[5608] | 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 | ! MODULE: math |
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| 6 | ! |
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| 7 | ! DESCRIPTION: |
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| 8 | !> @brief |
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| 9 | !> This module groups some useful mathematical function. |
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| 10 | !> |
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| 11 | !> @details |
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| 12 | !> |
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| 13 | !> to compute the mean of an array:<br/> |
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| 14 | !> @code |
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| 15 | !> dl_value=math_mean( dl_value, dd_fill ) |
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| 16 | !> @endcode |
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| 17 | !> - dl_value is 1D or 2D array |
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| 18 | !> - dd_fill is FillValue |
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| 19 | !> |
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| 20 | !> to compute the median of an array:<br/> |
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| 21 | !> @code |
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| 22 | !> dl_value=math_median( dl_value, dd_fill ) |
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| 23 | !> @endcode |
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| 24 | !> - dl_value is 1D or 2D array |
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| 25 | !> - dd_fill is FillValue |
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| 26 | !> |
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| 27 | !> to compute the mean without extremum of an array:<br/> |
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| 28 | !> @code |
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| 29 | !> dl_value=math_mwe( dl_value, id_next, dd_fill ) |
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| 30 | !> @endcode |
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| 31 | !> - dl_value is 1D or 2D array |
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| 32 | !> - id_next is the number of extremum to be removed |
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| 33 | !> - dd_fill is FillValue |
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| 34 | !> |
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| 35 | !> to sort an 1D array:<br/> |
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| 36 | !> @code |
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| 37 | !> CALL math_QsortC(dl_value) |
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| 38 | !> @endcode |
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| 39 | !> - dl_value is 1D array |
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| 40 | !> |
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| 41 | !> to correct phase angles to produce smoother phase:<br/> |
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| 42 | !> @code |
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| 43 | !> CALL math_unwrap(dl_value, [dl_discont]) |
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| 44 | !> @endcode |
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| 45 | !> - dl_value is 1D array |
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| 46 | !> - dl_discont maximum discontinuity between values, default pi |
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| 47 | !> |
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| 48 | !> to compute simple operation |
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| 49 | !> @code |
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| 50 | !> dl_res=math_compute(cl_var) |
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| 51 | !> @endcode |
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| 52 | !> - cl_var operation to compute (string of character) |
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| 53 | !> - dl_res result of the operation, real(dp) |
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| 54 | !> |
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| 55 | !> to compute first derivative of 1D array:<br/> |
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| 56 | !> @code |
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| 57 | !> dl_value(:)=math_deriv_1D( dd_value(:), dd_fill, [ld_discont] ) |
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| 58 | !> @endcode |
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| 59 | !> - dd_value is 1D array of variable |
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| 60 | !> - dd_fill is FillValue of variable |
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| 61 | !> - ld_discont is logical to take into account longitudinal |
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| 62 | !> East-West discontinuity [optional] |
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| 63 | !> |
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| 64 | !> to compute first derivative of 2D array:<br/> |
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| 65 | !> @code |
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| 66 | !> dl_value(:,:)=math_deriv_2D( dd_value(:,:), dd_fill, cd_dim, |
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| 67 | !> [ld_discont] ) |
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| 68 | !> @endcode |
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| 69 | !> - dd_value is 2D array of variable |
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| 70 | !> - dd_fill is FillValue of variable |
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| 71 | !> - cd_dim is character to compute derivative on first (I) or |
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| 72 | !> second (J) dimension |
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| 73 | !> - ld_discont is logical to take into account longitudinal |
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| 74 | !> East-West discontinuity [optional] |
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| 75 | !> |
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| 76 | !> to compute first derivative of 3D array:<br/> |
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| 77 | !> @code |
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| 78 | !> dl_value(:,:,:)=math_deriv_3D( dd_value(:,:,:), dd_fill, cd_dim, |
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| 79 | !> [ld_discont] ) |
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| 80 | !> @endcode |
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| 81 | !> - dd_value is 3D array of variable |
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| 82 | !> - dd_fill is FillValue of variable |
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| 83 | !> - cd_dim is character to compute derivative on first (I), second (J), |
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| 84 | !> or third (K) dimension |
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| 85 | !> - ld_discont is logical to take into account longitudinal East-West |
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| 86 | !> discontinuity [optional] |
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| 87 | !> |
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| 88 | !> |
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| 89 | !> @author |
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| 90 | !> J.Paul |
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| 91 | ! REVISION HISTORY: |
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| 92 | !> @date January, 2015 - Initial version |
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| 93 | ! |
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| 94 | !> @note Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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| 95 | !---------------------------------------------------------------------- |
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| 96 | MODULE math |
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| 97 | USE kind ! F90 kind parameter |
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| 98 | USE global ! global variable |
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| 99 | USE phycst ! physical constant |
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| 100 | USE fct ! basic useful function |
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| 101 | IMPLICIT NONE |
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| 102 | ! NOTE_avoid_public_variables_if_possible |
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| 103 | |
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| 104 | ! function and subroutine |
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| 105 | PUBLIC :: math_mean !< return mean of an array |
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| 106 | PUBLIC :: math_median !< return median of an array |
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| 107 | PUBLIC :: math_mwe !< return mean without extremum of an array |
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| 108 | PUBLIC :: math_QsortC !< sort an 1D array |
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| 109 | PUBLIC :: math_unwrap !< correct phase angles to produce smoother phase |
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| 110 | PUBLIC :: math_compute !< compute simple operation |
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| 111 | PUBLIC :: math_deriv_1D !< compute first derivative of 1D array |
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| 112 | PUBLIC :: math_deriv_2D !< compute first derivative of 2D array |
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| 113 | PUBLIC :: math_deriv_3D !< compute first derivative of 3D array |
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| 114 | |
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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 | !> @brief This function compute the mean of a 1D array. |
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| 144 | ! |
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| 145 | !> @author J.Paul |
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[5616] | 146 | !> @date January, 2015 - Initial Version |
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[5608] | 147 | ! |
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| 148 | !> @param[in] dd_array 1D array |
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| 149 | !> @param[in] dd_fill fillValue |
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| 150 | !> @return mean value, real(dp) |
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| 151 | !------------------------------------------------------------------- |
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| 152 | PURE REAL(dp) FUNCTION math__mean_1d(dd_array, dd_fill) |
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| 153 | IMPLICIT NONE |
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| 154 | ! Argument |
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| 155 | REAL(dp), DIMENSION(:), INTENT(IN) :: dd_array |
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| 156 | REAL(dp), INTENT(IN), OPTIONAL :: dd_fill |
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| 157 | |
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| 158 | ! local variable |
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| 159 | INTEGER(i4) :: il_count |
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| 160 | REAL(dp) :: dl_sum |
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| 161 | REAL(dp) :: dl_count |
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| 162 | !---------------------------------------------------------------- |
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| 163 | |
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| 164 | IF( PRESENT(dd_fill) )THEN |
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| 165 | il_count=COUNT(dd_array(:)/=dd_fill) |
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| 166 | IF( il_count > 0 )THEN |
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| 167 | dl_sum =SUM ( dd_array(:), dd_array(:)/= dd_fill ) |
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| 168 | dl_count=REAL( il_count, dp) |
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| 169 | |
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| 170 | math__mean_1d=dl_sum/dl_count |
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| 171 | ELSE |
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| 172 | math__mean_1d=dd_fill |
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| 173 | ENDIF |
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| 174 | ELSE |
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| 175 | il_count=SIZE(dd_array(:)) |
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| 176 | IF( il_count > 0 )THEN |
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| 177 | dl_sum =SUM ( dd_array(:) ) |
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| 178 | dl_count=REAL( il_count, dp) |
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| 179 | |
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| 180 | math__mean_1d=dl_sum/dl_count |
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| 181 | ELSE |
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| 182 | math__mean_1d=0 |
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| 183 | ENDIF |
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| 184 | ENDIF |
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| 185 | |
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| 186 | END FUNCTION math__mean_1d |
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| 187 | !------------------------------------------------------------------- |
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| 188 | !> @brief This function compute the mean of a 2D array. |
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| 189 | ! |
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| 190 | !> @author J.Paul |
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[5616] | 191 | !> @date January, 2015 - Initial Version |
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[5608] | 192 | ! |
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| 193 | !> @param[in] dd_array 2D array |
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| 194 | !> @param[in] dd_fill fillValue |
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| 195 | !> @return mean value, real(dp) |
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| 196 | !------------------------------------------------------------------- |
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| 197 | PURE REAL(dp) FUNCTION math__mean_2d(dd_array, dd_fill) |
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| 198 | IMPLICIT NONE |
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| 199 | ! Argument |
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| 200 | REAL(dp), DIMENSION(:,:), INTENT(IN) :: dd_array |
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| 201 | REAL(dp), INTENT(IN), OPTIONAL :: dd_fill |
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| 202 | |
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| 203 | ! local variable |
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| 204 | INTEGER(i4) :: il_count |
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| 205 | |
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| 206 | REAL(dp), DIMENSION(:), ALLOCATABLE :: dl_list |
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| 207 | !---------------------------------------------------------------- |
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| 208 | |
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| 209 | IF( PRESENT(dd_fill) )THEN |
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| 210 | il_count=COUNT(dd_array(:,:)/=dd_fill) |
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| 211 | IF( il_count > 0 )THEN |
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| 212 | ALLOCATE( dl_list(il_count) ) |
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| 213 | dl_list(:)=PACK(dd_array(:,:),dd_array(:,:)/=dd_fill) |
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| 214 | ELSE |
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| 215 | math__mean_2d=dd_fill |
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| 216 | ENDIF |
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| 217 | ELSE |
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| 218 | il_count=SIZE(dd_array) |
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| 219 | IF( il_count > 0 )THEN |
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| 220 | ALLOCATE( dl_list(il_count) ) |
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| 221 | dl_list(:)=PACK(dd_array(:,:), MASK=.TRUE.) |
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| 222 | ELSE |
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| 223 | math__mean_2d=0 |
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| 224 | ENDIF |
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| 225 | ENDIF |
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| 226 | |
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| 227 | IF( ALLOCATED(dl_list) )THEN |
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| 228 | math__mean_2d=math_mean(dl_list(:)) |
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| 229 | DEALLOCATE( dl_list ) |
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| 230 | ENDIF |
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| 231 | |
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| 232 | END FUNCTION math__mean_2d |
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| 233 | !------------------------------------------------------------------- |
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| 234 | !> @brief This function compute the median of a 1D array. |
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| 235 | ! |
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| 236 | !> @author J.Paul |
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[5616] | 237 | !> @date January, 2015 - Initial Version |
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[5608] | 238 | ! |
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| 239 | !> @param[in] dd_array 1D array |
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| 240 | !> @param[in] dd_fill fillValue |
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| 241 | !> @return median value, real(dp) |
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| 242 | !------------------------------------------------------------------- |
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| 243 | PURE REAL(dp) FUNCTION math__median_1d(dd_array, dd_fill) |
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| 244 | IMPLICIT NONE |
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| 245 | ! Argument |
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| 246 | REAL(dp), DIMENSION(:), INTENT(IN) :: dd_array |
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| 247 | REAL(dp), INTENT(IN), OPTIONAL :: dd_fill |
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| 248 | |
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| 249 | ! local variable |
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| 250 | INTEGER(i4) :: il_count |
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| 251 | |
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| 252 | REAL(dp), DIMENSION(:), ALLOCATABLE :: dl_list |
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| 253 | !---------------------------------------------------------------- |
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| 254 | |
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| 255 | IF( PRESENT(dd_fill) )THEN |
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| 256 | il_count=COUNT(dd_array(:)/=dd_fill) |
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| 257 | IF( il_count > 0 )THEN |
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| 258 | ALLOCATE( dl_list(il_count) ) |
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| 259 | dl_list(:)=PACK(dd_array(:),dd_array(:)/=dd_fill) |
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| 260 | ELSE |
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| 261 | math__median_1d=dd_fill |
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| 262 | ENDIF |
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| 263 | ELSE |
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| 264 | il_count=SIZE(dd_array(:)) |
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| 265 | IF( il_count > 0 )THEN |
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| 266 | ALLOCATE( dl_list(il_count) ) |
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| 267 | dl_list(:)=dd_array(:) |
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| 268 | ELSE |
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| 269 | math__median_1d=0 |
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| 270 | ENDIF |
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| 271 | ENDIF |
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| 272 | |
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| 273 | IF( ALLOCATED(dl_list) )THEN |
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| 274 | CALL math_QsortC(dl_list(:)) |
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| 275 | |
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| 276 | IF( MOD(il_count,2) == 0 )THEN |
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| 277 | math__median_1d=(dl_list(il_count/2+1)+dl_list(il_count/2))/2_dp |
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| 278 | ELSE |
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| 279 | math__median_1d=dl_list(il_count/2+1) |
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| 280 | ENDIF |
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| 281 | |
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| 282 | DEALLOCATE(dl_list) |
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| 283 | ENDIF |
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| 284 | |
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| 285 | END FUNCTION math__median_1d |
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| 286 | !------------------------------------------------------------------- |
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| 287 | !> @brief This function compute the median of a 2D array. |
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| 288 | ! |
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| 289 | !> @author J.Paul |
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[5616] | 290 | !> @date January, 2015 - Initial Version |
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[5608] | 291 | ! |
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| 292 | !> @param[in] dd_array 2D array |
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| 293 | !> @param[in] dd_fill fillValue |
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| 294 | !> @return median value, real(dp) |
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| 295 | !------------------------------------------------------------------- |
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| 296 | PURE REAL(dp) FUNCTION math__median_2d(dd_array, dd_fill) |
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| 297 | IMPLICIT NONE |
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| 298 | ! Argument |
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| 299 | REAL(dp), DIMENSION(:,:), INTENT(IN) :: dd_array |
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| 300 | REAL(dp), INTENT(IN), OPTIONAL :: dd_fill |
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| 301 | |
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| 302 | ! local variable |
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| 303 | INTEGER(i4) :: il_count |
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| 304 | |
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| 305 | REAL(dp), DIMENSION(:), ALLOCATABLE :: dl_list |
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| 306 | !---------------------------------------------------------------- |
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| 307 | |
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| 308 | IF( PRESENT(dd_fill) )THEN |
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| 309 | il_count=COUNT(dd_array(:,:)/=dd_fill) |
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| 310 | IF( il_count > 0 )THEN |
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| 311 | ALLOCATE( dl_list(il_count) ) |
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| 312 | dl_list(:)=PACK(dd_array(:,:),dd_array(:,:)/=dd_fill) |
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| 313 | ELSE |
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| 314 | math__median_2d=dd_fill |
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| 315 | ENDIF |
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| 316 | ELSE |
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| 317 | il_count=SIZE(dd_array(:,:)) |
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| 318 | IF( il_count > 0 )THEN |
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| 319 | ALLOCATE( dl_list(il_count) ) |
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| 320 | dl_list(:)=PACK(dd_array(:,:), MASK=.TRUE.) |
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| 321 | ELSE |
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| 322 | math__median_2d=0 |
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| 323 | ENDIF |
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| 324 | ENDIF |
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| 325 | |
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| 326 | IF( ALLOCATED(dl_list) )THEN |
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| 327 | math__median_2d=math_median(dl_list(:)) |
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| 328 | DEALLOCATE(dl_list) |
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| 329 | ENDIF |
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| 330 | |
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| 331 | END FUNCTION math__median_2d |
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| 332 | !------------------------------------------------------------------- |
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| 333 | !> @brief This function compute the mean without extremum of a 1D array. |
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| 334 | ! |
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| 335 | !> @author J.Paul |
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[5616] | 336 | !> @date January, 2015 - Initial Version |
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[5608] | 337 | ! |
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| 338 | !> @param[in] dd_array 1D array |
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| 339 | !> @param[in] id_next number of extremum to be removed |
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| 340 | !> @param[in] dd_fill fillValue |
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| 341 | !> @return median value, real(dp) |
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| 342 | !------------------------------------------------------------------- |
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| 343 | PURE REAL(dp) FUNCTION math__mwe_1d(dd_array, id_next, dd_fill) |
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| 344 | IMPLICIT NONE |
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| 345 | ! Argument |
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| 346 | REAL(dp), DIMENSION(:), INTENT(IN) :: dd_array |
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| 347 | INTEGER(i4) , INTENT(IN), OPTIONAL :: id_next |
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| 348 | REAL(dp), INTENT(IN), OPTIONAL :: dd_fill |
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| 349 | |
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| 350 | ! local variable |
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| 351 | INTEGER(i4) :: il_next |
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| 352 | INTEGER(i4) :: il_count |
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| 353 | INTEGER(i4) :: il_size |
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| 354 | |
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| 355 | REAL(dp), DIMENSION(:), ALLOCATABLE :: dl_list |
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| 356 | !---------------------------------------------------------------- |
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| 357 | |
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| 358 | il_next=2 |
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| 359 | IF( PRESENT(id_next) ) il_next=id_next |
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| 360 | |
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| 361 | il_size=SIZE(dd_array(:)) |
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| 362 | IF( PRESENT(dd_fill) )THEN |
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| 363 | il_count=COUNT(dd_array(:)/=dd_fill) |
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| 364 | IF( il_count > 0 )THEN |
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| 365 | ALLOCATE( dl_list(il_count) ) |
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| 366 | dl_list(:)=PACK(dd_array(:),dd_array(:)/=dd_fill) |
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| 367 | ELSE |
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| 368 | math__mwe_1d=dd_fill |
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| 369 | ENDIF |
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| 370 | ELSE |
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| 371 | il_count=SIZE(dd_array(:)) |
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| 372 | IF( il_count > 0 )THEN |
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| 373 | ALLOCATE( dl_list(il_count) ) |
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| 374 | dl_list(:)=dd_array(:) |
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| 375 | ELSE |
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| 376 | math__mwe_1d=0 |
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| 377 | ENDIF |
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| 378 | ENDIF |
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| 379 | |
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| 380 | IF( ALLOCATED(dl_list) )THEN |
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| 381 | CALL math_QsortC(dl_list(:)) |
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| 382 | |
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| 383 | IF( il_count == il_size )THEN |
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| 384 | ! no fillValue |
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| 385 | math__mwe_1d=math_mean(dl_list(il_next+1:il_size-il_next)) |
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| 386 | ELSEIF( il_count > il_size-2*il_next )THEN |
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| 387 | ! remove one extremum each side |
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| 388 | math__mwe_1d=math_mean(dl_list(2:il_size-1)) |
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| 389 | ELSE ! il_count <= il_size-2*il_next |
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| 390 | ! more than 2*il_next fillValue |
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| 391 | ! compute mean only |
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| 392 | math__mwe_1d=math_mean(dl_list(:)) |
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| 393 | ENDIF |
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| 394 | |
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| 395 | DEALLOCATE(dl_list) |
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| 396 | ENDIF |
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| 397 | |
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| 398 | END FUNCTION math__mwe_1d |
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| 399 | !------------------------------------------------------------------- |
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| 400 | !> @brief This function compute the mean without extremum of a 2D array. |
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| 401 | ! |
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| 402 | !> @author J.Paul |
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[5616] | 403 | !> @date January, 2015 - Initial Version |
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[5608] | 404 | ! |
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| 405 | !> @param[in] dd_array 2D array |
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| 406 | !> @param[in] id_next number of extremum to be removed |
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| 407 | !> @param[in] dd_fill fillValue |
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| 408 | !> @return median value, real(dp) |
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| 409 | !------------------------------------------------------------------- |
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| 410 | PURE REAL(dp) FUNCTION math__mwe_2d(dd_array, id_next, dd_fill) |
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| 411 | IMPLICIT NONE |
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| 412 | ! Argument |
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| 413 | REAL(dp), DIMENSION(:,:), INTENT(IN) :: dd_array |
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| 414 | INTEGER(i4) , INTENT(IN), OPTIONAL :: id_next |
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| 415 | REAL(dp), INTENT(IN), OPTIONAL :: dd_fill |
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| 416 | |
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| 417 | ! local variable |
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| 418 | INTEGER(i4) :: il_count |
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| 419 | |
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| 420 | REAL(dp), DIMENSION(:), ALLOCATABLE :: dl_list |
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| 421 | !---------------------------------------------------------------- |
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| 422 | |
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| 423 | IF( PRESENT(dd_fill) )THEN |
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| 424 | il_count=COUNT(dd_array(:,:)/=dd_fill) |
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| 425 | IF( il_count > 0 )THEN |
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| 426 | ALLOCATE( dl_list(il_count) ) |
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| 427 | dl_list(:)=PACK(dd_array(:,:),dd_array(:,:)/=dd_fill) |
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| 428 | |
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| 429 | math__mwe_2d=math_mwe(dl_list(:), id_next) |
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| 430 | ELSE |
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| 431 | math__mwe_2d=dd_fill |
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| 432 | ENDIF |
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| 433 | ELSE |
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| 434 | il_count=SIZE(dd_array(:,:)) |
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| 435 | IF( il_count > 0 )THEN |
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| 436 | ALLOCATE( dl_list(il_count) ) |
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| 437 | dl_list(:)=PACK(dd_array(:,:), MASK=.TRUE.) |
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| 438 | |
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| 439 | math__mwe_2d=math_mwe(dl_list(:), id_next) |
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| 440 | ELSE |
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| 441 | math__mwe_2d=0 |
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| 442 | ENDIF |
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| 443 | ENDIF |
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| 444 | |
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| 445 | IF( ALLOCATED(dl_list) ) DEALLOCATE(dl_list) |
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| 446 | |
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| 447 | END FUNCTION math__mwe_2d |
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| 448 | !------------------------------------------------------------------- |
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| 449 | !> @brief This subroutine sort a 1D array. |
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| 450 | !> |
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| 451 | !> @details |
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| 452 | !> Recursive Fortran 95 quicksort routine |
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| 453 | !> sorts real numbers into ascending numerical order |
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| 454 | !> Author: Juli Rew, SCD Consulting (juliana@ucar.edu), 9/03 |
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| 455 | !> Based on algorithm from Cormen et al., Introduction to Algorithms, |
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| 456 | !> 1997 printing |
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| 457 | !> |
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| 458 | !> @author J.Paul |
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[5616] | 459 | !> @date January, 2015 - Rewrite with SIREN coding rules |
---|
[5608] | 460 | ! |
---|
| 461 | !> @param[inout] dd_array 1D array |
---|
| 462 | !------------------------------------------------------------------- |
---|
| 463 | PURE RECURSIVE SUBROUTINE math_QsortC(dd_array) |
---|
| 464 | IMPLICIT NONE |
---|
| 465 | ! Argument |
---|
| 466 | REAL(dp), DIMENSION(:), INTENT(INOUT) :: dd_array |
---|
| 467 | |
---|
| 468 | ! local variable |
---|
| 469 | INTEGER(i4) :: il_iq |
---|
| 470 | !---------------------------------------------------------------- |
---|
| 471 | |
---|
| 472 | IF( SIZE(dd_array(:)) > 1 )THEN |
---|
| 473 | CALL math__Partition(dd_array, il_iq) |
---|
| 474 | CALL math_QsortC(dd_array(:il_iq-1)) |
---|
| 475 | CALL math_QsortC(dd_array(il_iq:)) |
---|
| 476 | ENDIF |
---|
| 477 | |
---|
| 478 | END SUBROUTINE math_QsortC |
---|
| 479 | !------------------------------------------------------------------- |
---|
| 480 | !> @brief This subroutine partition a 1D array. |
---|
| 481 | !> |
---|
| 482 | !> @details |
---|
| 483 | !> Author: Juli Rew, SCD Consulting (juliana@ucar.edu), 9/03 |
---|
| 484 | !> Based on algorithm from Cormen et al., Introduction to Algorithms, |
---|
| 485 | !> 1997 printing |
---|
| 486 | !> |
---|
| 487 | !> @author J.Paul |
---|
[5616] | 488 | !> @date January, 2015 - Rewrite with SIREN coding rules |
---|
[5608] | 489 | ! |
---|
| 490 | !> @param[inout] dd_array 1D array |
---|
| 491 | !> @param[in] id_marker |
---|
| 492 | !------------------------------------------------------------------- |
---|
| 493 | PURE SUBROUTINE math__Partition(dd_array, id_marker) |
---|
| 494 | IMPLICIT NONE |
---|
| 495 | ! Argument |
---|
| 496 | REAL(dp) , DIMENSION(:), INTENT(INOUT) :: dd_array |
---|
| 497 | INTEGER(i4), INTENT( OUT) :: id_marker |
---|
| 498 | |
---|
| 499 | ! local variable |
---|
| 500 | REAL(dp) :: dl_temp |
---|
| 501 | REAL(dp) :: dl_x ! pivot point |
---|
| 502 | |
---|
| 503 | ! loop indices |
---|
| 504 | INTEGER(i4) :: ji |
---|
| 505 | INTEGER(i4) :: jj |
---|
| 506 | !---------------------------------------------------------------- |
---|
| 507 | |
---|
| 508 | dl_x = dd_array(1) |
---|
| 509 | ji= 0 |
---|
| 510 | jj= SIZE(dd_array(:)) + 1 |
---|
| 511 | |
---|
| 512 | DO |
---|
| 513 | jj=jj-1 |
---|
| 514 | DO |
---|
| 515 | IF( dd_array(jj) <= dl_x ) EXIT |
---|
| 516 | jj=jj-1 |
---|
| 517 | ENDDO |
---|
| 518 | ji=ji+1 |
---|
| 519 | DO |
---|
| 520 | IF( dd_array(jj) >= dl_x ) EXIT |
---|
| 521 | ji=ji+1 |
---|
| 522 | ENDDO |
---|
| 523 | IF( ji < jj )THEN |
---|
| 524 | ! exchange dd_array(ji) and dd_array(jj) |
---|
| 525 | dl_temp= dd_array(ji) |
---|
| 526 | dd_array(ji) = dd_array(jj) |
---|
| 527 | dd_array(jj) = dl_temp |
---|
| 528 | ELSEIF( ji==jj )THEN |
---|
| 529 | id_marker=ji+1 |
---|
| 530 | RETURN |
---|
| 531 | ELSE |
---|
| 532 | id_marker=ji |
---|
| 533 | RETURN |
---|
| 534 | ENDIF |
---|
| 535 | ENDDO |
---|
| 536 | |
---|
| 537 | END SUBROUTINE math__Partition |
---|
| 538 | !------------------------------------------------------------------- |
---|
| 539 | !> @brief This subroutine correct phase angles to produce smoother |
---|
| 540 | !> phase plots. |
---|
| 541 | !> |
---|
| 542 | !> @details |
---|
| 543 | !> This code is based on numpy unwrap function |
---|
| 544 | !> |
---|
| 545 | !> Unwrap by changing deltas between values to 2*pi complement. |
---|
| 546 | !> |
---|
| 547 | !> Unwrap radian phase `dd_array` by changing absolute jumps greater than |
---|
| 548 | !> `dd_discont` to their 2*pi complement. |
---|
| 549 | !> |
---|
| 550 | !> @note If the discontinuity in `dd_array` is smaller than ``pi``, |
---|
| 551 | !> but larger than `dd_discont`, no unwrapping is done because taking |
---|
| 552 | !> the 2*pi complement would only make the discontinuity larger. |
---|
| 553 | !> |
---|
| 554 | !> @author J.Paul |
---|
[5616] | 555 | !> @date Marsh, 2015 - Rewrite in fortran, with SIREN coding rules |
---|
[5608] | 556 | ! |
---|
| 557 | !> @param[inout] dd_array 1D array |
---|
| 558 | !> @param[in] dd_discont maximum discontinuity between values, default pi |
---|
| 559 | !------------------------------------------------------------------- |
---|
| 560 | PURE SUBROUTINE math_unwrap(dd_array, dd_discont) |
---|
| 561 | IMPLICIT NONE |
---|
| 562 | ! Argument |
---|
| 563 | REAL(dp) , DIMENSION(:), INTENT(INOUT) :: dd_array |
---|
| 564 | REAL(dp) , INTENT(IN ), OPTIONAL :: dd_discont |
---|
| 565 | |
---|
| 566 | ! local variable |
---|
| 567 | INTEGER(i4) :: il_size |
---|
| 568 | |
---|
| 569 | REAL(dp) :: dl_discont |
---|
| 570 | |
---|
| 571 | REAL(dp), DIMENSION(:), ALLOCATABLE :: dl_diff |
---|
| 572 | REAL(dp), DIMENSION(:), ALLOCATABLE :: dl_mod |
---|
| 573 | REAL(dp), DIMENSION(:), ALLOCATABLE :: dl_correct |
---|
| 574 | REAL(dp), DIMENSION(:), ALLOCATABLE :: dl_tmp |
---|
| 575 | |
---|
| 576 | ! loop indices |
---|
| 577 | INTEGER(i4) :: ji |
---|
| 578 | !---------------------------------------------------------------- |
---|
| 579 | dl_discont=dp_pi |
---|
| 580 | IF( PRESENT(dd_discont) ) dl_discont=dd_discont |
---|
| 581 | |
---|
| 582 | il_size=SIZE(dd_array) |
---|
| 583 | ALLOCATE(dl_diff(il_size-1)) |
---|
| 584 | DO ji=1,il_size-1 |
---|
| 585 | dl_diff(ji)=dd_array(ji+1)-dd_array(ji) |
---|
| 586 | ENDDO |
---|
| 587 | |
---|
| 588 | ALLOCATE(dl_mod(il_size-1)) |
---|
| 589 | DO ji=1,il_size-1 |
---|
| 590 | dl_mod(ji) = MOD(dl_diff(ji) + dp_pi, 2*dp_pi) - dp_pi |
---|
| 591 | ENDDO |
---|
| 592 | |
---|
| 593 | WHERE( (dl_mod(:) == -dp_pi) .AND. (dl_diff(:) > 0._dp ) ) |
---|
| 594 | dl_mod(:)=dp_pi |
---|
| 595 | END WHERE |
---|
| 596 | |
---|
| 597 | ALLOCATE(dl_correct(il_size-1)) |
---|
| 598 | dl_correct(:)=dl_mod(:)-dl_diff(:) |
---|
| 599 | |
---|
| 600 | DEALLOCATE(dl_mod) |
---|
| 601 | |
---|
| 602 | WHERE( ABS(dl_diff(:)) < dl_discont ) |
---|
| 603 | dl_correct(:)=0._dp |
---|
| 604 | END WHERE |
---|
| 605 | |
---|
| 606 | DEALLOCATE(dl_diff) |
---|
| 607 | |
---|
| 608 | ALLOCATE(dl_tmp(il_size)) |
---|
| 609 | dl_tmp(:)=dd_array(:) |
---|
| 610 | |
---|
| 611 | DO ji=1,il_size-1 |
---|
| 612 | dd_array(ji+1)=dl_tmp(ji+1)+SUM(dl_correct(1:ji)) |
---|
| 613 | ENDDO |
---|
| 614 | |
---|
| 615 | DEALLOCATE(dl_correct) |
---|
| 616 | DEALLOCATE(dl_tmp) |
---|
| 617 | |
---|
| 618 | END SUBROUTINE math_unwrap |
---|
| 619 | !------------------------------------------------------------------- |
---|
| 620 | !> @brief This function compute simple operation |
---|
| 621 | !> |
---|
| 622 | !> @details |
---|
| 623 | !> - operation should be write as a string of character. |
---|
| 624 | !> - operators allowed are : +,-,*,/ |
---|
| 625 | !> - to ordered operation you should use parentheses |
---|
| 626 | !> |
---|
| 627 | !> exemples: '1e6/(16/122)', '(3/2)*(2+1)' |
---|
| 628 | !> |
---|
| 629 | !> @author J.Paul |
---|
[5616] | 630 | !> @date June, 2015 - initial version |
---|
[5608] | 631 | ! |
---|
| 632 | !> @param[in] cd_var operation to compute (string of character) |
---|
| 633 | !> @return result of the operation, real(dp) |
---|
| 634 | !------------------------------------------------------------------- |
---|
| 635 | REAL(dp) RECURSIVE FUNCTION math_compute(cd_var) RESULT(dd_res) |
---|
| 636 | IMPLICIT NONE |
---|
| 637 | ! Argument |
---|
| 638 | CHARACTER(LEN=*), INTENT(IN) :: cd_var |
---|
| 639 | |
---|
| 640 | ! local variables |
---|
| 641 | CHARACTER(LEN=lc) :: cl_var |
---|
| 642 | CHARACTER(LEN=lc) :: cl_str1 |
---|
| 643 | CHARACTER(LEN=lc) :: cl_str2 |
---|
| 644 | |
---|
| 645 | INTEGER(i4) :: il_ind |
---|
| 646 | ! loop indices |
---|
| 647 | !---------------------------------------------------------------- |
---|
| 648 | |
---|
| 649 | |
---|
| 650 | IF(fct_is_real(cd_var))THEN |
---|
| 651 | READ(cd_var,*) dd_res |
---|
| 652 | ELSE |
---|
| 653 | |
---|
| 654 | |
---|
| 655 | CALL math__parentheses(cd_var, cl_var) |
---|
| 656 | |
---|
| 657 | IF(fct_is_real(cl_var))THEN |
---|
| 658 | READ(cl_var,*) dd_res |
---|
| 659 | ELSE |
---|
| 660 | il_ind=SCAN(TRIM(cl_var),'*') |
---|
| 661 | IF( il_ind /= 0 )THEN |
---|
| 662 | cl_str1=cl_var(1:il_ind-1) |
---|
| 663 | cl_str2=cl_var(il_ind+1:) |
---|
| 664 | dd_res=math_compute(cl_str1)*math_compute(cl_str2) |
---|
| 665 | ELSE |
---|
| 666 | il_ind=SCAN(TRIM(cl_var),'/') |
---|
| 667 | IF( il_ind /= 0 )THEN |
---|
| 668 | cl_str1=cl_var(1:il_ind-1) |
---|
| 669 | cl_str2=cl_var(il_ind+1:) |
---|
| 670 | dd_res=math_compute(cl_str1)/math_compute(cl_str2) |
---|
| 671 | ELSE |
---|
| 672 | il_ind=SCAN(TRIM(cl_var),'+') |
---|
| 673 | IF( il_ind /= 0 )THEN |
---|
| 674 | cl_str1=cl_var(1:il_ind-1) |
---|
| 675 | cl_str2=cl_var(il_ind+1:) |
---|
| 676 | dd_res=math_compute(cl_str1)+math_compute(cl_str2) |
---|
| 677 | ELSE |
---|
| 678 | il_ind=SCAN(TRIM(cl_var),'-') |
---|
| 679 | IF( il_ind /= 0 )THEN |
---|
| 680 | cl_str1=cl_var(1:il_ind-1) |
---|
| 681 | cl_str2=cl_var(il_ind+1:) |
---|
| 682 | dd_res=math_compute(cl_str1)-math_compute(cl_str2) |
---|
| 683 | ELSE |
---|
| 684 | dd_res=dp_fill |
---|
| 685 | ENDIF |
---|
| 686 | ENDIF |
---|
| 687 | ENDIF |
---|
| 688 | ENDIF |
---|
| 689 | ENDIF |
---|
| 690 | ENDIF |
---|
| 691 | |
---|
| 692 | END FUNCTION math_compute |
---|
| 693 | !------------------------------------------------------------------- |
---|
| 694 | !> @brief This subroutine replace sub string inside parentheses |
---|
| 695 | !> by the value of the operation inside. |
---|
| 696 | !> |
---|
| 697 | !> @details |
---|
| 698 | !> exemple : |
---|
| 699 | !> - '2.6+(3/2)' => '2.6+1.5000' |
---|
| 700 | !> |
---|
| 701 | !> @author J.Paul |
---|
[5616] | 702 | !> @date June, 2015 - initial version |
---|
[5608] | 703 | ! |
---|
| 704 | !> @param[in] cd_varin string of character with operation inside |
---|
| 705 | !> parentheses |
---|
| 706 | !> @param[out] cd_varout string of character with result of |
---|
| 707 | !> operation inside parentheses |
---|
| 708 | !------------------------------------------------------------------- |
---|
| 709 | SUBROUTINE math__parentheses(cd_varin, cd_varout) |
---|
| 710 | IMPLICIT NONE |
---|
| 711 | ! Argument |
---|
| 712 | CHARACTER(LEN=*) , INTENT(IN) :: cd_varin |
---|
| 713 | CHARACTER(LEN=lc), INTENT(OUT) :: cd_varout |
---|
| 714 | ! local variables |
---|
| 715 | CHARACTER(LEN=lc) :: cl_cpt |
---|
| 716 | INTEGER(i4) :: il_ind |
---|
| 717 | INTEGER(i4) :: il_count |
---|
| 718 | ! loop indices |
---|
| 719 | INTEGER(i4) :: ji |
---|
| 720 | !---------------------------------------------------------------- |
---|
| 721 | il_ind=INDEX(cd_varin,'(') |
---|
| 722 | IF( il_ind /= 0 )THEN |
---|
| 723 | il_count=0 |
---|
| 724 | DO ji=il_ind+1,LEN(cd_varin) |
---|
| 725 | IF( cd_varin(ji:ji) == '(' )THEN |
---|
| 726 | il_count=il_count+1 |
---|
| 727 | ELSEIF( cd_varin(ji:ji) == ')' )THEN |
---|
| 728 | IF( il_count == 0 )THEN |
---|
| 729 | WRITE(cl_cpt,*) math_compute(cd_varin(il_ind+1:ji-1)) |
---|
| 730 | cd_varout=TRIM(cd_varin(1:il_ind-1))//TRIM(ADJUSTL(cl_cpt))//& |
---|
| 731 | & TRIM(cd_varin(ji+1:)) |
---|
| 732 | EXIT |
---|
| 733 | ELSE |
---|
| 734 | il_count=il_count-1 |
---|
| 735 | ENDIF |
---|
| 736 | ENDIF |
---|
| 737 | ENDDO |
---|
| 738 | ELSE |
---|
| 739 | cd_varout=TRIM(cd_varin) |
---|
| 740 | ENDIF |
---|
| 741 | |
---|
| 742 | END SUBROUTINE math__parentheses |
---|
| 743 | !------------------------------------------------------------------- |
---|
| 744 | !> @brief |
---|
| 745 | !> This function compute derivative of 1D array. |
---|
| 746 | !> |
---|
| 747 | !> @details |
---|
| 748 | !> optionaly you could specify to take into account east west discontinuity |
---|
| 749 | !> (-180° 180° or 0° 360° for longitude variable) |
---|
| 750 | !> |
---|
| 751 | !> @author J.Paul |
---|
[5616] | 752 | !> @date November, 2013 - Initial Version |
---|
[5608] | 753 | ! |
---|
| 754 | !> @param[in] dd_value 1D array of variable to be extrapolated |
---|
| 755 | !> @param[in] dd_fill FillValue of variable |
---|
| 756 | !> @param[in] ld_discont logical to take into account east west discontinuity |
---|
| 757 | !------------------------------------------------------------------- |
---|
| 758 | PURE FUNCTION math_deriv_1D( dd_value, dd_fill, ld_discont ) |
---|
| 759 | |
---|
| 760 | IMPLICIT NONE |
---|
| 761 | ! Argument |
---|
| 762 | REAL(dp) , DIMENSION(:), INTENT(IN) :: dd_value |
---|
| 763 | REAL(dp) , INTENT(IN) :: dd_fill |
---|
| 764 | LOGICAL , INTENT(IN), OPTIONAL :: ld_discont |
---|
| 765 | |
---|
| 766 | ! function |
---|
| 767 | REAL(dp), DIMENSION(SIZE(dd_value,DIM=1) ) :: math_deriv_1D |
---|
| 768 | |
---|
| 769 | ! local variable |
---|
| 770 | INTEGER(i4) :: il_imin |
---|
| 771 | INTEGER(i4) :: il_imax |
---|
| 772 | INTEGER(i4), DIMENSION(1) :: il_shape |
---|
| 773 | |
---|
| 774 | REAL(dp) :: dl_min |
---|
| 775 | REAL(dp) :: dl_max |
---|
| 776 | REAL(dp) , DIMENSION(:), ALLOCATABLE :: dl_value |
---|
| 777 | |
---|
| 778 | LOGICAL :: ll_discont |
---|
| 779 | |
---|
| 780 | ! loop indices |
---|
| 781 | INTEGER(i4) :: ji |
---|
| 782 | |
---|
| 783 | INTEGER(i4) :: i1 |
---|
| 784 | INTEGER(i4) :: i2 |
---|
| 785 | !---------------------------------------------------------------- |
---|
| 786 | ! init |
---|
| 787 | math_deriv_1D(:)=dd_fill |
---|
| 788 | |
---|
| 789 | ll_discont=.FALSE. |
---|
| 790 | IF( PRESENT(ld_discont) ) ll_discont=ld_discont |
---|
| 791 | |
---|
| 792 | il_shape(:)=SHAPE(dd_value(:)) |
---|
| 793 | |
---|
| 794 | ALLOCATE( dl_value(3)) |
---|
| 795 | |
---|
| 796 | ! compute derivative in i-direction |
---|
| 797 | DO ji=1,il_shape(1) |
---|
| 798 | |
---|
| 799 | il_imin=MAX(ji-1,1) |
---|
| 800 | il_imax=MIN(ji+1,il_shape(1)) |
---|
| 801 | |
---|
| 802 | IF( il_imin==ji-1 .AND. il_imax==ji+1 )THEN |
---|
| 803 | i1=1 ; i2=3 |
---|
| 804 | ELSEIF( il_imin==ji .AND. il_imax==ji+1 )THEN |
---|
| 805 | i1=1 ; i2=2 |
---|
| 806 | ELSEIF( il_imin==ji-1 .AND. il_imax==ji )THEN |
---|
| 807 | i1=2 ; i2=3 |
---|
| 808 | ENDIF |
---|
| 809 | |
---|
| 810 | dl_value(i1:i2)=dd_value(il_imin:il_imax) |
---|
| 811 | IF( il_imin == 1 )THEN |
---|
| 812 | dl_value(:)=EOSHIFT( dl_value(:), & |
---|
| 813 | & DIM=1, & |
---|
| 814 | & SHIFT=-1, & |
---|
| 815 | & BOUNDARY=dl_value(1) ) |
---|
| 816 | ENDIF |
---|
| 817 | IF( il_imax == il_shape(1) )THEN |
---|
| 818 | dl_value(:)=EOSHIFT( dl_value(:), & |
---|
| 819 | & DIM=1, & |
---|
| 820 | & SHIFT=1, & |
---|
| 821 | & BOUNDARY=dl_value(3)) |
---|
| 822 | ENDIF |
---|
| 823 | |
---|
| 824 | IF( ll_discont )THEN |
---|
| 825 | dl_min=MINVAL( dl_value(:), dl_value(:)/=dd_fill ) |
---|
| 826 | dl_max=MAXVAL( dl_value(:), dl_value(:)/=dd_fill ) |
---|
| 827 | IF( dl_min < -170_dp .AND. dl_max > 170_dp )THEN |
---|
| 828 | WHERE( dl_value(:) < 0._dp ) |
---|
| 829 | dl_value(:) = dl_value(:)+360._dp |
---|
| 830 | END WHERE |
---|
| 831 | ELSEIF( dl_min < 10_dp .AND. dl_max > 350_dp )THEN |
---|
| 832 | WHERE( dl_value(:) > 180._dp ) |
---|
| 833 | dl_value(:) = dl_value(:)-180._dp |
---|
| 834 | END WHERE |
---|
| 835 | ENDIF |
---|
| 836 | ENDIF |
---|
| 837 | |
---|
| 838 | IF( dl_value( 2) /= dd_fill .AND. & ! ji |
---|
| 839 | & dl_value( 3) /= dd_fill .AND. & ! ji+1 |
---|
| 840 | & dl_value( 1) /= dd_fill )THEN ! ji-1 |
---|
| 841 | |
---|
| 842 | math_deriv_1D(ji)=& |
---|
| 843 | & ( dl_value(3) - dl_value(1) ) / & |
---|
| 844 | & REAL( il_imax-il_imin ,dp) |
---|
| 845 | |
---|
| 846 | ENDIF |
---|
| 847 | |
---|
| 848 | ENDDO |
---|
| 849 | |
---|
| 850 | DEALLOCATE( dl_value ) |
---|
| 851 | |
---|
| 852 | END FUNCTION math_deriv_1D |
---|
| 853 | !------------------------------------------------------------------- |
---|
| 854 | !> @brief |
---|
| 855 | !> This function compute derivative of 2D array. |
---|
| 856 | !> you have to specify in which direction derivative have to be computed: |
---|
| 857 | !> first (I) or second (J) dimension. |
---|
| 858 | !> |
---|
| 859 | !> @details |
---|
| 860 | !> optionaly you could specify to take into account east west discontinuity |
---|
| 861 | !> (-180° 180° or 0° 360° for longitude variable) |
---|
| 862 | !> |
---|
| 863 | !> @author J.Paul |
---|
[5616] | 864 | !> @date November, 2013 - Initial Version |
---|
[5608] | 865 | ! |
---|
| 866 | !> @param[in] dd_value 2D array of variable to be extrapolated |
---|
| 867 | !> @param[in] dd_fill FillValue of variable |
---|
| 868 | !> @param[in] cd_dim compute derivative on first (I) or second (J) dimension |
---|
| 869 | !> @param[in] ld_discont logical to take into account east west discontinuity |
---|
| 870 | !------------------------------------------------------------------- |
---|
| 871 | FUNCTION math_deriv_2D( dd_value, dd_fill, cd_dim, ld_discont ) |
---|
| 872 | |
---|
| 873 | IMPLICIT NONE |
---|
| 874 | ! Argument |
---|
| 875 | REAL(dp) , DIMENSION(:,:), INTENT(IN) :: dd_value |
---|
| 876 | REAL(dp) , INTENT(IN) :: dd_fill |
---|
| 877 | CHARACTER(LEN=*) , INTENT(IN) :: cd_dim |
---|
| 878 | LOGICAL , INTENT(IN), OPTIONAL :: ld_discont |
---|
| 879 | |
---|
| 880 | ! function |
---|
| 881 | REAL(dp), DIMENSION(SIZE(dd_value,DIM=1), & |
---|
| 882 | & SIZE(dd_value,DIM=2) ) :: math_deriv_2D |
---|
| 883 | |
---|
| 884 | ! local variable |
---|
| 885 | INTEGER(i4) :: il_imin |
---|
| 886 | INTEGER(i4) :: il_imax |
---|
| 887 | INTEGER(i4) :: il_jmin |
---|
| 888 | INTEGER(i4) :: il_jmax |
---|
| 889 | INTEGER(i4), DIMENSION(2) :: il_shape |
---|
| 890 | |
---|
| 891 | REAL(dp) :: dl_min |
---|
| 892 | REAL(dp) :: dl_max |
---|
| 893 | REAL(dp) , DIMENSION(:,:), ALLOCATABLE :: dl_value |
---|
| 894 | |
---|
| 895 | LOGICAL :: ll_discont |
---|
| 896 | |
---|
| 897 | ! loop indices |
---|
| 898 | INTEGER(i4) :: ji |
---|
| 899 | INTEGER(i4) :: jj |
---|
| 900 | |
---|
| 901 | INTEGER(i4) :: i1 |
---|
| 902 | INTEGER(i4) :: i2 |
---|
| 903 | |
---|
| 904 | INTEGER(i4) :: j1 |
---|
| 905 | INTEGER(i4) :: j2 |
---|
| 906 | !---------------------------------------------------------------- |
---|
| 907 | ! init |
---|
| 908 | math_deriv_2D(:,:)=dd_fill |
---|
| 909 | |
---|
| 910 | ll_discont=.FALSE. |
---|
| 911 | IF( PRESENT(ld_discont) ) ll_discont=ld_discont |
---|
| 912 | |
---|
| 913 | il_shape(:)=SHAPE(dd_value(:,:)) |
---|
| 914 | |
---|
| 915 | SELECT CASE(TRIM(fct_upper(cd_dim))) |
---|
| 916 | |
---|
| 917 | CASE('I') |
---|
| 918 | |
---|
| 919 | ALLOCATE( dl_value(3,il_shape(2)) ) |
---|
| 920 | ! compute derivative in i-direction |
---|
| 921 | DO ji=1,il_shape(1) |
---|
| 922 | |
---|
| 923 | ! init |
---|
| 924 | dl_value(:,:)=dd_fill |
---|
| 925 | |
---|
| 926 | il_imin=MAX(ji-1,1) |
---|
| 927 | il_imax=MIN(ji+1,il_shape(1)) |
---|
| 928 | |
---|
| 929 | IF( il_imin==ji-1 .AND. il_imax==ji+1 )THEN |
---|
| 930 | i1=1 ; i2=3 |
---|
| 931 | ELSEIF( il_imin==ji .AND. il_imax==ji+1 )THEN |
---|
| 932 | i1=1 ; i2=2 |
---|
| 933 | ELSEIF( il_imin==ji-1 .AND. il_imax==ji )THEN |
---|
| 934 | i1=2 ; i2=3 |
---|
| 935 | ENDIF |
---|
| 936 | |
---|
| 937 | dl_value(i1:i2,:)=dd_value(il_imin:il_imax,:) |
---|
| 938 | IF( il_imin == 1 )THEN |
---|
| 939 | dl_value(:,:)=EOSHIFT( dl_value(:,:), & |
---|
| 940 | & DIM=1, & |
---|
| 941 | & SHIFT=-1, & |
---|
| 942 | & BOUNDARY=dl_value(1,:) ) |
---|
| 943 | ENDIF |
---|
| 944 | IF( il_imax == il_shape(1) )THEN |
---|
| 945 | dl_value(:,:)=EOSHIFT( dl_value(:,:), & |
---|
| 946 | & DIM=1, & |
---|
| 947 | & SHIFT=1, & |
---|
| 948 | & BOUNDARY=dl_value(3,:)) |
---|
| 949 | ENDIF |
---|
| 950 | |
---|
| 951 | IF( ll_discont )THEN |
---|
| 952 | dl_min=MINVAL( dl_value(:,:), dl_value(:,:)/=dd_fill ) |
---|
| 953 | dl_max=MAXVAL( dl_value(:,:), dl_value(:,:)/=dd_fill ) |
---|
| 954 | IF( dl_min < -170_dp .AND. dl_max > 170_dp )THEN |
---|
| 955 | WHERE( dl_value(:,:) < 0_dp ) |
---|
| 956 | dl_value(:,:) = dl_value(:,:)+360._dp |
---|
| 957 | END WHERE |
---|
| 958 | ELSEIF( dl_min < 10_dp .AND. dl_max > 350_dp )THEN |
---|
| 959 | WHERE( dl_value(:,:) > 180 ) |
---|
| 960 | dl_value(:,:) = dl_value(:,:)-180._dp |
---|
| 961 | END WHERE |
---|
| 962 | ENDIF |
---|
| 963 | ENDIF |
---|
| 964 | |
---|
| 965 | WHERE( dl_value(2,:) /= dd_fill .AND. & ! ji |
---|
| 966 | & dl_value(3,:) /= dd_fill .AND. & ! ji+1 |
---|
| 967 | & dl_value(1,:) /= dd_fill ) ! ji-1 |
---|
| 968 | |
---|
| 969 | math_deriv_2D(ji,:)=& |
---|
| 970 | & ( dl_value(3,:) - dl_value(1,:) ) / & |
---|
| 971 | & REAL( il_imax-il_imin,dp) |
---|
| 972 | |
---|
| 973 | END WHERE |
---|
| 974 | |
---|
| 975 | ENDDO |
---|
| 976 | |
---|
| 977 | CASE('J') |
---|
| 978 | |
---|
| 979 | ALLOCATE( dl_value(il_shape(1),3) ) |
---|
| 980 | ! compute derivative in j-direction |
---|
| 981 | DO jj=1,il_shape(2) |
---|
| 982 | |
---|
| 983 | il_jmin=MAX(jj-1,1) |
---|
| 984 | il_jmax=MIN(jj+1,il_shape(2)) |
---|
| 985 | |
---|
| 986 | IF( il_jmin==jj-1 .AND. il_jmax==jj+1 )THEN |
---|
| 987 | j1=1 ; j2=3 |
---|
| 988 | ELSEIF( il_jmin==jj .AND. il_jmax==jj+1 )THEN |
---|
| 989 | j1=1 ; j2=2 |
---|
| 990 | ELSEIF( il_jmin==jj-1 .AND. il_jmax==jj )THEN |
---|
| 991 | j1=2 ; j2=3 |
---|
| 992 | ENDIF |
---|
| 993 | |
---|
| 994 | dl_value(:,j1:j2)=dd_value(:,il_jmin:il_jmax) |
---|
| 995 | IF( il_jmin == 1 )THEN |
---|
| 996 | dl_value(:,:)=EOSHIFT( dl_value(:,:), & |
---|
| 997 | & DIM=2, & |
---|
| 998 | & SHIFT=-1, & |
---|
| 999 | & BOUNDARY=dl_value(:,1)) |
---|
| 1000 | ENDIF |
---|
| 1001 | IF( il_jmax == il_shape(2) )THEN |
---|
| 1002 | dl_value(:,:)=EOSHIFT( dl_value(:,:), & |
---|
| 1003 | & DIM=2, & |
---|
| 1004 | & SHIFT=1, & |
---|
| 1005 | & BOUNDARY=dl_value(:,3)) |
---|
| 1006 | ENDIF |
---|
| 1007 | |
---|
| 1008 | IF( ll_discont )THEN |
---|
| 1009 | dl_min=MINVAL( dl_value(:,:), dl_value(:,:)/=dd_fill ) |
---|
| 1010 | dl_max=MAXVAL( dl_value(:,:), dl_value(:,:)/=dd_fill ) |
---|
| 1011 | IF( dl_min < -170_dp .AND. dl_max > 170_dp )THEN |
---|
| 1012 | WHERE( dl_value(:,:) < 0_dp ) |
---|
| 1013 | dl_value(:,:) = dl_value(:,:)+360._dp |
---|
| 1014 | END WHERE |
---|
| 1015 | ELSEIF( dl_min < 10_dp .AND. dl_max > 350_dp )THEN |
---|
| 1016 | WHERE( dl_value(:,:) > 180 ) |
---|
| 1017 | dl_value(:,:) = dl_value(:,:)-180._dp |
---|
| 1018 | END WHERE |
---|
| 1019 | ENDIF |
---|
| 1020 | ENDIF |
---|
| 1021 | |
---|
| 1022 | WHERE( dl_value(:, 2) /= dd_fill .AND. & ! jj |
---|
| 1023 | & dl_value(:, 3) /= dd_fill .AND. & ! jj+1 |
---|
| 1024 | & dl_value(:, 1) /= dd_fill ) ! jj-1 |
---|
| 1025 | |
---|
| 1026 | math_deriv_2D(:,jj)=& |
---|
| 1027 | & ( dl_value(:,3) - dl_value(:,1) ) / & |
---|
| 1028 | & REAL(il_jmax-il_jmin,dp) |
---|
| 1029 | |
---|
| 1030 | END WHERE |
---|
| 1031 | |
---|
| 1032 | ENDDO |
---|
| 1033 | |
---|
| 1034 | END SELECT |
---|
| 1035 | |
---|
| 1036 | DEALLOCATE( dl_value ) |
---|
| 1037 | |
---|
| 1038 | END FUNCTION math_deriv_2D |
---|
| 1039 | !------------------------------------------------------------------- |
---|
| 1040 | !> @brief |
---|
| 1041 | !> This function compute derivative of 3D array. |
---|
| 1042 | !> you have to specify in which direction derivative have to be computed: |
---|
| 1043 | !> first (I), second (J) or third (K) dimension. |
---|
| 1044 | !> |
---|
| 1045 | !> @details |
---|
| 1046 | !> optionaly you could specify to take into account east west discontinuity |
---|
| 1047 | !> (-180° 180° or 0° 360° for longitude variable) |
---|
| 1048 | !> |
---|
| 1049 | !> @author J.Paul |
---|
[5616] | 1050 | !> @date November, 2013 - Initial Version |
---|
[5608] | 1051 | ! |
---|
| 1052 | !> @param[inout] dd_value 3D array of variable to be extrapolated |
---|
| 1053 | !> @param[in] dd_fill FillValue of variable |
---|
| 1054 | !> @param[in] cd_dim compute derivative on first (I) second (J) or third (K) dimension |
---|
| 1055 | !> @param[in] ld_discont logical to take into account east west discontinuity |
---|
| 1056 | !------------------------------------------------------------------- |
---|
| 1057 | PURE FUNCTION math_deriv_3D( dd_value, dd_fill, cd_dim, ld_discont ) |
---|
| 1058 | |
---|
| 1059 | IMPLICIT NONE |
---|
| 1060 | ! Argument |
---|
| 1061 | REAL(dp) , DIMENSION(:,:,:), INTENT(IN) :: dd_value |
---|
| 1062 | REAL(dp) , INTENT(IN) :: dd_fill |
---|
| 1063 | CHARACTER(LEN=*) , INTENT(IN) :: cd_dim |
---|
| 1064 | LOGICAL , INTENT(IN), OPTIONAL :: ld_discont |
---|
| 1065 | |
---|
| 1066 | ! function |
---|
| 1067 | REAL(dp), DIMENSION(SIZE(dd_value,DIM=1), & |
---|
| 1068 | & SIZE(dd_value,DIM=2), & |
---|
| 1069 | & SIZE(dd_value,DIM=3)) :: math_deriv_3D |
---|
| 1070 | |
---|
| 1071 | ! local variable |
---|
| 1072 | INTEGER(i4) :: il_imin |
---|
| 1073 | INTEGER(i4) :: il_imax |
---|
| 1074 | INTEGER(i4) :: il_jmin |
---|
| 1075 | INTEGER(i4) :: il_jmax |
---|
| 1076 | INTEGER(i4) :: il_kmin |
---|
| 1077 | INTEGER(i4) :: il_kmax |
---|
| 1078 | INTEGER(i4), DIMENSION(3) :: il_shape |
---|
| 1079 | |
---|
| 1080 | REAL(dp) :: dl_min |
---|
| 1081 | REAL(dp) :: dl_max |
---|
| 1082 | REAL(dp) , DIMENSION(:,:,:), ALLOCATABLE :: dl_value |
---|
| 1083 | |
---|
| 1084 | LOGICAL :: ll_discont |
---|
| 1085 | |
---|
| 1086 | ! loop indices |
---|
| 1087 | INTEGER(i4) :: ji |
---|
| 1088 | INTEGER(i4) :: jj |
---|
| 1089 | INTEGER(i4) :: jk |
---|
| 1090 | |
---|
| 1091 | INTEGER(i4) :: i1 |
---|
| 1092 | INTEGER(i4) :: i2 |
---|
| 1093 | |
---|
| 1094 | INTEGER(i4) :: j1 |
---|
| 1095 | INTEGER(i4) :: j2 |
---|
| 1096 | |
---|
| 1097 | INTEGER(i4) :: k1 |
---|
| 1098 | INTEGER(i4) :: k2 |
---|
| 1099 | !---------------------------------------------------------------- |
---|
| 1100 | ! init |
---|
| 1101 | math_deriv_3D(:,:,:)=dd_fill |
---|
| 1102 | |
---|
| 1103 | ll_discont=.FALSE. |
---|
| 1104 | IF( PRESENT(ld_discont) ) ll_discont=ld_discont |
---|
| 1105 | |
---|
| 1106 | il_shape(:)=SHAPE(dd_value(:,:,:)) |
---|
| 1107 | |
---|
| 1108 | |
---|
| 1109 | SELECT CASE(TRIM(fct_upper(cd_dim))) |
---|
| 1110 | |
---|
| 1111 | CASE('I') |
---|
| 1112 | |
---|
| 1113 | ALLOCATE( dl_value(3,il_shape(2),il_shape(3)) ) |
---|
| 1114 | ! compute derivative in i-direction |
---|
| 1115 | DO ji=1,il_shape(1) |
---|
| 1116 | |
---|
| 1117 | il_imin=MAX(ji-1,1) |
---|
| 1118 | il_imax=MIN(ji+1,il_shape(1)) |
---|
| 1119 | |
---|
| 1120 | IF( il_imin==ji-1 .AND. il_imax==ji+1 )THEN |
---|
| 1121 | i1=1 ; i2=3 |
---|
| 1122 | ELSEIF( il_imin==ji .AND. il_imax==ji+1 )THEN |
---|
| 1123 | i1=1 ; i2=2 |
---|
| 1124 | ELSEIF( il_imin==ji-1 .AND. il_imax==ji )THEN |
---|
| 1125 | i1=2 ; i2=3 |
---|
| 1126 | ENDIF |
---|
| 1127 | |
---|
| 1128 | dl_value(i1:i2,:,:)=dd_value(il_imin:il_imax,:,:) |
---|
| 1129 | IF( il_imin == 1 )THEN |
---|
| 1130 | dl_value(:,:,:)=EOSHIFT( dl_value(:,:,:), & |
---|
| 1131 | & DIM=1, & |
---|
| 1132 | & SHIFT=-1, & |
---|
| 1133 | & BOUNDARY=dl_value(1,:,:) ) |
---|
| 1134 | ENDIF |
---|
| 1135 | IF( il_imax == il_shape(1) )THEN |
---|
| 1136 | dl_value(:,:,:)=EOSHIFT( dl_value(:,:,:), & |
---|
| 1137 | & DIM=1, & |
---|
| 1138 | & SHIFT=1, & |
---|
| 1139 | & BOUNDARY=dl_value(3,:,:)) |
---|
| 1140 | ENDIF |
---|
| 1141 | |
---|
| 1142 | IF( ll_discont )THEN |
---|
| 1143 | dl_min=MINVAL( dl_value(:,:,:), dl_value(:,:,:)/=dd_fill ) |
---|
| 1144 | dl_max=MAXVAL( dl_value(:,:,:), dl_value(:,:,:)/=dd_fill ) |
---|
| 1145 | IF( dl_min < -170_dp .AND. dl_max > 170_dp )THEN |
---|
| 1146 | WHERE( dl_value(:,:,:) < 0_dp ) |
---|
| 1147 | dl_value(:,:,:) = dl_value(:,:,:)+360._dp |
---|
| 1148 | END WHERE |
---|
| 1149 | ELSEIF( dl_min < 10_dp .AND. dl_max > 350_dp )THEN |
---|
| 1150 | WHERE( dl_value(:,:,:) > 180 ) |
---|
| 1151 | dl_value(:,:,:) = dl_value(:,:,:)-180._dp |
---|
| 1152 | END WHERE |
---|
| 1153 | ENDIF |
---|
| 1154 | ENDIF |
---|
| 1155 | |
---|
| 1156 | WHERE( dl_value(2,:,:) /= dd_fill .AND. & ! ji |
---|
| 1157 | & dl_value(3,:,:) /= dd_fill .AND. & !ji+1 |
---|
| 1158 | & dl_value(1,:,:) /= dd_fill ) !ji-1 |
---|
| 1159 | |
---|
| 1160 | math_deriv_3D(ji,:,:)= & |
---|
| 1161 | & ( dl_value(3,:,:) - dl_value(1,:,:) ) / & |
---|
| 1162 | & REAL( il_imax-il_imin ,dp) |
---|
| 1163 | |
---|
| 1164 | END WHERE |
---|
| 1165 | |
---|
| 1166 | ENDDO |
---|
| 1167 | |
---|
| 1168 | CASE('J') |
---|
| 1169 | |
---|
| 1170 | ALLOCATE( dl_value(il_shape(1),3,il_shape(3)) ) |
---|
| 1171 | ! compute derivative in j-direction |
---|
| 1172 | DO jj=1,il_shape(2) |
---|
| 1173 | |
---|
| 1174 | il_jmin=MAX(jj-1,1) |
---|
| 1175 | il_jmax=MIN(jj+1,il_shape(2)) |
---|
| 1176 | |
---|
| 1177 | IF( il_jmin==jj-1 .AND. il_jmax==jj+1 )THEN |
---|
| 1178 | j1=1 ; j2=3 |
---|
| 1179 | ELSEIF( il_jmin==jj .AND. il_jmax==jj+1 )THEN |
---|
| 1180 | j1=1 ; j2=2 |
---|
| 1181 | ELSEIF( il_jmin==jj-1 .AND. il_jmax==jj )THEN |
---|
| 1182 | j1=2 ; j2=3 |
---|
| 1183 | ENDIF |
---|
| 1184 | |
---|
| 1185 | dl_value(:,j1:j2,:)=dd_value(:,il_jmin:il_jmax,:) |
---|
| 1186 | IF( il_jmin == 1 )THEN |
---|
| 1187 | dl_value(:,:,:)=EOSHIFT( dl_value(:,:,:), & |
---|
| 1188 | & DIM=2, & |
---|
| 1189 | & SHIFT=-1, & |
---|
| 1190 | & BOUNDARY=dl_value(:,1,:) ) |
---|
| 1191 | ENDIF |
---|
| 1192 | IF( il_jmax == il_shape(2) )THEN |
---|
| 1193 | dl_value(:,:,:)=EOSHIFT( dl_value(:,:,:), & |
---|
| 1194 | & DIM=2, & |
---|
| 1195 | & SHIFT=1, & |
---|
| 1196 | & BOUNDARY=dl_value(:,3,:)) |
---|
| 1197 | ENDIF |
---|
| 1198 | |
---|
| 1199 | IF( ll_discont )THEN |
---|
| 1200 | dl_min=MINVAL( dl_value(:,:,:), dl_value(:,:,:)/=dd_fill ) |
---|
| 1201 | dl_max=MAXVAL( dl_value(:,:,:), dl_value(:,:,:)/=dd_fill ) |
---|
| 1202 | IF( dl_min < -170_dp .AND. dl_max > 170_dp )THEN |
---|
| 1203 | WHERE( dl_value(:,:,:) < 0_dp ) |
---|
| 1204 | dl_value(:,:,:) = dl_value(:,:,:)+360._dp |
---|
| 1205 | END WHERE |
---|
| 1206 | ELSEIF( dl_min < 10_dp .AND. dl_max > 350_dp )THEN |
---|
| 1207 | WHERE( dl_value(:,:,:) > 180 ) |
---|
| 1208 | dl_value(:,:,:) = dl_value(:,:,:)-180._dp |
---|
| 1209 | END WHERE |
---|
| 1210 | ENDIF |
---|
| 1211 | ENDIF |
---|
| 1212 | |
---|
| 1213 | WHERE( dl_value(:, 2,:) /= dd_fill .AND. & ! jj |
---|
| 1214 | & dl_value(:, 3,:) /= dd_fill .AND. & ! jj+1 |
---|
| 1215 | & dl_value(:, 1,:) /= dd_fill ) ! jj-1 |
---|
| 1216 | |
---|
| 1217 | math_deriv_3D(:,jj,:)=& |
---|
| 1218 | & ( dl_value(:,3,:) - dl_value(:,1,:) ) / & |
---|
| 1219 | & REAL( il_jmax - il_jmin ,dp) |
---|
| 1220 | |
---|
| 1221 | END WHERE |
---|
| 1222 | |
---|
| 1223 | ENDDO |
---|
| 1224 | |
---|
| 1225 | CASE('K') |
---|
| 1226 | ! compute derivative in k-direction |
---|
| 1227 | DO jk=1,il_shape(3) |
---|
| 1228 | |
---|
| 1229 | il_kmin=MAX(jk-1,1) |
---|
| 1230 | il_kmax=MIN(jk+1,il_shape(3)) |
---|
| 1231 | |
---|
| 1232 | IF( il_kmin==jk-1 .AND. il_kmax==jk+1 )THEN |
---|
| 1233 | k1=1 ; k2=3 |
---|
| 1234 | ELSEIF( il_kmin==jk .AND. il_kmax==jk+1 )THEN |
---|
| 1235 | k1=1 ; k2=2 |
---|
| 1236 | ELSEIF( il_kmin==jk-1 .AND. il_kmax==jk )THEN |
---|
| 1237 | k1=2 ; k2=3 |
---|
| 1238 | ENDIF |
---|
| 1239 | |
---|
| 1240 | dl_value(:,:,k1:k2)=dd_value(:,:,il_kmin:il_kmax) |
---|
| 1241 | IF( il_kmin == 1 )THEN |
---|
| 1242 | dl_value(:,:,:)=EOSHIFT( dl_value(:,:,:), & |
---|
| 1243 | & DIM=3, & |
---|
| 1244 | & SHIFT=-1, & |
---|
| 1245 | & BOUNDARY=dl_value(:,:,1) ) |
---|
| 1246 | ENDIF |
---|
| 1247 | IF( il_kmax == il_shape(3) )THEN |
---|
| 1248 | dl_value(:,:,:)=EOSHIFT( dl_value(:,:,:), & |
---|
| 1249 | & DIM=3, & |
---|
| 1250 | & SHIFT=1, & |
---|
| 1251 | & BOUNDARY=dl_value(:,:,3)) |
---|
| 1252 | ENDIF |
---|
| 1253 | |
---|
| 1254 | IF( ll_discont )THEN |
---|
| 1255 | dl_min=MINVAL( dl_value(:,:,:), dl_value(:,:,:)/=dd_fill ) |
---|
| 1256 | dl_max=MAXVAL( dl_value(:,:,:), dl_value(:,:,:)/=dd_fill ) |
---|
| 1257 | IF( dl_min < -170_dp .AND. dl_max > 170_dp )THEN |
---|
| 1258 | WHERE( dl_value(:,:,:) < 0_dp ) |
---|
| 1259 | dl_value(:,:,:) = dl_value(:,:,:)+360._dp |
---|
| 1260 | END WHERE |
---|
| 1261 | ELSEIF( dl_min < 10_dp .AND. dl_max > 350_dp )THEN |
---|
| 1262 | WHERE( dl_value(:,:,:) > 180 ) |
---|
| 1263 | dl_value(:,:,:) = dl_value(:,:,:)-180._dp |
---|
| 1264 | END WHERE |
---|
| 1265 | ENDIF |
---|
| 1266 | ENDIF |
---|
| 1267 | |
---|
| 1268 | WHERE( dl_value(:,:, 2) /= dd_fill .AND. & ! jk |
---|
| 1269 | & dl_value(:,:, 3) /= dd_fill .AND. & ! jk+1 |
---|
| 1270 | & dl_value(:,:, 1) /= dd_fill ) ! jk-1 |
---|
| 1271 | |
---|
| 1272 | math_deriv_3D(:,:,jk)=& |
---|
| 1273 | & ( dl_value(:,:,3) - dl_value(:,:,1) ) / & |
---|
| 1274 | & REAL( il_kmax-il_kmin,dp) |
---|
| 1275 | |
---|
| 1276 | END WHERE |
---|
| 1277 | |
---|
| 1278 | ENDDO |
---|
| 1279 | |
---|
| 1280 | END SELECT |
---|
| 1281 | |
---|
| 1282 | DEALLOCATE( dl_value ) |
---|
| 1283 | |
---|
| 1284 | END FUNCTION math_deriv_3D |
---|
| 1285 | END MODULE math |
---|