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NORTRIP_maths.f90
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NORTRIP_maths.f90
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!Maths functions used in NORTRIP
!==========================================================================
function sd_func(val,n_val,nodata_val)
implicit none
!Functions
real mean_func
!Input
integer n_val
real :: val(n_val)
real :: nodata_val
!Output
real sd_func
!Internal
real :: mean_val
integer :: max_index
integer :: i
integer :: count
real :: s
max_index=size(val)
mean_val=mean_func(val,n_val,nodata_val)
s=0
count=0
do i=1,max_index
if (val(i).ne.nodata_val) then
s=s+(val(i)-mean_val)**2
count=count+1
endif
enddo
if (count.gt.1) then
sd_func=sqrt(s/(count-1))
else
sd_func=nodata_val
endif
end function sd_func
!==========================================================================
function mean_func(val,n_val,nodata_val)
!implicit none
!Input
!real, allocatable :: val(:)
integer n_val
real :: val(n_val)
real :: nodata_val
!Output
real mean_func
!Internal
real :: mean_val
integer :: max_index
integer :: i
integer :: count
max_index=size(val)
mean_val=0
count=0
do i=1,max_index
if (val(i).ne.nodata_val) then
mean_val=mean_val+val(i)
count=count+1
endif
enddo
if (count.gt.0) then
mean_func=mean_val/count
else
mean_func=nodata_val
endif
end function mean_func
!==========================================================================
function cov_func(val1,val2,n_val,nodata_val)
implicit none
!Input
integer n_val
real :: val1(n_val)
real :: val2(n_val)
real :: nodata_val
!Output
real cov_func
!Internal
real :: mean_val1
real :: mean_val2
integer :: max_index1,max_index2
integer :: i
integer :: count
real :: s
max_index1=size(val1)
max_index2=size(val2)
if (max_index1.ne.max_index2) then
cov_func=nodata_val
return
endif
count=0
mean_val1=0
mean_val2=0
do i=1,max_index1
if (val1(i).ne.nodata_val.and.val2(i).ne.nodata_val) then
mean_val1=mean_val1+val1(i)
mean_val2=mean_val2+val2(i)
count=count+1
endif
enddo
if (count.gt.0) then
mean_val1=mean_val1/count
mean_val2=mean_val2/count
else
mean_val1=nodata_val
mean_val2=nodata_val
cov_func=nodata_val
return
endif
s=0
do i=1,max_index1
if (val1(i).ne.nodata_val.and.val2(i).ne.nodata_val) then
s=s+(val1(i)-mean_val1)*(val2(i)-mean_val2)
count=count+1
endif
enddo
if (count.gt.1) then
cov_func=s/(count-1)
else
cov_func=nodata_val
endif
end function cov_func
!==========================================================================
function correlation_func(val1,val2,n_val,nodata_val)
implicit none
!Input
integer n_val
real :: val1(n_val)
real :: val2(n_val)
real :: nodata_val
!Output
real correlation_func
!Internal
real :: s_val1
real :: s_val2
real :: cov_val
real :: mean_val1
real :: mean_val2
integer :: count
integer :: max_index1,max_index2
integer i
max_index1=size(val1)
max_index2=size(val2)
if (max_index1.ne.max_index2) then
correlation_func=nodata_val
return
endif
mean_val1=0
mean_val2=0
count=0
do i=1,max_index1
if (val1(i).ne.nodata_val.and.val2(i).ne.nodata_val) then
mean_val1=mean_val1+val1(i)
mean_val2=mean_val2+val2(i)
count=count+1
endif
enddo
if (count.gt.0) then
mean_val1=mean_val1/count
mean_val2=mean_val2/count
else
mean_val1=nodata_val
mean_val2=nodata_val
correlation_func=nodata_val
return
endif
s_val1=0
s_val2=0
cov_val=0
do i=1,max_index1
if (val1(i).ne.nodata_val.and.val2(i).ne.nodata_val) then
cov_val=cov_val+(val1(i)-mean_val1)*(val2(i)-mean_val2)
s_val1=s_val1+(val1(i)-mean_val1)**2
s_val2=s_val2+(val2(i)-mean_val2)**2
endif
enddo
if (count.gt.1.and.s_val1.gt.0.and.s_val2.gt.0) then
correlation_func=cov_val/(sqrt(s_val1)*sqrt(s_val2))
else
correlation_func=nodata_val
endif
end function correlation_func
!==========================================================================
function rsquare_func(val1,val2,n_val,nodata_val)
!This is just correlation**2, which it is if it is in regard to linear fitting
implicit none
!Functions
real correlation_func
!Input
integer n_val
real :: val1(n_val)
real :: val2(n_val)
real :: nodata_val
!Output
real rsquare_func
rsquare_func=correlation_func(val1,val2,n_val,nodata_val)
if (rsquare_func.ne.nodata_val) then
rsquare_func=rsquare_func**2
else
rsquare_func=nodata_val
endif
end function rsquare_func
!==========================================================================
function rmse_func(val1,val2,n_val,nodata_val)
implicit none
!Input
integer n_val
real :: val1(n_val)
real :: val2(n_val)
real :: nodata_val
!Output
real rmse_func
!Internal
integer :: max_index1,max_index2
integer :: i
integer :: count
real :: s
max_index1=size(val1)
max_index2=size(val2)
if (max_index1.ne.max_index2) then
rmse_func=nodata_val
return
endif
count=0
s=0
do i=1,max_index1
if (val1(i).ne.nodata_val.and.val2(i).ne.nodata_val) then
s=s+(val1(i)-val2(i))**2
count=count+1
endif
enddo
if (count.gt.0) then
rmse_func=sqrt(s/count)
else
rmse_func=nodata_val
endif
end function rmse_func
!==========================================================================
function percentile_func(val_in,n_val,percentile,nodata_val)
!Uses a simple sorting routine
!Percentile is a percentage
implicit none
!Input
integer n_val
real :: val_in(n_val)
real :: nodata_val
real :: percentile
!Output
real percentile_func
!Internal
integer :: max_index
integer :: i,j
integer :: count
real :: val_i,val_j
integer :: percentile_index
real :: val(n_val)
max_index=size(val_in,1)
val=val_in
!Bubble sort. Can be more effective if it doesn't bubble through the entire array
do i=2,max_index
val_i=val(i)
do j=i,2,-1
val_j=val(j-1)
if (val_i.lt.val_j) then
val(j-1)=val_i
val(j)=val_j
endif
enddo
enddo
!Remove nodata values
count=0
do i=1,max_index
if (val(i).ne.nodata_val) then
count=count+1
!write(*,*) count,i,max_index
val(count)=val(i)
endif
enddo
if (count.gt.0) then
percentile_index=max(int(percentile/100.*count+.5),1)
percentile_func=val(percentile_index)
else
percentile_func=nodata_val
endif
end function percentile_func
!==========================================================================
!Do not use yet. Need to reorganise like percentile_func so that val does not change
function nhigh_func(val,n_val,nhigh,nodata_val)
!Uses a simple sorting routine
!nhigh is a number
implicit none
!Input
integer n_val
real :: val(n_val)
real :: nodata_val
integer :: nhigh
!Output
real nhigh_func
!Internal
integer :: max_index
integer :: i,j
integer :: count
real :: val_i,val_j
integer :: nhigh_index
max_index=size(val)
!Bubble sort. Can be more effective if it doesn't bubble through the entire array
do i=2,max_index
val_i=val(i)
do j=i,2,-1
val_j=val(j-1)
if (val_i.lt.val_j) then
val(j-1)=val_i
val(j)=val_j
endif
enddo
enddo
!Remove nodata values
do i=1,max_index
if (val(i).ne.nodata_val) then
count=count+1
val(count)=val(i)
endif
enddo
if (count.gt.0) then
nhigh_index=max(count-nhigh+1,1)
nhigh_func=val(nhigh_index)
else
nhigh_func=nodata_val
endif
end function nhigh_func
!==========================================================================
function fb_func(val1,val2,n_val,nodata_val)
!Fractional bias function
implicit none
!Input
integer n_val
real :: val1(n_val)
real :: val2(n_val)
real :: nodata_val
!Output
real fb_func
!Internal
real :: mean_val1
real :: mean_val2
integer :: max_index1,max_index2
integer :: i
integer :: count
real :: s
max_index1=size(val1)
max_index2=size(val2)
if (max_index1.ne.max_index2) then
fb_func=nodata_val
return
endif
count=0
mean_val1=0
mean_val2=0
do i=1,max_index1
if (val1(i).ne.nodata_val.and.val2(i).ne.nodata_val) then
mean_val1=mean_val1+val1(i)
mean_val2=mean_val2+val2(i)
count=count+1
endif
enddo
if (count.gt.0) then
mean_val1=mean_val1/count
mean_val2=mean_val2/count
fb_func=(mean_val1-mean_val2)/(mean_val1+mean_val2)*2
else
mean_val1=nodata_val
mean_val2=nodata_val
fb_func=nodata_val
return
endif
end function fb_func
!==========================================================================
!==========================================================================
!subroutine daily_mean_sub()