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nrutil.f90
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MODULE nrutil
USE nrtype
IMPLICIT NONE
INTEGER(I4B), PARAMETER :: NPAR_ARTH=16,NPAR2_ARTH=8
INTEGER(I4B), PARAMETER :: NPAR_GEOP=4,NPAR2_GEOP=2
INTEGER(I4B), PARAMETER :: NPAR_CUMSUM=16
INTEGER(I4B), PARAMETER :: NPAR_CUMPROD=8
INTEGER(I4B), PARAMETER :: NPAR_POLY=8
INTEGER(I4B), PARAMETER :: NPAR_POLYTERM=8
INTERFACE array_copy
MODULE PROCEDURE array_copy_r, array_copy_d, array_copy_i
END INTERFACE
INTERFACE swap
MODULE PROCEDURE swap_i,swap_r,swap_rv,swap_c, &
swap_cv,swap_cm,swap_z,swap_zv,swap_zm, &
masked_swap_rs,masked_swap_rv,masked_swap_rm
END INTERFACE
INTERFACE reallocate
MODULE PROCEDURE reallocate_rv,reallocate_rm,&
reallocate_iv,reallocate_im,reallocate_hv
END INTERFACE
INTERFACE imaxloc
MODULE PROCEDURE imaxloc_r,imaxloc_i
END INTERFACE
INTERFACE assert
MODULE PROCEDURE assert1,assert2,assert3,assert4,assert_v
END INTERFACE
INTERFACE assert_eq
MODULE PROCEDURE assert_eq2,assert_eq3,assert_eq4,assert_eqn
END INTERFACE
INTERFACE arth
MODULE PROCEDURE arth_r, arth_d, arth_i
END INTERFACE
INTERFACE geop
MODULE PROCEDURE geop_r, geop_d, geop_i, geop_c, geop_dv
END INTERFACE
INTERFACE cumsum
MODULE PROCEDURE cumsum_r,cumsum_i
END INTERFACE
INTERFACE poly
MODULE PROCEDURE poly_rr,poly_rrv,poly_dd,poly_ddv,&
poly_rc,poly_cc,poly_msk_rrv,poly_msk_ddv
END INTERFACE
INTERFACE poly_term
MODULE PROCEDURE poly_term_rr,poly_term_cc
END INTERFACE
INTERFACE outerprod
MODULE PROCEDURE outerprod_r,outerprod_d
END INTERFACE
INTERFACE outerdiff
MODULE PROCEDURE outerdiff_r,outerdiff_d,outerdiff_i
END INTERFACE
INTERFACE scatter_add
MODULE PROCEDURE scatter_add_r,scatter_add_d
END INTERFACE
INTERFACE scatter_max
MODULE PROCEDURE scatter_max_r,scatter_max_d
END INTERFACE
INTERFACE diagadd
MODULE PROCEDURE diagadd_rv,diagadd_r
END INTERFACE
INTERFACE diagmult
MODULE PROCEDURE diagmult_rv,diagmult_r
END INTERFACE
INTERFACE get_diag
MODULE PROCEDURE get_diag_rv, get_diag_dv
END INTERFACE
INTERFACE put_diag
MODULE PROCEDURE put_diag_rv, put_diag_r
END INTERFACE
CONTAINS
!BL
SUBROUTINE array_copy_r(src,dest,n_copied,n_not_copied)
REAL(SP), DIMENSION(:), INTENT(IN) :: src
REAL(SP), DIMENSION(:), INTENT(OUT) :: dest
INTEGER(I4B), INTENT(OUT) :: n_copied, n_not_copied
n_copied=min(size(src),size(dest))
n_not_copied=size(src)-n_copied
dest(1:n_copied)=src(1:n_copied)
END SUBROUTINE array_copy_r
!BL
SUBROUTINE array_copy_d(src,dest,n_copied,n_not_copied)
REAL(DP), DIMENSION(:), INTENT(IN) :: src
REAL(DP), DIMENSION(:), INTENT(OUT) :: dest
INTEGER(I4B), INTENT(OUT) :: n_copied, n_not_copied
n_copied=min(size(src),size(dest))
n_not_copied=size(src)-n_copied
dest(1:n_copied)=src(1:n_copied)
END SUBROUTINE array_copy_d
!BL
SUBROUTINE array_copy_i(src,dest,n_copied,n_not_copied)
INTEGER(I4B), DIMENSION(:), INTENT(IN) :: src
INTEGER(I4B), DIMENSION(:), INTENT(OUT) :: dest
INTEGER(I4B), INTENT(OUT) :: n_copied, n_not_copied
n_copied=min(size(src),size(dest))
n_not_copied=size(src)-n_copied
dest(1:n_copied)=src(1:n_copied)
END SUBROUTINE array_copy_i
!BL
!BL
SUBROUTINE swap_i(a,b)
INTEGER(I4B), INTENT(INOUT) :: a,b
INTEGER(I4B) :: dum
dum=a
a=b
b=dum
END SUBROUTINE swap_i
!BL
SUBROUTINE swap_r(a,b)
REAL(SP), INTENT(INOUT) :: a,b
REAL(SP) :: dum
dum=a
a=b
b=dum
END SUBROUTINE swap_r
!BL
SUBROUTINE swap_rv(a,b)
REAL(SP), DIMENSION(:), INTENT(INOUT) :: a,b
REAL(SP), DIMENSION(SIZE(a)) :: dum
dum=a
a=b
b=dum
END SUBROUTINE swap_rv
!BL
SUBROUTINE swap_c(a,b)
COMPLEX(SPC), INTENT(INOUT) :: a,b
COMPLEX(SPC) :: dum
dum=a
a=b
b=dum
END SUBROUTINE swap_c
!BL
SUBROUTINE swap_cv(a,b)
COMPLEX(SPC), DIMENSION(:), INTENT(INOUT) :: a,b
COMPLEX(SPC), DIMENSION(SIZE(a)) :: dum
dum=a
a=b
b=dum
END SUBROUTINE swap_cv
!BL
SUBROUTINE swap_cm(a,b)
COMPLEX(SPC), DIMENSION(:,:), INTENT(INOUT) :: a,b
COMPLEX(SPC), DIMENSION(size(a,1),size(a,2)) :: dum
dum=a
a=b
b=dum
END SUBROUTINE swap_cm
!BL
SUBROUTINE swap_z(a,b)
COMPLEX(DPC), INTENT(INOUT) :: a,b
COMPLEX(DPC) :: dum
dum=a
a=b
b=dum
END SUBROUTINE swap_z
!BL
SUBROUTINE swap_zv(a,b)
COMPLEX(DPC), DIMENSION(:), INTENT(INOUT) :: a,b
COMPLEX(DPC), DIMENSION(SIZE(a)) :: dum
dum=a
a=b
b=dum
END SUBROUTINE swap_zv
!BL
SUBROUTINE swap_zm(a,b)
COMPLEX(DPC), DIMENSION(:,:), INTENT(INOUT) :: a,b
COMPLEX(DPC), DIMENSION(size(a,1),size(a,2)) :: dum
dum=a
a=b
b=dum
END SUBROUTINE swap_zm
!BL
SUBROUTINE masked_swap_rs(a,b,mask)
REAL(SP), INTENT(INOUT) :: a,b
LOGICAL(LGT), INTENT(IN) :: mask
REAL(SP) :: swp
if (mask) then
swp=a
a=b
b=swp
end if
END SUBROUTINE masked_swap_rs
!BL
SUBROUTINE masked_swap_rv(a,b,mask)
REAL(SP), DIMENSION(:), INTENT(INOUT) :: a,b
LOGICAL(LGT), DIMENSION(:), INTENT(IN) :: mask
REAL(SP), DIMENSION(size(a)) :: swp
where (mask)
swp=a
a=b
b=swp
end where
END SUBROUTINE masked_swap_rv
!BL
SUBROUTINE masked_swap_rm(a,b,mask)
REAL(SP), DIMENSION(:,:), INTENT(INOUT) :: a,b
LOGICAL(LGT), DIMENSION(:,:), INTENT(IN) :: mask
REAL(SP), DIMENSION(size(a,1),size(a,2)) :: swp
where (mask)
swp=a
a=b
b=swp
end where
END SUBROUTINE masked_swap_rm
!BL
!BL
FUNCTION reallocate_rv(p,n)
REAL(SP), DIMENSION(:), POINTER :: p, reallocate_rv
INTEGER(I4B), INTENT(IN) :: n
INTEGER(I4B) :: nold,ierr
allocate(reallocate_rv(n),stat=ierr)
if (ierr /= 0) call &
nrerror('reallocate_rv: problem in attempt to allocate memory')
if (.not. associated(p)) RETURN
nold=size(p)
reallocate_rv(1:min(nold,n))=p(1:min(nold,n))
deallocate(p)
END FUNCTION reallocate_rv
!BL
FUNCTION reallocate_iv(p,n)
INTEGER(I4B), DIMENSION(:), POINTER :: p, reallocate_iv
INTEGER(I4B), INTENT(IN) :: n
INTEGER(I4B) :: nold,ierr
allocate(reallocate_iv(n),stat=ierr)
if (ierr /= 0) call &
nrerror('reallocate_iv: problem in attempt to allocate memory')
if (.not. associated(p)) RETURN
nold=size(p)
reallocate_iv(1:min(nold,n))=p(1:min(nold,n))
deallocate(p)
END FUNCTION reallocate_iv
!BL
FUNCTION reallocate_hv(p,n)
CHARACTER(1), DIMENSION(:), POINTER :: p, reallocate_hv
INTEGER(I4B), INTENT(IN) :: n
INTEGER(I4B) :: nold,ierr
allocate(reallocate_hv(n),stat=ierr)
if (ierr /= 0) call &
nrerror('reallocate_hv: problem in attempt to allocate memory')
if (.not. associated(p)) RETURN
nold=size(p)
reallocate_hv(1:min(nold,n))=p(1:min(nold,n))
deallocate(p)
END FUNCTION reallocate_hv
!BL
FUNCTION reallocate_rm(p,n,m)
REAL(SP), DIMENSION(:,:), POINTER :: p, reallocate_rm
INTEGER(I4B), INTENT(IN) :: n,m
INTEGER(I4B) :: nold,mold,ierr
allocate(reallocate_rm(n,m),stat=ierr)
if (ierr /= 0) call &
nrerror('reallocate_rm: problem in attempt to allocate memory')
if (.not. associated(p)) RETURN
nold=size(p,1)
mold=size(p,2)
reallocate_rm(1:min(nold,n),1:min(mold,m))=&
p(1:min(nold,n),1:min(mold,m))
deallocate(p)
END FUNCTION reallocate_rm
!BL
FUNCTION reallocate_im(p,n,m)
INTEGER(I4B), DIMENSION(:,:), POINTER :: p, reallocate_im
INTEGER(I4B), INTENT(IN) :: n,m
INTEGER(I4B) :: nold,mold,ierr
allocate(reallocate_im(n,m),stat=ierr)
if (ierr /= 0) call &
nrerror('reallocate_im: problem in attempt to allocate memory')
if (.not. associated(p)) RETURN
nold=size(p,1)
mold=size(p,2)
reallocate_im(1:min(nold,n),1:min(mold,m))=&
p(1:min(nold,n),1:min(mold,m))
deallocate(p)
END FUNCTION reallocate_im
!BL
FUNCTION ifirstloc(mask)
LOGICAL(LGT), DIMENSION(:), INTENT(IN) :: mask
INTEGER(I4B) :: ifirstloc
INTEGER(I4B), DIMENSION(1) :: loc
loc=maxloc(merge(1,0,mask))
ifirstloc=loc(1)
if (.not. mask(ifirstloc)) ifirstloc=size(mask)+1
END FUNCTION ifirstloc
!BL
FUNCTION imaxloc_r(arr)
REAL(SP), DIMENSION(:), INTENT(IN) :: arr
INTEGER(I4B) :: imaxloc_r
INTEGER(I4B), DIMENSION(1) :: imax
imax=maxloc(arr(:))
imaxloc_r=imax(1)
END FUNCTION imaxloc_r
!BL
FUNCTION imaxloc_i(iarr)
INTEGER(I4B), DIMENSION(:), INTENT(IN) :: iarr
INTEGER(I4B), DIMENSION(1) :: imax
INTEGER(I4B) :: imaxloc_i
imax=maxloc(iarr(:))
imaxloc_i=imax(1)
END FUNCTION imaxloc_i
!BL
FUNCTION iminloc(arr)
REAL(SP), DIMENSION(:), INTENT(IN) :: arr
INTEGER(I4B), DIMENSION(1) :: imin
INTEGER(I4B) :: iminloc
imin=minloc(arr(:))
iminloc=imin(1)
END FUNCTION iminloc
!BL
SUBROUTINE assert1(n1,string)
CHARACTER(LEN=*), INTENT(IN) :: string
LOGICAL, INTENT(IN) :: n1
if (.not. n1) then
write (*,*) 'nrerror: an assertion failed with this tag:', &
string
STOP 'program terminated by assert1'
end if
END SUBROUTINE assert1
!BL
SUBROUTINE assert2(n1,n2,string)
CHARACTER(LEN=*), INTENT(IN) :: string
LOGICAL, INTENT(IN) :: n1,n2
if (.not. (n1 .and. n2)) then
write (*,*) 'nrerror: an assertion failed with this tag:', &
string
STOP 'program terminated by assert2'
end if
END SUBROUTINE assert2
!BL
SUBROUTINE assert3(n1,n2,n3,string)
CHARACTER(LEN=*), INTENT(IN) :: string
LOGICAL, INTENT(IN) :: n1,n2,n3
if (.not. (n1 .and. n2 .and. n3)) then
write (*,*) 'nrerror: an assertion failed with this tag:', &
string
STOP 'program terminated by assert3'
end if
END SUBROUTINE assert3
!BL
SUBROUTINE assert4(n1,n2,n3,n4,string)
CHARACTER(LEN=*), INTENT(IN) :: string
LOGICAL, INTENT(IN) :: n1,n2,n3,n4
if (.not. (n1 .and. n2 .and. n3 .and. n4)) then
write (*,*) 'nrerror: an assertion failed with this tag:', &
string
STOP 'program terminated by assert4'
end if
END SUBROUTINE assert4
!BL
SUBROUTINE assert_v(n,string)
CHARACTER(LEN=*), INTENT(IN) :: string
LOGICAL, DIMENSION(:), INTENT(IN) :: n
if (.not. all(n)) then
write (*,*) 'nrerror: an assertion failed with this tag:', &
string
STOP 'program terminated by assert_v'
end if
END SUBROUTINE assert_v
!BL
FUNCTION assert_eq2(n1,n2,string)
CHARACTER(LEN=*), INTENT(IN) :: string
INTEGER, INTENT(IN) :: n1,n2
INTEGER :: assert_eq2
if (n1 == n2) then
assert_eq2=n1
else
write (*,*) 'nrerror: an assert_eq failed with this tag:', &
string
STOP 'program terminated by assert_eq2'
end if
END FUNCTION assert_eq2
!BL
FUNCTION assert_eq3(n1,n2,n3,string)
CHARACTER(LEN=*), INTENT(IN) :: string
INTEGER, INTENT(IN) :: n1,n2,n3
INTEGER :: assert_eq3
if (n1 == n2 .and. n2 == n3) then
assert_eq3=n1
else
write (*,*) 'nrerror: an assert_eq failed with this tag:', &
string
STOP 'program terminated by assert_eq3'
end if
END FUNCTION assert_eq3
!BL
FUNCTION assert_eq4(n1,n2,n3,n4,string)
CHARACTER(LEN=*), INTENT(IN) :: string
INTEGER, INTENT(IN) :: n1,n2,n3,n4
INTEGER :: assert_eq4
if (n1 == n2 .and. n2 == n3 .and. n3 == n4) then
assert_eq4=n1
else
write (*,*) 'nrerror: an assert_eq failed with this tag:', &
string
STOP 'program terminated by assert_eq4'
end if
END FUNCTION assert_eq4
!BL
FUNCTION assert_eqn(nn,string)
CHARACTER(LEN=*), INTENT(IN) :: string
INTEGER, DIMENSION(:), INTENT(IN) :: nn
INTEGER :: assert_eqn
if (all(nn(2:) == nn(1))) then
assert_eqn=nn(1)
else
write (*,*) 'nrerror: an assert_eq failed with this tag:', &
string
STOP 'program terminated by assert_eqn'
end if
END FUNCTION assert_eqn
!BL
SUBROUTINE nrerror(string)
CHARACTER(LEN=*), INTENT(IN) :: string
write (*,*) 'nrerror: ',string
STOP 'program terminated by nrerror'
END SUBROUTINE nrerror
!BL
FUNCTION arth_r(first,increment,n)
REAL(SP), INTENT(IN) :: first,increment
INTEGER(I4B), INTENT(IN) :: n
REAL(SP), DIMENSION(n) :: arth_r
INTEGER(I4B) :: k,k2
REAL(SP) :: temp
if (n > 0) arth_r(1)=first
if (n <= NPAR_ARTH) then
do k=2,n
arth_r(k)=arth_r(k-1)+increment
end do
else
do k=2,NPAR2_ARTH
arth_r(k)=arth_r(k-1)+increment
end do
temp=increment*NPAR2_ARTH
k=NPAR2_ARTH
do
if (k >= n) exit
k2=k+k
arth_r(k+1:min(k2,n))=temp+arth_r(1:min(k,n-k))
temp=temp+temp
k=k2
end do
end if
END FUNCTION arth_r
!BL
FUNCTION arth_d(first,increment,n)
REAL(DP), INTENT(IN) :: first,increment
INTEGER(I4B), INTENT(IN) :: n
REAL(DP), DIMENSION(n) :: arth_d
INTEGER(I4B) :: k,k2
REAL(DP) :: temp
if (n > 0) arth_d(1)=first
if (n <= NPAR_ARTH) then
do k=2,n
arth_d(k)=arth_d(k-1)+increment
end do
else
do k=2,NPAR2_ARTH
arth_d(k)=arth_d(k-1)+increment
end do
temp=increment*NPAR2_ARTH
k=NPAR2_ARTH
do
if (k >= n) exit
k2=k+k
arth_d(k+1:min(k2,n))=temp+arth_d(1:min(k,n-k))
temp=temp+temp
k=k2
end do
end if
END FUNCTION arth_d
!BL
FUNCTION arth_i(first,increment,n)
INTEGER(I4B), INTENT(IN) :: first,increment,n
INTEGER(I4B), DIMENSION(n) :: arth_i
INTEGER(I4B) :: k,k2,temp
if (n > 0) arth_i(1)=first
if (n <= NPAR_ARTH) then
do k=2,n
arth_i(k)=arth_i(k-1)+increment
end do
else
do k=2,NPAR2_ARTH
arth_i(k)=arth_i(k-1)+increment
end do
temp=increment*NPAR2_ARTH
k=NPAR2_ARTH
do
if (k >= n) exit
k2=k+k
arth_i(k+1:min(k2,n))=temp+arth_i(1:min(k,n-k))
temp=temp+temp
k=k2
end do
end if
END FUNCTION arth_i
!BL
!BL
FUNCTION geop_r(first,factor,n)
REAL(SP), INTENT(IN) :: first,factor
INTEGER(I4B), INTENT(IN) :: n
REAL(SP), DIMENSION(n) :: geop_r
INTEGER(I4B) :: k,k2
REAL(SP) :: temp
if (n > 0) geop_r(1)=first
if (n <= NPAR_GEOP) then
do k=2,n
geop_r(k)=geop_r(k-1)*factor
end do
else
do k=2,NPAR2_GEOP
geop_r(k)=geop_r(k-1)*factor
end do
temp=factor**NPAR2_GEOP
k=NPAR2_GEOP
do
if (k >= n) exit
k2=k+k
geop_r(k+1:min(k2,n))=temp*geop_r(1:min(k,n-k))
temp=temp*temp
k=k2
end do
end if
END FUNCTION geop_r
!BL
FUNCTION geop_d(first,factor,n)
REAL(DP), INTENT(IN) :: first,factor
INTEGER(I4B), INTENT(IN) :: n
REAL(DP), DIMENSION(n) :: geop_d
INTEGER(I4B) :: k,k2
REAL(DP) :: temp
if (n > 0) geop_d(1)=first
if (n <= NPAR_GEOP) then
do k=2,n
geop_d(k)=geop_d(k-1)*factor
end do
else
do k=2,NPAR2_GEOP
geop_d(k)=geop_d(k-1)*factor
end do
temp=factor**NPAR2_GEOP
k=NPAR2_GEOP
do
if (k >= n) exit
k2=k+k
geop_d(k+1:min(k2,n))=temp*geop_d(1:min(k,n-k))
temp=temp*temp
k=k2
end do
end if
END FUNCTION geop_d
!BL
FUNCTION geop_i(first,factor,n)
INTEGER(I4B), INTENT(IN) :: first,factor,n
INTEGER(I4B), DIMENSION(n) :: geop_i
INTEGER(I4B) :: k,k2,temp
if (n > 0) geop_i(1)=first
if (n <= NPAR_GEOP) then
do k=2,n
geop_i(k)=geop_i(k-1)*factor
end do
else
do k=2,NPAR2_GEOP
geop_i(k)=geop_i(k-1)*factor
end do
temp=factor**NPAR2_GEOP
k=NPAR2_GEOP
do
if (k >= n) exit
k2=k+k
geop_i(k+1:min(k2,n))=temp*geop_i(1:min(k,n-k))
temp=temp*temp
k=k2
end do
end if
END FUNCTION geop_i
!BL
FUNCTION geop_c(first,factor,n)
COMPLEX(SP), INTENT(IN) :: first,factor
INTEGER(I4B), INTENT(IN) :: n
COMPLEX(SP), DIMENSION(n) :: geop_c
INTEGER(I4B) :: k,k2
COMPLEX(SP) :: temp
if (n > 0) geop_c(1)=first
if (n <= NPAR_GEOP) then
do k=2,n
geop_c(k)=geop_c(k-1)*factor
end do
else
do k=2,NPAR2_GEOP
geop_c(k)=geop_c(k-1)*factor
end do
temp=factor**NPAR2_GEOP
k=NPAR2_GEOP
do
if (k >= n) exit
k2=k+k
geop_c(k+1:min(k2,n))=temp*geop_c(1:min(k,n-k))
temp=temp*temp
k=k2
end do
end if
END FUNCTION geop_c
!BL
FUNCTION geop_dv(first,factor,n)
REAL(DP), DIMENSION(:), INTENT(IN) :: first,factor
INTEGER(I4B), INTENT(IN) :: n
REAL(DP), DIMENSION(size(first),n) :: geop_dv
INTEGER(I4B) :: k,k2
REAL(DP), DIMENSION(size(first)) :: temp
if (n > 0) geop_dv(:,1)=first(:)
if (n <= NPAR_GEOP) then
do k=2,n
geop_dv(:,k)=geop_dv(:,k-1)*factor(:)
end do
else
do k=2,NPAR2_GEOP
geop_dv(:,k)=geop_dv(:,k-1)*factor(:)
end do
temp=factor**NPAR2_GEOP
k=NPAR2_GEOP
do
if (k >= n) exit
k2=k+k
geop_dv(:,k+1:min(k2,n))=geop_dv(:,1:min(k,n-k))*&
spread(temp,2,size(geop_dv(:,1:min(k,n-k)),2))
temp=temp*temp
k=k2
end do
end if
END FUNCTION geop_dv
!BL
!BL
RECURSIVE FUNCTION cumsum_r(arr,seed) RESULT(ans)
REAL(SP), DIMENSION(:), INTENT(IN) :: arr
REAL(SP), OPTIONAL, INTENT(IN) :: seed
REAL(SP), DIMENSION(size(arr)) :: ans
INTEGER(I4B) :: n,j
REAL(SP) :: sd
n=size(arr)
if (n == 0_i4b) RETURN
sd=0.0_sp
if (present(seed)) sd=seed
ans(1)=arr(1)+sd
if (n < NPAR_CUMSUM) then
do j=2,n
ans(j)=ans(j-1)+arr(j)
end do
else
ans(2:n:2)=cumsum_r(arr(2:n:2)+arr(1:n-1:2),sd)
ans(3:n:2)=ans(2:n-1:2)+arr(3:n:2)
end if
END FUNCTION cumsum_r
!BL
RECURSIVE FUNCTION cumsum_i(arr,seed) RESULT(ans)
INTEGER(I4B), DIMENSION(:), INTENT(IN) :: arr
INTEGER(I4B), OPTIONAL, INTENT(IN) :: seed
INTEGER(I4B), DIMENSION(size(arr)) :: ans
INTEGER(I4B) :: n,j,sd
n=size(arr)
if (n == 0_i4b) RETURN
sd=0_i4b
if (present(seed)) sd=seed
ans(1)=arr(1)+sd
if (n < NPAR_CUMSUM) then
do j=2,n
ans(j)=ans(j-1)+arr(j)
end do
else
ans(2:n:2)=cumsum_i(arr(2:n:2)+arr(1:n-1:2),sd)
ans(3:n:2)=ans(2:n-1:2)+arr(3:n:2)
end if
END FUNCTION cumsum_i
!BL
!BL
RECURSIVE FUNCTION cumprod(arr,seed) RESULT(ans)
REAL(SP), DIMENSION(:), INTENT(IN) :: arr
REAL(SP), OPTIONAL, INTENT(IN) :: seed
REAL(SP), DIMENSION(size(arr)) :: ans
INTEGER(I4B) :: n,j
REAL(SP) :: sd
n=size(arr)
if (n == 0_i4b) RETURN
sd=1.0_sp
if (present(seed)) sd=seed
ans(1)=arr(1)*sd
if (n < NPAR_CUMPROD) then
do j=2,n
ans(j)=ans(j-1)*arr(j)
end do
else
ans(2:n:2)=cumprod(arr(2:n:2)*arr(1:n-1:2),sd)
ans(3:n:2)=ans(2:n-1:2)*arr(3:n:2)
end if
END FUNCTION cumprod
!BL
!BL
FUNCTION poly_rr(x,coeffs)
REAL(SP), INTENT(IN) :: x
REAL(SP), DIMENSION(:), INTENT(IN) :: coeffs
REAL(SP) :: poly_rr
REAL(SP) :: pow
REAL(SP), DIMENSION(:), ALLOCATABLE :: vec
INTEGER(I4B) :: i,n,nn
n=size(coeffs)
if (n <= 0) then
poly_rr=0.0_sp
else if (n < NPAR_POLY) then
poly_rr=coeffs(n)
do i=n-1,1,-1
poly_rr=x*poly_rr+coeffs(i)
end do
else
allocate(vec(n+1))
pow=x
vec(1:n)=coeffs
do
vec(n+1)=0.0_sp
nn=ishft(n+1,-1)
vec(1:nn)=vec(1:n:2)+pow*vec(2:n+1:2)
if (nn == 1) exit
pow=pow*pow
n=nn
end do
poly_rr=vec(1)
deallocate(vec)
end if
END FUNCTION poly_rr
!BL
FUNCTION poly_dd(x,coeffs)
REAL(DP), INTENT(IN) :: x
REAL(DP), DIMENSION(:), INTENT(IN) :: coeffs
REAL(DP) :: poly_dd
REAL(DP) :: pow
REAL(DP), DIMENSION(:), ALLOCATABLE :: vec
INTEGER(I4B) :: i,n,nn
n=size(coeffs)
if (n <= 0) then
poly_dd=0.0_dp
else if (n < NPAR_POLY) then
poly_dd=coeffs(n)
do i=n-1,1,-1
poly_dd=x*poly_dd+coeffs(i)
end do
else
allocate(vec(n+1))
pow=x
vec(1:n)=coeffs
do
vec(n+1)=0.0_dp
nn=ishft(n+1,-1)
vec(1:nn)=vec(1:n:2)+pow*vec(2:n+1:2)
if (nn == 1) exit
pow=pow*pow
n=nn
end do
poly_dd=vec(1)
deallocate(vec)
end if
END FUNCTION poly_dd
!BL
FUNCTION poly_rc(x,coeffs)
COMPLEX(SPC), INTENT(IN) :: x
REAL(SP), DIMENSION(:), INTENT(IN) :: coeffs
COMPLEX(SPC) :: poly_rc
COMPLEX(SPC) :: pow
COMPLEX(SPC), DIMENSION(:), ALLOCATABLE :: vec
INTEGER(I4B) :: i,n,nn
n=size(coeffs)
if (n <= 0) then
poly_rc=0.0_sp
else if (n < NPAR_POLY) then
poly_rc=coeffs(n)
do i=n-1,1,-1
poly_rc=x*poly_rc+coeffs(i)
end do
else
allocate(vec(n+1))
pow=x
vec(1:n)=coeffs
do
vec(n+1)=0.0_sp
nn=ishft(n+1,-1)
vec(1:nn)=vec(1:n:2)+pow*vec(2:n+1:2)
if (nn == 1) exit
pow=pow*pow
n=nn
end do
poly_rc=vec(1)
deallocate(vec)
end if
END FUNCTION poly_rc
!BL
FUNCTION poly_cc(x,coeffs)
COMPLEX(SPC), INTENT(IN) :: x
COMPLEX(SPC), DIMENSION(:), INTENT(IN) :: coeffs
COMPLEX(SPC) :: poly_cc
COMPLEX(SPC) :: pow
COMPLEX(SPC), DIMENSION(:), ALLOCATABLE :: vec
INTEGER(I4B) :: i,n,nn
n=size(coeffs)
if (n <= 0) then
poly_cc=0.0_sp
else if (n < NPAR_POLY) then
poly_cc=coeffs(n)
do i=n-1,1,-1
poly_cc=x*poly_cc+coeffs(i)
end do
else
allocate(vec(n+1))
pow=x
vec(1:n)=coeffs
do
vec(n+1)=0.0_sp
nn=ishft(n+1,-1)
vec(1:nn)=vec(1:n:2)+pow*vec(2:n+1:2)
if (nn == 1) exit
pow=pow*pow
n=nn
end do
poly_cc=vec(1)
deallocate(vec)
end if
END FUNCTION poly_cc
!BL
FUNCTION poly_rrv(x,coeffs)
REAL(SP), DIMENSION(:), INTENT(IN) :: coeffs,x
REAL(SP), DIMENSION(size(x)) :: poly_rrv
INTEGER(I4B) :: i,n,m
m=size(coeffs)
n=size(x)
if (m <= 0) then
poly_rrv=0.0_sp
else if (m < n .or. m < NPAR_POLY) then
poly_rrv=coeffs(m)
do i=m-1,1,-1
poly_rrv=x*poly_rrv+coeffs(i)
end do
else
do i=1,n
poly_rrv(i)=poly_rr(x(i),coeffs)
end do
end if
END FUNCTION poly_rrv
!BL
FUNCTION poly_ddv(x,coeffs)
REAL(DP), DIMENSION(:), INTENT(IN) :: coeffs,x
REAL(DP), DIMENSION(size(x)) :: poly_ddv
INTEGER(I4B) :: i,n,m
m=size(coeffs)
n=size(x)
if (m <= 0) then
poly_ddv=0.0_dp
else if (m < n .or. m < NPAR_POLY) then
poly_ddv=coeffs(m)
do i=m-1,1,-1
poly_ddv=x*poly_ddv+coeffs(i)
end do
else
do i=1,n
poly_ddv(i)=poly_dd(x(i),coeffs)
end do
end if
END FUNCTION poly_ddv
!BL
FUNCTION poly_msk_rrv(x,coeffs,mask)
REAL(SP), DIMENSION(:), INTENT(IN) :: coeffs,x
LOGICAL(LGT), DIMENSION(:), INTENT(IN) :: mask
REAL(SP), DIMENSION(size(x)) :: poly_msk_rrv
poly_msk_rrv=unpack(poly_rrv(pack(x,mask),coeffs),mask,0.0_sp)
END FUNCTION poly_msk_rrv
!BL
FUNCTION poly_msk_ddv(x,coeffs,mask)
REAL(DP), DIMENSION(:), INTENT(IN) :: coeffs,x
LOGICAL(LGT), DIMENSION(:), INTENT(IN) :: mask
REAL(DP), DIMENSION(size(x)) :: poly_msk_ddv
poly_msk_ddv=unpack(poly_ddv(pack(x,mask),coeffs),mask,0.0_dp)
END FUNCTION poly_msk_ddv
!BL
!BL
RECURSIVE FUNCTION poly_term_rr(a,b) RESULT(u)
REAL(SP), DIMENSION(:), INTENT(IN) :: a
REAL(SP), INTENT(IN) :: b
REAL(SP), DIMENSION(size(a)) :: u
INTEGER(I4B) :: n,j
n=size(a)
if (n <= 0) RETURN
u(1)=a(1)
if (n < NPAR_POLYTERM) then
do j=2,n
u(j)=a(j)+b*u(j-1)
end do
else
u(2:n:2)=poly_term_rr(a(2:n:2)+a(1:n-1:2)*b,b*b)
u(3:n:2)=a(3:n:2)+b*u(2:n-1:2)
end if
END FUNCTION poly_term_rr
!BL
RECURSIVE FUNCTION poly_term_cc(a,b) RESULT(u)
COMPLEX(SPC), DIMENSION(:), INTENT(IN) :: a
COMPLEX(SPC), INTENT(IN) :: b
COMPLEX(SPC), DIMENSION(size(a)) :: u
INTEGER(I4B) :: n,j
n=size(a)
if (n <= 0) RETURN
u(1)=a(1)
if (n < NPAR_POLYTERM) then
do j=2,n
u(j)=a(j)+b*u(j-1)
end do
else
u(2:n:2)=poly_term_cc(a(2:n:2)+a(1:n-1:2)*b,b*b)
u(3:n:2)=a(3:n:2)+b*u(2:n-1:2)
end if
END FUNCTION poly_term_cc
!BL
!BL
FUNCTION zroots_unity(n,nn)
INTEGER(I4B), INTENT(IN) :: n,nn
COMPLEX(SPC), DIMENSION(nn) :: zroots_unity
INTEGER(I4B) :: k
REAL(SP) :: theta
zroots_unity(1)=1.0
theta=TWOPI/n
k=1
do
if (k >= nn) exit
zroots_unity(k+1)=cmplx(cos(k*theta),sin(k*theta),SPC)
zroots_unity(k+2:min(2*k,nn))=zroots_unity(k+1)*&
zroots_unity(2:min(k,nn-k))
k=2*k
end do
END FUNCTION zroots_unity
!BL
FUNCTION outerprod_r(a,b)
REAL(SP), DIMENSION(:), INTENT(IN) :: a,b
REAL(SP), DIMENSION(size(a),size(b)) :: outerprod_r
outerprod_r = spread(a,dim=2,ncopies=size(b)) * &
spread(b,dim=1,ncopies=size(a))
END FUNCTION outerprod_r
!BL
FUNCTION outerprod_d(a,b)
REAL(DP), DIMENSION(:), INTENT(IN) :: a,b
REAL(DP), DIMENSION(size(a),size(b)) :: outerprod_d
outerprod_d = spread(a,dim=2,ncopies=size(b)) * &
spread(b,dim=1,ncopies=size(a))
END FUNCTION outerprod_d
!BL
FUNCTION outerdiv(a,b)
REAL(SP), DIMENSION(:), INTENT(IN) :: a,b
REAL(SP), DIMENSION(size(a),size(b)) :: outerdiv
outerdiv = spread(a,dim=2,ncopies=size(b)) / &
spread(b,dim=1,ncopies=size(a))
END FUNCTION outerdiv
!BL
FUNCTION outersum(a,b)
REAL(SP), DIMENSION(:), INTENT(IN) :: a,b
REAL(SP), DIMENSION(size(a),size(b)) :: outersum
outersum = spread(a,dim=2,ncopies=size(b)) + &
spread(b,dim=1,ncopies=size(a))
END FUNCTION outersum
!BL
FUNCTION outerdiff_r(a,b)
REAL(SP), DIMENSION(:), INTENT(IN) :: a,b
REAL(SP), DIMENSION(size(a),size(b)) :: outerdiff_r
outerdiff_r = spread(a,dim=2,ncopies=size(b)) - &
spread(b,dim=1,ncopies=size(a))
END FUNCTION outerdiff_r
!BL
FUNCTION outerdiff_d(a,b)
REAL(DP), DIMENSION(:), INTENT(IN) :: a,b
REAL(DP), DIMENSION(size(a),size(b)) :: outerdiff_d
outerdiff_d = spread(a,dim=2,ncopies=size(b)) - &
spread(b,dim=1,ncopies=size(a))
END FUNCTION outerdiff_d
!BL
FUNCTION outerdiff_i(a,b)
INTEGER(I4B), DIMENSION(:), INTENT(IN) :: a,b
INTEGER(I4B), DIMENSION(size(a),size(b)) :: outerdiff_i
outerdiff_i = spread(a,dim=2,ncopies=size(b)) - &
spread(b,dim=1,ncopies=size(a))
END FUNCTION outerdiff_i
!BL
FUNCTION outerand(a,b)
LOGICAL(LGT), DIMENSION(:), INTENT(IN) :: a,b
LOGICAL(LGT), DIMENSION(size(a),size(b)) :: outerand
outerand = spread(a,dim=2,ncopies=size(b)) .and. &
spread(b,dim=1,ncopies=size(a))
END FUNCTION outerand
!BL
SUBROUTINE scatter_add_r(dest,source,dest_index)
REAL(SP), DIMENSION(:), INTENT(OUT) :: dest
REAL(SP), DIMENSION(:), INTENT(IN) :: source
INTEGER(I4B), DIMENSION(:), INTENT(IN) :: dest_index
INTEGER(I4B) :: m,n,j,i
n=assert_eq2(size(source),size(dest_index),'scatter_add_r')
m=size(dest)
do j=1,n
i=dest_index(j)
if (i > 0 .and. i <= m) dest(i)=dest(i)+source(j)
end do
END SUBROUTINE scatter_add_r