
|
---|
| 2545 | return;
|
---|
| 2546 | }
|
---|
| 2547 | if( n==2 )
|
---|
| 2548 | {
|
---|
| 2549 | f = new complex[2];
|
---|
| 2550 | f[0].x = a[0]+a[1];
|
---|
| 2551 | f[0].y = 0;
|
---|
| 2552 | f[1].x = a[0]-a[1];
|
---|
| 2553 | f[1].y = 0;
|
---|
| 2554 | return;
|
---|
| 2555 | }
|
---|
| 2556 |
|
---|
| 2557 | //
|
---|
| 2558 | // Choose between odd-size and even-size FFTs
|
---|
| 2559 | //
|
---|
| 2560 | if( n%2==0 )
|
---|
| 2561 | {
|
---|
| 2562 |
|
---|
| 2563 | //
|
---|
| 2564 | // even-size real FFT, use reduction to the complex task
|
---|
| 2565 | //
|
---|
| 2566 | n2 = n/2;
|
---|
| 2567 | buf = new double[n];
|
---|
| 2568 | for(i_=0; i_<=n-1;i_++)
|
---|
| 2569 | {
|
---|
| 2570 | buf[i_] = a[i_];
|
---|
| 2571 | }
|
---|
| 2572 | ftbase.ftbasegeneratecomplexfftplan(n2, plan);
|
---|
| 2573 | ftbase.ftbaseexecuteplan(ref buf, 0, n2, plan);
|
---|
| 2574 | f = new complex[n];
|
---|
| 2575 | for(i=0; i<=n2; i++)
|
---|
| 2576 | {
|
---|
| 2577 | idx = 2*(i%n2);
|
---|
| 2578 | hn.x = buf[idx+0];
|
---|
| 2579 | hn.y = buf[idx+1];
|
---|
| 2580 | idx = 2*((n2-i)%n2);
|
---|
| 2581 | hmnc.x = buf[idx+0];
|
---|
| 2582 | hmnc.y = -buf[idx+1];
|
---|
| 2583 | v.x = -Math.Sin(-(2*Math.PI*i/n));
|
---|
| 2584 | v.y = Math.Cos(-(2*Math.PI*i/n));
|
---|
| 2585 | f[i] = hn+hmnc-v*(hn-hmnc);
|
---|
| 2586 | f[i].x = 0.5*f[i].x;
|
---|
| 2587 | f[i].y = 0.5*f[i].y;
|
---|
| 2588 | }
|
---|
| 2589 | for(i=n2+1; i<=n-1; i++)
|
---|
| 2590 | {
|
---|
| 2591 | f[i] = math.conj(f[n-i]);
|
---|
| 2592 | }
|
---|
| 2593 | }
|
---|
| 2594 | else
|
---|
| 2595 | {
|
---|
| 2596 |
|
---|
| 2597 | //
|
---|
| 2598 | // use complex FFT
|
---|
| 2599 | //
|
---|
| 2600 | f = new complex[n];
|
---|
| 2601 | for(i=0; i<=n-1; i++)
|
---|
| 2602 | {
|
---|
| 2603 | f[i] = a[i];
|
---|
| 2604 | }
|
---|
| 2605 | fftc1d(ref f, n);
|
---|
| 2606 | }
|
---|
| 2607 | }
|
---|
| 2608 |
|
---|
| 2609 |
|
---|
| 2610 | /*************************************************************************
|
---|
| 2611 | 1-dimensional real inverse FFT.
|
---|
| 2612 |
|
---|
| 2613 | Algorithm has O(N*logN) complexity for any N (composite or prime).
|
---|
| 2614 |
|
---|
| 2615 | INPUT PARAMETERS
|
---|
| 2616 | F - array[0..floor(N/2)] - frequencies from forward real FFT
|
---|
| 2617 | N - problem size
|
---|
| 2618 |
|
---|
| 2619 | OUTPUT PARAMETERS
|
---|
| 2620 | A - inverse DFT of a input array, array[0..N-1]
|
---|
| 2621 |
|
---|
| 2622 | NOTE:
|
---|
| 2623 | F[] should satisfy symmetry property F[k] = conj(F[N-k]), so just one
|
---|
| 2624 | half of frequencies array is needed - elements from 0 to floor(N/2). F[0]
|
---|
| 2625 | is ALWAYS real. If N is even F[floor(N/2)] is real too. If N is odd, then
|
---|
| 2626 | F[floor(N/2)] has no special properties.
|
---|
| 2627 |
|
---|
| 2628 | Relying on properties noted above, FFTR1DInv subroutine uses only elements
|
---|
| 2629 | from 0th to floor(N/2)-th. It ignores imaginary part of F[0], and in case
|
---|
| 2630 | N is even it ignores imaginary part of F[floor(N/2)] too.
|
---|
| 2631 |
|
---|
| 2632 | When you call this function using full arguments list - "FFTR1DInv(F,N,A)"
|
---|
| 2633 | - you can pass either either frequencies array with N elements or reduced
|
---|
| 2634 | array with roughly N/2 elements - subroutine will successfully transform
|
---|
| 2635 | both.
|
---|
| 2636 |
|
---|
| 2637 | If you call this function using reduced arguments list - "FFTR1DInv(F,A)"
|
---|
| 2638 | - you must pass FULL array with N elements (although higher N/2 are still
|
---|
| 2639 | not used) because array size is used to automatically determine FFT length
|
---|
| 2640 |
|
---|
| 2641 |
|
---|
| 2642 | -- ALGLIB --
|
---|
| 2643 | Copyright 01.06.2009 by Bochkanov Sergey
|
---|
| 2644 | *************************************************************************/
|
---|
| 2645 | public static void fftr1dinv(complex[] f,
|
---|
| 2646 | int n,
|
---|
| 2647 | ref double[] a)
|
---|
| 2648 | {
|
---|
| 2649 | int i = 0;
|
---|
| 2650 | double[] h = new double[0];
|
---|
| 2651 | complex[] fh = new complex[0];
|
---|
| 2652 |
|
---|
| 2653 | a = new double[0];
|
---|
| 2654 |
|
---|
| 2655 | ap.assert(n>0, "FFTR1DInv: incorrect N!");
|
---|
| 2656 | ap.assert(ap.len(f)>=(int)Math.Floor((double)n/(double)2)+1, "FFTR1DInv: Length(F)<Floor(N/2)+1!");
|
---|
| 2657 | ap.assert(math.isfinite(f[0].x), "FFTR1DInv: F contains infinite or NAN values!");
|
---|
| 2658 | for(i=1; i<=(int)Math.Floor((double)n/(double)2)-1; i++)
|
---|
| 2659 | {
|
---|
| 2660 | ap.assert(math.isfinite(f[i].x) & math.isfinite(f[i].y), "FFTR1DInv: F contains infinite or NAN values!");
|
---|
| 2661 | }
|
---|
| 2662 | ap.assert(math.isfinite(f[(int)Math.Floor((double)n/(double)2)].x), "FFTR1DInv: F contains infinite or NAN values!");
|
---|
| 2663 | if( n%2!=0 )
|
---|
| 2664 | {
|
---|
| 2665 | ap.assert(math.isfinite(f[(int)Math.Floor((double)n/(double)2)].y), "FFTR1DInv: F contains infinite or NAN values!");
|
---|
| 2666 | }
|
---|
| 2667 |
|
---|
| 2668 | //
|
---|
| 2669 | // Special case: N=1, FFT is just identity transform.
|
---|
| 2670 | // After this block we assume that N is strictly greater than 1.
|
---|
| 2671 | //
|
---|
| 2672 | if( n==1 )
|
---|
| 2673 | {
|
---|
| 2674 | a = new double[1];
|
---|
| 2675 | a[0] = f[0].x;
|
---|
| 2676 | return;
|
---|
| 2677 | }
|
---|
| 2678 |
|
---|
| 2679 | //
|
---|
| 2680 | // inverse real FFT is reduced to the inverse real FHT,
|
---|
| 2681 | // which is reduced to the forward real FHT,
|
---|
| 2682 | // which is reduced to the forward real FFT.
|
---|
| 2683 | //
|
---|
| 2684 | // Don't worry, it is really compact and efficient reduction :)
|
---|
| 2685 | //
|
---|
| 2686 | h = new double[n];
|
---|
| 2687 | a = new double[n];
|
---|
| 2688 | h[0] = f[0].x;
|
---|
| 2689 | for(i=1; i<=(int)Math.Floor((double)n/(double)2)-1; i++)
|
---|
| 2690 | {
|
---|
| 2691 | h[i] = f[i].x-f[i].y;
|
---|
| 2692 | h[n-i] = f[i].x+f[i].y;
|
---|
| 2693 | }
|
---|
| 2694 | if( n%2==0 )
|
---|
| 2695 | {
|
---|
| 2696 | h[(int)Math.Floor((double)n/(double)2)] = f[(int)Math.Floor((double)n/(double)2)].x;
|
---|
| 2697 | }
|
---|
| 2698 | else
|
---|
| 2699 | {
|
---|
| 2700 | 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;
|
---|
| 2701 | 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;
|
---|
| 2702 | }
|
---|
| 2703 | fftr1d(h, n, ref fh);
|
---|
| 2704 | for(i=0; i<=n-1; i++)
|
---|
| 2705 | {
|
---|
| 2706 | a[i] = (fh[i].x-fh[i].y)/n;
|
---|
| 2707 | }
|
---|
| 2708 | }
|
---|
| 2709 |
|
---|
| 2710 |
|
---|
| 2711 | /*************************************************************************
|
---|
| 2712 | Internal subroutine. Never call it directly!
|
---|
| 2713 |
|
---|
| 2714 |
|
---|
| 2715 | -- ALGLIB --
|
---|
| 2716 | Copyright 01.06.2009 by Bochkanov Sergey
|
---|
| 2717 | *************************************************************************/
|
---|
| 2718 | public static void fftr1dinternaleven(ref double[] a,
|
---|
| 2719 | int n,
|
---|
| 2720 | ref double[] buf,
|
---|
| 2721 | ftbase.ftplan plan)
|
---|
| 2722 | {
|
---|
| 2723 | double x = 0;
|
---|
| 2724 | double y = 0;
|
---|
| 2725 | int i = 0;
|
---|
| 2726 | int n2 = 0;
|
---|
| 2727 | int idx = 0;
|
---|
| 2728 | complex hn = 0;
|
---|
| 2729 | complex hmnc = 0;
|
---|
| 2730 | complex v = 0;
|
---|
| 2731 | int i_ = 0;
|
---|
| 2732 |
|
---|
| 2733 | ap.assert(n>0 & n%2==0, "FFTR1DEvenInplace: incorrect N!");
|
---|
| 2734 |
|
---|
| 2735 | //
|
---|
| 2736 | // Special cases:
|
---|
| 2737 | // * N=2
|
---|
| 2738 | //
|
---|
| 2739 | // After this block we assume that N is strictly greater than 2
|
---|
| 2740 | //
|
---|
| 2741 | if( n==2 )
|
---|
| 2742 | {
|
---|
| 2743 | x = a[0]+a[1];
|
---|
| 2744 | y = a[0]-a[1];
|
---|
| 2745 | a[0] = x;
|
---|
| 2746 | a[1] = y;
|
---|
| 2747 | return;
|
---|
| 2748 | }
|
---|
| 2749 |
|
---|
| 2750 | //
|
---|
| 2751 | // even-size real FFT, use reduction to the complex task
|
---|
| 2752 | //
|
---|
| 2753 | n2 = n/2;
|
---|
| 2754 | for(i_=0; i_<=n-1;i_++)
|
---|
| 2755 | {
|
---|
| 2756 | buf[i_] = a[i_];
|
---|
| 2757 | }
|
---|
| 2758 | ftbase.ftbaseexecuteplan(ref buf, 0, n2, plan);
|
---|
| 2759 | a[0] = buf[0]+buf[1];
|
---|
| 2760 | for(i=1; i<=n2-1; i++)
|
---|
| 2761 | {
|
---|
| 2762 | idx = 2*(i%n2);
|
---|
| 2763 | hn.x = buf[idx+0];
|
---|
| 2764 | hn.y = buf[idx+1];
|
---|
| 2765 | idx = 2*(n2-i);
|
---|
| 2766 | hmnc.x = buf[idx+0];
|
---|
| 2767 | hmnc.y = -buf[idx+1];
|
---|
| 2768 | v.x = -Math.Sin(-(2*Math.PI*i/n));
|
---|
| 2769 | v.y = Math.Cos(-(2*Math.PI*i/n));
|
---|
| 2770 | v = hn+hmnc-v*(hn-hmnc);
|
---|
| 2771 | a[2*i+0] = 0.5*v.x;
|
---|
| 2772 | a[2*i+1] = 0.5*v.y;
|
---|
| 2773 | }
|
---|
| 2774 | a[1] = buf[0]-buf[1];
|
---|
| 2775 | }
|
---|
| 2776 |
|
---|
| 2777 |
|
---|
| 2778 | /*************************************************************************
|
---|
| 2779 | Internal subroutine. Never call it directly!
|
---|
| 2780 |
|
---|
| 2781 |
|
---|
| 2782 | -- ALGLIB --
|
---|
| 2783 | Copyright 01.06.2009 by Bochkanov Sergey
|
---|
| 2784 | *************************************************************************/
|
---|
| 2785 | public static void fftr1dinvinternaleven(ref double[] a,
|
---|
| 2786 | int n,
|
---|
| 2787 | ref double[] buf,
|
---|
| 2788 | ftbase.ftplan plan)
|
---|
| 2789 | {
|
---|
| 2790 | double x = 0;
|
---|
| 2791 | double y = 0;
|
---|
| 2792 | double t = 0;
|
---|
| 2793 | int i = 0;
|
---|
| 2794 | int n2 = 0;
|
---|
| 2795 |
|
---|
| 2796 | ap.assert(n>0 & n%2==0, "FFTR1DInvInternalEven: incorrect N!");
|
---|
| 2797 |
|
---|
| 2798 | //
|
---|
| 2799 | // Special cases:
|
---|
| 2800 | // * N=2
|
---|
| 2801 | //
|
---|
| 2802 | // After this block we assume that N is strictly greater than 2
|
---|
| 2803 | //
|
---|
| 2804 | if( n==2 )
|
---|
| 2805 | {
|
---|
| 2806 | x = 0.5*(a[0]+a[1]);
|
---|
| 2807 | y = 0.5*(a[0]-a[1]);
|
---|
| 2808 | a[0] = x;
|
---|
| 2809 | a[1] = y;
|
---|
| 2810 | return;
|
---|
| 2811 | }
|
---|
| 2812 |
|
---|
| 2813 | //
|
---|
| 2814 | // inverse real FFT is reduced to the inverse real FHT,
|
---|
| 2815 | // which is reduced to the forward real FHT,
|
---|
| 2816 | // which is reduced to the forward real FFT.
|
---|
| 2817 | //
|
---|
| 2818 | // Don't worry, it is really compact and efficient reduction :)
|
---|
| 2819 | //
|
---|
| 2820 | n2 = n/2;
|
---|
| 2821 | buf[0] = a[0];
|
---|
| 2822 | for(i=1; i<=n2-1; i++)
|
---|
| 2823 | {
|
---|
| 2824 | x = a[2*i+0];
|
---|
| 2825 | y = a[2*i+1];
|
---|
| 2826 | buf[i] = x-y;
|
---|
| 2827 | buf[n-i] = x+y;
|
---|
| 2828 | }
|
---|
| 2829 | buf[n2] = a[1];
|
---|
| 2830 | fftr1dinternaleven(ref buf, n, ref a, plan);
|
---|
| 2831 | a[0] = buf[0]/n;
|
---|
| 2832 | t = (double)1/(double)n;
|
---|
| 2833 | for(i=1; i<=n2-1; i++)
|
---|
| 2834 | {
|
---|
| 2835 | x = buf[2*i+0];
|
---|
| 2836 | y = buf[2*i+1];
|
---|
| 2837 | a[i] = t*(x-y);
|
---|
| 2838 | a[n-i] = t*(x+y);
|
---|
| 2839 | }
|
---|
| 2840 | a[n2] = buf[1]/n;
|
---|
| 2841 | }
|
---|
| 2842 |
|
---|
| 2843 |
|
---|
| 2844 | }
|
---|
| 2845 | public class corr
|
---|
| 2846 | {
|
---|
| 2847 | public static void corrc1d(complex[] signal,
|
---|
| 2848 | int n,
|
---|
| 2849 | complex[] pattern,
|
---|
| 2850 | int m,
|
---|
| 2851 | ref complex[] r)
|
---|
| 2852 | {
|
---|
| 2853 | complex[] p = new complex[0];
|
---|
| 2854 | complex[] b = new complex[0];
|
---|
| 2855 | int i = 0;
|
---|
| 2856 | int i_ = 0;
|
---|
| 2857 | int i1_ = 0;
|
---|
| 2858 |
|
---|
| 2859 | r = new complex[0];
|
---|
| 2860 |
|
---|
| 2861 | ap.assert(n>0 & m>0, "CorrC1D: incorrect N or M!");
|
---|
| 2862 | p = new complex[m];
|
---|
| 2863 | for(i=0; i<=m-1; i++)
|
---|
| 2864 | {
|
---|
| 2865 | p[m-1-i] = math.conj(pattern[i]);
|
---|
| 2866 | }
|
---|
| 2867 | conv.convc1d(p, m, signal, n, ref b);
|
---|
| 2868 | r = new complex[m+n-1];
|
---|
| 2869 | i1_ = (m-1) - (0);
|
---|
| 2870 | for(i_=0; i_<=n-1;i_++)
|
---|
| 2871 | {
|
---|
| 2872 | r[i_] = b[i_+i1_];
|
---|
| 2873 | }
|
---|
| 2874 | if( m+n-2>=n )
|
---|
| 2875 | {
|
---|
| 2876 | i1_ = (0) - (n);
|
---|
| 2877 | for(i_=n; i_<=m+n-2;i_++)
|
---|
| 2878 | {
|
---|
| 2879 | r[i_] = b[i_+i1_];
|
---|
| 2880 | }
|
---|
| 2881 | }
|
---|
| 2882 | }
|
---|
| 2883 |
|
---|
| 2884 |
|
---|
| 2885 | public static void corrc1dcircular(complex[] signal,
|
---|
| 2886 | int m,
|
---|
| 2887 | complex[] pattern,
|
---|
| 2888 | int n,
|
---|
| 2889 | ref complex[] c)
|
---|
| 2890 | {
|
---|
| 2891 | complex[] p = new complex[0];
|
---|
| 2892 | complex[] b = new complex[0];
|
---|
| 2893 | int i1 = 0;
|
---|
| 2894 | int i2 = 0;
|
---|
| 2895 | int i = 0;
|
---|
| 2896 | int j2 = 0;
|
---|
| 2897 | int i_ = 0;
|
---|
| 2898 | int i1_ = 0;
|
---|
| 2899 |
|
---|
| 2900 | c = new complex[0];
|
---|
| 2901 |
|
---|
| 2902 | ap.assert(n>0 & m>0, "ConvC1DCircular: incorrect N or M!");
|
---|
| 2903 |
|
---|
| 2904 | //
|
---|
| 2905 | // normalize task: make M>=N,
|
---|
| 2906 | // so A will be longer (at least - not shorter) that B.
|
---|
| 2907 | //
|
---|
| 2908 | if( m<n )
|
---|
| 2909 | {
|
---|
| 2910 | b = new complex[m];
|
---|
| 2911 | for(i1=0; i1<=m-1; i1++)
|
---|
| 2912 | {
|
---|
| 2913 | b[i1] = 0;
|
---|
| 2914 | }
|
---|
| 2915 | i1 = 0;
|
---|
| 2916 | while( i1<n )
|
---|
| 2917 | {
|
---|
| 2918 | i2 = Math.Min(i1+m-1, n-1);
|
---|
| 2919 | j2 = i2-i1;
|
---|
| 2920 | i1_ = (i1) - (0);
|
---|
| 2921 | for(i_=0; i_<=j2;i_++)
|
---|
| 2922 | {
|
---|
| 2923 | b[i_] = b[i_] + pattern[i_+i1_];
|
---|
| 2924 | }
|
---|
| 2925 | i1 = i1+m;
|
---|
| 2926 | }
|
---|
| 2927 | corrc1dcircular(signal, m, b, m, ref c);
|
---|
| 2928 | return;
|
---|
| 2929 | }
|
---|
| 2930 |
|
---|
| 2931 | //
|
---|
| 2932 | // Task is normalized
|
---|
| 2933 | //
|
---|
| 2934 | p = new complex[n];
|
---|
| 2935 | for(i=0; i<=n-1; i++)
|
---|
| 2936 | {
|
---|
| 2937 | p[n-1-i] = math.conj(pattern[i]);
|
---|
| 2938 | }
|
---|
| 2939 | conv.convc1dcircular(signal, m, p, n, ref b);
|
---|
| 2940 | c = new complex[m];
|
---|
| 2941 | i1_ = (n-1) - (0);
|
---|
| 2942 | for(i_=0; i_<=m-n;i_++)
|
---|
| 2943 | {
|
---|
| 2944 | c[i_] = b[i_+i1_];
|
---|
| 2945 | }
|
---|
| 2946 | if( m-n+1<=m-1 )
|
---|
| 2947 | {
|
---|
| 2948 | i1_ = (0) - (m-n+1);
|
---|
| 2949 | for(i_=m-n+1; i_<=m-1;i_++)
|
---|
| 2950 | {
|
---|
| 2951 | c[i_] = b[i_+i1_];
|
---|
| 2952 | }
|
---|
| 2953 | }
|
---|
| 2954 | }
|
---|
| 2955 |
|
---|
| 2956 |
|
---|
| 2957 | public static void corrr1d(double[] signal,
|
---|
| 2958 | int n,
|
---|
| 2959 | double[] pattern,
|
---|
| 2960 | int m,
|
---|
| 2961 | ref double[] r)
|
---|
| 2962 | {
|
---|
| 2963 | double[] p = new double[0];
|
---|
| 2964 | double[] b = new double[0];
|
---|
| 2965 | int i = 0;
|
---|
| 2966 | int i_ = 0;
|
---|
| 2967 | int i1_ = 0;
|
---|
| 2968 |
|
---|
| 2969 | r = new double[0];
|
---|
| 2970 |
|
---|
| 2971 | ap.assert(n>0 & m>0, "CorrR1D: incorrect N or M!");
|
---|
| 2972 | p = new double[m];
|
---|
| 2973 | for(i=0; i<=m-1; i++)
|
---|
| 2974 | {
|
---|
| 2975 | p[m-1-i] = pattern[i];
|
---|
| 2976 | }
|
---|
| 2977 | conv.convr1d(p, m, signal, n, ref b);
|
---|
| 2978 | r = new double[m+n-1];
|
---|
| 2979 | i1_ = (m-1) - (0);
|
---|
| 2980 | for(i_=0; i_<=n-1;i_++)
|
---|
| 2981 | {
|
---|
| 2982 | r[i_] = b[i_+i1_];
|
---|
| 2983 | }
|
---|
| 2984 | if( m+n-2>=n )
|
---|
| 2985 | {
|
---|
| 2986 | i1_ = (0) - (n);
|
---|
| 2987 | for(i_=n; i_<=m+n-2;i_++)
|
---|
| 2988 | {
|
---|
| 2989 | r[i_] = b[i_+i1_];
|
---|
| 2990 | }
|
---|
| 2991 | }
|
---|
| 2992 | }
|
---|
| 2993 |
|
---|
| 2994 |
|
---|
| 2995 | public static void corrr1dcircular(double[] signal,
|
---|
| 2996 | int m,
|
---|
| 2997 | double[] pattern,
|
---|
| 2998 | int n,
|
---|
| 2999 | ref double[] c)
|
---|
| 3000 | {
|
---|
| 3001 | double[] p = new double[0];
|
---|
| 3002 | double[] b = new double[0];
|
---|
| 3003 | int i1 = 0;
|
---|
| 3004 | int i2 = 0;
|
---|
| 3005 | int i = 0;
|
---|
| 3006 | int j2 = 0;
|
---|
| 3007 | int i_ = 0;
|
---|
| 3008 | int i1_ = 0;
|
---|
| 3009 |
|
---|
| 3010 | c = new double[0];
|
---|
| 3011 |
|
---|
| 3012 | ap.assert(n>0 & m>0, "ConvC1DCircular: incorrect N or M!");
|
---|
| 3013 |
|
---|
| 3014 | //
|
---|
| 3015 | // normalize task: make M>=N,
|
---|
| 3016 | // so A will be longer (at least - not shorter) that B.
|
---|
| 3017 | //
|
---|
| 3018 | if( m<n )
|
---|
| 3019 | {
|
---|
| 3020 | b = new double[m];
|
---|
| 3021 | for(i1=0; i1<=m-1; i1++)
|
---|
| 3022 | {
|
---|
| 3023 | b[i1] = 0;
|
---|
| 3024 | }
|
---|
| 3025 | i1 = 0;
|
---|
| 3026 | while( i1<n )
|
---|
| 3027 | {
|
---|
| 3028 | i2 = Math.Min(i1+m-1, n-1);
|
---|
| 3029 | j2 = i2-i1;
|
---|
| 3030 | i1_ = (i1) - (0);
|
---|
| 3031 | for(i_=0; i_<=j2;i_++)
|
---|
| 3032 | {
|
---|
| 3033 | b[i_] = b[i_] + pattern[i_+i1_];
|
---|
| 3034 | }
|
---|
| 3035 | i1 = i1+m;
|
---|
| 3036 | }
|
---|
| 3037 | corrr1dcircular(signal, m, b, m, ref c);
|
---|
| 3038 | return;
|
---|
| 3039 | }
|
---|
| 3040 |
|
---|
| 3041 | //
|
---|
| 3042 | // Task is normalized
|
---|
| 3043 | //
|
---|
| 3044 | p = new double[n];
|
---|
| 3045 | for(i=0; i<=n-1; i++)
|
---|
| 3046 | {
|
---|
| 3047 | p[n-1-i] = pattern[i];
|
---|
| 3048 | }
|
---|
| 3049 | conv.convr1dcircular(signal, m, p, n, ref b);
|
---|
| 3050 | c = new double[m];
|
---|
| 3051 | i1_ = (n-1) - (0);
|
---|
| 3052 | for(i_=0; i_<=m-n;i_++)
|
---|
| 3053 | {
|
---|
| 3054 | c[i_] = b[i_+i1_];
|
---|
| 3055 | }
|
---|
| 3056 | if( m-n+1<=m-1 )
|
---|
| 3057 | {
|
---|
| 3058 | i1_ = (0) - (m-n+1);
|
---|
| 3059 | for(i_=m-n+1; i_<=m-1;i_++)
|
---|
| 3060 | {
|
---|
| 3061 | c[i_] = b[i_+i1_];
|
---|
| 3062 | }
|
---|
| 3063 | }
|
---|
| 3064 | }
|
---|
| 3065 |
|
---|
| 3066 |
|
---|
| 3067 | }
|
---|
| 3068 | public class fht
|
---|
| 3069 | {
|
---|
| 3070 | /*************************************************************************
|
---|
| 3071 | 1-dimensional Fast Hartley Transform.
|
---|
| 3072 |
|
---|
| 3073 | Algorithm has O(N*logN) complexity for any N (composite or prime).
|
---|
| 3074 |
|
---|
| 3075 | INPUT PARAMETERS
|
---|
| 3076 | A - array[0..N-1] - real function to be transformed
|
---|
| 3077 | N - problem size
|
---|
| 3078 |
|
---|
| 3079 | OUTPUT PARAMETERS
|
---|
| 3080 | A - FHT of a input array, array[0..N-1],
|
---|
| 3081 | A_out[k] = sum(A_in[j]*(cos(2*pi*j*k/N)+sin(2*pi*j*k/N)), j=0..N-1)
|
---|
| 3082 |
|
---|
| 3083 |
|
---|
| 3084 | -- ALGLIB --
|
---|
| 3085 | Copyright 04.06.2009 by Bochkanov Sergey
|
---|
| 3086 | *************************************************************************/
|
---|
| 3087 | public static void fhtr1d(ref double[] a,
|
---|
| 3088 | int n)
|
---|
| 3089 | {
|
---|
| 3090 | ftbase.ftplan plan = new ftbase.ftplan();
|
---|
| 3091 | int i = 0;
|
---|
| 3092 | complex[] fa = new complex[0];
|
---|
| 3093 |
|
---|
| 3094 | ap.assert(n>0, "FHTR1D: incorrect N!");
|
---|
| 3095 |
|
---|
| 3096 | //
|
---|
| 3097 | // Special case: N=1, FHT is just identity transform.
|
---|
| 3098 | // After this block we assume that N is strictly greater than 1.
|
---|
| 3099 | //
|
---|
| 3100 | if( n==1 )
|
---|
| 3101 | {
|
---|
| 3102 | return;
|
---|
| 3103 | }
|
---|
| 3104 |
|
---|
| 3105 | //
|
---|
| 3106 | // Reduce FHt to real FFT
|
---|
| 3107 | //
|
---|
| 3108 | fft.fftr1d(a, n, ref fa);
|
---|
| 3109 | for(i=0; i<=n-1; i++)
|
---|
| 3110 | {
|
---|
| 3111 | a[i] = fa[i].x-fa[i].y;
|
---|
| 3112 | }
|
---|
| 3113 | }
|
---|
| 3114 |
|
---|
| 3115 |
|
---|
| 3116 | /*************************************************************************
|
---|
| 3117 | 1-dimensional inverse FHT.
|
---|
| 3118 |
|
---|
| 3119 | Algorithm has O(N*logN) complexity for any N (composite or prime).
|
---|
| 3120 |
|
---|
| 3121 | INPUT PARAMETERS
|
---|
| 3122 | A - array[0..N-1] - complex array to be transformed
|
---|
| 3123 | N - problem size
|
---|
| 3124 |
|
---|
| 3125 | OUTPUT PARAMETERS
|
---|
| 3126 | A - inverse FHT of a input array, array[0..N-1]
|
---|
| 3127 |
|
---|
| 3128 |
|
---|
| 3129 | -- ALGLIB --
|
---|
| 3130 | Copyright 29.05.2009 by Bochkanov Sergey
|
---|
| 3131 | *************************************************************************/
|
---|
| 3132 | public static void fhtr1dinv(ref double[] a,
|
---|
| 3133 | int n)
|
---|
| 3134 | {
|
---|
| 3135 | int i = 0;
|
---|
| 3136 |
|
---|
| 3137 | ap.assert(n>0, "FHTR1DInv: incorrect N!");
|
---|
| 3138 |
|
---|
| 3139 | //
|
---|
| 3140 | // Special case: N=1, iFHT is just identity transform.
|
---|
| 3141 | // After this block we assume that N is strictly greater than 1.
|
---|
| 3142 | //
|
---|
| 3143 | if( n==1 )
|
---|
| 3144 | {
|
---|
| 3145 | return;
|
---|
| 3146 | }
|
---|
| 3147 |
|
---|
| 3148 | //
|
---|
| 3149 | // Inverse FHT can be expressed in terms of the FHT as
|
---|
| 3150 | //
|
---|
| 3151 | // invfht(x) = fht(x)/N
|
---|
| 3152 | //
|
---|
| 3153 | fhtr1d(ref a, n);
|
---|
| 3154 | for(i=0; i<=n-1; i++)
|
---|
| 3155 | {
|
---|
| 3156 | a[i] = a[i]/n;
|
---|
| 3157 | }
|
---|
| 3158 | }
|
---|
| 3159 |
|
---|
| 3160 |
|
---|
| 3161 | }
|
---|
| 3162 | }
|
---|
| 3163 |
|
---|