[5037] | 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: interp |
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| 6 | ! |
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| 7 | ! DESCRIPTION: |
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| 8 | !> @brief |
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| 9 | !> This module manage cubic interpolation on regular grid. |
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| 10 | !> |
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| 11 | !> |
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| 12 | !> @details |
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| 13 | !> to compute cubic interpolation:<br/> |
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| 14 | !> @code |
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| 15 | !> CALL interp_cubic_fill(dd_value, dd_fill, id_detect, id_rho, ld_even [,ld_discont] ) |
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| 16 | !> @endcode |
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| 17 | !> - dd_value is 2D array of variable value |
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| 18 | !> - dd_fill is the FillValue of variable |
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| 19 | !> - id_detect is 2D array of point to be interpolated (see interp module) |
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| 20 | !> - id_rho is array of refinment factor |
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| 21 | !> - ld_even indicates even refinment or not |
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| 22 | !> - ld_discont indicates longitudinal discontinuity (-180°/180°, 0°/360°) or not |
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| 23 | !> |
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| 24 | !> @author |
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| 25 | !> J.Paul |
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| 26 | ! REVISION HISTORY: |
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| 27 | !> @date September, 2014 -Initial version |
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[5609] | 28 | !> @date June, 2015 |
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| 29 | !> - use math module |
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[5037] | 30 | !> |
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| 31 | !> @note Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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| 32 | !---------------------------------------------------------------------- |
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| 33 | MODULE interp_cubic |
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| 34 | |
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| 35 | USE netcdf ! nf90 library |
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| 36 | USE global ! global variable |
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| 37 | USE kind ! F90 kind parameter |
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| 38 | USE logger ! log file manager |
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| 39 | USE fct ! basic useful function |
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[5609] | 40 | USE math ! mathematical function |
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[5037] | 41 | |
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| 42 | IMPLICIT NONE |
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| 43 | ! NOTE_avoid_public_variables_if_possible |
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| 44 | |
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| 45 | ! type and variable |
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| 46 | |
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| 47 | ! function and subroutine |
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| 48 | PUBLIC :: interp_cubic_fill !< compute interpolation using cubic method |
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| 49 | |
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| 50 | PRIVATE :: interp_cubic__2D !< compute bicubic interpolation on 2D gid |
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| 51 | PRIVATE :: interp_cubic__1D !< compute cubic interpolation on 1D gid |
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| 52 | PRIVATE :: interp_cubic__2D_coef !< compute coefficient for bicubic interpolation |
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| 53 | PRIVATE :: interp_cubic__2D_fill !< fill value using bicubic interpolation |
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| 54 | PRIVATE :: interp_cubic__1D_coef !< compute coefficient for cubic interpolation |
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| 55 | PRIVATE :: interp_cubic__1D_fill !< fill value using cubic interpolation |
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| 56 | PRIVATE :: interp_cubic__get_weight2D !< compute interpoaltion weight for 2D array |
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| 57 | PRIVATE :: interp_cubic__get_weight1D !< compute interpoaltion weight for 1D array |
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| 58 | |
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| 59 | CONTAINS |
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| 60 | !------------------------------------------------------------------- |
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| 61 | !> @brief |
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| 62 | !> This subroutine compute horizontal cubic interpolation on 4D array of value. |
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| 63 | !> |
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| 64 | !> @author J.Paul |
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[5609] | 65 | !> @date September, 2014 - Initial Version |
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| 66 | !> @date July, 2015 |
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| 67 | !> - reinitialise detect array for each level |
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[5037] | 68 | !> |
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| 69 | !> @param[inout] dd_value 2D array of variable value |
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| 70 | !> @param[in] dd_fill FillValue of variable |
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| 71 | !> @param[inout] id_detect 2D array of point to be interpolated |
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| 72 | !> @param[in] id_rho array of refinment factor |
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| 73 | !> @param[in] ld_even even refinment or not |
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| 74 | !> @param[in] ld_discont longitudinal discontinuity (-180°/180°, 0°/360°) or not |
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| 75 | !------------------------------------------------------------------- |
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| 76 | SUBROUTINE interp_cubic_fill(dd_value, dd_fill, id_detect, & |
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| 77 | & id_rho, ld_even, ld_discont ) |
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| 78 | IMPLICIT NONE |
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| 79 | ! Argument |
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| 80 | REAL(dp) , DIMENSION(:,:,:,:), INTENT(INOUT) :: dd_value |
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| 81 | REAL(dp) , INTENT(IN ) :: dd_fill |
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| 82 | INTEGER(I4) , DIMENSION(:,:,:) , INTENT(INOUT) :: id_detect |
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| 83 | INTEGER(I4) , DIMENSION(:) , INTENT(IN ) :: id_rho |
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| 84 | LOGICAL , DIMENSION(:) , INTENT(IN ) :: ld_even |
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| 85 | LOGICAL , INTENT(IN ), OPTIONAL :: ld_discont |
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| 86 | |
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| 87 | ! local variable |
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[5609] | 88 | INTEGER(i4), DIMENSION(4) :: il_shape |
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[5037] | 89 | |
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[5609] | 90 | INTEGER(I4), DIMENSION(:,:,:), ALLOCATABLE :: il_detect |
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[5037] | 91 | |
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[5609] | 92 | LOGICAL :: ll_discont |
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| 93 | |
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| 94 | REAL(dp) , DIMENSION(:,:) , ALLOCATABLE :: dl_weight_IJ |
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| 95 | REAL(dp) , DIMENSION(:,:) , ALLOCATABLE :: dl_weight_I |
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| 96 | REAL(dp) , DIMENSION(:,:) , ALLOCATABLE :: dl_weight_J |
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[5037] | 97 | |
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| 98 | ! loop indices |
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| 99 | INTEGER(i4) :: ji |
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| 100 | INTEGER(i4) :: jj |
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| 101 | INTEGER(i4) :: jk |
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| 102 | INTEGER(i4) :: jl |
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| 103 | !---------------------------------------------------------------- |
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| 104 | ll_discont=.FALSE. |
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| 105 | IF( PRESENT(ld_discont) ) ll_discont=ld_discont |
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| 106 | |
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| 107 | il_shape(:)=SHAPE(dd_value) |
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| 108 | |
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| 109 | ! compute vect2D |
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| 110 | ALLOCATE(dl_weight_IJ(16,((id_rho(jp_I)+1)*(id_rho(jp_J)+1))) ) |
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| 111 | CALL interp_cubic__get_weight2D(dl_weight_IJ(:,:), & |
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| 112 | & id_rho(:), ld_even(:)) |
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| 113 | |
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| 114 | ALLOCATE( dl_weight_I( 4,((id_rho(jp_I)+1) )) ) |
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| 115 | ALLOCATE( dl_weight_J( 4,( (id_rho(jp_J)+1))) ) |
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| 116 | CALL interp_cubic__get_weight1D(dl_weight_I(:,:), & |
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| 117 | & id_rho(jp_I), ld_even(jp_I)) |
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| 118 | CALL interp_cubic__get_weight1D(dl_weight_J(:,:), & |
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| 119 | & id_rho(jp_J), ld_even(jp_J)) |
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| 120 | |
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[5609] | 121 | ALLOCATE(il_detect(il_shape(1),il_shape(2),il_shape(3))) |
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| 122 | |
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[5037] | 123 | DO jl=1,il_shape(4) |
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[5609] | 124 | il_detect(:,:,:)=id_detect(:,:,:) |
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[5037] | 125 | ! loop on vertical level |
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| 126 | DO jk=1,il_shape(3) |
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| 127 | |
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| 128 | ! I-J plan |
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| 129 | CALL interp_cubic__2D(dd_value(:,:,jk,jl), dd_fill, & |
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[5609] | 130 | & il_detect(:,:,jk), & |
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[5037] | 131 | & dl_weight_IJ(:,:), & |
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| 132 | & id_rho(jp_I), id_rho(jp_J), & |
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| 133 | & ll_discont) |
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[5609] | 134 | IF( ANY(il_detect(:,:,jk)==1) )THEN |
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[5037] | 135 | ! I direction |
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| 136 | DO jj=1,il_shape(2) |
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| 137 | CALL interp_cubic__1D( dd_value(:,jj,jk,jl), dd_fill, & |
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[5609] | 138 | & il_detect(:,jj,jk), & |
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[5037] | 139 | & dl_weight_I(:,:), & |
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| 140 | & id_rho(jp_I), ll_discont ) |
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| 141 | ENDDO |
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[5609] | 142 | IF( ALL(il_detect(:,:,jk)==0) )THEN |
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[5037] | 143 | CYCLE |
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| 144 | ELSE |
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| 145 | ! J direction |
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| 146 | DO ji=1,il_shape(1) |
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| 147 | CALL interp_cubic__1D( dd_value(ji,:,jk,jl), dd_fill, & |
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[5609] | 148 | & il_detect(ji,:,jk), & |
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[5037] | 149 | & dl_weight_J(:,:), & |
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| 150 | & id_rho(jp_J), ll_discont ) |
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| 151 | ENDDO |
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| 152 | ENDIF |
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| 153 | ENDIF |
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| 154 | |
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| 155 | ENDDO |
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| 156 | ENDDO |
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| 157 | |
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[5609] | 158 | id_detect(:,:,:)=il_detect(:,:,:) |
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| 159 | DEALLOCATE(il_detect) |
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| 160 | |
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[5037] | 161 | DEALLOCATE(dl_weight_IJ) |
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| 162 | DEALLOCATE(dl_weight_I) |
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| 163 | DEALLOCATE(dl_weight_J) |
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| 164 | |
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| 165 | END SUBROUTINE interp_cubic_fill |
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| 166 | !------------------------------------------------------------------- |
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| 167 | !> @brief |
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| 168 | !> This subroutine compute cubic interpolation on 2D array of value. |
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| 169 | !> |
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| 170 | !> @details |
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| 171 | !> |
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| 172 | !> @author J.Paul |
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[5609] | 173 | !> @date September, 2014 - Initial Version |
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[5037] | 174 | !> |
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| 175 | !> @param[inout] dd_value 2D array of variable value |
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| 176 | !> @param[in] dd_fill FillValue of variable |
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| 177 | !> @param[inout] id_detect 2D array of point to be interpolated |
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| 178 | !> @param[in] id_rhoi refinment factor in i-direction |
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| 179 | !> @param[in] id_rhoj refinment factor in j-direction |
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| 180 | !> @param[in] id_rhok refinment factor in k-direction |
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| 181 | !> @param[in] ld_even even refinment or not |
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| 182 | !> @param[in] ld_discont longitudinal discontinuity (-180°/180°, 0°/360°) or not |
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| 183 | !------------------------------------------------------------------- |
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| 184 | SUBROUTINE interp_cubic__2D( dd_value, dd_fill, & |
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| 185 | & id_detect, & |
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| 186 | & dd_weight, & |
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| 187 | & id_rhoi, id_rhoj, & |
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| 188 | & ld_discont ) |
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| 189 | |
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| 190 | IMPLICIT NONE |
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| 191 | ! Argument |
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| 192 | REAL(dp) , DIMENSION(:,:), INTENT(INOUT) :: dd_value |
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| 193 | REAL(dp) , INTENT(IN ) :: dd_fill |
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| 194 | INTEGER(I4) , DIMENSION(:,:), INTENT(INOUT) :: id_detect |
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[5609] | 195 | REAL(dp) , DIMENSION(:,:), INTENT(IN ) :: dd_weight |
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[5037] | 196 | INTEGER(I4) , INTENT(IN ) :: id_rhoi |
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| 197 | INTEGER(I4) , INTENT(IN ) :: id_rhoj |
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| 198 | LOGICAL , INTENT(IN ) :: ld_discont |
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| 199 | |
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| 200 | ! local variable |
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| 201 | INTEGER(I4) :: il_xextra |
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| 202 | INTEGER(I4) :: il_yextra |
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| 203 | INTEGER(i4), DIMENSION(2) :: il_shape |
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| 204 | INTEGER(i4), DIMENSION(2) :: il_dim |
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| 205 | |
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| 206 | REAL(dp) :: dl_min |
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| 207 | REAL(dp) :: dl_max |
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| 208 | REAL(dp) , DIMENSION(:) , ALLOCATABLE :: dl_coef |
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| 209 | REAL(dp) , DIMENSION(:,:), ALLOCATABLE :: dl_coarse |
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| 210 | REAL(dp) , DIMENSION(:,:), ALLOCATABLE :: dl_tmp |
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| 211 | REAL(dp) , DIMENSION(:,:), ALLOCATABLE :: dl_dfdx |
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| 212 | REAL(dp) , DIMENSION(:,:), ALLOCATABLE :: dl_dfdy |
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| 213 | REAL(dp) , DIMENSION(:,:), ALLOCATABLE :: dl_d2fdxy |
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| 214 | |
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| 215 | ! loop indices |
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| 216 | INTEGER(i4) :: ji |
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| 217 | INTEGER(i4) :: jj |
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| 218 | INTEGER(i4) :: ii |
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| 219 | INTEGER(i4) :: ij |
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| 220 | |
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| 221 | !---------------------------------------------------------------- |
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| 222 | |
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| 223 | IF( ANY(id_detect(:,:)==1) )THEN |
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| 224 | il_shape(:)=SHAPE(dd_value) |
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| 225 | |
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| 226 | ! compute coarse grid dimension |
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| 227 | il_xextra=id_rhoi-1 |
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| 228 | il_dim(1)=(il_shape(1)+il_xextra)/id_rhoi |
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| 229 | |
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| 230 | il_yextra=id_rhoj-1 |
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| 231 | il_dim(2)=(il_shape(2)+il_yextra)/id_rhoj |
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| 232 | |
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| 233 | ALLOCATE( dl_coarse(il_dim(1),il_dim(2)) ) |
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| 234 | |
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| 235 | ! value on coarse grid |
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| 236 | dl_coarse(:,:)=dd_value( 1:il_shape(1):id_rhoi, & |
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| 237 | & 1:il_shape(2):id_rhoj ) |
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| 238 | |
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| 239 | ALLOCATE( dl_dfdx( il_dim(1),il_dim(2)), & |
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| 240 | & dl_dfdy( il_dim(1),il_dim(2)), & |
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| 241 | & dl_d2fdxy(il_dim(1),il_dim(2)) ) |
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| 242 | |
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| 243 | ! compute derivative on coarse grid |
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[5609] | 244 | dl_dfdx(:,:)=math_deriv_2D(dl_coarse(:,:), dd_fill, 'I', ld_discont) |
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| 245 | dl_dfdy(:,:)=math_deriv_2D(dl_coarse(:,:), dd_fill, 'J', ld_discont) |
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[5037] | 246 | |
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| 247 | ! compute cross derivative on coarse grid |
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[5609] | 248 | dl_d2fdxy(:,:)=math_deriv_2D(dl_dfdx(:,:), dd_fill, 'J', ld_discont) |
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[5037] | 249 | |
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| 250 | ALLOCATE( dl_tmp(2,2) ) |
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| 251 | ALLOCATE( dl_coef(16) ) |
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| 252 | |
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| 253 | DO jj=1,il_shape(2)-1,id_rhoj |
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| 254 | ij=((jj-1)/id_rhoj)+1 |
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| 255 | DO ji=1,il_shape(1)-1,id_rhoi |
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| 256 | ii=((ji-1)/id_rhoi)+1 |
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| 257 | |
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| 258 | ! check if point to be interpolated |
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| 259 | IF( ALL(id_detect(ji:ji+id_rhoi, & |
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| 260 | & jj:jj+id_rhoj)==0) ) CYCLE |
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| 261 | ! check data needed to interpolate |
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| 262 | IF( ANY(dl_coarse(ii:ii+1,ij:ij+1)==dd_fill) .OR. & |
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| 263 | & ANY( dl_dfdx(ii:ii+1,ij:ij+1)==dd_fill) .OR. & |
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| 264 | & ANY( dl_dfdy(ii:ii+1,ij:ij+1)==dd_fill) .OR. & |
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| 265 | & ANY(dl_d2fdxy(ii:ii+1,ij:ij+1)==dd_fill) ) CYCLE |
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| 266 | |
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| 267 | dl_tmp(:,:)=dl_coarse(ii:ii+1,ij:ij+1) |
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| 268 | ! check longitude discontinuity |
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| 269 | IF( ld_discont )THEN |
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| 270 | |
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| 271 | dl_min=MINVAL( dl_tmp(:,:), dl_tmp(:,:)/=dd_fill ) |
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| 272 | dl_max=MAXVAL( dl_tmp(:,:), dl_tmp(:,:)/=dd_fill ) |
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| 273 | IF( dl_min < -170_dp .AND. dl_max > 170_dp )THEN |
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| 274 | WHERE( dl_tmp(:,:) < 0_dp ) |
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| 275 | dl_tmp(:,:) = dl_tmp(:,:)+360._dp |
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| 276 | END WHERE |
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| 277 | ELSEIF( dl_min < 10_dp .AND. dl_max > 350_dp )THEN |
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| 278 | WHERE( dl_tmp(:,:) > 180_dp ) |
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| 279 | dl_tmp(:,:) = dl_tmp(:,:)-180._dp |
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| 280 | END WHERE |
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| 281 | ENDIF |
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| 282 | |
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| 283 | ENDIF |
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| 284 | |
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| 285 | ! compute bicubic coefficient |
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| 286 | dl_coef(:)=interp_cubic__2D_coef(dl_tmp(:,:),& |
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| 287 | & dl_dfdx( ii:ii+1,ij:ij+1),& |
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| 288 | & dl_dfdy( ii:ii+1,ij:ij+1),& |
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| 289 | & dl_d2fdxy(ii:ii+1,ij:ij+1),& |
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| 290 | & dd_fill ) |
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| 291 | |
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| 292 | ! compute value on detetected point |
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| 293 | CALL interp_cubic__2D_fill(dd_value( ji:ji+id_rhoi, & |
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| 294 | & jj:jj+id_rhoj ), & |
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| 295 | & id_detect(ji:ji+id_rhoi, & |
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| 296 | & jj:jj+id_rhoj ), & |
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| 297 | & dd_weight(:,:), dl_coef(:),& |
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| 298 | & dd_fill, id_rhoi, id_rhoj ) |
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| 299 | |
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| 300 | IF( ld_discont )THEN |
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| 301 | WHERE( dd_value( ji:ji+id_rhoi, & |
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| 302 | & jj:jj+id_rhoj ) >= 180._dp .AND. & |
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| 303 | & dd_value( ji:ji+id_rhoi, & |
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| 304 | & jj:jj+id_rhoj ) /= dd_fill ) |
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| 305 | dd_value( ji:ji+id_rhoi, & |
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| 306 | & jj:jj+id_rhoj ) = & |
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| 307 | & dd_value( ji:ji+id_rhoi, & |
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| 308 | & jj:jj+id_rhoj ) - 360._dp |
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| 309 | END WHERE |
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| 310 | ENDIF |
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| 311 | |
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| 312 | ENDDO |
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| 313 | ENDDO |
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| 314 | |
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| 315 | DEALLOCATE(dl_coef) |
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| 316 | DEALLOCATE(dl_tmp ) |
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| 317 | |
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| 318 | DEALLOCATE(dl_dfdx, & |
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| 319 | & dl_dfdy, & |
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| 320 | & dl_d2fdxy ) |
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| 321 | |
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| 322 | DEALLOCATE( dl_coarse ) |
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| 323 | ENDIF |
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| 324 | |
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| 325 | END SUBROUTINE interp_cubic__2D |
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| 326 | !------------------------------------------------------------------- |
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| 327 | !> @brief |
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| 328 | !> This subroutine compute cubic interpolation on 1D array of value. |
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| 329 | !> |
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| 330 | !> @details |
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| 331 | !> |
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| 332 | !> @author J.Paul |
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[5609] | 333 | !> @date September, 2014 - Initial Version |
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[5037] | 334 | !> |
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| 335 | !> @param[inout] dd_value 1D array of variable value |
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| 336 | !> @param[in] dd_fill FillValue of variable |
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| 337 | !> @param[inout] id_detect 1D array of point to be interpolated |
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| 338 | !> @param[in] id_rhoi refinment factor |
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| 339 | !> @param[in] ld_even even refinment or not |
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| 340 | !> @param[in] ld_discont longitudinal discontinuity (-180°/180°, 0°/360°) or not |
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| 341 | !------------------------------------------------------------------- |
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| 342 | SUBROUTINE interp_cubic__1D( dd_value, dd_fill, & |
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| 343 | & id_detect, & |
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| 344 | & dd_weight, & |
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| 345 | & id_rhoi, & |
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| 346 | & ld_discont ) |
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| 347 | |
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| 348 | IMPLICIT NONE |
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| 349 | ! Argument |
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| 350 | REAL(dp) , DIMENSION(:) , INTENT(INOUT) :: dd_value |
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| 351 | REAL(dp) , INTENT(IN ) :: dd_fill |
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| 352 | INTEGER(I4) , DIMENSION(:) , INTENT(INOUT) :: id_detect |
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[5609] | 353 | REAL(dp) , DIMENSION(:,:), INTENT(IN ) :: dd_weight |
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[5037] | 354 | INTEGER(I4) , INTENT(IN ) :: id_rhoi |
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| 355 | LOGICAL , INTENT(IN ) :: ld_discont |
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| 356 | |
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| 357 | ! local variable |
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| 358 | INTEGER(I4) :: il_xextra |
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| 359 | INTEGER(i4), DIMENSION(1) :: il_shape |
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| 360 | INTEGER(i4), DIMENSION(1) :: il_dim |
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| 361 | |
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| 362 | REAL(dp) :: dl_min |
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| 363 | REAL(dp) :: dl_max |
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| 364 | REAL(dp) , DIMENSION(:), ALLOCATABLE :: dl_coef |
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| 365 | REAL(dp) , DIMENSION(:), ALLOCATABLE :: dl_coarse |
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| 366 | REAL(dp) , DIMENSION(:), ALLOCATABLE :: dl_tmp |
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| 367 | REAL(dp) , DIMENSION(:), ALLOCATABLE :: dl_dfdx |
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| 368 | |
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| 369 | ! loop indices |
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| 370 | INTEGER(i4) :: ji |
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| 371 | INTEGER(i4) :: ii |
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| 372 | |
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| 373 | !---------------------------------------------------------------- |
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| 374 | |
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| 375 | IF( ANY(id_detect(:)==1) )THEN |
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| 376 | il_shape(:)=SHAPE(dd_value) |
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| 377 | |
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| 378 | ! compute coarse grid dimension |
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| 379 | il_xextra=id_rhoi-1 |
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| 380 | il_dim(1)=(il_shape(1)+il_xextra)/id_rhoi |
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| 381 | |
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| 382 | ALLOCATE( dl_coarse(il_dim(1)) ) |
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| 383 | |
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| 384 | ! value on coarse grid |
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| 385 | dl_coarse(:)=dd_value( 1:il_shape(1):id_rhoi ) |
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| 386 | |
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| 387 | ALLOCATE( dl_dfdx(il_dim(1)) ) |
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| 388 | |
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| 389 | ! compute derivative on coarse grid |
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[5609] | 390 | dl_dfdx(:)=math_deriv_1D(dl_coarse(:), dd_fill, ld_discont) |
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[5037] | 391 | |
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| 392 | ALLOCATE( dl_tmp(2) ) |
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| 393 | ALLOCATE( dl_coef(4) ) |
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| 394 | |
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| 395 | DO ji=1,il_shape(1)-1,id_rhoi |
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| 396 | ii=((ji-1)/id_rhoi)+1 |
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| 397 | |
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| 398 | ! check if point to be interpolated |
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| 399 | IF( ALL(id_detect(ji:ji+id_rhoi)==0) ) CYCLE |
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| 400 | ! check data needed to interpolate |
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| 401 | IF( ANY(dl_coarse(ii:ii+1)==dd_fill) .OR. & |
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| 402 | & ANY( dl_dfdx(ii:ii+1)==dd_fill) ) CYCLE |
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| 403 | ! check longitude discontinuity |
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| 404 | dl_tmp(:)=dl_coarse(ii:ii+1) |
---|
| 405 | IF( ld_discont )THEN |
---|
| 406 | |
---|
| 407 | dl_min=MINVAL( dl_tmp(:), dl_tmp(:)/=dd_fill ) |
---|
| 408 | dl_max=MAXVAL( dl_tmp(:), dl_tmp(:)/=dd_fill ) |
---|
| 409 | IF( dl_min < -170_dp .AND. dl_max > 170_dp )THEN |
---|
| 410 | WHERE( dl_tmp(:) < 0_dp ) |
---|
| 411 | dl_tmp(:) = dl_tmp(:)+360._dp |
---|
| 412 | END WHERE |
---|
| 413 | ELSEIF( dl_min < 10_dp .AND. dl_max > 350_dp )THEN |
---|
| 414 | WHERE( dl_tmp(:) > 180_dp ) |
---|
| 415 | dl_tmp(:) = dl_tmp(:)-180._dp |
---|
| 416 | END WHERE |
---|
| 417 | ENDIF |
---|
| 418 | |
---|
| 419 | ENDIF |
---|
| 420 | |
---|
| 421 | ! compute bicubic coefficient |
---|
| 422 | dl_coef(:)=interp_cubic__1D_coef(dl_tmp(:), & |
---|
| 423 | & dl_dfdx(ii:ii+1),& |
---|
| 424 | & dd_fill ) |
---|
| 425 | |
---|
| 426 | ! compute value on detetected point |
---|
| 427 | CALL interp_cubic__1D_fill( dd_value( ji:ji+id_rhoi ), & |
---|
| 428 | & id_detect(ji:ji+id_rhoi ), & |
---|
| 429 | & dd_weight(:,:), dl_coef(:), & |
---|
| 430 | & dd_fill, id_rhoi ) |
---|
| 431 | |
---|
| 432 | IF( ld_discont )THEN |
---|
| 433 | WHERE( dd_value( ji:ji+id_rhoi ) >= 180._dp .AND. & |
---|
| 434 | & dd_value( ji:ji+id_rhoi ) /= dd_fill ) |
---|
| 435 | dd_value(ji:ji+id_rhoi) = dd_value(ji:ji+id_rhoi) - 360._dp |
---|
| 436 | END WHERE |
---|
| 437 | ENDIF |
---|
| 438 | |
---|
| 439 | ENDDO |
---|
| 440 | |
---|
| 441 | DEALLOCATE(dl_coef) |
---|
| 442 | DEALLOCATE(dl_tmp ) |
---|
| 443 | |
---|
| 444 | DEALLOCATE(dl_dfdx ) |
---|
| 445 | DEALLOCATE( dl_coarse ) |
---|
| 446 | ENDIF |
---|
| 447 | |
---|
| 448 | END SUBROUTINE interp_cubic__1D |
---|
| 449 | !------------------------------------------------------------------- |
---|
| 450 | !> @brief |
---|
| 451 | !> This subroutine compute 2D array of coefficient for cubic interpolation. |
---|
| 452 | !> |
---|
| 453 | !> @author J.Paul |
---|
[5609] | 454 | !> @date September, 2014 - Initial Version |
---|
[5037] | 455 | !> |
---|
| 456 | !> @param[in] dd_value 2D array of value |
---|
| 457 | !> @param[in] dd_dfdx 2D array of first derivative in i-direction |
---|
| 458 | !> @param[in] dd_dfdy 2D array of first derivative in j-direction |
---|
| 459 | !> @param[in] dd_d2fdxy 2D array of cross derivative in i-j-direction |
---|
| 460 | !> @param[in] dd_fill FillValue of variable |
---|
| 461 | !------------------------------------------------------------------- |
---|
| 462 | FUNCTION interp_cubic__2D_coef( dd_value, & |
---|
| 463 | & dd_dfdx, & |
---|
| 464 | & dd_dfdy, & |
---|
| 465 | & dd_d2fdxy,& |
---|
| 466 | & dd_fill ) |
---|
| 467 | IMPLICIT NONE |
---|
| 468 | ! Argument |
---|
| 469 | REAL(dp), DIMENSION(:,:), INTENT(IN) :: dd_value |
---|
| 470 | REAL(dp), DIMENSION(:,:), INTENT(IN) :: dd_dfdx |
---|
| 471 | REAL(dp), DIMENSION(:,:), INTENT(IN) :: dd_dfdy |
---|
| 472 | REAL(dp), DIMENSION(:,:), INTENT(IN) :: dd_d2fdxy |
---|
| 473 | REAL(dp) , INTENT(IN) :: dd_fill |
---|
| 474 | |
---|
| 475 | ! function |
---|
| 476 | REAL(dp), DIMENSION(16) :: interp_cubic__2D_coef |
---|
| 477 | |
---|
| 478 | ! local variable |
---|
| 479 | REAL(dp), DIMENSION(16,16), PARAMETER :: dl_matrix = RESHAPE( & |
---|
| 480 | & (/ 1 , 0 ,-3 , 2 , 0 , 0 , 0 , 0 ,-3 , 0 , 9 ,-6 , 2 , 0 ,-6 , 4 ,& |
---|
| 481 | 0 , 0 , 3 ,-2 , 0 , 0 , 0 , 0 , 0 , 0 ,-9 , 6 , 0 , 0 , 6 ,-4 ,& |
---|
| 482 | 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 3 , 0 ,-9 , 6 ,-2 , 0 , 6 ,-4 ,& |
---|
| 483 | 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 9 ,-6 , 0 , 0 ,-6 , 4 ,& |
---|
| 484 | 0 , 1 ,-2 , 1 , 0 , 0 , 0 , 0 , 0 ,-3 , 6 ,-3 , 0 , 2 ,-4 , 2 ,& |
---|
| 485 | 0 , 0 ,-1 , 1 , 0 , 0 , 0 , 0 , 0 , 0 , 3 ,-3 , 0 , 0 ,-2 , 2 ,& |
---|
| 486 | 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 3 ,-6 , 3 , 0 ,-2 , 4 ,-2 ,& |
---|
| 487 | 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 ,-3 , 3 , 0 , 0 , 2 ,-2 ,& |
---|
| 488 | 0 , 0 , 0 , 0 , 1 , 0 ,-3 , 2 ,-2 , 0 , 6 ,-4 , 1 , 0 ,-3 , 2 ,& |
---|
| 489 | 0 , 0 , 0 , 0 , 0 , 0 , 3 ,-2 , 0 , 0 ,-6 , 4 , 0 , 0 , 3 ,-2 ,& |
---|
| 490 | 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 ,-1 , 0 , 3 ,-2 , 1 , 0 ,-3 , 2 ,& |
---|
| 491 | 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 ,-3 , 2 , 0 , 0 , 3 ,-2 ,& |
---|
| 492 | 0 , 0 , 0 , 0 , 0 , 1 ,-2 , 1 , 0 ,-2 , 4 ,-2 , 0 , 1 ,-2 , 1 ,& |
---|
| 493 | 0 , 0 , 0 , 0 , 0 , 0 ,-1 , 1 , 0 , 0 , 2 ,-2 , 0 , 0 ,-1 , 1 ,& |
---|
| 494 | 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 ,-1 , 2 ,-1 , 0 , 1 ,-2 , 1 ,& |
---|
| 495 | 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 1 ,-1 , 0 , 0 ,-1 , 1 /), & |
---|
| 496 | & (/ 16, 16 /) ) |
---|
| 497 | |
---|
| 498 | REAL(dp), DIMENSION(16) :: dl_vect |
---|
| 499 | |
---|
| 500 | !---------------------------------------------------------------- |
---|
| 501 | ! init |
---|
| 502 | interp_cubic__2D_coef(:)=dd_fill |
---|
| 503 | |
---|
| 504 | dl_vect( 1: 4)=PACK(dd_value(:,:),.TRUE. ) |
---|
| 505 | dl_vect( 5: 8)=PACK(dd_dfdx(:,:),.TRUE. ) |
---|
| 506 | dl_vect( 9:12)=PACK(dd_dfdy(:,:),.TRUE. ) |
---|
| 507 | dl_vect(13:16)=PACK(dd_d2fdxy(:,:),.TRUE. ) |
---|
| 508 | |
---|
| 509 | interp_cubic__2D_coef(:)=MATMUL(dl_matrix(:,:),dl_vect(:)) |
---|
| 510 | |
---|
| 511 | END FUNCTION interp_cubic__2D_coef |
---|
| 512 | !------------------------------------------------------------------- |
---|
| 513 | !> @brief |
---|
| 514 | !> This subroutine compute cubic interpolation of a 2D array of value. |
---|
| 515 | !> |
---|
| 516 | !> @author J.Paul |
---|
[5609] | 517 | !> @date September, 2014 - Initial Version |
---|
[5037] | 518 | !> |
---|
| 519 | !> @param[inout] dd_value 2D array of mixed grid value |
---|
| 520 | !> @param[inout] id_detect 2D array of point to be interpolated |
---|
| 521 | !> @param[in] dd_coef 2D array of coefficient |
---|
| 522 | !> @param[in] dd_fill FillValue of variable |
---|
| 523 | !> @param[in] ld_even even refinment or not |
---|
| 524 | !> @param[in] id_rhoi refinement factor in i-direction |
---|
| 525 | !> @param[in] id_rhoj refinement factor in j-direction |
---|
| 526 | !------------------------------------------------------------------- |
---|
| 527 | SUBROUTINE interp_cubic__2D_fill( dd_value, id_detect, & |
---|
| 528 | & dd_weight, dd_coef, & |
---|
| 529 | & dd_fill, id_rhoi, id_rhoj ) |
---|
| 530 | IMPLICIT NONE |
---|
| 531 | ! Argument |
---|
| 532 | REAL(dp) , DIMENSION(:,:), INTENT(INOUT) :: dd_value |
---|
| 533 | INTEGER(i4) , DIMENSION(:,:), INTENT(INOUT) :: id_detect |
---|
| 534 | REAL(dp) , DIMENSION(:,:), INTENT(IN ) :: dd_weight |
---|
| 535 | REAL(dp) , DIMENSION(:) , INTENT(IN ) :: dd_coef |
---|
| 536 | REAL(dp) , INTENT(IN ) :: dd_fill |
---|
| 537 | INTEGER(I4) , INTENT(IN ) :: id_rhoi |
---|
| 538 | INTEGER(I4) , INTENT(IN ) :: id_rhoj |
---|
| 539 | |
---|
| 540 | ! local variable |
---|
| 541 | |
---|
| 542 | ! loop indices |
---|
| 543 | INTEGER(i4) :: ii |
---|
| 544 | |
---|
| 545 | INTEGER(i4) :: ji |
---|
| 546 | INTEGER(i4) :: jj |
---|
| 547 | !---------------------------------------------------------------- |
---|
| 548 | |
---|
| 549 | IF( ANY( dd_coef(:)==dd_fill ) )THEN |
---|
| 550 | CALL logger_error("INTERP CUBIC FILL: fill value detected in coef . "//& |
---|
| 551 | & "can not compute interpolation.") |
---|
| 552 | ELSE |
---|
| 553 | |
---|
| 554 | ii=0 |
---|
| 555 | DO jj=1,id_rhoj+1 |
---|
| 556 | DO ji=1,id_rhoi+1 |
---|
| 557 | |
---|
| 558 | ii=ii+1 |
---|
| 559 | IF(id_detect(ji,jj)==1)THEN |
---|
| 560 | |
---|
| 561 | dd_value(ji,jj)=DOT_PRODUCT(dd_coef(:),dd_weight(:,ii)) |
---|
| 562 | id_detect(ji,jj)=0 |
---|
| 563 | |
---|
| 564 | ENDIF |
---|
| 565 | |
---|
| 566 | ENDDO |
---|
| 567 | ENDDO |
---|
| 568 | |
---|
| 569 | ENDIF |
---|
| 570 | |
---|
| 571 | END SUBROUTINE interp_cubic__2D_fill |
---|
| 572 | !------------------------------------------------------------------- |
---|
| 573 | !> @brief |
---|
| 574 | !> This subroutine compute 1D array of coefficient for cubic interpolation. |
---|
| 575 | !> |
---|
| 576 | !> @details |
---|
| 577 | !> |
---|
| 578 | !> @author J.Paul |
---|
[5609] | 579 | !> @date September, 2014 - Initial Version |
---|
[5037] | 580 | !> |
---|
| 581 | !> @param[in] dd_value 1D array of value |
---|
| 582 | !> @param[in] dd_dfdx 1D array of first derivative |
---|
| 583 | !> @param[in] dd_fill FillValue of variable |
---|
| 584 | !------------------------------------------------------------------- |
---|
| 585 | FUNCTION interp_cubic__1D_coef( dd_value, & |
---|
| 586 | & dd_dfdx, & |
---|
| 587 | & dd_fill ) |
---|
| 588 | IMPLICIT NONE |
---|
| 589 | ! Argument |
---|
| 590 | REAL(dp), DIMENSION(:) , INTENT(IN) :: dd_value |
---|
| 591 | REAL(dp), DIMENSION(:) , INTENT(IN) :: dd_dfdx |
---|
| 592 | REAL(dp) , INTENT(IN) :: dd_fill |
---|
| 593 | |
---|
| 594 | ! function |
---|
| 595 | REAL(dp), DIMENSION(4) :: interp_cubic__1D_coef |
---|
| 596 | |
---|
| 597 | ! local variable |
---|
| 598 | REAL(dp), DIMENSION(4,4), PARAMETER :: dl_matrix = RESHAPE( & |
---|
| 599 | & (/ 1 ,-1 ,-3 , 2 ,& |
---|
| 600 | 0 , 1 , 3 ,-2 ,& |
---|
| 601 | 0 , 0 ,-2 , 1 ,& |
---|
| 602 | 0 , 0 ,-1 , 1 /), & |
---|
| 603 | & (/ 4, 4 /) ) |
---|
| 604 | |
---|
| 605 | REAL(dp), DIMENSION(4) :: dl_vect |
---|
| 606 | |
---|
| 607 | !---------------------------------------------------------------- |
---|
| 608 | ! init |
---|
| 609 | interp_cubic__1D_coef(:)=dd_fill |
---|
| 610 | |
---|
| 611 | dl_vect( 1: 2)=PACK(dd_value(:),.TRUE. ) |
---|
| 612 | dl_vect( 3: 4)=PACK(dd_dfdx(:),.TRUE. ) |
---|
| 613 | |
---|
| 614 | interp_cubic__1D_coef(:)=MATMUL(dl_matrix(:,:),dl_vect(:)) |
---|
| 615 | |
---|
| 616 | END FUNCTION interp_cubic__1D_coef |
---|
| 617 | !------------------------------------------------------------------- |
---|
| 618 | !> @brief |
---|
| 619 | !> This subroutine compute cubic interpolation of a 1D array of value. |
---|
| 620 | !> |
---|
| 621 | !> @author J.Paul |
---|
[5609] | 622 | !> @date September, 2014 - Initial Version |
---|
[5037] | 623 | !> |
---|
| 624 | !> @param[inout] dd_value 1D array of mixed grid value |
---|
| 625 | !> @param[inout] id_detect 1D array of point to be interpolated |
---|
| 626 | !> @param[in] dd_coef 1D array of coefficient |
---|
| 627 | !> @param[in] dd_fill FillValue of variable |
---|
| 628 | !> @param[in] ld_even even refinment or not |
---|
| 629 | !> @param[in] id_rho refinement factor |
---|
| 630 | !------------------------------------------------------------------- |
---|
| 631 | SUBROUTINE interp_cubic__1D_fill( dd_value, id_detect, & |
---|
| 632 | & dd_weight, dd_coef, & |
---|
| 633 | & dd_fill, id_rhoi ) |
---|
| 634 | IMPLICIT NONE |
---|
| 635 | ! Argument |
---|
| 636 | REAL(dp) , DIMENSION(:) , INTENT(INOUT) :: dd_value |
---|
| 637 | INTEGER(i4) , DIMENSION(:) , INTENT(INOUT) :: id_detect |
---|
| 638 | REAL(dp) , DIMENSION(:,:), INTENT(IN ) :: dd_weight |
---|
| 639 | REAL(dp) , DIMENSION(4) , INTENT(IN ) :: dd_coef |
---|
| 640 | REAL(dp) , INTENT(IN ) :: dd_fill |
---|
| 641 | INTEGER(I4) , INTENT(IN ) :: id_rhoi |
---|
| 642 | |
---|
| 643 | ! local variable |
---|
| 644 | |
---|
| 645 | ! loop indices |
---|
| 646 | INTEGER(i4) :: ji |
---|
| 647 | !---------------------------------------------------------------- |
---|
| 648 | |
---|
| 649 | IF( ANY( dd_coef(:)==dd_fill ) )THEN |
---|
| 650 | CALL logger_error("INTERP CUBIC FILL: fill value detected. "//& |
---|
| 651 | & "can not compute interpolation") |
---|
| 652 | ELSE |
---|
| 653 | |
---|
| 654 | DO ji=1,id_rhoi+1 |
---|
| 655 | |
---|
| 656 | IF(id_detect(ji)==1)THEN |
---|
| 657 | |
---|
| 658 | dd_value(ji)=DOT_PRODUCT(dd_coef(:),dd_weight(:,ji)) |
---|
| 659 | id_detect(ji)=0 |
---|
| 660 | |
---|
| 661 | ENDIF |
---|
| 662 | |
---|
| 663 | ENDDO |
---|
| 664 | |
---|
| 665 | ENDIF |
---|
| 666 | |
---|
| 667 | END SUBROUTINE interp_cubic__1D_fill |
---|
| 668 | !------------------------------------------------------------------- |
---|
| 669 | !> @brief |
---|
| 670 | !> This subroutine compute interpoaltion weight for 2D array. |
---|
| 671 | !> |
---|
| 672 | !> @author J.Paul |
---|
[5609] | 673 | !> @date September, 2014 - Initial Version |
---|
[5037] | 674 | !> |
---|
| 675 | !> @param[in] dd_weight interpolation weight of 2D array |
---|
| 676 | !> @param[in] ld_even even refinment or not |
---|
| 677 | !> @param[in] id_rho refinement factor |
---|
| 678 | !------------------------------------------------------------------- |
---|
| 679 | SUBROUTINE interp_cubic__get_weight2D(dd_weight, & |
---|
| 680 | & id_rho, ld_even) |
---|
| 681 | IMPLICIT NONE |
---|
| 682 | ! Argument |
---|
| 683 | REAL(dp) , DIMENSION(:,:), INTENT(INOUT) :: dd_weight |
---|
| 684 | INTEGER(I4), DIMENSION(:) , INTENT(IN ) :: id_rho |
---|
| 685 | LOGICAL , DIMENSION(:) , INTENT(IN ) :: ld_even |
---|
| 686 | |
---|
| 687 | ! local variable |
---|
| 688 | REAL(dp) :: dl_dx |
---|
| 689 | REAL(dp) :: dl_x |
---|
| 690 | REAL(dp) :: dl_x2 |
---|
| 691 | REAL(dp) :: dl_x3 |
---|
| 692 | REAL(dp) :: dl_dy |
---|
| 693 | REAL(dp) :: dl_y |
---|
| 694 | REAL(dp) :: dl_y2 |
---|
| 695 | REAL(dp) :: dl_y3 |
---|
| 696 | |
---|
| 697 | ! loop indices |
---|
| 698 | INTEGER(i4) :: ii |
---|
| 699 | |
---|
| 700 | INTEGER(i4) :: ji |
---|
| 701 | INTEGER(i4) :: jj |
---|
| 702 | !---------------------------------------------------------------- |
---|
| 703 | |
---|
| 704 | IF( ld_even(jp_I) )THEN |
---|
| 705 | dl_dx=1./REAL(id_rho(jp_I)-1) |
---|
| 706 | ELSE ! odd refinement |
---|
| 707 | dl_dx=1./REAL(id_rho(jp_I)) |
---|
| 708 | ENDIF |
---|
| 709 | |
---|
| 710 | IF( ld_even(jp_J) )THEN |
---|
| 711 | dl_dy=1./REAL(id_rho(jp_J)-1) |
---|
| 712 | ELSE ! odd refinement |
---|
| 713 | dl_dy=1./REAL(id_rho(jp_J)) |
---|
| 714 | ENDIF |
---|
| 715 | |
---|
| 716 | ii=0 |
---|
| 717 | DO jj=1,id_rho(jp_J)+1 |
---|
| 718 | |
---|
| 719 | IF( ld_even(jp_J) )THEN |
---|
| 720 | dl_y=(jj-1)*dl_dy - dl_dy*0.5 |
---|
| 721 | ELSE ! odd refinement |
---|
| 722 | dl_y=(jj-1)*dl_dy |
---|
| 723 | ENDIF |
---|
| 724 | dl_y2=dl_y*dl_y |
---|
| 725 | dl_y3=dl_y2*dl_y |
---|
| 726 | |
---|
| 727 | DO ji=1,id_rho(jp_I)+1 |
---|
| 728 | |
---|
| 729 | ! iter |
---|
| 730 | ii=ii+1 |
---|
| 731 | |
---|
| 732 | IF( ld_even(jp_I) )THEN |
---|
| 733 | dl_x=(ji-1)*dl_dx - dl_dx*0.5 |
---|
| 734 | ELSE ! odd refinement |
---|
| 735 | dl_x=(ji-1)*dl_dx |
---|
| 736 | ENDIF |
---|
| 737 | dl_x2=dl_x*dl_x |
---|
| 738 | dl_x3=dl_x2*dl_x |
---|
| 739 | |
---|
| 740 | dd_weight(:,ii)=(/1._dp, dl_x , dl_x2 , dl_x3 , & |
---|
| 741 | & dl_y , dl_x*dl_y , dl_x2*dl_y , dl_x3*dl_y , & |
---|
| 742 | & dl_y2, dl_x*dl_y2, dl_x2*dl_y2, dl_x3*dl_y2, & |
---|
| 743 | & dl_y3, dl_x*dl_y3, dl_x2*dl_y3, dl_x3*dl_y3 /) |
---|
| 744 | |
---|
| 745 | ENDDO |
---|
| 746 | ENDDO |
---|
| 747 | |
---|
| 748 | END SUBROUTINE interp_cubic__get_weight2D |
---|
| 749 | !------------------------------------------------------------------- |
---|
| 750 | !> @brief |
---|
| 751 | !> This subroutine compute interpoaltion weight for 1D array. |
---|
| 752 | !> |
---|
| 753 | !> @author J.Paul |
---|
[5609] | 754 | !> @date September, 2014 - Initial Version |
---|
[5037] | 755 | !> |
---|
| 756 | !> @param[in] dd_weight interpolation weight of 1D array |
---|
| 757 | !> @param[in] ld_even even refinment or not |
---|
| 758 | !> @param[in] id_rho refinement factor |
---|
| 759 | !------------------------------------------------------------------- |
---|
| 760 | SUBROUTINE interp_cubic__get_weight1D(dd_weight, & |
---|
| 761 | & id_rho, ld_even) |
---|
| 762 | IMPLICIT NONE |
---|
| 763 | ! Argument |
---|
| 764 | REAL(dp) , DIMENSION(:,:), INTENT(INOUT) :: dd_weight |
---|
| 765 | INTEGER(I4) , INTENT(IN ) :: id_rho |
---|
| 766 | LOGICAL , INTENT(IN ) :: ld_even |
---|
| 767 | ! local variable |
---|
| 768 | REAL(dp) :: dl_dx |
---|
| 769 | REAL(dp) :: dl_x |
---|
| 770 | REAL(dp) :: dl_x2 |
---|
| 771 | REAL(dp) :: dl_x3 |
---|
| 772 | ! loop indices |
---|
| 773 | INTEGER(i4) :: ji |
---|
| 774 | !---------------------------------------------------------------- |
---|
| 775 | |
---|
| 776 | IF( ld_even )THEN |
---|
| 777 | dl_dx=1./REAL(id_rho-1) |
---|
| 778 | ELSE ! odd refinement |
---|
| 779 | dl_dx=1./REAL(id_rho) |
---|
| 780 | ENDIF |
---|
| 781 | |
---|
| 782 | DO ji=1,id_rho+1 |
---|
| 783 | IF( ld_even )THEN |
---|
| 784 | dl_x=(ji-1)*dl_dx - dl_dx*0.5 |
---|
| 785 | ELSE ! odd refinement |
---|
| 786 | dl_x=(ji-1)*dl_dx |
---|
| 787 | ENDIF |
---|
| 788 | dl_x2=dl_x*dl_x |
---|
| 789 | dl_x3=dl_x2*dl_x |
---|
| 790 | |
---|
| 791 | dd_weight(:,ji)=(/1._dp, dl_x, dl_x2, dl_x3 /) |
---|
| 792 | ENDDO |
---|
| 793 | |
---|
| 794 | END SUBROUTINE interp_cubic__get_weight1D |
---|
| 795 | END MODULE interp_cubic |
---|