1 | /*************************************************************************
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2 | ALGLIB 3.11.0 (source code generated 2017-05-11)
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3 | Copyright (c) Sergey Bochkanov (ALGLIB project).
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4 |
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5 | >>> SOURCE LICENSE >>>
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6 | This program is free software; you can redistribute it and/or modify
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7 | it under the terms of the GNU General Public License as published by
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8 | the Free Software Foundation (www.fsf.org); either version 2 of the
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9 | License, or (at your option) any later version.
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10 |
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11 | This program is distributed in the hope that it will be useful,
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12 | but WITHOUT ANY WARRANTY; without even the implied warranty of
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13 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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14 | GNU General Public License for more details.
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15 |
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16 | A copy of the GNU General Public License is available at
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17 | http://www.fsf.org/licensing/licenses
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18 | >>> END OF LICENSE >>>
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19 | *************************************************************************/
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20 | #pragma warning disable 162
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21 | #pragma warning disable 164
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22 | #pragma warning disable 219
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23 | using System;
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24 |
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25 | public partial class alglib
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26 | {
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27 |
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28 |
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29 | /*************************************************************************
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30 | 1-dimensional complex FFT.
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31 |
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32 | Array size N may be arbitrary number (composite or prime). Composite N's
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33 | are handled with cache-oblivious variation of a Cooley-Tukey algorithm.
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34 | Small prime-factors are transformed using hard coded codelets (similar to
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35 | FFTW codelets, but without low-level optimization), large prime-factors
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36 | are handled with Bluestein's algorithm.
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37 |
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38 | Fastests transforms are for smooth N's (prime factors are 2, 3, 5 only),
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39 | most fast for powers of 2. When N have prime factors larger than these,
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40 | but orders of magnitude smaller than N, computations will be about 4 times
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41 | slower than for nearby highly composite N's. When N itself is prime, speed
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42 | will be 6 times lower.
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43 |
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44 | Algorithm has O(N*logN) complexity for any N (composite or prime).
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45 |
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46 | INPUT PARAMETERS
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47 | A - array[0..N-1] - complex function to be transformed
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48 | N - problem size
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49 |
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50 | OUTPUT PARAMETERS
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51 | A - DFT of a input array, array[0..N-1]
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52 | A_out[j] = SUM(A_in[k]*exp(-2*pi*sqrt(-1)*j*k/N), k = 0..N-1)
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53 |
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54 |
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55 | -- ALGLIB --
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56 | Copyright 29.05.2009 by Bochkanov Sergey
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57 | *************************************************************************/
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58 | public static void fftc1d(ref complex[] a, int n)
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59 | {
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60 |
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61 | fft.fftc1d(ref a, n);
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62 | return;
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63 | }
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64 | public static void fftc1d(ref complex[] a)
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65 | {
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66 | int n;
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67 |
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68 |
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69 | n = ap.len(a);
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70 | fft.fftc1d(ref a, n);
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71 |
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72 | return;
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73 | }
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74 |
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75 | /*************************************************************************
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76 | 1-dimensional complex inverse FFT.
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77 |
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78 | Array size N may be arbitrary number (composite or prime). Algorithm has
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79 | O(N*logN) complexity for any N (composite or prime).
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80 |
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81 | See FFTC1D() description for more information about algorithm performance.
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82 |
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83 | INPUT PARAMETERS
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84 | A - array[0..N-1] - complex array to be transformed
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85 | N - problem size
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86 |
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87 | OUTPUT PARAMETERS
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88 | A - inverse DFT of a input array, array[0..N-1]
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89 | A_out[j] = SUM(A_in[k]/N*exp(+2*pi*sqrt(-1)*j*k/N), k = 0..N-1)
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90 |
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91 |
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92 | -- ALGLIB --
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93 | Copyright 29.05.2009 by Bochkanov Sergey
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94 | *************************************************************************/
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95 | public static void fftc1dinv(ref complex[] a, int n)
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96 | {
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97 |
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98 | fft.fftc1dinv(ref a, n);
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99 | return;
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100 | }
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101 | public static void fftc1dinv(ref complex[] a)
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102 | {
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103 | int n;
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104 |
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105 |
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106 | n = ap.len(a);
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107 | fft.fftc1dinv(ref a, n);
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108 |
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109 | return;
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110 | }
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111 |
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112 | /*************************************************************************
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113 | 1-dimensional real FFT.
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114 |
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115 | Algorithm has O(N*logN) complexity for any N (composite or prime).
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116 |
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117 | INPUT PARAMETERS
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118 | A - array[0..N-1] - real function to be transformed
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119 | N - problem size
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120 |
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121 | OUTPUT PARAMETERS
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122 | F - DFT of a input array, array[0..N-1]
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123 | F[j] = SUM(A[k]*exp(-2*pi*sqrt(-1)*j*k/N), k = 0..N-1)
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124 |
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125 | NOTE:
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126 | F[] satisfies symmetry property F[k] = conj(F[N-k]), so just one half
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127 | of array is usually needed. But for convinience subroutine returns full
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128 | complex array (with frequencies above N/2), so its result may be used by
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129 | other FFT-related subroutines.
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130 |
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131 |
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132 | -- ALGLIB --
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133 | Copyright 01.06.2009 by Bochkanov Sergey
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134 | *************************************************************************/
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135 | public static void fftr1d(double[] a, int n, out complex[] f)
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136 | {
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137 | f = new complex[0];
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138 | fft.fftr1d(a, n, ref f);
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139 | return;
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140 | }
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141 | public static void fftr1d(double[] a, out complex[] f)
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142 | {
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143 | int n;
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144 |
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145 | f = new complex[0];
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146 | n = ap.len(a);
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147 | fft.fftr1d(a, n, ref f);
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148 |
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149 | return;
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150 | }
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151 |
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152 | /*************************************************************************
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153 | 1-dimensional real inverse FFT.
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154 |
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155 | Algorithm has O(N*logN) complexity for any N (composite or prime).
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156 |
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157 | INPUT PARAMETERS
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158 | F - array[0..floor(N/2)] - frequencies from forward real FFT
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159 | N - problem size
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160 |
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161 | OUTPUT PARAMETERS
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162 | A - inverse DFT of a input array, array[0..N-1]
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163 |
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164 | NOTE:
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165 | F[] should satisfy symmetry property F[k] = conj(F[N-k]), so just one
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166 | half of frequencies array is needed - elements from 0 to floor(N/2). F[0]
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167 | is ALWAYS real. If N is even F[floor(N/2)] is real too. If N is odd, then
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168 | F[floor(N/2)] has no special properties.
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169 |
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170 | Relying on properties noted above, FFTR1DInv subroutine uses only elements
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171 | from 0th to floor(N/2)-th. It ignores imaginary part of F[0], and in case
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172 | N is even it ignores imaginary part of F[floor(N/2)] too.
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173 |
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174 | When you call this function using full arguments list - "FFTR1DInv(F,N,A)"
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175 | - you can pass either either frequencies array with N elements or reduced
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176 | array with roughly N/2 elements - subroutine will successfully transform
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177 | both.
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178 |
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179 | If you call this function using reduced arguments list - "FFTR1DInv(F,A)"
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180 | - you must pass FULL array with N elements (although higher N/2 are still
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181 | not used) because array size is used to automatically determine FFT length
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182 |
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183 |
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184 | -- ALGLIB --
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185 | Copyright 01.06.2009 by Bochkanov Sergey
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186 | *************************************************************************/
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187 | public static void fftr1dinv(complex[] f, int n, out double[] a)
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188 | {
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189 | a = new double[0];
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190 | fft.fftr1dinv(f, n, ref a);
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191 | return;
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192 | }
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193 | public static void fftr1dinv(complex[] f, out double[] a)
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194 | {
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195 | int n;
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196 |
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197 | a = new double[0];
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198 | n = ap.len(f);
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199 | fft.fftr1dinv(f, n, ref a);
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200 |
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201 | return;
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202 | }
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203 |
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204 | }
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205 | public partial class alglib
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206 | {
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207 |
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208 |
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209 | /*************************************************************************
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210 | 1-dimensional Fast Hartley Transform.
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211 |
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212 | Algorithm has O(N*logN) complexity for any N (composite or prime).
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213 |
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214 | INPUT PARAMETERS
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215 | A - array[0..N-1] - real function to be transformed
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216 | N - problem size
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217 |
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218 | OUTPUT PARAMETERS
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219 | A - FHT of a input array, array[0..N-1],
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220 | A_out[k] = sum(A_in[j]*(cos(2*pi*j*k/N)+sin(2*pi*j*k/N)), j=0..N-1)
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221 |
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222 |
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223 | -- ALGLIB --
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224 | Copyright 04.06.2009 by Bochkanov Sergey
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225 | *************************************************************************/
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226 | public static void fhtr1d(ref double[] a, int n)
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227 | {
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228 |
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229 | fht.fhtr1d(ref a, n);
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230 | return;
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231 | }
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232 |
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233 | /*************************************************************************
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234 | 1-dimensional inverse FHT.
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235 |
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236 | Algorithm has O(N*logN) complexity for any N (composite or prime).
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237 |
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238 | INPUT PARAMETERS
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239 | A - array[0..N-1] - complex array to be transformed
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240 | N - problem size
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241 |
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242 | OUTPUT PARAMETERS
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243 | A - inverse FHT of a input array, array[0..N-1]
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244 |
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245 |
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246 | -- ALGLIB --
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247 | Copyright 29.05.2009 by Bochkanov Sergey
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248 | *************************************************************************/
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249 | public static void fhtr1dinv(ref double[] a, int n)
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250 | {
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251 |
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252 | fht.fhtr1dinv(ref a, n);
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253 | return;
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254 | }
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255 |
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256 | }
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257 | public partial class alglib
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258 | {
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259 |
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260 |
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261 | /*************************************************************************
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262 | 1-dimensional complex convolution.
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263 |
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264 | For given A/B returns conv(A,B) (non-circular). Subroutine can automatically
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265 | choose between three implementations: straightforward O(M*N) formula for
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266 | very small N (or M), overlap-add algorithm for cases where max(M,N) is
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267 | significantly larger than min(M,N), but O(M*N) algorithm is too slow, and
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268 | general FFT-based formula for cases where two previois algorithms are too
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269 | slow.
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270 |
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271 | Algorithm has max(M,N)*log(max(M,N)) complexity for any M/N.
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272 |
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273 | INPUT PARAMETERS
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274 | A - array[0..M-1] - complex function to be transformed
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275 | M - problem size
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276 | B - array[0..N-1] - complex function to be transformed
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277 | N - problem size
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278 |
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279 | OUTPUT PARAMETERS
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280 | R - convolution: A*B. array[0..N+M-2].
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281 |
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282 | NOTE:
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283 | It is assumed that A is zero at T<0, B is zero too. If one or both
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284 | functions have non-zero values at negative T's, you can still use this
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285 | subroutine - just shift its result correspondingly.
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286 |
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287 | -- ALGLIB --
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288 | Copyright 21.07.2009 by Bochkanov Sergey
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289 | *************************************************************************/
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290 | public static void convc1d(complex[] a, int m, complex[] b, int n, out complex[] r)
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291 | {
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292 | r = new complex[0];
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293 | conv.convc1d(a, m, b, n, ref r);
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294 | return;
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295 | }
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296 |
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297 | /*************************************************************************
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298 | 1-dimensional complex non-circular deconvolution (inverse of ConvC1D()).
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299 |
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300 | Algorithm has M*log(M)) complexity for any M (composite or prime).
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301 |
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302 | INPUT PARAMETERS
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303 | A - array[0..M-1] - convolved signal, A = conv(R, B)
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304 | M - convolved signal length
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305 | B - array[0..N-1] - response
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306 | N - response length, N<=M
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307 |
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308 | OUTPUT PARAMETERS
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309 | R - deconvolved signal. array[0..M-N].
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310 |
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311 | NOTE:
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312 | deconvolution is unstable process and may result in division by zero
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313 | (if your response function is degenerate, i.e. has zero Fourier coefficient).
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314 |
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315 | NOTE:
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316 | It is assumed that A is zero at T<0, B is zero too. If one or both
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317 | functions have non-zero values at negative T's, you can still use this
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318 | subroutine - just shift its result correspondingly.
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319 |
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320 | -- ALGLIB --
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321 | Copyright 21.07.2009 by Bochkanov Sergey
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322 | *************************************************************************/
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323 | public static void convc1dinv(complex[] a, int m, complex[] b, int n, out complex[] r)
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324 | {
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325 | r = new complex[0];
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326 | conv.convc1dinv(a, m, b, n, ref r);
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327 | return;
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328 | }
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329 |
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330 | /*************************************************************************
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331 | 1-dimensional circular complex convolution.
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332 |
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333 | For given S/R returns conv(S,R) (circular). Algorithm has linearithmic
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334 | complexity for any M/N.
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335 |
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336 | IMPORTANT: normal convolution is commutative, i.e. it is symmetric -
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337 | conv(A,B)=conv(B,A). Cyclic convolution IS NOT. One function - S - is a
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338 | signal, periodic function, and another - R - is a response, non-periodic
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339 | function with limited length.
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340 |
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341 | INPUT PARAMETERS
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342 | S - array[0..M-1] - complex periodic signal
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343 | M - problem size
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344 | B - array[0..N-1] - complex non-periodic response
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345 | N - problem size
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346 |
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347 | OUTPUT PARAMETERS
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348 | R - convolution: A*B. array[0..M-1].
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349 |
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350 | NOTE:
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351 | It is assumed that B is zero at T<0. If it has non-zero values at
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352 | negative T's, you can still use this subroutine - just shift its result
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353 | correspondingly.
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354 |
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355 | -- ALGLIB --
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356 | Copyright 21.07.2009 by Bochkanov Sergey
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357 | *************************************************************************/
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358 | public static void convc1dcircular(complex[] s, int m, complex[] r, int n, out complex[] c)
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359 | {
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360 | c = new complex[0];
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361 | conv.convc1dcircular(s, m, r, n, ref c);
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362 | return;
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363 | }
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364 |
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365 | /*************************************************************************
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366 | 1-dimensional circular complex deconvolution (inverse of ConvC1DCircular()).
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367 |
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368 | Algorithm has M*log(M)) complexity for any M (composite or prime).
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369 |
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370 | INPUT PARAMETERS
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371 | A - array[0..M-1] - convolved periodic signal, A = conv(R, B)
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372 | M - convolved signal length
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373 | B - array[0..N-1] - non-periodic response
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374 | N - response length
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375 |
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376 | OUTPUT PARAMETERS
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377 | R - deconvolved signal. array[0..M-1].
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378 |
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379 | NOTE:
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380 | deconvolution is unstable process and may result in division by zero
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381 | (if your response function is degenerate, i.e. has zero Fourier coefficient).
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382 |
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383 | NOTE:
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384 | It is assumed that B is zero at T<0. If it has non-zero values at
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385 | negative T's, you can still use this subroutine - just shift its result
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386 | correspondingly.
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387 |
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388 | -- ALGLIB --
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389 | Copyright 21.07.2009 by Bochkanov Sergey
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390 | *************************************************************************/
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391 | public static void convc1dcircularinv(complex[] a, int m, complex[] b, int n, out complex[] r)
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392 | {
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393 | r = new complex[0];
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394 | conv.convc1dcircularinv(a, m, b, n, ref r);
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395 | return;
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396 | }
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397 |
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398 | /*************************************************************************
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399 | 1-dimensional real convolution.
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400 |
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401 | Analogous to ConvC1D(), see ConvC1D() comments for more details.
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402 |
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403 | INPUT PARAMETERS
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404 | A - array[0..M-1] - real function to be transformed
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405 | M - problem size
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406 | B - array[0..N-1] - real function to be transformed
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407 | N - problem size
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408 |
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409 | OUTPUT PARAMETERS
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410 | R - convolution: A*B. array[0..N+M-2].
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411 |
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412 | NOTE:
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413 | It is assumed that A is zero at T<0, B is zero too. If one or both
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414 | functions have non-zero values at negative T's, you can still use this
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415 | subroutine - just shift its result correspondingly.
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416 |
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417 | -- ALGLIB --
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418 | Copyright 21.07.2009 by Bochkanov Sergey
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419 | *************************************************************************/
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420 | public static void convr1d(double[] a, int m, double[] b, int n, out double[] r)
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421 | {
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422 | r = new double[0];
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423 | conv.convr1d(a, m, b, n, ref r);
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424 | return;
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425 | }
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426 |
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427 | /*************************************************************************
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428 | 1-dimensional real deconvolution (inverse of ConvC1D()).
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429 |
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430 | Algorithm has M*log(M)) complexity for any M (composite or prime).
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431 |
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432 | INPUT PARAMETERS
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433 | A - array[0..M-1] - convolved signal, A = conv(R, B)
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434 | M - convolved signal length
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435 | B - array[0..N-1] - response
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436 | N - response length, N<=M
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437 |
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438 | OUTPUT PARAMETERS
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439 | R - deconvolved signal. array[0..M-N].
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440 |
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441 | NOTE:
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442 | deconvolution is unstable process and may result in division by zero
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443 | (if your response function is degenerate, i.e. has zero Fourier coefficient).
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444 |
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445 | NOTE:
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446 | It is assumed that A is zero at T<0, B is zero too. If one or both
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447 | functions have non-zero values at negative T's, you can still use this
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448 | subroutine - just shift its result correspondingly.
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449 |
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450 | -- ALGLIB --
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451 | Copyright 21.07.2009 by Bochkanov Sergey
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452 | *************************************************************************/
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453 | public static void convr1dinv(double[] a, int m, double[] b, int n, out double[] r)
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454 | {
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455 | r = new double[0];
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456 | conv.convr1dinv(a, m, b, n, ref r);
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457 | return;
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458 | }
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459 |
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460 | /*************************************************************************
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461 | 1-dimensional circular real convolution.
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462 |
|
---|
463 | Analogous to ConvC1DCircular(), see ConvC1DCircular() comments for more details.
|
---|
464 |
|
---|
465 | INPUT PARAMETERS
|
---|
466 | S - array[0..M-1] - real signal
|
---|
467 | M - problem size
|
---|
468 | B - array[0..N-1] - real response
|
---|
469 | N - problem size
|
---|
470 |
|
---|
471 | OUTPUT PARAMETERS
|
---|
472 | R - convolution: A*B. array[0..M-1].
|
---|
473 |
|
---|
474 | NOTE:
|
---|
475 | It is assumed that B is zero at T<0. If it has non-zero values at
|
---|
476 | negative T's, you can still use this subroutine - just shift its result
|
---|
477 | correspondingly.
|
---|
478 |
|
---|
479 | -- ALGLIB --
|
---|
480 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
481 | *************************************************************************/
|
---|
482 | public static void convr1dcircular(double[] s, int m, double[] r, int n, out double[] c)
|
---|
483 | {
|
---|
484 | c = new double[0];
|
---|
485 | conv.convr1dcircular(s, m, r, n, ref c);
|
---|
486 | return;
|
---|
487 | }
|
---|
488 |
|
---|
489 | /*************************************************************************
|
---|
490 | 1-dimensional complex deconvolution (inverse of ConvC1D()).
|
---|
491 |
|
---|
492 | Algorithm has M*log(M)) complexity for any M (composite or prime).
|
---|
493 |
|
---|
494 | INPUT PARAMETERS
|
---|
495 | A - array[0..M-1] - convolved signal, A = conv(R, B)
|
---|
496 | M - convolved signal length
|
---|
497 | B - array[0..N-1] - response
|
---|
498 | N - response length
|
---|
499 |
|
---|
500 | OUTPUT PARAMETERS
|
---|
501 | R - deconvolved signal. array[0..M-N].
|
---|
502 |
|
---|
503 | NOTE:
|
---|
504 | deconvolution is unstable process and may result in division by zero
|
---|
505 | (if your response function is degenerate, i.e. has zero Fourier coefficient).
|
---|
506 |
|
---|
507 | NOTE:
|
---|
508 | It is assumed that B is zero at T<0. If it has non-zero values at
|
---|
509 | negative T's, you can still use this subroutine - just shift its result
|
---|
510 | correspondingly.
|
---|
511 |
|
---|
512 | -- ALGLIB --
|
---|
513 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
514 | *************************************************************************/
|
---|
515 | public static void convr1dcircularinv(double[] a, int m, double[] b, int n, out double[] r)
|
---|
516 | {
|
---|
517 | r = new double[0];
|
---|
518 | conv.convr1dcircularinv(a, m, b, n, ref r);
|
---|
519 | return;
|
---|
520 | }
|
---|
521 |
|
---|
522 | }
|
---|
523 | public partial class alglib
|
---|
524 | {
|
---|
525 |
|
---|
526 |
|
---|
527 | /*************************************************************************
|
---|
528 | 1-dimensional complex cross-correlation.
|
---|
529 |
|
---|
530 | For given Pattern/Signal returns corr(Pattern,Signal) (non-circular).
|
---|
531 |
|
---|
532 | Correlation is calculated using reduction to convolution. Algorithm with
|
---|
533 | max(N,N)*log(max(N,N)) complexity is used (see ConvC1D() for more info
|
---|
534 | about performance).
|
---|
535 |
|
---|
536 | IMPORTANT:
|
---|
537 | for historical reasons subroutine accepts its parameters in reversed
|
---|
538 | order: CorrC1D(Signal, Pattern) = Pattern x Signal (using traditional
|
---|
539 | definition of cross-correlation, denoting cross-correlation as "x").
|
---|
540 |
|
---|
541 | INPUT PARAMETERS
|
---|
542 | Signal - array[0..N-1] - complex function to be transformed,
|
---|
543 | signal containing pattern
|
---|
544 | N - problem size
|
---|
545 | Pattern - array[0..M-1] - complex function to be transformed,
|
---|
546 | pattern to search withing signal
|
---|
547 | M - problem size
|
---|
548 |
|
---|
549 | OUTPUT PARAMETERS
|
---|
550 | R - cross-correlation, array[0..N+M-2]:
|
---|
551 | * positive lags are stored in R[0..N-1],
|
---|
552 | R[i] = sum(conj(pattern[j])*signal[i+j]
|
---|
553 | * negative lags are stored in R[N..N+M-2],
|
---|
554 | R[N+M-1-i] = sum(conj(pattern[j])*signal[-i+j]
|
---|
555 |
|
---|
556 | NOTE:
|
---|
557 | It is assumed that pattern domain is [0..M-1]. If Pattern is non-zero
|
---|
558 | on [-K..M-1], you can still use this subroutine, just shift result by K.
|
---|
559 |
|
---|
560 | -- ALGLIB --
|
---|
561 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
562 | *************************************************************************/
|
---|
563 | public static void corrc1d(complex[] signal, int n, complex[] pattern, int m, out complex[] r)
|
---|
564 | {
|
---|
565 | r = new complex[0];
|
---|
566 | corr.corrc1d(signal, n, pattern, m, ref r);
|
---|
567 | return;
|
---|
568 | }
|
---|
569 |
|
---|
570 | /*************************************************************************
|
---|
571 | 1-dimensional circular complex cross-correlation.
|
---|
572 |
|
---|
573 | For given Pattern/Signal returns corr(Pattern,Signal) (circular).
|
---|
574 | Algorithm has linearithmic complexity for any M/N.
|
---|
575 |
|
---|
576 | IMPORTANT:
|
---|
577 | for historical reasons subroutine accepts its parameters in reversed
|
---|
578 | order: CorrC1DCircular(Signal, Pattern) = Pattern x Signal (using
|
---|
579 | traditional definition of cross-correlation, denoting cross-correlation
|
---|
580 | as "x").
|
---|
581 |
|
---|
582 | INPUT PARAMETERS
|
---|
583 | Signal - array[0..N-1] - complex function to be transformed,
|
---|
584 | periodic signal containing pattern
|
---|
585 | N - problem size
|
---|
586 | Pattern - array[0..M-1] - complex function to be transformed,
|
---|
587 | non-periodic pattern to search withing signal
|
---|
588 | M - problem size
|
---|
589 |
|
---|
590 | OUTPUT PARAMETERS
|
---|
591 | R - convolution: A*B. array[0..M-1].
|
---|
592 |
|
---|
593 |
|
---|
594 | -- ALGLIB --
|
---|
595 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
596 | *************************************************************************/
|
---|
597 | public static void corrc1dcircular(complex[] signal, int m, complex[] pattern, int n, out complex[] c)
|
---|
598 | {
|
---|
599 | c = new complex[0];
|
---|
600 | corr.corrc1dcircular(signal, m, pattern, n, ref c);
|
---|
601 | return;
|
---|
602 | }
|
---|
603 |
|
---|
604 | /*************************************************************************
|
---|
605 | 1-dimensional real cross-correlation.
|
---|
606 |
|
---|
607 | For given Pattern/Signal returns corr(Pattern,Signal) (non-circular).
|
---|
608 |
|
---|
609 | Correlation is calculated using reduction to convolution. Algorithm with
|
---|
610 | max(N,N)*log(max(N,N)) complexity is used (see ConvC1D() for more info
|
---|
611 | about performance).
|
---|
612 |
|
---|
613 | IMPORTANT:
|
---|
614 | for historical reasons subroutine accepts its parameters in reversed
|
---|
615 | order: CorrR1D(Signal, Pattern) = Pattern x Signal (using traditional
|
---|
616 | definition of cross-correlation, denoting cross-correlation as "x").
|
---|
617 |
|
---|
618 | INPUT PARAMETERS
|
---|
619 | Signal - array[0..N-1] - real function to be transformed,
|
---|
620 | signal containing pattern
|
---|
621 | N - problem size
|
---|
622 | Pattern - array[0..M-1] - real function to be transformed,
|
---|
623 | pattern to search withing signal
|
---|
624 | M - problem size
|
---|
625 |
|
---|
626 | OUTPUT PARAMETERS
|
---|
627 | R - cross-correlation, array[0..N+M-2]:
|
---|
628 | * positive lags are stored in R[0..N-1],
|
---|
629 | R[i] = sum(pattern[j]*signal[i+j]
|
---|
630 | * negative lags are stored in R[N..N+M-2],
|
---|
631 | R[N+M-1-i] = sum(pattern[j]*signal[-i+j]
|
---|
632 |
|
---|
633 | NOTE:
|
---|
634 | It is assumed that pattern domain is [0..M-1]. If Pattern is non-zero
|
---|
635 | on [-K..M-1], you can still use this subroutine, just shift result by K.
|
---|
636 |
|
---|
637 | -- ALGLIB --
|
---|
638 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
639 | *************************************************************************/
|
---|
640 | public static void corrr1d(double[] signal, int n, double[] pattern, int m, out double[] r)
|
---|
641 | {
|
---|
642 | r = new double[0];
|
---|
643 | corr.corrr1d(signal, n, pattern, m, ref r);
|
---|
644 | return;
|
---|
645 | }
|
---|
646 |
|
---|
647 | /*************************************************************************
|
---|
648 | 1-dimensional circular real cross-correlation.
|
---|
649 |
|
---|
650 | For given Pattern/Signal returns corr(Pattern,Signal) (circular).
|
---|
651 | Algorithm has linearithmic complexity for any M/N.
|
---|
652 |
|
---|
653 | IMPORTANT:
|
---|
654 | for historical reasons subroutine accepts its parameters in reversed
|
---|
655 | order: CorrR1DCircular(Signal, Pattern) = Pattern x Signal (using
|
---|
656 | traditional definition of cross-correlation, denoting cross-correlation
|
---|
657 | as "x").
|
---|
658 |
|
---|
659 | INPUT PARAMETERS
|
---|
660 | Signal - array[0..N-1] - real function to be transformed,
|
---|
661 | periodic signal containing pattern
|
---|
662 | N - problem size
|
---|
663 | Pattern - array[0..M-1] - real function to be transformed,
|
---|
664 | non-periodic pattern to search withing signal
|
---|
665 | M - problem size
|
---|
666 |
|
---|
667 | OUTPUT PARAMETERS
|
---|
668 | R - convolution: A*B. array[0..M-1].
|
---|
669 |
|
---|
670 |
|
---|
671 | -- ALGLIB --
|
---|
672 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
673 | *************************************************************************/
|
---|
674 | public static void corrr1dcircular(double[] signal, int m, double[] pattern, int n, out double[] c)
|
---|
675 | {
|
---|
676 | c = new double[0];
|
---|
677 | corr.corrr1dcircular(signal, m, pattern, n, ref c);
|
---|
678 | return;
|
---|
679 | }
|
---|
680 |
|
---|
681 | }
|
---|
682 | public partial class alglib
|
---|
683 | {
|
---|
684 | public class fft
|
---|
685 | {
|
---|
686 | /*************************************************************************
|
---|
687 | 1-dimensional complex FFT.
|
---|
688 |
|
---|
689 | Array size N may be arbitrary number (composite or prime). Composite N's
|
---|
690 | are handled with cache-oblivious variation of a Cooley-Tukey algorithm.
|
---|
691 | Small prime-factors are transformed using hard coded codelets (similar to
|
---|
692 | FFTW codelets, but without low-level optimization), large prime-factors
|
---|
693 | are handled with Bluestein's algorithm.
|
---|
694 |
|
---|
695 | Fastests transforms are for smooth N's (prime factors are 2, 3, 5 only),
|
---|
696 | most fast for powers of 2. When N have prime factors larger than these,
|
---|
697 | but orders of magnitude smaller than N, computations will be about 4 times
|
---|
698 | slower than for nearby highly composite N's. When N itself is prime, speed
|
---|
699 | will be 6 times lower.
|
---|
700 |
|
---|
701 | Algorithm has O(N*logN) complexity for any N (composite or prime).
|
---|
702 |
|
---|
703 | INPUT PARAMETERS
|
---|
704 | A - array[0..N-1] - complex function to be transformed
|
---|
705 | N - problem size
|
---|
706 |
|
---|
707 | OUTPUT PARAMETERS
|
---|
708 | A - DFT of a input array, array[0..N-1]
|
---|
709 | A_out[j] = SUM(A_in[k]*exp(-2*pi*sqrt(-1)*j*k/N), k = 0..N-1)
|
---|
710 |
|
---|
711 |
|
---|
712 | -- ALGLIB --
|
---|
713 | Copyright 29.05.2009 by Bochkanov Sergey
|
---|
714 | *************************************************************************/
|
---|
715 | public static void fftc1d(ref complex[] a,
|
---|
716 | int n)
|
---|
717 | {
|
---|
718 | ftbase.fasttransformplan plan = new ftbase.fasttransformplan();
|
---|
719 | int i = 0;
|
---|
720 | double[] buf = new double[0];
|
---|
721 |
|
---|
722 | alglib.ap.assert(n>0, "FFTC1D: incorrect N!");
|
---|
723 | alglib.ap.assert(alglib.ap.len(a)>=n, "FFTC1D: Length(A)<N!");
|
---|
724 | alglib.ap.assert(apserv.isfinitecvector(a, n), "FFTC1D: A contains infinite or NAN values!");
|
---|
725 |
|
---|
726 | //
|
---|
727 | // Special case: N=1, FFT is just identity transform.
|
---|
728 | // After this block we assume that N is strictly greater than 1.
|
---|
729 | //
|
---|
730 | if( n==1 )
|
---|
731 | {
|
---|
732 | return;
|
---|
733 | }
|
---|
734 |
|
---|
735 | //
|
---|
736 | // convert input array to the more convinient format
|
---|
737 | //
|
---|
738 | buf = new double[2*n];
|
---|
739 | for(i=0; i<=n-1; i++)
|
---|
740 | {
|
---|
741 | buf[2*i+0] = a[i].x;
|
---|
742 | buf[2*i+1] = a[i].y;
|
---|
743 | }
|
---|
744 |
|
---|
745 | //
|
---|
746 | // Generate plan and execute it.
|
---|
747 | //
|
---|
748 | // Plan is a combination of a successive factorizations of N and
|
---|
749 | // precomputed data. It is much like a FFTW plan, but is not stored
|
---|
750 | // between subroutine calls and is much simpler.
|
---|
751 | //
|
---|
752 | ftbase.ftcomplexfftplan(n, 1, plan);
|
---|
753 | ftbase.ftapplyplan(plan, buf, 0, 1);
|
---|
754 |
|
---|
755 | //
|
---|
756 | // result
|
---|
757 | //
|
---|
758 | for(i=0; i<=n-1; i++)
|
---|
759 | {
|
---|
760 | a[i].x = buf[2*i+0];
|
---|
761 | a[i].y = buf[2*i+1];
|
---|
762 | }
|
---|
763 | }
|
---|
764 |
|
---|
765 |
|
---|
766 | /*************************************************************************
|
---|
767 | 1-dimensional complex inverse FFT.
|
---|
768 |
|
---|
769 | Array size N may be arbitrary number (composite or prime). Algorithm has
|
---|
770 | O(N*logN) complexity for any N (composite or prime).
|
---|
771 |
|
---|
772 | See FFTC1D() description for more information about algorithm performance.
|
---|
773 |
|
---|
774 | INPUT PARAMETERS
|
---|
775 | A - array[0..N-1] - complex array to be transformed
|
---|
776 | N - problem size
|
---|
777 |
|
---|
778 | OUTPUT PARAMETERS
|
---|
779 | A - inverse DFT of a input array, array[0..N-1]
|
---|
780 | A_out[j] = SUM(A_in[k]/N*exp(+2*pi*sqrt(-1)*j*k/N), k = 0..N-1)
|
---|
781 |
|
---|
782 |
|
---|
783 | -- ALGLIB --
|
---|
784 | Copyright 29.05.2009 by Bochkanov Sergey
|
---|
785 | *************************************************************************/
|
---|
786 | public static void fftc1dinv(ref complex[] a,
|
---|
787 | int n)
|
---|
788 | {
|
---|
789 | int i = 0;
|
---|
790 |
|
---|
791 | alglib.ap.assert(n>0, "FFTC1DInv: incorrect N!");
|
---|
792 | alglib.ap.assert(alglib.ap.len(a)>=n, "FFTC1DInv: Length(A)<N!");
|
---|
793 | alglib.ap.assert(apserv.isfinitecvector(a, n), "FFTC1DInv: A contains infinite or NAN values!");
|
---|
794 |
|
---|
795 | //
|
---|
796 | // Inverse DFT can be expressed in terms of the DFT as
|
---|
797 | //
|
---|
798 | // invfft(x) = fft(x')'/N
|
---|
799 | //
|
---|
800 | // here x' means conj(x).
|
---|
801 | //
|
---|
802 | for(i=0; i<=n-1; i++)
|
---|
803 | {
|
---|
804 | a[i].y = -a[i].y;
|
---|
805 | }
|
---|
806 | fftc1d(ref a, n);
|
---|
807 | for(i=0; i<=n-1; i++)
|
---|
808 | {
|
---|
809 | a[i].x = a[i].x/n;
|
---|
810 | a[i].y = -(a[i].y/n);
|
---|
811 | }
|
---|
812 | }
|
---|
813 |
|
---|
814 |
|
---|
815 | /*************************************************************************
|
---|
816 | 1-dimensional real FFT.
|
---|
817 |
|
---|
818 | Algorithm has O(N*logN) complexity for any N (composite or prime).
|
---|
819 |
|
---|
820 | INPUT PARAMETERS
|
---|
821 | A - array[0..N-1] - real function to be transformed
|
---|
822 | N - problem size
|
---|
823 |
|
---|
824 | OUTPUT PARAMETERS
|
---|
825 | F - DFT of a input array, array[0..N-1]
|
---|
826 | F[j] = SUM(A[k]*exp(-2*pi*sqrt(-1)*j*k/N), k = 0..N-1)
|
---|
827 |
|
---|
828 | NOTE:
|
---|
829 | F[] satisfies symmetry property F[k] = conj(F[N-k]), so just one half
|
---|
830 | of array is usually needed. But for convinience subroutine returns full
|
---|
831 | complex array (with frequencies above N/2), so its result may be used by
|
---|
832 | other FFT-related subroutines.
|
---|
833 |
|
---|
834 |
|
---|
835 | -- ALGLIB --
|
---|
836 | Copyright 01.06.2009 by Bochkanov Sergey
|
---|
837 | *************************************************************************/
|
---|
838 | public static void fftr1d(double[] a,
|
---|
839 | int n,
|
---|
840 | ref complex[] f)
|
---|
841 | {
|
---|
842 | int i = 0;
|
---|
843 | int n2 = 0;
|
---|
844 | int idx = 0;
|
---|
845 | complex hn = 0;
|
---|
846 | complex hmnc = 0;
|
---|
847 | complex v = 0;
|
---|
848 | double[] buf = new double[0];
|
---|
849 | ftbase.fasttransformplan plan = new ftbase.fasttransformplan();
|
---|
850 | int i_ = 0;
|
---|
851 |
|
---|
852 | f = new complex[0];
|
---|
853 |
|
---|
854 | alglib.ap.assert(n>0, "FFTR1D: incorrect N!");
|
---|
855 | alglib.ap.assert(alglib.ap.len(a)>=n, "FFTR1D: Length(A)<N!");
|
---|
856 | alglib.ap.assert(apserv.isfinitevector(a, n), "FFTR1D: A contains infinite or NAN values!");
|
---|
857 |
|
---|
858 | //
|
---|
859 | // Special cases:
|
---|
860 | // * N=1, FFT is just identity transform.
|
---|
861 | // * N=2, FFT is simple too
|
---|
862 | //
|
---|
863 | // After this block we assume that N is strictly greater than 2
|
---|
864 | //
|
---|
865 | if( n==1 )
|
---|
866 | {
|
---|
867 | f = new complex[1];
|
---|
868 | f[0] = a[0];
|
---|
869 | return;
|
---|
870 | }
|
---|
871 | if( n==2 )
|
---|
872 | {
|
---|
873 | f = new complex[2];
|
---|
874 | f[0].x = a[0]+a[1];
|
---|
875 | f[0].y = 0;
|
---|
876 | f[1].x = a[0]-a[1];
|
---|
877 | f[1].y = 0;
|
---|
878 | return;
|
---|
879 | }
|
---|
880 |
|
---|
881 | //
|
---|
882 | // Choose between odd-size and even-size FFTs
|
---|
883 | //
|
---|
884 | if( n%2==0 )
|
---|
885 | {
|
---|
886 |
|
---|
887 | //
|
---|
888 | // even-size real FFT, use reduction to the complex task
|
---|
889 | //
|
---|
890 | n2 = n/2;
|
---|
891 | buf = new double[n];
|
---|
892 | for(i_=0; i_<=n-1;i_++)
|
---|
893 | {
|
---|
894 | buf[i_] = a[i_];
|
---|
895 | }
|
---|
896 | ftbase.ftcomplexfftplan(n2, 1, plan);
|
---|
897 | ftbase.ftapplyplan(plan, buf, 0, 1);
|
---|
898 | f = new complex[n];
|
---|
899 | for(i=0; i<=n2; i++)
|
---|
900 | {
|
---|
901 | idx = 2*(i%n2);
|
---|
902 | hn.x = buf[idx+0];
|
---|
903 | hn.y = buf[idx+1];
|
---|
904 | idx = 2*((n2-i)%n2);
|
---|
905 | hmnc.x = buf[idx+0];
|
---|
906 | hmnc.y = -buf[idx+1];
|
---|
907 | v.x = -Math.Sin(-(2*Math.PI*i/n));
|
---|
908 | v.y = Math.Cos(-(2*Math.PI*i/n));
|
---|
909 | f[i] = hn+hmnc-v*(hn-hmnc);
|
---|
910 | f[i].x = 0.5*f[i].x;
|
---|
911 | f[i].y = 0.5*f[i].y;
|
---|
912 | }
|
---|
913 | for(i=n2+1; i<=n-1; i++)
|
---|
914 | {
|
---|
915 | f[i] = math.conj(f[n-i]);
|
---|
916 | }
|
---|
917 | }
|
---|
918 | else
|
---|
919 | {
|
---|
920 |
|
---|
921 | //
|
---|
922 | // use complex FFT
|
---|
923 | //
|
---|
924 | f = new complex[n];
|
---|
925 | for(i=0; i<=n-1; i++)
|
---|
926 | {
|
---|
927 | f[i] = a[i];
|
---|
928 | }
|
---|
929 | fftc1d(ref f, n);
|
---|
930 | }
|
---|
931 | }
|
---|
932 |
|
---|
933 |
|
---|
934 | /*************************************************************************
|
---|
935 | 1-dimensional real inverse FFT.
|
---|
936 |
|
---|
937 | Algorithm has O(N*logN) complexity for any N (composite or prime).
|
---|
938 |
|
---|
939 | INPUT PARAMETERS
|
---|
940 | F - array[0..floor(N/2)] - frequencies from forward real FFT
|
---|
941 | N - problem size
|
---|
942 |
|
---|
943 | OUTPUT PARAMETERS
|
---|
944 | A - inverse DFT of a input array, array[0..N-1]
|
---|
945 |
|
---|
946 | NOTE:
|
---|
947 | F[] should satisfy symmetry property F[k] = conj(F[N-k]), so just one
|
---|
948 | half of frequencies array is needed - elements from 0 to floor(N/2). F[0]
|
---|
949 | is ALWAYS real. If N is even F[floor(N/2)] is real too. If N is odd, then
|
---|
950 | F[floor(N/2)] has no special properties.
|
---|
951 |
|
---|
952 | Relying on properties noted above, FFTR1DInv subroutine uses only elements
|
---|
953 | from 0th to floor(N/2)-th. It ignores imaginary part of F[0], and in case
|
---|
954 | N is even it ignores imaginary part of F[floor(N/2)] too.
|
---|
955 |
|
---|
956 | When you call this function using full arguments list - "FFTR1DInv(F,N,A)"
|
---|
957 | - you can pass either either frequencies array with N elements or reduced
|
---|
958 | array with roughly N/2 elements - subroutine will successfully transform
|
---|
959 | both.
|
---|
960 |
|
---|
961 | If you call this function using reduced arguments list - "FFTR1DInv(F,A)"
|
---|
962 | - you must pass FULL array with N elements (although higher N/2 are still
|
---|
963 | not used) because array size is used to automatically determine FFT length
|
---|
964 |
|
---|
965 |
|
---|
966 | -- ALGLIB --
|
---|
967 | Copyright 01.06.2009 by Bochkanov Sergey
|
---|
968 | *************************************************************************/
|
---|
969 | public static void fftr1dinv(complex[] f,
|
---|
970 | int n,
|
---|
971 | ref double[] a)
|
---|
972 | {
|
---|
973 | int i = 0;
|
---|
974 | double[] h = new double[0];
|
---|
975 | complex[] fh = new complex[0];
|
---|
976 |
|
---|
977 | a = new double[0];
|
---|
978 |
|
---|
979 | alglib.ap.assert(n>0, "FFTR1DInv: incorrect N!");
|
---|
980 | alglib.ap.assert(alglib.ap.len(f)>=(int)Math.Floor((double)n/(double)2)+1, "FFTR1DInv: Length(F)<Floor(N/2)+1!");
|
---|
981 | alglib.ap.assert(math.isfinite(f[0].x), "FFTR1DInv: F contains infinite or NAN values!");
|
---|
982 | for(i=1; i<=(int)Math.Floor((double)n/(double)2)-1; i++)
|
---|
983 | {
|
---|
984 | alglib.ap.assert(math.isfinite(f[i].x) && math.isfinite(f[i].y), "FFTR1DInv: F contains infinite or NAN values!");
|
---|
985 | }
|
---|
986 | alglib.ap.assert(math.isfinite(f[(int)Math.Floor((double)n/(double)2)].x), "FFTR1DInv: F contains infinite or NAN values!");
|
---|
987 | if( n%2!=0 )
|
---|
988 | {
|
---|
989 | alglib.ap.assert(math.isfinite(f[(int)Math.Floor((double)n/(double)2)].y), "FFTR1DInv: F contains infinite or NAN values!");
|
---|
990 | }
|
---|
991 |
|
---|
992 | //
|
---|
993 | // Special case: N=1, FFT is just identity transform.
|
---|
994 | // After this block we assume that N is strictly greater than 1.
|
---|
995 | //
|
---|
996 | if( n==1 )
|
---|
997 | {
|
---|
998 | a = new double[1];
|
---|
999 | a[0] = f[0].x;
|
---|
1000 | return;
|
---|
1001 | }
|
---|
1002 |
|
---|
1003 | //
|
---|
1004 | // inverse real FFT is reduced to the inverse real FHT,
|
---|
1005 | // which is reduced to the forward real FHT,
|
---|
1006 | // which is reduced to the forward real FFT.
|
---|
1007 | //
|
---|
1008 | // Don't worry, it is really compact and efficient reduction :)
|
---|
1009 | //
|
---|
1010 | h = new double[n];
|
---|
1011 | a = new double[n];
|
---|
1012 | h[0] = f[0].x;
|
---|
1013 | for(i=1; i<=(int)Math.Floor((double)n/(double)2)-1; i++)
|
---|
1014 | {
|
---|
1015 | h[i] = f[i].x-f[i].y;
|
---|
1016 | h[n-i] = f[i].x+f[i].y;
|
---|
1017 | }
|
---|
1018 | if( n%2==0 )
|
---|
1019 | {
|
---|
1020 | h[(int)Math.Floor((double)n/(double)2)] = f[(int)Math.Floor((double)n/(double)2)].x;
|
---|
1021 | }
|
---|
1022 | else
|
---|
1023 | {
|
---|
1024 | 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;
|
---|
1025 | 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;
|
---|
1026 | }
|
---|
1027 | fftr1d(h, n, ref fh);
|
---|
1028 | for(i=0; i<=n-1; i++)
|
---|
1029 | {
|
---|
1030 | a[i] = (fh[i].x-fh[i].y)/n;
|
---|
1031 | }
|
---|
1032 | }
|
---|
1033 |
|
---|
1034 |
|
---|
1035 | /*************************************************************************
|
---|
1036 | Internal subroutine. Never call it directly!
|
---|
1037 |
|
---|
1038 |
|
---|
1039 | -- ALGLIB --
|
---|
1040 | Copyright 01.06.2009 by Bochkanov Sergey
|
---|
1041 | *************************************************************************/
|
---|
1042 | public static void fftr1dinternaleven(ref double[] a,
|
---|
1043 | int n,
|
---|
1044 | ref double[] buf,
|
---|
1045 | ftbase.fasttransformplan plan)
|
---|
1046 | {
|
---|
1047 | double x = 0;
|
---|
1048 | double y = 0;
|
---|
1049 | int i = 0;
|
---|
1050 | int n2 = 0;
|
---|
1051 | int idx = 0;
|
---|
1052 | complex hn = 0;
|
---|
1053 | complex hmnc = 0;
|
---|
1054 | complex v = 0;
|
---|
1055 | int i_ = 0;
|
---|
1056 |
|
---|
1057 | alglib.ap.assert(n>0 && n%2==0, "FFTR1DEvenInplace: incorrect N!");
|
---|
1058 |
|
---|
1059 | //
|
---|
1060 | // Special cases:
|
---|
1061 | // * N=2
|
---|
1062 | //
|
---|
1063 | // After this block we assume that N is strictly greater than 2
|
---|
1064 | //
|
---|
1065 | if( n==2 )
|
---|
1066 | {
|
---|
1067 | x = a[0]+a[1];
|
---|
1068 | y = a[0]-a[1];
|
---|
1069 | a[0] = x;
|
---|
1070 | a[1] = y;
|
---|
1071 | return;
|
---|
1072 | }
|
---|
1073 |
|
---|
1074 | //
|
---|
1075 | // even-size real FFT, use reduction to the complex task
|
---|
1076 | //
|
---|
1077 | n2 = n/2;
|
---|
1078 | for(i_=0; i_<=n-1;i_++)
|
---|
1079 | {
|
---|
1080 | buf[i_] = a[i_];
|
---|
1081 | }
|
---|
1082 | ftbase.ftapplyplan(plan, buf, 0, 1);
|
---|
1083 | a[0] = buf[0]+buf[1];
|
---|
1084 | for(i=1; i<=n2-1; i++)
|
---|
1085 | {
|
---|
1086 | idx = 2*(i%n2);
|
---|
1087 | hn.x = buf[idx+0];
|
---|
1088 | hn.y = buf[idx+1];
|
---|
1089 | idx = 2*(n2-i);
|
---|
1090 | hmnc.x = buf[idx+0];
|
---|
1091 | hmnc.y = -buf[idx+1];
|
---|
1092 | v.x = -Math.Sin(-(2*Math.PI*i/n));
|
---|
1093 | v.y = Math.Cos(-(2*Math.PI*i/n));
|
---|
1094 | v = hn+hmnc-v*(hn-hmnc);
|
---|
1095 | a[2*i+0] = 0.5*v.x;
|
---|
1096 | a[2*i+1] = 0.5*v.y;
|
---|
1097 | }
|
---|
1098 | a[1] = buf[0]-buf[1];
|
---|
1099 | }
|
---|
1100 |
|
---|
1101 |
|
---|
1102 | /*************************************************************************
|
---|
1103 | Internal subroutine. Never call it directly!
|
---|
1104 |
|
---|
1105 |
|
---|
1106 | -- ALGLIB --
|
---|
1107 | Copyright 01.06.2009 by Bochkanov Sergey
|
---|
1108 | *************************************************************************/
|
---|
1109 | public static void fftr1dinvinternaleven(ref double[] a,
|
---|
1110 | int n,
|
---|
1111 | ref double[] buf,
|
---|
1112 | ftbase.fasttransformplan plan)
|
---|
1113 | {
|
---|
1114 | double x = 0;
|
---|
1115 | double y = 0;
|
---|
1116 | double t = 0;
|
---|
1117 | int i = 0;
|
---|
1118 | int n2 = 0;
|
---|
1119 |
|
---|
1120 | alglib.ap.assert(n>0 && n%2==0, "FFTR1DInvInternalEven: incorrect N!");
|
---|
1121 |
|
---|
1122 | //
|
---|
1123 | // Special cases:
|
---|
1124 | // * N=2
|
---|
1125 | //
|
---|
1126 | // After this block we assume that N is strictly greater than 2
|
---|
1127 | //
|
---|
1128 | if( n==2 )
|
---|
1129 | {
|
---|
1130 | x = 0.5*(a[0]+a[1]);
|
---|
1131 | y = 0.5*(a[0]-a[1]);
|
---|
1132 | a[0] = x;
|
---|
1133 | a[1] = y;
|
---|
1134 | return;
|
---|
1135 | }
|
---|
1136 |
|
---|
1137 | //
|
---|
1138 | // inverse real FFT is reduced to the inverse real FHT,
|
---|
1139 | // which is reduced to the forward real FHT,
|
---|
1140 | // which is reduced to the forward real FFT.
|
---|
1141 | //
|
---|
1142 | // Don't worry, it is really compact and efficient reduction :)
|
---|
1143 | //
|
---|
1144 | n2 = n/2;
|
---|
1145 | buf[0] = a[0];
|
---|
1146 | for(i=1; i<=n2-1; i++)
|
---|
1147 | {
|
---|
1148 | x = a[2*i+0];
|
---|
1149 | y = a[2*i+1];
|
---|
1150 | buf[i] = x-y;
|
---|
1151 | buf[n-i] = x+y;
|
---|
1152 | }
|
---|
1153 | buf[n2] = a[1];
|
---|
1154 | fftr1dinternaleven(ref buf, n, ref a, plan);
|
---|
1155 | a[0] = buf[0]/n;
|
---|
1156 | t = (double)1/(double)n;
|
---|
1157 | for(i=1; i<=n2-1; i++)
|
---|
1158 | {
|
---|
1159 | x = buf[2*i+0];
|
---|
1160 | y = buf[2*i+1];
|
---|
1161 | a[i] = t*(x-y);
|
---|
1162 | a[n-i] = t*(x+y);
|
---|
1163 | }
|
---|
1164 | a[n2] = buf[1]/n;
|
---|
1165 | }
|
---|
1166 |
|
---|
1167 |
|
---|
1168 | }
|
---|
1169 | public class fht
|
---|
1170 | {
|
---|
1171 | /*************************************************************************
|
---|
1172 | 1-dimensional Fast Hartley Transform.
|
---|
1173 |
|
---|
1174 | Algorithm has O(N*logN) complexity for any N (composite or prime).
|
---|
1175 |
|
---|
1176 | INPUT PARAMETERS
|
---|
1177 | A - array[0..N-1] - real function to be transformed
|
---|
1178 | N - problem size
|
---|
1179 |
|
---|
1180 | OUTPUT PARAMETERS
|
---|
1181 | A - FHT of a input array, array[0..N-1],
|
---|
1182 | A_out[k] = sum(A_in[j]*(cos(2*pi*j*k/N)+sin(2*pi*j*k/N)), j=0..N-1)
|
---|
1183 |
|
---|
1184 |
|
---|
1185 | -- ALGLIB --
|
---|
1186 | Copyright 04.06.2009 by Bochkanov Sergey
|
---|
1187 | *************************************************************************/
|
---|
1188 | public static void fhtr1d(ref double[] a,
|
---|
1189 | int n)
|
---|
1190 | {
|
---|
1191 | int i = 0;
|
---|
1192 | complex[] fa = new complex[0];
|
---|
1193 |
|
---|
1194 | alglib.ap.assert(n>0, "FHTR1D: incorrect N!");
|
---|
1195 |
|
---|
1196 | //
|
---|
1197 | // Special case: N=1, FHT is just identity transform.
|
---|
1198 | // After this block we assume that N is strictly greater than 1.
|
---|
1199 | //
|
---|
1200 | if( n==1 )
|
---|
1201 | {
|
---|
1202 | return;
|
---|
1203 | }
|
---|
1204 |
|
---|
1205 | //
|
---|
1206 | // Reduce FHt to real FFT
|
---|
1207 | //
|
---|
1208 | fft.fftr1d(a, n, ref fa);
|
---|
1209 | for(i=0; i<=n-1; i++)
|
---|
1210 | {
|
---|
1211 | a[i] = fa[i].x-fa[i].y;
|
---|
1212 | }
|
---|
1213 | }
|
---|
1214 |
|
---|
1215 |
|
---|
1216 | /*************************************************************************
|
---|
1217 | 1-dimensional inverse FHT.
|
---|
1218 |
|
---|
1219 | Algorithm has O(N*logN) complexity for any N (composite or prime).
|
---|
1220 |
|
---|
1221 | INPUT PARAMETERS
|
---|
1222 | A - array[0..N-1] - complex array to be transformed
|
---|
1223 | N - problem size
|
---|
1224 |
|
---|
1225 | OUTPUT PARAMETERS
|
---|
1226 | A - inverse FHT of a input array, array[0..N-1]
|
---|
1227 |
|
---|
1228 |
|
---|
1229 | -- ALGLIB --
|
---|
1230 | Copyright 29.05.2009 by Bochkanov Sergey
|
---|
1231 | *************************************************************************/
|
---|
1232 | public static void fhtr1dinv(ref double[] a,
|
---|
1233 | int n)
|
---|
1234 | {
|
---|
1235 | int i = 0;
|
---|
1236 |
|
---|
1237 | alglib.ap.assert(n>0, "FHTR1DInv: incorrect N!");
|
---|
1238 |
|
---|
1239 | //
|
---|
1240 | // Special case: N=1, iFHT is just identity transform.
|
---|
1241 | // After this block we assume that N is strictly greater than 1.
|
---|
1242 | //
|
---|
1243 | if( n==1 )
|
---|
1244 | {
|
---|
1245 | return;
|
---|
1246 | }
|
---|
1247 |
|
---|
1248 | //
|
---|
1249 | // Inverse FHT can be expressed in terms of the FHT as
|
---|
1250 | //
|
---|
1251 | // invfht(x) = fht(x)/N
|
---|
1252 | //
|
---|
1253 | fhtr1d(ref a, n);
|
---|
1254 | for(i=0; i<=n-1; i++)
|
---|
1255 | {
|
---|
1256 | a[i] = a[i]/n;
|
---|
1257 | }
|
---|
1258 | }
|
---|
1259 |
|
---|
1260 |
|
---|
1261 | }
|
---|
1262 | public class conv
|
---|
1263 | {
|
---|
1264 | /*************************************************************************
|
---|
1265 | 1-dimensional complex convolution.
|
---|
1266 |
|
---|
1267 | For given A/B returns conv(A,B) (non-circular). Subroutine can automatically
|
---|
1268 | choose between three implementations: straightforward O(M*N) formula for
|
---|
1269 | very small N (or M), overlap-add algorithm for cases where max(M,N) is
|
---|
1270 | significantly larger than min(M,N), but O(M*N) algorithm is too slow, and
|
---|
1271 | general FFT-based formula for cases where two previois algorithms are too
|
---|
1272 | slow.
|
---|
1273 |
|
---|
1274 | Algorithm has max(M,N)*log(max(M,N)) complexity for any M/N.
|
---|
1275 |
|
---|
1276 | INPUT PARAMETERS
|
---|
1277 | A - array[0..M-1] - complex function to be transformed
|
---|
1278 | M - problem size
|
---|
1279 | B - array[0..N-1] - complex function to be transformed
|
---|
1280 | N - problem size
|
---|
1281 |
|
---|
1282 | OUTPUT PARAMETERS
|
---|
1283 | R - convolution: A*B. array[0..N+M-2].
|
---|
1284 |
|
---|
1285 | NOTE:
|
---|
1286 | It is assumed that A is zero at T<0, B is zero too. If one or both
|
---|
1287 | functions have non-zero values at negative T's, you can still use this
|
---|
1288 | subroutine - just shift its result correspondingly.
|
---|
1289 |
|
---|
1290 | -- ALGLIB --
|
---|
1291 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
1292 | *************************************************************************/
|
---|
1293 | public static void convc1d(complex[] a,
|
---|
1294 | int m,
|
---|
1295 | complex[] b,
|
---|
1296 | int n,
|
---|
1297 | ref complex[] r)
|
---|
1298 | {
|
---|
1299 | r = new complex[0];
|
---|
1300 |
|
---|
1301 | alglib.ap.assert(n>0 && m>0, "ConvC1D: incorrect N or M!");
|
---|
1302 |
|
---|
1303 | //
|
---|
1304 | // normalize task: make M>=N,
|
---|
1305 | // so A will be longer that B.
|
---|
1306 | //
|
---|
1307 | if( m<n )
|
---|
1308 | {
|
---|
1309 | convc1d(b, n, a, m, ref r);
|
---|
1310 | return;
|
---|
1311 | }
|
---|
1312 | convc1dx(a, m, b, n, false, -1, 0, ref r);
|
---|
1313 | }
|
---|
1314 |
|
---|
1315 |
|
---|
1316 | /*************************************************************************
|
---|
1317 | 1-dimensional complex non-circular deconvolution (inverse of ConvC1D()).
|
---|
1318 |
|
---|
1319 | Algorithm has M*log(M)) complexity for any M (composite or prime).
|
---|
1320 |
|
---|
1321 | INPUT PARAMETERS
|
---|
1322 | A - array[0..M-1] - convolved signal, A = conv(R, B)
|
---|
1323 | M - convolved signal length
|
---|
1324 | B - array[0..N-1] - response
|
---|
1325 | N - response length, N<=M
|
---|
1326 |
|
---|
1327 | OUTPUT PARAMETERS
|
---|
1328 | R - deconvolved signal. array[0..M-N].
|
---|
1329 |
|
---|
1330 | NOTE:
|
---|
1331 | deconvolution is unstable process and may result in division by zero
|
---|
1332 | (if your response function is degenerate, i.e. has zero Fourier coefficient).
|
---|
1333 |
|
---|
1334 | NOTE:
|
---|
1335 | It is assumed that A is zero at T<0, B is zero too. If one or both
|
---|
1336 | functions have non-zero values at negative T's, you can still use this
|
---|
1337 | subroutine - just shift its result correspondingly.
|
---|
1338 |
|
---|
1339 | -- ALGLIB --
|
---|
1340 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
1341 | *************************************************************************/
|
---|
1342 | public static void convc1dinv(complex[] a,
|
---|
1343 | int m,
|
---|
1344 | complex[] b,
|
---|
1345 | int n,
|
---|
1346 | ref complex[] r)
|
---|
1347 | {
|
---|
1348 | int i = 0;
|
---|
1349 | int p = 0;
|
---|
1350 | double[] buf = new double[0];
|
---|
1351 | double[] buf2 = new double[0];
|
---|
1352 | ftbase.fasttransformplan plan = new ftbase.fasttransformplan();
|
---|
1353 | complex c1 = 0;
|
---|
1354 | complex c2 = 0;
|
---|
1355 | complex c3 = 0;
|
---|
1356 | double t = 0;
|
---|
1357 |
|
---|
1358 | r = new complex[0];
|
---|
1359 |
|
---|
1360 | alglib.ap.assert((n>0 && m>0) && n<=m, "ConvC1DInv: incorrect N or M!");
|
---|
1361 | p = ftbase.ftbasefindsmooth(m);
|
---|
1362 | ftbase.ftcomplexfftplan(p, 1, plan);
|
---|
1363 | buf = new double[2*p];
|
---|
1364 | for(i=0; i<=m-1; i++)
|
---|
1365 | {
|
---|
1366 | buf[2*i+0] = a[i].x;
|
---|
1367 | buf[2*i+1] = a[i].y;
|
---|
1368 | }
|
---|
1369 | for(i=m; i<=p-1; i++)
|
---|
1370 | {
|
---|
1371 | buf[2*i+0] = 0;
|
---|
1372 | buf[2*i+1] = 0;
|
---|
1373 | }
|
---|
1374 | buf2 = new double[2*p];
|
---|
1375 | for(i=0; i<=n-1; i++)
|
---|
1376 | {
|
---|
1377 | buf2[2*i+0] = b[i].x;
|
---|
1378 | buf2[2*i+1] = b[i].y;
|
---|
1379 | }
|
---|
1380 | for(i=n; i<=p-1; i++)
|
---|
1381 | {
|
---|
1382 | buf2[2*i+0] = 0;
|
---|
1383 | buf2[2*i+1] = 0;
|
---|
1384 | }
|
---|
1385 | ftbase.ftapplyplan(plan, buf, 0, 1);
|
---|
1386 | ftbase.ftapplyplan(plan, buf2, 0, 1);
|
---|
1387 | for(i=0; i<=p-1; i++)
|
---|
1388 | {
|
---|
1389 | c1.x = buf[2*i+0];
|
---|
1390 | c1.y = buf[2*i+1];
|
---|
1391 | c2.x = buf2[2*i+0];
|
---|
1392 | c2.y = buf2[2*i+1];
|
---|
1393 | c3 = c1/c2;
|
---|
1394 | buf[2*i+0] = c3.x;
|
---|
1395 | buf[2*i+1] = -c3.y;
|
---|
1396 | }
|
---|
1397 | ftbase.ftapplyplan(plan, buf, 0, 1);
|
---|
1398 | t = (double)1/(double)p;
|
---|
1399 | r = new complex[m-n+1];
|
---|
1400 | for(i=0; i<=m-n; i++)
|
---|
1401 | {
|
---|
1402 | r[i].x = t*buf[2*i+0];
|
---|
1403 | r[i].y = -(t*buf[2*i+1]);
|
---|
1404 | }
|
---|
1405 | }
|
---|
1406 |
|
---|
1407 |
|
---|
1408 | /*************************************************************************
|
---|
1409 | 1-dimensional circular complex convolution.
|
---|
1410 |
|
---|
1411 | For given S/R returns conv(S,R) (circular). Algorithm has linearithmic
|
---|
1412 | complexity for any M/N.
|
---|
1413 |
|
---|
1414 | IMPORTANT: normal convolution is commutative, i.e. it is symmetric -
|
---|
1415 | conv(A,B)=conv(B,A). Cyclic convolution IS NOT. One function - S - is a
|
---|
1416 | signal, periodic function, and another - R - is a response, non-periodic
|
---|
1417 | function with limited length.
|
---|
1418 |
|
---|
1419 | INPUT PARAMETERS
|
---|
1420 | S - array[0..M-1] - complex periodic signal
|
---|
1421 | M - problem size
|
---|
1422 | B - array[0..N-1] - complex non-periodic response
|
---|
1423 | N - problem size
|
---|
1424 |
|
---|
1425 | OUTPUT PARAMETERS
|
---|
1426 | R - convolution: A*B. array[0..M-1].
|
---|
1427 |
|
---|
1428 | NOTE:
|
---|
1429 | It is assumed that B is zero at T<0. If it has non-zero values at
|
---|
1430 | negative T's, you can still use this subroutine - just shift its result
|
---|
1431 | correspondingly.
|
---|
1432 |
|
---|
1433 | -- ALGLIB --
|
---|
1434 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
1435 | *************************************************************************/
|
---|
1436 | public static void convc1dcircular(complex[] s,
|
---|
1437 | int m,
|
---|
1438 | complex[] r,
|
---|
1439 | int n,
|
---|
1440 | ref complex[] c)
|
---|
1441 | {
|
---|
1442 | complex[] buf = new complex[0];
|
---|
1443 | int i1 = 0;
|
---|
1444 | int i2 = 0;
|
---|
1445 | int j2 = 0;
|
---|
1446 | int i_ = 0;
|
---|
1447 | int i1_ = 0;
|
---|
1448 |
|
---|
1449 | c = new complex[0];
|
---|
1450 |
|
---|
1451 | alglib.ap.assert(n>0 && m>0, "ConvC1DCircular: incorrect N or M!");
|
---|
1452 |
|
---|
1453 | //
|
---|
1454 | // normalize task: make M>=N,
|
---|
1455 | // so A will be longer (at least - not shorter) that B.
|
---|
1456 | //
|
---|
1457 | if( m<n )
|
---|
1458 | {
|
---|
1459 | buf = new complex[m];
|
---|
1460 | for(i1=0; i1<=m-1; i1++)
|
---|
1461 | {
|
---|
1462 | buf[i1] = 0;
|
---|
1463 | }
|
---|
1464 | i1 = 0;
|
---|
1465 | while( i1<n )
|
---|
1466 | {
|
---|
1467 | i2 = Math.Min(i1+m-1, n-1);
|
---|
1468 | j2 = i2-i1;
|
---|
1469 | i1_ = (i1) - (0);
|
---|
1470 | for(i_=0; i_<=j2;i_++)
|
---|
1471 | {
|
---|
1472 | buf[i_] = buf[i_] + r[i_+i1_];
|
---|
1473 | }
|
---|
1474 | i1 = i1+m;
|
---|
1475 | }
|
---|
1476 | convc1dcircular(s, m, buf, m, ref c);
|
---|
1477 | return;
|
---|
1478 | }
|
---|
1479 | convc1dx(s, m, r, n, true, -1, 0, ref c);
|
---|
1480 | }
|
---|
1481 |
|
---|
1482 |
|
---|
1483 | /*************************************************************************
|
---|
1484 | 1-dimensional circular complex deconvolution (inverse of ConvC1DCircular()).
|
---|
1485 |
|
---|
1486 | Algorithm has M*log(M)) complexity for any M (composite or prime).
|
---|
1487 |
|
---|
1488 | INPUT PARAMETERS
|
---|
1489 | A - array[0..M-1] - convolved periodic signal, A = conv(R, B)
|
---|
1490 | M - convolved signal length
|
---|
1491 | B - array[0..N-1] - non-periodic response
|
---|
1492 | N - response length
|
---|
1493 |
|
---|
1494 | OUTPUT PARAMETERS
|
---|
1495 | R - deconvolved signal. array[0..M-1].
|
---|
1496 |
|
---|
1497 | NOTE:
|
---|
1498 | deconvolution is unstable process and may result in division by zero
|
---|
1499 | (if your response function is degenerate, i.e. has zero Fourier coefficient).
|
---|
1500 |
|
---|
1501 | NOTE:
|
---|
1502 | It is assumed that B is zero at T<0. If it has non-zero values at
|
---|
1503 | negative T's, you can still use this subroutine - just shift its result
|
---|
1504 | correspondingly.
|
---|
1505 |
|
---|
1506 | -- ALGLIB --
|
---|
1507 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
1508 | *************************************************************************/
|
---|
1509 | public static void convc1dcircularinv(complex[] a,
|
---|
1510 | int m,
|
---|
1511 | complex[] b,
|
---|
1512 | int n,
|
---|
1513 | ref complex[] r)
|
---|
1514 | {
|
---|
1515 | int i = 0;
|
---|
1516 | int i1 = 0;
|
---|
1517 | int i2 = 0;
|
---|
1518 | int j2 = 0;
|
---|
1519 | double[] buf = new double[0];
|
---|
1520 | double[] buf2 = new double[0];
|
---|
1521 | complex[] cbuf = new complex[0];
|
---|
1522 | ftbase.fasttransformplan plan = new ftbase.fasttransformplan();
|
---|
1523 | complex c1 = 0;
|
---|
1524 | complex c2 = 0;
|
---|
1525 | complex c3 = 0;
|
---|
1526 | double t = 0;
|
---|
1527 | int i_ = 0;
|
---|
1528 | int i1_ = 0;
|
---|
1529 |
|
---|
1530 | r = new complex[0];
|
---|
1531 |
|
---|
1532 | alglib.ap.assert(n>0 && m>0, "ConvC1DCircularInv: incorrect N or M!");
|
---|
1533 |
|
---|
1534 | //
|
---|
1535 | // normalize task: make M>=N,
|
---|
1536 | // so A will be longer (at least - not shorter) that B.
|
---|
1537 | //
|
---|
1538 | if( m<n )
|
---|
1539 | {
|
---|
1540 | cbuf = new complex[m];
|
---|
1541 | for(i=0; i<=m-1; i++)
|
---|
1542 | {
|
---|
1543 | cbuf[i] = 0;
|
---|
1544 | }
|
---|
1545 | i1 = 0;
|
---|
1546 | while( i1<n )
|
---|
1547 | {
|
---|
1548 | i2 = Math.Min(i1+m-1, n-1);
|
---|
1549 | j2 = i2-i1;
|
---|
1550 | i1_ = (i1) - (0);
|
---|
1551 | for(i_=0; i_<=j2;i_++)
|
---|
1552 | {
|
---|
1553 | cbuf[i_] = cbuf[i_] + b[i_+i1_];
|
---|
1554 | }
|
---|
1555 | i1 = i1+m;
|
---|
1556 | }
|
---|
1557 | convc1dcircularinv(a, m, cbuf, m, ref r);
|
---|
1558 | return;
|
---|
1559 | }
|
---|
1560 |
|
---|
1561 | //
|
---|
1562 | // Task is normalized
|
---|
1563 | //
|
---|
1564 | ftbase.ftcomplexfftplan(m, 1, plan);
|
---|
1565 | buf = new double[2*m];
|
---|
1566 | for(i=0; i<=m-1; i++)
|
---|
1567 | {
|
---|
1568 | buf[2*i+0] = a[i].x;
|
---|
1569 | buf[2*i+1] = a[i].y;
|
---|
1570 | }
|
---|
1571 | buf2 = new double[2*m];
|
---|
1572 | for(i=0; i<=n-1; i++)
|
---|
1573 | {
|
---|
1574 | buf2[2*i+0] = b[i].x;
|
---|
1575 | buf2[2*i+1] = b[i].y;
|
---|
1576 | }
|
---|
1577 | for(i=n; i<=m-1; i++)
|
---|
1578 | {
|
---|
1579 | buf2[2*i+0] = 0;
|
---|
1580 | buf2[2*i+1] = 0;
|
---|
1581 | }
|
---|
1582 | ftbase.ftapplyplan(plan, buf, 0, 1);
|
---|
1583 | ftbase.ftapplyplan(plan, buf2, 0, 1);
|
---|
1584 | for(i=0; i<=m-1; i++)
|
---|
1585 | {
|
---|
1586 | c1.x = buf[2*i+0];
|
---|
1587 | c1.y = buf[2*i+1];
|
---|
1588 | c2.x = buf2[2*i+0];
|
---|
1589 | c2.y = buf2[2*i+1];
|
---|
1590 | c3 = c1/c2;
|
---|
1591 | buf[2*i+0] = c3.x;
|
---|
1592 | buf[2*i+1] = -c3.y;
|
---|
1593 | }
|
---|
1594 | ftbase.ftapplyplan(plan, buf, 0, 1);
|
---|
1595 | t = (double)1/(double)m;
|
---|
1596 | r = new complex[m];
|
---|
1597 | for(i=0; i<=m-1; i++)
|
---|
1598 | {
|
---|
1599 | r[i].x = t*buf[2*i+0];
|
---|
1600 | r[i].y = -(t*buf[2*i+1]);
|
---|
1601 | }
|
---|
1602 | }
|
---|
1603 |
|
---|
1604 |
|
---|
1605 | /*************************************************************************
|
---|
1606 | 1-dimensional real convolution.
|
---|
1607 |
|
---|
1608 | Analogous to ConvC1D(), see ConvC1D() comments for more details.
|
---|
1609 |
|
---|
1610 | INPUT PARAMETERS
|
---|
1611 | A - array[0..M-1] - real function to be transformed
|
---|
1612 | M - problem size
|
---|
1613 | B - array[0..N-1] - real function to be transformed
|
---|
1614 | N - problem size
|
---|
1615 |
|
---|
1616 | OUTPUT PARAMETERS
|
---|
1617 | R - convolution: A*B. array[0..N+M-2].
|
---|
1618 |
|
---|
1619 | NOTE:
|
---|
1620 | It is assumed that A is zero at T<0, B is zero too. If one or both
|
---|
1621 | functions have non-zero values at negative T's, you can still use this
|
---|
1622 | subroutine - just shift its result correspondingly.
|
---|
1623 |
|
---|
1624 | -- ALGLIB --
|
---|
1625 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
1626 | *************************************************************************/
|
---|
1627 | public static void convr1d(double[] a,
|
---|
1628 | int m,
|
---|
1629 | double[] b,
|
---|
1630 | int n,
|
---|
1631 | ref double[] r)
|
---|
1632 | {
|
---|
1633 | r = new double[0];
|
---|
1634 |
|
---|
1635 | alglib.ap.assert(n>0 && m>0, "ConvR1D: incorrect N or M!");
|
---|
1636 |
|
---|
1637 | //
|
---|
1638 | // normalize task: make M>=N,
|
---|
1639 | // so A will be longer that B.
|
---|
1640 | //
|
---|
1641 | if( m<n )
|
---|
1642 | {
|
---|
1643 | convr1d(b, n, a, m, ref r);
|
---|
1644 | return;
|
---|
1645 | }
|
---|
1646 | convr1dx(a, m, b, n, false, -1, 0, ref r);
|
---|
1647 | }
|
---|
1648 |
|
---|
1649 |
|
---|
1650 | /*************************************************************************
|
---|
1651 | 1-dimensional real deconvolution (inverse of ConvC1D()).
|
---|
1652 |
|
---|
1653 | Algorithm has M*log(M)) complexity for any M (composite or prime).
|
---|
1654 |
|
---|
1655 | INPUT PARAMETERS
|
---|
1656 | A - array[0..M-1] - convolved signal, A = conv(R, B)
|
---|
1657 | M - convolved signal length
|
---|
1658 | B - array[0..N-1] - response
|
---|
1659 | N - response length, N<=M
|
---|
1660 |
|
---|
1661 | OUTPUT PARAMETERS
|
---|
1662 | R - deconvolved signal. array[0..M-N].
|
---|
1663 |
|
---|
1664 | NOTE:
|
---|
1665 | deconvolution is unstable process and may result in division by zero
|
---|
1666 | (if your response function is degenerate, i.e. has zero Fourier coefficient).
|
---|
1667 |
|
---|
1668 | NOTE:
|
---|
1669 | It is assumed that A is zero at T<0, B is zero too. If one or both
|
---|
1670 | functions have non-zero values at negative T's, you can still use this
|
---|
1671 | subroutine - just shift its result correspondingly.
|
---|
1672 |
|
---|
1673 | -- ALGLIB --
|
---|
1674 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
1675 | *************************************************************************/
|
---|
1676 | public static void convr1dinv(double[] a,
|
---|
1677 | int m,
|
---|
1678 | double[] b,
|
---|
1679 | int n,
|
---|
1680 | ref double[] r)
|
---|
1681 | {
|
---|
1682 | int i = 0;
|
---|
1683 | int p = 0;
|
---|
1684 | double[] buf = new double[0];
|
---|
1685 | double[] buf2 = new double[0];
|
---|
1686 | double[] buf3 = new double[0];
|
---|
1687 | ftbase.fasttransformplan plan = new ftbase.fasttransformplan();
|
---|
1688 | complex c1 = 0;
|
---|
1689 | complex c2 = 0;
|
---|
1690 | complex c3 = 0;
|
---|
1691 | int i_ = 0;
|
---|
1692 |
|
---|
1693 | r = new double[0];
|
---|
1694 |
|
---|
1695 | alglib.ap.assert((n>0 && m>0) && n<=m, "ConvR1DInv: incorrect N or M!");
|
---|
1696 | p = ftbase.ftbasefindsmootheven(m);
|
---|
1697 | buf = new double[p];
|
---|
1698 | for(i_=0; i_<=m-1;i_++)
|
---|
1699 | {
|
---|
1700 | buf[i_] = a[i_];
|
---|
1701 | }
|
---|
1702 | for(i=m; i<=p-1; i++)
|
---|
1703 | {
|
---|
1704 | buf[i] = 0;
|
---|
1705 | }
|
---|
1706 | buf2 = new double[p];
|
---|
1707 | for(i_=0; i_<=n-1;i_++)
|
---|
1708 | {
|
---|
1709 | buf2[i_] = b[i_];
|
---|
1710 | }
|
---|
1711 | for(i=n; i<=p-1; i++)
|
---|
1712 | {
|
---|
1713 | buf2[i] = 0;
|
---|
1714 | }
|
---|
1715 | buf3 = new double[p];
|
---|
1716 | ftbase.ftcomplexfftplan(p/2, 1, plan);
|
---|
1717 | fft.fftr1dinternaleven(ref buf, p, ref buf3, plan);
|
---|
1718 | fft.fftr1dinternaleven(ref buf2, p, ref buf3, plan);
|
---|
1719 | buf[0] = buf[0]/buf2[0];
|
---|
1720 | buf[1] = buf[1]/buf2[1];
|
---|
1721 | for(i=1; i<=p/2-1; i++)
|
---|
1722 | {
|
---|
1723 | c1.x = buf[2*i+0];
|
---|
1724 | c1.y = buf[2*i+1];
|
---|
1725 | c2.x = buf2[2*i+0];
|
---|
1726 | c2.y = buf2[2*i+1];
|
---|
1727 | c3 = c1/c2;
|
---|
1728 | buf[2*i+0] = c3.x;
|
---|
1729 | buf[2*i+1] = c3.y;
|
---|
1730 | }
|
---|
1731 | fft.fftr1dinvinternaleven(ref buf, p, ref buf3, plan);
|
---|
1732 | r = new double[m-n+1];
|
---|
1733 | for(i_=0; i_<=m-n;i_++)
|
---|
1734 | {
|
---|
1735 | r[i_] = buf[i_];
|
---|
1736 | }
|
---|
1737 | }
|
---|
1738 |
|
---|
1739 |
|
---|
1740 | /*************************************************************************
|
---|
1741 | 1-dimensional circular real convolution.
|
---|
1742 |
|
---|
1743 | Analogous to ConvC1DCircular(), see ConvC1DCircular() comments for more details.
|
---|
1744 |
|
---|
1745 | INPUT PARAMETERS
|
---|
1746 | S - array[0..M-1] - real signal
|
---|
1747 | M - problem size
|
---|
1748 | B - array[0..N-1] - real response
|
---|
1749 | N - problem size
|
---|
1750 |
|
---|
1751 | OUTPUT PARAMETERS
|
---|
1752 | R - convolution: A*B. array[0..M-1].
|
---|
1753 |
|
---|
1754 | NOTE:
|
---|
1755 | It is assumed that B is zero at T<0. If it has non-zero values at
|
---|
1756 | negative T's, you can still use this subroutine - just shift its result
|
---|
1757 | correspondingly.
|
---|
1758 |
|
---|
1759 | -- ALGLIB --
|
---|
1760 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
1761 | *************************************************************************/
|
---|
1762 | public static void convr1dcircular(double[] s,
|
---|
1763 | int m,
|
---|
1764 | double[] r,
|
---|
1765 | int n,
|
---|
1766 | ref double[] c)
|
---|
1767 | {
|
---|
1768 | double[] buf = new double[0];
|
---|
1769 | int i1 = 0;
|
---|
1770 | int i2 = 0;
|
---|
1771 | int j2 = 0;
|
---|
1772 | int i_ = 0;
|
---|
1773 | int i1_ = 0;
|
---|
1774 |
|
---|
1775 | c = new double[0];
|
---|
1776 |
|
---|
1777 | alglib.ap.assert(n>0 && m>0, "ConvC1DCircular: incorrect N or M!");
|
---|
1778 |
|
---|
1779 | //
|
---|
1780 | // normalize task: make M>=N,
|
---|
1781 | // so A will be longer (at least - not shorter) that B.
|
---|
1782 | //
|
---|
1783 | if( m<n )
|
---|
1784 | {
|
---|
1785 | buf = new double[m];
|
---|
1786 | for(i1=0; i1<=m-1; i1++)
|
---|
1787 | {
|
---|
1788 | buf[i1] = 0;
|
---|
1789 | }
|
---|
1790 | i1 = 0;
|
---|
1791 | while( i1<n )
|
---|
1792 | {
|
---|
1793 | i2 = Math.Min(i1+m-1, n-1);
|
---|
1794 | j2 = i2-i1;
|
---|
1795 | i1_ = (i1) - (0);
|
---|
1796 | for(i_=0; i_<=j2;i_++)
|
---|
1797 | {
|
---|
1798 | buf[i_] = buf[i_] + r[i_+i1_];
|
---|
1799 | }
|
---|
1800 | i1 = i1+m;
|
---|
1801 | }
|
---|
1802 | convr1dcircular(s, m, buf, m, ref c);
|
---|
1803 | return;
|
---|
1804 | }
|
---|
1805 |
|
---|
1806 | //
|
---|
1807 | // reduce to usual convolution
|
---|
1808 | //
|
---|
1809 | convr1dx(s, m, r, n, true, -1, 0, ref c);
|
---|
1810 | }
|
---|
1811 |
|
---|
1812 |
|
---|
1813 | /*************************************************************************
|
---|
1814 | 1-dimensional complex deconvolution (inverse of ConvC1D()).
|
---|
1815 |
|
---|
1816 | Algorithm has M*log(M)) complexity for any M (composite or prime).
|
---|
1817 |
|
---|
1818 | INPUT PARAMETERS
|
---|
1819 | A - array[0..M-1] - convolved signal, A = conv(R, B)
|
---|
1820 | M - convolved signal length
|
---|
1821 | B - array[0..N-1] - response
|
---|
1822 | N - response length
|
---|
1823 |
|
---|
1824 | OUTPUT PARAMETERS
|
---|
1825 | R - deconvolved signal. array[0..M-N].
|
---|
1826 |
|
---|
1827 | NOTE:
|
---|
1828 | deconvolution is unstable process and may result in division by zero
|
---|
1829 | (if your response function is degenerate, i.e. has zero Fourier coefficient).
|
---|
1830 |
|
---|
1831 | NOTE:
|
---|
1832 | It is assumed that B is zero at T<0. If it has non-zero values at
|
---|
1833 | negative T's, you can still use this subroutine - just shift its result
|
---|
1834 | correspondingly.
|
---|
1835 |
|
---|
1836 | -- ALGLIB --
|
---|
1837 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
1838 | *************************************************************************/
|
---|
1839 | public static void convr1dcircularinv(double[] a,
|
---|
1840 | int m,
|
---|
1841 | double[] b,
|
---|
1842 | int n,
|
---|
1843 | ref double[] r)
|
---|
1844 | {
|
---|
1845 | int i = 0;
|
---|
1846 | int i1 = 0;
|
---|
1847 | int i2 = 0;
|
---|
1848 | int j2 = 0;
|
---|
1849 | double[] buf = new double[0];
|
---|
1850 | double[] buf2 = new double[0];
|
---|
1851 | double[] buf3 = new double[0];
|
---|
1852 | complex[] cbuf = new complex[0];
|
---|
1853 | complex[] cbuf2 = new complex[0];
|
---|
1854 | ftbase.fasttransformplan plan = new ftbase.fasttransformplan();
|
---|
1855 | complex c1 = 0;
|
---|
1856 | complex c2 = 0;
|
---|
1857 | complex c3 = 0;
|
---|
1858 | int i_ = 0;
|
---|
1859 | int i1_ = 0;
|
---|
1860 |
|
---|
1861 | r = new double[0];
|
---|
1862 |
|
---|
1863 | alglib.ap.assert(n>0 && m>0, "ConvR1DCircularInv: incorrect N or M!");
|
---|
1864 |
|
---|
1865 | //
|
---|
1866 | // normalize task: make M>=N,
|
---|
1867 | // so A will be longer (at least - not shorter) that B.
|
---|
1868 | //
|
---|
1869 | if( m<n )
|
---|
1870 | {
|
---|
1871 | buf = new double[m];
|
---|
1872 | for(i=0; i<=m-1; i++)
|
---|
1873 | {
|
---|
1874 | buf[i] = 0;
|
---|
1875 | }
|
---|
1876 | i1 = 0;
|
---|
1877 | while( i1<n )
|
---|
1878 | {
|
---|
1879 | i2 = Math.Min(i1+m-1, n-1);
|
---|
1880 | j2 = i2-i1;
|
---|
1881 | i1_ = (i1) - (0);
|
---|
1882 | for(i_=0; i_<=j2;i_++)
|
---|
1883 | {
|
---|
1884 | buf[i_] = buf[i_] + b[i_+i1_];
|
---|
1885 | }
|
---|
1886 | i1 = i1+m;
|
---|
1887 | }
|
---|
1888 | convr1dcircularinv(a, m, buf, m, ref r);
|
---|
1889 | return;
|
---|
1890 | }
|
---|
1891 |
|
---|
1892 | //
|
---|
1893 | // Task is normalized
|
---|
1894 | //
|
---|
1895 | if( m%2==0 )
|
---|
1896 | {
|
---|
1897 |
|
---|
1898 | //
|
---|
1899 | // size is even, use fast even-size FFT
|
---|
1900 | //
|
---|
1901 | buf = new double[m];
|
---|
1902 | for(i_=0; i_<=m-1;i_++)
|
---|
1903 | {
|
---|
1904 | buf[i_] = a[i_];
|
---|
1905 | }
|
---|
1906 | buf2 = new double[m];
|
---|
1907 | for(i_=0; i_<=n-1;i_++)
|
---|
1908 | {
|
---|
1909 | buf2[i_] = b[i_];
|
---|
1910 | }
|
---|
1911 | for(i=n; i<=m-1; i++)
|
---|
1912 | {
|
---|
1913 | buf2[i] = 0;
|
---|
1914 | }
|
---|
1915 | buf3 = new double[m];
|
---|
1916 | ftbase.ftcomplexfftplan(m/2, 1, plan);
|
---|
1917 | fft.fftr1dinternaleven(ref buf, m, ref buf3, plan);
|
---|
1918 | fft.fftr1dinternaleven(ref buf2, m, ref buf3, plan);
|
---|
1919 | buf[0] = buf[0]/buf2[0];
|
---|
1920 | buf[1] = buf[1]/buf2[1];
|
---|
1921 | for(i=1; i<=m/2-1; i++)
|
---|
1922 | {
|
---|
1923 | c1.x = buf[2*i+0];
|
---|
1924 | c1.y = buf[2*i+1];
|
---|
1925 | c2.x = buf2[2*i+0];
|
---|
1926 | c2.y = buf2[2*i+1];
|
---|
1927 | c3 = c1/c2;
|
---|
1928 | buf[2*i+0] = c3.x;
|
---|
1929 | buf[2*i+1] = c3.y;
|
---|
1930 | }
|
---|
1931 | fft.fftr1dinvinternaleven(ref buf, m, ref buf3, plan);
|
---|
1932 | r = new double[m];
|
---|
1933 | for(i_=0; i_<=m-1;i_++)
|
---|
1934 | {
|
---|
1935 | r[i_] = buf[i_];
|
---|
1936 | }
|
---|
1937 | }
|
---|
1938 | else
|
---|
1939 | {
|
---|
1940 |
|
---|
1941 | //
|
---|
1942 | // odd-size, use general real FFT
|
---|
1943 | //
|
---|
1944 | fft.fftr1d(a, m, ref cbuf);
|
---|
1945 | buf2 = new double[m];
|
---|
1946 | for(i_=0; i_<=n-1;i_++)
|
---|
1947 | {
|
---|
1948 | buf2[i_] = b[i_];
|
---|
1949 | }
|
---|
1950 | for(i=n; i<=m-1; i++)
|
---|
1951 | {
|
---|
1952 | buf2[i] = 0;
|
---|
1953 | }
|
---|
1954 | fft.fftr1d(buf2, m, ref cbuf2);
|
---|
1955 | for(i=0; i<=(int)Math.Floor((double)m/(double)2); i++)
|
---|
1956 | {
|
---|
1957 | cbuf[i] = cbuf[i]/cbuf2[i];
|
---|
1958 | }
|
---|
1959 | fft.fftr1dinv(cbuf, m, ref r);
|
---|
1960 | }
|
---|
1961 | }
|
---|
1962 |
|
---|
1963 |
|
---|
1964 | /*************************************************************************
|
---|
1965 | 1-dimensional complex convolution.
|
---|
1966 |
|
---|
1967 | Extended subroutine which allows to choose convolution algorithm.
|
---|
1968 | Intended for internal use, ALGLIB users should call ConvC1D()/ConvC1DCircular().
|
---|
1969 |
|
---|
1970 | INPUT PARAMETERS
|
---|
1971 | A - array[0..M-1] - complex function to be transformed
|
---|
1972 | M - problem size
|
---|
1973 | B - array[0..N-1] - complex function to be transformed
|
---|
1974 | N - problem size, N<=M
|
---|
1975 | Alg - algorithm type:
|
---|
1976 | *-2 auto-select Q for overlap-add
|
---|
1977 | *-1 auto-select algorithm and parameters
|
---|
1978 | * 0 straightforward formula for small N's
|
---|
1979 | * 1 general FFT-based code
|
---|
1980 | * 2 overlap-add with length Q
|
---|
1981 | Q - length for overlap-add
|
---|
1982 |
|
---|
1983 | OUTPUT PARAMETERS
|
---|
1984 | R - convolution: A*B. array[0..N+M-1].
|
---|
1985 |
|
---|
1986 | -- ALGLIB --
|
---|
1987 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
1988 | *************************************************************************/
|
---|
1989 | public static void convc1dx(complex[] a,
|
---|
1990 | int m,
|
---|
1991 | complex[] b,
|
---|
1992 | int n,
|
---|
1993 | bool circular,
|
---|
1994 | int alg,
|
---|
1995 | int q,
|
---|
1996 | ref complex[] r)
|
---|
1997 | {
|
---|
1998 | int i = 0;
|
---|
1999 | int j = 0;
|
---|
2000 | int p = 0;
|
---|
2001 | int ptotal = 0;
|
---|
2002 | int i1 = 0;
|
---|
2003 | int i2 = 0;
|
---|
2004 | int j1 = 0;
|
---|
2005 | int j2 = 0;
|
---|
2006 | complex[] bbuf = new complex[0];
|
---|
2007 | complex v = 0;
|
---|
2008 | double ax = 0;
|
---|
2009 | double ay = 0;
|
---|
2010 | double bx = 0;
|
---|
2011 | double by = 0;
|
---|
2012 | double t = 0;
|
---|
2013 | double tx = 0;
|
---|
2014 | double ty = 0;
|
---|
2015 | double flopcand = 0;
|
---|
2016 | double flopbest = 0;
|
---|
2017 | int algbest = 0;
|
---|
2018 | ftbase.fasttransformplan plan = new ftbase.fasttransformplan();
|
---|
2019 | double[] buf = new double[0];
|
---|
2020 | double[] buf2 = new double[0];
|
---|
2021 | int i_ = 0;
|
---|
2022 | int i1_ = 0;
|
---|
2023 |
|
---|
2024 | r = new complex[0];
|
---|
2025 |
|
---|
2026 | alglib.ap.assert(n>0 && m>0, "ConvC1DX: incorrect N or M!");
|
---|
2027 | alglib.ap.assert(n<=m, "ConvC1DX: N<M assumption is false!");
|
---|
2028 |
|
---|
2029 | //
|
---|
2030 | // Auto-select
|
---|
2031 | //
|
---|
2032 | if( alg==-1 || alg==-2 )
|
---|
2033 | {
|
---|
2034 |
|
---|
2035 | //
|
---|
2036 | // Initial candidate: straightforward implementation.
|
---|
2037 | //
|
---|
2038 | // If we want to use auto-fitted overlap-add,
|
---|
2039 | // flop count is initialized by large real number - to force
|
---|
2040 | // another algorithm selection
|
---|
2041 | //
|
---|
2042 | algbest = 0;
|
---|
2043 | if( alg==-1 )
|
---|
2044 | {
|
---|
2045 | flopbest = 2*m*n;
|
---|
2046 | }
|
---|
2047 | else
|
---|
2048 | {
|
---|
2049 | flopbest = math.maxrealnumber;
|
---|
2050 | }
|
---|
2051 |
|
---|
2052 | //
|
---|
2053 | // Another candidate - generic FFT code
|
---|
2054 | //
|
---|
2055 | if( alg==-1 )
|
---|
2056 | {
|
---|
2057 | if( circular && ftbase.ftbaseissmooth(m) )
|
---|
2058 | {
|
---|
2059 |
|
---|
2060 | //
|
---|
2061 | // special code for circular convolution of a sequence with a smooth length
|
---|
2062 | //
|
---|
2063 | flopcand = 3*ftbase.ftbasegetflopestimate(m)+6*m;
|
---|
2064 | if( (double)(flopcand)<(double)(flopbest) )
|
---|
2065 | {
|
---|
2066 | algbest = 1;
|
---|
2067 | flopbest = flopcand;
|
---|
2068 | }
|
---|
2069 | }
|
---|
2070 | else
|
---|
2071 | {
|
---|
2072 |
|
---|
2073 | //
|
---|
2074 | // general cyclic/non-cyclic convolution
|
---|
2075 | //
|
---|
2076 | p = ftbase.ftbasefindsmooth(m+n-1);
|
---|
2077 | flopcand = 3*ftbase.ftbasegetflopestimate(p)+6*p;
|
---|
2078 | if( (double)(flopcand)<(double)(flopbest) )
|
---|
2079 | {
|
---|
2080 | algbest = 1;
|
---|
2081 | flopbest = flopcand;
|
---|
2082 | }
|
---|
2083 | }
|
---|
2084 | }
|
---|
2085 |
|
---|
2086 | //
|
---|
2087 | // Another candidate - overlap-add
|
---|
2088 | //
|
---|
2089 | q = 1;
|
---|
2090 | ptotal = 1;
|
---|
2091 | while( ptotal<n )
|
---|
2092 | {
|
---|
2093 | ptotal = ptotal*2;
|
---|
2094 | }
|
---|
2095 | while( ptotal<=m+n-1 )
|
---|
2096 | {
|
---|
2097 | p = ptotal-n+1;
|
---|
2098 | flopcand = (int)Math.Ceiling((double)m/(double)p)*(2*ftbase.ftbasegetflopestimate(ptotal)+8*ptotal);
|
---|
2099 | if( (double)(flopcand)<(double)(flopbest) )
|
---|
2100 | {
|
---|
2101 | flopbest = flopcand;
|
---|
2102 | algbest = 2;
|
---|
2103 | q = p;
|
---|
2104 | }
|
---|
2105 | ptotal = ptotal*2;
|
---|
2106 | }
|
---|
2107 | alg = algbest;
|
---|
2108 | convc1dx(a, m, b, n, circular, alg, q, ref r);
|
---|
2109 | return;
|
---|
2110 | }
|
---|
2111 |
|
---|
2112 | //
|
---|
2113 | // straightforward formula for
|
---|
2114 | // circular and non-circular convolutions.
|
---|
2115 | //
|
---|
2116 | // Very simple code, no further comments needed.
|
---|
2117 | //
|
---|
2118 | if( alg==0 )
|
---|
2119 | {
|
---|
2120 |
|
---|
2121 | //
|
---|
2122 | // Special case: N=1
|
---|
2123 | //
|
---|
2124 | if( n==1 )
|
---|
2125 | {
|
---|
2126 | r = new complex[m];
|
---|
2127 | v = b[0];
|
---|
2128 | for(i_=0; i_<=m-1;i_++)
|
---|
2129 | {
|
---|
2130 | r[i_] = v*a[i_];
|
---|
2131 | }
|
---|
2132 | return;
|
---|
2133 | }
|
---|
2134 |
|
---|
2135 | //
|
---|
2136 | // use straightforward formula
|
---|
2137 | //
|
---|
2138 | if( circular )
|
---|
2139 | {
|
---|
2140 |
|
---|
2141 | //
|
---|
2142 | // circular convolution
|
---|
2143 | //
|
---|
2144 | r = new complex[m];
|
---|
2145 | v = b[0];
|
---|
2146 | for(i_=0; i_<=m-1;i_++)
|
---|
2147 | {
|
---|
2148 | r[i_] = v*a[i_];
|
---|
2149 | }
|
---|
2150 | for(i=1; i<=n-1; i++)
|
---|
2151 | {
|
---|
2152 | v = b[i];
|
---|
2153 | i1 = 0;
|
---|
2154 | i2 = i-1;
|
---|
2155 | j1 = m-i;
|
---|
2156 | j2 = m-1;
|
---|
2157 | i1_ = (j1) - (i1);
|
---|
2158 | for(i_=i1; i_<=i2;i_++)
|
---|
2159 | {
|
---|
2160 | r[i_] = r[i_] + v*a[i_+i1_];
|
---|
2161 | }
|
---|
2162 | i1 = i;
|
---|
2163 | i2 = m-1;
|
---|
2164 | j1 = 0;
|
---|
2165 | j2 = m-i-1;
|
---|
2166 | i1_ = (j1) - (i1);
|
---|
2167 | for(i_=i1; i_<=i2;i_++)
|
---|
2168 | {
|
---|
2169 | r[i_] = r[i_] + v*a[i_+i1_];
|
---|
2170 | }
|
---|
2171 | }
|
---|
2172 | }
|
---|
2173 | else
|
---|
2174 | {
|
---|
2175 |
|
---|
2176 | //
|
---|
2177 | // non-circular convolution
|
---|
2178 | //
|
---|
2179 | r = new complex[m+n-1];
|
---|
2180 | for(i=0; i<=m+n-2; i++)
|
---|
2181 | {
|
---|
2182 | r[i] = 0;
|
---|
2183 | }
|
---|
2184 | for(i=0; i<=n-1; i++)
|
---|
2185 | {
|
---|
2186 | v = b[i];
|
---|
2187 | i1_ = (0) - (i);
|
---|
2188 | for(i_=i; i_<=i+m-1;i_++)
|
---|
2189 | {
|
---|
2190 | r[i_] = r[i_] + v*a[i_+i1_];
|
---|
2191 | }
|
---|
2192 | }
|
---|
2193 | }
|
---|
2194 | return;
|
---|
2195 | }
|
---|
2196 |
|
---|
2197 | //
|
---|
2198 | // general FFT-based code for
|
---|
2199 | // circular and non-circular convolutions.
|
---|
2200 | //
|
---|
2201 | // First, if convolution is circular, we test whether M is smooth or not.
|
---|
2202 | // If it is smooth, we just use M-length FFT to calculate convolution.
|
---|
2203 | // If it is not, we calculate non-circular convolution and wrap it arount.
|
---|
2204 | //
|
---|
2205 | // IF convolution is non-circular, we use zero-padding + FFT.
|
---|
2206 | //
|
---|
2207 | if( alg==1 )
|
---|
2208 | {
|
---|
2209 | if( circular && ftbase.ftbaseissmooth(m) )
|
---|
2210 | {
|
---|
2211 |
|
---|
2212 | //
|
---|
2213 | // special code for circular convolution with smooth M
|
---|
2214 | //
|
---|
2215 | ftbase.ftcomplexfftplan(m, 1, plan);
|
---|
2216 | buf = new double[2*m];
|
---|
2217 | for(i=0; i<=m-1; i++)
|
---|
2218 | {
|
---|
2219 | buf[2*i+0] = a[i].x;
|
---|
2220 | buf[2*i+1] = a[i].y;
|
---|
2221 | }
|
---|
2222 | buf2 = new double[2*m];
|
---|
2223 | for(i=0; i<=n-1; i++)
|
---|
2224 | {
|
---|
2225 | buf2[2*i+0] = b[i].x;
|
---|
2226 | buf2[2*i+1] = b[i].y;
|
---|
2227 | }
|
---|
2228 | for(i=n; i<=m-1; i++)
|
---|
2229 | {
|
---|
2230 | buf2[2*i+0] = 0;
|
---|
2231 | buf2[2*i+1] = 0;
|
---|
2232 | }
|
---|
2233 | ftbase.ftapplyplan(plan, buf, 0, 1);
|
---|
2234 | ftbase.ftapplyplan(plan, buf2, 0, 1);
|
---|
2235 | for(i=0; i<=m-1; i++)
|
---|
2236 | {
|
---|
2237 | ax = buf[2*i+0];
|
---|
2238 | ay = buf[2*i+1];
|
---|
2239 | bx = buf2[2*i+0];
|
---|
2240 | by = buf2[2*i+1];
|
---|
2241 | tx = ax*bx-ay*by;
|
---|
2242 | ty = ax*by+ay*bx;
|
---|
2243 | buf[2*i+0] = tx;
|
---|
2244 | buf[2*i+1] = -ty;
|
---|
2245 | }
|
---|
2246 | ftbase.ftapplyplan(plan, buf, 0, 1);
|
---|
2247 | t = (double)1/(double)m;
|
---|
2248 | r = new complex[m];
|
---|
2249 | for(i=0; i<=m-1; i++)
|
---|
2250 | {
|
---|
2251 | r[i].x = t*buf[2*i+0];
|
---|
2252 | r[i].y = -(t*buf[2*i+1]);
|
---|
2253 | }
|
---|
2254 | }
|
---|
2255 | else
|
---|
2256 | {
|
---|
2257 |
|
---|
2258 | //
|
---|
2259 | // M is non-smooth, general code (circular/non-circular):
|
---|
2260 | // * first part is the same for circular and non-circular
|
---|
2261 | // convolutions. zero padding, FFTs, inverse FFTs
|
---|
2262 | // * second part differs:
|
---|
2263 | // * for non-circular convolution we just copy array
|
---|
2264 | // * for circular convolution we add array tail to its head
|
---|
2265 | //
|
---|
2266 | p = ftbase.ftbasefindsmooth(m+n-1);
|
---|
2267 | ftbase.ftcomplexfftplan(p, 1, plan);
|
---|
2268 | buf = new double[2*p];
|
---|
2269 | for(i=0; i<=m-1; i++)
|
---|
2270 | {
|
---|
2271 | buf[2*i+0] = a[i].x;
|
---|
2272 | buf[2*i+1] = a[i].y;
|
---|
2273 | }
|
---|
2274 | for(i=m; i<=p-1; i++)
|
---|
2275 | {
|
---|
2276 | buf[2*i+0] = 0;
|
---|
2277 | buf[2*i+1] = 0;
|
---|
2278 | }
|
---|
2279 | buf2 = new double[2*p];
|
---|
2280 | for(i=0; i<=n-1; i++)
|
---|
2281 | {
|
---|
2282 | buf2[2*i+0] = b[i].x;
|
---|
2283 | buf2[2*i+1] = b[i].y;
|
---|
2284 | }
|
---|
2285 | for(i=n; i<=p-1; i++)
|
---|
2286 | {
|
---|
2287 | buf2[2*i+0] = 0;
|
---|
2288 | buf2[2*i+1] = 0;
|
---|
2289 | }
|
---|
2290 | ftbase.ftapplyplan(plan, buf, 0, 1);
|
---|
2291 | ftbase.ftapplyplan(plan, buf2, 0, 1);
|
---|
2292 | for(i=0; i<=p-1; i++)
|
---|
2293 | {
|
---|
2294 | ax = buf[2*i+0];
|
---|
2295 | ay = buf[2*i+1];
|
---|
2296 | bx = buf2[2*i+0];
|
---|
2297 | by = buf2[2*i+1];
|
---|
2298 | tx = ax*bx-ay*by;
|
---|
2299 | ty = ax*by+ay*bx;
|
---|
2300 | buf[2*i+0] = tx;
|
---|
2301 | buf[2*i+1] = -ty;
|
---|
2302 | }
|
---|
2303 | ftbase.ftapplyplan(plan, buf, 0, 1);
|
---|
2304 | t = (double)1/(double)p;
|
---|
2305 | if( circular )
|
---|
2306 | {
|
---|
2307 |
|
---|
2308 | //
|
---|
2309 | // circular, add tail to head
|
---|
2310 | //
|
---|
2311 | r = new complex[m];
|
---|
2312 | for(i=0; i<=m-1; i++)
|
---|
2313 | {
|
---|
2314 | r[i].x = t*buf[2*i+0];
|
---|
2315 | r[i].y = -(t*buf[2*i+1]);
|
---|
2316 | }
|
---|
2317 | for(i=m; i<=m+n-2; i++)
|
---|
2318 | {
|
---|
2319 | r[i-m].x = r[i-m].x+t*buf[2*i+0];
|
---|
2320 | r[i-m].y = r[i-m].y-t*buf[2*i+1];
|
---|
2321 | }
|
---|
2322 | }
|
---|
2323 | else
|
---|
2324 | {
|
---|
2325 |
|
---|
2326 | //
|
---|
2327 | // non-circular, just copy
|
---|
2328 | //
|
---|
2329 | r = new complex[m+n-1];
|
---|
2330 | for(i=0; i<=m+n-2; i++)
|
---|
2331 | {
|
---|
2332 | r[i].x = t*buf[2*i+0];
|
---|
2333 | r[i].y = -(t*buf[2*i+1]);
|
---|
2334 | }
|
---|
2335 | }
|
---|
2336 | }
|
---|
2337 | return;
|
---|
2338 | }
|
---|
2339 |
|
---|
2340 | //
|
---|
2341 | // overlap-add method for
|
---|
2342 | // circular and non-circular convolutions.
|
---|
2343 | //
|
---|
2344 | // First part of code (separate FFTs of input blocks) is the same
|
---|
2345 | // for all types of convolution. Second part (overlapping outputs)
|
---|
2346 | // differs for different types of convolution. We just copy output
|
---|
2347 | // when convolution is non-circular. We wrap it around, if it is
|
---|
2348 | // circular.
|
---|
2349 | //
|
---|
2350 | if( alg==2 )
|
---|
2351 | {
|
---|
2352 | buf = new double[2*(q+n-1)];
|
---|
2353 |
|
---|
2354 | //
|
---|
2355 | // prepare R
|
---|
2356 | //
|
---|
2357 | if( circular )
|
---|
2358 | {
|
---|
2359 | r = new complex[m];
|
---|
2360 | for(i=0; i<=m-1; i++)
|
---|
2361 | {
|
---|
2362 | r[i] = 0;
|
---|
2363 | }
|
---|
2364 | }
|
---|
2365 | else
|
---|
2366 | {
|
---|
2367 | r = new complex[m+n-1];
|
---|
2368 | for(i=0; i<=m+n-2; i++)
|
---|
2369 | {
|
---|
2370 | r[i] = 0;
|
---|
2371 | }
|
---|
2372 | }
|
---|
2373 |
|
---|
2374 | //
|
---|
2375 | // pre-calculated FFT(B)
|
---|
2376 | //
|
---|
2377 | bbuf = new complex[q+n-1];
|
---|
2378 | for(i_=0; i_<=n-1;i_++)
|
---|
2379 | {
|
---|
2380 | bbuf[i_] = b[i_];
|
---|
2381 | }
|
---|
2382 | for(j=n; j<=q+n-2; j++)
|
---|
2383 | {
|
---|
2384 | bbuf[j] = 0;
|
---|
2385 | }
|
---|
2386 | fft.fftc1d(ref bbuf, q+n-1);
|
---|
2387 |
|
---|
2388 | //
|
---|
2389 | // prepare FFT plan for chunks of A
|
---|
2390 | //
|
---|
2391 | ftbase.ftcomplexfftplan(q+n-1, 1, plan);
|
---|
2392 |
|
---|
2393 | //
|
---|
2394 | // main overlap-add cycle
|
---|
2395 | //
|
---|
2396 | i = 0;
|
---|
2397 | while( i<=m-1 )
|
---|
2398 | {
|
---|
2399 | p = Math.Min(q, m-i);
|
---|
2400 | for(j=0; j<=p-1; j++)
|
---|
2401 | {
|
---|
2402 | buf[2*j+0] = a[i+j].x;
|
---|
2403 | buf[2*j+1] = a[i+j].y;
|
---|
2404 | }
|
---|
2405 | for(j=p; j<=q+n-2; j++)
|
---|
2406 | {
|
---|
2407 | buf[2*j+0] = 0;
|
---|
2408 | buf[2*j+1] = 0;
|
---|
2409 | }
|
---|
2410 | ftbase.ftapplyplan(plan, buf, 0, 1);
|
---|
2411 | for(j=0; j<=q+n-2; j++)
|
---|
2412 | {
|
---|
2413 | ax = buf[2*j+0];
|
---|
2414 | ay = buf[2*j+1];
|
---|
2415 | bx = bbuf[j].x;
|
---|
2416 | by = bbuf[j].y;
|
---|
2417 | tx = ax*bx-ay*by;
|
---|
2418 | ty = ax*by+ay*bx;
|
---|
2419 | buf[2*j+0] = tx;
|
---|
2420 | buf[2*j+1] = -ty;
|
---|
2421 | }
|
---|
2422 | ftbase.ftapplyplan(plan, buf, 0, 1);
|
---|
2423 | t = (double)1/(double)(q+n-1);
|
---|
2424 | if( circular )
|
---|
2425 | {
|
---|
2426 | j1 = Math.Min(i+p+n-2, m-1)-i;
|
---|
2427 | j2 = j1+1;
|
---|
2428 | }
|
---|
2429 | else
|
---|
2430 | {
|
---|
2431 | j1 = p+n-2;
|
---|
2432 | j2 = j1+1;
|
---|
2433 | }
|
---|
2434 | for(j=0; j<=j1; j++)
|
---|
2435 | {
|
---|
2436 | r[i+j].x = r[i+j].x+buf[2*j+0]*t;
|
---|
2437 | r[i+j].y = r[i+j].y-buf[2*j+1]*t;
|
---|
2438 | }
|
---|
2439 | for(j=j2; j<=p+n-2; j++)
|
---|
2440 | {
|
---|
2441 | r[j-j2].x = r[j-j2].x+buf[2*j+0]*t;
|
---|
2442 | r[j-j2].y = r[j-j2].y-buf[2*j+1]*t;
|
---|
2443 | }
|
---|
2444 | i = i+p;
|
---|
2445 | }
|
---|
2446 | return;
|
---|
2447 | }
|
---|
2448 | }
|
---|
2449 |
|
---|
2450 |
|
---|
2451 | /*************************************************************************
|
---|
2452 | 1-dimensional real convolution.
|
---|
2453 |
|
---|
2454 | Extended subroutine which allows to choose convolution algorithm.
|
---|
2455 | Intended for internal use, ALGLIB users should call ConvR1D().
|
---|
2456 |
|
---|
2457 | INPUT PARAMETERS
|
---|
2458 | A - array[0..M-1] - complex function to be transformed
|
---|
2459 | M - problem size
|
---|
2460 | B - array[0..N-1] - complex function to be transformed
|
---|
2461 | N - problem size, N<=M
|
---|
2462 | Alg - algorithm type:
|
---|
2463 | *-2 auto-select Q for overlap-add
|
---|
2464 | *-1 auto-select algorithm and parameters
|
---|
2465 | * 0 straightforward formula for small N's
|
---|
2466 | * 1 general FFT-based code
|
---|
2467 | * 2 overlap-add with length Q
|
---|
2468 | Q - length for overlap-add
|
---|
2469 |
|
---|
2470 | OUTPUT PARAMETERS
|
---|
2471 | R - convolution: A*B. array[0..N+M-1].
|
---|
2472 |
|
---|
2473 | -- ALGLIB --
|
---|
2474 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
2475 | *************************************************************************/
|
---|
2476 | public static void convr1dx(double[] a,
|
---|
2477 | int m,
|
---|
2478 | double[] b,
|
---|
2479 | int n,
|
---|
2480 | bool circular,
|
---|
2481 | int alg,
|
---|
2482 | int q,
|
---|
2483 | ref double[] r)
|
---|
2484 | {
|
---|
2485 | double v = 0;
|
---|
2486 | int i = 0;
|
---|
2487 | int j = 0;
|
---|
2488 | int p = 0;
|
---|
2489 | int ptotal = 0;
|
---|
2490 | int i1 = 0;
|
---|
2491 | int i2 = 0;
|
---|
2492 | int j1 = 0;
|
---|
2493 | int j2 = 0;
|
---|
2494 | double ax = 0;
|
---|
2495 | double ay = 0;
|
---|
2496 | double bx = 0;
|
---|
2497 | double by = 0;
|
---|
2498 | double tx = 0;
|
---|
2499 | double ty = 0;
|
---|
2500 | double flopcand = 0;
|
---|
2501 | double flopbest = 0;
|
---|
2502 | int algbest = 0;
|
---|
2503 | ftbase.fasttransformplan plan = new ftbase.fasttransformplan();
|
---|
2504 | double[] buf = new double[0];
|
---|
2505 | double[] buf2 = new double[0];
|
---|
2506 | double[] buf3 = new double[0];
|
---|
2507 | int i_ = 0;
|
---|
2508 | int i1_ = 0;
|
---|
2509 |
|
---|
2510 | r = new double[0];
|
---|
2511 |
|
---|
2512 | alglib.ap.assert(n>0 && m>0, "ConvC1DX: incorrect N or M!");
|
---|
2513 | alglib.ap.assert(n<=m, "ConvC1DX: N<M assumption is false!");
|
---|
2514 |
|
---|
2515 | //
|
---|
2516 | // handle special cases
|
---|
2517 | //
|
---|
2518 | if( Math.Min(m, n)<=2 )
|
---|
2519 | {
|
---|
2520 | alg = 0;
|
---|
2521 | }
|
---|
2522 |
|
---|
2523 | //
|
---|
2524 | // Auto-select
|
---|
2525 | //
|
---|
2526 | if( alg<0 )
|
---|
2527 | {
|
---|
2528 |
|
---|
2529 | //
|
---|
2530 | // Initial candidate: straightforward implementation.
|
---|
2531 | //
|
---|
2532 | // If we want to use auto-fitted overlap-add,
|
---|
2533 | // flop count is initialized by large real number - to force
|
---|
2534 | // another algorithm selection
|
---|
2535 | //
|
---|
2536 | algbest = 0;
|
---|
2537 | if( alg==-1 )
|
---|
2538 | {
|
---|
2539 | flopbest = 0.15*m*n;
|
---|
2540 | }
|
---|
2541 | else
|
---|
2542 | {
|
---|
2543 | flopbest = math.maxrealnumber;
|
---|
2544 | }
|
---|
2545 |
|
---|
2546 | //
|
---|
2547 | // Another candidate - generic FFT code
|
---|
2548 | //
|
---|
2549 | if( alg==-1 )
|
---|
2550 | {
|
---|
2551 | if( (circular && ftbase.ftbaseissmooth(m)) && m%2==0 )
|
---|
2552 | {
|
---|
2553 |
|
---|
2554 | //
|
---|
2555 | // special code for circular convolution of a sequence with a smooth length
|
---|
2556 | //
|
---|
2557 | flopcand = 3*ftbase.ftbasegetflopestimate(m/2)+(double)(6*m)/(double)2;
|
---|
2558 | if( (double)(flopcand)<(double)(flopbest) )
|
---|
2559 | {
|
---|
2560 | algbest = 1;
|
---|
2561 | flopbest = flopcand;
|
---|
2562 | }
|
---|
2563 | }
|
---|
2564 | else
|
---|
2565 | {
|
---|
2566 |
|
---|
2567 | //
|
---|
2568 | // general cyclic/non-cyclic convolution
|
---|
2569 | //
|
---|
2570 | p = ftbase.ftbasefindsmootheven(m+n-1);
|
---|
2571 | flopcand = 3*ftbase.ftbasegetflopestimate(p/2)+(double)(6*p)/(double)2;
|
---|
2572 | if( (double)(flopcand)<(double)(flopbest) )
|
---|
2573 | {
|
---|
2574 | algbest = 1;
|
---|
2575 | flopbest = flopcand;
|
---|
2576 | }
|
---|
2577 | }
|
---|
2578 | }
|
---|
2579 |
|
---|
2580 | //
|
---|
2581 | // Another candidate - overlap-add
|
---|
2582 | //
|
---|
2583 | q = 1;
|
---|
2584 | ptotal = 1;
|
---|
2585 | while( ptotal<n )
|
---|
2586 | {
|
---|
2587 | ptotal = ptotal*2;
|
---|
2588 | }
|
---|
2589 | while( ptotal<=m+n-1 )
|
---|
2590 | {
|
---|
2591 | p = ptotal-n+1;
|
---|
2592 | flopcand = (int)Math.Ceiling((double)m/(double)p)*(2*ftbase.ftbasegetflopestimate(ptotal/2)+1*(ptotal/2));
|
---|
2593 | if( (double)(flopcand)<(double)(flopbest) )
|
---|
2594 | {
|
---|
2595 | flopbest = flopcand;
|
---|
2596 | algbest = 2;
|
---|
2597 | q = p;
|
---|
2598 | }
|
---|
2599 | ptotal = ptotal*2;
|
---|
2600 | }
|
---|
2601 | alg = algbest;
|
---|
2602 | convr1dx(a, m, b, n, circular, alg, q, ref r);
|
---|
2603 | return;
|
---|
2604 | }
|
---|
2605 |
|
---|
2606 | //
|
---|
2607 | // straightforward formula for
|
---|
2608 | // circular and non-circular convolutions.
|
---|
2609 | //
|
---|
2610 | // Very simple code, no further comments needed.
|
---|
2611 | //
|
---|
2612 | if( alg==0 )
|
---|
2613 | {
|
---|
2614 |
|
---|
2615 | //
|
---|
2616 | // Special case: N=1
|
---|
2617 | //
|
---|
2618 | if( n==1 )
|
---|
2619 | {
|
---|
2620 | r = new double[m];
|
---|
2621 | v = b[0];
|
---|
2622 | for(i_=0; i_<=m-1;i_++)
|
---|
2623 | {
|
---|
2624 | r[i_] = v*a[i_];
|
---|
2625 | }
|
---|
2626 | return;
|
---|
2627 | }
|
---|
2628 |
|
---|
2629 | //
|
---|
2630 | // use straightforward formula
|
---|
2631 | //
|
---|
2632 | if( circular )
|
---|
2633 | {
|
---|
2634 |
|
---|
2635 | //
|
---|
2636 | // circular convolution
|
---|
2637 | //
|
---|
2638 | r = new double[m];
|
---|
2639 | v = b[0];
|
---|
2640 | for(i_=0; i_<=m-1;i_++)
|
---|
2641 | {
|
---|
2642 | r[i_] = v*a[i_];
|
---|
2643 | }
|
---|
2644 | for(i=1; i<=n-1; i++)
|
---|
2645 | {
|
---|
2646 | v = b[i];
|
---|
2647 | i1 = 0;
|
---|
2648 | i2 = i-1;
|
---|
2649 | j1 = m-i;
|
---|
2650 | j2 = m-1;
|
---|
2651 | i1_ = (j1) - (i1);
|
---|
2652 | for(i_=i1; i_<=i2;i_++)
|
---|
2653 | {
|
---|
2654 | r[i_] = r[i_] + v*a[i_+i1_];
|
---|
2655 | }
|
---|
2656 | i1 = i;
|
---|
2657 | i2 = m-1;
|
---|
2658 | j1 = 0;
|
---|
2659 | j2 = m-i-1;
|
---|
2660 | i1_ = (j1) - (i1);
|
---|
2661 | for(i_=i1; i_<=i2;i_++)
|
---|
2662 | {
|
---|
2663 | r[i_] = r[i_] + v*a[i_+i1_];
|
---|
2664 | }
|
---|
2665 | }
|
---|
2666 | }
|
---|
2667 | else
|
---|
2668 | {
|
---|
2669 |
|
---|
2670 | //
|
---|
2671 | // non-circular convolution
|
---|
2672 | //
|
---|
2673 | r = new double[m+n-1];
|
---|
2674 | for(i=0; i<=m+n-2; i++)
|
---|
2675 | {
|
---|
2676 | r[i] = 0;
|
---|
2677 | }
|
---|
2678 | for(i=0; i<=n-1; i++)
|
---|
2679 | {
|
---|
2680 | v = b[i];
|
---|
2681 | i1_ = (0) - (i);
|
---|
2682 | for(i_=i; i_<=i+m-1;i_++)
|
---|
2683 | {
|
---|
2684 | r[i_] = r[i_] + v*a[i_+i1_];
|
---|
2685 | }
|
---|
2686 | }
|
---|
2687 | }
|
---|
2688 | return;
|
---|
2689 | }
|
---|
2690 |
|
---|
2691 | //
|
---|
2692 | // general FFT-based code for
|
---|
2693 | // circular and non-circular convolutions.
|
---|
2694 | //
|
---|
2695 | // First, if convolution is circular, we test whether M is smooth or not.
|
---|
2696 | // If it is smooth, we just use M-length FFT to calculate convolution.
|
---|
2697 | // If it is not, we calculate non-circular convolution and wrap it arount.
|
---|
2698 | //
|
---|
2699 | // If convolution is non-circular, we use zero-padding + FFT.
|
---|
2700 | //
|
---|
2701 | // We assume that M+N-1>2 - we should call small case code otherwise
|
---|
2702 | //
|
---|
2703 | if( alg==1 )
|
---|
2704 | {
|
---|
2705 | alglib.ap.assert(m+n-1>2, "ConvR1DX: internal error!");
|
---|
2706 | if( (circular && ftbase.ftbaseissmooth(m)) && m%2==0 )
|
---|
2707 | {
|
---|
2708 |
|
---|
2709 | //
|
---|
2710 | // special code for circular convolution with smooth even M
|
---|
2711 | //
|
---|
2712 | buf = new double[m];
|
---|
2713 | for(i_=0; i_<=m-1;i_++)
|
---|
2714 | {
|
---|
2715 | buf[i_] = a[i_];
|
---|
2716 | }
|
---|
2717 | buf2 = new double[m];
|
---|
2718 | for(i_=0; i_<=n-1;i_++)
|
---|
2719 | {
|
---|
2720 | buf2[i_] = b[i_];
|
---|
2721 | }
|
---|
2722 | for(i=n; i<=m-1; i++)
|
---|
2723 | {
|
---|
2724 | buf2[i] = 0;
|
---|
2725 | }
|
---|
2726 | buf3 = new double[m];
|
---|
2727 | ftbase.ftcomplexfftplan(m/2, 1, plan);
|
---|
2728 | fft.fftr1dinternaleven(ref buf, m, ref buf3, plan);
|
---|
2729 | fft.fftr1dinternaleven(ref buf2, m, ref buf3, plan);
|
---|
2730 | buf[0] = buf[0]*buf2[0];
|
---|
2731 | buf[1] = buf[1]*buf2[1];
|
---|
2732 | for(i=1; i<=m/2-1; i++)
|
---|
2733 | {
|
---|
2734 | ax = buf[2*i+0];
|
---|
2735 | ay = buf[2*i+1];
|
---|
2736 | bx = buf2[2*i+0];
|
---|
2737 | by = buf2[2*i+1];
|
---|
2738 | tx = ax*bx-ay*by;
|
---|
2739 | ty = ax*by+ay*bx;
|
---|
2740 | buf[2*i+0] = tx;
|
---|
2741 | buf[2*i+1] = ty;
|
---|
2742 | }
|
---|
2743 | fft.fftr1dinvinternaleven(ref buf, m, ref buf3, plan);
|
---|
2744 | r = new double[m];
|
---|
2745 | for(i_=0; i_<=m-1;i_++)
|
---|
2746 | {
|
---|
2747 | r[i_] = buf[i_];
|
---|
2748 | }
|
---|
2749 | }
|
---|
2750 | else
|
---|
2751 | {
|
---|
2752 |
|
---|
2753 | //
|
---|
2754 | // M is non-smooth or non-even, general code (circular/non-circular):
|
---|
2755 | // * first part is the same for circular and non-circular
|
---|
2756 | // convolutions. zero padding, FFTs, inverse FFTs
|
---|
2757 | // * second part differs:
|
---|
2758 | // * for non-circular convolution we just copy array
|
---|
2759 | // * for circular convolution we add array tail to its head
|
---|
2760 | //
|
---|
2761 | p = ftbase.ftbasefindsmootheven(m+n-1);
|
---|
2762 | buf = new double[p];
|
---|
2763 | for(i_=0; i_<=m-1;i_++)
|
---|
2764 | {
|
---|
2765 | buf[i_] = a[i_];
|
---|
2766 | }
|
---|
2767 | for(i=m; i<=p-1; i++)
|
---|
2768 | {
|
---|
2769 | buf[i] = 0;
|
---|
2770 | }
|
---|
2771 | buf2 = new double[p];
|
---|
2772 | for(i_=0; i_<=n-1;i_++)
|
---|
2773 | {
|
---|
2774 | buf2[i_] = b[i_];
|
---|
2775 | }
|
---|
2776 | for(i=n; i<=p-1; i++)
|
---|
2777 | {
|
---|
2778 | buf2[i] = 0;
|
---|
2779 | }
|
---|
2780 | buf3 = new double[p];
|
---|
2781 | ftbase.ftcomplexfftplan(p/2, 1, plan);
|
---|
2782 | fft.fftr1dinternaleven(ref buf, p, ref buf3, plan);
|
---|
2783 | fft.fftr1dinternaleven(ref buf2, p, ref buf3, plan);
|
---|
2784 | buf[0] = buf[0]*buf2[0];
|
---|
2785 | buf[1] = buf[1]*buf2[1];
|
---|
2786 | for(i=1; i<=p/2-1; i++)
|
---|
2787 | {
|
---|
2788 | ax = buf[2*i+0];
|
---|
2789 | ay = buf[2*i+1];
|
---|
2790 | bx = buf2[2*i+0];
|
---|
2791 | by = buf2[2*i+1];
|
---|
2792 | tx = ax*bx-ay*by;
|
---|
2793 | ty = ax*by+ay*bx;
|
---|
2794 | buf[2*i+0] = tx;
|
---|
2795 | buf[2*i+1] = ty;
|
---|
2796 | }
|
---|
2797 | fft.fftr1dinvinternaleven(ref buf, p, ref buf3, plan);
|
---|
2798 | if( circular )
|
---|
2799 | {
|
---|
2800 |
|
---|
2801 | //
|
---|
2802 | // circular, add tail to head
|
---|
2803 | //
|
---|
2804 | r = new double[m];
|
---|
2805 | for(i_=0; i_<=m-1;i_++)
|
---|
2806 | {
|
---|
2807 | r[i_] = buf[i_];
|
---|
2808 | }
|
---|
2809 | if( n>=2 )
|
---|
2810 | {
|
---|
2811 | i1_ = (m) - (0);
|
---|
2812 | for(i_=0; i_<=n-2;i_++)
|
---|
2813 | {
|
---|
2814 | r[i_] = r[i_] + buf[i_+i1_];
|
---|
2815 | }
|
---|
2816 | }
|
---|
2817 | }
|
---|
2818 | else
|
---|
2819 | {
|
---|
2820 |
|
---|
2821 | //
|
---|
2822 | // non-circular, just copy
|
---|
2823 | //
|
---|
2824 | r = new double[m+n-1];
|
---|
2825 | for(i_=0; i_<=m+n-2;i_++)
|
---|
2826 | {
|
---|
2827 | r[i_] = buf[i_];
|
---|
2828 | }
|
---|
2829 | }
|
---|
2830 | }
|
---|
2831 | return;
|
---|
2832 | }
|
---|
2833 |
|
---|
2834 | //
|
---|
2835 | // overlap-add method
|
---|
2836 | //
|
---|
2837 | if( alg==2 )
|
---|
2838 | {
|
---|
2839 | alglib.ap.assert((q+n-1)%2==0, "ConvR1DX: internal error!");
|
---|
2840 | buf = new double[q+n-1];
|
---|
2841 | buf2 = new double[q+n-1];
|
---|
2842 | buf3 = new double[q+n-1];
|
---|
2843 | ftbase.ftcomplexfftplan((q+n-1)/2, 1, plan);
|
---|
2844 |
|
---|
2845 | //
|
---|
2846 | // prepare R
|
---|
2847 | //
|
---|
2848 | if( circular )
|
---|
2849 | {
|
---|
2850 | r = new double[m];
|
---|
2851 | for(i=0; i<=m-1; i++)
|
---|
2852 | {
|
---|
2853 | r[i] = 0;
|
---|
2854 | }
|
---|
2855 | }
|
---|
2856 | else
|
---|
2857 | {
|
---|
2858 | r = new double[m+n-1];
|
---|
2859 | for(i=0; i<=m+n-2; i++)
|
---|
2860 | {
|
---|
2861 | r[i] = 0;
|
---|
2862 | }
|
---|
2863 | }
|
---|
2864 |
|
---|
2865 | //
|
---|
2866 | // pre-calculated FFT(B)
|
---|
2867 | //
|
---|
2868 | for(i_=0; i_<=n-1;i_++)
|
---|
2869 | {
|
---|
2870 | buf2[i_] = b[i_];
|
---|
2871 | }
|
---|
2872 | for(j=n; j<=q+n-2; j++)
|
---|
2873 | {
|
---|
2874 | buf2[j] = 0;
|
---|
2875 | }
|
---|
2876 | fft.fftr1dinternaleven(ref buf2, q+n-1, ref buf3, plan);
|
---|
2877 |
|
---|
2878 | //
|
---|
2879 | // main overlap-add cycle
|
---|
2880 | //
|
---|
2881 | i = 0;
|
---|
2882 | while( i<=m-1 )
|
---|
2883 | {
|
---|
2884 | p = Math.Min(q, m-i);
|
---|
2885 | i1_ = (i) - (0);
|
---|
2886 | for(i_=0; i_<=p-1;i_++)
|
---|
2887 | {
|
---|
2888 | buf[i_] = a[i_+i1_];
|
---|
2889 | }
|
---|
2890 | for(j=p; j<=q+n-2; j++)
|
---|
2891 | {
|
---|
2892 | buf[j] = 0;
|
---|
2893 | }
|
---|
2894 | fft.fftr1dinternaleven(ref buf, q+n-1, ref buf3, plan);
|
---|
2895 | buf[0] = buf[0]*buf2[0];
|
---|
2896 | buf[1] = buf[1]*buf2[1];
|
---|
2897 | for(j=1; j<=(q+n-1)/2-1; j++)
|
---|
2898 | {
|
---|
2899 | ax = buf[2*j+0];
|
---|
2900 | ay = buf[2*j+1];
|
---|
2901 | bx = buf2[2*j+0];
|
---|
2902 | by = buf2[2*j+1];
|
---|
2903 | tx = ax*bx-ay*by;
|
---|
2904 | ty = ax*by+ay*bx;
|
---|
2905 | buf[2*j+0] = tx;
|
---|
2906 | buf[2*j+1] = ty;
|
---|
2907 | }
|
---|
2908 | fft.fftr1dinvinternaleven(ref buf, q+n-1, ref buf3, plan);
|
---|
2909 | if( circular )
|
---|
2910 | {
|
---|
2911 | j1 = Math.Min(i+p+n-2, m-1)-i;
|
---|
2912 | j2 = j1+1;
|
---|
2913 | }
|
---|
2914 | else
|
---|
2915 | {
|
---|
2916 | j1 = p+n-2;
|
---|
2917 | j2 = j1+1;
|
---|
2918 | }
|
---|
2919 | i1_ = (0) - (i);
|
---|
2920 | for(i_=i; i_<=i+j1;i_++)
|
---|
2921 | {
|
---|
2922 | r[i_] = r[i_] + buf[i_+i1_];
|
---|
2923 | }
|
---|
2924 | if( p+n-2>=j2 )
|
---|
2925 | {
|
---|
2926 | i1_ = (j2) - (0);
|
---|
2927 | for(i_=0; i_<=p+n-2-j2;i_++)
|
---|
2928 | {
|
---|
2929 | r[i_] = r[i_] + buf[i_+i1_];
|
---|
2930 | }
|
---|
2931 | }
|
---|
2932 | i = i+p;
|
---|
2933 | }
|
---|
2934 | return;
|
---|
2935 | }
|
---|
2936 | }
|
---|
2937 |
|
---|
2938 |
|
---|
2939 | }
|
---|
2940 | public class corr
|
---|
2941 | {
|
---|
2942 | /*************************************************************************
|
---|
2943 | 1-dimensional complex cross-correlation.
|
---|
2944 |
|
---|
2945 | For given Pattern/Signal returns corr(Pattern,Signal) (non-circular).
|
---|
2946 |
|
---|
2947 | Correlation is calculated using reduction to convolution. Algorithm with
|
---|
2948 | max(N,N)*log(max(N,N)) complexity is used (see ConvC1D() for more info
|
---|
2949 | about performance).
|
---|
2950 |
|
---|
2951 | IMPORTANT:
|
---|
2952 | for historical reasons subroutine accepts its parameters in reversed
|
---|
2953 | order: CorrC1D(Signal, Pattern) = Pattern x Signal (using traditional
|
---|
2954 | definition of cross-correlation, denoting cross-correlation as "x").
|
---|
2955 |
|
---|
2956 | INPUT PARAMETERS
|
---|
2957 | Signal - array[0..N-1] - complex function to be transformed,
|
---|
2958 | signal containing pattern
|
---|
2959 | N - problem size
|
---|
2960 | Pattern - array[0..M-1] - complex function to be transformed,
|
---|
2961 | pattern to search withing signal
|
---|
2962 | M - problem size
|
---|
2963 |
|
---|
2964 | OUTPUT PARAMETERS
|
---|
2965 | R - cross-correlation, array[0..N+M-2]:
|
---|
2966 | * positive lags are stored in R[0..N-1],
|
---|
2967 | R[i] = sum(conj(pattern[j])*signal[i+j]
|
---|
2968 | * negative lags are stored in R[N..N+M-2],
|
---|
2969 | R[N+M-1-i] = sum(conj(pattern[j])*signal[-i+j]
|
---|
2970 |
|
---|
2971 | NOTE:
|
---|
2972 | It is assumed that pattern domain is [0..M-1]. If Pattern is non-zero
|
---|
2973 | on [-K..M-1], you can still use this subroutine, just shift result by K.
|
---|
2974 |
|
---|
2975 | -- ALGLIB --
|
---|
2976 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
2977 | *************************************************************************/
|
---|
2978 | public static void corrc1d(complex[] signal,
|
---|
2979 | int n,
|
---|
2980 | complex[] pattern,
|
---|
2981 | int m,
|
---|
2982 | ref complex[] r)
|
---|
2983 | {
|
---|
2984 | complex[] p = new complex[0];
|
---|
2985 | complex[] b = new complex[0];
|
---|
2986 | int i = 0;
|
---|
2987 | int i_ = 0;
|
---|
2988 | int i1_ = 0;
|
---|
2989 |
|
---|
2990 | r = new complex[0];
|
---|
2991 |
|
---|
2992 | alglib.ap.assert(n>0 && m>0, "CorrC1D: incorrect N or M!");
|
---|
2993 | p = new complex[m];
|
---|
2994 | for(i=0; i<=m-1; i++)
|
---|
2995 | {
|
---|
2996 | p[m-1-i] = math.conj(pattern[i]);
|
---|
2997 | }
|
---|
2998 | conv.convc1d(p, m, signal, n, ref b);
|
---|
2999 | r = new complex[m+n-1];
|
---|
3000 | i1_ = (m-1) - (0);
|
---|
3001 | for(i_=0; i_<=n-1;i_++)
|
---|
3002 | {
|
---|
3003 | r[i_] = b[i_+i1_];
|
---|
3004 | }
|
---|
3005 | if( m+n-2>=n )
|
---|
3006 | {
|
---|
3007 | i1_ = (0) - (n);
|
---|
3008 | for(i_=n; i_<=m+n-2;i_++)
|
---|
3009 | {
|
---|
3010 | r[i_] = b[i_+i1_];
|
---|
3011 | }
|
---|
3012 | }
|
---|
3013 | }
|
---|
3014 |
|
---|
3015 |
|
---|
3016 | /*************************************************************************
|
---|
3017 | 1-dimensional circular complex cross-correlation.
|
---|
3018 |
|
---|
3019 | For given Pattern/Signal returns corr(Pattern,Signal) (circular).
|
---|
3020 | Algorithm has linearithmic complexity for any M/N.
|
---|
3021 |
|
---|
3022 | IMPORTANT:
|
---|
3023 | for historical reasons subroutine accepts its parameters in reversed
|
---|
3024 | order: CorrC1DCircular(Signal, Pattern) = Pattern x Signal (using
|
---|
3025 | traditional definition of cross-correlation, denoting cross-correlation
|
---|
3026 | as "x").
|
---|
3027 |
|
---|
3028 | INPUT PARAMETERS
|
---|
3029 | Signal - array[0..N-1] - complex function to be transformed,
|
---|
3030 | periodic signal containing pattern
|
---|
3031 | N - problem size
|
---|
3032 | Pattern - array[0..M-1] - complex function to be transformed,
|
---|
3033 | non-periodic pattern to search withing signal
|
---|
3034 | M - problem size
|
---|
3035 |
|
---|
3036 | OUTPUT PARAMETERS
|
---|
3037 | R - convolution: A*B. array[0..M-1].
|
---|
3038 |
|
---|
3039 |
|
---|
3040 | -- ALGLIB --
|
---|
3041 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
3042 | *************************************************************************/
|
---|
3043 | public static void corrc1dcircular(complex[] signal,
|
---|
3044 | int m,
|
---|
3045 | complex[] pattern,
|
---|
3046 | int n,
|
---|
3047 | ref complex[] c)
|
---|
3048 | {
|
---|
3049 | complex[] p = new complex[0];
|
---|
3050 | complex[] b = new complex[0];
|
---|
3051 | int i1 = 0;
|
---|
3052 | int i2 = 0;
|
---|
3053 | int i = 0;
|
---|
3054 | int j2 = 0;
|
---|
3055 | int i_ = 0;
|
---|
3056 | int i1_ = 0;
|
---|
3057 |
|
---|
3058 | c = new complex[0];
|
---|
3059 |
|
---|
3060 | alglib.ap.assert(n>0 && m>0, "ConvC1DCircular: incorrect N or M!");
|
---|
3061 |
|
---|
3062 | //
|
---|
3063 | // normalize task: make M>=N,
|
---|
3064 | // so A will be longer (at least - not shorter) that B.
|
---|
3065 | //
|
---|
3066 | if( m<n )
|
---|
3067 | {
|
---|
3068 | b = new complex[m];
|
---|
3069 | for(i1=0; i1<=m-1; i1++)
|
---|
3070 | {
|
---|
3071 | b[i1] = 0;
|
---|
3072 | }
|
---|
3073 | i1 = 0;
|
---|
3074 | while( i1<n )
|
---|
3075 | {
|
---|
3076 | i2 = Math.Min(i1+m-1, n-1);
|
---|
3077 | j2 = i2-i1;
|
---|
3078 | i1_ = (i1) - (0);
|
---|
3079 | for(i_=0; i_<=j2;i_++)
|
---|
3080 | {
|
---|
3081 | b[i_] = b[i_] + pattern[i_+i1_];
|
---|
3082 | }
|
---|
3083 | i1 = i1+m;
|
---|
3084 | }
|
---|
3085 | corrc1dcircular(signal, m, b, m, ref c);
|
---|
3086 | return;
|
---|
3087 | }
|
---|
3088 |
|
---|
3089 | //
|
---|
3090 | // Task is normalized
|
---|
3091 | //
|
---|
3092 | p = new complex[n];
|
---|
3093 | for(i=0; i<=n-1; i++)
|
---|
3094 | {
|
---|
3095 | p[n-1-i] = math.conj(pattern[i]);
|
---|
3096 | }
|
---|
3097 | conv.convc1dcircular(signal, m, p, n, ref b);
|
---|
3098 | c = new complex[m];
|
---|
3099 | i1_ = (n-1) - (0);
|
---|
3100 | for(i_=0; i_<=m-n;i_++)
|
---|
3101 | {
|
---|
3102 | c[i_] = b[i_+i1_];
|
---|
3103 | }
|
---|
3104 | if( m-n+1<=m-1 )
|
---|
3105 | {
|
---|
3106 | i1_ = (0) - (m-n+1);
|
---|
3107 | for(i_=m-n+1; i_<=m-1;i_++)
|
---|
3108 | {
|
---|
3109 | c[i_] = b[i_+i1_];
|
---|
3110 | }
|
---|
3111 | }
|
---|
3112 | }
|
---|
3113 |
|
---|
3114 |
|
---|
3115 | /*************************************************************************
|
---|
3116 | 1-dimensional real cross-correlation.
|
---|
3117 |
|
---|
3118 | For given Pattern/Signal returns corr(Pattern,Signal) (non-circular).
|
---|
3119 |
|
---|
3120 | Correlation is calculated using reduction to convolution. Algorithm with
|
---|
3121 | max(N,N)*log(max(N,N)) complexity is used (see ConvC1D() for more info
|
---|
3122 | about performance).
|
---|
3123 |
|
---|
3124 | IMPORTANT:
|
---|
3125 | for historical reasons subroutine accepts its parameters in reversed
|
---|
3126 | order: CorrR1D(Signal, Pattern) = Pattern x Signal (using traditional
|
---|
3127 | definition of cross-correlation, denoting cross-correlation as "x").
|
---|
3128 |
|
---|
3129 | INPUT PARAMETERS
|
---|
3130 | Signal - array[0..N-1] - real function to be transformed,
|
---|
3131 | signal containing pattern
|
---|
3132 | N - problem size
|
---|
3133 | Pattern - array[0..M-1] - real function to be transformed,
|
---|
3134 | pattern to search withing signal
|
---|
3135 | M - problem size
|
---|
3136 |
|
---|
3137 | OUTPUT PARAMETERS
|
---|
3138 | R - cross-correlation, array[0..N+M-2]:
|
---|
3139 | * positive lags are stored in R[0..N-1],
|
---|
3140 | R[i] = sum(pattern[j]*signal[i+j]
|
---|
3141 | * negative lags are stored in R[N..N+M-2],
|
---|
3142 | R[N+M-1-i] = sum(pattern[j]*signal[-i+j]
|
---|
3143 |
|
---|
3144 | NOTE:
|
---|
3145 | It is assumed that pattern domain is [0..M-1]. If Pattern is non-zero
|
---|
3146 | on [-K..M-1], you can still use this subroutine, just shift result by K.
|
---|
3147 |
|
---|
3148 | -- ALGLIB --
|
---|
3149 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
3150 | *************************************************************************/
|
---|
3151 | public static void corrr1d(double[] signal,
|
---|
3152 | int n,
|
---|
3153 | double[] pattern,
|
---|
3154 | int m,
|
---|
3155 | ref double[] r)
|
---|
3156 | {
|
---|
3157 | double[] p = new double[0];
|
---|
3158 | double[] b = new double[0];
|
---|
3159 | int i = 0;
|
---|
3160 | int i_ = 0;
|
---|
3161 | int i1_ = 0;
|
---|
3162 |
|
---|
3163 | r = new double[0];
|
---|
3164 |
|
---|
3165 | alglib.ap.assert(n>0 && m>0, "CorrR1D: incorrect N or M!");
|
---|
3166 | p = new double[m];
|
---|
3167 | for(i=0; i<=m-1; i++)
|
---|
3168 | {
|
---|
3169 | p[m-1-i] = pattern[i];
|
---|
3170 | }
|
---|
3171 | conv.convr1d(p, m, signal, n, ref b);
|
---|
3172 | r = new double[m+n-1];
|
---|
3173 | i1_ = (m-1) - (0);
|
---|
3174 | for(i_=0; i_<=n-1;i_++)
|
---|
3175 | {
|
---|
3176 | r[i_] = b[i_+i1_];
|
---|
3177 | }
|
---|
3178 | if( m+n-2>=n )
|
---|
3179 | {
|
---|
3180 | i1_ = (0) - (n);
|
---|
3181 | for(i_=n; i_<=m+n-2;i_++)
|
---|
3182 | {
|
---|
3183 | r[i_] = b[i_+i1_];
|
---|
3184 | }
|
---|
3185 | }
|
---|
3186 | }
|
---|
3187 |
|
---|
3188 |
|
---|
3189 | /*************************************************************************
|
---|
3190 | 1-dimensional circular real cross-correlation.
|
---|
3191 |
|
---|
3192 | For given Pattern/Signal returns corr(Pattern,Signal) (circular).
|
---|
3193 | Algorithm has linearithmic complexity for any M/N.
|
---|
3194 |
|
---|
3195 | IMPORTANT:
|
---|
3196 | for historical reasons subroutine accepts its parameters in reversed
|
---|
3197 | order: CorrR1DCircular(Signal, Pattern) = Pattern x Signal (using
|
---|
3198 | traditional definition of cross-correlation, denoting cross-correlation
|
---|
3199 | as "x").
|
---|
3200 |
|
---|
3201 | INPUT PARAMETERS
|
---|
3202 | Signal - array[0..N-1] - real function to be transformed,
|
---|
3203 | periodic signal containing pattern
|
---|
3204 | N - problem size
|
---|
3205 | Pattern - array[0..M-1] - real function to be transformed,
|
---|
3206 | non-periodic pattern to search withing signal
|
---|
3207 | M - problem size
|
---|
3208 |
|
---|
3209 | OUTPUT PARAMETERS
|
---|
3210 | R - convolution: A*B. array[0..M-1].
|
---|
3211 |
|
---|
3212 |
|
---|
3213 | -- ALGLIB --
|
---|
3214 | Copyright 21.07.2009 by Bochkanov Sergey
|
---|
3215 | *************************************************************************/
|
---|
3216 | public static void corrr1dcircular(double[] signal,
|
---|
3217 | int m,
|
---|
3218 | double[] pattern,
|
---|
3219 | int n,
|
---|
3220 | ref double[] c)
|
---|
3221 | {
|
---|
3222 | double[] p = new double[0];
|
---|
3223 | double[] b = new double[0];
|
---|
3224 | int i1 = 0;
|
---|
3225 | int i2 = 0;
|
---|
3226 | int i = 0;
|
---|
3227 | int j2 = 0;
|
---|
3228 | int i_ = 0;
|
---|
3229 | int i1_ = 0;
|
---|
3230 |
|
---|
3231 | c = new double[0];
|
---|
3232 |
|
---|
3233 | alglib.ap.assert(n>0 && m>0, "ConvC1DCircular: incorrect N or M!");
|
---|
3234 |
|
---|
3235 | //
|
---|
3236 | // normalize task: make M>=N,
|
---|
3237 | // so A will be longer (at least - not shorter) that B.
|
---|
3238 | //
|
---|
3239 | if( m<n )
|
---|
3240 | {
|
---|
3241 | b = new double[m];
|
---|
3242 | for(i1=0; i1<=m-1; i1++)
|
---|
3243 | {
|
---|
3244 | b[i1] = 0;
|
---|
3245 | }
|
---|
3246 | i1 = 0;
|
---|
3247 | while( i1<n )
|
---|
3248 | {
|
---|
3249 | i2 = Math.Min(i1+m-1, n-1);
|
---|
3250 | j2 = i2-i1;
|
---|
3251 | i1_ = (i1) - (0);
|
---|
3252 | for(i_=0; i_<=j2;i_++)
|
---|
3253 | {
|
---|
3254 | b[i_] = b[i_] + pattern[i_+i1_];
|
---|
3255 | }
|
---|
3256 | i1 = i1+m;
|
---|
3257 | }
|
---|
3258 | corrr1dcircular(signal, m, b, m, ref c);
|
---|
3259 | return;
|
---|
3260 | }
|
---|
3261 |
|
---|
3262 | //
|
---|
3263 | // Task is normalized
|
---|
3264 | //
|
---|
3265 | p = new double[n];
|
---|
3266 | for(i=0; i<=n-1; i++)
|
---|
3267 | {
|
---|
3268 | p[n-1-i] = pattern[i];
|
---|
3269 | }
|
---|
3270 | conv.convr1dcircular(signal, m, p, n, ref b);
|
---|
3271 | c = new double[m];
|
---|
3272 | i1_ = (n-1) - (0);
|
---|
3273 | for(i_=0; i_<=m-n;i_++)
|
---|
3274 | {
|
---|
3275 | c[i_] = b[i_+i1_];
|
---|
3276 | }
|
---|
3277 | if( m-n+1<=m-1 )
|
---|
3278 | {
|
---|
3279 | i1_ = (0) - (m-n+1);
|
---|
3280 | for(i_=m-n+1; i_<=m-1;i_++)
|
---|
3281 | {
|
---|
3282 | c[i_] = b[i_+i1_];
|
---|
3283 | }
|
---|
3284 | }
|
---|
3285 | }
|
---|
3286 |
|
---|
3287 |
|
---|
3288 | }
|
---|
3289 | }
|
---|
3290 |
|
---|