[5609] | 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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[12080] | 10 | !> |
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[5609] | 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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[12080] | 89 | !> |
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[5609] | 90 | !> @date January, 2015 - Initial version |
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[12080] | 91 | !> |
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| 92 | !> @note Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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[5609] | 93 | !---------------------------------------------------------------------- |
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| 94 | MODULE math |
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[12080] | 95 | |
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[5609] | 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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[12080] | 113 | PUBLIC :: math_ortho !< compute orthodome distance |
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| 114 | PUBLIC :: math_euclid !< compute euclidian distance |
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[5609] | 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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[12080] | 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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[5609] | 145 | !------------------------------------------------------------------- |
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| 146 | !> @brief This function compute the mean of a 1D array. |
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[12080] | 147 | !> |
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[5609] | 148 | !> @author J.Paul |
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[5617] | 149 | !> @date January, 2015 - Initial Version |
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[12080] | 150 | !> |
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[5609] | 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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[12080] | 155 | |
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[5609] | 156 | IMPLICIT NONE |
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[12080] | 157 | |
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[5609] | 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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[12080] | 162 | ! function |
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| 163 | REAL(dp) :: df_mean |
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| 164 | |
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[5609] | 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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[12080] | 177 | df_mean=dl_sum/dl_count |
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[5609] | 178 | ELSE |
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[12080] | 179 | df_mean=dd_fill |
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[5609] | 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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[12080] | 187 | df_mean=dl_sum/dl_count |
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[5609] | 188 | ELSE |
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[12080] | 189 | df_mean=0 |
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[5609] | 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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[12080] | 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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[5609] | 197 | !------------------------------------------------------------------- |
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| 198 | !> @brief This function compute the mean of a 2D array. |
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[12080] | 199 | !> |
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[5609] | 200 | !> @author J.Paul |
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[5617] | 201 | !> @date January, 2015 - Initial Version |
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[12080] | 202 | !> |
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[5609] | 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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[12080] | 207 | |
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[5609] | 208 | IMPLICIT NONE |
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[12080] | 209 | |
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[5609] | 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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[12080] | 214 | ! function |
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| 215 | REAL(dp) :: df_mean |
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| 216 | |
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[5609] | 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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[12080] | 229 | df_mean=dd_fill |
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[5609] | 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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[12080] | 237 | df_mean=0 |
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[5609] | 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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[12080] | 242 | df_mean=math_mean(dl_list(:)) |
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[5609] | 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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[12080] | 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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[5609] | 250 | !------------------------------------------------------------------- |
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| 251 | !> @brief This function compute the median of a 1D array. |
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[12080] | 252 | !> |
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[5609] | 253 | !> @author J.Paul |
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[5617] | 254 | !> @date January, 2015 - Initial Version |
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[12080] | 255 | !> |
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[5609] | 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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[12080] | 260 | |
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[5609] | 261 | IMPLICIT NONE |
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[12080] | 262 | |
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[5609] | 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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[12080] | 267 | ! function |
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| 268 | REAL(dp) :: df_median |
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| 269 | |
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[5609] | 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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[12080] | 282 | df_median=dd_fill |
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[5609] | 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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[12080] | 290 | df_median=0 |
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[5609] | 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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[12080] | 298 | df_median=(dl_list(il_count/2+1)+dl_list(il_count/2))/2_dp |
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[5609] | 299 | ELSE |
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[12080] | 300 | df_median=dl_list(il_count/2+1) |
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[5609] | 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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[12080] | 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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[5609] | 310 | !------------------------------------------------------------------- |
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| 311 | !> @brief This function compute the median of a 2D array. |
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[12080] | 312 | !> |
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[5609] | 313 | !> @author J.Paul |
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[5617] | 314 | !> @date January, 2015 - Initial Version |
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[12080] | 315 | !> |
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[5609] | 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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[12080] | 320 | |
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[5609] | 321 | IMPLICIT NONE |
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[12080] | 322 | |
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[5609] | 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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[12080] | 327 | ! funtion |
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| 328 | REAL(dp) :: df_median |
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| 329 | |
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[5609] | 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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[12080] | 342 | df_median=dd_fill |
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[5609] | 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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[12080] | 350 | df_median=0 |
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[5609] | 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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[12080] | 355 | df_median=math_median(dl_list(:)) |
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[5609] | 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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[12080] | 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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[5609] | 363 | !------------------------------------------------------------------- |
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| 364 | !> @brief This function compute the mean without extremum of a 1D array. |
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[12080] | 365 | !> |
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[5609] | 366 | !> @author J.Paul |
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[5617] | 367 | !> @date January, 2015 - Initial Version |
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[12080] | 368 | !> |
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[5609] | 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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[12080] | 374 | |
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[5609] | 375 | IMPLICIT NONE |
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[12080] | 376 | |
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[5609] | 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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[12080] | 382 | ! function |
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| 383 | REAL(dp) :: df_mwe |
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| 384 | |
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[5609] | 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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[12080] | 403 | df_mwe=dd_fill |
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[5609] | 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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[12080] | 411 | df_mwe=0 |
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[5609] | 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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[12080] | 420 | df_mwe=math_mean(dl_list(il_next+1:il_size-il_next)) |
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[5609] | 421 | ELSEIF( il_count > il_size-2*il_next )THEN |
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| 422 | ! remove one extremum each side |
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[12080] | 423 | df_mwe=math_mean(dl_list(2:il_size-1)) |
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[5609] | 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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[12080] | 427 | df_mwe=math_mean(dl_list(:)) |
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[5609] | 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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[12080] | 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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[5609] | 437 | !------------------------------------------------------------------- |
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| 438 | !> @brief This function compute the mean without extremum of a 2D array. |
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[12080] | 439 | !> |
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[5609] | 440 | !> @author J.Paul |
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[5617] | 441 | !> @date January, 2015 - Initial Version |
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[12080] | 442 | !> |
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[5609] | 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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[12080] | 448 | |
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[5609] | 449 | IMPLICIT NONE |
---|
[12080] | 450 | |
---|
[5609] | 451 | ! Argument |
---|
| 452 | REAL(dp), DIMENSION(:,:), INTENT(IN) :: dd_array |
---|
| 453 | INTEGER(i4) , INTENT(IN), OPTIONAL :: id_next |
---|
| 454 | REAL(dp), INTENT(IN), OPTIONAL :: dd_fill |
---|
| 455 | |
---|
[12080] | 456 | ! function |
---|
| 457 | REAL(dp) :: df_mwe |
---|
| 458 | |
---|
[5609] | 459 | ! local variable |
---|
| 460 | INTEGER(i4) :: il_count |
---|
| 461 | |
---|
| 462 | REAL(dp), DIMENSION(:), ALLOCATABLE :: dl_list |
---|
| 463 | !---------------------------------------------------------------- |
---|
| 464 | |
---|
| 465 | IF( PRESENT(dd_fill) )THEN |
---|
| 466 | il_count=COUNT(dd_array(:,:)/=dd_fill) |
---|
| 467 | IF( il_count > 0 )THEN |
---|
| 468 | ALLOCATE( dl_list(il_count) ) |
---|
| 469 | dl_list(:)=PACK(dd_array(:,:),dd_array(:,:)/=dd_fill) |
---|
| 470 | |
---|
[12080] | 471 | df_mwe=math_mwe(dl_list(:), id_next) |
---|
[5609] | 472 | ELSE |
---|
[12080] | 473 | df_mwe=dd_fill |
---|
[5609] | 474 | ENDIF |
---|
| 475 | ELSE |
---|
| 476 | il_count=SIZE(dd_array(:,:)) |
---|
| 477 | IF( il_count > 0 )THEN |
---|
| 478 | ALLOCATE( dl_list(il_count) ) |
---|
| 479 | dl_list(:)=PACK(dd_array(:,:), MASK=.TRUE.) |
---|
| 480 | |
---|
[12080] | 481 | df_mwe=math_mwe(dl_list(:), id_next) |
---|
[5609] | 482 | ELSE |
---|
[12080] | 483 | df_mwe=0 |
---|
[5609] | 484 | ENDIF |
---|
| 485 | ENDIF |
---|
| 486 | |
---|
| 487 | IF( ALLOCATED(dl_list) ) DEALLOCATE(dl_list) |
---|
| 488 | |
---|
| 489 | END FUNCTION math__mwe_2d |
---|
[12080] | 490 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 491 | PURE RECURSIVE SUBROUTINE math_QsortC(dd_array) |
---|
[5609] | 492 | !------------------------------------------------------------------- |
---|
| 493 | !> @brief This subroutine sort a 1D array. |
---|
| 494 | !> |
---|
| 495 | !> @details |
---|
| 496 | !> Recursive Fortran 95 quicksort routine |
---|
| 497 | !> sorts real numbers into ascending numerical order |
---|
| 498 | !> Author: Juli Rew, SCD Consulting (juliana@ucar.edu), 9/03 |
---|
| 499 | !> Based on algorithm from Cormen et al., Introduction to Algorithms, |
---|
| 500 | !> 1997 printing |
---|
| 501 | !> |
---|
| 502 | !> @author J.Paul |
---|
[5617] | 503 | !> @date January, 2015 - Rewrite with SIREN coding rules |
---|
[12080] | 504 | !> |
---|
[5609] | 505 | !> @param[inout] dd_array 1D array |
---|
| 506 | !------------------------------------------------------------------- |
---|
[12080] | 507 | |
---|
[5609] | 508 | IMPLICIT NONE |
---|
[12080] | 509 | |
---|
[5609] | 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 |
---|
[12080] | 524 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 525 | PURE SUBROUTINE math__Partition(dd_array, id_marker) |
---|
[5609] | 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 |
---|
[5617] | 535 | !> @date January, 2015 - Rewrite with SIREN coding rules |
---|
[12080] | 536 | !> @date November, 2017 |
---|
| 537 | !> - use the correct loop index to look for element bigger than pivot point. |
---|
| 538 | !> |
---|
[5609] | 539 | !> @param[inout] dd_array 1D array |
---|
| 540 | !> @param[in] id_marker |
---|
| 541 | !------------------------------------------------------------------- |
---|
[12080] | 542 | |
---|
[5609] | 543 | IMPLICIT NONE |
---|
[12080] | 544 | |
---|
[5609] | 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 |
---|
[12080] | 570 | IF( dd_array(ji) >= dl_x ) EXIT |
---|
[5609] | 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 |
---|
[12080] | 588 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 589 | PURE SUBROUTINE math_unwrap(dd_array, dd_discont) |
---|
[5609] | 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 |
---|
[5617] | 607 | !> @date Marsh, 2015 - Rewrite in fortran, with SIREN coding rules |
---|
[12080] | 608 | !> |
---|
[5609] | 609 | !> @param[inout] dd_array 1D array |
---|
| 610 | !> @param[in] dd_discont maximum discontinuity between values, default pi |
---|
| 611 | !------------------------------------------------------------------- |
---|
[12080] | 612 | |
---|
[5609] | 613 | IMPLICIT NONE |
---|
[12080] | 614 | |
---|
[5609] | 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 |
---|
[12080] | 672 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 673 | RECURSIVE FUNCTION math_compute(cd_var) & |
---|
| 674 | & RESULT(df_res) |
---|
[5609] | 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 |
---|
[5617] | 686 | !> @date June, 2015 - initial version |
---|
[12080] | 687 | !> |
---|
[5609] | 688 | !> @param[in] cd_var operation to compute (string of character) |
---|
| 689 | !> @return result of the operation, real(dp) |
---|
| 690 | !------------------------------------------------------------------- |
---|
[12080] | 691 | |
---|
[5609] | 692 | IMPLICIT NONE |
---|
[12080] | 693 | |
---|
[5609] | 694 | ! Argument |
---|
| 695 | CHARACTER(LEN=*), INTENT(IN) :: cd_var |
---|
| 696 | |
---|
[12080] | 697 | ! fucntion |
---|
| 698 | REAL(dp) :: df_res |
---|
| 699 | |
---|
[5609] | 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 |
---|
[12080] | 711 | READ(cd_var,*) df_res |
---|
[5609] | 712 | ELSE |
---|
| 713 | |
---|
| 714 | |
---|
| 715 | CALL math__parentheses(cd_var, cl_var) |
---|
| 716 | |
---|
| 717 | IF(fct_is_real(cl_var))THEN |
---|
[12080] | 718 | READ(cl_var,*) df_res |
---|
[5609] | 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:) |
---|
[12080] | 724 | df_res=math_compute(cl_str1)*math_compute(cl_str2) |
---|
[5609] | 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:) |
---|
[12080] | 730 | df_res=math_compute(cl_str1)/math_compute(cl_str2) |
---|
[5609] | 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:) |
---|
[12080] | 736 | df_res=math_compute(cl_str1)+math_compute(cl_str2) |
---|
[5609] | 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:) |
---|
[12080] | 742 | df_res=math_compute(cl_str1)-math_compute(cl_str2) |
---|
[5609] | 743 | ELSE |
---|
[12080] | 744 | df_res=dp_fill |
---|
[5609] | 745 | ENDIF |
---|
| 746 | ENDIF |
---|
| 747 | ENDIF |
---|
| 748 | ENDIF |
---|
| 749 | ENDIF |
---|
| 750 | ENDIF |
---|
| 751 | |
---|
| 752 | END FUNCTION math_compute |
---|
[12080] | 753 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 754 | SUBROUTINE math__parentheses(cd_varin, cd_varout) |
---|
[5609] | 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 |
---|
[5617] | 764 | !> @date June, 2015 - initial version |
---|
[12080] | 765 | !> |
---|
[5609] | 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 | !------------------------------------------------------------------- |
---|
[12080] | 771 | |
---|
[5609] | 772 | IMPLICIT NONE |
---|
[12080] | 773 | |
---|
[5609] | 774 | ! Argument |
---|
| 775 | CHARACTER(LEN=*) , INTENT(IN) :: cd_varin |
---|
| 776 | CHARACTER(LEN=lc), INTENT(OUT) :: cd_varout |
---|
[12080] | 777 | |
---|
[5609] | 778 | ! local variables |
---|
| 779 | CHARACTER(LEN=lc) :: cl_cpt |
---|
| 780 | INTEGER(i4) :: il_ind |
---|
| 781 | INTEGER(i4) :: il_count |
---|
[12080] | 782 | |
---|
[5609] | 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 |
---|
[12080] | 808 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 809 | PURE FUNCTION math_deriv_1D(dd_value, dd_fill, ld_discont) & |
---|
| 810 | & RESULT (df_deriv) |
---|
[5609] | 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 |
---|
[5617] | 820 | !> @date November, 2013 - Initial Version |
---|
[12080] | 821 | !> |
---|
[5609] | 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 |
---|
[12080] | 828 | |
---|
[5609] | 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 |
---|
[12080] | 835 | REAL(dp), DIMENSION(SIZE(dd_value,DIM=1) ) :: df_deriv |
---|
[5609] | 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 |
---|
[12080] | 855 | df_deriv(:)=dd_fill |
---|
[5609] | 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 | |
---|
[12080] | 910 | df_deriv(ji)= (dl_value(3) - dl_value(1)) / REAL(il_imax-il_imin,dp) |
---|
[5609] | 911 | |
---|
| 912 | ENDIF |
---|
| 913 | |
---|
| 914 | ENDDO |
---|
| 915 | |
---|
| 916 | DEALLOCATE( dl_value ) |
---|
| 917 | |
---|
| 918 | END FUNCTION math_deriv_1D |
---|
[12080] | 919 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 920 | FUNCTION math_deriv_2D(dd_value, dd_fill, cd_dim, ld_discont) & |
---|
| 921 | & RESULT (df_deriv) |
---|
[5609] | 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 |
---|
[5617] | 933 | !> @date November, 2013 - Initial Version |
---|
[12080] | 934 | !> |
---|
[5609] | 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 |
---|
[12080] | 942 | |
---|
[5609] | 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), & |
---|
[12080] | 951 | & SIZE(dd_value,DIM=2) ) :: df_deriv |
---|
[5609] | 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 |
---|
[12080] | 977 | df_deriv(:,:)=dd_fill |
---|
[5609] | 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(:,:), & |
---|
[12080] | 1009 | & DIM=1, & |
---|
| 1010 | & SHIFT=-1, & |
---|
| 1011 | & BOUNDARY=dl_value(1,:) ) |
---|
[5609] | 1012 | ENDIF |
---|
| 1013 | IF( il_imax == il_shape(1) )THEN |
---|
| 1014 | dl_value(:,:)=EOSHIFT( dl_value(:,:), & |
---|
[12080] | 1015 | & DIM=1, & |
---|
| 1016 | & SHIFT=1, & |
---|
| 1017 | & BOUNDARY=dl_value(3,:)) |
---|
[5609] | 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 |
---|
[12080] | 1035 | & dl_value(3,:) /= dd_fill .AND. & ! ji+1 |
---|
| 1036 | & dl_value(1,:) /= dd_fill ) ! ji-1 |
---|
[5609] | 1037 | |
---|
[12080] | 1038 | df_deriv(ji,:)= (dl_value(3,:) - dl_value(1,:)) / REAL(il_imax-il_imin,dp) |
---|
[5609] | 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(:,:), & |
---|
[12080] | 1064 | & DIM=2, & |
---|
| 1065 | & SHIFT=-1, & |
---|
| 1066 | & BOUNDARY=dl_value(:,1)) |
---|
[5609] | 1067 | ENDIF |
---|
| 1068 | IF( il_jmax == il_shape(2) )THEN |
---|
| 1069 | dl_value(:,:)=EOSHIFT( dl_value(:,:), & |
---|
[12080] | 1070 | & DIM=2, & |
---|
| 1071 | & SHIFT=1, & |
---|
| 1072 | & BOUNDARY=dl_value(:,3)) |
---|
[5609] | 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 |
---|
[12080] | 1090 | & dl_value(:, 3) /= dd_fill .AND. & ! jj+1 |
---|
| 1091 | & dl_value(:, 1) /= dd_fill ) ! jj-1 |
---|
[5609] | 1092 | |
---|
[12080] | 1093 | df_deriv(:,jj)= (dl_value(:,3) - dl_value(:,1)) / REAL(il_jmax-il_jmin,dp) |
---|
[5609] | 1094 | |
---|
| 1095 | END WHERE |
---|
| 1096 | |
---|
| 1097 | ENDDO |
---|
| 1098 | |
---|
| 1099 | END SELECT |
---|
| 1100 | |
---|
| 1101 | DEALLOCATE( dl_value ) |
---|
| 1102 | |
---|
| 1103 | END FUNCTION math_deriv_2D |
---|
[12080] | 1104 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1105 | PURE FUNCTION math_deriv_3D(dd_value, dd_fill, cd_dim, ld_discont) & |
---|
| 1106 | & RESULT (df_deriv) |
---|
[5609] | 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 |
---|
[5617] | 1118 | !> @date November, 2013 - Initial Version |
---|
[12080] | 1119 | !> |
---|
[5609] | 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 |
---|
[12080] | 1127 | |
---|
[5609] | 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), & |
---|
[12080] | 1137 | & SIZE(dd_value,DIM=3)) :: df_deriv |
---|
[5609] | 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 |
---|
[12080] | 1169 | df_deriv(:,:,:)=dd_fill |
---|
[5609] | 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(:,:,:), & |
---|
[12080] | 1199 | & DIM=1, & |
---|
| 1200 | & SHIFT=-1, & |
---|
| 1201 | & BOUNDARY=dl_value(1,:,:) ) |
---|
[5609] | 1202 | ENDIF |
---|
| 1203 | IF( il_imax == il_shape(1) )THEN |
---|
| 1204 | dl_value(:,:,:)=EOSHIFT( dl_value(:,:,:), & |
---|
[12080] | 1205 | & DIM=1, & |
---|
| 1206 | & SHIFT=1, & |
---|
| 1207 | & BOUNDARY=dl_value(3,:,:)) |
---|
[5609] | 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 |
---|
[12080] | 1225 | & dl_value(3,:,:) /= dd_fill .AND. & !ji+1 |
---|
| 1226 | & dl_value(1,:,:) /= dd_fill ) !ji-1 |
---|
[5609] | 1227 | |
---|
[12080] | 1228 | df_deriv(ji,:,:)= (dl_value(3,:,:) - dl_value(1,:,:)) / REAL(il_imax-il_imin,dp) |
---|
[5609] | 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(:,:,:), & |
---|
[12080] | 1254 | & DIM=2, & |
---|
| 1255 | & SHIFT=-1, & |
---|
| 1256 | & BOUNDARY=dl_value(:,1,:) ) |
---|
[5609] | 1257 | ENDIF |
---|
| 1258 | IF( il_jmax == il_shape(2) )THEN |
---|
| 1259 | dl_value(:,:,:)=EOSHIFT( dl_value(:,:,:), & |
---|
[12080] | 1260 | & DIM=2, & |
---|
| 1261 | & SHIFT=1, & |
---|
| 1262 | & BOUNDARY=dl_value(:,3,:)) |
---|
[5609] | 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 |
---|
[12080] | 1281 | & dl_value(:, 1,:) /= dd_fill ) ! jj-1 |
---|
[5609] | 1282 | |
---|
[12080] | 1283 | df_deriv(:,jj,:)= (dl_value(:,3,:) - dl_value(:,1,:)) / REAL(il_jmax - il_jmin,dp) |
---|
[5609] | 1284 | |
---|
| 1285 | END WHERE |
---|
| 1286 | |
---|
| 1287 | ENDDO |
---|
| 1288 | |
---|
| 1289 | CASE('K') |
---|
[6393] | 1290 | |
---|
| 1291 | ALLOCATE( dl_value(il_shape(1),il_shape(2),3) ) |
---|
[5609] | 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(:,:,:), & |
---|
[12080] | 1309 | & DIM=3, & |
---|
| 1310 | & SHIFT=-1, & |
---|
| 1311 | & BOUNDARY=dl_value(:,:,1) ) |
---|
[5609] | 1312 | ENDIF |
---|
| 1313 | IF( il_kmax == il_shape(3) )THEN |
---|
| 1314 | dl_value(:,:,:)=EOSHIFT( dl_value(:,:,:), & |
---|
[12080] | 1315 | & DIM=3, & |
---|
| 1316 | & SHIFT=1, & |
---|
| 1317 | & BOUNDARY=dl_value(:,:,3)) |
---|
[5609] | 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 | |
---|
[6393] | 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 |
---|
[5609] | 1337 | |
---|
[12080] | 1338 | df_deriv(:,:,jk)= (dl_value(:,:,3) - dl_value(:,:,1)) / REAL(il_kmax-il_kmin,dp) |
---|
[5609] | 1339 | |
---|
| 1340 | END WHERE |
---|
| 1341 | |
---|
| 1342 | ENDDO |
---|
| 1343 | |
---|
| 1344 | END SELECT |
---|
| 1345 | |
---|
| 1346 | DEALLOCATE( dl_value ) |
---|
| 1347 | |
---|
| 1348 | END FUNCTION math_deriv_3D |
---|
[12080] | 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 |
---|
| 1430 | !---------------------------------------------------------------- |
---|
| 1431 | |
---|
| 1432 | dl_lata=(dd_latm-0.5)*dp_deg2rad |
---|
| 1433 | dl_lona=(dd_lonm-0.5)*dp_deg2rad |
---|
| 1434 | |
---|
| 1435 | xa = dp_rearth * COS(dl_lata) * COS(dl_lona) |
---|
| 1436 | ya = dp_rearth * COS(dl_lata) * SIN(dl_lona) |
---|
| 1437 | za = dp_rearth * SIN(dl_lata) |
---|
| 1438 | |
---|
| 1439 | dl_latb=(dd_latm+0.5)*dp_deg2rad |
---|
| 1440 | dl_lonb=(dd_lonm+0.5)*dp_deg2rad |
---|
| 1441 | |
---|
| 1442 | xb = dp_rearth * COS(dl_latb) * COS(dl_lonb) |
---|
| 1443 | yb = dp_rearth * COS(dl_latb) * SIN(dl_lonb) |
---|
| 1444 | zb = dp_rearth * SIN(dl_latb) |
---|
| 1445 | |
---|
| 1446 | df_euclid = ((xb-xa)**2 + (yb-ya)**2 + (zb-za)**2) |
---|
| 1447 | |
---|
| 1448 | END FUNCTION math_euclid |
---|
| 1449 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
[5609] | 1450 | END MODULE math |
---|