1 | /* |
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2 | * PairCorrelation.c |
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3 | * twoyukawa |
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4 | * |
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5 | * Created by Marcus Hennig on 5/9/10. |
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6 | * Copyright 2010 __MyCompanyName__. All rights reserved. |
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7 | * |
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8 | */ |
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9 | |
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10 | #include "2Y_PairCorrelation.h" |
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11 | #include <stdio.h> |
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12 | #include <stdlib.h> |
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13 | #include <math.h> |
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14 | //#include <gsl/gsl_errno.h> |
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15 | //#include <gsl/gsl_fft_real.h> |
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16 | |
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17 | /* |
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18 | =================================================================================================== |
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19 | |
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20 | Source: J.B.Hayter: A Program for the fast bi-directional transforms |
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21 | between g(r) and S(Q), ILL internal scientific report, October 1979 |
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22 | |
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23 | The transformation between structure factor and pair correlation |
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24 | function is given by |
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25 | |
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26 | g(x) = 1 + 1 / (12*pi*phi*x) * int( [S(q)-q]*q*sin(q*x), { 0, inf } ) |
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27 | |
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28 | where phi is the volume frcation, x and q are dimensionless variables, |
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29 | scaled by the radius a of the particles: |
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30 | |
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31 | r = x * a; |
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32 | Q = q / a |
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33 | |
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34 | Discretizing the integral leads to |
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35 | |
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36 | x[k] = 2*pi*k / (N * dq) |
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37 | g(x[k]) = 1 + N*dq^3 / (24*pi^2*phi*k) * Im{ sum(S[n]*exp(2*pi*i*n*k/N),{n,0,N-1}) } |
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38 | |
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39 | where S[n] = n*(S(q[n])-1) with q[n]=n * dq |
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40 | |
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41 | =================================================================================================== |
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42 | */ |
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43 | |
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44 | /* |
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45 | int PairCorrelation_GSL( double phi, double dq, double* Sq, double* dr, double* gr, int N ) |
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46 | { |
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47 | double* data = malloc( sizeof(double) * N ); |
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48 | int n; |
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49 | for ( n = 0; n < N; n++ ) |
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50 | data[n] = n * ( Sq[n] - 1 ); |
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51 | |
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52 | // data[k] -> sum( data[n] * exp(-2*pi*i*n*k/N), {n, 0, N-1 }) |
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53 | int stride = 1; |
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54 | int error = gsl_fft_real_radix2_transform( data, stride, N ); |
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55 | |
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56 | // if no errors detected |
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57 | if ( error == GSL_SUCCESS ) |
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58 | { |
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59 | double alpha = N * pow( dq, 3 ) / ( 24 * M_PI * M_PI * phi ); |
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60 | |
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61 | |
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62 | *dr = 2 * M_PI / ( N * dq ); |
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63 | int k; |
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64 | double real, imag; |
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65 | for ( k = 0; k < N; k++ ) |
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66 | { |
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67 | // the solutions of the transform is stored in data, |
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68 | // consult GSL manual for more details |
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69 | if ( k == 0 || k == N / 2) |
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70 | { |
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71 | real = data[k]; |
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72 | imag = 0; |
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73 | } |
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74 | else if ( k < N / 2 ) |
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75 | { |
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76 | real = data[k]; |
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77 | imag = data[N-k]; |
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78 | } |
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79 | else if ( k > N / 2 ) |
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80 | { |
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81 | real = data[N-k]; |
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82 | imag = -data[k]; |
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83 | } |
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84 | |
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85 | if ( k == 0 ) |
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86 | gr[k] = 0; |
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87 | else |
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88 | gr[k] = 1. + alpha / k * (-imag); |
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89 | } |
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90 | } |
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91 | // if N is not a power of two |
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92 | else if ( error == GSL_EDOM ) |
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93 | { |
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94 | printf( "N is not a power of 2\n" ); |
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95 | } |
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96 | else |
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97 | { |
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98 | printf( "Could not perform DFT (discrete fourier transform)\n" ); |
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99 | } |
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100 | // release allocated memory |
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101 | free( data ); |
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102 | |
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103 | // return error value |
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104 | return error; |
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105 | } |
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106 | */ |
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107 | |
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108 | |
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109 | // this uses numerical recipes for the FFT |
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110 | // |
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111 | int PairCorrelation( double phi, double dq, double* Sq, double* dr, double* gr, int N ) |
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112 | { |
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113 | double* data = malloc( sizeof(double) * N * 2); |
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114 | int n,error,k; |
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115 | double alpha,real,imag; |
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116 | double Pi = 3.14159265358979323846264338327950288; /* pi */ |
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117 | |
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118 | |
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119 | for ( n = 0; n < N; n++ ) { |
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120 | data[2*n] = n * ( Sq[n] - 1 ); |
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121 | data[2*n+1] = 0; |
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122 | } |
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123 | // printf("start of new fft\n"); |
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124 | |
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125 | // data[k] -> sum( data[n] * exp(-2*pi*i*n*k/N), {n, 0, N-1 }) |
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126 | // int error = gsl_fft_real_radix2_transform( data, stride, N ); |
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127 | error = 1; |
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128 | dfour1( data-1, N, 1 ); //N is the number of complex points |
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129 | |
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130 | // printf("dfour1 is done\n"); |
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131 | |
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132 | // if no errors detected |
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133 | if ( error == 1 ) |
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134 | { |
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135 | alpha = N * pow( dq, 3 ) / ( 24 * Pi * Pi * phi ); |
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136 | |
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137 | *dr = 2 * Pi / ( N * dq ); |
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138 | for ( k = 0; k < N; k++ ) |
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139 | { |
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140 | // the solutions of the transform is stored in data, |
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141 | // consult GSL manual for more details |
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142 | if ( 2*k == 0 || 2*k == 2*N / 2) |
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143 | { |
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144 | real = data[2*k]; |
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145 | imag = 0; |
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146 | } |
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147 | else if ( 2*k < 2*N / 2 ) |
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148 | { |
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149 | real = data[2*k]; |
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150 | imag = data[2*k+1]; |
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151 | } |
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152 | else if ( 2*k > 2*N / 2 ) |
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153 | { |
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154 | real = data[2*k]; |
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155 | imag = -data[2*k+1]; |
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156 | } |
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157 | |
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158 | if ( k == 0 ) |
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159 | gr[k] = 0; |
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160 | else |
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161 | // gr[k] = 1. + alpha / k * (-imag); //if using GSL |
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162 | gr[k] = 1. + alpha / k * (imag); //if using NR |
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163 | } |
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164 | } |
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165 | |
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166 | // release allocated memory |
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167 | free( data ); |
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168 | |
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169 | // printf(" done with FFT assignment -- Using Numerical Recipes, not GSL\n"); |
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170 | |
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171 | // return error value |
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172 | return error; |
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173 | } |
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174 | |
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175 | |
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176 | // isign == 1 means no scaling of output. isign == -1 multiplies output by nn |
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177 | // |
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178 | // |
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179 | #define SWAP(a,b) tempr=(a);(a)=(b);(b)=tempr |
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180 | |
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181 | void dfour1(double data[], unsigned long nn, int isign) |
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182 | { |
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183 | unsigned long n,mmax,m,j,istep,i; |
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184 | double wtemp,wr,wpr,wpi,wi,theta; |
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185 | double tempr,tempi; |
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186 | |
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187 | n=nn << 1; |
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188 | j=1; |
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189 | for (i=1;i<n;i+=2) { |
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190 | if (j > i) { |
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191 | SWAP(data[j],data[i]); |
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192 | SWAP(data[j+1],data[i+1]); |
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193 | } |
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194 | m=n >> 1; |
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195 | while (m >= 2 && j > m) { |
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196 | j -= m; |
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197 | m >>= 1; |
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198 | } |
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199 | j += m; |
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200 | } |
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201 | mmax=2; |
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202 | while (n > mmax) { |
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203 | istep=mmax << 1; |
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204 | theta=isign*(6.28318530717959/mmax); |
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205 | wtemp=sin(0.5*theta); |
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206 | wpr = -2.0*wtemp*wtemp; |
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207 | wpi=sin(theta); |
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208 | wr=1.0; |
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209 | wi=0.0; |
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210 | for (m=1;m<mmax;m+=2) { |
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211 | for (i=m;i<=n;i+=istep) { |
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212 | j=i+mmax; |
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213 | tempr=wr*data[j]-wi*data[j+1]; |
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214 | tempi=wr*data[j+1]+wi*data[j]; |
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215 | data[j]=data[i]-tempr; |
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216 | data[j+1]=data[i+1]-tempi; |
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217 | data[i] += tempr; |
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218 | data[i+1] += tempi; |
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219 | } |
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220 | wr=(wtemp=wr)*wpr-wi*wpi+wr; |
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221 | wi=wi*wpr+wtemp*wpi+wi; |
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222 | } |
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223 | mmax=istep; |
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224 | } |
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225 | } |
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226 | #undef SWAP |
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