| 1 | MODULE filtre |
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| 2 | |
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| 3 | REAL, DIMENSION(:,:,:), ALLOCATABLE :: matriceun,matriceus,matricevn |
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| 4 | REAL, DIMENSION(:,:,:), ALLOCATABLE :: matricevs,matrinvn,matrinvs |
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| 5 | |
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| 6 | CONTAINS |
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| 7 | |
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| 8 | SUBROUTINE inifilr |
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| 9 | ! |
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| 10 | ! ... H. Upadhyaya, O.Sharma ... |
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| 11 | ! |
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| 12 | IMPLICIT NONE |
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| 13 | ! |
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| 14 | ! version 3 ..... |
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| 15 | |
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| 16 | ! Correction le 28/10/97 P. Le Van . |
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| 17 | ! ------------------------------------------------------------------- |
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| 18 | #include "dimensions.h" |
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| 19 | #include "paramet.h" |
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| 20 | ! ------------------------------------------------------------------- |
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| 21 | #include "comgeom.h" |
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| 22 | #include "coefils.h" |
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| 23 | #include "logic.h" |
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| 24 | #include "serre.h" |
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| 25 | |
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| 26 | REAL dlonu(iim),dlatu(jjm) |
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| 27 | REAL rlamda( iim ), eignvl( iim ) |
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| 28 | ! |
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| 29 | |
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| 30 | REAL lamdamax,pi,cof |
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| 31 | INTEGER i,j,modemax,imx,k,kf,ii |
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| 32 | REAL dymin,dxmin,colat0 |
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| 33 | REAL eignft(iim,iim), coff |
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| 34 | |
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| 35 | LOGICAL, SAVE :: first_call_inifilr = .TRUE. |
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| 36 | |
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| 37 | #ifdef CRAY |
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| 38 | INTEGER ISMIN |
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| 39 | EXTERNAL ISMIN |
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| 40 | INTEGER iymin |
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| 41 | INTEGER ixmineq |
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| 42 | #endif |
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| 43 | EXTERNAL inifgn |
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| 44 | ! |
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| 45 | ! ------------------------------------------------------------ |
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| 46 | ! This routine computes the eigenfunctions of the laplacien |
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| 47 | ! on the stretched grid, and the filtering coefficients |
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| 48 | ! |
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| 49 | ! We designate: |
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| 50 | ! eignfn eigenfunctions of the discrete laplacien |
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| 51 | ! eigenvl eigenvalues |
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| 52 | ! jfiltn indexof the last scalar line filtered in NH |
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| 53 | ! jfilts index of the first line filtered in SH |
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| 54 | ! modfrst index of the mode from WHERE modes are filtered |
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| 55 | ! modemax maximum number of modes ( im ) |
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| 56 | ! coefil filtering coefficients ( lamda_max*COS(rlat)/lamda ) |
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| 57 | ! sdd SQRT( dx ) |
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| 58 | ! |
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| 59 | ! the modes are filtered from modfrst to modemax |
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| 60 | ! |
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| 61 | !----------------------------------------------------------- |
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| 62 | ! |
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| 63 | |
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| 64 | pi = 2. * ASIN( 1. ) |
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| 65 | |
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| 66 | DO i = 1,iim |
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| 67 | dlonu(i) = xprimu( i ) |
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| 68 | ENDDO |
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| 69 | ! |
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| 70 | CALL inifgn(eignvl) |
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| 71 | ! |
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| 72 | PRINT *,' EIGNVL ' |
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| 73 | PRINT 250,eignvl |
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| 74 | 250 FORMAT( 1x,5e13.6) |
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| 75 | ! |
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| 76 | ! compute eigenvalues and eigenfunctions |
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| 77 | ! |
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| 78 | ! |
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| 79 | !................................................................. |
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| 80 | ! |
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| 81 | ! compute the filtering coefficients for scalar lines and |
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| 82 | ! meridional wind v-lines |
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| 83 | ! |
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| 84 | ! we filter all those latitude lines WHERE coefil < 1 |
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| 85 | ! NO FILTERING AT POLES |
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| 86 | ! |
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| 87 | ! colat0 is to be used when alpha (stretching coefficient) |
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| 88 | ! is set equal to zero for the regular grid CASE |
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| 89 | ! |
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| 90 | ! ....... Calcul de colat0 ......... |
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| 91 | ! ..... colat0 = minimum de ( 0.5, min dy/ min dx ) ... |
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| 92 | ! |
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| 93 | ! |
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| 94 | DO j = 1,jjm |
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| 95 | dlatu( j ) = rlatu( j ) - rlatu( j+1 ) |
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| 96 | ENDDO |
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| 97 | ! |
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| 98 | #ifdef CRAY |
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| 99 | iymin = ISMIN( jjm, dlatu, 1 ) |
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| 100 | ixmineq = ISMIN( iim, dlonu, 1 ) |
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| 101 | dymin = dlatu( iymin ) |
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| 102 | dxmin = dlonu( ixmineq ) |
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| 103 | #else |
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| 104 | dxmin = dlonu(1) |
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| 105 | DO i = 2, iim |
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| 106 | dxmin = MIN( dxmin,dlonu(i) ) |
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| 107 | ENDDO |
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| 108 | dymin = dlatu(1) |
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| 109 | DO j = 2, jjm |
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| 110 | dymin = MIN( dymin,dlatu(j) ) |
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| 111 | ENDDO |
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| 112 | #endif |
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| 113 | ! |
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| 114 | ! |
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| 115 | colat0 = MIN( 0.5, dymin/dxmin ) |
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| 116 | ! |
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| 117 | IF( .NOT.fxyhypb.AND.ysinus ) THEN |
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| 118 | colat0 = 0.6 |
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| 119 | ! ...... a revoir pour ysinus ! ....... |
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| 120 | alphax = 0. |
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| 121 | ENDIF |
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| 122 | ! |
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| 123 | PRINT 50, colat0,alphax |
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| 124 | 50 FORMAT(/15x,' Inifilr colat0 alphax ',2e16.7) |
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| 125 | ! |
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| 126 | IF(alphax.EQ.1. ) THEN |
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| 127 | PRINT *,' Inifilr alphax doit etre < a 1. Corriger ' |
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| 128 | STOP |
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| 129 | ENDIF |
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| 130 | ! |
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| 131 | lamdamax = iim / ( pi * colat0 * ( 1. - alphax ) ) |
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| 132 | |
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| 133 | ! ... Correction le 28/10/97 ( P.Le Van ) .. |
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| 134 | ! |
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| 135 | DO i = 2,iim |
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| 136 | rlamda( i ) = lamdamax/ SQRT( ABS( eignvl(i) ) ) |
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| 137 | ENDDO |
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| 138 | ! |
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| 139 | |
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| 140 | DO j = 1,jjm |
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| 141 | DO i = 1,iim |
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| 142 | coefilu( i,j ) = 0.0 |
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| 143 | coefilv( i,j ) = 0.0 |
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| 144 | coefilu2( i,j ) = 0.0 |
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| 145 | coefilv2( i,j ) = 0.0 |
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| 146 | ENDDO |
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| 147 | ENDDO |
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| 148 | |
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| 149 | ! |
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| 150 | ! ... Determination de jfiltnu,jfiltnv,jfiltsu,jfiltsv .... |
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| 151 | ! ......................................................... |
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| 152 | ! |
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| 153 | modemax = iim |
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| 154 | |
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| 155 | !!!! imx = modemax - 4 * (modemax/iim) |
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| 156 | |
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| 157 | imx = iim |
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| 158 | ! |
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| 159 | PRINT *,' TRUNCATION AT ',imx |
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| 160 | ! |
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| 161 | DO j = 2, jjm/2+1 |
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| 162 | cof = COS( rlatu(j) )/ colat0 |
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| 163 | IF ( cof .LT. 1. ) THEN |
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| 164 | IF( rlamda(imx) * COS(rlatu(j) ).LT.1. ) jfiltnu= j |
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| 165 | ENDIF |
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| 166 | |
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| 167 | cof = COS( rlatu(jjp1-j+1) )/ colat0 |
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| 168 | IF ( cof .LT. 1. ) THEN |
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| 169 | IF( rlamda(imx) * COS(rlatu(jjp1-j+1) ).LT.1. ) & |
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| 170 | jfiltsu= jjp1-j+1 |
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| 171 | ENDIF |
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| 172 | ENDDO |
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| 173 | ! |
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| 174 | DO j = 1, jjm/2 |
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| 175 | cof = COS( rlatv(j) )/ colat0 |
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| 176 | IF ( cof .LT. 1. ) THEN |
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| 177 | IF( rlamda(imx) * COS(rlatv(j) ).LT.1. ) jfiltnv= j |
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| 178 | ENDIF |
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| 179 | |
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| 180 | cof = COS( rlatv(jjm-j+1) )/ colat0 |
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| 181 | IF ( cof .LT. 1. ) THEN |
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| 182 | IF( rlamda(imx) * COS(rlatv(jjm-j+1) ).LT.1. ) & |
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| 183 | jfiltsv= jjm-j+1 |
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| 184 | ENDIF |
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| 185 | ENDDO |
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| 186 | ! |
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| 187 | |
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| 188 | IF ( jfiltnu.LE.0 ) jfiltnu=1 |
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| 189 | IF( jfiltnu.GT. jjm/2 +1 ) THEN |
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| 190 | PRINT *,' jfiltnu en dehors des valeurs acceptables ' ,jfiltnu |
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| 191 | STOP |
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| 192 | ENDIF |
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| 193 | |
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| 194 | IF( jfiltsu.LE.0) jfiltsu=1 |
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| 195 | IF( jfiltsu.GT. jjm +1 ) THEN |
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| 196 | PRINT *,' jfiltsu en dehors des valeurs acceptables ' ,jfiltsu |
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| 197 | STOP |
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| 198 | ENDIF |
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| 199 | |
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| 200 | IF( jfiltnv.LE.0) jfiltnv=1 |
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| 201 | IF( jfiltnv.GT. jjm/2 ) THEN |
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| 202 | PRINT *,' jfiltnv en dehors des valeurs acceptables ' ,jfiltnv |
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| 203 | STOP |
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| 204 | ENDIF |
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| 205 | |
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| 206 | IF( jfiltsv.LE.0) jfiltsv=1 |
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| 207 | IF( jfiltsv.GT. jjm ) THEN |
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| 208 | PRINT *,' jfiltsv en dehors des valeurs acceptables ' ,jfiltsv |
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| 209 | STOP |
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| 210 | ENDIF |
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| 211 | |
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| 212 | PRINT *,' jfiltnv jfiltsv jfiltnu jfiltsu ' , & |
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| 213 | jfiltnv,jfiltsv,jfiltnu,jfiltsu |
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| 214 | |
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| 215 | IF(first_call_inifilr) THEN |
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| 216 | ALLOCATE(matriceun(iim,iim,jfiltnu)) |
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| 217 | ALLOCATE(matriceus(iim,iim,jfiltsu)) |
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| 218 | ALLOCATE(matricevn(iim,iim,jfiltnv)) |
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| 219 | ALLOCATE(matricevs(iim,iim,jfiltsv)) |
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| 220 | ALLOCATE( matrinvn(iim,iim,jfiltnu)) |
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| 221 | ALLOCATE( matrinvs(iim,iim,jfiltsu)) |
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| 222 | first_call_inifilr = .FALSE. |
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| 223 | ENDIF |
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| 224 | |
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| 225 | ! |
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| 226 | ! ... Determination de coefilu,coefilv,n=modfrstu,modfrstv .... |
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| 227 | !................................................................ |
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| 228 | ! |
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| 229 | ! |
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| 230 | DO j = 1,jjm |
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| 231 | modfrstu( j ) = iim |
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| 232 | modfrstv( j ) = iim |
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| 233 | ENDDO |
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| 234 | ! |
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| 235 | DO j = 2,jfiltnu |
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| 236 | DO k = 2,modemax |
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| 237 | cof = rlamda(k) * COS( rlatu(j) ) |
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| 238 | IF ( cof .LT. 1. ) GOTO 82 |
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| 239 | ENDDO |
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| 240 | GOTO 84 |
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| 241 | 82 modfrstu( j ) = k |
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| 242 | ! |
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| 243 | kf = modfrstu( j ) |
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| 244 | DO k = kf , modemax |
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| 245 | cof = rlamda(k) * COS( rlatu(j) ) |
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| 246 | coefilu(k,j) = cof - 1. |
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| 247 | coefilu2(k,j) = cof*cof - 1. |
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| 248 | ENDDO |
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| 249 | 84 CONTINUE |
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| 250 | ENDDO |
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| 251 | ! |
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| 252 | ! |
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| 253 | DO j = 1,jfiltnv |
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| 254 | ! |
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| 255 | DO k = 2,modemax |
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| 256 | cof = rlamda(k) * COS( rlatv(j) ) |
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| 257 | IF ( cof .LT. 1. ) GOTO 87 |
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| 258 | ENDDO |
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| 259 | GOTO 89 |
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| 260 | 87 modfrstv( j ) = k |
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| 261 | ! |
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| 262 | kf = modfrstv( j ) |
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| 263 | DO k = kf , modemax |
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| 264 | cof = rlamda(k) * COS( rlatv(j) ) |
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| 265 | coefilv(k,j) = cof - 1. |
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| 266 | coefilv2(k,j) = cof*cof - 1. |
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| 267 | ENDDO |
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| 268 | 89 CONTINUE |
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| 269 | ENDDO |
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| 270 | ! |
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| 271 | DO j = jfiltsu,jjm |
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| 272 | DO k = 2,modemax |
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| 273 | cof = rlamda(k) * COS( rlatu(j) ) |
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| 274 | IF ( cof .LT. 1. ) GOTO 92 |
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| 275 | ENDDO |
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| 276 | GOTO 94 |
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| 277 | 92 modfrstu( j ) = k |
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| 278 | ! |
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| 279 | kf = modfrstu( j ) |
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| 280 | DO k = kf , modemax |
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| 281 | cof = rlamda(k) * COS( rlatu(j) ) |
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| 282 | coefilu(k,j) = cof - 1. |
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| 283 | coefilu2(k,j) = cof*cof - 1. |
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| 284 | ENDDO |
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| 285 | 94 CONTINUE |
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| 286 | ENDDO |
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| 287 | ! |
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| 288 | DO j = jfiltsv,jjm |
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| 289 | DO k = 2,modemax |
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| 290 | cof = rlamda(k) * COS( rlatv(j) ) |
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| 291 | IF ( cof .LT. 1. ) GOTO 97 |
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| 292 | ENDDO |
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| 293 | GOTO 99 |
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| 294 | 97 modfrstv( j ) = k |
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| 295 | ! |
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| 296 | kf = modfrstv( j ) |
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| 297 | DO k = kf , modemax |
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| 298 | cof = rlamda(k) * COS( rlatv(j) ) |
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| 299 | coefilv(k,j) = cof - 1. |
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| 300 | coefilv2(k,j) = cof*cof - 1. |
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| 301 | ENDDO |
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| 302 | 99 CONTINUE |
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| 303 | ENDDO |
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| 304 | ! |
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| 305 | |
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| 306 | IF(jfiltnv.GE.jjm/2 .OR. jfiltnu.GE.jjm/2)THEN |
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| 307 | |
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| 308 | IF(jfiltnv.EQ.jfiltsv)jfiltsv=1+jfiltnv |
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| 309 | IF(jfiltnu.EQ.jfiltsu)jfiltsu=1+jfiltnu |
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| 310 | |
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| 311 | PRINT *,'jfiltnv jfiltsv jfiltnu jfiltsu' , & |
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| 312 | jfiltnv,jfiltsv,jfiltnu,jfiltsu |
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| 313 | ENDIF |
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| 314 | |
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| 315 | PRINT *,' Modes premiers v ' |
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| 316 | PRINT 334,modfrstv |
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| 317 | PRINT *,' Modes premiers u ' |
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| 318 | PRINT 334,modfrstu |
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| 319 | |
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| 320 | ! |
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| 321 | ! ................................................................... |
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| 322 | ! |
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| 323 | ! ... Calcul de la matrice filtre 'matriceu' pour les champs situes |
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| 324 | ! sur la grille scalaire ........ |
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| 325 | ! ................................................................... |
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| 326 | ! |
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| 327 | DO j = 2, jfiltnu |
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| 328 | |
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| 329 | DO i=1,iim |
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| 330 | coff = coefilu(i,j) |
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| 331 | IF( i.LT.modfrstu(j) ) coff = 0. |
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| 332 | DO k=1,iim |
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| 333 | eignft(i,k) = eignfnv(k,i) * coff |
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| 334 | ENDDO |
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| 335 | ENDDO |
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| 336 | #ifdef CRAY |
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| 337 | CALL MXM( eignfnv,iim,eignft,iim,matriceun(1,1,j),iim ) |
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| 338 | #else |
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| 339 | #ifdef BLAS |
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| 340 | CALL SGEMM ('N', 'N', iim, iim, iim, 1.0, & |
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| 341 | eignfnv, iim, eignft, iim, 0.0, matriceun(1,1,j), iim) |
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| 342 | #else |
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| 343 | DO k = 1, iim |
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| 344 | DO i = 1, iim |
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| 345 | matriceun(i,k,j) = 0.0 |
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| 346 | DO ii = 1, iim |
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| 347 | matriceun(i,k,j) = matriceun(i,k,j) & |
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| 348 | + eignfnv(i,ii)*eignft(ii,k) |
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| 349 | ENDDO |
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| 350 | ENDDO |
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| 351 | ENDDO |
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| 352 | #endif |
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| 353 | #endif |
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| 354 | |
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| 355 | ENDDO |
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| 356 | |
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| 357 | DO j = jfiltsu, jjm |
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| 358 | |
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| 359 | DO i=1,iim |
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| 360 | coff = coefilu(i,j) |
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| 361 | IF( i.LT.modfrstu(j) ) coff = 0. |
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| 362 | DO k=1,iim |
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| 363 | eignft(i,k) = eignfnv(k,i) * coff |
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| 364 | ENDDO |
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| 365 | ENDDO |
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| 366 | #ifdef CRAY |
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| 367 | CALL MXM(eignfnv,iim,eignft,iim,matriceus(1,1,j-jfiltsu+1),iim) |
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| 368 | #else |
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| 369 | #ifdef BLAS |
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| 370 | CALL SGEMM ('N', 'N', iim, iim, iim, 1.0, & |
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| 371 | eignfnv, iim, eignft, iim, 0.0, & |
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| 372 | matriceus(1,1,j-jfiltsu+1), iim) |
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| 373 | #else |
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| 374 | DO k = 1, iim |
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| 375 | DO i = 1, iim |
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| 376 | matriceus(i,k,j-jfiltsu+1) = 0.0 |
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| 377 | DO ii = 1, iim |
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| 378 | matriceus(i,k,j-jfiltsu+1) = matriceus(i,k,j-jfiltsu+1) & |
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| 379 | + eignfnv(i,ii)*eignft(ii,k) |
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| 380 | ENDDO |
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| 381 | ENDDO |
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| 382 | ENDDO |
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| 383 | #endif |
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| 384 | #endif |
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| 385 | |
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| 386 | ENDDO |
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| 387 | |
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| 388 | ! ................................................................... |
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| 389 | ! |
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| 390 | ! ... Calcul de la matrice filtre 'matricev' pour les champs situes |
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| 391 | ! sur la grille de V ou de Z ........ |
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| 392 | ! ................................................................... |
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| 393 | ! |
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| 394 | DO j = 1, jfiltnv |
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| 395 | |
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| 396 | DO i = 1, iim |
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| 397 | coff = coefilv(i,j) |
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| 398 | IF( i.LT.modfrstv(j) ) coff = 0. |
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| 399 | DO k = 1, iim |
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| 400 | eignft(i,k) = eignfnu(k,i) * coff |
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| 401 | ENDDO |
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| 402 | ENDDO |
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| 403 | #ifdef CRAY |
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| 404 | CALL MXM( eignfnu,iim,eignft,iim,matricevn(1,1,j),iim ) |
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| 405 | #else |
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| 406 | #ifdef BLAS |
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| 407 | CALL SGEMM ('N', 'N', iim, iim, iim, 1.0, & |
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| 408 | eignfnu, iim, eignft, iim, 0.0, matricevn(1,1,j), iim) |
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| 409 | #else |
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| 410 | DO k = 1, iim |
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| 411 | DO i = 1, iim |
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| 412 | matricevn(i,k,j) = 0.0 |
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| 413 | DO ii = 1, iim |
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| 414 | matricevn(i,k,j) = matricevn(i,k,j) & |
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| 415 | + eignfnu(i,ii)*eignft(ii,k) |
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| 416 | ENDDO |
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| 417 | ENDDO |
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| 418 | ENDDO |
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| 419 | #endif |
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| 420 | #endif |
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| 421 | |
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| 422 | ENDDO |
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| 423 | |
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| 424 | DO j = jfiltsv, jjm |
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| 425 | |
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| 426 | DO i = 1, iim |
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| 427 | coff = coefilv(i,j) |
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| 428 | IF( i.LT.modfrstv(j) ) coff = 0. |
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| 429 | DO k = 1, iim |
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| 430 | eignft(i,k) = eignfnu(k,i) * coff |
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| 431 | ENDDO |
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| 432 | ENDDO |
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| 433 | #ifdef CRAY |
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| 434 | CALL MXM(eignfnu,iim,eignft,iim,matricevs(1,1,j-jfiltsv+1),iim) |
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| 435 | #else |
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| 436 | #ifdef BLAS |
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| 437 | CALL SGEMM ('N', 'N', iim, iim, iim, 1.0, & |
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| 438 | eignfnu, iim, eignft, iim, 0.0, & |
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| 439 | matricevs(1,1,j-jfiltsv+1), iim) |
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| 440 | #else |
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| 441 | DO k = 1, iim |
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| 442 | DO i = 1, iim |
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| 443 | matricevs(i,k,j-jfiltsv+1) = 0.0 |
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| 444 | DO ii = 1, iim |
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| 445 | matricevs(i,k,j-jfiltsv+1) = matricevs(i,k,j-jfiltsv+1) & |
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| 446 | + eignfnu(i,ii)*eignft(ii,k) |
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| 447 | ENDDO |
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| 448 | ENDDO |
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| 449 | ENDDO |
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| 450 | #endif |
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| 451 | #endif |
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| 452 | |
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| 453 | ENDDO |
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| 454 | |
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| 455 | ! ................................................................... |
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| 456 | ! |
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| 457 | ! ... Calcul de la matrice filtre 'matrinv' pour les champs situes |
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| 458 | ! sur la grille scalaire , pour le filtre inverse ........ |
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| 459 | ! ................................................................... |
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| 460 | ! |
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| 461 | DO j = 2, jfiltnu |
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| 462 | |
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| 463 | DO i = 1,iim |
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| 464 | coff = coefilu(i,j)/ ( 1. + coefilu(i,j) ) |
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| 465 | IF( i.LT.modfrstu(j) ) coff = 0. |
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| 466 | DO k=1,iim |
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| 467 | eignft(i,k) = eignfnv(k,i) * coff |
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| 468 | ENDDO |
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| 469 | ENDDO |
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| 470 | #ifdef CRAY |
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| 471 | CALL MXM( eignfnv,iim,eignft,iim,matrinvn(1,1,j),iim ) |
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| 472 | #else |
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| 473 | #ifdef BLAS |
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| 474 | CALL SGEMM ('N', 'N', iim, iim, iim, 1.0, & |
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| 475 | eignfnv, iim, eignft, iim, 0.0, matrinvn(1,1,j), iim) |
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| 476 | #else |
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| 477 | DO k = 1, iim |
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| 478 | DO i = 1, iim |
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| 479 | matrinvn(i,k,j) = 0.0 |
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| 480 | DO ii = 1, iim |
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| 481 | matrinvn(i,k,j) = matrinvn(i,k,j) & |
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| 482 | + eignfnv(i,ii)*eignft(ii,k) |
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| 483 | ENDDO |
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| 484 | ENDDO |
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| 485 | ENDDO |
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| 486 | #endif |
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| 487 | #endif |
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| 488 | |
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| 489 | ENDDO |
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| 490 | |
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| 491 | DO j = jfiltsu, jjm |
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| 492 | |
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| 493 | DO i = 1,iim |
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| 494 | coff = coefilu(i,j) / ( 1. + coefilu(i,j) ) |
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| 495 | IF( i.LT.modfrstu(j) ) coff = 0. |
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| 496 | DO k=1,iim |
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| 497 | eignft(i,k) = eignfnv(k,i) * coff |
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| 498 | ENDDO |
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| 499 | ENDDO |
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| 500 | #ifdef CRAY |
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| 501 | CALL MXM(eignfnv,iim,eignft,iim,matrinvs(1,1,j-jfiltsu+1),iim) |
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| 502 | #else |
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| 503 | #ifdef BLAS |
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| 504 | CALL SGEMM ('N', 'N', iim, iim, iim, 1.0, & |
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| 505 | eignfnv, iim, eignft, iim, 0.0, matrinvs(1,1,j-jfiltsu+1), iim) |
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| 506 | #else |
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| 507 | DO k = 1, iim |
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| 508 | DO i = 1, iim |
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| 509 | matrinvs(i,k,j-jfiltsu+1) = 0.0 |
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| 510 | DO ii = 1, iim |
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| 511 | matrinvs(i,k,j-jfiltsu+1) = matrinvs(i,k,j-jfiltsu+1) & |
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| 512 | + eignfnv(i,ii)*eignft(ii,k) |
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| 513 | ENDDO |
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| 514 | ENDDO |
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| 515 | ENDDO |
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| 516 | #endif |
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| 517 | #endif |
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| 518 | |
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| 519 | ENDDO |
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| 520 | |
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| 521 | ! ................................................................... |
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| 522 | |
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| 523 | ! |
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| 524 | 334 FORMAT(1x,24i3) |
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| 525 | 755 FORMAT(1x,6f10.3,i3) |
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| 526 | |
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| 527 | RETURN |
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| 528 | END SUBROUTINE inifilr |
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| 529 | |
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| 530 | END MODULE filtre |
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