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MODULE regr_conserv_m |
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USE assert_eq_m, ONLY: assert_eq |
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USE assert_m, ONLY: assert |
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USE interpolation, ONLY: locate |
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IMPLICIT NONE |
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! Purpose: Each procedure regrids a piecewise linear function (not necessarily |
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! continuous) by averaging it. This is a conservative regridding. |
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! The regridding operation is done along dimension "ix" of the input |
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! field "vs". Input are positions of cell edges. |
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! Remarks: |
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! * The target grid should be included in the source grid: |
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! no extrapolation is allowed. |
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! * Field on target grid "vt" has same rank, slopes and averages as "vs". |
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! * If optional argument "slope" is not given, 0 is assumed for slopes. |
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! Then the regridding is first order instead of second. |
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! * "vs" and "vt" have the same dimensions except Nr. ix (ns for vs, nt for vt) |
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! Argument Type Description |
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!------------------------------------------------------------------------------- |
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! INTEGER, INTENT(IN) :: ix Scalar dimension regridded <=rank(vs) |
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! REAL, INTENT(IN) :: vs(*) Rank>=1 averages in source grid cells |
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! REAL, INTENT(IN) :: xs(:) Vector(ns+1) edges of source grid, asc. order |
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! REAL, INTENT(IN) :: xt(:) Vector(nt+1) edges of target grid, asc. order |
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! REAL, INTENT(OUT) :: vt(*) Rank>=1 regridded field |
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! [REAL, INTENT(IN) :: slope] Rank>=1 slopes in source grid cells |
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INTERFACE regr_conserv |
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! The procedures differ only from the rank of the input/output fields. |
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MODULE PROCEDURE regr1_conserv, regr2_conserv, regr3_conserv, & |
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regr4_conserv, regr5_conserv |
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END INTERFACE |
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PRIVATE |
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PUBLIC :: regr_conserv |
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CONTAINS |
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!------------------------------------------------------------------------------- |
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! |
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SUBROUTINE regr1_conserv(ix, vs, xs, xt, vt, slope) |
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! |
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!------------------------------------------------------------------------------- |
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! Arguments: |
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INTEGER, INTENT(IN) :: ix |
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REAL, INTENT(IN) :: vs(:) |
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REAL, INTENT(IN) :: xs(:), xt(:) |
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REAL, INTENT(OUT) :: vt(:) |
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REAL, OPTIONAL, INTENT(IN) :: slope(:) |
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!------------------------------------------------------------------------------- |
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! Local variables: |
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INTEGER :: is, it, ns, nt |
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REAL :: co, idt |
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LOGICAL :: lslope |
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!------------------------------------------------------------------------------- |
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lslope=PRESENT(slope) |
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CALL check_size(ix,SHAPE(vs),SHAPE(vt),xs,xt,ns,nt) |
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is=locate(xs,xt(1)) !--- 1<= is <= ns (no extrapolation) |
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vt(:)=0. |
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DO it=1, nt; idt=1./(xt(it+1)-xt(it)) |
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IF(xt(it+1)<=xs(is+1)) THEN !--- xs(is)<=xt(it)<=xt(it+1)<=xs(is+1) |
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CALL mean_lin(xt(it),xt(it+1)) |
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ELSE |
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CALL mean_lin(xt(it),xs(is+1)); is=is+1 |
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DO WHILE(xs(is+1)<xt(it+1)) !--- 1<=is<=ns-1 |
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CALL mean_lin(xs(is),xs(is+1)); is=is+1 |
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END DO |
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CALL mean_lin(xs(is),xt(it+1)) !--- 1<=is<=ns |
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END IF |
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IF(xs(is+1)==xt(it+1)) is=is+1 !--- 1<=is<=ns .OR. it==nt |
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END DO |
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CONTAINS |
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!------------------------------------------------------------------------------- |
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SUBROUTINE mean_lin(a,b) ! mean [a,b] of the linear function in [xs(is),xs(is+1)] |
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!------------------------------------------------------------------------------- |
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! Arguments: |
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REAL, INTENT(IN) :: a, b |
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!------------------------------------------------------------------------------- |
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IF(lslope.AND.(a/=xs(is).OR.b/=xs(is+1))) THEN; co=0. |
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IF(a==xt(it )) co=co+xt(it )-xs(is ) |
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IF(b==xt(it+1)) co=co+xt(it+1)-xs(is+1) |
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vt(it) = vt(it)+idt*(b-a)*(vs(is)+co*slope(is)/2.) |
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ELSE |
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vt(it) = vt(it)+idt*(b-a)* vs(is) |
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END IF |
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END SUBROUTINE mean_lin |
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!------------------------------------------------------------------------------- |
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END SUBROUTINE regr1_conserv |
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! |
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!------------------------------------------------------------------------------- |
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!------------------------------------------------------------------------------- |
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! |
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SUBROUTINE regr2_conserv(ix, vs, xs, xt, vt, slope) |
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! |
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!------------------------------------------------------------------------------- |
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! Arguments: |
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INTEGER, INTENT(IN) :: ix |
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REAL, INTENT(IN) :: vs(:,:) |
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REAL, INTENT(IN) :: xs(:), xt(:) |
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REAL, INTENT(OUT) :: vt(:,:) |
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REAL, OPTIONAL, INTENT(IN) :: slope(:,:) |
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!------------------------------------------------------------------------------- |
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! Local variables: |
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INTEGER :: is, it, ns, nt |
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REAL :: co, idt |
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LOGICAL :: lslope |
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!------------------------------------------------------------------------------- |
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lslope=PRESENT(slope) |
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CALL check_size(ix,SHAPE(vs),SHAPE(vt),xs,xt,ns,nt) |
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is=locate(xs,xt(1)) ! 1 <= is <= ns, because we forbid extrapolation |
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vt(:,:)=0. |
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DO it=1, nt; idt=1./(xt(it+1)-xt(it)) |
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IF(xt(it+1)<=xs(is+1)) THEN !--- xs(is)<=xt(it)<=xt(it+1)<=xs(is+1) |
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CALL mean_lin(xt(it),xt(it+1)) |
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ELSE |
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CALL mean_lin(xt(it),xs(is+1)); is=is+1 |
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DO WHILE(xs(is+1)<xt(it+1)) !--- 1<=is<=ns-1 |
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CALL mean_lin(xs(is),xs(is+1)); is=is+1 |
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END DO |
128 |
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CALL mean_lin(xs(is),xt(it+1)) !--- 1<=is<=ns |
129 |
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END IF |
130 |
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IF(xs(is+1)==xt(it+1)) is=is+1 !--- 1<=is<=ns .OR. it==nt |
131 |
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END DO |
132 |
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133 |
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CONTAINS |
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135 |
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!------------------------------------------------------------------------------- |
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SUBROUTINE mean_lin(a,b) ! mean [a,b] of the linear function in [xs(is),xs(is+1)] |
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!------------------------------------------------------------------------------- |
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! Arguments: |
139 |
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REAL, INTENT(IN) :: a, b |
140 |
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!------------------------------------------------------------------------------- |
141 |
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IF(lslope.AND.(a/=xs(is).OR.b/=xs(is+1))) THEN; co=0. |
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IF(a==xt(it )) co=co+xt(it )-xs(is ) |
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IF(b==xt(it+1)) co=co+xt(it+1)-xs(is+1) |
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IF(ix==1) vt(it,:) = vt(it,:)+idt*(b-a)*(vs(is,:)+co*slope(is,:)/2.) |
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IF(ix==2) vt(:,it) = vt(:,it)+idt*(b-a)*(vs(:,is)+co*slope(:,is)/2.) |
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ELSE |
147 |
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IF(ix==1) vt(it,:) = vt(it,:)+idt*(b-a)* vs(is,:) |
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IF(ix==2) vt(:,it) = vt(:,it)+idt*(b-a)* vs(:,is) |
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END IF |
150 |
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151 |
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END SUBROUTINE mean_lin |
152 |
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!------------------------------------------------------------------------------- |
153 |
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154 |
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END SUBROUTINE regr2_conserv |
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! |
156 |
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!------------------------------------------------------------------------------- |
157 |
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158 |
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159 |
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!------------------------------------------------------------------------------- |
160 |
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! |
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SUBROUTINE regr3_conserv(ix, vs, xs, xt, vt, slope) |
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! |
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!------------------------------------------------------------------------------- |
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! Arguments: |
165 |
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INTEGER, INTENT(IN) :: ix |
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REAL, INTENT(IN) :: vs(:,:,:) |
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REAL, INTENT(IN) :: xs(:), xt(:) |
168 |
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REAL, INTENT(OUT) :: vt(:,:,:) |
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REAL, OPTIONAL, INTENT(IN) :: slope(:,:,:) |
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!------------------------------------------------------------------------------- |
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! Local variables: |
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INTEGER :: is, it, ns, nt |
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REAL :: co, idt |
174 |
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LOGICAL :: lslope |
175 |
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!------------------------------------------------------------------------------- |
176 |
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lslope=PRESENT(slope) |
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CALL check_size(ix,SHAPE(vs),SHAPE(vt),xs,xt,ns,nt) |
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is=locate(xs,xt(1)) ! 1 <= is <= ns, because we forbid extrapolation |
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vt(:,:,:)=0. |
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DO it=1, nt; idt=1./(xt(it+1)-xt(it)) |
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IF(xt(it+1)<=xs(is+1)) THEN !--- xs(is)<=xt(it)<=xt(it+1)<=xs(is+1) |
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CALL mean_lin(xt(it),xt(it+1)) |
183 |
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ELSE |
184 |
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CALL mean_lin(xt(it),xs(is+1)); is=is+1 |
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DO WHILE(xs(is+1)<xt(it+1)) !--- 1<=is<=ns-1 |
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CALL mean_lin(xs(is),xs(is+1)); is=is+1 |
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END DO |
188 |
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CALL mean_lin(xs(is),xt(it+1)) !--- 1<=is<=ns |
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END IF |
190 |
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IF(xs(is+1)==xt(it+1)) is=is+1 !--- 1<=is<=ns .OR. it==nt |
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END DO |
192 |
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193 |
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CONTAINS |
194 |
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195 |
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!------------------------------------------------------------------------------- |
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SUBROUTINE mean_lin(a,b) ! mean [a,b] of the linear function in [xs(is),xs(is+1)] |
197 |
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!------------------------------------------------------------------------------- |
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! Arguments: |
199 |
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REAL, INTENT(IN) :: a, b |
200 |
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!------------------------------------------------------------------------------- |
201 |
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IF(lslope.AND.(a/=xs(is).OR.b/=xs(is+1))) THEN; co=0. |
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IF(a==xt(it )) co=co+xt(it )-xs(is ) |
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IF(b==xt(it+1)) co=co+xt(it+1)-xs(is+1) |
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IF(ix==1) vt(it,:,:) = vt(it,:,:)+idt*(b-a)*(vs(is,:,:)+co*slope(is,:,:)/2.) |
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IF(ix==2) vt(:,it,:) = vt(:,it,:)+idt*(b-a)*(vs(:,is,:)+co*slope(:,is,:)/2.) |
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IF(ix==3) vt(:,:,it) = vt(:,:,it)+idt*(b-a)*(vs(:,:,is)+co*slope(:,:,is)/2.) |
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ELSE |
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IF(ix==1) vt(it,:,:) = vt(it,:,:)+idt*(b-a)* vs(is,:,:) |
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IF(ix==2) vt(:,it,:) = vt(:,it,:)+idt*(b-a)* vs(:,is,:) |
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IF(ix==3) vt(:,:,it) = vt(:,:,it)+idt*(b-a)* vs(:,:,is) |
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END IF |
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213 |
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END SUBROUTINE mean_lin |
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!------------------------------------------------------------------------------- |
215 |
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216 |
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END SUBROUTINE regr3_conserv |
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! |
218 |
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!------------------------------------------------------------------------------- |
219 |
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220 |
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221 |
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!------------------------------------------------------------------------------- |
222 |
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! |
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SUBROUTINE regr4_conserv(ix, vs, xs, xt, vt, slope) |
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! |
225 |
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!------------------------------------------------------------------------------- |
226 |
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! Arguments: |
227 |
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INTEGER, INTENT(IN) :: ix |
228 |
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REAL, INTENT(IN) :: vs(:,:,:,:) |
229 |
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REAL, INTENT(IN) :: xs(:), xt(:) |
230 |
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REAL, INTENT(OUT) :: vt(:,:,:,:) |
231 |
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REAL, OPTIONAL, INTENT(IN) :: slope(:,:,:,:) |
232 |
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!------------------------------------------------------------------------------- |
233 |
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! Local variables: |
234 |
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INTEGER :: is, it, ns, nt |
235 |
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REAL :: co, idt |
236 |
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LOGICAL :: lslope |
237 |
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!------------------------------------------------------------------------------- |
238 |
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lslope=PRESENT(slope) |
239 |
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CALL check_size(ix,SHAPE(vs),SHAPE(vt),xs,xt,ns,nt) |
240 |
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is=locate(xs,xt(1)) ! 1 <= is <= ns, because we forbid extrapolation |
241 |
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vt(:,:,:,:)=0. |
242 |
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DO it=1, nt; idt=1./(xt(it+1)-xt(it)) |
243 |
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IF(xt(it+1)<=xs(is+1)) THEN !--- xs(is)<=xt(it)<=xt(it+1)<=xs(is+1) |
244 |
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CALL mean_lin(xt(it),xt(it+1)) |
245 |
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ELSE |
246 |
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CALL mean_lin(xt(it),xs(is+1)); is=is+1 |
247 |
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DO WHILE(xs(is+1)<xt(it+1)) !--- 1<=is<=ns-1 |
248 |
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CALL mean_lin(xs(is),xs(is+1)); is=is+1 |
249 |
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END DO |
250 |
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CALL mean_lin(xs(is),xt(it+1)) !--- 1<=is<=ns |
251 |
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END IF |
252 |
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IF(xs(is+1)==xt(it+1)) is=is+1 !--- 1<=is<=ns .OR. it==nt |
253 |
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END DO |
254 |
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255 |
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CONTAINS |
256 |
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257 |
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!------------------------------------------------------------------------------- |
258 |
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SUBROUTINE mean_lin(a,b) ! mean [a,b] of the linear function in [xs(is),xs(is+1)] |
259 |
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!------------------------------------------------------------------------------- |
260 |
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! Arguments: |
261 |
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REAL, INTENT(IN) :: a, b |
262 |
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!------------------------------------------------------------------------------- |
263 |
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IF(lslope.AND.(a/=xs(is).OR.b/=xs(is+1))) THEN; co=0. |
264 |
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IF(a==xt(it )) co=co+xt(it )-xs(is ) |
265 |
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IF(b==xt(it+1)) co=co+xt(it+1)-xs(is+1) |
266 |
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IF(ix==1) vt(it,:,:,:) = vt(it,:,:,:)+idt*(b-a)*(vs(is,:,:,:)+co*slope(is,:,:,:)/2.) |
267 |
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IF(ix==2) vt(:,it,:,:) = vt(:,it,:,:)+idt*(b-a)*(vs(:,is,:,:)+co*slope(:,is,:,:)/2.) |
268 |
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IF(ix==3) vt(:,:,it,:) = vt(:,:,it,:)+idt*(b-a)*(vs(:,:,is,:)+co*slope(:,:,is,:)/2.) |
269 |
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IF(ix==4) vt(:,:,:,it) = vt(:,:,:,it)+idt*(b-a)*(vs(:,:,:,is)+co*slope(:,:,:,is)/2.) |
270 |
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ELSE |
271 |
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IF(ix==1) vt(it,:,:,:) = vt(it,:,:,:)+idt*(b-a)* vs(is,:,:,:) |
272 |
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IF(ix==2) vt(:,it,:,:) = vt(:,it,:,:)+idt*(b-a)* vs(:,is,:,:) |
273 |
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IF(ix==3) vt(:,:,it,:) = vt(:,:,it,:)+idt*(b-a)* vs(:,:,is,:) |
274 |
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IF(ix==4) vt(:,:,:,it) = vt(:,:,:,it)+idt*(b-a)* vs(:,:,:,is) |
275 |
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END IF |
276 |
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277 |
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END SUBROUTINE mean_lin |
278 |
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!------------------------------------------------------------------------------- |
279 |
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280 |
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END SUBROUTINE regr4_conserv |
281 |
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! |
282 |
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!------------------------------------------------------------------------------- |
283 |
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284 |
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285 |
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!------------------------------------------------------------------------------- |
286 |
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! |
287 |
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SUBROUTINE regr5_conserv(ix, vs, xs, xt, vt, slope) |
288 |
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! |
289 |
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!------------------------------------------------------------------------------- |
290 |
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! Arguments: |
291 |
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INTEGER, INTENT(IN) :: ix |
292 |
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REAL, INTENT(IN) :: vs(:,:,:,:,:) |
293 |
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REAL, INTENT(IN) :: xs(:), xt(:) |
294 |
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REAL, INTENT(OUT) :: vt(:,:,:,:,:) |
295 |
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REAL, OPTIONAL, INTENT(IN) :: slope(:,:,:,:,:) |
296 |
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!------------------------------------------------------------------------------- |
297 |
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! Local variables: |
298 |
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INTEGER :: is, it, ns, nt |
299 |
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REAL :: co, idt |
300 |
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LOGICAL :: lslope |
301 |
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!------------------------------------------------------------------------------- |
302 |
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lslope=PRESENT(slope) |
303 |
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CALL check_size(ix,SHAPE(vs),SHAPE(vt),xs,xt,ns,nt) |
304 |
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is=locate(xs,xt(1)) ! 1 <= is <= ns, because we forbid extrapolation |
305 |
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vt(:,:,:,:,:)=0. |
306 |
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DO it=1, nt; idt=1./(xt(it+1)-xt(it)) |
307 |
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IF(xt(it+1)<=xs(is+1)) THEN !--- xs(is)<=xt(it)<=xt(it+1)<=xs(is+1) |
308 |
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CALL mean_lin(xt(it),xt(it+1)) |
309 |
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ELSE |
310 |
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CALL mean_lin(xt(it),xs(is+1)); is=is+1 |
311 |
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DO WHILE(xs(is+1)<xt(it+1)) !--- 1<=is<=ns-1 |
312 |
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CALL mean_lin(xs(is),xs(is+1)); is=is+1 |
313 |
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END DO |
314 |
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CALL mean_lin(xs(is),xt(it+1)) !--- 1<=is<=ns |
315 |
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END IF |
316 |
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IF(xs(is+1)==xt(it+1)) is=is+1 !--- 1<=is<=ns .OR. it==nt |
317 |
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END DO |
318 |
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319 |
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CONTAINS |
320 |
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321 |
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!------------------------------------------------------------------------------- |
322 |
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SUBROUTINE mean_lin(a,b) ! mean [a,b] of the linear function in [xs(is),xs(is+1)] |
323 |
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!------------------------------------------------------------------------------- |
324 |
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! Arguments: |
325 |
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REAL, INTENT(IN) :: a, b |
326 |
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!------------------------------------------------------------------------------- |
327 |
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IF(lslope.AND.(a/=xs(is).OR.b/=xs(is+1))) THEN; co=0. |
328 |
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IF(a==xt(it )) co=co+xt(it )-xs(is ) |
329 |
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IF(b==xt(it+1)) co=co+xt(it+1)-xs(is+1) |
330 |
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IF(ix==1) vt(it,:,:,:,:) = vt(it,:,:,:,:)+idt*(b-a)*(vs(is,:,:,:,:)+co*slope(is,:,:,:,:)/2.) |
331 |
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IF(ix==2) vt(:,it,:,:,:) = vt(:,it,:,:,:)+idt*(b-a)*(vs(:,is,:,:,:)+co*slope(:,is,:,:,:)/2.) |
332 |
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IF(ix==3) vt(:,:,it,:,:) = vt(:,:,it,:,:)+idt*(b-a)*(vs(:,:,is,:,:)+co*slope(:,:,is,:,:)/2.) |
333 |
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IF(ix==4) vt(:,:,:,it,:) = vt(:,:,:,it,:)+idt*(b-a)*(vs(:,:,:,is,:)+co*slope(:,:,:,is,:)/2.) |
334 |
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IF(ix==5) vt(:,:,:,:,it) = vt(:,:,:,:,it)+idt*(b-a)*(vs(:,:,:,:,is)+co*slope(:,:,:,:,is)/2.) |
335 |
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ELSE |
336 |
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IF(ix==1) vt(it,:,:,:,:) = vt(it,:,:,:,:)+idt*(b-a)* vs(is,:,:,:,:) |
337 |
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IF(ix==2) vt(:,it,:,:,:) = vt(:,it,:,:,:)+idt*(b-a)* vs(:,is,:,:,:) |
338 |
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IF(ix==3) vt(:,:,it,:,:) = vt(:,:,it,:,:)+idt*(b-a)* vs(:,:,is,:,:) |
339 |
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IF(ix==4) vt(:,:,:,it,:) = vt(:,:,:,it,:)+idt*(b-a)* vs(:,:,:,is,:) |
340 |
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IF(ix==5) vt(:,:,:,:,it) = vt(:,:,:,:,it)+idt*(b-a)* vs(:,:,:,:,is) |
341 |
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END IF |
342 |
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343 |
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END SUBROUTINE mean_lin |
344 |
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!------------------------------------------------------------------------------- |
345 |
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346 |
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END SUBROUTINE regr5_conserv |
347 |
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! |
348 |
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!------------------------------------------------------------------------------- |
349 |
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350 |
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351 |
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!------------------------------------------------------------------------------- |
352 |
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! |
353 |
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SUBROUTINE check_size(ix,svs,svt,xs,xt,ns,nt) |
354 |
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! |
355 |
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!------------------------------------------------------------------------------- |
356 |
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! Arguments: |
357 |
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INTEGER, INTENT(IN) :: ix, svs(:), svt(:) |
358 |
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REAL, INTENT(IN) :: xs(:), xt(:) |
359 |
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INTEGER, INTENT(OUT) :: ns, nt |
360 |
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!------------------------------------------------------------------------------- |
361 |
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! Local variables: |
362 |
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INTEGER :: rk, is, ii, n |
363 |
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CHARACTER(LEN=80) :: sub, msg |
364 |
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!------------------------------------------------------------------------------- |
365 |
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WRITE(sub,'(a,2i0,a)')"regr",SIZE(svs),ix,"_conserv" |
366 |
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rk=assert_eq(SIZE(svs),SIZE(svt),TRIM(sub)//': inconsistent ranks') |
367 |
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WRITE(msg,'(a,2(i0,a))')TRIM(sub)//": ix (",ix,") exceeds field rank (",rk,")" |
368 |
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CALL assert(ix>=1.AND.ix<=rk,msg) |
369 |
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ii=0 |
370 |
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DO is=1,rk; IF(is==ix) CYCLE |
371 |
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WRITE(msg,'(a,i0)')TRIM(sub)//" n",is |
372 |
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n=assert_eq(svs(is),svt(is),msg) |
373 |
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ii=ii+1 |
374 |
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END DO |
375 |
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ns=assert_eq(svs(ix),SIZE(xs)-1,TRIM(sub)//" ns") |
376 |
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nt=assert_eq(svt(ix),SIZE(xt)-1,TRIM(sub)//" nt") |
377 |
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378 |
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!--- Quick check on sort order: |
379 |
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CALL assert(xs(1)<xs(2), TRIM(sub)//": xs bad order") |
380 |
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CALL assert(xt(1)<xt(2), TRIM(sub)//": xt bad order") |
381 |
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CALL assert(xs(1)<=xt(1).AND.xt(nt+1)<=xs(ns+1), TRIM(sub)//": extrapolation") |
382 |
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383 |
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END SUBROUTINE check_size |
384 |
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! |
385 |
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!------------------------------------------------------------------------------- |
386 |
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387 |
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388 |
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END MODULE regr_conserv_m |