1 | !> @file temperton_fft_mod.f90 |
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2 | !------------------------------------------------------------------------------! |
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3 | ! |
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4 | ! Current revisions: |
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5 | ! ----------------- |
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6 | ! |
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7 | ! |
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8 | ! Former revisions: |
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9 | ! ----------------- |
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10 | ! $Id: temperton_fft_mod.f90 4370 2020-01-10 14:00:44Z raasch $ |
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11 | ! unused variables removed |
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12 | ! |
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13 | ! 4366 2020-01-09 08:12:43Z raasch |
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14 | ! vectorized routines added |
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15 | ! |
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16 | ! 4182 2019-08-22 15:20:23Z scharf |
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17 | ! Corrected "Former revisions" section |
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18 | ! |
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19 | ! 3725 2019-02-07 10:11:02Z raasch |
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20 | ! GOTO statements replaced, file re-formatted corresponding to coding standards |
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21 | ! |
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22 | ! Revision 1.1 2003/03/12 16:41:59 raasch |
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23 | ! Initial revision |
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24 | ! |
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25 | ! |
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26 | ! Description: |
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27 | ! ------------ |
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28 | !> Fast Fourier transformation developed by Clive Temperton, ECMWF. |
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29 | !------------------------------------------------------------------------------! |
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30 | MODULE temperton_fft |
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31 | |
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32 | USE kinds |
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33 | |
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34 | IMPLICIT NONE |
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35 | |
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36 | PRIVATE |
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37 | |
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38 | ! |
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39 | !-- No interfaces for the serial routines, because these are still writte in FORTRAN77 |
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40 | INTERFACE fft991cy_vec |
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41 | MODULE PROCEDURE fft991cy_vec |
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42 | END INTERFACE fft991cy_vec |
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43 | |
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44 | INTERFACE qpassm_vec |
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45 | MODULE PROCEDURE qpassm_vec |
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46 | END INTERFACE qpassm_vec |
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47 | |
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48 | INTERFACE rpassm_vec |
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49 | MODULE PROCEDURE rpassm_vec |
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50 | END INTERFACE rpassm_vec |
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51 | |
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52 | PUBLIC set99, fft991cy, fft991cy_vec |
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53 | |
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54 | INTEGER(iwp), PARAMETER :: nfft = 32 !< maximum length of calls to *fft |
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55 | INTEGER(iwp), PARAMETER :: nout = 6 !< standard output stream |
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56 | |
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57 | CONTAINS |
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58 | |
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59 | !------------------------------------------------------------------------------! |
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60 | ! Description: |
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61 | ! ------------ |
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62 | !> Calls Fortran-versions of fft's. |
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63 | !> |
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64 | !> Method: |
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65 | !> |
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66 | !> Subroutine 'fft991cy' - multiple fast real periodic transform |
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67 | !> supersedes previous routine 'fft991cy'. |
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68 | !> |
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69 | !> Real transform of length n performed by removing redundant |
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70 | !> operations from complex transform of length n. |
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71 | !> |
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72 | !> a is the array containing input & output data. |
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73 | !> work is an area of size (n+1)*min(lot,nfft). |
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74 | !> trigs is a previously prepared list of trig function values. |
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75 | !> ifax is a previously prepared list of factors of n. |
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76 | !> inc is the increment within each data 'vector' |
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77 | !> (e.g. inc=1 for consecutively stored data). |
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78 | !> jump is the increment between the start of each data vector. |
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79 | !> n is the length of the data vectors. |
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80 | !> lot is the number of data vectors. |
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81 | !> isign = +1 for transform from spectral to gridpoint |
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82 | !> = -1 for transform from gridpoint to spectral. |
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83 | !> |
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84 | !> ordering of coefficients: |
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85 | !> a(0),b(0),a(1),b(1),a(2),b(2),.,a(n/2),b(n/2) |
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86 | !> where b(0)=b(n/2)=0; (n+2) locations required. |
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87 | !> |
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88 | !> ordering of data: |
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89 | !> x(0),x(1),x(2),.,x(n-1), 0 , 0 ; (n+2) locations required. |
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90 | !> |
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91 | !> Vectorization is achieved on cray by doing the transforms |
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92 | !> in parallel. |
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93 | !> |
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94 | !> n must be composed of factors 2,3 & 5 but does not have to be even. |
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95 | !> |
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96 | !> definition of transforms: |
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97 | !> |
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98 | !> isign=+1: x(j)=sum(k=0,.,n-1)(c(k)*exp(2*i*j*k*pi/n)) |
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99 | !> where c(k)=a(k)+i*b(k) and c(n-k)=a(k)-i*b(k) |
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100 | !> |
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101 | !> isign=-1: a(k)=(1/n)*sum(j=0,.,n-1)(x(j)*cos(2*j*k*pi/n)) |
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102 | !> b(k)=-(1/n)*sum(j=0,.,n-1)(x(j)*sin(2*j*k*pi/n)) |
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103 | !> |
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104 | !> calls fortran-versions of fft's !!! |
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105 | !> dimension a(n),work(n),trigs(n),ifax(1) |
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106 | !------------------------------------------------------------------------------! |
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107 | SUBROUTINE fft991cy( a, work, trigs, ifax, inc, jump, n, lot, isign ) |
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108 | |
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109 | USE kinds |
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110 | |
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111 | IMPLICIT NONE |
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112 | |
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113 | INTEGER(iwp) :: inc !< |
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114 | INTEGER(iwp) :: isign !< |
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115 | INTEGER(iwp) :: jump !< |
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116 | INTEGER(iwp) :: lot !< |
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117 | INTEGER(iwp) :: n !< |
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118 | |
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119 | REAL(wp) :: a(*) !< |
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120 | REAL(wp) :: trigs(*) !< |
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121 | REAL(wp) :: work(*) !< |
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122 | INTEGER(iwp) :: ifax(*) !< |
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123 | |
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124 | INTEGER(iwp) :: i !< |
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125 | INTEGER(iwp) :: ia !< |
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126 | INTEGER(iwp) :: ibase !< |
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127 | INTEGER(iwp) :: ierr !< |
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128 | INTEGER(iwp) :: ifac !< |
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129 | INTEGER(iwp) :: igo !< |
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130 | INTEGER(iwp) :: ii !< |
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131 | INTEGER(iwp) :: istart !< |
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132 | INTEGER(iwp) :: ix !< |
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133 | INTEGER(iwp) :: iz !< |
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134 | INTEGER(iwp) :: j !< |
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135 | INTEGER(iwp) :: jbase !< |
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136 | INTEGER(iwp) :: jj !< |
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137 | INTEGER(iwp) :: k !< |
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138 | INTEGER(iwp) :: la !< |
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139 | INTEGER(iwp) :: nb !< |
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140 | INTEGER(iwp) :: nblox !< |
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141 | INTEGER(iwp) :: nfax !< |
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142 | INTEGER(iwp) :: nvex !< |
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143 | INTEGER(iwp) :: nx !< |
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144 | |
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145 | |
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146 | IF ( ifax(10) /= n ) CALL set99( trigs, ifax, n ) |
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147 | nfax = ifax(1) |
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148 | nx = n + 1 |
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149 | IF ( MOD(n,2) == 1 ) nx = n |
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150 | nblox = 1 + (lot-1) / nfft |
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151 | nvex = lot - (nblox-1) * nfft |
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152 | |
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153 | |
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154 | IF ( isign == 1 ) THEN |
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155 | ! |
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156 | !-- Backward fft: spectral to gridpoint transform |
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157 | |
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158 | istart = 1 |
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159 | DO nb = 1, nblox |
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160 | |
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161 | ia = istart |
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162 | i = istart |
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163 | !DIR$ IVDEP |
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164 | !CDIR NODEP |
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165 | !OCL NOVREC |
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166 | DO j = 1, nvex |
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167 | a(i+inc) = 0.5_wp * a(i) |
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168 | i = i + jump |
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169 | ENDDO |
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170 | IF ( MOD(n,2) /= 1 ) THEN |
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171 | i = istart + n * inc |
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172 | DO j = 1, nvex |
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173 | a(i) = 0.5_wp * a(i) |
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174 | i = i + jump |
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175 | ENDDO |
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176 | ENDIF |
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177 | ia = istart + inc |
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178 | la = 1 |
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179 | igo = + 1 |
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180 | |
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181 | DO k = 1, nfax |
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182 | |
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183 | ifac = ifax(k+1) |
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184 | ierr = -1 |
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185 | IF ( igo /= -1 ) THEN |
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186 | CALL rpassm( a(ia), a(ia+la*inc), work(1), work(ifac*la+1), trigs, inc, 1, jump, & |
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187 | nx, nvex, n, ifac, la, ierr ) |
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188 | ELSE |
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189 | CALL rpassm( work(1), work(la+1), a(ia), a(ia+ifac*la*inc), trigs, 1, inc, nx, & |
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190 | jump, nvex, n, ifac, la, ierr ) |
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191 | ENDIF |
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192 | ! |
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193 | !-- Following messages shouldn't appear in PALM applications |
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194 | IF ( ierr /= 0 ) THEN |
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195 | SELECT CASE (ierr) |
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196 | CASE (:-1) |
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197 | WRITE (nout,'(A,I5,A)') ' Vector length =',nvex,', greater than nfft' |
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198 | CASE (0) |
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199 | WRITE (nout,'(A,I3,A)') ' Factor =',ifac,', not catered for' |
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200 | CASE (1:) |
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201 | WRITE (nout,'(A,I3,A)') ' Factor =',ifac,', only catered for if la*ifac=n' |
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202 | END SELECT |
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203 | RETURN |
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204 | ENDIF |
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205 | |
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206 | la = ifac * la |
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207 | igo = -igo |
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208 | ia = istart |
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209 | |
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210 | ENDDO |
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211 | ! |
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212 | !-- If necessary, copy results back to a |
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213 | IF ( MOD(nfax,2) /= 0 ) THEN |
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214 | ibase = 1 |
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215 | jbase = ia |
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216 | DO jj = 1, nvex |
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217 | i = ibase |
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218 | j = jbase |
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219 | DO ii = 1, n |
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220 | a(j) = work(i) |
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221 | i = i + 1 |
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222 | j = j + inc |
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223 | ENDDO |
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224 | ibase = ibase + nx |
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225 | jbase = jbase + jump |
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226 | ENDDO |
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227 | ENDIF |
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228 | ! |
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229 | !-- Fill in zeros at end |
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230 | ix = istart + n*inc |
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231 | !DIR$ IVDEP |
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232 | !CDIR NODEP |
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233 | !OCL NOVREC |
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234 | DO j = 1, nvex |
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235 | a(ix) = 0.0_wp |
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236 | a(ix+inc) = 0.0_wp |
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237 | ix = ix + jump |
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238 | ENDDO |
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239 | istart = istart + nvex*jump |
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240 | nvex = nfft |
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241 | |
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242 | ENDDO |
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243 | |
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244 | ELSEIF ( isign == -1 ) THEN |
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245 | ! |
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246 | !-- Forward fft: gridpoint to spectral transform |
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247 | istart = 1 |
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248 | DO nb = 1, nblox |
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249 | ia = istart |
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250 | la = n |
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251 | igo = + 1 |
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252 | |
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253 | DO k = 1, nfax |
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254 | |
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255 | ifac = ifax(nfax+2-k) |
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256 | la = la / ifac |
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257 | ierr = -1 |
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258 | IF ( igo /= -1 ) THEN |
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259 | CALL qpassm( a(ia), a(ia+ifac*la*inc), work(1), work(la+1), trigs, inc, 1, jump, & |
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260 | nx, nvex, n, ifac, la, ierr ) |
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261 | ELSE |
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262 | CALL qpassm( work(1), work(ifac*la+1), a(ia), a(ia+la*inc), trigs, 1, inc, nx, & |
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263 | jump, nvex, n, ifac, la, ierr ) |
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264 | ENDIF |
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265 | ! |
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266 | !-- Following messages shouldn't appear in PALM applications |
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267 | IF ( ierr /= 0 ) THEN |
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268 | SELECT CASE (ierr) |
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269 | CASE (:-1) |
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270 | WRITE (nout,'(A,I5,A)') ' Vector length =',nvex,', greater than nfft' |
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271 | CASE (0) |
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272 | WRITE (nout,'(A,I3,A)') ' Factor =',ifac,', not catered for' |
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273 | CASE (1:) |
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274 | WRITE (nout,'(A,I3,A)') ' Factor =',ifac,', only catered for if la*ifac=n' |
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275 | END SELECT |
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276 | RETURN |
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277 | ENDIF |
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278 | |
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279 | igo = -igo |
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280 | ia = istart + inc |
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281 | |
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282 | ENDDO |
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283 | ! |
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284 | !-- If necessary, copy results back to a |
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285 | IF ( MOD(nfax,2) /= 0 ) THEN |
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286 | ibase = 1 |
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287 | jbase = ia |
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288 | DO jj = 1, nvex |
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289 | i = ibase |
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290 | j = jbase |
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291 | DO ii = 1, n |
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292 | a(j) = work(i) |
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293 | i = i + 1 |
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294 | j = j + inc |
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295 | ENDDO |
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296 | ibase = ibase + nx |
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297 | jbase = jbase + jump |
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298 | ENDDO |
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299 | ENDIF |
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300 | ! |
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301 | !-- Shift a(0) and fill in zero imag parts |
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302 | ix = istart |
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303 | !DIR$ IVDEP |
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304 | !CDIR NODEP |
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305 | !OCL NOVREC |
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306 | DO j = 1, nvex |
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307 | a(ix) = a(ix+inc) |
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308 | a(ix+inc) = 0.0_wp |
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309 | ix = ix + jump |
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310 | ENDDO |
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311 | IF ( MOD(n,2) /= 1 ) THEN |
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312 | iz = istart + (n+1) * inc |
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313 | DO j = 1, nvex |
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314 | a(iz) = 0.0_wp |
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315 | iz = iz + jump |
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316 | ENDDO |
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317 | ENDIF |
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318 | istart = istart + nvex * jump |
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319 | nvex = nfft |
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320 | |
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321 | ENDDO |
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322 | |
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323 | ENDIF |
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324 | |
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325 | END SUBROUTINE fft991cy |
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326 | |
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327 | !------------------------------------------------------------------------------! |
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328 | ! Description: |
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329 | ! ------------ |
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330 | !> Performs one pass through data as part of |
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331 | !> multiple real fft (fourier analysis) routine. |
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332 | !> |
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333 | !> Method: |
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334 | !> |
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335 | !> a is first real input vector |
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336 | !> equivalence b(1) with a(ifac*la*inc1+1) |
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337 | !> c is first real output vector |
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338 | !> equivalence d(1) with c(la*inc2+1) |
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339 | !> trigs is a precalculated list of sines & cosines |
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340 | !> inc1 is the addressing increment for a |
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341 | !> inc2 is the addressing increment for c |
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342 | !> inc3 is the increment between input vectors a |
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343 | !> inc4 is the increment between output vectors c |
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344 | !> lot is the number of vectors |
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345 | !> n is the length of the vectors |
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346 | !> ifac is the current factor of n |
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347 | !> la = n/(product of factors used so far) |
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348 | !> ierr is an error indicator: |
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349 | !> 0 - pass completed without error |
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350 | !> 1 - lot greater than nfft |
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351 | !> 2 - ifac not catered for |
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352 | !> 3 - ifac only catered for if la=n/ifac |
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353 | !------------------------------------------------------------------------------! |
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354 | SUBROUTINE qpassm( a, b, c, d, trigs, inc1, inc2, inc3, inc4, lot, n, ifac, la, ierr ) |
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355 | |
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356 | USE kinds |
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357 | |
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358 | IMPLICIT NONE |
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359 | |
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360 | INTEGER(iwp) :: ierr !< |
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361 | INTEGER(iwp) :: ifac !< |
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362 | INTEGER(iwp) :: inc1 !< |
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363 | INTEGER(iwp) :: inc2 !< |
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364 | INTEGER(iwp) :: inc3 !< |
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365 | INTEGER(iwp) :: inc4 !< |
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366 | INTEGER(iwp) :: la !< |
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367 | INTEGER(iwp) :: lot !< |
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368 | INTEGER(iwp) :: n !< |
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369 | |
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370 | ! |
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371 | !-- Arrays are dimensioned with n |
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372 | REAL(wp) :: a(*) !< |
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373 | REAL(wp) :: b(*) !< |
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374 | REAL(wp) :: c(*) !< |
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375 | REAL(wp) :: d(*) !< |
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376 | REAL(wp) :: trigs(*) !< |
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377 | |
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378 | REAL(wp) :: a0 !< |
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379 | REAL(wp) :: a1 !< |
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380 | REAL(wp) :: a10 !< |
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381 | REAL(wp) :: a11 !< |
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382 | REAL(wp) :: a2 !< |
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383 | REAL(wp) :: a20 !< |
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384 | REAL(wp) :: a21 !< |
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385 | REAL(wp) :: a3 !< |
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386 | REAL(wp) :: a4 !< |
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387 | REAL(wp) :: a5 !< |
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388 | REAL(wp) :: a6 !< |
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389 | REAL(wp) :: b0 !< |
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390 | REAL(wp) :: b1 !< |
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391 | REAL(wp) :: b10 !< |
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392 | REAL(wp) :: b11 !< |
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393 | REAL(wp) :: b2 !< |
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394 | REAL(wp) :: b20 !< |
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395 | REAL(wp) :: b21 !< |
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396 | REAL(wp) :: b3 !< |
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397 | REAL(wp) :: b4 !< |
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398 | REAL(wp) :: b5 !< |
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399 | REAL(wp) :: b6 !< |
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400 | REAL(wp) :: c1 !< |
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401 | REAL(wp) :: c2 !< |
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402 | REAL(wp) :: c3 !< |
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403 | REAL(wp) :: c4 !< |
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404 | REAL(wp) :: c5 !< |
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405 | REAL(wp) :: qrt5 !< |
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406 | REAL(wp) :: s1 !< |
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407 | REAL(wp) :: s2 !< |
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408 | REAL(wp) :: s3 !< |
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409 | REAL(wp) :: s4 !< |
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410 | REAL(wp) :: s5 !< |
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411 | REAL(wp) :: sin36 !< |
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412 | REAL(wp) :: sin45 !< |
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413 | REAL(wp) :: sin60 !< |
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414 | REAL(wp) :: sin72 !< |
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415 | REAL(wp) :: z !< |
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416 | REAL(wp) :: zqrt5 !< |
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417 | REAL(wp) :: zsin36 !< |
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418 | REAL(wp) :: zsin45 !< |
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419 | REAL(wp) :: zsin60 !< |
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420 | REAL(wp) :: zsin72 !< |
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421 | |
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422 | INTEGER(iwp) :: i !< |
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423 | INTEGER(iwp) :: ia !< |
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424 | INTEGER(iwp) :: ib !< |
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425 | INTEGER(iwp) :: ibase !< |
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426 | INTEGER(iwp) :: ic !< |
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427 | INTEGER(iwp) :: id !< |
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428 | INTEGER(iwp) :: ie !< |
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429 | INTEGER(iwp) :: if !< |
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430 | INTEGER(iwp) :: ig !< |
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431 | INTEGER(iwp) :: igo !< |
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432 | INTEGER(iwp) :: ih !< |
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433 | INTEGER(iwp) :: iink !< |
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434 | INTEGER(iwp) :: ijk !< |
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435 | INTEGER(iwp) :: ijump !< |
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436 | INTEGER(iwp) :: j !< |
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437 | INTEGER(iwp) :: ja !< |
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438 | INTEGER(iwp) :: jb !< |
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439 | INTEGER(iwp) :: jbase !< |
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440 | INTEGER(iwp) :: jc !< |
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441 | INTEGER(iwp) :: jd !< |
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442 | INTEGER(iwp) :: je !< |
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443 | INTEGER(iwp) :: jf !< |
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444 | INTEGER(iwp) :: jink !< |
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445 | INTEGER(iwp) :: k !< |
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446 | INTEGER(iwp) :: kb !< |
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447 | INTEGER(iwp) :: kc !< |
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448 | INTEGER(iwp) :: kd !< |
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449 | INTEGER(iwp) :: ke !< |
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450 | INTEGER(iwp) :: kf !< |
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451 | INTEGER(iwp) :: kstop !< |
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452 | INTEGER(iwp) :: l !< |
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453 | INTEGER(iwp) :: m !< |
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454 | |
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455 | |
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456 | DATA sin36/0.587785252292473_wp/, sin72/0.951056516295154_wp/, & |
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457 | qrt5/0.559016994374947_wp/, sin60/0.866025403784437_wp/ |
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458 | |
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459 | |
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460 | ierr = 0 |
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461 | |
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462 | IF ( lot > nfft ) THEN |
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463 | ierr = 1 |
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464 | RETURN |
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465 | ENDIF |
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466 | |
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467 | m = n / ifac |
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468 | iink = la * inc1 |
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469 | jink = la * inc2 |
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470 | ijump = (ifac-1) * iink |
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471 | kstop = ( n-ifac ) / ( 2*ifac ) |
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472 | |
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473 | ibase = 0 |
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474 | jbase = 0 |
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475 | igo = ifac - 1 |
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476 | IF ( igo == 7 ) igo = 6 |
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477 | |
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478 | IF (igo < 1 .OR. igo > 6 ) THEN |
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479 | ierr = 2 |
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480 | RETURN |
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481 | ENDIF |
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482 | |
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483 | |
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484 | SELECT CASE ( igo ) |
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485 | |
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486 | ! |
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487 | !-- Coding for factor 2 |
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488 | CASE ( 1 ) |
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489 | ia = 1 |
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490 | ib = ia + iink |
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491 | ja = 1 |
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492 | jb = ja + (2*m-la) * inc2 |
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493 | |
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494 | IF ( la /= m ) THEN |
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495 | |
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496 | DO l = 1, la |
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497 | i = ibase |
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498 | j = jbase |
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499 | !DIR$ IVDEP |
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500 | !CDIR NODEP |
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501 | !OCL NOVREC |
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502 | DO ijk = 1, lot |
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503 | c(ja+j) = a(ia+i) + a(ib+i) |
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504 | c(jb+j) = a(ia+i) - a(ib+i) |
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505 | i = i + inc3 |
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506 | j = j + inc4 |
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507 | ENDDO |
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508 | ibase = ibase + inc1 |
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509 | jbase = jbase + inc2 |
---|
510 | ENDDO |
---|
511 | |
---|
512 | ja = ja + jink |
---|
513 | jink = 2 * jink |
---|
514 | jb = jb - jink |
---|
515 | ibase = ibase + ijump |
---|
516 | ijump = 2 * ijump + iink |
---|
517 | |
---|
518 | IF ( ja /= jb ) THEN |
---|
519 | |
---|
520 | DO k = la, kstop, la |
---|
521 | kb = k + k |
---|
522 | c1 = trigs(kb+1) |
---|
523 | s1 = trigs(kb+2) |
---|
524 | jbase = 0 |
---|
525 | DO l = 1, la |
---|
526 | i = ibase |
---|
527 | j = jbase |
---|
528 | !DIR$ IVDEP |
---|
529 | !CDIR NODEP |
---|
530 | !OCL NOVREC |
---|
531 | DO ijk = 1, lot |
---|
532 | c(ja+j) = a(ia+i) + (c1*a(ib+i)+s1*b(ib+i)) |
---|
533 | c(jb+j) = a(ia+i) - (c1*a(ib+i)+s1*b(ib+i)) |
---|
534 | d(ja+j) = (c1*b(ib+i)-s1*a(ib+i)) + b(ia+i) |
---|
535 | d(jb+j) = (c1*b(ib+i)-s1*a(ib+i)) - b(ia+i) |
---|
536 | i = i + inc3 |
---|
537 | j = j + inc4 |
---|
538 | ENDDO |
---|
539 | ibase = ibase + inc1 |
---|
540 | jbase = jbase + inc2 |
---|
541 | ENDDO |
---|
542 | |
---|
543 | ibase = ibase + ijump |
---|
544 | ja = ja + jink |
---|
545 | jb = jb - jink |
---|
546 | ENDDO |
---|
547 | |
---|
548 | IF ( ja > jb ) RETURN |
---|
549 | |
---|
550 | ENDIF |
---|
551 | |
---|
552 | jbase = 0 |
---|
553 | DO l = 1, la |
---|
554 | i = ibase |
---|
555 | j = jbase |
---|
556 | !DIR$ IVDEP |
---|
557 | !CDIR NODEP |
---|
558 | !OCL NOVREC |
---|
559 | DO ijk = 1, lot |
---|
560 | c(ja+j) = a(ia+i) |
---|
561 | d(ja+j) = -a(ib+i) |
---|
562 | i = i + inc3 |
---|
563 | j = j + inc4 |
---|
564 | |
---|
565 | ENDDO |
---|
566 | ibase = ibase + inc1 |
---|
567 | jbase = jbase + inc2 |
---|
568 | ENDDO |
---|
569 | |
---|
570 | ELSE |
---|
571 | |
---|
572 | z = 1.0_wp/REAL(n,KIND=wp) |
---|
573 | DO l = 1, la |
---|
574 | i = ibase |
---|
575 | j = jbase |
---|
576 | !DIR$ IVDEP |
---|
577 | !CDIR NODEP |
---|
578 | !OCL NOVREC |
---|
579 | DO ijk = 1, lot |
---|
580 | c(ja+j) = z*(a(ia+i)+a(ib+i)) |
---|
581 | c(jb+j) = z*(a(ia+i)-a(ib+i)) |
---|
582 | i = i + inc3 |
---|
583 | j = j + inc4 |
---|
584 | ENDDO |
---|
585 | ibase = ibase + inc1 |
---|
586 | jbase = jbase + inc2 |
---|
587 | ENDDO |
---|
588 | |
---|
589 | ENDIF |
---|
590 | |
---|
591 | ! |
---|
592 | !-- Coding for factor 3 |
---|
593 | CASE ( 2 ) |
---|
594 | |
---|
595 | ia = 1 |
---|
596 | ib = ia + iink |
---|
597 | ic = ib + iink |
---|
598 | ja = 1 |
---|
599 | jb = ja + (2*m-la) * inc2 |
---|
600 | jc = jb |
---|
601 | |
---|
602 | IF ( la /= m ) THEN |
---|
603 | |
---|
604 | DO l = 1, la |
---|
605 | i = ibase |
---|
606 | j = jbase |
---|
607 | !DIR$ IVDEP |
---|
608 | !CDIR NODEP |
---|
609 | !OCL NOVREC |
---|
610 | DO ijk = 1, lot |
---|
611 | c(ja+j) = a(ia+i) + (a(ib+i)+a(ic+i)) |
---|
612 | c(jb+j) = a(ia+i) - 0.5_wp*(a(ib+i)+a(ic+i)) |
---|
613 | d(jb+j) = sin60*(a(ic+i)-a(ib+i)) |
---|
614 | i = i + inc3 |
---|
615 | j = j + inc4 |
---|
616 | ENDDO |
---|
617 | ibase = ibase + inc1 |
---|
618 | jbase = jbase + inc2 |
---|
619 | ENDDO |
---|
620 | |
---|
621 | ja = ja + jink |
---|
622 | jink = 2 * jink |
---|
623 | jb = jb + jink |
---|
624 | jc = jc - jink |
---|
625 | ibase = ibase + ijump |
---|
626 | ijump = 2 * ijump + iink |
---|
627 | |
---|
628 | IF ( ja /= jc ) THEN |
---|
629 | |
---|
630 | DO k = la, kstop, la |
---|
631 | kb = k + k |
---|
632 | kc = kb + kb |
---|
633 | c1 = trigs(kb+1) |
---|
634 | s1 = trigs(kb+2) |
---|
635 | c2 = trigs(kc+1) |
---|
636 | s2 = trigs(kc+2) |
---|
637 | |
---|
638 | jbase = 0 |
---|
639 | DO l = 1, la |
---|
640 | i = ibase |
---|
641 | j = jbase |
---|
642 | !DIR$ IVDEP |
---|
643 | !CDIR NODEP |
---|
644 | !OCL NOVREC |
---|
645 | DO ijk = 1, lot |
---|
646 | a1 = (c1*a(ib+i)+s1*b(ib+i)) + (c2*a(ic+i)+s2*b(ic+i)) |
---|
647 | b1 = (c1*b(ib+i)-s1*a(ib+i)) + (c2*b(ic+i)-s2*a(ic+i)) |
---|
648 | a2 = a(ia+i) - 0.5_wp*a1 |
---|
649 | b2 = b(ia+i) - 0.5_wp*b1 |
---|
650 | a3 = sin60*((c1*a(ib+i)+s1*b(ib+i))-(c2*a(ic+i)+s2*b(ic+i))) |
---|
651 | b3 = sin60*((c1*b(ib+i)-s1*a(ib+i))-(c2*b(ic+i)-s2*a(ic+i))) |
---|
652 | c(ja+j) = a(ia+i) + a1 |
---|
653 | d(ja+j) = b(ia+i) + b1 |
---|
654 | c(jb+j) = a2 + b3 |
---|
655 | d(jb+j) = b2 - a3 |
---|
656 | c(jc+j) = a2 - b3 |
---|
657 | d(jc+j) = -(b2+a3) |
---|
658 | i = i + inc3 |
---|
659 | j = j + inc4 |
---|
660 | ENDDO |
---|
661 | ibase = ibase + inc1 |
---|
662 | jbase = jbase + inc2 |
---|
663 | ENDDO |
---|
664 | ibase = ibase + ijump |
---|
665 | ja = ja + jink |
---|
666 | jb = jb + jink |
---|
667 | jc = jc - jink |
---|
668 | ENDDO |
---|
669 | |
---|
670 | IF ( ja > jc ) RETURN |
---|
671 | |
---|
672 | ENDIF |
---|
673 | |
---|
674 | jbase = 0 |
---|
675 | DO l = 1, la |
---|
676 | i = ibase |
---|
677 | j = jbase |
---|
678 | !DIR$ IVDEP |
---|
679 | !CDIR NODEP |
---|
680 | !OCL NOVREC |
---|
681 | DO ijk = 1, lot |
---|
682 | c(ja+j) = a(ia+i) + 0.5_wp*(a(ib+i)-a(ic+i)) |
---|
683 | d(ja+j) = -sin60*(a(ib+i)+a(ic+i)) |
---|
684 | c(jb+j) = a(ia+i) - (a(ib+i)-a(ic+i)) |
---|
685 | i = i + inc3 |
---|
686 | j = j + inc4 |
---|
687 | ENDDO |
---|
688 | ibase = ibase + inc1 |
---|
689 | jbase = jbase + inc2 |
---|
690 | ENDDO |
---|
691 | |
---|
692 | ELSE |
---|
693 | |
---|
694 | z = 1.0_wp / REAL( n, KIND=wp ) |
---|
695 | zsin60 = z*sin60 |
---|
696 | DO l = 1, la |
---|
697 | i = ibase |
---|
698 | j = jbase |
---|
699 | !DIR$ IVDEP |
---|
700 | !CDIR NODEP |
---|
701 | !OCL NOVREC |
---|
702 | DO ijk = 1, lot |
---|
703 | c(ja+j) = z*(a(ia+i)+(a(ib+i)+a(ic+i))) |
---|
704 | c(jb+j) = z*(a(ia+i)-0.5_wp*(a(ib+i)+a(ic+i))) |
---|
705 | d(jb+j) = zsin60*(a(ic+i)-a(ib+i)) |
---|
706 | i = i + inc3 |
---|
707 | j = j + inc4 |
---|
708 | ENDDO |
---|
709 | ibase = ibase + inc1 |
---|
710 | jbase = jbase + inc2 |
---|
711 | ENDDO |
---|
712 | |
---|
713 | ENDIF |
---|
714 | |
---|
715 | ! |
---|
716 | !-- Coding for factor 4 |
---|
717 | CASE ( 3 ) |
---|
718 | |
---|
719 | ia = 1 |
---|
720 | ib = ia + iink |
---|
721 | ic = ib + iink |
---|
722 | id = ic + iink |
---|
723 | ja = 1 |
---|
724 | jb = ja + (2*m-la) * inc2 |
---|
725 | jc = jb + 2*m*inc2 |
---|
726 | jd = jb |
---|
727 | |
---|
728 | IF ( la /= m ) THEN |
---|
729 | |
---|
730 | DO l = 1, la |
---|
731 | |
---|
732 | i = ibase |
---|
733 | j = jbase |
---|
734 | !DIR$ IVDEP |
---|
735 | !CDIR NODEP |
---|
736 | !OCL NOVREC |
---|
737 | DO ijk = 1, lot |
---|
738 | c(ja+j) = (a(ia+i)+a(ic+i)) + (a(ib+i)+a(id+i)) |
---|
739 | c(jc+j) = (a(ia+i)+a(ic+i)) - (a(ib+i)+a(id+i)) |
---|
740 | c(jb+j) = a(ia+i) - a(ic+i) |
---|
741 | d(jb+j) = a(id+i) - a(ib+i) |
---|
742 | i = i + inc3 |
---|
743 | j = j + inc4 |
---|
744 | ENDDO |
---|
745 | ibase = ibase + inc1 |
---|
746 | jbase = jbase + inc2 |
---|
747 | ENDDO |
---|
748 | |
---|
749 | ja = ja + jink |
---|
750 | jink = 2 * jink |
---|
751 | jb = jb + jink |
---|
752 | jc = jc - jink |
---|
753 | jd = jd - jink |
---|
754 | ibase = ibase + ijump |
---|
755 | ijump = 2 * ijump + iink |
---|
756 | |
---|
757 | IF ( jb /= jc ) THEN |
---|
758 | |
---|
759 | DO k = la, kstop, la |
---|
760 | kb = k + k |
---|
761 | kc = kb + kb |
---|
762 | kd = kc + kb |
---|
763 | c1 = trigs(kb+1) |
---|
764 | s1 = trigs(kb+2) |
---|
765 | c2 = trigs(kc+1) |
---|
766 | s2 = trigs(kc+2) |
---|
767 | c3 = trigs(kd+1) |
---|
768 | s3 = trigs(kd+2) |
---|
769 | jbase = 0 |
---|
770 | DO l = 1, la |
---|
771 | i = ibase |
---|
772 | j = jbase |
---|
773 | !DIR$ IVDEP |
---|
774 | !CDIR NODEP |
---|
775 | !OCL NOVREC |
---|
776 | DO ijk = 1, lot |
---|
777 | a0 = a(ia+i) + (c2*a(ic+i)+s2*b(ic+i)) |
---|
778 | a2 = a(ia+i) - (c2*a(ic+i)+s2*b(ic+i)) |
---|
779 | a1 = (c1*a(ib+i)+s1*b(ib+i)) + (c3*a(id+i)+s3*b(id+i)) |
---|
780 | a3 = (c1*a(ib+i)+s1*b(ib+i)) - (c3*a(id+i)+s3*b(id+i)) |
---|
781 | b0 = b(ia+i) + (c2*b(ic+i)-s2*a(ic+i)) |
---|
782 | b2 = b(ia+i) - (c2*b(ic+i)-s2*a(ic+i)) |
---|
783 | b1 = (c1*b(ib+i)-s1*a(ib+i)) + (c3*b(id+i)-s3*a(id+i)) |
---|
784 | b3 = (c1*b(ib+i)-s1*a(ib+i)) - (c3*b(id+i)-s3*a(id+i)) |
---|
785 | c(ja+j) = a0 + a1 |
---|
786 | c(jc+j) = a0 - a1 |
---|
787 | d(ja+j) = b0 + b1 |
---|
788 | d(jc+j) = b1 - b0 |
---|
789 | c(jb+j) = a2 + b3 |
---|
790 | c(jd+j) = a2 - b3 |
---|
791 | d(jb+j) = b2 - a3 |
---|
792 | d(jd+j) = -(b2+a3) |
---|
793 | i = i + inc3 |
---|
794 | j = j + inc4 |
---|
795 | ENDDO |
---|
796 | ibase = ibase + inc1 |
---|
797 | jbase = jbase + inc2 |
---|
798 | ENDDO |
---|
799 | ibase = ibase + ijump |
---|
800 | ja = ja + jink |
---|
801 | jb = jb + jink |
---|
802 | jc = jc - jink |
---|
803 | jd = jd - jink |
---|
804 | ENDDO |
---|
805 | |
---|
806 | IF ( jb > jc ) RETURN |
---|
807 | |
---|
808 | ENDIF |
---|
809 | |
---|
810 | sin45 = SQRT( 0.5_wp ) |
---|
811 | jbase = 0 |
---|
812 | DO l = 1, la |
---|
813 | i = ibase |
---|
814 | j = jbase |
---|
815 | !DIR$ IVDEP |
---|
816 | !CDIR NODEP |
---|
817 | !OCL NOVREC |
---|
818 | DO ijk = 1, lot |
---|
819 | c(ja+j) = a(ia+i) + sin45*(a(ib+i)-a(id+i)) |
---|
820 | c(jb+j) = a(ia+i) - sin45*(a(ib+i)-a(id+i)) |
---|
821 | d(ja+j) = -a(ic+i) - sin45*(a(ib+i)+a(id+i)) |
---|
822 | d(jb+j) = a(ic+i) - sin45*(a(ib+i)+a(id+i)) |
---|
823 | i = i + inc3 |
---|
824 | j = j + inc4 |
---|
825 | ENDDO |
---|
826 | ibase = ibase + inc1 |
---|
827 | jbase = jbase + inc2 |
---|
828 | ENDDO |
---|
829 | |
---|
830 | ELSE |
---|
831 | |
---|
832 | z = 1.0_wp / REAL( n, KIND=wp ) |
---|
833 | DO l = 1, la |
---|
834 | i = ibase |
---|
835 | j = jbase |
---|
836 | !DIR$ IVDEP |
---|
837 | !CDIR NODEP |
---|
838 | !OCL NOVREC |
---|
839 | DO ijk = 1, lot |
---|
840 | c(ja+j) = z*((a(ia+i)+a(ic+i))+(a(ib+i)+a(id+i))) |
---|
841 | c(jc+j) = z*((a(ia+i)+a(ic+i))-(a(ib+i)+a(id+i))) |
---|
842 | c(jb+j) = z*(a(ia+i)-a(ic+i)) |
---|
843 | d(jb+j) = z*(a(id+i)-a(ib+i)) |
---|
844 | i = i + inc3 |
---|
845 | j = j + inc4 |
---|
846 | ENDDO |
---|
847 | ibase = ibase + inc1 |
---|
848 | jbase = jbase + inc2 |
---|
849 | ENDDO |
---|
850 | |
---|
851 | ENDIF |
---|
852 | |
---|
853 | ! |
---|
854 | !-- Coding for factor 5 |
---|
855 | CASE ( 4 ) |
---|
856 | |
---|
857 | ia = 1 |
---|
858 | ib = ia + iink |
---|
859 | ic = ib + iink |
---|
860 | id = ic + iink |
---|
861 | ie = id + iink |
---|
862 | ja = 1 |
---|
863 | jb = ja + (2*m-la) * inc2 |
---|
864 | jc = jb + 2*m*inc2 |
---|
865 | jd = jc |
---|
866 | je = jb |
---|
867 | |
---|
868 | IF ( la /= m ) THEN |
---|
869 | |
---|
870 | DO l = 1, la |
---|
871 | i = ibase |
---|
872 | j = jbase |
---|
873 | !DIR$ IVDEP |
---|
874 | !CDIR NODEP |
---|
875 | !OCL NOVREC |
---|
876 | DO ijk = 1, lot |
---|
877 | a1 = a(ib+i) + a(ie+i) |
---|
878 | a3 = a(ib+i) - a(ie+i) |
---|
879 | a2 = a(ic+i) + a(id+i) |
---|
880 | a4 = a(ic+i) - a(id+i) |
---|
881 | a5 = a(ia+i) - 0.25_wp*(a1+a2) |
---|
882 | a6 = qrt5*(a1-a2) |
---|
883 | c(ja+j) = a(ia+i) + (a1+a2) |
---|
884 | c(jb+j) = a5 + a6 |
---|
885 | c(jc+j) = a5 - a6 |
---|
886 | d(jb+j) = -sin72*a3 - sin36*a4 |
---|
887 | d(jc+j) = -sin36*a3 + sin72*a4 |
---|
888 | i = i + inc3 |
---|
889 | j = j + inc4 |
---|
890 | ENDDO |
---|
891 | ibase = ibase + inc1 |
---|
892 | jbase = jbase + inc2 |
---|
893 | ENDDO |
---|
894 | |
---|
895 | ja = ja + jink |
---|
896 | jink = 2 * jink |
---|
897 | jb = jb + jink |
---|
898 | jc = jc + jink |
---|
899 | jd = jd - jink |
---|
900 | je = je - jink |
---|
901 | ibase = ibase + ijump |
---|
902 | ijump = 2 * ijump + iink |
---|
903 | |
---|
904 | IF ( jb /= jd ) THEN |
---|
905 | |
---|
906 | DO k = la, kstop, la |
---|
907 | kb = k + k |
---|
908 | kc = kb + kb |
---|
909 | kd = kc + kb |
---|
910 | ke = kd + kb |
---|
911 | c1 = trigs(kb+1) |
---|
912 | s1 = trigs(kb+2) |
---|
913 | c2 = trigs(kc+1) |
---|
914 | s2 = trigs(kc+2) |
---|
915 | c3 = trigs(kd+1) |
---|
916 | s3 = trigs(kd+2) |
---|
917 | c4 = trigs(ke+1) |
---|
918 | s4 = trigs(ke+2) |
---|
919 | jbase = 0 |
---|
920 | DO l = 1, la |
---|
921 | i = ibase |
---|
922 | j = jbase |
---|
923 | !DIR$ IVDEP |
---|
924 | !CDIR NODEP |
---|
925 | !OCL NOVREC |
---|
926 | DO ijk = 1, lot |
---|
927 | a1 = (c1*a(ib+i)+s1*b(ib+i)) + (c4*a(ie+i)+s4*b(ie+i)) |
---|
928 | a3 = (c1*a(ib+i)+s1*b(ib+i)) - (c4*a(ie+i)+s4*b(ie+i)) |
---|
929 | a2 = (c2*a(ic+i)+s2*b(ic+i)) + (c3*a(id+i)+s3*b(id+i)) |
---|
930 | a4 = (c2*a(ic+i)+s2*b(ic+i)) - (c3*a(id+i)+s3*b(id+i)) |
---|
931 | b1 = (c1*b(ib+i)-s1*a(ib+i)) + (c4*b(ie+i)-s4*a(ie+i)) |
---|
932 | b3 = (c1*b(ib+i)-s1*a(ib+i)) - (c4*b(ie+i)-s4*a(ie+i)) |
---|
933 | b2 = (c2*b(ic+i)-s2*a(ic+i)) + (c3*b(id+i)-s3*a(id+i)) |
---|
934 | b4 = (c2*b(ic+i)-s2*a(ic+i)) - (c3*b(id+i)-s3*a(id+i)) |
---|
935 | a5 = a(ia+i) - 0.25_wp*(a1+a2) |
---|
936 | a6 = qrt5*(a1-a2) |
---|
937 | b5 = b(ia+i) - 0.25_wp*(b1+b2) |
---|
938 | b6 = qrt5*(b1-b2) |
---|
939 | a10 = a5 + a6 |
---|
940 | a20 = a5 - a6 |
---|
941 | b10 = b5 + b6 |
---|
942 | b20 = b5 - b6 |
---|
943 | a11 = sin72*b3 + sin36*b4 |
---|
944 | a21 = sin36*b3 - sin72*b4 |
---|
945 | b11 = sin72*a3 + sin36*a4 |
---|
946 | b21 = sin36*a3 - sin72*a4 |
---|
947 | c(ja+j) = a(ia+i) + (a1+a2) |
---|
948 | c(jb+j) = a10 + a11 |
---|
949 | c(je+j) = a10 - a11 |
---|
950 | c(jc+j) = a20 + a21 |
---|
951 | c(jd+j) = a20 - a21 |
---|
952 | d(ja+j) = b(ia+i) + (b1+b2) |
---|
953 | d(jb+j) = b10 - b11 |
---|
954 | d(je+j) = -(b10+b11) |
---|
955 | d(jc+j) = b20 - b21 |
---|
956 | d(jd+j) = -(b20+b21) |
---|
957 | i = i + inc3 |
---|
958 | j = j + inc4 |
---|
959 | ENDDO |
---|
960 | ibase = ibase + inc1 |
---|
961 | jbase = jbase + inc2 |
---|
962 | ENDDO |
---|
963 | ibase = ibase + ijump |
---|
964 | ja = ja + jink |
---|
965 | jb = jb + jink |
---|
966 | jc = jc + jink |
---|
967 | jd = jd - jink |
---|
968 | je = je - jink |
---|
969 | ENDDO |
---|
970 | |
---|
971 | IF ( jb > jd ) RETURN |
---|
972 | |
---|
973 | ENDIF |
---|
974 | |
---|
975 | jbase = 0 |
---|
976 | DO l = 1, la |
---|
977 | i = ibase |
---|
978 | j = jbase |
---|
979 | !DIR$ IVDEP |
---|
980 | !CDIR NODEP |
---|
981 | !OCL NOVREC |
---|
982 | DO ijk = 1, lot |
---|
983 | a1 = a(ib+i) + a(ie+i) |
---|
984 | a3 = a(ib+i) - a(ie+i) |
---|
985 | a2 = a(ic+i) + a(id+i) |
---|
986 | a4 = a(ic+i) - a(id+i) |
---|
987 | a5 = a(ia+i) + 0.25_wp*(a3-a4) |
---|
988 | a6 = qrt5*(a3+a4) |
---|
989 | c(ja+j) = a5 + a6 |
---|
990 | c(jb+j) = a5 - a6 |
---|
991 | c(jc+j) = a(ia+i) - (a3-a4) |
---|
992 | d(ja+j) = -sin36*a1 - sin72*a2 |
---|
993 | d(jb+j) = -sin72*a1 + sin36*a2 |
---|
994 | i = i + inc3 |
---|
995 | j = j + inc4 |
---|
996 | ENDDO |
---|
997 | ibase = ibase + inc1 |
---|
998 | jbase = jbase + inc2 |
---|
999 | ENDDO |
---|
1000 | |
---|
1001 | ELSE |
---|
1002 | |
---|
1003 | z = 1.0_wp / REAL( n, KIND=wp ) |
---|
1004 | zqrt5 = z * qrt5 |
---|
1005 | zsin36 = z * sin36 |
---|
1006 | zsin72 = z * sin72 |
---|
1007 | DO l = 1, la |
---|
1008 | i = ibase |
---|
1009 | j = jbase |
---|
1010 | !DIR$ IVDEP |
---|
1011 | !CDIR NODEP |
---|
1012 | !OCL NOVREC |
---|
1013 | DO ijk = 1, lot |
---|
1014 | a1 = a(ib+i) + a(ie+i) |
---|
1015 | a3 = a(ib+i) - a(ie+i) |
---|
1016 | a2 = a(ic+i) + a(id+i) |
---|
1017 | a4 = a(ic+i) - a(id+i) |
---|
1018 | a5 = z*(a(ia+i)-0.25_wp*(a1+a2)) |
---|
1019 | a6 = zqrt5*(a1-a2) |
---|
1020 | c(ja+j) = z*(a(ia+i)+(a1+a2)) |
---|
1021 | c(jb+j) = a5 + a6 |
---|
1022 | c(jc+j) = a5 - a6 |
---|
1023 | d(jb+j) = -zsin72*a3 - zsin36*a4 |
---|
1024 | d(jc+j) = -zsin36*a3 + zsin72*a4 |
---|
1025 | i = i + inc3 |
---|
1026 | j = j + inc4 |
---|
1027 | ENDDO |
---|
1028 | ibase = ibase + inc1 |
---|
1029 | jbase = jbase + inc2 |
---|
1030 | ENDDO |
---|
1031 | |
---|
1032 | ENDIF |
---|
1033 | |
---|
1034 | ! |
---|
1035 | !-- Coding for factor 6 |
---|
1036 | CASE ( 5 ) |
---|
1037 | |
---|
1038 | ia = 1 |
---|
1039 | ib = ia + iink |
---|
1040 | ic = ib + iink |
---|
1041 | id = ic + iink |
---|
1042 | ie = id + iink |
---|
1043 | if = ie + iink |
---|
1044 | ja = 1 |
---|
1045 | jb = ja + (2*m-la) * inc2 |
---|
1046 | jc = jb + 2*m*inc2 |
---|
1047 | jd = jc + 2*m*inc2 |
---|
1048 | je = jc |
---|
1049 | jf = jb |
---|
1050 | |
---|
1051 | IF ( la /= m ) THEN |
---|
1052 | |
---|
1053 | DO l = 1, la |
---|
1054 | i = ibase |
---|
1055 | j = jbase |
---|
1056 | !DIR$ IVDEP |
---|
1057 | !CDIR NODEP |
---|
1058 | !OCL NOVREC |
---|
1059 | DO ijk = 1, lot |
---|
1060 | a11 = (a(ic+i)+a(if+i)) + (a(ib+i)+a(ie+i)) |
---|
1061 | c(ja+j) = (a(ia+i)+a(id+i)) + a11 |
---|
1062 | c(jc+j) = (a(ia+i)+a(id+i)-0.5_wp*a11) |
---|
1063 | d(jc+j) = sin60*((a(ic+i)+a(if+i))-(a(ib+i)+a(ie+i))) |
---|
1064 | a11 = (a(ic+i)-a(if+i)) + (a(ie+i)-a(ib+i)) |
---|
1065 | c(jb+j) = (a(ia+i)-a(id+i)) - 0.5_wp*a11 |
---|
1066 | d(jb+j) = sin60*((a(ie+i)-a(ib+i))-(a(ic+i)-a(if+i))) |
---|
1067 | c(jd+j) = (a(ia+i)-a(id+i)) + a11 |
---|
1068 | i = i + inc3 |
---|
1069 | j = j + inc4 |
---|
1070 | ENDDO |
---|
1071 | ibase = ibase + inc1 |
---|
1072 | jbase = jbase + inc2 |
---|
1073 | ENDDO |
---|
1074 | ja = ja + jink |
---|
1075 | jink = 2 * jink |
---|
1076 | jb = jb + jink |
---|
1077 | jc = jc + jink |
---|
1078 | jd = jd - jink |
---|
1079 | je = je - jink |
---|
1080 | jf = jf - jink |
---|
1081 | ibase = ibase + ijump |
---|
1082 | ijump = 2 * ijump + iink |
---|
1083 | |
---|
1084 | IF ( jc /= jd ) THEN |
---|
1085 | |
---|
1086 | DO k = la, kstop, la |
---|
1087 | kb = k + k |
---|
1088 | kc = kb + kb |
---|
1089 | kd = kc + kb |
---|
1090 | ke = kd + kb |
---|
1091 | kf = ke + kb |
---|
1092 | c1 = trigs(kb+1) |
---|
1093 | s1 = trigs(kb+2) |
---|
1094 | c2 = trigs(kc+1) |
---|
1095 | s2 = trigs(kc+2) |
---|
1096 | c3 = trigs(kd+1) |
---|
1097 | s3 = trigs(kd+2) |
---|
1098 | c4 = trigs(ke+1) |
---|
1099 | s4 = trigs(ke+2) |
---|
1100 | c5 = trigs(kf+1) |
---|
1101 | s5 = trigs(kf+2) |
---|
1102 | jbase = 0 |
---|
1103 | DO l = 1, la |
---|
1104 | i = ibase |
---|
1105 | j = jbase |
---|
1106 | !DIR$ IVDEP |
---|
1107 | !CDIR NODEP |
---|
1108 | !OCL NOVREC |
---|
1109 | DO ijk = 1, lot |
---|
1110 | a1 = c1*a(ib+i) + s1*b(ib+i) |
---|
1111 | b1 = c1*b(ib+i) - s1*a(ib+i) |
---|
1112 | a2 = c2*a(ic+i) + s2*b(ic+i) |
---|
1113 | b2 = c2*b(ic+i) - s2*a(ic+i) |
---|
1114 | a3 = c3*a(id+i) + s3*b(id+i) |
---|
1115 | b3 = c3*b(id+i) - s3*a(id+i) |
---|
1116 | a4 = c4*a(ie+i) + s4*b(ie+i) |
---|
1117 | b4 = c4*b(ie+i) - s4*a(ie+i) |
---|
1118 | a5 = c5*a(if+i) + s5*b(if+i) |
---|
1119 | b5 = c5*b(if+i) - s5*a(if+i) |
---|
1120 | a11 = (a2+a5) + (a1+a4) |
---|
1121 | a20 = (a(ia+i)+a3) - 0.5_wp*a11 |
---|
1122 | a21 = sin60*((a2+a5)-(a1+a4)) |
---|
1123 | b11 = (b2+b5) + (b1+b4) |
---|
1124 | b20 = (b(ia+i)+b3) - 0.5_wp*b11 |
---|
1125 | b21 = sin60*((b2+b5)-(b1+b4)) |
---|
1126 | c(ja+j) = (a(ia+i)+a3) + a11 |
---|
1127 | d(ja+j) = (b(ia+i)+b3) + b11 |
---|
1128 | c(jc+j) = a20 - b21 |
---|
1129 | d(jc+j) = a21 + b20 |
---|
1130 | c(je+j) = a20 + b21 |
---|
1131 | d(je+j) = a21 - b20 |
---|
1132 | a11 = (a2-a5) + (a4-a1) |
---|
1133 | a20 = (a(ia+i)-a3) - 0.5_wp*a11 |
---|
1134 | a21 = sin60*((a4-a1)-(a2-a5)) |
---|
1135 | b11 = (b5-b2) - (b4-b1) |
---|
1136 | b20 = (b3-b(ia+i)) - 0.5_wp*b11 |
---|
1137 | b21 = sin60*((b5-b2)+(b4-b1)) |
---|
1138 | c(jb+j) = a20 - b21 |
---|
1139 | d(jb+j) = a21 - b20 |
---|
1140 | c(jd+j) = a11 + (a(ia+i)-a3) |
---|
1141 | d(jd+j) = b11 + (b3-b(ia+i)) |
---|
1142 | c(jf+j) = a20 + b21 |
---|
1143 | d(jf+j) = a21 + b20 |
---|
1144 | i = i + inc3 |
---|
1145 | j = j + inc4 |
---|
1146 | ENDDO |
---|
1147 | ibase = ibase + inc1 |
---|
1148 | jbase = jbase + inc2 |
---|
1149 | ENDDO |
---|
1150 | ibase = ibase + ijump |
---|
1151 | ja = ja + jink |
---|
1152 | jb = jb + jink |
---|
1153 | jc = jc + jink |
---|
1154 | jd = jd - jink |
---|
1155 | je = je - jink |
---|
1156 | jf = jf - jink |
---|
1157 | ENDDO |
---|
1158 | |
---|
1159 | IF ( jc > jd ) RETURN |
---|
1160 | |
---|
1161 | ENDIF |
---|
1162 | |
---|
1163 | jbase = 0 |
---|
1164 | DO l = 1, la |
---|
1165 | i = ibase |
---|
1166 | j = jbase |
---|
1167 | !DIR$ IVDEP |
---|
1168 | !CDIR NODEP |
---|
1169 | !OCL NOVREC |
---|
1170 | DO ijk = 1, lot |
---|
1171 | c(ja+j) = (a(ia+i)+0.5_wp*(a(ic+i)-a(ie+i))) + sin60*(a(ib+i)-a(if+i)) |
---|
1172 | d(ja+j) = -(a(id+i)+0.5_wp*(a(ib+i)+a(if+i))) - sin60*(a(ic+i)+a(ie+i)) |
---|
1173 | c(jb+j) = a(ia+i) - (a(ic+i)-a(ie+i)) |
---|
1174 | d(jb+j) = a(id+i) - (a(ib+i)+a(if+i)) |
---|
1175 | c(jc+j) = (a(ia+i)+0.5_wp*(a(ic+i)-a(ie+i))) - sin60*(a(ib+i)-a(if+i)) |
---|
1176 | d(jc+j) = -(a(id+i)+0.5_wp*(a(ib+i)+a(if+i))) + sin60*(a(ic+i)+a(ie+i)) |
---|
1177 | i = i + inc3 |
---|
1178 | j = j + inc4 |
---|
1179 | ENDDO |
---|
1180 | ibase = ibase + inc1 |
---|
1181 | jbase = jbase + inc2 |
---|
1182 | ENDDO |
---|
1183 | |
---|
1184 | ELSE |
---|
1185 | |
---|
1186 | z = 1.0_wp/REAL(n,KIND=wp) |
---|
1187 | zsin60 = z*sin60 |
---|
1188 | DO l = 1, la |
---|
1189 | i = ibase |
---|
1190 | j = jbase |
---|
1191 | !DIR$ IVDEP |
---|
1192 | !CDIR NODEP |
---|
1193 | !OCL NOVREC |
---|
1194 | DO ijk = 1, lot |
---|
1195 | a11 = (a(ic+i)+a(if+i)) + (a(ib+i)+a(ie+i)) |
---|
1196 | c(ja+j) = z*((a(ia+i)+a(id+i))+a11) |
---|
1197 | c(jc+j) = z*((a(ia+i)+a(id+i))-0.5_wp*a11) |
---|
1198 | d(jc+j) = zsin60*((a(ic+i)+a(if+i))-(a(ib+i)+a(ie+i))) |
---|
1199 | a11 = (a(ic+i)-a(if+i)) + (a(ie+i)-a(ib+i)) |
---|
1200 | c(jb+j) = z*((a(ia+i)-a(id+i))-0.5_wp*a11) |
---|
1201 | d(jb+j) = zsin60*((a(ie+i)-a(ib+i))-(a(ic+i)-a(if+i))) |
---|
1202 | c(jd+j) = z*((a(ia+i)-a(id+i))+a11) |
---|
1203 | i = i + inc3 |
---|
1204 | j = j + inc4 |
---|
1205 | ENDDO |
---|
1206 | ibase = ibase + inc1 |
---|
1207 | jbase = jbase + inc2 |
---|
1208 | ENDDO |
---|
1209 | |
---|
1210 | ENDIF |
---|
1211 | |
---|
1212 | ! |
---|
1213 | !-- Coding for factor 8 |
---|
1214 | CASE ( 6 ) |
---|
1215 | |
---|
1216 | IF ( la /= m ) THEN |
---|
1217 | ierr = 3 |
---|
1218 | RETURN |
---|
1219 | ENDIF |
---|
1220 | |
---|
1221 | ia = 1 |
---|
1222 | ib = ia + iink |
---|
1223 | ic = ib + iink |
---|
1224 | id = ic + iink |
---|
1225 | ie = id + iink |
---|
1226 | if = ie + iink |
---|
1227 | ig = if + iink |
---|
1228 | ih = ig + iink |
---|
1229 | ja = 1 |
---|
1230 | jb = ja + la * inc2 |
---|
1231 | jc = jb + 2*m*inc2 |
---|
1232 | jd = jc + 2*m*inc2 |
---|
1233 | je = jd + 2*m*inc2 |
---|
1234 | z = 1.0_wp / REAL( n, KIND=wp ) |
---|
1235 | zsin45 = z * SQRT( 0.5_wp ) |
---|
1236 | |
---|
1237 | DO l = 1, la |
---|
1238 | i = ibase |
---|
1239 | j = jbase |
---|
1240 | |
---|
1241 | !DIR$ IVDEP |
---|
1242 | !CDIR NODEP |
---|
1243 | !OCL NOVREC |
---|
1244 | DO ijk = 1, lot |
---|
1245 | c(ja+j) = z*(((a(ia+i)+a(ie+i))+(a(ic+i)+a(ig+i)))+((a(id+i)+ a(ih+i))+(a(ib+i)+a(if+i)))) |
---|
1246 | c(je+j) = z*(((a(ia+i)+a(ie+i))+(a(ic+i)+a(ig+i)))-((a(id+i)+ a(ih+i))+(a(ib+i)+a(if+i)))) |
---|
1247 | c(jc+j) = z*((a(ia+i)+a(ie+i))-(a(ic+i)+a(ig+i))) |
---|
1248 | d(jc+j) = z*((a(id+i)+a(ih+i))-(a(ib+i)+a(if+i))) |
---|
1249 | c(jb+j) = z*(a(ia+i)-a(ie+i)) + zsin45*((a(ih+i)-a(id+i))-(a(if+i)-a(ib+i))) |
---|
1250 | c(jd+j) = z*(a(ia+i)-a(ie+i)) - zsin45*((a(ih+i)-a(id+i))-(a(if+i)-a(ib+i))) |
---|
1251 | d(jb+j) = zsin45*((a(ih+i)-a(id+i))+(a(if+i)-a(ib+i))) + z*(a(ig+i)-a(ic+i)) |
---|
1252 | d(jd+j) = zsin45*((a(ih+i)-a(id+i))+(a(if+i)-a(ib+i))) - z*(a(ig+i)-a(ic+i)) |
---|
1253 | i = i + inc3 |
---|
1254 | j = j + inc4 |
---|
1255 | ENDDO |
---|
1256 | ibase = ibase + inc1 |
---|
1257 | jbase = jbase + inc2 |
---|
1258 | ENDDO |
---|
1259 | |
---|
1260 | END SELECT |
---|
1261 | |
---|
1262 | END SUBROUTINE qpassm |
---|
1263 | |
---|
1264 | !------------------------------------------------------------------------------! |
---|
1265 | ! Description: |
---|
1266 | ! ------------ |
---|
1267 | !> Same as qpassm, but for backward fft |
---|
1268 | !------------------------------------------------------------------------------! |
---|
1269 | SUBROUTINE rpassm( a, b, c, d, trigs, inc1, inc2, inc3, inc4, lot, n, ifac, la, ierr ) |
---|
1270 | |
---|
1271 | USE kinds |
---|
1272 | |
---|
1273 | IMPLICIT NONE |
---|
1274 | |
---|
1275 | INTEGER(iwp) :: ierr !< |
---|
1276 | INTEGER(iwp) :: ifac !< |
---|
1277 | INTEGER(iwp) :: inc1 !< |
---|
1278 | INTEGER(iwp) :: inc2 !< |
---|
1279 | INTEGER(iwp) :: inc3 !< |
---|
1280 | INTEGER(iwp) :: inc4 !< |
---|
1281 | INTEGER(iwp) :: la !< |
---|
1282 | INTEGER(iwp) :: lot !< |
---|
1283 | INTEGER(iwp) :: n !< |
---|
1284 | ! |
---|
1285 | !-- Arrays are dimensioned with n |
---|
1286 | REAL(wp) :: a(*) !< |
---|
1287 | REAL(wp) :: b(*) !< |
---|
1288 | REAL(wp) :: c(*) !< |
---|
1289 | REAL(wp) :: d(*) !< |
---|
1290 | REAL(wp) :: trigs(*) !< |
---|
1291 | |
---|
1292 | REAL(wp) :: c1 !< |
---|
1293 | REAL(wp) :: c2 !< |
---|
1294 | REAL(wp) :: c3 !< |
---|
1295 | REAL(wp) :: c4 !< |
---|
1296 | REAL(wp) :: c5 !< |
---|
1297 | REAL(wp) :: qqrt5 !< |
---|
1298 | REAL(wp) :: qrt5 !< |
---|
1299 | REAL(wp) :: s1 !< |
---|
1300 | REAL(wp) :: s2 !< |
---|
1301 | REAL(wp) :: s3 !< |
---|
1302 | REAL(wp) :: s4 !< |
---|
1303 | REAL(wp) :: s5 !< |
---|
1304 | REAL(wp) :: sin36 !< |
---|
1305 | REAL(wp) :: sin45 !< |
---|
1306 | REAL(wp) :: sin60 !< |
---|
1307 | REAL(wp) :: sin72 !< |
---|
1308 | REAL(wp) :: ssin36 !< |
---|
1309 | REAL(wp) :: ssin45 !< |
---|
1310 | REAL(wp) :: ssin60 !< |
---|
1311 | REAL(wp) :: ssin72 !< |
---|
1312 | |
---|
1313 | INTEGER(iwp) :: i !< |
---|
1314 | INTEGER(iwp) :: ia !< |
---|
1315 | INTEGER(iwp) :: ib !< |
---|
1316 | INTEGER(iwp) :: ibase !< |
---|
1317 | INTEGER(iwp) :: ic !< |
---|
1318 | INTEGER(iwp) :: id !< |
---|
1319 | INTEGER(iwp) :: ie !< |
---|
1320 | INTEGER(iwp) :: if !< |
---|
1321 | INTEGER(iwp) :: igo !< |
---|
1322 | INTEGER(iwp) :: iink !< |
---|
1323 | INTEGER(iwp) :: ijk !< |
---|
1324 | INTEGER(iwp) :: j !< |
---|
1325 | INTEGER(iwp) :: ja !< |
---|
1326 | INTEGER(iwp) :: jb !< |
---|
1327 | INTEGER(iwp) :: jbase !< |
---|
1328 | INTEGER(iwp) :: jc !< |
---|
1329 | INTEGER(iwp) :: jd !< |
---|
1330 | INTEGER(iwp) :: je !< |
---|
1331 | INTEGER(iwp) :: jf !< |
---|
1332 | INTEGER(iwp) :: jg !< |
---|
1333 | INTEGER(iwp) :: jh !< |
---|
1334 | INTEGER(iwp) :: jink !< |
---|
1335 | INTEGER(iwp) :: jump !< |
---|
1336 | INTEGER(iwp) :: k !< |
---|
1337 | INTEGER(iwp) :: kb !< |
---|
1338 | INTEGER(iwp) :: kc !< |
---|
1339 | INTEGER(iwp) :: kd !< |
---|
1340 | INTEGER(iwp) :: ke !< |
---|
1341 | INTEGER(iwp) :: kf !< |
---|
1342 | INTEGER(iwp) :: kstop !< |
---|
1343 | INTEGER(iwp) :: l !< |
---|
1344 | INTEGER(iwp) :: m !< |
---|
1345 | |
---|
1346 | REAL(wp) :: a10(nfft) !< |
---|
1347 | REAL(wp) :: a11(nfft) !< |
---|
1348 | REAL(wp) :: a20(nfft) !< |
---|
1349 | REAL(wp) :: a21(nfft) !< |
---|
1350 | REAL(wp) :: b10(nfft) !< |
---|
1351 | REAL(wp) :: b11(nfft) !< |
---|
1352 | REAL(wp) :: b20(nfft) !< |
---|
1353 | REAL(wp) :: b21(nfft) !< |
---|
1354 | |
---|
1355 | |
---|
1356 | DATA sin36/0.587785252292473_wp/, sin72/0.951056516295154_wp/, & |
---|
1357 | qrt5/0.559016994374947_wp/, sin60/0.866025403784437_wp/ |
---|
1358 | |
---|
1359 | |
---|
1360 | ierr = 0 |
---|
1361 | |
---|
1362 | m = n / ifac |
---|
1363 | iink = la * inc1 |
---|
1364 | jink = la * inc2 |
---|
1365 | jump = (ifac-1) * jink |
---|
1366 | kstop = (n-ifac) / (2*ifac) |
---|
1367 | |
---|
1368 | IF ( lot > nfft ) THEN |
---|
1369 | ierr = 1 |
---|
1370 | RETURN |
---|
1371 | ENDIF |
---|
1372 | ibase = 0 |
---|
1373 | jbase = 0 |
---|
1374 | igo = ifac - 1 |
---|
1375 | IF ( igo == 7 ) igo = 6 |
---|
1376 | IF ( igo < 1 .OR. igo > 6 ) THEN |
---|
1377 | ierr = 2 |
---|
1378 | RETURN |
---|
1379 | ENDIF |
---|
1380 | |
---|
1381 | |
---|
1382 | SELECT CASE ( igo ) |
---|
1383 | ! |
---|
1384 | !-- Coding for factor 2 |
---|
1385 | CASE ( 1 ) |
---|
1386 | |
---|
1387 | ia = 1 |
---|
1388 | ib = ia + (2*m-la) * inc1 |
---|
1389 | ja = 1 |
---|
1390 | jb = ja + jink |
---|
1391 | |
---|
1392 | IF ( la /= m ) THEN |
---|
1393 | |
---|
1394 | DO l = 1, la |
---|
1395 | i = ibase |
---|
1396 | j = jbase |
---|
1397 | !DIR$ IVDEP |
---|
1398 | !CDIR NODEP |
---|
1399 | !OCL NOVREC |
---|
1400 | DO ijk = 1, lot |
---|
1401 | c(ja+j) = a(ia+i) + a(ib+i) |
---|
1402 | c(jb+j) = a(ia+i) - a(ib+i) |
---|
1403 | i = i + inc3 |
---|
1404 | j = j + inc4 |
---|
1405 | ENDDO |
---|
1406 | ibase = ibase + inc1 |
---|
1407 | jbase = jbase + inc2 |
---|
1408 | ENDDO |
---|
1409 | |
---|
1410 | ia = ia + iink |
---|
1411 | iink = 2 * iink |
---|
1412 | ib = ib - iink |
---|
1413 | ibase = 0 |
---|
1414 | jbase = jbase + jump |
---|
1415 | jump = 2 * jump + jink |
---|
1416 | |
---|
1417 | IF ( ia /= ib ) THEN |
---|
1418 | |
---|
1419 | DO k = la, kstop, la |
---|
1420 | kb = k + k |
---|
1421 | c1 = trigs(kb+1) |
---|
1422 | s1 = trigs(kb+2) |
---|
1423 | ibase = 0 |
---|
1424 | DO l = 1, la |
---|
1425 | i = ibase |
---|
1426 | j = jbase |
---|
1427 | !DIR$ IVDEP |
---|
1428 | !CDIR NODEP |
---|
1429 | !OCL NOVREC |
---|
1430 | DO ijk = 1, lot |
---|
1431 | c(ja+j) = a(ia+i) + a(ib+i) |
---|
1432 | d(ja+j) = b(ia+i) - b(ib+i) |
---|
1433 | c(jb+j) = c1*(a(ia+i)-a(ib+i)) - s1*(b(ia+i)+b(ib+i)) |
---|
1434 | d(jb+j) = s1*(a(ia+i)-a(ib+i)) + c1*(b(ia+i)+b(ib+i)) |
---|
1435 | i = i + inc3 |
---|
1436 | j = j + inc4 |
---|
1437 | ENDDO |
---|
1438 | ibase = ibase + inc1 |
---|
1439 | jbase = jbase + inc2 |
---|
1440 | ENDDO |
---|
1441 | ia = ia + iink |
---|
1442 | ib = ib - iink |
---|
1443 | jbase = jbase + jump |
---|
1444 | ENDDO |
---|
1445 | |
---|
1446 | IF ( ia > ib ) RETURN |
---|
1447 | |
---|
1448 | ENDIF |
---|
1449 | |
---|
1450 | ibase = 0 |
---|
1451 | DO l = 1, la |
---|
1452 | i = ibase |
---|
1453 | j = jbase |
---|
1454 | !DIR$ IVDEP |
---|
1455 | !CDIR NODEP |
---|
1456 | !OCL NOVREC |
---|
1457 | DO ijk = 1, lot |
---|
1458 | c(ja+j) = a(ia+i) |
---|
1459 | c(jb+j) = -b(ia+i) |
---|
1460 | i = i + inc3 |
---|
1461 | j = j + inc4 |
---|
1462 | ENDDO |
---|
1463 | ibase = ibase + inc1 |
---|
1464 | jbase = jbase + inc2 |
---|
1465 | ENDDO |
---|
1466 | |
---|
1467 | ELSE |
---|
1468 | |
---|
1469 | DO l = 1, la |
---|
1470 | i = ibase |
---|
1471 | j = jbase |
---|
1472 | !DIR$ IVDEP |
---|
1473 | !CDIR NODEP |
---|
1474 | !OCL NOVREC |
---|
1475 | DO ijk = 1, lot |
---|
1476 | c(ja+j) = 2.0_wp*(a(ia+i)+a(ib+i)) |
---|
1477 | c(jb+j) = 2.0_wp*(a(ia+i)-a(ib+i)) |
---|
1478 | i = i + inc3 |
---|
1479 | j = j + inc4 |
---|
1480 | ENDDO |
---|
1481 | ibase = ibase + inc1 |
---|
1482 | jbase = jbase + inc2 |
---|
1483 | ENDDO |
---|
1484 | |
---|
1485 | ENDIF |
---|
1486 | |
---|
1487 | ! |
---|
1488 | !-- Coding for factor 3 |
---|
1489 | CASE ( 2 ) |
---|
1490 | |
---|
1491 | ia = 1 |
---|
1492 | ib = ia + (2*m-la) * inc1 |
---|
1493 | ic = ib |
---|
1494 | ja = 1 |
---|
1495 | jb = ja + jink |
---|
1496 | jc = jb + jink |
---|
1497 | |
---|
1498 | IF ( la /= m ) THEN |
---|
1499 | |
---|
1500 | DO l = 1, la |
---|
1501 | i = ibase |
---|
1502 | j = jbase |
---|
1503 | !DIR$ IVDEP |
---|
1504 | !CDIR NODEP |
---|
1505 | !OCL NOVREC |
---|
1506 | DO ijk = 1, lot |
---|
1507 | c(ja+j) = a(ia+i) + a(ib+i) |
---|
1508 | c(jb+j) = (a(ia+i)-0.5_wp*a(ib+i)) - (sin60*(b(ib+i))) |
---|
1509 | c(jc+j) = (a(ia+i)-0.5_wp*a(ib+i)) + (sin60*(b(ib+i))) |
---|
1510 | i = i + inc3 |
---|
1511 | j = j + inc4 |
---|
1512 | ENDDO |
---|
1513 | ibase = ibase + inc1 |
---|
1514 | jbase = jbase + inc2 |
---|
1515 | ENDDO |
---|
1516 | ia = ia + iink |
---|
1517 | iink = 2 * iink |
---|
1518 | ib = ib + iink |
---|
1519 | ic = ic - iink |
---|
1520 | jbase = jbase + jump |
---|
1521 | jump = 2 * jump + jink |
---|
1522 | |
---|
1523 | IF ( ia /= ic ) THEN |
---|
1524 | |
---|
1525 | DO k = la, kstop, la |
---|
1526 | kb = k + k |
---|
1527 | kc = kb + kb |
---|
1528 | c1 = trigs(kb+1) |
---|
1529 | s1 = trigs(kb+2) |
---|
1530 | c2 = trigs(kc+1) |
---|
1531 | s2 = trigs(kc+2) |
---|
1532 | ibase = 0 |
---|
1533 | DO l = 1, la |
---|
1534 | i = ibase |
---|
1535 | j = jbase |
---|
1536 | !DIR$ IVDEP |
---|
1537 | !CDIR NODEP |
---|
1538 | !OCL NOVREC |
---|
1539 | DO ijk = 1, lot |
---|
1540 | c(ja+j) = a(ia+i) + (a(ib+i)+a(ic+i)) |
---|
1541 | d(ja+j) = b(ia+i) + (b(ib+i)-b(ic+i)) |
---|
1542 | c(jb+j) = c1*((a(ia+i)-0.5_wp*(a(ib+i)+a(ic+i)))-(sin60*(b(ib+i)+ b(ic+i)))) & |
---|
1543 | - s1*((b(ia+i)-0.5_wp*(b(ib+i)-b(ic+i)))+(sin60*(a(ib+i)- a(ic+i)))) |
---|
1544 | d(jb+j) = s1*((a(ia+i)-0.5_wp*(a(ib+i)+a(ic+i)))-(sin60*(b(ib+i)+ b(ic+i)))) & |
---|
1545 | + c1*((b(ia+i)-0.5_wp*(b(ib+i)-b(ic+i)))+(sin60*(a(ib+i)- a(ic+i)))) |
---|
1546 | c(jc+j) = c2*((a(ia+i)-0.5_wp*(a(ib+i)+a(ic+i)))+(sin60*(b(ib+i)+ b(ic+i)))) & |
---|
1547 | - s2*((b(ia+i)-0.5_wp*(b(ib+i)-b(ic+i)))-(sin60*(a(ib+i)- a(ic+i)))) |
---|
1548 | d(jc+j) = s2*((a(ia+i)-0.5_wp*(a(ib+i)+a(ic+i)))+(sin60*(b(ib+i)+ b(ic+i)))) & |
---|
1549 | + c2*((b(ia+i)-0.5_wp*(b(ib+i)-b(ic+i)))-(sin60*(a(ib+i)- a(ic+i)))) |
---|
1550 | i = i + inc3 |
---|
1551 | j = j + inc4 |
---|
1552 | ENDDO |
---|
1553 | ibase = ibase + inc1 |
---|
1554 | jbase = jbase + inc2 |
---|
1555 | ENDDO |
---|
1556 | ia = ia + iink |
---|
1557 | ib = ib + iink |
---|
1558 | ic = ic - iink |
---|
1559 | jbase = jbase + jump |
---|
1560 | ENDDO |
---|
1561 | |
---|
1562 | IF ( ia > ic ) RETURN |
---|
1563 | |
---|
1564 | ENDIF |
---|
1565 | |
---|
1566 | ibase = 0 |
---|
1567 | DO l = 1, la |
---|
1568 | i = ibase |
---|
1569 | j = jbase |
---|
1570 | !DIR$ IVDEP |
---|
1571 | !CDIR NODEP |
---|
1572 | !OCL NOVREC |
---|
1573 | DO ijk = 1, lot |
---|
1574 | c(ja+j) = a(ia+i) + a(ib+i) |
---|
1575 | c(jb+j) = (0.5_wp*a(ia+i)-a(ib+i)) - (sin60*b(ia+i)) |
---|
1576 | c(jc+j) = -(0.5_wp*a(ia+i)-a(ib+i)) - (sin60*b(ia+i)) |
---|
1577 | i = i + inc3 |
---|
1578 | j = j + inc4 |
---|
1579 | ENDDO |
---|
1580 | ibase = ibase + inc1 |
---|
1581 | jbase = jbase + inc2 |
---|
1582 | ENDDO |
---|
1583 | |
---|
1584 | ELSE |
---|
1585 | |
---|
1586 | ssin60 = 2.0_wp * sin60 |
---|
1587 | DO l = 1, la |
---|
1588 | i = ibase |
---|
1589 | j = jbase |
---|
1590 | !DIR$ IVDEP |
---|
1591 | !CDIR NODEP |
---|
1592 | !OCL NOVREC |
---|
1593 | DO ijk = 1, lot |
---|
1594 | c(ja+j) = 2.0_wp*(a(ia+i)+a(ib+i)) |
---|
1595 | c(jb+j) = (2.0_wp*a(ia+i)-a(ib+i)) - (ssin60*b(ib+i)) |
---|
1596 | c(jc+j) = (2.0_wp*a(ia+i)-a(ib+i)) + (ssin60*b(ib+i)) |
---|
1597 | i = i + inc3 |
---|
1598 | j = j + inc4 |
---|
1599 | ENDDO |
---|
1600 | ibase = ibase + inc1 |
---|
1601 | jbase = jbase + inc2 |
---|
1602 | ENDDO |
---|
1603 | |
---|
1604 | ENDIF |
---|
1605 | |
---|
1606 | ! |
---|
1607 | !-- Coding for factor 4 |
---|
1608 | CASE ( 3 ) |
---|
1609 | |
---|
1610 | ia = 1 |
---|
1611 | ib = ia + (2*m-la) * inc1 |
---|
1612 | ic = ib + 2*m*inc1 |
---|
1613 | id = ib |
---|
1614 | ja = 1 |
---|
1615 | jb = ja + jink |
---|
1616 | jc = jb + jink |
---|
1617 | jd = jc + jink |
---|
1618 | |
---|
1619 | IF ( la /= m ) THEN |
---|
1620 | |
---|
1621 | DO l = 1, la |
---|
1622 | i = ibase |
---|
1623 | j = jbase |
---|
1624 | !DIR$ IVDEP |
---|
1625 | !CDIR NODEP |
---|
1626 | !OCL NOVREC |
---|
1627 | DO ijk = 1, lot |
---|
1628 | c(ja+j) = (a(ia+i)+a(ic+i)) + a(ib+i) |
---|
1629 | c(jb+j) = (a(ia+i)-a(ic+i)) - b(ib+i) |
---|
1630 | c(jc+j) = (a(ia+i)+a(ic+i)) - a(ib+i) |
---|
1631 | c(jd+j) = (a(ia+i)-a(ic+i)) + b(ib+i) |
---|
1632 | i = i + inc3 |
---|
1633 | j = j + inc4 |
---|
1634 | ENDDO |
---|
1635 | ibase = ibase + inc1 |
---|
1636 | jbase = jbase + inc2 |
---|
1637 | ENDDO |
---|
1638 | ia = ia + iink |
---|
1639 | iink = 2 * iink |
---|
1640 | ib = ib + iink |
---|
1641 | ic = ic - iink |
---|
1642 | id = id - iink |
---|
1643 | jbase = jbase + jump |
---|
1644 | jump = 2 * jump + jink |
---|
1645 | |
---|
1646 | IF ( ib /= ic ) THEN |
---|
1647 | |
---|
1648 | DO k = la, kstop, la |
---|
1649 | kb = k + k |
---|
1650 | kc = kb + kb |
---|
1651 | kd = kc + kb |
---|
1652 | c1 = trigs(kb+1) |
---|
1653 | s1 = trigs(kb+2) |
---|
1654 | c2 = trigs(kc+1) |
---|
1655 | s2 = trigs(kc+2) |
---|
1656 | c3 = trigs(kd+1) |
---|
1657 | s3 = trigs(kd+2) |
---|
1658 | ibase = 0 |
---|
1659 | DO l = 1, la |
---|
1660 | i = ibase |
---|
1661 | j = jbase |
---|
1662 | !DIR$ IVDEP |
---|
1663 | !CDIR NODEP |
---|
1664 | !OCL NOVREC |
---|
1665 | DO ijk = 1, lot |
---|
1666 | c(ja+j) = (a(ia+i)+a(ic+i)) + (a(ib+i)+a(id+i)) |
---|
1667 | d(ja+j) = (b(ia+i)-b(ic+i)) + (b(ib+i)-b(id+i)) |
---|
1668 | c(jc+j) = c2*((a(ia+i)+a(ic+i))-(a(ib+i)+a(id+i))) - s2*((b(ia+i)-b(ic+i))& |
---|
1669 | -(b(ib+i)-b(id+i))) |
---|
1670 | d(jc+j) = s2*((a(ia+i)+a(ic+i))-(a(ib+i)+a(id+i))) + c2*((b(ia+i)-b(ic+i))& |
---|
1671 | -(b(ib+i)-b(id+i))) |
---|
1672 | c(jb+j) = c1*((a(ia+i)-a(ic+i))-(b(ib+i)+b(id+i))) - s1*((b(ia+i)+b(ic+i))& |
---|
1673 | +(a(ib+i)-a(id+i))) |
---|
1674 | d(jb+j) = s1*((a(ia+i)-a(ic+i))-(b(ib+i)+b(id+i))) + c1*((b(ia+i)+b(ic+i))& |
---|
1675 | +(a(ib+i)-a(id+i))) |
---|
1676 | c(jd+j) = c3*((a(ia+i)-a(ic+i))+(b(ib+i)+b(id+i))) - s3*((b(ia+i)+b(ic+i))& |
---|
1677 | -(a(ib+i)-a(id+i))) |
---|
1678 | d(jd+j) = s3*((a(ia+i)-a(ic+i))+(b(ib+i)+b(id+i))) + c3*((b(ia+i)+b(ic+i))& |
---|
1679 | -(a(ib+i)-a(id+i))) |
---|
1680 | i = i + inc3 |
---|
1681 | j = j + inc4 |
---|
1682 | ENDDO |
---|
1683 | ibase = ibase + inc1 |
---|
1684 | jbase = jbase + inc2 |
---|
1685 | ENDDO |
---|
1686 | ia = ia + iink |
---|
1687 | ib = ib + iink |
---|
1688 | ic = ic - iink |
---|
1689 | id = id - iink |
---|
1690 | jbase = jbase + jump |
---|
1691 | ENDDO |
---|
1692 | |
---|
1693 | IF ( ib > ic ) RETURN |
---|
1694 | |
---|
1695 | ENDIF |
---|
1696 | |
---|
1697 | ibase = 0 |
---|
1698 | sin45 = SQRT( 0.5_wp ) |
---|
1699 | DO l = 1, la |
---|
1700 | i = ibase |
---|
1701 | j = jbase |
---|
1702 | !DIR$ IVDEP |
---|
1703 | !CDIR NODEP |
---|
1704 | !OCL NOVREC |
---|
1705 | DO ijk = 1, lot |
---|
1706 | c(ja+j) = a(ia+i) + a(ib+i) |
---|
1707 | c(jb+j) = sin45*((a(ia+i)-a(ib+i))-(b(ia+i)+b(ib+i))) |
---|
1708 | c(jc+j) = b(ib+i) - b(ia+i) |
---|
1709 | c(jd+j) = -sin45*((a(ia+i)-a(ib+i))+(b(ia+i)+b(ib+i))) |
---|
1710 | i = i + inc3 |
---|
1711 | j = j + inc4 |
---|
1712 | ENDDO |
---|
1713 | ibase = ibase + inc1 |
---|
1714 | jbase = jbase + inc2 |
---|
1715 | ENDDO |
---|
1716 | |
---|
1717 | ELSE |
---|
1718 | |
---|
1719 | DO l = 1, la |
---|
1720 | i = ibase |
---|
1721 | j = jbase |
---|
1722 | !DIR$ IVDEP |
---|
1723 | !CDIR NODEP |
---|
1724 | !OCL NOVREC |
---|
1725 | DO ijk = 1, lot |
---|
1726 | c(ja+j) = 2.0_wp*((a(ia+i)+a(ic+i))+a(ib+i)) |
---|
1727 | c(jb+j) = 2.0_wp*((a(ia+i)-a(ic+i))-b(ib+i)) |
---|
1728 | c(jc+j) = 2.0_wp*((a(ia+i)+a(ic+i))-a(ib+i)) |
---|
1729 | c(jd+j) = 2.0_wp*((a(ia+i)-a(ic+i))+b(ib+i)) |
---|
1730 | i = i + inc3 |
---|
1731 | j = j + inc4 |
---|
1732 | ENDDO |
---|
1733 | ibase = ibase + inc1 |
---|
1734 | jbase = jbase + inc2 |
---|
1735 | ENDDO |
---|
1736 | |
---|
1737 | ENDIF |
---|
1738 | |
---|
1739 | ! |
---|
1740 | !-- Coding for factor 5 |
---|
1741 | CASE ( 4 ) |
---|
1742 | |
---|
1743 | ia = 1 |
---|
1744 | ib = ia + (2*m-la) * inc1 |
---|
1745 | ic = ib + 2*m*inc1 |
---|
1746 | id = ic |
---|
1747 | ie = ib |
---|
1748 | ja = 1 |
---|
1749 | jb = ja + jink |
---|
1750 | jc = jb + jink |
---|
1751 | jd = jc + jink |
---|
1752 | je = jd + jink |
---|
1753 | |
---|
1754 | IF ( la /= m ) THEN |
---|
1755 | |
---|
1756 | DO l = 1, la |
---|
1757 | i = ibase |
---|
1758 | j = jbase |
---|
1759 | !DIR$ IVDEP |
---|
1760 | !CDIR NODEP |
---|
1761 | !OCL NOVREC |
---|
1762 | DO ijk = 1, lot |
---|
1763 | c(ja+j) = a(ia+i) + (a(ib+i)+a(ic+i)) |
---|
1764 | c(jb+j) = ((a(ia+i)-0.25_wp*(a(ib+i)+a(ic+i)))+qrt5*(a(ib+i)-a(ic+i))) - & |
---|
1765 | (sin72*b(ib+i)+sin36*b(ic+i)) |
---|
1766 | c(jc+j) = ((a(ia+i)-0.25_wp*(a(ib+i)+a(ic+i)))-qrt5*(a(ib+i)-a(ic+i))) - & |
---|
1767 | (sin36*b(ib+i)-sin72*b(ic+i)) |
---|
1768 | c(jd+j) = ((a(ia+i)-0.25_wp*(a(ib+i)+a(ic+i)))-qrt5*(a(ib+i)-a(ic+i))) + & |
---|
1769 | (sin36*b(ib+i)-sin72*b(ic+i)) |
---|
1770 | c(je+j) = ((a(ia+i)-0.25_wp*(a(ib+i)+a(ic+i)))+qrt5*(a(ib+i)-a(ic+i))) + & |
---|
1771 | (sin72*b(ib+i)+sin36*b(ic+i)) |
---|
1772 | i = i + inc3 |
---|
1773 | j = j + inc4 |
---|
1774 | ENDDO |
---|
1775 | ibase = ibase + inc1 |
---|
1776 | jbase = jbase + inc2 |
---|
1777 | ENDDO |
---|
1778 | ia = ia + iink |
---|
1779 | iink = 2 * iink |
---|
1780 | ib = ib + iink |
---|
1781 | ic = ic + iink |
---|
1782 | id = id - iink |
---|
1783 | ie = ie - iink |
---|
1784 | jbase = jbase + jump |
---|
1785 | jump = 2 * jump + jink |
---|
1786 | |
---|
1787 | IF ( ib /= id ) THEN |
---|
1788 | |
---|
1789 | DO k = la, kstop, la |
---|
1790 | kb = k + k |
---|
1791 | kc = kb + kb |
---|
1792 | kd = kc + kb |
---|
1793 | ke = kd + kb |
---|
1794 | c1 = trigs(kb+1) |
---|
1795 | s1 = trigs(kb+2) |
---|
1796 | c2 = trigs(kc+1) |
---|
1797 | s2 = trigs(kc+2) |
---|
1798 | c3 = trigs(kd+1) |
---|
1799 | s3 = trigs(kd+2) |
---|
1800 | c4 = trigs(ke+1) |
---|
1801 | s4 = trigs(ke+2) |
---|
1802 | ibase = 0 |
---|
1803 | DO l = 1, la |
---|
1804 | i = ibase |
---|
1805 | j = jbase |
---|
1806 | !DIR$ IVDEP |
---|
1807 | !CDIR NODEP |
---|
1808 | !OCL NOVREC |
---|
1809 | DO ijk = 1, lot |
---|
1810 | a10(ijk) = (a(ia+i)-0.25_wp*((a(ib+i)+a(ie+i))+(a(ic+i)+a(id+i)))) + & |
---|
1811 | qrt5*((a(ib+i)+a(ie+i))-(a(ic+i)+a(id+i))) |
---|
1812 | a20(ijk) = (a(ia+i)-0.25_wp*((a(ib+i)+a(ie+i))+(a(ic+i)+a(id+i)))) - & |
---|
1813 | qrt5*((a(ib+i)+a(ie+i))-(a(ic+i)+a(id+i))) |
---|
1814 | b10(ijk) = (b(ia+i)-0.25_wp*((b(ib+i)-b(ie+i))+(b(ic+i)-b(id+i)))) + & |
---|
1815 | qrt5*((b(ib+i)-b(ie+i))-(b(ic+i)-b(id+i))) |
---|
1816 | b20(ijk) = (b(ia+i)-0.25_wp*((b(ib+i)-b(ie+i))+(b(ic+i)-b(id+i)))) - & |
---|
1817 | qrt5*((b(ib+i)-b(ie+i))-(b(ic+i)-b(id+i))) |
---|
1818 | a11(ijk) = sin72*(b(ib+i)+b(ie+i)) + sin36*(b(ic+i)+b(id+i)) |
---|
1819 | a21(ijk) = sin36*(b(ib+i)+b(ie+i)) - sin72*(b(ic+i)+b(id+i)) |
---|
1820 | b11(ijk) = sin72*(a(ib+i)-a(ie+i)) + sin36*(a(ic+i)-a(id+i)) |
---|
1821 | b21(ijk) = sin36*(a(ib+i)-a(ie+i)) - sin72*(a(ic+i)-a(id+i)) |
---|
1822 | c(ja+j) = a(ia+i) + ((a(ib+i)+a(ie+i))+(a(ic+i)+a(id+i))) |
---|
1823 | d(ja+j) = b(ia+i) + ((b(ib+i)-b(ie+i))+(b(ic+i)-b(id+i))) |
---|
1824 | c(jb+j) = c1*(a10(ijk)-a11(ijk)) - s1*(b10(ijk)+b11(ijk)) |
---|
1825 | d(jb+j) = s1*(a10(ijk)-a11(ijk)) + c1*(b10(ijk)+b11(ijk)) |
---|
1826 | c(je+j) = c4*(a10(ijk)+a11(ijk)) - s4*(b10(ijk)-b11(ijk)) |
---|
1827 | d(je+j) = s4*(a10(ijk)+a11(ijk)) + c4*(b10(ijk)-b11(ijk)) |
---|
1828 | c(jc+j) = c2*(a20(ijk)-a21(ijk)) - s2*(b20(ijk)+b21(ijk)) |
---|
1829 | d(jc+j) = s2*(a20(ijk)-a21(ijk)) + c2*(b20(ijk)+b21(ijk)) |
---|
1830 | c(jd+j) = c3*(a20(ijk)+a21(ijk)) - s3*(b20(ijk)-b21(ijk)) |
---|
1831 | d(jd+j) = s3*(a20(ijk)+a21(ijk)) + c3*(b20(ijk)-b21(ijk)) |
---|
1832 | |
---|
1833 | i = i + inc3 |
---|
1834 | j = j + inc4 |
---|
1835 | ENDDO |
---|
1836 | ibase = ibase + inc1 |
---|
1837 | jbase = jbase + inc2 |
---|
1838 | ENDDO |
---|
1839 | ia = ia + iink |
---|
1840 | ib = ib + iink |
---|
1841 | ic = ic + iink |
---|
1842 | id = id - iink |
---|
1843 | ie = ie - iink |
---|
1844 | jbase = jbase + jump |
---|
1845 | ENDDO |
---|
1846 | |
---|
1847 | IF ( ib > id ) RETURN |
---|
1848 | |
---|
1849 | ENDIF |
---|
1850 | |
---|
1851 | ibase = 0 |
---|
1852 | DO l = 1, la |
---|
1853 | i = ibase |
---|
1854 | j = jbase |
---|
1855 | !DIR$ IVDEP |
---|
1856 | !CDIR NODEP |
---|
1857 | !OCL NOVREC |
---|
1858 | DO ijk = 1, lot |
---|
1859 | c(ja+j) = (a(ia+i)+a(ib+i)) + a(ic+i) |
---|
1860 | c(jb+j) = (qrt5*(a(ia+i)-a(ib+i))+(0.25_wp*(a(ia+i)+a(ib+i))-a(ic+i))) - & |
---|
1861 | (sin36*b(ia+i)+sin72*b(ib+i)) |
---|
1862 | c(je+j) = -(qrt5*(a(ia+i)-a(ib+i))+(0.25_wp*(a(ia+i)+a(ib+i))-a(ic+i))) - & |
---|
1863 | (sin36*b(ia+i)+sin72*b(ib+i)) |
---|
1864 | c(jc+j) = (qrt5*(a(ia+i)-a(ib+i))-(0.25_wp*(a(ia+i)+a(ib+i))-a(ic+i))) - & |
---|
1865 | (sin72*b(ia+i)-sin36*b(ib+i)) |
---|
1866 | c(jd+j) = -(qrt5*(a(ia+i)-a(ib+i))-(0.25_wp*(a(ia+i)+a(ib+i))-a(ic+i))) - & |
---|
1867 | (sin72*b(ia+i)-sin36*b(ib+i)) |
---|
1868 | i = i + inc3 |
---|
1869 | j = j + inc4 |
---|
1870 | ENDDO |
---|
1871 | ibase = ibase + inc1 |
---|
1872 | jbase = jbase + inc2 |
---|
1873 | ENDDO |
---|
1874 | |
---|
1875 | ELSE |
---|
1876 | |
---|
1877 | qqrt5 = 2.0_wp * qrt5 |
---|
1878 | ssin36 = 2.0_wp * sin36 |
---|
1879 | ssin72 = 2.0_wp * sin72 |
---|
1880 | DO l = 1, la |
---|
1881 | i = ibase |
---|
1882 | j = jbase |
---|
1883 | !DIR$ IVDEP |
---|
1884 | !CDIR NODEP |
---|
1885 | !OCL NOVREC |
---|
1886 | DO ijk = 1, lot |
---|
1887 | c(ja+j) = 2.0_wp*(a(ia+i)+(a(ib+i)+a(ic+i))) |
---|
1888 | c(jb+j) = (2.0_wp*(a(ia+i)-0.25_wp*(a(ib+i)+a(ic+i)))+qqrt5*(a(ib+i)-a(ic+i))) & |
---|
1889 | - (ssin72*b(ib+i)+ssin36*b(ic+i)) |
---|
1890 | c(jc+j) = (2.0_wp*(a(ia+i)-0.25_wp*(a(ib+i)+a(ic+i)))-qqrt5*(a(ib+i)-a(ic+i))) & |
---|
1891 | - (ssin36*b(ib+i)-ssin72*b(ic+i)) |
---|
1892 | c(jd+j) = (2.0_wp*(a(ia+i)-0.25_wp*(a(ib+i)+a(ic+i)))-qqrt5*(a(ib+i)-a(ic+i))) & |
---|
1893 | + (ssin36*b(ib+i)-ssin72*b(ic+i)) |
---|
1894 | c(je+j) = (2.0_wp*(a(ia+i)-0.25_wp*(a(ib+i)+a(ic+i)))+qqrt5*(a(ib+i)-a(ic+i))) & |
---|
1895 | + (ssin72*b(ib+i)+ssin36*b(ic+i)) |
---|
1896 | i = i + inc3 |
---|
1897 | j = j + inc4 |
---|
1898 | ENDDO |
---|
1899 | ibase = ibase + inc1 |
---|
1900 | jbase = jbase + inc2 |
---|
1901 | ENDDO |
---|
1902 | |
---|
1903 | ENDIF |
---|
1904 | |
---|
1905 | ! |
---|
1906 | !-- Coding for factor 6 |
---|
1907 | CASE ( 5 ) |
---|
1908 | |
---|
1909 | ia = 1 |
---|
1910 | ib = ia + (2*m-la) * inc1 |
---|
1911 | ic = ib + 2*m*inc1 |
---|
1912 | id = ic + 2*m*inc1 |
---|
1913 | ie = ic |
---|
1914 | if = ib |
---|
1915 | ja = 1 |
---|
1916 | jb = ja + jink |
---|
1917 | jc = jb + jink |
---|
1918 | jd = jc + jink |
---|
1919 | je = jd + jink |
---|
1920 | jf = je + jink |
---|
1921 | |
---|
1922 | IF ( la /= m ) THEN |
---|
1923 | |
---|
1924 | DO l = 1, la |
---|
1925 | i = ibase |
---|
1926 | j = jbase |
---|
1927 | !DIR$ IVDEP |
---|
1928 | !CDIR NODEP |
---|
1929 | !OCL NOVREC |
---|
1930 | DO ijk = 1, lot |
---|
1931 | c(ja+j) = (a(ia+i)+a(id+i)) + (a(ib+i)+a(ic+i)) |
---|
1932 | c(jd+j) = (a(ia+i)-a(id+i)) - (a(ib+i)-a(ic+i)) |
---|
1933 | c(jb+j) = ((a(ia+i)-a(id+i))+0.5_wp*(a(ib+i)-a(ic+i))) - (sin60*(b(ib+i)+b(ic+i))) |
---|
1934 | c(jf+j) = ((a(ia+i)-a(id+i))+0.5_wp*(a(ib+i)-a(ic+i))) + (sin60*(b(ib+i)+b(ic+i))) |
---|
1935 | c(jc+j) = ((a(ia+i)+a(id+i))-0.5_wp*(a(ib+i)+a(ic+i))) - (sin60*(b(ib+i)-b(ic+i))) |
---|
1936 | c(je+j) = ((a(ia+i)+a(id+i))-0.5_wp*(a(ib+i)+a(ic+i))) + (sin60*(b(ib+i)-b(ic+i))) |
---|
1937 | i = i + inc3 |
---|
1938 | j = j + inc4 |
---|
1939 | ENDDO |
---|
1940 | ibase = ibase + inc1 |
---|
1941 | jbase = jbase + inc2 |
---|
1942 | ENDDO |
---|
1943 | ia = ia + iink |
---|
1944 | iink = 2 * iink |
---|
1945 | ib = ib + iink |
---|
1946 | ic = ic + iink |
---|
1947 | id = id - iink |
---|
1948 | ie = ie - iink |
---|
1949 | if = if - iink |
---|
1950 | jbase = jbase + jump |
---|
1951 | jump = 2 * jump + jink |
---|
1952 | |
---|
1953 | IF ( ic /= id ) THEN |
---|
1954 | |
---|
1955 | DO k = la, kstop, la |
---|
1956 | kb = k + k |
---|
1957 | kc = kb + kb |
---|
1958 | kd = kc + kb |
---|
1959 | ke = kd + kb |
---|
1960 | kf = ke + kb |
---|
1961 | c1 = trigs(kb+1) |
---|
1962 | s1 = trigs(kb+2) |
---|
1963 | c2 = trigs(kc+1) |
---|
1964 | s2 = trigs(kc+2) |
---|
1965 | c3 = trigs(kd+1) |
---|
1966 | s3 = trigs(kd+2) |
---|
1967 | c4 = trigs(ke+1) |
---|
1968 | s4 = trigs(ke+2) |
---|
1969 | c5 = trigs(kf+1) |
---|
1970 | s5 = trigs(kf+2) |
---|
1971 | ibase = 0 |
---|
1972 | DO l = 1, la |
---|
1973 | i = ibase |
---|
1974 | j = jbase |
---|
1975 | !DIR$ IVDEP |
---|
1976 | !CDIR NODEP |
---|
1977 | !OCL NOVREC |
---|
1978 | DO ijk = 1, lot |
---|
1979 | a11(ijk) = (a(ie+i)+a(ib+i)) + (a(ic+i)+a(if+i)) |
---|
1980 | a20(ijk) = (a(ia+i)+a(id+i)) - 0.5_wp*a11(ijk) |
---|
1981 | a21(ijk) = sin60*((a(ie+i)+a(ib+i))-(a(ic+i)+a(if+i))) |
---|
1982 | b11(ijk) = (b(ib+i)-b(ie+i)) + (b(ic+i)-b(if+i)) |
---|
1983 | b20(ijk) = (b(ia+i)-b(id+i)) - 0.5_wp*b11(ijk) |
---|
1984 | b21(ijk) = sin60*((b(ib+i)-b(ie+i))-(b(ic+i)-b(if+i))) |
---|
1985 | |
---|
1986 | c(ja+j) = (a(ia+i)+a(id+i)) + a11(ijk) |
---|
1987 | d(ja+j) = (b(ia+i)-b(id+i)) + b11(ijk) |
---|
1988 | c(jc+j) = c2*(a20(ijk)-b21(ijk)) - s2*(b20(ijk)+a21(ijk)) |
---|
1989 | d(jc+j) = s2*(a20(ijk)-b21(ijk)) + c2*(b20(ijk)+a21(ijk)) |
---|
1990 | c(je+j) = c4*(a20(ijk)+b21(ijk)) - s4*(b20(ijk)-a21(ijk)) |
---|
1991 | d(je+j) = s4*(a20(ijk)+b21(ijk)) + c4*(b20(ijk)-a21(ijk)) |
---|
1992 | |
---|
1993 | a11(ijk) = (a(ie+i)-a(ib+i)) + (a(ic+i)-a(if+i)) |
---|
1994 | b11(ijk) = (b(ie+i)+b(ib+i)) - (b(ic+i)+b(if+i)) |
---|
1995 | a20(ijk) = (a(ia+i)-a(id+i)) - 0.5_wp*a11(ijk) |
---|
1996 | a21(ijk) = sin60*((a(ie+i)-a(ib+i))-(a(ic+i)-a(if+i))) |
---|
1997 | b20(ijk) = (b(ia+i)+b(id+i)) + 0.5_wp*b11(ijk) |
---|
1998 | b21(ijk) = sin60*((b(ie+i)+b(ib+i))+(b(ic+i)+b(if+i))) |
---|
1999 | |
---|
2000 | c(jd+j) = c3*((a(ia+i)-a(id+i))+a11(ijk)) - s3*((b(ia+i)+b(id+i))-b11(ijk)) |
---|
2001 | d(jd+j) = s3*((a(ia+i)-a(id+i))+a11(ijk)) + c3*((b(ia+i)+b(id+i))-b11(ijk)) |
---|
2002 | c(jb+j) = c1*(a20(ijk)-b21(ijk)) - s1*(b20(ijk)-a21(ijk)) |
---|
2003 | d(jb+j) = s1*(a20(ijk)-b21(ijk)) + c1*(b20(ijk)-a21(ijk)) |
---|
2004 | c(jf+j) = c5*(a20(ijk)+b21(ijk)) - s5*(b20(ijk)+a21(ijk)) |
---|
2005 | d(jf+j) = s5*(a20(ijk)+b21(ijk)) + c5*(b20(ijk)+a21(ijk)) |
---|
2006 | |
---|
2007 | i = i + inc3 |
---|
2008 | j = j + inc4 |
---|
2009 | ENDDO |
---|
2010 | ibase = ibase + inc1 |
---|
2011 | jbase = jbase + inc2 |
---|
2012 | ENDDO |
---|
2013 | ia = ia + iink |
---|
2014 | ib = ib + iink |
---|
2015 | ic = ic + iink |
---|
2016 | id = id - iink |
---|
2017 | ie = ie - iink |
---|
2018 | if = if - iink |
---|
2019 | jbase = jbase + jump |
---|
2020 | ENDDO |
---|
2021 | |
---|
2022 | IF ( ic > id ) RETURN |
---|
2023 | |
---|
2024 | ENDIF |
---|
2025 | |
---|
2026 | ibase = 0 |
---|
2027 | DO l = 1, la |
---|
2028 | i = ibase |
---|
2029 | j = jbase |
---|
2030 | !DIR$ IVDEP |
---|
2031 | !CDIR NODEP |
---|
2032 | !OCL NOVREC |
---|
2033 | DO ijk = 1, lot |
---|
2034 | c(ja+j) = a(ib+i) + (a(ia+i)+a(ic+i)) |
---|
2035 | c(jd+j) = b(ib+i) - (b(ia+i)+b(ic+i)) |
---|
2036 | c(jb+j) = (sin60*(a(ia+i)-a(ic+i))) - (0.5_wp*(b(ia+i)+b(ic+i))+b(ib+i)) |
---|
2037 | c(jf+j) = -(sin60*(a(ia+i)-a(ic+i))) - (0.5_wp*(b(ia+i)+b(ic+i))+b(ib+i)) |
---|
2038 | c(jc+j) = sin60*(b(ic+i)-b(ia+i)) + (0.5_wp*(a(ia+i)+a(ic+i))-a(ib+i)) |
---|
2039 | c(je+j) = sin60*(b(ic+i)-b(ia+i)) - (0.5_wp*(a(ia+i)+a(ic+i))-a(ib+i)) |
---|
2040 | i = i + inc3 |
---|
2041 | j = j + inc4 |
---|
2042 | ENDDO |
---|
2043 | ibase = ibase + inc1 |
---|
2044 | jbase = jbase + inc2 |
---|
2045 | ENDDO |
---|
2046 | |
---|
2047 | ELSE |
---|
2048 | |
---|
2049 | ssin60 = 2.0_wp * sin60 |
---|
2050 | DO l = 1, la |
---|
2051 | i = ibase |
---|
2052 | j = jbase |
---|
2053 | !DIR$ IVDEP |
---|
2054 | !CDIR NODEP |
---|
2055 | !OCL NOVREC |
---|
2056 | DO ijk = 1, lot |
---|
2057 | c(ja+j) = (2.0_wp*(a(ia+i)+a(id+i))) + (2.0_wp*(a(ib+i)+a(ic+i))) |
---|
2058 | c(jd+j) = (2.0_wp*(a(ia+i)-a(id+i))) - (2.0_wp*(a(ib+i)-a(ic+i))) |
---|
2059 | c(jb+j) = (2.0_wp*(a(ia+i)-a(id+i))+(a(ib+i)-a(ic+i))) - (ssin60*(b(ib+i)+b(ic+i))) |
---|
2060 | c(jf+j) = (2.0_wp*(a(ia+i)-a(id+i))+(a(ib+i)-a(ic+i))) + (ssin60*(b(ib+i)+b(ic+i))) |
---|
2061 | c(jc+j) = (2.0_wp*(a(ia+i)+a(id+i))-(a(ib+i)+a(ic+i))) - (ssin60*(b(ib+i)-b(ic+i))) |
---|
2062 | c(je+j) = (2.0_wp*(a(ia+i)+a(id+i))-(a(ib+i)+a(ic+i))) + (ssin60*(b(ib+i)-b(ic+i))) |
---|
2063 | i = i + inc3 |
---|
2064 | j = j + inc4 |
---|
2065 | ENDDO |
---|
2066 | ibase = ibase + inc1 |
---|
2067 | jbase = jbase + inc2 |
---|
2068 | ENDDO |
---|
2069 | |
---|
2070 | ENDIF |
---|
2071 | |
---|
2072 | ! |
---|
2073 | !-- Coding for factor 8 |
---|
2074 | CASE ( 6 ) |
---|
2075 | |
---|
2076 | IF ( la /= m ) THEN |
---|
2077 | ierr = 3 |
---|
2078 | RETURN |
---|
2079 | ENDIF |
---|
2080 | |
---|
2081 | ia = 1 |
---|
2082 | ib = ia + la*inc1 |
---|
2083 | ic = ib + 2*la*inc1 |
---|
2084 | id = ic + 2*la*inc1 |
---|
2085 | ie = id + 2*la*inc1 |
---|
2086 | ja = 1 |
---|
2087 | jb = ja + jink |
---|
2088 | jc = jb + jink |
---|
2089 | jd = jc + jink |
---|
2090 | je = jd + jink |
---|
2091 | jf = je + jink |
---|
2092 | jg = jf + jink |
---|
2093 | jh = jg + jink |
---|
2094 | ssin45 = SQRT( 2.0_wp ) |
---|
2095 | |
---|
2096 | DO l = 1, la |
---|
2097 | i = ibase |
---|
2098 | j = jbase |
---|
2099 | !DIR$ IVDEP |
---|
2100 | !CDIR NODEP |
---|
2101 | !OCL NOVREC |
---|
2102 | DO ijk = 1, lot |
---|
2103 | c(ja+j) = 2.0_wp*(((a(ia+i)+a(ie+i))+a(ic+i))+(a(ib+i)+a(id+i))) |
---|
2104 | c(je+j) = 2.0_wp*(((a(ia+i)+a(ie+i))+a(ic+i))-(a(ib+i)+a(id+i))) |
---|
2105 | c(jc+j) = 2.0_wp*(((a(ia+i)+a(ie+i))-a(ic+i))-(b(ib+i)-b(id+i))) |
---|
2106 | c(jg+j) = 2.0_wp*(((a(ia+i)+a(ie+i))-a(ic+i))+(b(ib+i)-b(id+i))) |
---|
2107 | c(jb+j) = 2.0_wp*((a(ia+i)-a(ie+i))-b(ic+i)) + ssin45*((a(ib+i)-a(id+i))-(b(ib+i)+b(id+i))) |
---|
2108 | c(jf+j) = 2.0_wp*((a(ia+i)-a(ie+i))-b(ic+i)) - ssin45*((a(ib+i)-a(id+i))-(b(ib+i)+b(id+i))) |
---|
2109 | c(jd+j) = 2.0_wp*((a(ia+i)-a(ie+i))+b(ic+i)) - ssin45*((a(ib+i)-a(id+i))+(b(ib+i)+b(id+i))) |
---|
2110 | c(jh+j) = 2.0_wp*((a(ia+i)-a(ie+i))+b(ic+i)) + ssin45*((a(ib+i)-a(id+i))+(b(ib+i)+b(id+i))) |
---|
2111 | i = i + inc3 |
---|
2112 | j = j + inc4 |
---|
2113 | ENDDO |
---|
2114 | ibase = ibase + inc1 |
---|
2115 | jbase = jbase + inc2 |
---|
2116 | ENDDO |
---|
2117 | |
---|
2118 | END SELECT |
---|
2119 | |
---|
2120 | END SUBROUTINE rpassm |
---|
2121 | |
---|
2122 | !------------------------------------------------------------------------------! |
---|
2123 | ! Description: |
---|
2124 | ! ------------ |
---|
2125 | !> Computes factors of n & trigonometric functins required by fft99 & fft991cy |
---|
2126 | !> Method: Dimension trigs(n),ifax(1),jfax(10),lfax(7) |
---|
2127 | !> subroutine 'set99' - computes factors of n & trigonometric |
---|
2128 | !> functins required by fft99 & fft991cy |
---|
2129 | !------------------------------------------------------------------------------! |
---|
2130 | SUBROUTINE set99( trigs, ifax, n ) |
---|
2131 | |
---|
2132 | |
---|
2133 | USE control_parameters, & |
---|
2134 | ONLY: message_string |
---|
2135 | |
---|
2136 | USE kinds |
---|
2137 | |
---|
2138 | IMPLICIT NONE |
---|
2139 | |
---|
2140 | INTEGER(iwp) :: n !< |
---|
2141 | |
---|
2142 | INTEGER(iwp) :: ifax(*) !< |
---|
2143 | REAL(wp) :: trigs(*) !< |
---|
2144 | |
---|
2145 | |
---|
2146 | REAL(wp) :: angle !< |
---|
2147 | REAL(wp) :: del !< |
---|
2148 | INTEGER(iwp) :: i !< |
---|
2149 | INTEGER(iwp) :: ifac !< |
---|
2150 | INTEGER(iwp) :: ixxx !< |
---|
2151 | INTEGER(iwp) :: k !< |
---|
2152 | INTEGER(iwp) :: l !< |
---|
2153 | INTEGER(iwp) :: nfax !< |
---|
2154 | INTEGER(iwp) :: nhl !< |
---|
2155 | INTEGER(iwp) :: nil !< |
---|
2156 | INTEGER(iwp) :: nu !< |
---|
2157 | |
---|
2158 | INTEGER(iwp) :: jfax(10) !< |
---|
2159 | INTEGER(iwp) :: lfax(7) !< |
---|
2160 | |
---|
2161 | DATA lfax / 6, 8, 5, 4, 3, 2, 1 / |
---|
2162 | |
---|
2163 | |
---|
2164 | ixxx = 1 |
---|
2165 | |
---|
2166 | del = 4.0_wp * ASIN( 1.0_wp ) / REAL( n, KIND=wp ) |
---|
2167 | nil = 0 |
---|
2168 | nhl = (n/2) - 1 |
---|
2169 | DO k = nil, nhl |
---|
2170 | angle = REAL( k, KIND=wp ) * del |
---|
2171 | trigs(2*k+1) = COS( angle ) |
---|
2172 | trigs(2*k+2) = SIN( angle ) |
---|
2173 | ENDDO |
---|
2174 | |
---|
2175 | ! |
---|
2176 | !-- Find factors of n (8,6,5,4,3,2; only one 8 allowed). |
---|
2177 | !-- Look for sixes first, store factors in descending order. |
---|
2178 | nu = n |
---|
2179 | ifac = 6 |
---|
2180 | k = 0 |
---|
2181 | l = 1 |
---|
2182 | |
---|
2183 | DO |
---|
2184 | |
---|
2185 | IF ( MOD( nu, ifac ) == 0 ) THEN |
---|
2186 | k = k + 1 |
---|
2187 | jfax(k) = ifac |
---|
2188 | IF ( ifac == 8 .AND. k /= 1 ) THEN |
---|
2189 | jfax(1) = 8 |
---|
2190 | jfax(k) = 6 |
---|
2191 | ENDIF |
---|
2192 | nu = nu/ifac |
---|
2193 | IF ( nu == 1 ) EXIT |
---|
2194 | IF ( ifac /= 8 ) CYCLE |
---|
2195 | ENDIF |
---|
2196 | |
---|
2197 | l = l + 1 |
---|
2198 | ifac = lfax(l) |
---|
2199 | IF (ifac < 2 ) THEN |
---|
2200 | message_string = 'number of gridpoints along x or/and y ' // & |
---|
2201 | 'contain illegal factors' // & |
---|
2202 | '&only factors 2, 3, 5 are allowed' |
---|
2203 | CALL message( 'temperton_fft', 'PA0311', 1, 2, 0, 6, 0 ) |
---|
2204 | RETURN |
---|
2205 | ENDIF |
---|
2206 | |
---|
2207 | ENDDO |
---|
2208 | ! |
---|
2209 | !-- Now reverse order of factors |
---|
2210 | nfax = k |
---|
2211 | ifax(1) = nfax |
---|
2212 | DO i = 1, nfax |
---|
2213 | ifax(nfax+2-i) = jfax(i) |
---|
2214 | ENDDO |
---|
2215 | ifax(10) = n |
---|
2216 | |
---|
2217 | END SUBROUTINE set99 |
---|
2218 | |
---|
2219 | |
---|
2220 | SUBROUTINE fft991cy_vec( a, work, trigs, ifax, n, isign ) |
---|
2221 | |
---|
2222 | USE kinds |
---|
2223 | |
---|
2224 | IMPLICIT NONE |
---|
2225 | |
---|
2226 | REAL(wp),DIMENSION(:,:) :: a !< |
---|
2227 | REAL(wp),DIMENSION(:) :: trigs !< |
---|
2228 | REAL(wp),DIMENSION(:,:) :: work !< |
---|
2229 | INTEGER(iwp),DIMENSION(:),INTENT(IN) :: ifax !< |
---|
2230 | |
---|
2231 | INTEGER(iwp) :: inc !< |
---|
2232 | INTEGER(iwp) :: isign !< |
---|
2233 | INTEGER(iwp) :: jump !< |
---|
2234 | INTEGER(iwp) :: lot !< |
---|
2235 | INTEGER(iwp) :: n !< |
---|
2236 | |
---|
2237 | |
---|
2238 | INTEGER(iwp) :: i !< |
---|
2239 | INTEGER(iwp) :: ia !< |
---|
2240 | INTEGER(iwp) :: ibase !< |
---|
2241 | INTEGER(iwp) :: ierr !< |
---|
2242 | INTEGER(iwp) :: ifac !< |
---|
2243 | INTEGER(iwp) :: igo !< |
---|
2244 | INTEGER(iwp) :: ii !< |
---|
2245 | INTEGER(iwp) :: istart !< |
---|
2246 | INTEGER(iwp) :: ix !< |
---|
2247 | INTEGER(iwp) :: iz !< |
---|
2248 | INTEGER(iwp) :: j !< |
---|
2249 | INTEGER(iwp) :: jbase !< |
---|
2250 | INTEGER(iwp) :: k !< |
---|
2251 | INTEGER(iwp) :: la !< |
---|
2252 | INTEGER(iwp) :: nfax !< |
---|
2253 | INTEGER(iwp) :: nvex !< |
---|
2254 | INTEGER(iwp) :: nx !< |
---|
2255 | |
---|
2256 | |
---|
2257 | inc = 1 |
---|
2258 | jump = n |
---|
2259 | lot = 1 |
---|
2260 | |
---|
2261 | IF ( ifax(10) /= n ) CALL set99( trigs, ifax, n ) |
---|
2262 | nfax = ifax(1) |
---|
2263 | nx = n + 1 |
---|
2264 | IF ( MOD(n,2) == 1 ) nx = n |
---|
2265 | nvex = 1 |
---|
2266 | |
---|
2267 | IF ( isign == 1 ) THEN |
---|
2268 | ! |
---|
2269 | !-- Backward fft: spectral to gridpoint transform |
---|
2270 | |
---|
2271 | istart = 1 |
---|
2272 | ia = istart |
---|
2273 | i = istart |
---|
2274 | a(:,i+inc) = 0.5_wp * a(:,i) |
---|
2275 | IF ( MOD(n,2) /= 1 ) THEN |
---|
2276 | i = istart + n * inc |
---|
2277 | a(:,i) = 0.5_wp * a(:,i) |
---|
2278 | ENDIF |
---|
2279 | ia = istart + inc |
---|
2280 | la = 1 |
---|
2281 | igo = + 1 |
---|
2282 | |
---|
2283 | DO k = 1, nfax |
---|
2284 | |
---|
2285 | ifac = ifax(k+1) |
---|
2286 | ierr = -1 |
---|
2287 | IF ( igo /= -1 ) THEN |
---|
2288 | CALL rpassm_vec( a(:,ia:), a(:,ia+la*inc:), work, work(:,ifac*la+1:), trigs, inc, 1, & |
---|
2289 | n, ifac, la, ierr ) |
---|
2290 | ELSE |
---|
2291 | CALL rpassm_vec( work, work(:,la+1:), a(:,ia:), a(:,ia+ifac*la*inc:), trigs, 1, inc, & |
---|
2292 | n, ifac, la, ierr ) |
---|
2293 | ENDIF |
---|
2294 | ! |
---|
2295 | !-- Following messages shouldn't appear in PALM applications |
---|
2296 | IF ( ierr /= 0 ) THEN |
---|
2297 | SELECT CASE (ierr) |
---|
2298 | CASE (:-1) |
---|
2299 | WRITE (nout,'(A,I5,A)') ' Vector length =',nvex,', greater than nfft' |
---|
2300 | CASE (0) |
---|
2301 | WRITE (nout,'(A,I3,A)') ' Factor =',ifac,', not catered for' |
---|
2302 | CASE (1:) |
---|
2303 | WRITE (nout,'(A,I3,A)') ' Factor =',ifac,', only catered for if la*ifac=n' |
---|
2304 | END SELECT |
---|
2305 | RETURN |
---|
2306 | ENDIF |
---|
2307 | |
---|
2308 | la = ifac * la |
---|
2309 | igo = -igo |
---|
2310 | ia = istart |
---|
2311 | |
---|
2312 | ENDDO |
---|
2313 | ! |
---|
2314 | !-- If necessary, copy results back to a |
---|
2315 | IF ( MOD(nfax,2) /= 0 ) THEN |
---|
2316 | ibase = 1 |
---|
2317 | jbase = ia |
---|
2318 | i = ibase |
---|
2319 | j = jbase |
---|
2320 | DO ii = 1, n |
---|
2321 | a(:,j) = work(:,i) |
---|
2322 | i = i + 1 |
---|
2323 | j = j + inc |
---|
2324 | ENDDO |
---|
2325 | ENDIF |
---|
2326 | ! |
---|
2327 | !-- Fill in zeros at end |
---|
2328 | ix = istart + n*inc |
---|
2329 | a(:,ix) = 0.0_wp |
---|
2330 | a(:,ix+inc) = 0.0_wp |
---|
2331 | |
---|
2332 | ELSEIF ( isign == -1 ) THEN |
---|
2333 | ! |
---|
2334 | !-- Forward fft: gridpoint to spectral transform |
---|
2335 | istart = 1 |
---|
2336 | ia = istart |
---|
2337 | la = n |
---|
2338 | igo = + 1 |
---|
2339 | |
---|
2340 | DO k = 1, nfax |
---|
2341 | |
---|
2342 | ifac = ifax(nfax+2-k) |
---|
2343 | la = la / ifac |
---|
2344 | ierr = -1 |
---|
2345 | |
---|
2346 | IF ( igo /= -1 ) THEN |
---|
2347 | CALL qpassm_vec( a(:,ia:), a(:,ia+ifac*la*inc:), work, work(:,la+1:), trigs, inc, 1, & |
---|
2348 | n, ifac, la, ierr ) |
---|
2349 | ELSE |
---|
2350 | CALL qpassm_vec( work, work(:,ifac*la+1:), a(:,ia:), a(:,ia+la*inc:), trigs, 1, inc, & |
---|
2351 | n, ifac, la, ierr ) |
---|
2352 | ENDIF |
---|
2353 | |
---|
2354 | ! |
---|
2355 | !-- Following messages shouldn't appear in PALM applications |
---|
2356 | IF ( ierr /= 0 ) THEN |
---|
2357 | SELECT CASE (ierr) |
---|
2358 | CASE (0) |
---|
2359 | WRITE (nout,'(A,I3,A)') ' Factor =',ifac,', not catered for' |
---|
2360 | CASE (1:) |
---|
2361 | WRITE (nout,'(A,I3,A)') ' Factor =',ifac,', only catered for if la*ifac=n' |
---|
2362 | END SELECT |
---|
2363 | RETURN |
---|
2364 | ENDIF |
---|
2365 | |
---|
2366 | igo = -igo |
---|
2367 | ia = istart + inc |
---|
2368 | |
---|
2369 | ENDDO |
---|
2370 | ! |
---|
2371 | !-- If necessary, copy results back to a |
---|
2372 | IF ( MOD(nfax,2) /= 0 ) THEN |
---|
2373 | ibase = 1 |
---|
2374 | jbase = ia |
---|
2375 | i = ibase |
---|
2376 | j = jbase |
---|
2377 | DO ii = 1, n |
---|
2378 | a(:,j) = work(:,i) |
---|
2379 | i = i + 1 |
---|
2380 | j = j + inc |
---|
2381 | ENDDO |
---|
2382 | ENDIF |
---|
2383 | ! |
---|
2384 | !-- Shift a(0) and fill in zero imag parts |
---|
2385 | ix = istart |
---|
2386 | a(:,ix) = a(:,ix+inc) |
---|
2387 | a(:,ix+inc) = 0.0_wp |
---|
2388 | |
---|
2389 | IF ( MOD(n,2) /= 1 ) THEN |
---|
2390 | iz = istart + (n+1) * inc |
---|
2391 | a(:,iz) = 0.0_wp |
---|
2392 | ENDIF |
---|
2393 | |
---|
2394 | ENDIF |
---|
2395 | |
---|
2396 | END SUBROUTINE fft991cy_vec |
---|
2397 | |
---|
2398 | !------------------------------------------------------------------------------! |
---|
2399 | ! Description: |
---|
2400 | ! ------------ |
---|
2401 | !> Performs one pass through data as part of |
---|
2402 | !> multiple real fft (fourier analysis) routine. |
---|
2403 | !> |
---|
2404 | !> Method: |
---|
2405 | !> |
---|
2406 | !> a is first real input vector |
---|
2407 | !> equivalence b(1) with a(ifac*la*inc1+1) |
---|
2408 | !> c is first real output vector |
---|
2409 | !> equivalence d(1) with c(la*inc2+1) |
---|
2410 | !> trigs is a precalculated list of sines & cosines |
---|
2411 | !> inc1 is the addressing increment for a |
---|
2412 | !> inc2 is the addressing increment for c |
---|
2413 | !> inc3 is the increment between input vectors a |
---|
2414 | !> inc4 is the increment between output vectors c |
---|
2415 | !> lot is the number of vectors |
---|
2416 | !> n is the length of the vectors |
---|
2417 | !> ifac is the current factor of n |
---|
2418 | !> la = n/(product of factors used so far) |
---|
2419 | !> ierr is an error indicator: |
---|
2420 | !> 0 - pass completed without error |
---|
2421 | !> 1 - lot greater than nfft |
---|
2422 | !> 2 - ifac not catered for |
---|
2423 | !> 3 - ifac only catered for if la=n/ifac |
---|
2424 | !------------------------------------------------------------------------------! |
---|
2425 | SUBROUTINE qpassm_vec( a, b, c, d, trigs, inc1, inc2, n, ifac, la, ierr ) |
---|
2426 | |
---|
2427 | USE kinds |
---|
2428 | |
---|
2429 | IMPLICIT NONE |
---|
2430 | |
---|
2431 | INTEGER(iwp),INTENT(IN) :: ifac !< |
---|
2432 | INTEGER(iwp),INTENT(IN) :: inc1 !< |
---|
2433 | INTEGER(iwp),INTENT(IN) :: inc2 !< |
---|
2434 | INTEGER(iwp),INTENT(IN) :: la !< |
---|
2435 | INTEGER(iwp),INTENT(IN) :: n !< |
---|
2436 | INTEGER(iwp),INTENT(OUT) :: ierr !< |
---|
2437 | |
---|
2438 | ! |
---|
2439 | !-- Arrays are dimensioned with n |
---|
2440 | REAL(wp),DIMENSION(:,:) :: a !< |
---|
2441 | REAL(wp),DIMENSION(:,:) :: b !< |
---|
2442 | REAL(wp),DIMENSION(:,:) :: c !< |
---|
2443 | REAL(wp),DIMENSION(:,:) :: d !< |
---|
2444 | REAL(wp),DIMENSION(:),INTENT(IN) :: trigs !< |
---|
2445 | |
---|
2446 | REAL(wp) :: a0 !< |
---|
2447 | REAL(wp) :: a1 !< |
---|
2448 | REAL(wp) :: a10 !< |
---|
2449 | REAL(wp) :: a11 !< |
---|
2450 | REAL(wp) :: a2 !< |
---|
2451 | REAL(wp) :: a20 !< |
---|
2452 | REAL(wp) :: a21 !< |
---|
2453 | REAL(wp) :: a3 !< |
---|
2454 | REAL(wp) :: a4 !< |
---|
2455 | REAL(wp) :: a5 !< |
---|
2456 | REAL(wp) :: a6 !< |
---|
2457 | REAL(wp) :: b0 !< |
---|
2458 | REAL(wp) :: b1 !< |
---|
2459 | REAL(wp) :: b10 !< |
---|
2460 | REAL(wp) :: b11 !< |
---|
2461 | REAL(wp) :: b2 !< |
---|
2462 | REAL(wp) :: b20 !< |
---|
2463 | REAL(wp) :: b21 !< |
---|
2464 | REAL(wp) :: b3 !< |
---|
2465 | REAL(wp) :: b4 !< |
---|
2466 | REAL(wp) :: b5 !< |
---|
2467 | REAL(wp) :: b6 !< |
---|
2468 | REAL(wp) :: c1 !< |
---|
2469 | REAL(wp) :: c2 !< |
---|
2470 | REAL(wp) :: c3 !< |
---|
2471 | REAL(wp) :: c4 !< |
---|
2472 | REAL(wp) :: c5 !< |
---|
2473 | REAL(wp) :: qrt5 !< |
---|
2474 | REAL(wp) :: s1 !< |
---|
2475 | REAL(wp) :: s2 !< |
---|
2476 | REAL(wp) :: s3 !< |
---|
2477 | REAL(wp) :: s4 !< |
---|
2478 | REAL(wp) :: s5 !< |
---|
2479 | REAL(wp) :: sin36 !< |
---|
2480 | REAL(wp) :: sin45 !< |
---|
2481 | REAL(wp) :: sin60 !< |
---|
2482 | REAL(wp) :: sin72 !< |
---|
2483 | REAL(wp) :: z !< |
---|
2484 | REAL(wp) :: zqrt5 !< |
---|
2485 | REAL(wp) :: zsin36 !< |
---|
2486 | REAL(wp) :: zsin45 !< |
---|
2487 | REAL(wp) :: zsin60 !< |
---|
2488 | REAL(wp) :: zsin72 !< |
---|
2489 | |
---|
2490 | INTEGER(iwp) :: i !< |
---|
2491 | INTEGER(iwp) :: ia !< |
---|
2492 | INTEGER(iwp) :: ib !< |
---|
2493 | INTEGER(iwp) :: ibase !< |
---|
2494 | INTEGER(iwp) :: ic !< |
---|
2495 | INTEGER(iwp) :: id !< |
---|
2496 | INTEGER(iwp) :: ie !< |
---|
2497 | INTEGER(iwp) :: if !< |
---|
2498 | INTEGER(iwp) :: ig !< |
---|
2499 | INTEGER(iwp) :: igo !< |
---|
2500 | INTEGER(iwp) :: ih !< |
---|
2501 | INTEGER(iwp) :: iink !< |
---|
2502 | INTEGER(iwp) :: ijump !< |
---|
2503 | INTEGER(iwp) :: ipl !< loop index parallel loop |
---|
2504 | INTEGER(iwp) :: j !< |
---|
2505 | INTEGER(iwp) :: ja !< |
---|
2506 | INTEGER(iwp) :: jb !< |
---|
2507 | INTEGER(iwp) :: jbase !< |
---|
2508 | INTEGER(iwp) :: jc !< |
---|
2509 | INTEGER(iwp) :: jd !< |
---|
2510 | INTEGER(iwp) :: je !< |
---|
2511 | INTEGER(iwp) :: jf !< |
---|
2512 | INTEGER(iwp) :: jink !< |
---|
2513 | INTEGER(iwp) :: k !< |
---|
2514 | INTEGER(iwp) :: kb !< |
---|
2515 | INTEGER(iwp) :: kc !< |
---|
2516 | INTEGER(iwp) :: kd !< |
---|
2517 | INTEGER(iwp) :: ke !< |
---|
2518 | INTEGER(iwp) :: kf !< |
---|
2519 | INTEGER(iwp) :: kstop !< |
---|
2520 | INTEGER(iwp) :: l !< |
---|
2521 | INTEGER(iwp) :: m !< |
---|
2522 | |
---|
2523 | |
---|
2524 | DATA sin36/0.587785252292473_wp/, sin72/0.951056516295154_wp/, & |
---|
2525 | qrt5/0.559016994374947_wp/, sin60/0.866025403784437_wp/ |
---|
2526 | |
---|
2527 | |
---|
2528 | ierr = 0 |
---|
2529 | |
---|
2530 | m = n / ifac |
---|
2531 | iink = la * inc1 |
---|
2532 | jink = la * inc2 |
---|
2533 | ijump = (ifac-1) * iink |
---|
2534 | kstop = ( n-ifac ) / ( 2*ifac ) |
---|
2535 | |
---|
2536 | ibase = 0 |
---|
2537 | jbase = 0 |
---|
2538 | igo = ifac - 1 |
---|
2539 | IF ( igo == 7 ) igo = 6 |
---|
2540 | |
---|
2541 | IF (igo < 1 .OR. igo > 6 ) THEN |
---|
2542 | ierr = 2 |
---|
2543 | RETURN |
---|
2544 | ENDIF |
---|
2545 | |
---|
2546 | |
---|
2547 | SELECT CASE ( igo ) |
---|
2548 | |
---|
2549 | ! |
---|
2550 | !-- Coding for factor 2 |
---|
2551 | CASE ( 1 ) |
---|
2552 | ia = 1 |
---|
2553 | ib = ia + iink |
---|
2554 | ja = 1 |
---|
2555 | jb = ja + (2*m-la) * inc2 |
---|
2556 | |
---|
2557 | IF ( la /= m ) THEN |
---|
2558 | |
---|
2559 | DO l = 1, la |
---|
2560 | i = ibase |
---|
2561 | j = jbase |
---|
2562 | c(:,ja+j) = a(:,ia+i) + a(:,ib+i) |
---|
2563 | c(:,jb+j) = a(:,ia+i) - a(:,ib+i) |
---|
2564 | ibase = ibase + inc1 |
---|
2565 | jbase = jbase + inc2 |
---|
2566 | ENDDO |
---|
2567 | |
---|
2568 | ja = ja + jink |
---|
2569 | jink = 2 * jink |
---|
2570 | jb = jb - jink |
---|
2571 | ibase = ibase + ijump |
---|
2572 | ijump = 2 * ijump + iink |
---|
2573 | |
---|
2574 | IF ( ja /= jb ) THEN |
---|
2575 | |
---|
2576 | DO k = la, kstop, la |
---|
2577 | kb = k + k |
---|
2578 | c1 = trigs(kb+1) |
---|
2579 | s1 = trigs(kb+2) |
---|
2580 | jbase = 0 |
---|
2581 | DO l = 1, la |
---|
2582 | i = ibase |
---|
2583 | j = jbase |
---|
2584 | c(:,ja+j) = a(:,ia+i) + (c1*a(:,ib+i)+s1*b(:,ib+i)) |
---|
2585 | c(:,jb+j) = a(:,ia+i) - (c1*a(:,ib+i)+s1*b(:,ib+i)) |
---|
2586 | d(:,ja+j) = (c1*b(:,ib+i)-s1*a(:,ib+i)) + b(:,ia+i) |
---|
2587 | d(:,jb+j) = (c1*b(:,ib+i)-s1*a(:,ib+i)) - b(:,ia+i) |
---|
2588 | ibase = ibase + inc1 |
---|
2589 | jbase = jbase + inc2 |
---|
2590 | ENDDO |
---|
2591 | |
---|
2592 | ibase = ibase + ijump |
---|
2593 | ja = ja + jink |
---|
2594 | jb = jb - jink |
---|
2595 | ENDDO |
---|
2596 | |
---|
2597 | IF ( ja > jb ) RETURN |
---|
2598 | |
---|
2599 | ENDIF |
---|
2600 | |
---|
2601 | jbase = 0 |
---|
2602 | DO l = 1, la |
---|
2603 | i = ibase |
---|
2604 | j = jbase |
---|
2605 | c(:,ja+j) = a(:,ia+i) |
---|
2606 | d(:,ja+j) = -a(:,ib+i) |
---|
2607 | ibase = ibase + inc1 |
---|
2608 | jbase = jbase + inc2 |
---|
2609 | ENDDO |
---|
2610 | |
---|
2611 | ELSE |
---|
2612 | |
---|
2613 | z = 1.0_wp/REAL(n,KIND=wp) |
---|
2614 | DO l = 1, la |
---|
2615 | i = ibase |
---|
2616 | j = jbase |
---|
2617 | c(:,ja+j) = z*(a(:,ia+i)+a(:,ib+i)) |
---|
2618 | c(:,jb+j) = z*(a(:,ia+i)-a(:,ib+i)) |
---|
2619 | ibase = ibase + inc1 |
---|
2620 | jbase = jbase + inc2 |
---|
2621 | ENDDO |
---|
2622 | |
---|
2623 | ENDIF |
---|
2624 | |
---|
2625 | ! |
---|
2626 | !-- Coding for factor 3 |
---|
2627 | CASE ( 2 ) |
---|
2628 | |
---|
2629 | ia = 1 |
---|
2630 | ib = ia + iink |
---|
2631 | ic = ib + iink |
---|
2632 | ja = 1 |
---|
2633 | jb = ja + (2*m-la) * inc2 |
---|
2634 | jc = jb |
---|
2635 | |
---|
2636 | IF ( la /= m ) THEN |
---|
2637 | |
---|
2638 | DO l = 1, la |
---|
2639 | i = ibase |
---|
2640 | j = jbase |
---|
2641 | c(:,ja+j) = a(:,ia+i) + (a(:,ib+i)+a(:,ic+i)) |
---|
2642 | c(:,jb+j) = a(:,ia+i) - 0.5_wp*(a(:,ib+i)+a(:,ic+i)) |
---|
2643 | d(:,jb+j) = sin60*(a(:,ic+i)-a(:,ib+i)) |
---|
2644 | ibase = ibase + inc1 |
---|
2645 | jbase = jbase + inc2 |
---|
2646 | ENDDO |
---|
2647 | |
---|
2648 | ja = ja + jink |
---|
2649 | jink = 2 * jink |
---|
2650 | jb = jb + jink |
---|
2651 | jc = jc - jink |
---|
2652 | ibase = ibase + ijump |
---|
2653 | ijump = 2 * ijump + iink |
---|
2654 | |
---|
2655 | IF ( ja /= jc ) THEN |
---|
2656 | |
---|
2657 | DO k = la, kstop, la |
---|
2658 | kb = k + k |
---|
2659 | kc = kb + kb |
---|
2660 | c1 = trigs(kb+1) |
---|
2661 | s1 = trigs(kb+2) |
---|
2662 | c2 = trigs(kc+1) |
---|
2663 | s2 = trigs(kc+2) |
---|
2664 | |
---|
2665 | jbase = 0 |
---|
2666 | DO l = 1, la |
---|
2667 | i = ibase |
---|
2668 | j = jbase |
---|
2669 | DO ipl = 1, SIZE(a,1) |
---|
2670 | a1 = (c1*a(ipl,ib+i)+s1*b(ipl,ib+i)) + (c2*a(ipl,ic+i)+s2*b(ipl,ic+i)) |
---|
2671 | b1 = (c1*b(ipl,ib+i)-s1*a(ipl,ib+i)) + (c2*b(ipl,ic+i)-s2*a(ipl,ic+i)) |
---|
2672 | a2 = a(ipl,ia+i) - 0.5_wp*a1 |
---|
2673 | b2 = b(ipl,ia+i) - 0.5_wp*b1 |
---|
2674 | a3 = sin60*((c1*a(ipl,ib+i)+s1*b(ipl,ib+i))-(c2*a(ipl,ic+i)+s2*b(ipl,ic+i))) |
---|
2675 | b3 = sin60*((c1*b(ipl,ib+i)-s1*a(ipl,ib+i))-(c2*b(ipl,ic+i)-s2*a(ipl,ic+i))) |
---|
2676 | c(ipl,ja+j) = a(ipl,ia+i) + a1 |
---|
2677 | d(ipl,ja+j) = b(ipl,ia+i) + b1 |
---|
2678 | c(ipl,jb+j) = a2 + b3 |
---|
2679 | d(ipl,jb+j) = b2 - a3 |
---|
2680 | c(ipl,jc+j) = a2 - b3 |
---|
2681 | d(ipl,jc+j) = -(b2+a3) |
---|
2682 | ENDDO |
---|
2683 | ibase = ibase + inc1 |
---|
2684 | jbase = jbase + inc2 |
---|
2685 | ENDDO |
---|
2686 | ibase = ibase + ijump |
---|
2687 | ja = ja + jink |
---|
2688 | jb = jb + jink |
---|
2689 | jc = jc - jink |
---|
2690 | ENDDO |
---|
2691 | |
---|
2692 | IF ( ja > jc ) RETURN |
---|
2693 | |
---|
2694 | ENDIF |
---|
2695 | |
---|
2696 | jbase = 0 |
---|
2697 | DO l = 1, la |
---|
2698 | i = ibase |
---|
2699 | j = jbase |
---|
2700 | c(:,ja+j) = a(:,ia+i) + 0.5_wp*(a(:,ib+i)-a(:,ic+i)) |
---|
2701 | d(:,ja+j) = -sin60*(a(:,ib+i)+a(:,ic+i)) |
---|
2702 | c(:,jb+j) = a(:,ia+i) - (a(:,ib+i)-a(:,ic+i)) |
---|
2703 | ibase = ibase + inc1 |
---|
2704 | jbase = jbase + inc2 |
---|
2705 | ENDDO |
---|
2706 | |
---|
2707 | ELSE |
---|
2708 | |
---|
2709 | z = 1.0_wp / REAL( n, KIND=wp ) |
---|
2710 | zsin60 = z*sin60 |
---|
2711 | DO l = 1, la |
---|
2712 | i = ibase |
---|
2713 | j = jbase |
---|
2714 | c(:,ja+j) = z*(a(:,ia+i)+(a(:,ib+i)+a(:,ic+i))) |
---|
2715 | c(:,jb+j) = z*(a(:,ia+i)-0.5_wp*(a(:,ib+i)+a(:,ic+i))) |
---|
2716 | d(:,jb+j) = zsin60*(a(:,ic+i)-a(:,ib+i)) |
---|
2717 | ibase = ibase + inc1 |
---|
2718 | jbase = jbase + inc2 |
---|
2719 | ENDDO |
---|
2720 | |
---|
2721 | ENDIF |
---|
2722 | |
---|
2723 | ! |
---|
2724 | !-- Coding for factor 4 |
---|
2725 | CASE ( 3 ) |
---|
2726 | |
---|
2727 | ia = 1 |
---|
2728 | ib = ia + iink |
---|
2729 | ic = ib + iink |
---|
2730 | id = ic + iink |
---|
2731 | ja = 1 |
---|
2732 | jb = ja + (2*m-la) * inc2 |
---|
2733 | jc = jb + 2*m*inc2 |
---|
2734 | jd = jb |
---|
2735 | |
---|
2736 | IF ( la /= m ) THEN |
---|
2737 | |
---|
2738 | DO l = 1, la |
---|
2739 | |
---|
2740 | i = ibase |
---|
2741 | j = jbase |
---|
2742 | c(:,ja+j) = (a(:,ia+i)+a(:,ic+i)) + (a(:,ib+i)+a(:,id+i)) |
---|
2743 | c(:,jc+j) = (a(:,ia+i)+a(:,ic+i)) - (a(:,ib+i)+a(:,id+i)) |
---|
2744 | c(:,jb+j) = a(:,ia+i) - a(:,ic+i) |
---|
2745 | d(:,jb+j) = a(:,id+i) - a(:,ib+i) |
---|
2746 | ibase = ibase + inc1 |
---|
2747 | jbase = jbase + inc2 |
---|
2748 | ENDDO |
---|
2749 | |
---|
2750 | ja = ja + jink |
---|
2751 | jink = 2 * jink |
---|
2752 | jb = jb + jink |
---|
2753 | jc = jc - jink |
---|
2754 | jd = jd - jink |
---|
2755 | ibase = ibase + ijump |
---|
2756 | ijump = 2 * ijump + iink |
---|
2757 | |
---|
2758 | IF ( jb /= jc ) THEN |
---|
2759 | |
---|
2760 | DO k = la, kstop, la |
---|
2761 | kb = k + k |
---|
2762 | kc = kb + kb |
---|
2763 | kd = kc + kb |
---|
2764 | c1 = trigs(kb+1) |
---|
2765 | s1 = trigs(kb+2) |
---|
2766 | c2 = trigs(kc+1) |
---|
2767 | s2 = trigs(kc+2) |
---|
2768 | c3 = trigs(kd+1) |
---|
2769 | s3 = trigs(kd+2) |
---|
2770 | jbase = 0 |
---|
2771 | DO l = 1, la |
---|
2772 | i = ibase |
---|
2773 | j = jbase |
---|
2774 | DO ipl = 1, SIZE(a,1) |
---|
2775 | a0 = a(ipl,ia+i) + (c2*a(ipl,ic+i)+s2*b(ipl,ic+i)) |
---|
2776 | a2 = a(ipl,ia+i) - (c2*a(ipl,ic+i)+s2*b(ipl,ic+i)) |
---|
2777 | a1 = (c1*a(ipl,ib+i)+s1*b(ipl,ib+i)) + (c3*a(ipl,id+i)+s3*b(ipl,id+i)) |
---|
2778 | a3 = (c1*a(ipl,ib+i)+s1*b(ipl,ib+i)) - (c3*a(ipl,id+i)+s3*b(ipl,id+i)) |
---|
2779 | b0 = b(ipl,ia+i) + (c2*b(ipl,ic+i)-s2*a(ipl,ic+i)) |
---|
2780 | b2 = b(ipl,ia+i) - (c2*b(ipl,ic+i)-s2*a(ipl,ic+i)) |
---|
2781 | b1 = (c1*b(ipl,ib+i)-s1*a(ipl,ib+i)) + (c3*b(ipl,id+i)-s3*a(ipl,id+i)) |
---|
2782 | b3 = (c1*b(ipl,ib+i)-s1*a(ipl,ib+i)) - (c3*b(ipl,id+i)-s3*a(ipl,id+i)) |
---|
2783 | c(ipl,ja+j) = a0 + a1 |
---|
2784 | c(ipl,jc+j) = a0 - a1 |
---|
2785 | d(ipl,ja+j) = b0 + b1 |
---|
2786 | d(ipl,jc+j) = b1 - b0 |
---|
2787 | c(ipl,jb+j) = a2 + b3 |
---|
2788 | c(ipl,jd+j) = a2 - b3 |
---|
2789 | d(ipl,jb+j) = b2 - a3 |
---|
2790 | d(ipl,jd+j) = -(b2+a3) |
---|
2791 | ENDDO |
---|
2792 | ibase = ibase + inc1 |
---|
2793 | jbase = jbase + inc2 |
---|
2794 | ENDDO |
---|
2795 | ibase = ibase + ijump |
---|
2796 | ja = ja + jink |
---|
2797 | jb = jb + jink |
---|
2798 | jc = jc - jink |
---|
2799 | jd = jd - jink |
---|
2800 | ENDDO |
---|
2801 | |
---|
2802 | IF ( jb > jc ) RETURN |
---|
2803 | |
---|
2804 | ENDIF |
---|
2805 | |
---|
2806 | sin45 = SQRT( 0.5_wp ) |
---|
2807 | jbase = 0 |
---|
2808 | DO l = 1, la |
---|
2809 | i = ibase |
---|
2810 | j = jbase |
---|
2811 | c(:,ja+j) = a(:,ia+i) + sin45*(a(:,ib+i)-a(:,id+i)) |
---|
2812 | c(:,jb+j) = a(:,ia+i) - sin45*(a(:,ib+i)-a(:,id+i)) |
---|
2813 | d(:,ja+j) = -a(:,ic+i) - sin45*(a(:,ib+i)+a(:,id+i)) |
---|
2814 | d(:,jb+j) = a(:,ic+i) - sin45*(a(:,ib+i)+a(:,id+i)) |
---|
2815 | ibase = ibase + inc1 |
---|
2816 | jbase = jbase + inc2 |
---|
2817 | ENDDO |
---|
2818 | |
---|
2819 | ELSE |
---|
2820 | |
---|
2821 | z = 1.0_wp / REAL( n, KIND=wp ) |
---|
2822 | DO l = 1, la |
---|
2823 | i = ibase |
---|
2824 | j = jbase |
---|
2825 | c(:,ja+j) = z*((a(:,ia+i)+a(:,ic+i))+(a(:,ib+i)+a(:,id+i))) |
---|
2826 | c(:,jc+j) = z*((a(:,ia+i)+a(:,ic+i))-(a(:,ib+i)+a(:,id+i))) |
---|
2827 | c(:,jb+j) = z*(a(:,ia+i)-a(:,ic+i)) |
---|
2828 | d(:,jb+j) = z*(a(:,id+i)-a(:,ib+i)) |
---|
2829 | ibase = ibase + inc1 |
---|
2830 | jbase = jbase + inc2 |
---|
2831 | ENDDO |
---|
2832 | |
---|
2833 | ENDIF |
---|
2834 | |
---|
2835 | ! |
---|
2836 | !-- Coding for factor 5 |
---|
2837 | CASE ( 4 ) |
---|
2838 | |
---|
2839 | ia = 1 |
---|
2840 | ib = ia + iink |
---|
2841 | ic = ib + iink |
---|
2842 | id = ic + iink |
---|
2843 | ie = id + iink |
---|
2844 | ja = 1 |
---|
2845 | jb = ja + (2*m-la) * inc2 |
---|
2846 | jc = jb + 2*m*inc2 |
---|
2847 | jd = jc |
---|
2848 | je = jb |
---|
2849 | |
---|
2850 | IF ( la /= m ) THEN |
---|
2851 | |
---|
2852 | DO l = 1, la |
---|
2853 | i = ibase |
---|
2854 | j = jbase |
---|
2855 | DO ipl = 1, SIZE(a,1) |
---|
2856 | a1 = a(ipl,ib+i) + a(ipl,ie+i) |
---|
2857 | a3 = a(ipl,ib+i) - a(ipl,ie+i) |
---|
2858 | a2 = a(ipl,ic+i) + a(ipl,id+i) |
---|
2859 | a4 = a(ipl,ic+i) - a(ipl,id+i) |
---|
2860 | a5 = a(ipl,ia+i) - 0.25_wp*(a1+a2) |
---|
2861 | a6 = qrt5*(a1-a2) |
---|
2862 | c(ipl,ja+j) = a(ipl,ia+i) + (a1+a2) |
---|
2863 | c(ipl,jb+j) = a5 + a6 |
---|
2864 | c(ipl,jc+j) = a5 - a6 |
---|
2865 | d(ipl,jb+j) = -sin72*a3 - sin36*a4 |
---|
2866 | d(ipl,jc+j) = -sin36*a3 + sin72*a4 |
---|
2867 | ENDDO |
---|
2868 | ibase = ibase + inc1 |
---|
2869 | jbase = jbase + inc2 |
---|
2870 | ENDDO |
---|
2871 | |
---|
2872 | ja = ja + jink |
---|
2873 | jink = 2 * jink |
---|
2874 | jb = jb + jink |
---|
2875 | jc = jc + jink |
---|
2876 | jd = jd - jink |
---|
2877 | je = je - jink |
---|
2878 | ibase = ibase + ijump |
---|
2879 | ijump = 2 * ijump + iink |
---|
2880 | |
---|
2881 | IF ( jb /= jd ) THEN |
---|
2882 | |
---|
2883 | DO k = la, kstop, la |
---|
2884 | kb = k + k |
---|
2885 | kc = kb + kb |
---|
2886 | kd = kc + kb |
---|
2887 | ke = kd + kb |
---|
2888 | c1 = trigs(kb+1) |
---|
2889 | s1 = trigs(kb+2) |
---|
2890 | c2 = trigs(kc+1) |
---|
2891 | s2 = trigs(kc+2) |
---|
2892 | c3 = trigs(kd+1) |
---|
2893 | s3 = trigs(kd+2) |
---|
2894 | c4 = trigs(ke+1) |
---|
2895 | s4 = trigs(ke+2) |
---|
2896 | jbase = 0 |
---|
2897 | DO l = 1, la |
---|
2898 | i = ibase |
---|
2899 | j = jbase |
---|
2900 | DO ipl = 1, SIZE(a,1) |
---|
2901 | a1 = (c1*a(ipl,ib+i)+s1*b(ipl,ib+i)) + (c4*a(ipl,ie+i)+s4*b(ipl,ie+i)) |
---|
2902 | a3 = (c1*a(ipl,ib+i)+s1*b(ipl,ib+i)) - (c4*a(ipl,ie+i)+s4*b(ipl,ie+i)) |
---|
2903 | a2 = (c2*a(ipl,ic+i)+s2*b(ipl,ic+i)) + (c3*a(ipl,id+i)+s3*b(ipl,id+i)) |
---|
2904 | a4 = (c2*a(ipl,ic+i)+s2*b(ipl,ic+i)) - (c3*a(ipl,id+i)+s3*b(ipl,id+i)) |
---|
2905 | b1 = (c1*b(ipl,ib+i)-s1*a(ipl,ib+i)) + (c4*b(ipl,ie+i)-s4*a(ipl,ie+i)) |
---|
2906 | b3 = (c1*b(ipl,ib+i)-s1*a(ipl,ib+i)) - (c4*b(ipl,ie+i)-s4*a(ipl,ie+i)) |
---|
2907 | b2 = (c2*b(ipl,ic+i)-s2*a(ipl,ic+i)) + (c3*b(ipl,id+i)-s3*a(ipl,id+i)) |
---|
2908 | b4 = (c2*b(ipl,ic+i)-s2*a(ipl,ic+i)) - (c3*b(ipl,id+i)-s3*a(ipl,id+i)) |
---|
2909 | a5 = a(ipl,ia+i) - 0.25_wp*(a1+a2) |
---|
2910 | a6 = qrt5*(a1-a2) |
---|
2911 | b5 = b(ipl,ia+i) - 0.25_wp*(b1+b2) |
---|
2912 | b6 = qrt5*(b1-b2) |
---|
2913 | a10 = a5 + a6 |
---|
2914 | a20 = a5 - a6 |
---|
2915 | b10 = b5 + b6 |
---|
2916 | b20 = b5 - b6 |
---|
2917 | a11 = sin72*b3 + sin36*b4 |
---|
2918 | a21 = sin36*b3 - sin72*b4 |
---|
2919 | b11 = sin72*a3 + sin36*a4 |
---|
2920 | b21 = sin36*a3 - sin72*a4 |
---|
2921 | c(ipl,ja+j) = a(ipl,ia+i) + (a1+a2) |
---|
2922 | c(ipl,jb+j) = a10 + a11 |
---|
2923 | c(ipl,je+j) = a10 - a11 |
---|
2924 | c(ipl,jc+j) = a20 + a21 |
---|
2925 | c(ipl,jd+j) = a20 - a21 |
---|
2926 | d(ipl,ja+j) = b(ipl,ia+i) + (b1+b2) |
---|
2927 | d(ipl,jb+j) = b10 - b11 |
---|
2928 | d(ipl,je+j) = -(b10+b11) |
---|
2929 | d(ipl,jc+j) = b20 - b21 |
---|
2930 | d(ipl,jd+j) = -(b20+b21) |
---|
2931 | ENDDO |
---|
2932 | ibase = ibase + inc1 |
---|
2933 | jbase = jbase + inc2 |
---|
2934 | ENDDO |
---|
2935 | ibase = ibase + ijump |
---|
2936 | ja = ja + jink |
---|
2937 | jb = jb + jink |
---|
2938 | jc = jc + jink |
---|
2939 | jd = jd - jink |
---|
2940 | je = je - jink |
---|
2941 | ENDDO |
---|
2942 | |
---|
2943 | IF ( jb > jd ) RETURN |
---|
2944 | |
---|
2945 | ENDIF |
---|
2946 | |
---|
2947 | jbase = 0 |
---|
2948 | DO l = 1, la |
---|
2949 | i = ibase |
---|
2950 | j = jbase |
---|
2951 | DO ipl = 1, SIZE(a,1) |
---|
2952 | a1 = a(ipl,ib+i) + a(ipl,ie+i) |
---|
2953 | a3 = a(ipl,ib+i) - a(ipl,ie+i) |
---|
2954 | a2 = a(ipl,ic+i) + a(ipl,id+i) |
---|
2955 | a4 = a(ipl,ic+i) - a(ipl,id+i) |
---|
2956 | a5 = a(ipl,ia+i) + 0.25_wp*(a3-a4) |
---|
2957 | a6 = qrt5*(a3+a4) |
---|
2958 | c(ipl,ja+j) = a5 + a6 |
---|
2959 | c(ipl,jb+j) = a5 - a6 |
---|
2960 | c(ipl,jc+j) = a(ipl,ia+i) - (a3-a4) |
---|
2961 | d(ipl,ja+j) = -sin36*a1 - sin72*a2 |
---|
2962 | d(ipl,jb+j) = -sin72*a1 + sin36*a2 |
---|
2963 | ENDDO |
---|
2964 | ibase = ibase + inc1 |
---|
2965 | jbase = jbase + inc2 |
---|
2966 | ENDDO |
---|
2967 | |
---|
2968 | ELSE |
---|
2969 | |
---|
2970 | z = 1.0_wp / REAL( n, KIND=wp ) |
---|
2971 | zqrt5 = z * qrt5 |
---|
2972 | zsin36 = z * sin36 |
---|
2973 | zsin72 = z * sin72 |
---|
2974 | DO l = 1, la |
---|
2975 | i = ibase |
---|
2976 | j = jbase |
---|
2977 | DO ipl = 1, SIZE(a,1) |
---|
2978 | a1 = a(ipl,ib+i) + a(ipl,ie+i) |
---|
2979 | a3 = a(ipl,ib+i) - a(ipl,ie+i) |
---|
2980 | a2 = a(ipl,ic+i) + a(ipl,id+i) |
---|
2981 | a4 = a(ipl,ic+i) - a(ipl,id+i) |
---|
2982 | a5 = z*(a(ipl,ia+i)-0.25_wp*(a1+a2)) |
---|
2983 | a6 = zqrt5*(a1-a2) |
---|
2984 | c(ipl,ja+j) = z*(a(ipl,ia+i)+(a1+a2)) |
---|
2985 | c(ipl,jb+j) = a5 + a6 |
---|
2986 | c(ipl,jc+j) = a5 - a6 |
---|
2987 | d(ipl,jb+j) = -zsin72*a3 - zsin36*a4 |
---|
2988 | d(ipl,jc+j) = -zsin36*a3 + zsin72*a4 |
---|
2989 | ENDDO |
---|
2990 | ibase = ibase + inc1 |
---|
2991 | jbase = jbase + inc2 |
---|
2992 | ENDDO |
---|
2993 | |
---|
2994 | ENDIF |
---|
2995 | |
---|
2996 | ! |
---|
2997 | !-- Coding for factor 6 |
---|
2998 | CASE ( 5 ) |
---|
2999 | |
---|
3000 | ia = 1 |
---|
3001 | ib = ia + iink |
---|
3002 | ic = ib + iink |
---|
3003 | id = ic + iink |
---|
3004 | ie = id + iink |
---|
3005 | if = ie + iink |
---|
3006 | ja = 1 |
---|
3007 | jb = ja + (2*m-la) * inc2 |
---|
3008 | jc = jb + 2*m*inc2 |
---|
3009 | jd = jc + 2*m*inc2 |
---|
3010 | je = jc |
---|
3011 | jf = jb |
---|
3012 | |
---|
3013 | IF ( la /= m ) THEN |
---|
3014 | |
---|
3015 | DO l = 1, la |
---|
3016 | i = ibase |
---|
3017 | j = jbase |
---|
3018 | DO ipl = 1, SIZE(a,1) |
---|
3019 | a11 = (a(ipl,ic+i)+a(ipl,if+i)) + (a(ipl,ib+i)+a(ipl,ie+i)) |
---|
3020 | c(ipl,ja+j) = (a(ipl,ia+i)+a(ipl,id+i)) + a11 |
---|
3021 | c(ipl,jc+j) = (a(ipl,ia+i)+a(ipl,id+i)-0.5_wp*a11) |
---|
3022 | d(ipl,jc+j) = sin60*((a(ipl,ic+i)+a(ipl,if+i))-(a(ipl,ib+i)+a(ipl,ie+i))) |
---|
3023 | a11 = (a(ipl,ic+i)-a(ipl,if+i)) + (a(ipl,ie+i)-a(ipl,ib+i)) |
---|
3024 | c(ipl,jb+j) = (a(ipl,ia+i)-a(ipl,id+i)) - 0.5_wp*a11 |
---|
3025 | d(ipl,jb+j) = sin60*((a(ipl,ie+i)-a(ipl,ib+i))-(a(ipl,ic+i)-a(ipl,if+i))) |
---|
3026 | c(ipl,jd+j) = (a(ipl,ia+i)-a(ipl,id+i)) + a11 |
---|
3027 | END DO |
---|
3028 | ibase = ibase + inc1 |
---|
3029 | jbase = jbase + inc2 |
---|
3030 | ENDDO |
---|
3031 | ja = ja + jink |
---|
3032 | jink = 2 * jink |
---|
3033 | jb = jb + jink |
---|
3034 | jc = jc + jink |
---|
3035 | jd = jd - jink |
---|
3036 | je = je - jink |
---|
3037 | jf = jf - jink |
---|
3038 | ibase = ibase + ijump |
---|
3039 | ijump = 2 * ijump + iink |
---|
3040 | |
---|
3041 | IF ( jc /= jd ) THEN |
---|
3042 | |
---|
3043 | DO k = la, kstop, la |
---|
3044 | kb = k + k |
---|
3045 | kc = kb + kb |
---|
3046 | kd = kc + kb |
---|
3047 | ke = kd + kb |
---|
3048 | kf = ke + kb |
---|
3049 | c1 = trigs(kb+1) |
---|
3050 | s1 = trigs(kb+2) |
---|
3051 | c2 = trigs(kc+1) |
---|
3052 | s2 = trigs(kc+2) |
---|
3053 | c3 = trigs(kd+1) |
---|
3054 | s3 = trigs(kd+2) |
---|
3055 | c4 = trigs(ke+1) |
---|
3056 | s4 = trigs(ke+2) |
---|
3057 | c5 = trigs(kf+1) |
---|
3058 | s5 = trigs(kf+2) |
---|
3059 | jbase = 0 |
---|
3060 | DO l = 1, la |
---|
3061 | i = ibase |
---|
3062 | j = jbase |
---|
3063 | DO ipl = 1, SIZE(a,1) |
---|
3064 | a1 = c1*a(ipl,ib+i) + s1*b(ipl,ib+i) |
---|
3065 | b1 = c1*b(ipl,ib+i) - s1*a(ipl,ib+i) |
---|
3066 | a2 = c2*a(ipl,ic+i) + s2*b(ipl,ic+i) |
---|
3067 | b2 = c2*b(ipl,ic+i) - s2*a(ipl,ic+i) |
---|
3068 | a3 = c3*a(ipl,id+i) + s3*b(ipl,id+i) |
---|
3069 | b3 = c3*b(ipl,id+i) - s3*a(ipl,id+i) |
---|
3070 | a4 = c4*a(ipl,ie+i) + s4*b(ipl,ie+i) |
---|
3071 | b4 = c4*b(ipl,ie+i) - s4*a(ipl,ie+i) |
---|
3072 | a5 = c5*a(ipl,if+i) + s5*b(ipl,if+i) |
---|
3073 | b5 = c5*b(ipl,if+i) - s5*a(ipl,if+i) |
---|
3074 | a11 = (a2+a5) + (a1+a4) |
---|
3075 | a20 = (a(ipl,ia+i)+a3) - 0.5_wp*a11 |
---|
3076 | a21 = sin60*((a2+a5)-(a1+a4)) |
---|
3077 | b11 = (b2+b5) + (b1+b4) |
---|
3078 | b20 = (b(ipl,ia+i)+b3) - 0.5_wp*b11 |
---|
3079 | b21 = sin60*((b2+b5)-(b1+b4)) |
---|
3080 | c(ipl,ja+j) = (a(ipl,ia+i)+a3) + a11 |
---|
3081 | d(ipl,ja+j) = (b(ipl,ia+i)+b3) + b11 |
---|
3082 | c(ipl,jc+j) = a20 - b21 |
---|
3083 | d(ipl,jc+j) = a21 + b20 |
---|
3084 | c(ipl,je+j) = a20 + b21 |
---|
3085 | d(ipl,je+j) = a21 - b20 |
---|
3086 | a11 = (a2-a5) + (a4-a1) |
---|
3087 | a20 = (a(ipl,ia+i)-a3) - 0.5_wp*a11 |
---|
3088 | a21 = sin60*((a4-a1)-(a2-a5)) |
---|
3089 | b11 = (b5-b2) - (b4-b1) |
---|
3090 | b20 = (b3-b(ipl,ia+i)) - 0.5_wp*b11 |
---|
3091 | b21 = sin60*((b5-b2)+(b4-b1)) |
---|
3092 | c(ipl,jb+j) = a20 - b21 |
---|
3093 | d(ipl,jb+j) = a21 - b20 |
---|
3094 | c(ipl,jd+j) = a11 + (a(ipl,ia+i)-a3) |
---|
3095 | d(ipl,jd+j) = b11 + (b3-b(ipl,ia+i)) |
---|
3096 | c(ipl,jf+j) = a20 + b21 |
---|
3097 | d(ipl,jf+j) = a21 + b20 |
---|
3098 | ENDDO |
---|
3099 | ibase = ibase + inc1 |
---|
3100 | jbase = jbase + inc2 |
---|
3101 | ENDDO |
---|
3102 | ibase = ibase + ijump |
---|
3103 | ja = ja + jink |
---|
3104 | jb = jb + jink |
---|
3105 | jc = jc + jink |
---|
3106 | jd = jd - jink |
---|
3107 | je = je - jink |
---|
3108 | jf = jf - jink |
---|
3109 | ENDDO |
---|
3110 | |
---|
3111 | IF ( jc > jd ) RETURN |
---|
3112 | |
---|
3113 | ENDIF |
---|
3114 | |
---|
3115 | jbase = 0 |
---|
3116 | DO l = 1, la |
---|
3117 | i = ibase |
---|
3118 | j = jbase |
---|
3119 | c(:,ja+j) = (a(:,ia+i)+0.5_wp*(a(:,ic+i)-a(:,ie+i))) + sin60*(a(:,ib+i)-a(:,if+i)) |
---|
3120 | d(:,ja+j) = -(a(:,id+i)+0.5_wp*(a(:,ib+i)+a(:,if+i))) - sin60*(a(:,ic+i)+a(:,ie+i)) |
---|
3121 | c(:,jb+j) = a(:,ia+i) - (a(:,ic+i)-a(:,ie+i)) |
---|
3122 | d(:,jb+j) = a(:,id+i) - (a(:,ib+i)+a(:,if+i)) |
---|
3123 | c(:,jc+j) = (a(:,ia+i)+0.5_wp*(a(:,ic+i)-a(:,ie+i))) - sin60*(a(:,ib+i)-a(:,if+i)) |
---|
3124 | d(:,jc+j) = -(a(:,id+i)+0.5_wp*(a(:,ib+i)+a(:,if+i))) + sin60*(a(:,ic+i)+a(:,ie+i)) |
---|
3125 | ibase = ibase + inc1 |
---|
3126 | jbase = jbase + inc2 |
---|
3127 | ENDDO |
---|
3128 | |
---|
3129 | ELSE |
---|
3130 | |
---|
3131 | z = 1.0_wp/REAL(n,KIND=wp) |
---|
3132 | zsin60 = z*sin60 |
---|
3133 | DO l = 1, la |
---|
3134 | i = ibase |
---|
3135 | j = jbase |
---|
3136 | DO ipl = 1, SIZE(a,1) |
---|
3137 | a11 = (a(ipl,ic+i)+a(ipl,if+i)) + (a(ipl,ib+i)+a(ipl,ie+i)) |
---|
3138 | c(ipl,ja+j) = z*((a(ipl,ia+i)+a(ipl,id+i))+a11) |
---|
3139 | c(ipl,jc+j) = z*((a(ipl,ia+i)+a(ipl,id+i))-0.5_wp*a11) |
---|
3140 | d(ipl,jc+j) = zsin60*((a(ipl,ic+i)+a(ipl,if+i))-(a(ipl,ib+i)+a(ipl,ie+i))) |
---|
3141 | a11 = (a(ipl,ic+i)-a(ipl,if+i)) + (a(ipl,ie+i)-a(ipl,ib+i)) |
---|
3142 | c(ipl,jb+j) = z*((a(ipl,ia+i)-a(ipl,id+i))-0.5_wp*a11) |
---|
3143 | d(ipl,jb+j) = zsin60*((a(ipl,ie+i)-a(ipl,ib+i))-(a(ipl,ic+i)-a(ipl,if+i))) |
---|
3144 | c(ipl,jd+j) = z*((a(ipl,ia+i)-a(ipl,id+i))+a11) |
---|
3145 | ENDDO |
---|
3146 | ibase = ibase + inc1 |
---|
3147 | jbase = jbase + inc2 |
---|
3148 | ENDDO |
---|
3149 | |
---|
3150 | ENDIF |
---|
3151 | |
---|
3152 | ! |
---|
3153 | !-- Coding for factor 8 |
---|
3154 | CASE ( 6 ) |
---|
3155 | |
---|
3156 | IF ( la /= m ) THEN |
---|
3157 | ierr = 3 |
---|
3158 | RETURN |
---|
3159 | ENDIF |
---|
3160 | |
---|
3161 | ia = 1 |
---|
3162 | ib = ia + iink |
---|
3163 | ic = ib + iink |
---|
3164 | id = ic + iink |
---|
3165 | ie = id + iink |
---|
3166 | if = ie + iink |
---|
3167 | ig = if + iink |
---|
3168 | ih = ig + iink |
---|
3169 | ja = 1 |
---|
3170 | jb = ja + la * inc2 |
---|
3171 | jc = jb + 2*m*inc2 |
---|
3172 | jd = jc + 2*m*inc2 |
---|
3173 | je = jd + 2*m*inc2 |
---|
3174 | z = 1.0_wp / REAL( n, KIND=wp ) |
---|
3175 | zsin45 = z * SQRT( 0.5_wp ) |
---|
3176 | |
---|
3177 | DO l = 1, la |
---|
3178 | i = ibase |
---|
3179 | j = jbase |
---|
3180 | c(:,ja+j) = z*(((a(:,ia+i)+a(:,ie+i))+(a(:,ic+i)+a(:,ig+i)))+((a(:,id+i)+ a(:,ih+i))+(a(:,ib+i)+a(:,if+i)))) |
---|
3181 | c(:,je+j) = z*(((a(:,ia+i)+a(:,ie+i))+(a(:,ic+i)+a(:,ig+i)))-((a(:,id+i)+ a(:,ih+i))+(a(:,ib+i)+a(:,if+i)))) |
---|
3182 | c(:,jc+j) = z*((a(:,ia+i)+a(:,ie+i))-(a(:,ic+i)+a(:,ig+i))) |
---|
3183 | d(:,jc+j) = z*((a(:,id+i)+a(:,ih+i))-(a(:,ib+i)+a(:,if+i))) |
---|
3184 | c(:,jb+j) = z*(a(:,ia+i)-a(:,ie+i)) + zsin45*((a(:,ih+i)-a(:,id+i))-(a(:,if+i)-a(:,ib+i))) |
---|
3185 | c(:,jd+j) = z*(a(:,ia+i)-a(:,ie+i)) - zsin45*((a(:,ih+i)-a(:,id+i))-(a(:,if+i)-a(:,ib+i))) |
---|
3186 | d(:,jb+j) = zsin45*((a(:,ih+i)-a(:,id+i))+(a(:,if+i)-a(:,ib+i))) + z*(a(:,ig+i)-a(:,ic+i)) |
---|
3187 | d(:,jd+j) = zsin45*((a(:,ih+i)-a(:,id+i))+(a(:,if+i)-a(:,ib+i))) - z*(a(:,ig+i)-a(:,ic+i)) |
---|
3188 | ibase = ibase + inc1 |
---|
3189 | jbase = jbase + inc2 |
---|
3190 | ENDDO |
---|
3191 | |
---|
3192 | END SELECT |
---|
3193 | |
---|
3194 | END SUBROUTINE qpassm_vec |
---|
3195 | |
---|
3196 | !------------------------------------------------------------------------------! |
---|
3197 | ! Description: |
---|
3198 | ! ------------ |
---|
3199 | !> Same as qpassm, but for backward fft |
---|
3200 | !------------------------------------------------------------------------------! |
---|
3201 | SUBROUTINE rpassm_vec(a, b, c, d, trigs, inc1, inc2, n, ifac, la, ierr ) |
---|
3202 | |
---|
3203 | USE kinds |
---|
3204 | |
---|
3205 | IMPLICIT NONE |
---|
3206 | |
---|
3207 | INTEGER(iwp) :: ierr !< |
---|
3208 | INTEGER(iwp) :: ifac !< |
---|
3209 | INTEGER(iwp) :: inc1 !< |
---|
3210 | INTEGER(iwp) :: inc2 !< |
---|
3211 | INTEGER(iwp) :: la !< |
---|
3212 | INTEGER(iwp) :: n !< |
---|
3213 | ! |
---|
3214 | !-- Arrays are dimensioned with n |
---|
3215 | REAL(wp),DIMENSION(:,:) :: a !< |
---|
3216 | REAL(wp),DIMENSION(:,:) :: b !< |
---|
3217 | REAL(wp),DIMENSION(:,:) :: c !< |
---|
3218 | REAL(wp),DIMENSION(:,:) :: d !< |
---|
3219 | REAL(wp),DIMENSION(:),INTENT(IN) :: trigs !< |
---|
3220 | |
---|
3221 | REAL(wp) :: c1 !< |
---|
3222 | REAL(wp) :: c2 !< |
---|
3223 | REAL(wp) :: c3 !< |
---|
3224 | REAL(wp) :: c4 !< |
---|
3225 | REAL(wp) :: c5 !< |
---|
3226 | REAL(wp) :: qqrt5 !< |
---|
3227 | REAL(wp) :: qrt5 !< |
---|
3228 | REAL(wp) :: s1 !< |
---|
3229 | REAL(wp) :: s2 !< |
---|
3230 | REAL(wp) :: s3 !< |
---|
3231 | REAL(wp) :: s4 !< |
---|
3232 | REAL(wp) :: s5 !< |
---|
3233 | REAL(wp) :: sin36 !< |
---|
3234 | REAL(wp) :: sin45 !< |
---|
3235 | REAL(wp) :: sin60 !< |
---|
3236 | REAL(wp) :: sin72 !< |
---|
3237 | REAL(wp) :: ssin36 !< |
---|
3238 | REAL(wp) :: ssin45 !< |
---|
3239 | REAL(wp) :: ssin60 !< |
---|
3240 | REAL(wp) :: ssin72 !< |
---|
3241 | |
---|
3242 | INTEGER(iwp) :: i !< |
---|
3243 | INTEGER(iwp) :: ia !< |
---|
3244 | INTEGER(iwp) :: ib !< |
---|
3245 | INTEGER(iwp) :: ibase !< |
---|
3246 | INTEGER(iwp) :: ic !< |
---|
3247 | INTEGER(iwp) :: id !< |
---|
3248 | INTEGER(iwp) :: ie !< |
---|
3249 | INTEGER(iwp) :: if !< |
---|
3250 | INTEGER(iwp) :: igo !< |
---|
3251 | INTEGER(iwp) :: iink !< |
---|
3252 | INTEGER(iwp) :: ipl !< loop index parallel loop |
---|
3253 | INTEGER(iwp) :: j !< |
---|
3254 | INTEGER(iwp) :: ja !< |
---|
3255 | INTEGER(iwp) :: jb !< |
---|
3256 | INTEGER(iwp) :: jbase !< |
---|
3257 | INTEGER(iwp) :: jc !< |
---|
3258 | INTEGER(iwp) :: jd !< |
---|
3259 | INTEGER(iwp) :: je !< |
---|
3260 | INTEGER(iwp) :: jf !< |
---|
3261 | INTEGER(iwp) :: jg !< |
---|
3262 | INTEGER(iwp) :: jh !< |
---|
3263 | INTEGER(iwp) :: jink !< |
---|
3264 | INTEGER(iwp) :: jump !< |
---|
3265 | INTEGER(iwp) :: k !< |
---|
3266 | INTEGER(iwp) :: kb !< |
---|
3267 | INTEGER(iwp) :: kc !< |
---|
3268 | INTEGER(iwp) :: kd !< |
---|
3269 | INTEGER(iwp) :: ke !< |
---|
3270 | INTEGER(iwp) :: kf !< |
---|
3271 | INTEGER(iwp) :: kstop !< |
---|
3272 | INTEGER(iwp) :: l !< |
---|
3273 | INTEGER(iwp) :: m !< |
---|
3274 | |
---|
3275 | REAL(wp) :: a10 !< |
---|
3276 | REAL(wp) :: a11 !< |
---|
3277 | REAL(wp) :: a20 !< |
---|
3278 | REAL(wp) :: a21 !< |
---|
3279 | REAL(wp) :: b10 !< |
---|
3280 | REAL(wp) :: b11 !< |
---|
3281 | REAL(wp) :: b20 !< |
---|
3282 | REAL(wp) :: b21 !< |
---|
3283 | |
---|
3284 | |
---|
3285 | DATA sin36/0.587785252292473_wp/, sin72/0.951056516295154_wp/, & |
---|
3286 | qrt5/0.559016994374947_wp/, sin60/0.866025403784437_wp/ |
---|
3287 | |
---|
3288 | |
---|
3289 | ierr = 0 |
---|
3290 | |
---|
3291 | m = n / ifac |
---|
3292 | iink = la * inc1 |
---|
3293 | jink = la * inc2 |
---|
3294 | jump = (ifac-1) * jink |
---|
3295 | kstop = (n-ifac) / (2*ifac) |
---|
3296 | |
---|
3297 | ibase = 0 |
---|
3298 | jbase = 0 |
---|
3299 | igo = ifac - 1 |
---|
3300 | IF ( igo == 7 ) igo = 6 |
---|
3301 | IF ( igo < 1 .OR. igo > 6 ) THEN |
---|
3302 | ierr = 2 |
---|
3303 | RETURN |
---|
3304 | ENDIF |
---|
3305 | |
---|
3306 | |
---|
3307 | SELECT CASE ( igo ) |
---|
3308 | ! |
---|
3309 | !-- Coding for factor 2 |
---|
3310 | CASE ( 1 ) |
---|
3311 | |
---|
3312 | ia = 1 |
---|
3313 | ib = ia + (2*m-la) * inc1 |
---|
3314 | ja = 1 |
---|
3315 | jb = ja + jink |
---|
3316 | |
---|
3317 | IF ( la /= m ) THEN |
---|
3318 | |
---|
3319 | DO l = 1, la |
---|
3320 | i = ibase |
---|
3321 | j = jbase |
---|
3322 | c(:,ja+j) = a(:,ia+i) + a(:,ib+i) |
---|
3323 | c(:,jb+j) = a(:,ia+i) - a(:,ib+i) |
---|
3324 | ibase = ibase + inc1 |
---|
3325 | jbase = jbase + inc2 |
---|
3326 | ENDDO |
---|
3327 | |
---|
3328 | ia = ia + iink |
---|
3329 | iink = 2 * iink |
---|
3330 | ib = ib - iink |
---|
3331 | ibase = 0 |
---|
3332 | jbase = jbase + jump |
---|
3333 | jump = 2 * jump + jink |
---|
3334 | |
---|
3335 | IF ( ia /= ib ) THEN |
---|
3336 | |
---|
3337 | DO k = la, kstop, la |
---|
3338 | kb = k + k |
---|
3339 | c1 = trigs(kb+1) |
---|
3340 | s1 = trigs(kb+2) |
---|
3341 | ibase = 0 |
---|
3342 | DO l = 1, la |
---|
3343 | i = ibase |
---|
3344 | j = jbase |
---|
3345 | c(:,ja+j) = a(:,ia+i) + a(:,ib+i) |
---|
3346 | d(:,ja+j) = b(:,ia+i) - b(:,ib+i) |
---|
3347 | c(:,jb+j) = c1*(a(:,ia+i)-a(:,ib+i)) - s1*(b(:,ia+i)+b(:,ib+i)) |
---|
3348 | d(:,jb+j) = s1*(a(:,ia+i)-a(:,ib+i)) + c1*(b(:,ia+i)+b(:,ib+i)) |
---|
3349 | ibase = ibase + inc1 |
---|
3350 | jbase = jbase + inc2 |
---|
3351 | ENDDO |
---|
3352 | ia = ia + iink |
---|
3353 | ib = ib - iink |
---|
3354 | jbase = jbase + jump |
---|
3355 | ENDDO |
---|
3356 | |
---|
3357 | IF ( ia > ib ) RETURN |
---|
3358 | |
---|
3359 | ENDIF |
---|
3360 | |
---|
3361 | ibase = 0 |
---|
3362 | DO l = 1, la |
---|
3363 | i = ibase |
---|
3364 | j = jbase |
---|
3365 | c(:,ja+j) = a(:,ia+i) |
---|
3366 | c(:,jb+j) = -b(:,ia+i) |
---|
3367 | ibase = ibase + inc1 |
---|
3368 | jbase = jbase + inc2 |
---|
3369 | ENDDO |
---|
3370 | |
---|
3371 | ELSE |
---|
3372 | |
---|
3373 | DO l = 1, la |
---|
3374 | i = ibase |
---|
3375 | j = jbase |
---|
3376 | c(:,ja+j) = 2.0_wp*(a(:,ia+i)+a(:,ib+i)) |
---|
3377 | c(:,jb+j) = 2.0_wp*(a(:,ia+i)-a(:,ib+i)) |
---|
3378 | ibase = ibase + inc1 |
---|
3379 | jbase = jbase + inc2 |
---|
3380 | ENDDO |
---|
3381 | |
---|
3382 | ENDIF |
---|
3383 | |
---|
3384 | ! |
---|
3385 | !-- Coding for factor 3 |
---|
3386 | CASE ( 2 ) |
---|
3387 | |
---|
3388 | ia = 1 |
---|
3389 | ib = ia + (2*m-la) * inc1 |
---|
3390 | ic = ib |
---|
3391 | ja = 1 |
---|
3392 | jb = ja + jink |
---|
3393 | jc = jb + jink |
---|
3394 | |
---|
3395 | IF ( la /= m ) THEN |
---|
3396 | |
---|
3397 | DO l = 1, la |
---|
3398 | i = ibase |
---|
3399 | j = jbase |
---|
3400 | c(:,ja+j) = a(:,ia+i) + a(:,ib+i) |
---|
3401 | c(:,jb+j) = (a(:,ia+i)-0.5_wp*a(:,ib+i)) - (sin60*(b(:,ib+i))) |
---|
3402 | c(:,jc+j) = (a(:,ia+i)-0.5_wp*a(:,ib+i)) + (sin60*(b(:,ib+i))) |
---|
3403 | ibase = ibase + inc1 |
---|
3404 | jbase = jbase + inc2 |
---|
3405 | ENDDO |
---|
3406 | ia = ia + iink |
---|
3407 | iink = 2 * iink |
---|
3408 | ib = ib + iink |
---|
3409 | ic = ic - iink |
---|
3410 | jbase = jbase + jump |
---|
3411 | jump = 2 * jump + jink |
---|
3412 | |
---|
3413 | IF ( ia /= ic ) THEN |
---|
3414 | |
---|
3415 | DO k = la, kstop, la |
---|
3416 | kb = k + k |
---|
3417 | kc = kb + kb |
---|
3418 | c1 = trigs(kb+1) |
---|
3419 | s1 = trigs(kb+2) |
---|
3420 | c2 = trigs(kc+1) |
---|
3421 | s2 = trigs(kc+2) |
---|
3422 | ibase = 0 |
---|
3423 | DO l = 1, la |
---|
3424 | i = ibase |
---|
3425 | j = jbase |
---|
3426 | c(:,ja+j) = a(:,ia+i) + (a(:,ib+i)+a(:,ic+i)) |
---|
3427 | d(:,ja+j) = b(:,ia+i) + (b(:,ib+i)-b(:,ic+i)) |
---|
3428 | c(:,jb+j) = c1*((a(:,ia+i)-0.5_wp*(a(:,ib+i)+a(:,ic+i)))-(sin60*(b(:,ib+i)+ b(:,ic+i)))) & |
---|
3429 | - s1*((b(:,ia+i)-0.5_wp*(b(:,ib+i)-b(:,ic+i)))+(sin60*(a(:,ib+i)- a(:,ic+i)))) |
---|
3430 | d(:,jb+j) = s1*((a(:,ia+i)-0.5_wp*(a(:,ib+i)+a(:,ic+i)))-(sin60*(b(:,ib+i)+ b(:,ic+i)))) & |
---|
3431 | + c1*((b(:,ia+i)-0.5_wp*(b(:,ib+i)-b(:,ic+i)))+(sin60*(a(:,ib+i)- a(:,ic+i)))) |
---|
3432 | c(:,jc+j) = c2*((a(:,ia+i)-0.5_wp*(a(:,ib+i)+a(:,ic+i)))+(sin60*(b(:,ib+i)+ b(:,ic+i)))) & |
---|
3433 | - s2*((b(:,ia+i)-0.5_wp*(b(:,ib+i)-b(:,ic+i)))-(sin60*(a(:,ib+i)- a(:,ic+i)))) |
---|
3434 | d(:,jc+j) = s2*((a(:,ia+i)-0.5_wp*(a(:,ib+i)+a(:,ic+i)))+(sin60*(b(:,ib+i)+ b(:,ic+i)))) & |
---|
3435 | + c2*((b(:,ia+i)-0.5_wp*(b(:,ib+i)-b(:,ic+i)))-(sin60*(a(:,ib+i)- a(:,ic+i)))) |
---|
3436 | ibase = ibase + inc1 |
---|
3437 | jbase = jbase + inc2 |
---|
3438 | ENDDO |
---|
3439 | ia = ia + iink |
---|
3440 | ib = ib + iink |
---|
3441 | ic = ic - iink |
---|
3442 | jbase = jbase + jump |
---|
3443 | ENDDO |
---|
3444 | |
---|
3445 | IF ( ia > ic ) RETURN |
---|
3446 | |
---|
3447 | ENDIF |
---|
3448 | |
---|
3449 | ibase = 0 |
---|
3450 | DO l = 1, la |
---|
3451 | i = ibase |
---|
3452 | j = jbase |
---|
3453 | c(:,ja+j) = a(:,ia+i) + a(:,ib+i) |
---|
3454 | c(:,jb+j) = (0.5_wp*a(:,ia+i)-a(:,ib+i)) - (sin60*b(:,ia+i)) |
---|
3455 | c(:,jc+j) = -(0.5_wp*a(:,ia+i)-a(:,ib+i)) - (sin60*b(:,ia+i)) |
---|
3456 | ibase = ibase + inc1 |
---|
3457 | jbase = jbase + inc2 |
---|
3458 | ENDDO |
---|
3459 | |
---|
3460 | ELSE |
---|
3461 | |
---|
3462 | ssin60 = 2.0_wp * sin60 |
---|
3463 | DO l = 1, la |
---|
3464 | i = ibase |
---|
3465 | j = jbase |
---|
3466 | c(:,ja+j) = 2.0_wp*(a(:,ia+i)+a(:,ib+i)) |
---|
3467 | c(:,jb+j) = (2.0_wp*a(:,ia+i)-a(:,ib+i)) - (ssin60*b(:,ib+i)) |
---|
3468 | c(:,jc+j) = (2.0_wp*a(:,ia+i)-a(:,ib+i)) + (ssin60*b(:,ib+i)) |
---|
3469 | ibase = ibase + inc1 |
---|
3470 | jbase = jbase + inc2 |
---|
3471 | ENDDO |
---|
3472 | |
---|
3473 | ENDIF |
---|
3474 | |
---|
3475 | ! |
---|
3476 | !-- Coding for factor 4 |
---|
3477 | CASE ( 3 ) |
---|
3478 | |
---|
3479 | ia = 1 |
---|
3480 | ib = ia + (2*m-la) * inc1 |
---|
3481 | ic = ib + 2*m*inc1 |
---|
3482 | id = ib |
---|
3483 | ja = 1 |
---|
3484 | jb = ja + jink |
---|
3485 | jc = jb + jink |
---|
3486 | jd = jc + jink |
---|
3487 | |
---|
3488 | IF ( la /= m ) THEN |
---|
3489 | |
---|
3490 | DO l = 1, la |
---|
3491 | i = ibase |
---|
|
---|