1 | !---------------------------------------------------------------------- |
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2 | ! NEMO system team, System and Interface for oceanic RElocable Nesting |
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3 | !---------------------------------------------------------------------- |
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4 | ! |
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5 | ! DESCRIPTION: |
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6 | !> @brief |
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7 | !> This module groups some useful mathematical function. |
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8 | !> |
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9 | !> @details |
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10 | !> |
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11 | !> to compute the mean of an array:<br/> |
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12 | !> @code |
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13 | !> dl_value=math_mean( dl_value, dd_fill ) |
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14 | !> @endcode |
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15 | !> - dl_value is 1D or 2D array |
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16 | !> - dd_fill is FillValue |
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17 | !> |
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18 | !> to compute the median of an array:<br/> |
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19 | !> @code |
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20 | !> dl_value=math_median( dl_value, dd_fill ) |
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21 | !> @endcode |
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22 | !> - dl_value is 1D or 2D array |
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23 | !> - dd_fill is FillValue |
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24 | !> |
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25 | !> to compute the mean without extremum of an array:<br/> |
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26 | !> @code |
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27 | !> dl_value=math_mwe( dl_value, id_next, dd_fill ) |
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28 | !> @endcode |
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29 | !> - dl_value is 1D or 2D array |
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30 | !> - id_next is the number of extremum to be removed |
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31 | !> - dd_fill is FillValue |
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32 | !> |
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33 | !> to sort an 1D array:<br/> |
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34 | !> @code |
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35 | !> CALL math_QsortC(dl_value) |
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36 | !> @endcode |
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37 | !> - dl_value is 1D array |
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38 | !> |
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39 | !> to correct phase angles to produce smoother phase:<br/> |
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40 | !> @code |
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41 | !> CALL math_unwrap(dl_value, [dl_discont]) |
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42 | !> @endcode |
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43 | !> - dl_value is 1D array |
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44 | !> - dl_discont maximum discontinuity between values, default pi |
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45 | !> |
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46 | !> to compute simple operation |
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47 | !> @code |
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48 | !> dl_res=math_compute(cl_var) |
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49 | !> @endcode |
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50 | !> - cl_var operation to compute (string of character) |
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51 | !> - dl_res result of the operation, real(dp) |
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52 | !> |
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53 | !> to compute first derivative of 1D array:<br/> |
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54 | !> @code |
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55 | !> dl_value(:)=math_deriv_1D( dd_value(:), dd_fill, [ld_discont] ) |
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56 | !> @endcode |
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57 | !> - dd_value is 1D array of variable |
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58 | !> - dd_fill is FillValue of variable |
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59 | !> - ld_discont is logical to take into account longitudinal |
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60 | !> East-West discontinuity [optional] |
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61 | !> |
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62 | !> to compute first derivative of 2D array:<br/> |
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63 | !> @code |
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64 | !> dl_value(:,:)=math_deriv_2D( dd_value(:,:), dd_fill, cd_dim, |
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65 | !> [ld_discont] ) |
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66 | !> @endcode |
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67 | !> - dd_value is 2D array of variable |
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68 | !> - dd_fill is FillValue of variable |
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69 | !> - cd_dim is character to compute derivative on first (I) or |
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70 | !> second (J) dimension |
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71 | !> - ld_discont is logical to take into account longitudinal |
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72 | !> East-West discontinuity [optional] |
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73 | !> |
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74 | !> to compute first derivative of 3D array:<br/> |
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75 | !> @code |
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76 | !> dl_value(:,:,:)=math_deriv_3D( dd_value(:,:,:), dd_fill, cd_dim, |
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77 | !> [ld_discont] ) |
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78 | !> @endcode |
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79 | !> - dd_value is 3D array of variable |
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80 | !> - dd_fill is FillValue of variable |
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81 | !> - cd_dim is character to compute derivative on first (I), second (J), |
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82 | !> or third (K) dimension |
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83 | !> - ld_discont is logical to take into account longitudinal East-West |
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84 | !> discontinuity [optional] |
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85 | !> |
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86 | !> |
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87 | !> @author |
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88 | !> J.Paul |
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89 | !> |
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90 | !> @date January, 2015 - Initial version |
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91 | !> |
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92 | !> @note Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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93 | !---------------------------------------------------------------------- |
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94 | MODULE math |
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95 | |
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96 | USE kind ! F90 kind parameter |
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97 | USE global ! global variable |
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98 | USE phycst ! physical constant |
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99 | USE fct ! basic useful function |
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100 | IMPLICIT NONE |
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101 | ! NOTE_avoid_public_variables_if_possible |
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102 | |
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103 | ! function and subroutine |
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104 | PUBLIC :: math_mean !< return mean of an array |
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105 | PUBLIC :: math_median !< return median of an array |
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106 | PUBLIC :: math_mwe !< return mean without extremum of an array |
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107 | PUBLIC :: math_QsortC !< sort an 1D array |
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108 | PUBLIC :: math_unwrap !< correct phase angles to produce smoother phase |
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109 | PUBLIC :: math_compute !< compute simple operation |
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110 | PUBLIC :: math_deriv_1D !< compute first derivative of 1D array |
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111 | PUBLIC :: math_deriv_2D !< compute first derivative of 2D array |
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112 | PUBLIC :: math_deriv_3D !< compute first derivative of 3D array |
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113 | PUBLIC :: math_ortho !< compute orthodome distance |
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114 | PUBLIC :: math_euclid !< compute euclidian distance |
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115 | |
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116 | PRIVATE :: math__Partition |
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117 | PRIVATE :: math__mean_1d |
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118 | PRIVATE :: math__mean_2d |
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119 | PRIVATE :: math__median_1d |
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120 | PRIVATE :: math__median_2d |
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121 | PRIVATE :: math__mwe_1d |
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122 | PRIVATE :: math__mwe_2d |
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123 | PRIVATE :: math__parentheses |
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124 | |
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125 | |
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126 | INTERFACE math_mean |
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127 | MODULE PROCEDURE math__mean_1d ! return mean of an array 1D |
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128 | MODULE PROCEDURE math__mean_2d ! return mean of an array 2D |
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129 | END INTERFACE math_mean |
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130 | |
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131 | INTERFACE math_median |
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132 | MODULE PROCEDURE math__median_1d ! return median of an array 1D |
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133 | MODULE PROCEDURE math__median_2d ! return median of an array 2D |
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134 | END INTERFACE math_median |
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135 | |
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136 | INTERFACE math_mwe |
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137 | MODULE PROCEDURE math__mwe_1d ! return mean without extremum of an array 1D |
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138 | MODULE PROCEDURE math__mwe_2d ! return mean without extremum of an array 2D |
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139 | END INTERFACE math_mwe |
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140 | |
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141 | CONTAINS |
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142 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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143 | PURE FUNCTION math__mean_1d(dd_array, dd_fill) & |
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144 | & RESULT (df_mean) |
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145 | !------------------------------------------------------------------- |
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146 | !> @brief This function compute the mean of a 1D array. |
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147 | !> |
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148 | !> @author J.Paul |
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149 | !> @date January, 2015 - Initial Version |
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150 | !> |
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151 | !> @param[in] dd_array 1D array |
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152 | !> @param[in] dd_fill fillValue |
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153 | !> @return mean value, real(dp) |
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154 | !------------------------------------------------------------------- |
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155 | |
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156 | IMPLICIT NONE |
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157 | |
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158 | ! Argument |
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159 | REAL(dp), DIMENSION(:), INTENT(IN) :: dd_array |
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160 | REAL(dp), INTENT(IN), OPTIONAL :: dd_fill |
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161 | |
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162 | ! function |
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163 | REAL(dp) :: df_mean |
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164 | |
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165 | ! local variable |
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166 | INTEGER(i4) :: il_count |
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167 | REAL(dp) :: dl_sum |
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168 | REAL(dp) :: dl_count |
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169 | !---------------------------------------------------------------- |
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170 | |
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171 | IF( PRESENT(dd_fill) )THEN |
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172 | il_count=COUNT(dd_array(:)/=dd_fill) |
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173 | IF( il_count > 0 )THEN |
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174 | dl_sum =SUM ( dd_array(:), dd_array(:)/= dd_fill ) |
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175 | dl_count=REAL( il_count, dp) |
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176 | |
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177 | df_mean=dl_sum/dl_count |
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178 | ELSE |
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179 | df_mean=dd_fill |
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180 | ENDIF |
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181 | ELSE |
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182 | il_count=SIZE(dd_array(:)) |
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183 | IF( il_count > 0 )THEN |
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184 | dl_sum =SUM ( dd_array(:) ) |
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185 | dl_count=REAL( il_count, dp) |
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186 | |
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187 | df_mean=dl_sum/dl_count |
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188 | ELSE |
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189 | df_mean=0 |
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190 | ENDIF |
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191 | ENDIF |
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192 | |
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193 | END FUNCTION math__mean_1d |
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194 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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195 | PURE FUNCTION math__mean_2d(dd_array, dd_fill) & |
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196 | & RESULT (df_mean) |
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197 | !------------------------------------------------------------------- |
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198 | !> @brief This function compute the mean of a 2D array. |
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199 | !> |
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200 | !> @author J.Paul |
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201 | !> @date January, 2015 - Initial Version |
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202 | !> |
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203 | !> @param[in] dd_array 2D array |
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204 | !> @param[in] dd_fill fillValue |
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205 | !> @return mean value, real(dp) |
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206 | !------------------------------------------------------------------- |
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207 | |
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208 | IMPLICIT NONE |
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209 | |
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210 | ! Argument |
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211 | REAL(dp), DIMENSION(:,:), INTENT(IN) :: dd_array |
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212 | REAL(dp), INTENT(IN), OPTIONAL :: dd_fill |
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213 | |
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214 | ! function |
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215 | REAL(dp) :: df_mean |
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216 | |
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217 | ! local variable |
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218 | INTEGER(i4) :: il_count |
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219 | |
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220 | REAL(dp), DIMENSION(:), ALLOCATABLE :: dl_list |
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221 | !---------------------------------------------------------------- |
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222 | |
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223 | IF( PRESENT(dd_fill) )THEN |
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224 | il_count=COUNT(dd_array(:,:)/=dd_fill) |
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225 | IF( il_count > 0 )THEN |
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226 | ALLOCATE( dl_list(il_count) ) |
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227 | dl_list(:)=PACK(dd_array(:,:),dd_array(:,:)/=dd_fill) |
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228 | ELSE |
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229 | df_mean=dd_fill |
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230 | ENDIF |
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231 | ELSE |
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232 | il_count=SIZE(dd_array) |
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233 | IF( il_count > 0 )THEN |
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234 | ALLOCATE( dl_list(il_count) ) |
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235 | dl_list(:)=PACK(dd_array(:,:), MASK=.TRUE.) |
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236 | ELSE |
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237 | df_mean=0 |
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238 | ENDIF |
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239 | ENDIF |
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240 | |
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241 | IF( ALLOCATED(dl_list) )THEN |
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242 | df_mean=math_mean(dl_list(:)) |
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243 | DEALLOCATE( dl_list ) |
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244 | ENDIF |
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245 | |
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246 | END FUNCTION math__mean_2d |
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247 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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248 | PURE FUNCTION math__median_1d(dd_array, dd_fill) & |
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249 | & RESULT (df_median) |
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250 | !------------------------------------------------------------------- |
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251 | !> @brief This function compute the median of a 1D array. |
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252 | !> |
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253 | !> @author J.Paul |
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254 | !> @date January, 2015 - Initial Version |
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255 | !> |
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256 | !> @param[in] dd_array 1D array |
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257 | !> @param[in] dd_fill fillValue |
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258 | !> @return median value, real(dp) |
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259 | !------------------------------------------------------------------- |
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260 | |
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261 | IMPLICIT NONE |
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262 | |
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263 | ! Argument |
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264 | REAL(dp), DIMENSION(:), INTENT(IN) :: dd_array |
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265 | REAL(dp), INTENT(IN), OPTIONAL :: dd_fill |
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266 | |
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267 | ! function |
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268 | REAL(dp) :: df_median |
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269 | |
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270 | ! local variable |
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271 | INTEGER(i4) :: il_count |
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272 | |
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273 | REAL(dp), DIMENSION(:), ALLOCATABLE :: dl_list |
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274 | !---------------------------------------------------------------- |
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275 | |
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276 | IF( PRESENT(dd_fill) )THEN |
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277 | il_count=COUNT(dd_array(:)/=dd_fill) |
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278 | IF( il_count > 0 )THEN |
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279 | ALLOCATE( dl_list(il_count) ) |
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280 | dl_list(:)=PACK(dd_array(:),dd_array(:)/=dd_fill) |
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281 | ELSE |
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282 | df_median=dd_fill |
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283 | ENDIF |
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284 | ELSE |
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285 | il_count=SIZE(dd_array(:)) |
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286 | IF( il_count > 0 )THEN |
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287 | ALLOCATE( dl_list(il_count) ) |
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288 | dl_list(:)=dd_array(:) |
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289 | ELSE |
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290 | df_median=0 |
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291 | ENDIF |
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292 | ENDIF |
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293 | |
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294 | IF( ALLOCATED(dl_list) )THEN |
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295 | CALL math_QsortC(dl_list(:)) |
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296 | |
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297 | IF( MOD(il_count,2) == 0 )THEN |
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298 | df_median=(dl_list(il_count/2+1)+dl_list(il_count/2))/2_dp |
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299 | ELSE |
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300 | df_median=dl_list(il_count/2+1) |
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301 | ENDIF |
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302 | |
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303 | DEALLOCATE(dl_list) |
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304 | ENDIF |
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305 | |
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306 | END FUNCTION math__median_1d |
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307 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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308 | PURE FUNCTION math__median_2d(dd_array, dd_fill) & |
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309 | & RESULT (df_median) |
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310 | !------------------------------------------------------------------- |
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311 | !> @brief This function compute the median of a 2D array. |
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312 | !> |
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313 | !> @author J.Paul |
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314 | !> @date January, 2015 - Initial Version |
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315 | !> |
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316 | !> @param[in] dd_array 2D array |
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317 | !> @param[in] dd_fill fillValue |
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318 | !> @return median value, real(dp) |
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319 | !------------------------------------------------------------------- |
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320 | |
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321 | IMPLICIT NONE |
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322 | |
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323 | ! Argument |
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324 | REAL(dp), DIMENSION(:,:), INTENT(IN) :: dd_array |
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325 | REAL(dp), INTENT(IN), OPTIONAL :: dd_fill |
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326 | |
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327 | ! funtion |
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328 | REAL(dp) :: df_median |
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329 | |
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330 | ! local variable |
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331 | INTEGER(i4) :: il_count |
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332 | |
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333 | REAL(dp), DIMENSION(:), ALLOCATABLE :: dl_list |
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334 | !---------------------------------------------------------------- |
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335 | |
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336 | IF( PRESENT(dd_fill) )THEN |
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337 | il_count=COUNT(dd_array(:,:)/=dd_fill) |
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338 | IF( il_count > 0 )THEN |
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339 | ALLOCATE( dl_list(il_count) ) |
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340 | dl_list(:)=PACK(dd_array(:,:),dd_array(:,:)/=dd_fill) |
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341 | ELSE |
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342 | df_median=dd_fill |
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343 | ENDIF |
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344 | ELSE |
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345 | il_count=SIZE(dd_array(:,:)) |
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346 | IF( il_count > 0 )THEN |
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347 | ALLOCATE( dl_list(il_count) ) |
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348 | dl_list(:)=PACK(dd_array(:,:), MASK=.TRUE.) |
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349 | ELSE |
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350 | df_median=0 |
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351 | ENDIF |
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352 | ENDIF |
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353 | |
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354 | IF( ALLOCATED(dl_list) )THEN |
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355 | df_median=math_median(dl_list(:)) |
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356 | DEALLOCATE(dl_list) |
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357 | ENDIF |
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358 | |
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359 | END FUNCTION math__median_2d |
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360 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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361 | PURE FUNCTION math__mwe_1d(dd_array, id_next, dd_fill) & |
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362 | & RESULT (df_mwe) |
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363 | !------------------------------------------------------------------- |
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364 | !> @brief This function compute the mean without extremum of a 1D array. |
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365 | !> |
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366 | !> @author J.Paul |
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367 | !> @date January, 2015 - Initial Version |
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368 | !> |
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369 | !> @param[in] dd_array 1D array |
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370 | !> @param[in] id_next number of extremum to be removed |
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371 | !> @param[in] dd_fill fillValue |
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372 | !> @return median value, real(dp) |
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373 | !------------------------------------------------------------------- |
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374 | |
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375 | IMPLICIT NONE |
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376 | |
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377 | ! Argument |
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378 | REAL(dp), DIMENSION(:), INTENT(IN) :: dd_array |
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379 | INTEGER(i4) , INTENT(IN), OPTIONAL :: id_next |
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380 | REAL(dp), INTENT(IN), OPTIONAL :: dd_fill |
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381 | |
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382 | ! function |
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383 | REAL(dp) :: df_mwe |
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384 | |
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385 | ! local variable |
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386 | INTEGER(i4) :: il_next |
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387 | INTEGER(i4) :: il_count |
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388 | INTEGER(i4) :: il_size |
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389 | |
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390 | REAL(dp), DIMENSION(:), ALLOCATABLE :: dl_list |
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391 | !---------------------------------------------------------------- |
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392 | |
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393 | il_next=2 |
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394 | IF( PRESENT(id_next) ) il_next=id_next |
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395 | |
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396 | il_size=SIZE(dd_array(:)) |
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397 | IF( PRESENT(dd_fill) )THEN |
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398 | il_count=COUNT(dd_array(:)/=dd_fill) |
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399 | IF( il_count > 0 )THEN |
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400 | ALLOCATE( dl_list(il_count) ) |
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401 | dl_list(:)=PACK(dd_array(:),dd_array(:)/=dd_fill) |
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402 | ELSE |
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403 | df_mwe=dd_fill |
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404 | ENDIF |
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405 | ELSE |
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406 | il_count=SIZE(dd_array(:)) |
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407 | IF( il_count > 0 )THEN |
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408 | ALLOCATE( dl_list(il_count) ) |
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409 | dl_list(:)=dd_array(:) |
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410 | ELSE |
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411 | df_mwe=0 |
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412 | ENDIF |
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413 | ENDIF |
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414 | |
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415 | IF( ALLOCATED(dl_list) )THEN |
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416 | CALL math_QsortC(dl_list(:)) |
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417 | |
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418 | IF( il_count == il_size )THEN |
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419 | ! no fillValue |
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420 | df_mwe=math_mean(dl_list(il_next+1:il_size-il_next)) |
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421 | ELSEIF( il_count > il_size-2*il_next )THEN |
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422 | ! remove one extremum each side |
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423 | df_mwe=math_mean(dl_list(2:il_size-1)) |
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424 | ELSE ! il_count <= il_size-2*il_next |
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425 | ! more than 2*il_next fillValue |
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426 | ! compute mean only |
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427 | df_mwe=math_mean(dl_list(:)) |
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428 | ENDIF |
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429 | |
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430 | DEALLOCATE(dl_list) |
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431 | ENDIF |
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432 | |
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433 | END FUNCTION math__mwe_1d |
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434 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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435 | PURE FUNCTION math__mwe_2d(dd_array, id_next, dd_fill) & |
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436 | & RESULT (df_mwe) |
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437 | !------------------------------------------------------------------- |
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438 | !> @brief This function compute the mean without extremum of a 2D array. |
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439 | !> |
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440 | !> @author J.Paul |
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441 | !> @date January, 2015 - Initial Version |
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442 | !> |
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443 | !> @param[in] dd_array 2D array |
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444 | !> @param[in] id_next number of extremum to be removed |
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445 | !> @param[in] dd_fill fillValue |
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446 | !> @return median value, real(dp) |
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447 | !------------------------------------------------------------------- |
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448 | |
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449 | IMPLICIT NONE |
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450 | |
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451 | ! Argument |
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452 | REAL(dp), DIMENSION(:,:), INTENT(IN) :: dd_array |
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453 | INTEGER(i4) , INTENT(IN), OPTIONAL :: id_next |
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454 | REAL(dp), INTENT(IN), OPTIONAL :: dd_fill |
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455 | |
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456 | ! function |
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457 | REAL(dp) :: df_mwe |
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458 | |
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459 | ! local variable |
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460 | INTEGER(i4) :: il_count |
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461 | |
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462 | REAL(dp), DIMENSION(:), ALLOCATABLE :: dl_list |
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463 | !---------------------------------------------------------------- |
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464 | |
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465 | IF( PRESENT(dd_fill) )THEN |
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466 | il_count=COUNT(dd_array(:,:)/=dd_fill) |
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467 | IF( il_count > 0 )THEN |
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468 | ALLOCATE( dl_list(il_count) ) |
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469 | dl_list(:)=PACK(dd_array(:,:),dd_array(:,:)/=dd_fill) |
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470 | |
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471 | df_mwe=math_mwe(dl_list(:), id_next) |
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472 | ELSE |
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473 | df_mwe=dd_fill |
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474 | ENDIF |
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475 | ELSE |
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476 | il_count=SIZE(dd_array(:,:)) |
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477 | IF( il_count > 0 )THEN |
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478 | ALLOCATE( dl_list(il_count) ) |
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479 | dl_list(:)=PACK(dd_array(:,:), MASK=.TRUE.) |
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480 | |
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481 | df_mwe=math_mwe(dl_list(:), id_next) |
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482 | ELSE |
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483 | df_mwe=0 |
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484 | ENDIF |
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485 | ENDIF |
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486 | |
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487 | IF( ALLOCATED(dl_list) ) DEALLOCATE(dl_list) |
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488 | |
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489 | END FUNCTION math__mwe_2d |
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490 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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491 | PURE RECURSIVE SUBROUTINE math_QsortC(dd_array) |
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492 | !------------------------------------------------------------------- |
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493 | !> @brief This subroutine sort a 1D array. |
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494 | !> |
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495 | !> @details |
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496 | !> Recursive Fortran 95 quicksort routine |
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497 | !> sorts real numbers into ascending numerical order |
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498 | !> Author: Juli Rew, SCD Consulting (juliana@ucar.edu), 9/03 |
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499 | !> Based on algorithm from Cormen et al., Introduction to Algorithms, |
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500 | !> 1997 printing |
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501 | !> |
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502 | !> @author J.Paul |
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503 | !> @date January, 2015 - Rewrite with SIREN coding rules |
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504 | !> |
---|
505 | !> @param[inout] dd_array 1D array |
---|
506 | !------------------------------------------------------------------- |
---|
507 | |
---|
508 | IMPLICIT NONE |
---|
509 | |
---|
510 | ! Argument |
---|
511 | REAL(dp), DIMENSION(:), INTENT(INOUT) :: dd_array |
---|
512 | |
---|
513 | ! local variable |
---|
514 | INTEGER(i4) :: il_iq |
---|
515 | !---------------------------------------------------------------- |
---|
516 | |
---|
517 | IF( SIZE(dd_array(:)) > 1 )THEN |
---|
518 | CALL math__Partition(dd_array, il_iq) |
---|
519 | CALL math_QsortC(dd_array(:il_iq-1)) |
---|
520 | CALL math_QsortC(dd_array(il_iq:)) |
---|
521 | ENDIF |
---|
522 | |
---|
523 | END SUBROUTINE math_QsortC |
---|
524 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
525 | PURE SUBROUTINE math__Partition(dd_array, id_marker) |
---|
526 | !------------------------------------------------------------------- |
---|
527 | !> @brief This subroutine partition a 1D array. |
---|
528 | !> |
---|
529 | !> @details |
---|
530 | !> Author: Juli Rew, SCD Consulting (juliana@ucar.edu), 9/03 |
---|
531 | !> Based on algorithm from Cormen et al., Introduction to Algorithms, |
---|
532 | !> 1997 printing |
---|
533 | !> |
---|
534 | !> @author J.Paul |
---|
535 | !> @date January, 2015 - Rewrite with SIREN coding rules |
---|
536 | !> @date November, 2017 |
---|
537 | !> - use the correct loop index to look for element bigger than pivot point. |
---|
538 | !> |
---|
539 | !> @param[inout] dd_array 1D array |
---|
540 | !> @param[in] id_marker |
---|
541 | !------------------------------------------------------------------- |
---|
542 | |
---|
543 | IMPLICIT NONE |
---|
544 | |
---|
545 | ! Argument |
---|
546 | REAL(dp) , DIMENSION(:), INTENT(INOUT) :: dd_array |
---|
547 | INTEGER(i4), INTENT( OUT) :: id_marker |
---|
548 | |
---|
549 | ! local variable |
---|
550 | REAL(dp) :: dl_temp |
---|
551 | REAL(dp) :: dl_x ! pivot point |
---|
552 | |
---|
553 | ! loop indices |
---|
554 | INTEGER(i4) :: ji |
---|
555 | INTEGER(i4) :: jj |
---|
556 | !---------------------------------------------------------------- |
---|
557 | |
---|
558 | dl_x = dd_array(1) |
---|
559 | ji= 0 |
---|
560 | jj= SIZE(dd_array(:)) + 1 |
---|
561 | |
---|
562 | DO |
---|
563 | jj=jj-1 |
---|
564 | DO |
---|
565 | IF( dd_array(jj) <= dl_x ) EXIT |
---|
566 | jj=jj-1 |
---|
567 | ENDDO |
---|
568 | ji=ji+1 |
---|
569 | DO |
---|
570 | IF( dd_array(ji) >= dl_x ) EXIT |
---|
571 | ji=ji+1 |
---|
572 | ENDDO |
---|
573 | IF( ji < jj )THEN |
---|
574 | ! exchange dd_array(ji) and dd_array(jj) |
---|
575 | dl_temp= dd_array(ji) |
---|
576 | dd_array(ji) = dd_array(jj) |
---|
577 | dd_array(jj) = dl_temp |
---|
578 | ELSEIF( ji==jj )THEN |
---|
579 | id_marker=ji+1 |
---|
580 | RETURN |
---|
581 | ELSE |
---|
582 | id_marker=ji |
---|
583 | RETURN |
---|
584 | ENDIF |
---|
585 | ENDDO |
---|
586 | |
---|
587 | END SUBROUTINE math__Partition |
---|
588 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
589 | PURE SUBROUTINE math_unwrap(dd_array, dd_discont) |
---|
590 | !------------------------------------------------------------------- |
---|
591 | !> @brief This subroutine correct phase angles to produce smoother |
---|
592 | !> phase plots. |
---|
593 | !> |
---|
594 | !> @details |
---|
595 | !> This code is based on numpy unwrap function |
---|
596 | !> |
---|
597 | !> Unwrap by changing deltas between values to 2*pi complement. |
---|
598 | !> |
---|
599 | !> Unwrap radian phase `dd_array` by changing absolute jumps greater than |
---|
600 | !> `dd_discont` to their 2*pi complement. |
---|
601 | !> |
---|
602 | !> @note If the discontinuity in `dd_array` is smaller than ``pi``, |
---|
603 | !> but larger than `dd_discont`, no unwrapping is done because taking |
---|
604 | !> the 2*pi complement would only make the discontinuity larger. |
---|
605 | !> |
---|
606 | !> @author J.Paul |
---|
607 | !> @date Marsh, 2015 - Rewrite in fortran, with SIREN coding rules |
---|
608 | !> |
---|
609 | !> @param[inout] dd_array 1D array |
---|
610 | !> @param[in] dd_discont maximum discontinuity between values, default pi |
---|
611 | !------------------------------------------------------------------- |
---|
612 | |
---|
613 | IMPLICIT NONE |
---|
614 | |
---|
615 | ! Argument |
---|
616 | REAL(dp) , DIMENSION(:), INTENT(INOUT) :: dd_array |
---|
617 | REAL(dp) , INTENT(IN ), OPTIONAL :: dd_discont |
---|
618 | |
---|
619 | ! local variable |
---|
620 | INTEGER(i4) :: il_size |
---|
621 | |
---|
622 | REAL(dp) :: dl_discont |
---|
623 | |
---|
624 | REAL(dp), DIMENSION(:), ALLOCATABLE :: dl_diff |
---|
625 | REAL(dp), DIMENSION(:), ALLOCATABLE :: dl_mod |
---|
626 | REAL(dp), DIMENSION(:), ALLOCATABLE :: dl_correct |
---|
627 | REAL(dp), DIMENSION(:), ALLOCATABLE :: dl_tmp |
---|
628 | |
---|
629 | ! loop indices |
---|
630 | INTEGER(i4) :: ji |
---|
631 | !---------------------------------------------------------------- |
---|
632 | dl_discont=dp_pi |
---|
633 | IF( PRESENT(dd_discont) ) dl_discont=dd_discont |
---|
634 | |
---|
635 | il_size=SIZE(dd_array) |
---|
636 | ALLOCATE(dl_diff(il_size-1)) |
---|
637 | DO ji=1,il_size-1 |
---|
638 | dl_diff(ji)=dd_array(ji+1)-dd_array(ji) |
---|
639 | ENDDO |
---|
640 | |
---|
641 | ALLOCATE(dl_mod(il_size-1)) |
---|
642 | DO ji=1,il_size-1 |
---|
643 | dl_mod(ji) = MOD(dl_diff(ji) + dp_pi, 2*dp_pi) - dp_pi |
---|
644 | ENDDO |
---|
645 | |
---|
646 | WHERE( (dl_mod(:) == -dp_pi) .AND. (dl_diff(:) > 0._dp ) ) |
---|
647 | dl_mod(:)=dp_pi |
---|
648 | END WHERE |
---|
649 | |
---|
650 | ALLOCATE(dl_correct(il_size-1)) |
---|
651 | dl_correct(:)=dl_mod(:)-dl_diff(:) |
---|
652 | |
---|
653 | DEALLOCATE(dl_mod) |
---|
654 | |
---|
655 | WHERE( ABS(dl_diff(:)) < dl_discont ) |
---|
656 | dl_correct(:)=0._dp |
---|
657 | END WHERE |
---|
658 | |
---|
659 | DEALLOCATE(dl_diff) |
---|
660 | |
---|
661 | ALLOCATE(dl_tmp(il_size)) |
---|
662 | dl_tmp(:)=dd_array(:) |
---|
663 | |
---|
664 | DO ji=1,il_size-1 |
---|
665 | dd_array(ji+1)=dl_tmp(ji+1)+SUM(dl_correct(1:ji)) |
---|
666 | ENDDO |
---|
667 | |
---|
668 | DEALLOCATE(dl_correct) |
---|
669 | DEALLOCATE(dl_tmp) |
---|
670 | |
---|
671 | END SUBROUTINE math_unwrap |
---|
672 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
673 | RECURSIVE FUNCTION math_compute(cd_var) & |
---|
674 | & RESULT(df_res) |
---|
675 | !------------------------------------------------------------------- |
---|
676 | !> @brief This function compute simple operation |
---|
677 | !> |
---|
678 | !> @details |
---|
679 | !> - operation should be write as a string of character. |
---|
680 | !> - operators allowed are : +,-,*,/ |
---|
681 | !> - to ordered operation you should use parentheses |
---|
682 | !> |
---|
683 | !> exemples: '1e6/(16/122)', '(3/2)*(2+1)' |
---|
684 | !> |
---|
685 | !> @author J.Paul |
---|
686 | !> @date June, 2015 - initial version |
---|
687 | !> |
---|
688 | !> @param[in] cd_var operation to compute (string of character) |
---|
689 | !> @return result of the operation, real(dp) |
---|
690 | !------------------------------------------------------------------- |
---|
691 | |
---|
692 | IMPLICIT NONE |
---|
693 | |
---|
694 | ! Argument |
---|
695 | CHARACTER(LEN=*), INTENT(IN) :: cd_var |
---|
696 | |
---|
697 | ! fucntion |
---|
698 | REAL(dp) :: df_res |
---|
699 | |
---|
700 | ! local variables |
---|
701 | CHARACTER(LEN=lc) :: cl_var |
---|
702 | CHARACTER(LEN=lc) :: cl_str1 |
---|
703 | CHARACTER(LEN=lc) :: cl_str2 |
---|
704 | |
---|
705 | INTEGER(i4) :: il_ind |
---|
706 | ! loop indices |
---|
707 | !---------------------------------------------------------------- |
---|
708 | |
---|
709 | |
---|
710 | IF(fct_is_real(cd_var))THEN |
---|
711 | READ(cd_var,*) df_res |
---|
712 | ELSE |
---|
713 | |
---|
714 | |
---|
715 | CALL math__parentheses(cd_var, cl_var) |
---|
716 | |
---|
717 | IF(fct_is_real(cl_var))THEN |
---|
718 | READ(cl_var,*) df_res |
---|
719 | ELSE |
---|
720 | il_ind=SCAN(TRIM(cl_var),'*') |
---|
721 | IF( il_ind /= 0 )THEN |
---|
722 | cl_str1=cl_var(1:il_ind-1) |
---|
723 | cl_str2=cl_var(il_ind+1:) |
---|
724 | df_res=math_compute(cl_str1)*math_compute(cl_str2) |
---|
725 | ELSE |
---|
726 | il_ind=SCAN(TRIM(cl_var),'/') |
---|
727 | IF( il_ind /= 0 )THEN |
---|
728 | cl_str1=cl_var(1:il_ind-1) |
---|
729 | cl_str2=cl_var(il_ind+1:) |
---|
730 | df_res=math_compute(cl_str1)/math_compute(cl_str2) |
---|
731 | ELSE |
---|
732 | il_ind=SCAN(TRIM(cl_var),'+') |
---|
733 | IF( il_ind /= 0 )THEN |
---|
734 | cl_str1=cl_var(1:il_ind-1) |
---|
735 | cl_str2=cl_var(il_ind+1:) |
---|
736 | df_res=math_compute(cl_str1)+math_compute(cl_str2) |
---|
737 | ELSE |
---|
738 | il_ind=SCAN(TRIM(cl_var),'-') |
---|
739 | IF( il_ind /= 0 )THEN |
---|
740 | cl_str1=cl_var(1:il_ind-1) |
---|
741 | cl_str2=cl_var(il_ind+1:) |
---|
742 | df_res=math_compute(cl_str1)-math_compute(cl_str2) |
---|
743 | ELSE |
---|
744 | df_res=dp_fill |
---|
745 | ENDIF |
---|
746 | ENDIF |
---|
747 | ENDIF |
---|
748 | ENDIF |
---|
749 | ENDIF |
---|
750 | ENDIF |
---|
751 | |
---|
752 | END FUNCTION math_compute |
---|
753 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
754 | SUBROUTINE math__parentheses(cd_varin, cd_varout) |
---|
755 | !------------------------------------------------------------------- |
---|
756 | !> @brief This subroutine replace sub string inside parentheses |
---|
757 | !> by the value of the operation inside. |
---|
758 | !> |
---|
759 | !> @details |
---|
760 | !> exemple : |
---|
761 | !> - '2.6+(3/2)' => '2.6+1.5000' |
---|
762 | !> |
---|
763 | !> @author J.Paul |
---|
764 | !> @date June, 2015 - initial version |
---|
765 | !> |
---|
766 | !> @param[in] cd_varin string of character with operation inside |
---|
767 | !> parentheses |
---|
768 | !> @param[out] cd_varout string of character with result of |
---|
769 | !> operation inside parentheses |
---|
770 | !------------------------------------------------------------------- |
---|
771 | |
---|
772 | IMPLICIT NONE |
---|
773 | |
---|
774 | ! Argument |
---|
775 | CHARACTER(LEN=*) , INTENT(IN) :: cd_varin |
---|
776 | CHARACTER(LEN=lc), INTENT(OUT) :: cd_varout |
---|
777 | |
---|
778 | ! local variables |
---|
779 | CHARACTER(LEN=lc) :: cl_cpt |
---|
780 | INTEGER(i4) :: il_ind |
---|
781 | INTEGER(i4) :: il_count |
---|
782 | |
---|
783 | ! loop indices |
---|
784 | INTEGER(i4) :: ji |
---|
785 | !---------------------------------------------------------------- |
---|
786 | il_ind=INDEX(cd_varin,'(') |
---|
787 | IF( il_ind /= 0 )THEN |
---|
788 | il_count=0 |
---|
789 | DO ji=il_ind+1,LEN(cd_varin) |
---|
790 | IF( cd_varin(ji:ji) == '(' )THEN |
---|
791 | il_count=il_count+1 |
---|
792 | ELSEIF( cd_varin(ji:ji) == ')' )THEN |
---|
793 | IF( il_count == 0 )THEN |
---|
794 | WRITE(cl_cpt,*) math_compute(cd_varin(il_ind+1:ji-1)) |
---|
795 | cd_varout=TRIM(cd_varin(1:il_ind-1))//TRIM(ADJUSTL(cl_cpt))//& |
---|
796 | & TRIM(cd_varin(ji+1:)) |
---|
797 | EXIT |
---|
798 | ELSE |
---|
799 | il_count=il_count-1 |
---|
800 | ENDIF |
---|
801 | ENDIF |
---|
802 | ENDDO |
---|
803 | ELSE |
---|
804 | cd_varout=TRIM(cd_varin) |
---|
805 | ENDIF |
---|
806 | |
---|
807 | END SUBROUTINE math__parentheses |
---|
808 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
809 | PURE FUNCTION math_deriv_1D(dd_value, dd_fill, ld_discont) & |
---|
810 | & RESULT (df_deriv) |
---|
811 | !------------------------------------------------------------------- |
---|
812 | !> @brief |
---|
813 | !> This function compute derivative of 1D array. |
---|
814 | !> |
---|
815 | !> @details |
---|
816 | !> optionaly you could specify to take into account east west discontinuity |
---|
817 | !> (-180° 180° or 0° 360° for longitude variable) |
---|
818 | !> |
---|
819 | !> @author J.Paul |
---|
820 | !> @date November, 2013 - Initial Version |
---|
821 | !> |
---|
822 | !> @param[in] dd_value 1D array of variable to be extrapolated |
---|
823 | !> @param[in] dd_fill FillValue of variable |
---|
824 | !> @param[in] ld_discont logical to take into account east west discontinuity |
---|
825 | !------------------------------------------------------------------- |
---|
826 | |
---|
827 | IMPLICIT NONE |
---|
828 | |
---|
829 | ! Argument |
---|
830 | REAL(dp) , DIMENSION(:), INTENT(IN) :: dd_value |
---|
831 | REAL(dp) , INTENT(IN) :: dd_fill |
---|
832 | LOGICAL , INTENT(IN), OPTIONAL :: ld_discont |
---|
833 | |
---|
834 | ! function |
---|
835 | REAL(dp), DIMENSION(SIZE(dd_value,DIM=1) ) :: df_deriv |
---|
836 | |
---|
837 | ! local variable |
---|
838 | INTEGER(i4) :: il_imin |
---|
839 | INTEGER(i4) :: il_imax |
---|
840 | INTEGER(i4), DIMENSION(1) :: il_shape |
---|
841 | |
---|
842 | REAL(dp) :: dl_min |
---|
843 | REAL(dp) :: dl_max |
---|
844 | REAL(dp) , DIMENSION(:), ALLOCATABLE :: dl_value |
---|
845 | |
---|
846 | LOGICAL :: ll_discont |
---|
847 | |
---|
848 | ! loop indices |
---|
849 | INTEGER(i4) :: ji |
---|
850 | |
---|
851 | INTEGER(i4) :: i1 |
---|
852 | INTEGER(i4) :: i2 |
---|
853 | !---------------------------------------------------------------- |
---|
854 | ! init |
---|
855 | df_deriv(:)=dd_fill |
---|
856 | |
---|
857 | ll_discont=.FALSE. |
---|
858 | IF( PRESENT(ld_discont) ) ll_discont=ld_discont |
---|
859 | |
---|
860 | il_shape(:)=SHAPE(dd_value(:)) |
---|
861 | |
---|
862 | ALLOCATE( dl_value(3)) |
---|
863 | |
---|
864 | ! compute derivative in i-direction |
---|
865 | DO ji=1,il_shape(1) |
---|
866 | |
---|
867 | il_imin=MAX(ji-1,1) |
---|
868 | il_imax=MIN(ji+1,il_shape(1)) |
---|
869 | |
---|
870 | IF( il_imin==ji-1 .AND. il_imax==ji+1 )THEN |
---|
871 | i1=1 ; i2=3 |
---|
872 | ELSEIF( il_imin==ji .AND. il_imax==ji+1 )THEN |
---|
873 | i1=1 ; i2=2 |
---|
874 | ELSEIF( il_imin==ji-1 .AND. il_imax==ji )THEN |
---|
875 | i1=2 ; i2=3 |
---|
876 | ENDIF |
---|
877 | |
---|
878 | dl_value(i1:i2)=dd_value(il_imin:il_imax) |
---|
879 | IF( il_imin == 1 )THEN |
---|
880 | dl_value(:)=EOSHIFT( dl_value(:), & |
---|
881 | & DIM=1, & |
---|
882 | & SHIFT=-1, & |
---|
883 | & BOUNDARY=dl_value(1) ) |
---|
884 | ENDIF |
---|
885 | IF( il_imax == il_shape(1) )THEN |
---|
886 | dl_value(:)=EOSHIFT( dl_value(:), & |
---|
887 | & DIM=1, & |
---|
888 | & SHIFT=1, & |
---|
889 | & BOUNDARY=dl_value(3)) |
---|
890 | ENDIF |
---|
891 | |
---|
892 | IF( ll_discont )THEN |
---|
893 | dl_min=MINVAL( dl_value(:), dl_value(:)/=dd_fill ) |
---|
894 | dl_max=MAXVAL( dl_value(:), dl_value(:)/=dd_fill ) |
---|
895 | IF( dl_min < -170_dp .AND. dl_max > 170_dp )THEN |
---|
896 | WHERE( dl_value(:) < 0._dp ) |
---|
897 | dl_value(:) = dl_value(:)+360._dp |
---|
898 | END WHERE |
---|
899 | ELSEIF( dl_min < 10_dp .AND. dl_max > 350_dp )THEN |
---|
900 | WHERE( dl_value(:) > 180._dp ) |
---|
901 | dl_value(:) = dl_value(:)-180._dp |
---|
902 | END WHERE |
---|
903 | ENDIF |
---|
904 | ENDIF |
---|
905 | |
---|
906 | IF( dl_value( 2) /= dd_fill .AND. & ! ji |
---|
907 | & dl_value( 3) /= dd_fill .AND. & ! ji+1 |
---|
908 | & dl_value( 1) /= dd_fill )THEN ! ji-1 |
---|
909 | |
---|
910 | df_deriv(ji)= (dl_value(3) - dl_value(1)) / REAL(il_imax-il_imin,dp) |
---|
911 | |
---|
912 | ENDIF |
---|
913 | |
---|
914 | ENDDO |
---|
915 | |
---|
916 | DEALLOCATE( dl_value ) |
---|
917 | |
---|
918 | END FUNCTION math_deriv_1D |
---|
919 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
920 | FUNCTION math_deriv_2D(dd_value, dd_fill, cd_dim, ld_discont) & |
---|
921 | & RESULT (df_deriv) |
---|
922 | !------------------------------------------------------------------- |
---|
923 | !> @brief |
---|
924 | !> This function compute derivative of 2D array. |
---|
925 | !> you have to specify in which direction derivative have to be computed: |
---|
926 | !> first (I) or second (J) dimension. |
---|
927 | !> |
---|
928 | !> @details |
---|
929 | !> optionaly you could specify to take into account east west discontinuity |
---|
930 | !> (-180° 180° or 0° 360° for longitude variable) |
---|
931 | !> |
---|
932 | !> @author J.Paul |
---|
933 | !> @date November, 2013 - Initial Version |
---|
934 | !> |
---|
935 | !> @param[in] dd_value 2D array of variable to be extrapolated |
---|
936 | !> @param[in] dd_fill FillValue of variable |
---|
937 | !> @param[in] cd_dim compute derivative on first (I) or second (J) dimension |
---|
938 | !> @param[in] ld_discont logical to take into account east west discontinuity |
---|
939 | !------------------------------------------------------------------- |
---|
940 | |
---|
941 | IMPLICIT NONE |
---|
942 | |
---|
943 | ! Argument |
---|
944 | REAL(dp) , DIMENSION(:,:), INTENT(IN) :: dd_value |
---|
945 | REAL(dp) , INTENT(IN) :: dd_fill |
---|
946 | CHARACTER(LEN=*) , INTENT(IN) :: cd_dim |
---|
947 | LOGICAL , INTENT(IN), OPTIONAL :: ld_discont |
---|
948 | |
---|
949 | ! function |
---|
950 | REAL(dp), DIMENSION(SIZE(dd_value,DIM=1), & |
---|
951 | & SIZE(dd_value,DIM=2) ) :: df_deriv |
---|
952 | |
---|
953 | ! local variable |
---|
954 | INTEGER(i4) :: il_imin |
---|
955 | INTEGER(i4) :: il_imax |
---|
956 | INTEGER(i4) :: il_jmin |
---|
957 | INTEGER(i4) :: il_jmax |
---|
958 | INTEGER(i4), DIMENSION(2) :: il_shape |
---|
959 | |
---|
960 | REAL(dp) :: dl_min |
---|
961 | REAL(dp) :: dl_max |
---|
962 | REAL(dp) , DIMENSION(:,:), ALLOCATABLE :: dl_value |
---|
963 | |
---|
964 | LOGICAL :: ll_discont |
---|
965 | |
---|
966 | ! loop indices |
---|
967 | INTEGER(i4) :: ji |
---|
968 | INTEGER(i4) :: jj |
---|
969 | |
---|
970 | INTEGER(i4) :: i1 |
---|
971 | INTEGER(i4) :: i2 |
---|
972 | |
---|
973 | INTEGER(i4) :: j1 |
---|
974 | INTEGER(i4) :: j2 |
---|
975 | !---------------------------------------------------------------- |
---|
976 | ! init |
---|
977 | df_deriv(:,:)=dd_fill |
---|
978 | |
---|
979 | ll_discont=.FALSE. |
---|
980 | IF( PRESENT(ld_discont) ) ll_discont=ld_discont |
---|
981 | |
---|
982 | il_shape(:)=SHAPE(dd_value(:,:)) |
---|
983 | |
---|
984 | SELECT CASE(TRIM(fct_upper(cd_dim))) |
---|
985 | |
---|
986 | CASE('I') |
---|
987 | |
---|
988 | ALLOCATE( dl_value(3,il_shape(2)) ) |
---|
989 | ! compute derivative in i-direction |
---|
990 | DO ji=1,il_shape(1) |
---|
991 | |
---|
992 | ! init |
---|
993 | dl_value(:,:)=dd_fill |
---|
994 | |
---|
995 | il_imin=MAX(ji-1,1) |
---|
996 | il_imax=MIN(ji+1,il_shape(1)) |
---|
997 | |
---|
998 | IF( il_imin==ji-1 .AND. il_imax==ji+1 )THEN |
---|
999 | i1=1 ; i2=3 |
---|
1000 | ELSEIF( il_imin==ji .AND. il_imax==ji+1 )THEN |
---|
1001 | i1=1 ; i2=2 |
---|
1002 | ELSEIF( il_imin==ji-1 .AND. il_imax==ji )THEN |
---|
1003 | i1=2 ; i2=3 |
---|
1004 | ENDIF |
---|
1005 | |
---|
1006 | dl_value(i1:i2,:)=dd_value(il_imin:il_imax,:) |
---|
1007 | IF( il_imin == 1 )THEN |
---|
1008 | dl_value(:,:)=EOSHIFT( dl_value(:,:), & |
---|
1009 | & DIM=1, & |
---|
1010 | & SHIFT=-1, & |
---|
1011 | & BOUNDARY=dl_value(1,:) ) |
---|
1012 | ENDIF |
---|
1013 | IF( il_imax == il_shape(1) )THEN |
---|
1014 | dl_value(:,:)=EOSHIFT( dl_value(:,:), & |
---|
1015 | & DIM=1, & |
---|
1016 | & SHIFT=1, & |
---|
1017 | & BOUNDARY=dl_value(3,:)) |
---|
1018 | ENDIF |
---|
1019 | |
---|
1020 | IF( ll_discont )THEN |
---|
1021 | dl_min=MINVAL( dl_value(:,:), dl_value(:,:)/=dd_fill ) |
---|
1022 | dl_max=MAXVAL( dl_value(:,:), dl_value(:,:)/=dd_fill ) |
---|
1023 | IF( dl_min < -170_dp .AND. dl_max > 170_dp )THEN |
---|
1024 | WHERE( dl_value(:,:) < 0_dp ) |
---|
1025 | dl_value(:,:) = dl_value(:,:)+360._dp |
---|
1026 | END WHERE |
---|
1027 | ELSEIF( dl_min < 10_dp .AND. dl_max > 350_dp )THEN |
---|
1028 | WHERE( dl_value(:,:) > 180 ) |
---|
1029 | dl_value(:,:) = dl_value(:,:)-180._dp |
---|
1030 | END WHERE |
---|
1031 | ENDIF |
---|
1032 | ENDIF |
---|
1033 | |
---|
1034 | WHERE( dl_value(2,:) /= dd_fill .AND. & ! ji |
---|
1035 | & dl_value(3,:) /= dd_fill .AND. & ! ji+1 |
---|
1036 | & dl_value(1,:) /= dd_fill ) ! ji-1 |
---|
1037 | |
---|
1038 | df_deriv(ji,:)= (dl_value(3,:) - dl_value(1,:)) / REAL(il_imax-il_imin,dp) |
---|
1039 | |
---|
1040 | END WHERE |
---|
1041 | |
---|
1042 | ENDDO |
---|
1043 | |
---|
1044 | CASE('J') |
---|
1045 | |
---|
1046 | ALLOCATE( dl_value(il_shape(1),3) ) |
---|
1047 | ! compute derivative in j-direction |
---|
1048 | DO jj=1,il_shape(2) |
---|
1049 | |
---|
1050 | il_jmin=MAX(jj-1,1) |
---|
1051 | il_jmax=MIN(jj+1,il_shape(2)) |
---|
1052 | |
---|
1053 | IF( il_jmin==jj-1 .AND. il_jmax==jj+1 )THEN |
---|
1054 | j1=1 ; j2=3 |
---|
1055 | ELSEIF( il_jmin==jj .AND. il_jmax==jj+1 )THEN |
---|
1056 | j1=1 ; j2=2 |
---|
1057 | ELSEIF( il_jmin==jj-1 .AND. il_jmax==jj )THEN |
---|
1058 | j1=2 ; j2=3 |
---|
1059 | ENDIF |
---|
1060 | |
---|
1061 | dl_value(:,j1:j2)=dd_value(:,il_jmin:il_jmax) |
---|
1062 | IF( il_jmin == 1 )THEN |
---|
1063 | dl_value(:,:)=EOSHIFT( dl_value(:,:), & |
---|
1064 | & DIM=2, & |
---|
1065 | & SHIFT=-1, & |
---|
1066 | & BOUNDARY=dl_value(:,1)) |
---|
1067 | ENDIF |
---|
1068 | IF( il_jmax == il_shape(2) )THEN |
---|
1069 | dl_value(:,:)=EOSHIFT( dl_value(:,:), & |
---|
1070 | & DIM=2, & |
---|
1071 | & SHIFT=1, & |
---|
1072 | & BOUNDARY=dl_value(:,3)) |
---|
1073 | ENDIF |
---|
1074 | |
---|
1075 | IF( ll_discont )THEN |
---|
1076 | dl_min=MINVAL( dl_value(:,:), dl_value(:,:)/=dd_fill ) |
---|
1077 | dl_max=MAXVAL( dl_value(:,:), dl_value(:,:)/=dd_fill ) |
---|
1078 | IF( dl_min < -170_dp .AND. dl_max > 170_dp )THEN |
---|
1079 | WHERE( dl_value(:,:) < 0_dp ) |
---|
1080 | dl_value(:,:) = dl_value(:,:)+360._dp |
---|
1081 | END WHERE |
---|
1082 | ELSEIF( dl_min < 10_dp .AND. dl_max > 350_dp )THEN |
---|
1083 | WHERE( dl_value(:,:) > 180 ) |
---|
1084 | dl_value(:,:) = dl_value(:,:)-180._dp |
---|
1085 | END WHERE |
---|
1086 | ENDIF |
---|
1087 | ENDIF |
---|
1088 | |
---|
1089 | WHERE( dl_value(:, 2) /= dd_fill .AND. & ! jj |
---|
1090 | & dl_value(:, 3) /= dd_fill .AND. & ! jj+1 |
---|
1091 | & dl_value(:, 1) /= dd_fill ) ! jj-1 |
---|
1092 | |
---|
1093 | df_deriv(:,jj)= (dl_value(:,3) - dl_value(:,1)) / REAL(il_jmax-il_jmin,dp) |
---|
1094 | |
---|
1095 | END WHERE |
---|
1096 | |
---|
1097 | ENDDO |
---|
1098 | |
---|
1099 | END SELECT |
---|
1100 | |
---|
1101 | DEALLOCATE( dl_value ) |
---|
1102 | |
---|
1103 | END FUNCTION math_deriv_2D |
---|
1104 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1105 | PURE FUNCTION math_deriv_3D(dd_value, dd_fill, cd_dim, ld_discont) & |
---|
1106 | & RESULT (df_deriv) |
---|
1107 | !------------------------------------------------------------------- |
---|
1108 | !> @brief |
---|
1109 | !> This function compute derivative of 3D array. |
---|
1110 | !> you have to specify in which direction derivative have to be computed: |
---|
1111 | !> first (I), second (J) or third (K) dimension. |
---|
1112 | !> |
---|
1113 | !> @details |
---|
1114 | !> optionaly you could specify to take into account east west discontinuity |
---|
1115 | !> (-180° 180° or 0° 360° for longitude variable) |
---|
1116 | !> |
---|
1117 | !> @author J.Paul |
---|
1118 | !> @date November, 2013 - Initial Version |
---|
1119 | !> |
---|
1120 | !> @param[inout] dd_value 3D array of variable to be extrapolated |
---|
1121 | !> @param[in] dd_fill FillValue of variable |
---|
1122 | !> @param[in] cd_dim compute derivative on first (I) second (J) or third (K) dimension |
---|
1123 | !> @param[in] ld_discont logical to take into account east west discontinuity |
---|
1124 | !------------------------------------------------------------------- |
---|
1125 | |
---|
1126 | IMPLICIT NONE |
---|
1127 | |
---|
1128 | ! Argument |
---|
1129 | REAL(dp) , DIMENSION(:,:,:), INTENT(IN) :: dd_value |
---|
1130 | REAL(dp) , INTENT(IN) :: dd_fill |
---|
1131 | CHARACTER(LEN=*) , INTENT(IN) :: cd_dim |
---|
1132 | LOGICAL , INTENT(IN), OPTIONAL :: ld_discont |
---|
1133 | |
---|
1134 | ! function |
---|
1135 | REAL(dp), DIMENSION(SIZE(dd_value,DIM=1), & |
---|
1136 | & SIZE(dd_value,DIM=2), & |
---|
1137 | & SIZE(dd_value,DIM=3)) :: df_deriv |
---|
1138 | |
---|
1139 | ! local variable |
---|
1140 | INTEGER(i4) :: il_imin |
---|
1141 | INTEGER(i4) :: il_imax |
---|
1142 | INTEGER(i4) :: il_jmin |
---|
1143 | INTEGER(i4) :: il_jmax |
---|
1144 | INTEGER(i4) :: il_kmin |
---|
1145 | INTEGER(i4) :: il_kmax |
---|
1146 | INTEGER(i4), DIMENSION(3) :: il_shape |
---|
1147 | |
---|
1148 | REAL(dp) :: dl_min |
---|
1149 | REAL(dp) :: dl_max |
---|
1150 | REAL(dp) , DIMENSION(:,:,:), ALLOCATABLE :: dl_value |
---|
1151 | |
---|
1152 | LOGICAL :: ll_discont |
---|
1153 | |
---|
1154 | ! loop indices |
---|
1155 | INTEGER(i4) :: ji |
---|
1156 | INTEGER(i4) :: jj |
---|
1157 | INTEGER(i4) :: jk |
---|
1158 | |
---|
1159 | INTEGER(i4) :: i1 |
---|
1160 | INTEGER(i4) :: i2 |
---|
1161 | |
---|
1162 | INTEGER(i4) :: j1 |
---|
1163 | INTEGER(i4) :: j2 |
---|
1164 | |
---|
1165 | INTEGER(i4) :: k1 |
---|
1166 | INTEGER(i4) :: k2 |
---|
1167 | !---------------------------------------------------------------- |
---|
1168 | ! init |
---|
1169 | df_deriv(:,:,:)=dd_fill |
---|
1170 | |
---|
1171 | ll_discont=.FALSE. |
---|
1172 | IF( PRESENT(ld_discont) ) ll_discont=ld_discont |
---|
1173 | |
---|
1174 | il_shape(:)=SHAPE(dd_value(:,:,:)) |
---|
1175 | |
---|
1176 | |
---|
1177 | SELECT CASE(TRIM(fct_upper(cd_dim))) |
---|
1178 | |
---|
1179 | CASE('I') |
---|
1180 | |
---|
1181 | ALLOCATE( dl_value(3,il_shape(2),il_shape(3)) ) |
---|
1182 | ! compute derivative in i-direction |
---|
1183 | DO ji=1,il_shape(1) |
---|
1184 | |
---|
1185 | il_imin=MAX(ji-1,1) |
---|
1186 | il_imax=MIN(ji+1,il_shape(1)) |
---|
1187 | |
---|
1188 | IF( il_imin==ji-1 .AND. il_imax==ji+1 )THEN |
---|
1189 | i1=1 ; i2=3 |
---|
1190 | ELSEIF( il_imin==ji .AND. il_imax==ji+1 )THEN |
---|
1191 | i1=1 ; i2=2 |
---|
1192 | ELSEIF( il_imin==ji-1 .AND. il_imax==ji )THEN |
---|
1193 | i1=2 ; i2=3 |
---|
1194 | ENDIF |
---|
1195 | |
---|
1196 | dl_value(i1:i2,:,:)=dd_value(il_imin:il_imax,:,:) |
---|
1197 | IF( il_imin == 1 )THEN |
---|
1198 | dl_value(:,:,:)=EOSHIFT( dl_value(:,:,:), & |
---|
1199 | & DIM=1, & |
---|
1200 | & SHIFT=-1, & |
---|
1201 | & BOUNDARY=dl_value(1,:,:) ) |
---|
1202 | ENDIF |
---|
1203 | IF( il_imax == il_shape(1) )THEN |
---|
1204 | dl_value(:,:,:)=EOSHIFT( dl_value(:,:,:), & |
---|
1205 | & DIM=1, & |
---|
1206 | & SHIFT=1, & |
---|
1207 | & BOUNDARY=dl_value(3,:,:)) |
---|
1208 | ENDIF |
---|
1209 | |
---|
1210 | IF( ll_discont )THEN |
---|
1211 | dl_min=MINVAL( dl_value(:,:,:), dl_value(:,:,:)/=dd_fill ) |
---|
1212 | dl_max=MAXVAL( dl_value(:,:,:), dl_value(:,:,:)/=dd_fill ) |
---|
1213 | IF( dl_min < -170_dp .AND. dl_max > 170_dp )THEN |
---|
1214 | WHERE( dl_value(:,:,:) < 0_dp ) |
---|
1215 | dl_value(:,:,:) = dl_value(:,:,:)+360._dp |
---|
1216 | END WHERE |
---|
1217 | ELSEIF( dl_min < 10_dp .AND. dl_max > 350_dp )THEN |
---|
1218 | WHERE( dl_value(:,:,:) > 180 ) |
---|
1219 | dl_value(:,:,:) = dl_value(:,:,:)-180._dp |
---|
1220 | END WHERE |
---|
1221 | ENDIF |
---|
1222 | ENDIF |
---|
1223 | |
---|
1224 | WHERE( dl_value(2,:,:) /= dd_fill .AND. & ! ji |
---|
1225 | & dl_value(3,:,:) /= dd_fill .AND. & !ji+1 |
---|
1226 | & dl_value(1,:,:) /= dd_fill ) !ji-1 |
---|
1227 | |
---|
1228 | df_deriv(ji,:,:)= (dl_value(3,:,:) - dl_value(1,:,:)) / REAL(il_imax-il_imin,dp) |
---|
1229 | |
---|
1230 | END WHERE |
---|
1231 | |
---|
1232 | ENDDO |
---|
1233 | |
---|
1234 | CASE('J') |
---|
1235 | |
---|
1236 | ALLOCATE( dl_value(il_shape(1),3,il_shape(3)) ) |
---|
1237 | ! compute derivative in j-direction |
---|
1238 | DO jj=1,il_shape(2) |
---|
1239 | |
---|
1240 | il_jmin=MAX(jj-1,1) |
---|
1241 | il_jmax=MIN(jj+1,il_shape(2)) |
---|
1242 | |
---|
1243 | IF( il_jmin==jj-1 .AND. il_jmax==jj+1 )THEN |
---|
1244 | j1=1 ; j2=3 |
---|
1245 | ELSEIF( il_jmin==jj .AND. il_jmax==jj+1 )THEN |
---|
1246 | j1=1 ; j2=2 |
---|
1247 | ELSEIF( il_jmin==jj-1 .AND. il_jmax==jj )THEN |
---|
1248 | j1=2 ; j2=3 |
---|
1249 | ENDIF |
---|
1250 | |
---|
1251 | dl_value(:,j1:j2,:)=dd_value(:,il_jmin:il_jmax,:) |
---|
1252 | IF( il_jmin == 1 )THEN |
---|
1253 | dl_value(:,:,:)=EOSHIFT( dl_value(:,:,:), & |
---|
1254 | & DIM=2, & |
---|
1255 | & SHIFT=-1, & |
---|
1256 | & BOUNDARY=dl_value(:,1,:) ) |
---|
1257 | ENDIF |
---|
1258 | IF( il_jmax == il_shape(2) )THEN |
---|
1259 | dl_value(:,:,:)=EOSHIFT( dl_value(:,:,:), & |
---|
1260 | & DIM=2, & |
---|
1261 | & SHIFT=1, & |
---|
1262 | & BOUNDARY=dl_value(:,3,:)) |
---|
1263 | ENDIF |
---|
1264 | |
---|
1265 | IF( ll_discont )THEN |
---|
1266 | dl_min=MINVAL( dl_value(:,:,:), dl_value(:,:,:)/=dd_fill ) |
---|
1267 | dl_max=MAXVAL( dl_value(:,:,:), dl_value(:,:,:)/=dd_fill ) |
---|
1268 | IF( dl_min < -170_dp .AND. dl_max > 170_dp )THEN |
---|
1269 | WHERE( dl_value(:,:,:) < 0_dp ) |
---|
1270 | dl_value(:,:,:) = dl_value(:,:,:)+360._dp |
---|
1271 | END WHERE |
---|
1272 | ELSEIF( dl_min < 10_dp .AND. dl_max > 350_dp )THEN |
---|
1273 | WHERE( dl_value(:,:,:) > 180 ) |
---|
1274 | dl_value(:,:,:) = dl_value(:,:,:)-180._dp |
---|
1275 | END WHERE |
---|
1276 | ENDIF |
---|
1277 | ENDIF |
---|
1278 | |
---|
1279 | WHERE( dl_value(:, 2,:) /= dd_fill .AND. & ! jj |
---|
1280 | & dl_value(:, 3,:) /= dd_fill .AND. & ! jj+1 |
---|
1281 | & dl_value(:, 1,:) /= dd_fill ) ! jj-1 |
---|
1282 | |
---|
1283 | df_deriv(:,jj,:)= (dl_value(:,3,:) - dl_value(:,1,:)) / REAL(il_jmax - il_jmin,dp) |
---|
1284 | |
---|
1285 | END WHERE |
---|
1286 | |
---|
1287 | ENDDO |
---|
1288 | |
---|
1289 | CASE('K') |
---|
1290 | |
---|
1291 | ALLOCATE( dl_value(il_shape(1),il_shape(2),3) ) |
---|
1292 | ! compute derivative in k-direction |
---|
1293 | DO jk=1,il_shape(3) |
---|
1294 | |
---|
1295 | il_kmin=MAX(jk-1,1) |
---|
1296 | il_kmax=MIN(jk+1,il_shape(3)) |
---|
1297 | |
---|
1298 | IF( il_kmin==jk-1 .AND. il_kmax==jk+1 )THEN |
---|
1299 | k1=1 ; k2=3 |
---|
1300 | ELSEIF( il_kmin==jk .AND. il_kmax==jk+1 )THEN |
---|
1301 | k1=1 ; k2=2 |
---|
1302 | ELSEIF( il_kmin==jk-1 .AND. il_kmax==jk )THEN |
---|
1303 | k1=2 ; k2=3 |
---|
1304 | ENDIF |
---|
1305 | |
---|
1306 | dl_value(:,:,k1:k2)=dd_value(:,:,il_kmin:il_kmax) |
---|
1307 | IF( il_kmin == 1 )THEN |
---|
1308 | dl_value(:,:,:)=EOSHIFT( dl_value(:,:,:), & |
---|
1309 | & DIM=3, & |
---|
1310 | & SHIFT=-1, & |
---|
1311 | & BOUNDARY=dl_value(:,:,1) ) |
---|
1312 | ENDIF |
---|
1313 | IF( il_kmax == il_shape(3) )THEN |
---|
1314 | dl_value(:,:,:)=EOSHIFT( dl_value(:,:,:), & |
---|
1315 | & DIM=3, & |
---|
1316 | & SHIFT=1, & |
---|
1317 | & BOUNDARY=dl_value(:,:,3)) |
---|
1318 | ENDIF |
---|
1319 | |
---|
1320 | IF( ll_discont )THEN |
---|
1321 | dl_min=MINVAL( dl_value(:,:,:), dl_value(:,:,:)/=dd_fill ) |
---|
1322 | dl_max=MAXVAL( dl_value(:,:,:), dl_value(:,:,:)/=dd_fill ) |
---|
1323 | IF( dl_min < -170_dp .AND. dl_max > 170_dp )THEN |
---|
1324 | WHERE( dl_value(:,:,:) < 0_dp ) |
---|
1325 | dl_value(:,:,:) = dl_value(:,:,:)+360._dp |
---|
1326 | END WHERE |
---|
1327 | ELSEIF( dl_min < 10_dp .AND. dl_max > 350_dp )THEN |
---|
1328 | WHERE( dl_value(:,:,:) > 180 ) |
---|
1329 | dl_value(:,:,:) = dl_value(:,:,:)-180._dp |
---|
1330 | END WHERE |
---|
1331 | ENDIF |
---|
1332 | ENDIF |
---|
1333 | |
---|
1334 | WHERE( dl_value(:,:,2) /= dd_fill .AND. & ! jk |
---|
1335 | & dl_value(:,:,3) /= dd_fill .AND. & ! jk+1 |
---|
1336 | & dl_value(:,:,1) /= dd_fill ) ! jk-1 |
---|
1337 | |
---|
1338 | df_deriv(:,:,jk)= (dl_value(:,:,3) - dl_value(:,:,1)) / REAL(il_kmax-il_kmin,dp) |
---|
1339 | |
---|
1340 | END WHERE |
---|
1341 | |
---|
1342 | ENDDO |
---|
1343 | |
---|
1344 | END SELECT |
---|
1345 | |
---|
1346 | DEALLOCATE( dl_value ) |
---|
1347 | |
---|
1348 | END FUNCTION math_deriv_3D |
---|
1349 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1350 | FUNCTION math_ortho(dd_latm) & |
---|
1351 | & RESULT(df_ortho) |
---|
1352 | !------------------------------------------------------------------- |
---|
1353 | !> @brief |
---|
1354 | !> This function compute orthodome distance between opposite point of a cell |
---|
1355 | !> of one degree. |
---|
1356 | !> |
---|
1357 | !> @details |
---|
1358 | !> |
---|
1359 | !> @author J.Paul |
---|
1360 | !> @date April, 2017 - Initial Version |
---|
1361 | !> |
---|
1362 | !> @param[in] dd_latm mean latitude of the cell |
---|
1363 | !> @return orthodome distance |
---|
1364 | !------------------------------------------------------------------- |
---|
1365 | |
---|
1366 | IMPLICIT NONE |
---|
1367 | |
---|
1368 | ! Argument |
---|
1369 | REAL(dp), TARGET :: dd_latm |
---|
1370 | |
---|
1371 | ! function |
---|
1372 | REAL(dp) :: df_ortho |
---|
1373 | |
---|
1374 | ! local |
---|
1375 | REAL(dp) :: dl_dlat |
---|
1376 | REAL(dp) :: dl_dlon |
---|
1377 | REAL(dp) :: dl_lat1 |
---|
1378 | REAL(dp) :: dl_lat2 |
---|
1379 | REAL(dp) :: dl_tmp |
---|
1380 | !---------------------------------------------------------------- |
---|
1381 | |
---|
1382 | ! one degree cell |
---|
1383 | dl_dlat= 1._dp * dp_deg2rad |
---|
1384 | dl_dlon= 1._dp * dp_deg2rad |
---|
1385 | |
---|
1386 | ! |
---|
1387 | dl_lat1 = (dd_latm - 0.5_dp) * dp_deg2rad |
---|
1388 | dl_lat2 = (dd_latm + 0.5_dp) * dp_deg2rad |
---|
1389 | |
---|
1390 | dl_tmp = SQRT( SIN(dl_dlat*0.5)**2 + & |
---|
1391 | & COS(dl_lat1)*COS(dl_lat2)*SIN(dl_dlon*0.5)**2 ) |
---|
1392 | |
---|
1393 | df_ortho= 2* dp_rearth * ASIN( dl_tmp ) |
---|
1394 | |
---|
1395 | END FUNCTION math_ortho |
---|
1396 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1397 | FUNCTION math_euclid(dd_lonm,dd_latm) & |
---|
1398 | & RESULT(df_euclid) |
---|
1399 | !------------------------------------------------------------------- |
---|
1400 | !> @brief |
---|
1401 | !> This function compute euclidian distance between opposite point of a cell |
---|
1402 | !> of one degree, center on (lonm,latm). |
---|
1403 | !> |
---|
1404 | !> @details |
---|
1405 | !> |
---|
1406 | !> @author J.Paul |
---|
1407 | !> @date April, 2017 - Initial Version |
---|
1408 | !> |
---|
1409 | !> @param[in] dd_lonm mean longitude of the cell |
---|
1410 | !> @param[in] dd_latm mean latitude of the cell |
---|
1411 | !> @return orthodome distance |
---|
1412 | !------------------------------------------------------------------- |
---|
1413 | |
---|
1414 | IMPLICIT NONE |
---|
1415 | |
---|
1416 | ! Argument |
---|
1417 | REAL(dp), TARGET :: dd_lonm |
---|
1418 | REAL(dp), TARGET :: dd_latm |
---|
1419 | |
---|
1420 | ! function |
---|
1421 | REAL(dp) :: df_euclid |
---|
1422 | |
---|
1423 | ! local |
---|
1424 | REAL(dp) :: dl_lata |
---|
1425 | REAL(dp) :: dl_lona |
---|
1426 | REAL(dp) :: dl_latb |
---|
1427 | REAL(dp) :: dl_lonb |
---|
1428 | REAL(dp) :: xa,ya,za |
---|
1429 | REAL(dp) :: xb,yb,zb |
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1430 | !---------------------------------------------------------------- |
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1431 | |
---|
1432 | dl_lata=(dd_latm-0.5)*dp_deg2rad |
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1433 | dl_lona=(dd_lonm-0.5)*dp_deg2rad |
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1434 | |
---|
1435 | xa = dp_rearth * COS(dl_lata) * COS(dl_lona) |
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1436 | ya = dp_rearth * COS(dl_lata) * SIN(dl_lona) |
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1437 | za = dp_rearth * SIN(dl_lata) |
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1438 | |
---|
1439 | dl_latb=(dd_latm+0.5)*dp_deg2rad |
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1440 | dl_lonb=(dd_lonm+0.5)*dp_deg2rad |
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1441 | |
---|
1442 | xb = dp_rearth * COS(dl_latb) * COS(dl_lonb) |
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1443 | yb = dp_rearth * COS(dl_latb) * SIN(dl_lonb) |
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1444 | zb = dp_rearth * SIN(dl_latb) |
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1445 | |
---|
1446 | df_euclid = ((xb-xa)**2 + (yb-ya)**2 + (zb-za)**2) |
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1447 | |
---|
1448 | END FUNCTION math_euclid |
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1449 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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1450 | END MODULE math |
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