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module fvn
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
! fvn : a f95 module replacement for some imsl routines
! it uses lapack for linear algebra
! it uses modified quadpack for integration
!
! William Daniau 2007
! william.daniau@femto-st.fr
!
! Routines naming scheme :
!
! fvn_x_name
! where x can be s : real
! d : real double precision
! c : complex
! z : double complex
!
!
! This piece of code is totally free! Do whatever you want with it. However
! if you find it usefull it would be kind to give credits ;-) Nevertheless, you
! may give credits to quadpack authors.
!
! Version 1.1
!
! TO DO LIST :
! + Order eigenvalues and vectors in decreasing eigenvalue's modulus order -> atm
! eigenvalues are given with no particular order.
! + Generic interface for fvn_x_name family -> fvn_name
! + Make some parameters optional, status for example
! + use f95 kinds "double complex" -> complex(kind=8)
! + unify quadpack routines
! + ...
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
implicit none
! All quadpack routines are private to the module
private :: d1mach,dqag,dqag_2d_inner,dqag_2d_outer,dqage,dqage_2d_inner, &
dqage_2d_outer,dqk15,dqk15_2d_inner,dqk15_2d_outer,dqk21,dqk21_2d_inner,dqk21_2d_outer, &
dqk31,dqk31_2d_inner,dqk31_2d_outer,dqk41,dqk41_2d_inner,dqk41_2d_outer, &
dqk51,dqk51_2d_inner,dqk51_2d_outer,dqk61,dqk61_2d_inner,dqk61_2d_outer,dqpsrt
contains
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
! Matrix inversion subroutines
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
subroutine fvn_s_matinv(d,a,inva,status)
!
! Matrix inversion of a real matrix using BLAS and LAPACK
!
! d (in) : matrix rank
! a (in) : input matrix
! inva (out) : inversed matrix
! status (ou) : =0 if something failed
!
integer, intent(in) :: d
real, intent(in) :: a(d,d)
real, intent(out) :: inva(d,d)
integer, intent(out) :: status
integer, allocatable :: ipiv(:)
real, allocatable :: work(:)
real twork(1)
integer :: info
integer :: lwork
status=1
allocate(ipiv(d))
! copy a into inva using BLAS
!call scopy(d*d,a,1,inva,1)
inva(:,:)=a(:,:)
! LU factorization using LAPACK
call sgetrf(d,d,inva,d,ipiv,info)
! if info is not equal to 0, something went wrong we exit setting status to 0
if (info /= 0) then
status=0
deallocate(ipiv)
return
end if
! we use the query fonction of xxxtri to obtain the optimal workspace size
call sgetri(d,inva,d,ipiv,twork,-1,info)
lwork=int(twork(1))
allocate(work(lwork))
! Matrix inversion using LAPACK
call sgetri(d,inva,d,ipiv,work,lwork,info)
! again if info is not equal to 0, we exit setting status to 0
if (info /= 0) then
status=0
end if
deallocate(work)
deallocate(ipiv)
end subroutine
subroutine fvn_d_matinv(d,a,inva,status)
!
! Matrix inversion of a double precision matrix using BLAS and LAPACK
!
! d (in) : matrix rank
! a (in) : input matrix
! inva (out) : inversed matrix
! status (ou) : =0 if something failed
!
integer, intent(in) :: d
double precision, intent(in) :: a(d,d)
double precision, intent(out) :: inva(d,d)
integer, intent(out) :: status
integer, allocatable :: ipiv(:)
double precision, allocatable :: work(:)
double precision :: twork(1)
integer :: info
integer :: lwork
status=1
allocate(ipiv(d))
! copy a into inva using BLAS
!call dcopy(d*d,a,1,inva,1)
inva(:,:)=a(:,:)
! LU factorization using LAPACK
call dgetrf(d,d,inva,d,ipiv,info)
! if info is not equal to 0, something went wrong we exit setting status to 0
if (info /= 0) then
status=0
deallocate(ipiv)
return
end if
! we use the query fonction of xxxtri to obtain the optimal workspace size
call dgetri(d,inva,d,ipiv,twork,-1,info)
lwork=int(twork(1))
allocate(work(lwork))
! Matrix inversion using LAPACK
call dgetri(d,inva,d,ipiv,work,lwork,info)
! again if info is not equal to 0, we exit setting status to 0
if (info /= 0) then
status=0
end if
deallocate(work)
deallocate(ipiv)
end subroutine
subroutine fvn_c_matinv(d,a,inva,status)
!
! Matrix inversion of a complex matrix using BLAS and LAPACK
!
! d (in) : matrix rank
! a (in) : input matrix
! inva (out) : inversed matrix
! status (ou) : =0 if something failed
!
integer, intent(in) :: d
complex, intent(in) :: a(d,d)
complex, intent(out) :: inva(d,d)
integer, intent(out) :: status
integer, allocatable :: ipiv(:)
complex, allocatable :: work(:)
complex :: twork(1)
integer :: info
integer :: lwork
status=1
allocate(ipiv(d))
! copy a into inva using BLAS
!call ccopy(d*d,a,1,inva,1)
inva(:,:)=a(:,:)
! LU factorization using LAPACK
call cgetrf(d,d,inva,d,ipiv,info)
! if info is not equal to 0, something went wrong we exit setting status to 0
if (info /= 0) then
status=0
deallocate(ipiv)
return
end if
! we use the query fonction of xxxtri to obtain the optimal workspace size
call cgetri(d,inva,d,ipiv,twork,-1,info)
lwork=int(twork(1))
allocate(work(lwork))
! Matrix inversion using LAPACK
call cgetri(d,inva,d,ipiv,work,lwork,info)
! again if info is not equal to 0, we exit setting status to 0
if (info /= 0) then
status=0
end if
deallocate(work)
deallocate(ipiv)
end subroutine
subroutine fvn_z_matinv(d,a,inva,status)
!
! Matrix inversion of a double complex matrix using BLAS and LAPACK
!
! d (in) : matrix rank
! a (in) : input matrix
! inva (out) : inversed matrix
! status (ou) : =0 if something failed
!
integer, intent(in) :: d
double complex, intent(in) :: a(d,d)
double complex, intent(out) :: inva(d,d)
integer, intent(out) :: status
integer, allocatable :: ipiv(:)
double complex, allocatable :: work(:)
double complex :: twork(1)
integer :: info
integer :: lwork
status=1
allocate(ipiv(d))
! copy a into inva using BLAS
!call zcopy(d*d,a,1,inva,1)
inva(:,:)=a(:,:)
! LU factorization using LAPACK
call zgetrf(d,d,inva,d,ipiv,info)
! if info is not equal to 0, something went wrong we exit setting status to 0
if (info /= 0) then
status=0
deallocate(ipiv)
return
end if
! we use the query fonction of xxxtri to obtain the optimal workspace size
call zgetri(d,inva,d,ipiv,twork,-1,info)
lwork=int(twork(1))
allocate(work(lwork))
! Matrix inversion using LAPACK
call zgetri(d,inva,d,ipiv,work,lwork,info)
! again if info is not equal to 0, we exit setting status to 0
if (info /= 0) then
status=0
end if
deallocate(work)
deallocate(ipiv)
end subroutine
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
! Determinants
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
function fvn_s_det(d,a,status)
!
! Evaluate the determinant of a square matrix using lapack LU factorization
!
! d (in) : matrix rank
! a (in) : The Matrix
! status (out) : =0 if LU factorization failed
!
integer, intent(in) :: d
real, intent(in) :: a(d,d)
integer, intent(out) :: status
real :: fvn_s_det
real, allocatable :: wc_a(:,:)
integer, allocatable :: ipiv(:)
integer :: info,i
status=1
allocate(wc_a(d,d))
allocate(ipiv(d))
wc_a(:,:)=a(:,:)
call sgetrf(d,d,wc_a,d,ipiv,info)
if (info/= 0) then
status=0
fvn_s_det=0.e0
deallocate(ipiv)
deallocate(wc_a)
return
end if
fvn_s_det=1.e0
do i=1,d
if (ipiv(i)==i) then
fvn_s_det=fvn_s_det*wc_a(i,i)
else
fvn_s_det=-fvn_s_det*wc_a(i,i)
end if
end do
deallocate(ipiv)
deallocate(wc_a)
end function
function fvn_d_det(d,a,status)
!
! Evaluate the determinant of a square matrix using lapack LU factorization
!
! d (in) : matrix rank
! a (in) : The Matrix
! status (out) : =0 if LU factorization failed
!
integer, intent(in) :: d
double precision, intent(in) :: a(d,d)
integer, intent(out) :: status
double precision :: fvn_d_det
double precision, allocatable :: wc_a(:,:)
integer, allocatable :: ipiv(:)
integer :: info,i
status=1
allocate(wc_a(d,d))
allocate(ipiv(d))
wc_a(:,:)=a(:,:)
call dgetrf(d,d,wc_a,d,ipiv,info)
if (info/= 0) then
status=0
fvn_d_det=0.d0
deallocate(ipiv)
deallocate(wc_a)
return
end if
fvn_d_det=1.d0
do i=1,d
if (ipiv(i)==i) then
fvn_d_det=fvn_d_det*wc_a(i,i)
else
fvn_d_det=-fvn_d_det*wc_a(i,i)
end if
end do
deallocate(ipiv)
deallocate(wc_a)
end function
function fvn_c_det(d,a,status) !
! Evaluate the determinant of a square matrix using lapack LU factorization
!
! d (in) : matrix rank
! a (in) : The Matrix
! status (out) : =0 if LU factorization failed
!
integer, intent(in) :: d
complex, intent(in) :: a(d,d)
integer, intent(out) :: status
complex :: fvn_c_det
complex, allocatable :: wc_a(:,:)
integer, allocatable :: ipiv(:)
integer :: info,i
status=1
allocate(wc_a(d,d))
allocate(ipiv(d))
wc_a(:,:)=a(:,:)
call cgetrf(d,d,wc_a,d,ipiv,info)
if (info/= 0) then
status=0
fvn_c_det=(0.e0,0.e0)
deallocate(ipiv)
deallocate(wc_a)
return
end if
fvn_c_det=(1.e0,0.e0)
do i=1,d
if (ipiv(i)==i) then
fvn_c_det=fvn_c_det*wc_a(i,i)
else
fvn_c_det=-fvn_c_det*wc_a(i,i)
end if
end do
deallocate(ipiv)
deallocate(wc_a)
end function
function fvn_z_det(d,a,status)
!
! Evaluate the determinant of a square matrix using lapack LU factorization
!
! d (in) : matrix rank
! a (in) : The Matrix
! det (out) : determinant
! status (out) : =0 if LU factorization failed
!
integer, intent(in) :: d
double complex, intent(in) :: a(d,d)
integer, intent(out) :: status
double complex :: fvn_z_det
double complex, allocatable :: wc_a(:,:)
integer, allocatable :: ipiv(:)
integer :: info,i
status=1
allocate(wc_a(d,d))
allocate(ipiv(d))
wc_a(:,:)=a(:,:)
call zgetrf(d,d,wc_a,d,ipiv,info)
if (info/= 0) then
status=0
fvn_z_det=(0.d0,0.d0)
deallocate(ipiv)
deallocate(wc_a)
return
end if
fvn_z_det=(1.d0,0.d0)
do i=1,d
if (ipiv(i)==i) then
fvn_z_det=fvn_z_det*wc_a(i,i)
else
fvn_z_det=-fvn_z_det*wc_a(i,i)
end if
end do
deallocate(ipiv)
deallocate(wc_a)
end function
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
! Condition test
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! 1-norm
! fonction lapack slange,dlange,clange,zlange pour obtenir la 1-norm
! fonction lapack sgecon,dgecon,cgecon,zgecon pour calculer la rcond
!
subroutine fvn_s_matcon(d,a,rcond,status)
! Matrix condition (reciprocal of condition number)
!
! d (in) : matrix rank
! a (in) : The Matrix
! rcond (out) : guess what
! status (out) : =0 if something went wrong
!
integer, intent(in) :: d
real, intent(in) :: a(d,d)
real, intent(out) :: rcond
integer, intent(out) :: status
real, allocatable :: work(:)
integer, allocatable :: iwork(:)
real :: anorm
real, allocatable :: wc_a(:,:) ! working copy of a
integer :: info
integer, allocatable :: ipiv(:)
real, external :: slange
status=1
anorm=slange('1',d,d,a,d,work) ! work is unallocated as it is only used when computing infinity norm
allocate(wc_a(d,d))
!call scopy(d*d,a,1,wc_a,1)
wc_a(:,:)=a(:,:)
allocate(ipiv(d))
call sgetrf(d,d,wc_a,d,ipiv,info)
if (info /= 0) then
status=0
deallocate(ipiv)
deallocate(wc_a)
return
end if
allocate(work(4*d))
allocate(iwork(d))
call sgecon('1',d,wc_a,d,anorm,rcond,work,iwork,info)
if (info /= 0) then
status=0
end if
deallocate(iwork)
deallocate(work)
deallocate(ipiv)
deallocate(wc_a)
end subroutine
subroutine fvn_d_matcon(d,a,rcond,status)
! Matrix condition (reciprocal of condition number)
!
! d (in) : matrix rank
! a (in) : The Matrix
! rcond (out) : guess what
! status (out) : =0 if something went wrong
!
integer, intent(in) :: d
double precision, intent(in) :: a(d,d)
double precision, intent(out) :: rcond
integer, intent(out) :: status
double precision, allocatable :: work(:)
integer, allocatable :: iwork(:)
double precision :: anorm
double precision, allocatable :: wc_a(:,:) ! working copy of a
integer :: info
integer, allocatable :: ipiv(:)
double precision, external :: dlange
status=1
anorm=dlange('1',d,d,a,d,work) ! work is unallocated as it is only used when computing infinity norm
allocate(wc_a(d,d))
!call dcopy(d*d,a,1,wc_a,1)
wc_a(:,:)=a(:,:)
allocate(ipiv(d))
call dgetrf(d,d,wc_a,d,ipiv,info)
if (info /= 0) then
status=0
deallocate(ipiv)
deallocate(wc_a)
return
end if
allocate(work(4*d))
allocate(iwork(d))
call dgecon('1',d,wc_a,d,anorm,rcond,work,iwork,info)
if (info /= 0) then
status=0
end if
deallocate(iwork)
deallocate(work)
deallocate(ipiv)
deallocate(wc_a)
end subroutine
subroutine fvn_c_matcon(d,a,rcond,status)
! Matrix condition (reciprocal of condition number)
!
! d (in) : matrix rank
! a (in) : The Matrix
! rcond (out) : guess what
! status (out) : =0 if something went wrong
!
integer, intent(in) :: d
complex, intent(in) :: a(d,d)
real, intent(out) :: rcond
integer, intent(out) :: status
real, allocatable :: rwork(:)
complex, allocatable :: work(:)
integer, allocatable :: iwork(:)
real :: anorm
complex, allocatable :: wc_a(:,:) ! working copy of a
integer :: info
integer, allocatable :: ipiv(:)
real, external :: clange
status=1
anorm=clange('1',d,d,a,d,rwork) ! rwork is unallocated as it is only used when computing infinity norm
allocate(wc_a(d,d))
!call ccopy(d*d,a,1,wc_a,1)
wc_a(:,:)=a(:,:)
allocate(ipiv(d))
call cgetrf(d,d,wc_a,d,ipiv,info)
if (info /= 0) then
status=0
deallocate(ipiv)
deallocate(wc_a)
return
end if
allocate(work(2*d))
allocate(rwork(2*d))
call cgecon('1',d,wc_a,d,anorm,rcond,work,rwork,info)
if (info /= 0) then
status=0
end if
deallocate(rwork)
deallocate(work)
deallocate(ipiv)
deallocate(wc_a)
end subroutine
subroutine fvn_z_matcon(d,a,rcond,status)
! Matrix condition (reciprocal of condition number)
!
! d (in) : matrix rank
! a (in) : The Matrix
! rcond (out) : guess what
! status (out) : =0 if something went wrong
!
integer, intent(in) :: d
double complex, intent(in) :: a(d,d)
double precision, intent(out) :: rcond
integer, intent(out) :: status
double complex, allocatable :: work(:)
double precision, allocatable :: rwork(:)
double precision :: anorm
double complex, allocatable :: wc_a(:,:) ! working copy of a
integer :: info
integer, allocatable :: ipiv(:)
double precision, external :: zlange
status=1
anorm=zlange('1',d,d,a,d,rwork) ! rwork is unallocated as it is only used when computing infinity norm
allocate(wc_a(d,d))
!call zcopy(d*d,a,1,wc_a,1)
wc_a(:,:)=a(:,:)
allocate(ipiv(d))
call zgetrf(d,d,wc_a,d,ipiv,info)
if (info /= 0) then
status=0
deallocate(ipiv)
deallocate(wc_a)
return
end if
allocate(work(2*d))
allocate(rwork(2*d))
call zgecon('1',d,wc_a,d,anorm,rcond,work,rwork,info)
if (info /= 0) then
status=0
end if
deallocate(rwork)
deallocate(work)
deallocate(ipiv)
deallocate(wc_a)
end subroutine
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
! Valeurs propres/ Vecteurs propre
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
subroutine fvn_s_matev(d,a,evala,eveca,status)
!
! integer d (in) : matrice rank
! real a(d,d) (in) : The Matrix
! complex evala(d) (out) : eigenvalues
! complex eveca(d,d) (out) : eveca(:,j) = jth eigenvector
! integer (out) : status =0 if something went wrong
!
! interfacing Lapack routine SGEEV
integer, intent(in) :: d
real, intent(in) :: a(d,d)
complex, intent(out) :: evala(d)
complex, intent(out) :: eveca(d,d)
integer, intent(out) :: status
real, allocatable :: wc_a(:,:) ! a working copy of a
integer :: info
integer :: lwork
real, allocatable :: wr(:),wi(:)
real :: vl ! unused but necessary for the call
real, allocatable :: vr(:,:)
real, allocatable :: work(:)
real :: twork(1)
integer i
integer j
! making a working copy of a
allocate(wc_a(d,d))
!call scopy(d*d,a,1,wc_a,1)
wc_a(:,:)=a(:,:)
allocate(wr(d))
allocate(wi(d))
allocate(vr(d,d))
! query optimal work size
call sgeev('N','V',d,wc_a,d,wr,wi,vl,1,vr,d,twork,-1,info)
lwork=int(twork(1))
allocate(work(lwork))
call sgeev('N','V',d,wc_a,d,wr,wi,vl,1,vr,d,work,lwork,info)
if (info /= 0) then
status=0
deallocate(work)
deallocate(vr)
deallocate(wi)
deallocate(wr)
deallocate(wc_a)
return
end if
! now fill in the results
i=1
do while(i<=d)
evala(i)=cmplx(wr(i),wi(i))
if (wi(i) == 0.) then ! eigenvalue is real
eveca(:,i)=cmplx(vr(:,i),0.)
else ! eigenvalue is complex
evala(i+1)=cmplx(wr(i+1),wi(i+1))
eveca(:,i)=cmplx(vr(:,i),vr(:,i+1))
eveca(:,i+1)=cmplx(vr(:,i),-vr(:,i+1))
i=i+1
end if
i=i+1
enddo
deallocate(work)
deallocate(vr)
deallocate(wi)
deallocate(wr)
deallocate(wc_a)
end subroutine
subroutine fvn_d_matev(d,a,evala,eveca,status)
!
! integer d (in) : matrice rank
! double precision a(d,d) (in) : The Matrix
! double complex evala(d) (out) : eigenvalues
! double complex eveca(d,d) (out) : eveca(:,j) = jth eigenvector
! integer (out) : status =0 if something went wrong
!
! interfacing Lapack routine DGEEV
integer, intent(in) :: d
double precision, intent(in) :: a(d,d)
double complex, intent(out) :: evala(d)
double complex, intent(out) :: eveca(d,d)
integer, intent(out) :: status
double precision, allocatable :: wc_a(:,:) ! a working copy of a
integer :: info
integer :: lwork
double precision, allocatable :: wr(:),wi(:)
double precision :: vl ! unused but necessary for the call
double precision, allocatable :: vr(:,:)
double precision, allocatable :: work(:)
double precision :: twork(1)
integer i
integer j
! making a working copy of a
allocate(wc_a(d,d))
!call dcopy(d*d,a,1,wc_a,1)
wc_a(:,:)=a(:,:)
allocate(wr(d))
allocate(wi(d))
allocate(vr(d,d))
! query optimal work size
call dgeev('N','V',d,wc_a,d,wr,wi,vl,1,vr,d,twork,-1,info)
lwork=int(twork(1))
allocate(work(lwork))
call dgeev('N','V',d,wc_a,d,wr,wi,vl,1,vr,d,work,lwork,info)
if (info /= 0) then
status=0
deallocate(work)
deallocate(vr)
deallocate(wi)
deallocate(wr)
deallocate(wc_a)
return
end if
! now fill in the results
i=1
do while(i<=d)
evala(i)=dcmplx(wr(i),wi(i))
if (wi(i) == 0.) then ! eigenvalue is real
eveca(:,i)=dcmplx(vr(:,i),0.)
else ! eigenvalue is complex
evala(i+1)=dcmplx(wr(i+1),wi(i+1))
eveca(:,i)=dcmplx(vr(:,i),vr(:,i+1))
eveca(:,i+1)=dcmplx(vr(:,i),-vr(:,i+1))
i=i+1
end if
i=i+1
enddo
deallocate(work)
deallocate(vr)
deallocate(wi)
deallocate(wr)
deallocate(wc_a)
end subroutine
subroutine fvn_c_matev(d,a,evala,eveca,status)
!
! integer d (in) : matrice rank
! complex a(d,d) (in) : The Matrix
! complex evala(d) (out) : eigenvalues
! complex eveca(d,d) (out) : eveca(:,j) = jth eigenvector
! integer (out) : status =0 if something went wrong
!
! interfacing Lapack routine CGEEV
integer, intent(in) :: d
complex, intent(in) :: a(d,d)
complex, intent(out) :: evala(d)
complex, intent(out) :: eveca(d,d)
integer, intent(out) :: status
complex, allocatable :: wc_a(:,:) ! a working copy of a
integer :: info
integer :: lwork
complex, allocatable :: work(:)
complex :: twork(1)
real, allocatable :: rwork(:)
complex :: vl ! unused but necessary for the call
status=1
! making a working copy of a
allocate(wc_a(d,d))
!call ccopy(d*d,a,1,wc_a,1)
wc_a(:,:)=a(:,:)
! query optimal work size
call cgeev('N','V',d,wc_a,d,evala,vl,1,eveca,d,twork,-1,rwork,info)
lwork=int(twork(1))
allocate(work(lwork))
allocate(rwork(2*d))
call cgeev('N','V',d,wc_a,d,evala,vl,1,eveca,d,work,lwork,rwork,info)
if (info /= 0) then
status=0
end if
deallocate(rwork)
deallocate(work)
deallocate(wc_a)
end subroutine
subroutine fvn_z_matev(d,a,evala,eveca,status)
!
! integer d (in) : matrice rank
! double complex a(d,d) (in) : The Matrix
! double complex evala(d) (out) : eigenvalues
! double complex eveca(d,d) (out) : eveca(:,j) = jth eigenvector
! integer (out) : status =0 if something went wrong
!
! interfacing Lapack routine ZGEEV
integer, intent(in) :: d
double complex, intent(in) :: a(d,d)
double complex, intent(out) :: evala(d)
double complex, intent(out) :: eveca(d,d)
integer, intent(out) :: status
double complex, allocatable :: wc_a(:,:) ! a working copy of a
integer :: info
integer :: lwork
double complex, allocatable :: work(:)
double complex :: twork(1)
double precision, allocatable :: rwork(:)
double complex :: vl ! unused but necessary for the call
status=1
! making a working copy of a
allocate(wc_a(d,d))
!call zcopy(d*d,a,1,wc_a,1)
wc_a(:,:)=a(:,:)
! query optimal work size
call zgeev('N','V',d,wc_a,d,evala,vl,1,eveca,d,twork,-1,rwork,info)
lwork=int(twork(1))
allocate(work(lwork))
allocate(rwork(2*d))
call zgeev('N','V',d,wc_a,d,evala,vl,1,eveca,d,work,lwork,rwork,info)
if (info /= 0) then
status=0
end if
deallocate(rwork)
deallocate(work)
deallocate(wc_a)
end subroutine
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
! Akima spline interpolation and spline evaluation
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Single precision
subroutine fvn_s_akima(n,x,y,br,co)
implicit none
integer, intent(in) :: n
real, intent(in) :: x(n)
real, intent(in) :: y(n)
real, intent(out) :: br(n)
real, intent(out) :: co(4,n)
real, allocatable :: var(:),z(:)
real :: wi_1,wi
integer :: i
real :: dx,a,b
! br is just a copy of x
br(:)=x(:)
allocate(var(n))
allocate(z(n))
! evaluate the variations
do i=1, n-1
var(i+2)=(y(i+1)-y(i))/(x(i+1)-x(i))
end do
var(n+2)=2.e0*var(n+1)-var(n)
var(n+3)=2.e0*var(n+2)-var(n+1)
var(2)=2.e0*var(3)-var(4)
var(1)=2.e0*var(2)-var(3)
do i = 1, n
wi_1=abs(var(i+3)-var(i+2))
wi=abs(var(i+1)-var(i))
if ((wi_1+wi).eq.0.e0) then
z(i)=(var(i+2)+var(i+1))/2.e0
else
z(i)=(wi_1*var(i+1)+wi*var(i+2))/(wi_1+wi)
end if
end do
do i=1, n-1
dx=x(i+1)-x(i)
a=(z(i+1)-z(i))*dx ! coeff intermediaires pour calcul wd
b=y(i+1)-y(i)-z(i)*dx ! coeff intermediaires pour calcul wd
co(1,i)=y(i)
co(2,i)=z(i)
!co(3,i)=-(a-3.*b)/dx**2 ! méthode wd
!co(4,i)=(a-2.*b)/dx**3 ! méthode wd
co(3,i)=(3.e0*var(i+2)-2.e0*z(i)-z(i+1))/dx ! méthode JP Moreau
co(4,i)=(z(i)+z(i+1)-2.e0*var(i+2))/dx**2 !
! les coefficients donnés par imsl sont co(3,i)*2 et co(4,i)*6
! etrangement la fonction csval corrige et donne la bonne valeur ...
end do
co(1,n)=y(n)
co(2,n)=z(n)
co(3,n)=0.e0
co(4,n)=0.e0
deallocate(z)
deallocate(var)
end subroutine
! Double precision
subroutine fvn_d_akima(n,x,y,br,co)
implicit none
integer, intent(in) :: n
double precision, intent(in) :: x(n)
double precision, intent(in) :: y(n)
double precision, intent(out) :: br(n)
double precision, intent(out) :: co(4,n)
double precision, allocatable :: var(:),z(:)
double precision :: wi_1,wi
integer :: i
double precision :: dx,a,b
! br is just a copy of x
br(:)=x(:)
allocate(var(n))
allocate(z(n))
! evaluate the variations
do i=1, n-1
var(i+2)=(y(i+1)-y(i))/(x(i+1)-x(i))
end do
var(n+2)=2.d0*var(n+1)-var(n)
var(n+3)=2.d0*var(n+2)-var(n+1)
var(2)=2.d0*var(3)-var(4)
var(1)=2.d0*var(2)-var(3)
do i = 1, n
wi_1=dabs(var(i+3)-var(i+2))
wi=dabs(var(i+1)-var(i))
if ((wi_1+wi).eq.0.d0) then
z(i)=(var(i+2)+var(i+1))/2.d0
else
z(i)=(wi_1*var(i+1)+wi*var(i+2))/(wi_1+wi)
end if
end do
do i=1, n-1
dx=x(i+1)-x(i)
a=(z(i+1)-z(i))*dx ! coeff intermediaires pour calcul wd
b=y(i+1)-y(i)-z(i)*dx ! coeff intermediaires pour calcul wd
co(1,i)=y(i)
co(2,i)=z(i)
!co(3,i)=-(a-3.*b)/dx**2 ! méthode wd
!co(4,i)=(a-2.*b)/dx**3 ! méthode wd
co(3,i)=(3.d0*var(i+2)-2.d0*z(i)-z(i+1))/dx ! méthode JP Moreau
co(4,i)=(z(i)+z(i+1)-2.d0*var(i+2))/dx**2 !
! les coefficients donnés par imsl sont co(3,i)*2 et co(4,i)*6
! etrangement la fonction csval corrige et donne la bonne valeur ...
end do
co(1,n)=y(n)
co(2,n)=z(n)
co(3,n)=0.d0
co(4,n)=0.d0
deallocate(z)
deallocate(var)
end subroutine
!
! Single precision spline evaluation
!
function fvn_s_spline_eval(x,n,br,co)
implicit none
real, intent(in) :: x ! x must be br(1)<= x <= br(n+1) otherwise value is extrapolated
integer, intent(in) :: n ! number of intervals
real, intent(in) :: br(n+1) ! breakpoints
real, intent(in) :: co(4,n+1) ! spline coeeficients
real :: fvn_s_spline_eval
integer :: i
real :: dx
if (x<=br(1)) then
i=1
else if (x>=br(n+1)) then
i=n
else
i=1
do while(x>=br(i))
i=i+1
end do
i=i-1
end if
dx=x-br(i)
fvn_s_spline_eval=co(1,i)+co(2,i)*dx+co(3,i)*dx**2+co(4,i)*dx**3
end function
! Double precision spline evaluation
function fvn_d_spline_eval(x,n,br,co)
implicit none
double precision, intent(in) :: x ! x must be br(1)<= x <= br(n+1) otherwise value is extrapolated
integer, intent(in) :: n ! number of intervals
double precision, intent(in) :: br(n+1) ! breakpoints
double precision, intent(in) :: co(4,n+1) ! spline coeeficients
double precision :: fvn_d_spline_eval
integer :: i
double precision :: dx
if (x<=br(1)) then
i=1
else if (x>=br(n+1)) then
i=n
else
i=1
do while(x>=br(i))
i=i+1
end do
i=i-1
end if
dx=x-br(i)
fvn_d_spline_eval=co(1,i)+co(2,i)*dx+co(3,i)*dx**2+co(4,i)*dx**3
end function
!
! Muller
!
!
!
! William Daniau 2007
!
! This routine is a fortran 90 port of Hans D. Mittelmann's routine muller.f
! http://plato.asu.edu/ftp/other_software/muller.f
!
! it can be used as a replacement for imsl routine dzanly with minor changes
!
!-----------------------------------------------------------------------
!
! purpose - zeros of an analytic complex function
! using the muller method with deflation
!
! usage - call fvn_z_muller (f,eps,eps1,kn,n,nguess,x,itmax,
! infer,ier)
!
! arguments f - a complex function subprogram, f(z), written
! by the user specifying the equation whose
! roots are to be found. f must appear in
! an external statement in the calling pro-
! gram.
! eps - 1st stopping criterion. let fp(z)=f(z)/p
! where p = (z-z(1))*(z-z(2))*,,,*(z-z(k-1))
! and z(1),...,z(k-1) are previously found
! roots. if ((cdabs(f(z)).le.eps) .and.
! (cdabs(fp(z)).le.eps)), then z is accepted
! as a root. (input)
! eps1 - 2nd stopping criterion. a root is accepted
! if two successive approximations to a given
! root agree within eps1. (input)
! note. if either or both of the stopping
! criteria are fulfilled, the root is
! accepted.
! kn - the number of known roots which must be stored
! in x(1),...,x(kn), prior to entry to muller
! nguess - the number of initial guesses provided. these
! guesses must be stored in x(kn+1),...,
! x(kn+nguess). nguess must be set equal
! to zero if no guesses are provided. (input)
! n - the number of new roots to be found by
! muller (input)
! x - a complex vector of length kn+n. x(1),...,
! x(kn) on input must contain any known
! roots. x(kn+1),..., x(kn+n) on input may,
! on user option, contain initial guesses for
! the n new roots which are to be computed.
! if the user does not provide an initial
! guess, zero is used.
! on output, x(kn+1),...,x(kn+n) contain the
! approximate roots found by muller.
! itmax - the maximum allowable number of iterations
! per root (input)
! infer - an integer vector of length kn+n. on
! output infer(j) contains the number of
! iterations used in finding the j-th root
! when convergence was achieved. if
! convergence was not obtained in itmax
! iterations, infer(j) will be greater than
! itmax (output).
! ier - error parameter (output)
! warning error
! ier = 33 indicates failure to converge with-
! in itmax iterations for at least one of
! the (n) new roots.
!
!
! remarks muller always returns the last approximation for root j
! in x(j). if the convergence criterion is satisfied,
! then infer(j) is less than or equal to itmax. if the
! convergence criterion is not satisified, then infer(j)
! is set to either itmax+1 or itmax+k, with k greater
! than 1. infer(j) = itmax+1 indicates that muller did
! not obtain convergence in the allowed number of iter-
! ations. in this case, the user may wish to set itmax
! to a larger value. infer(j) = itmax+k means that con-
! vergence was obtained (on iteration k) for the defla-
! ted function
! fp(z) = f(z)/((z-z(1)...(z-z(j-1)))
!
! but failed for f(z). in this case, better initial
! guesses might help or, it might be necessary to relax
! the convergence criterion.
!
!-----------------------------------------------------------------------
!
subroutine fvn_z_muller (f,eps,eps1,kn,nguess,n,x,itmax,infer,ier)
implicit none
double precision :: rzero,rten,rhun,rp01,ax,eps1,qz,eps,tpq
double complex :: d,dd,den,fprt,frt,h,rt,t1,t2,t3, &
tem,z0,z1,z2,bi,xx,xl,y0,y1,y2,x0, &
zero,p1,one,four,p5
double complex, external :: f
integer :: ickmax,kn,nguess,n,itmax,ier,knp1,knpn,i,l,ic, &
knpng,jk,ick,nn,lm1,errcode
double complex :: x(kn+n)
integer :: infer(kn+n)
data zero/(0.0,0.0)/,p1/(0.1,0.0)/, &
one/(1.0,0.0)/,four/(4.0,0.0)/, &
p5/(0.5,0.0)/, &
rzero/0.0/,rten/10.0/,rhun/100.0/, &
ax/0.1/,ickmax/3/,rp01/0.01/
ier = 0
if (n .lt. 1) then ! What the hell are doing here then ...
return
end if
!eps1 = rten **(-nsig)
eps1 = min(eps1,rp01)
knp1 = kn+1
knpn = kn+n
knpng = kn+nguess
do i=1,knpn
infer(i) = 0
if (i .gt. knpng) x(i) = zero
end do
l= knp1
ic=0
rloop: do while (l<=knpn) ! Main loop over new roots
jk = 0
ick = 0
xl = x(l)
icloop: do
ic = 0
h = ax
h = p1*h
if (cdabs(xl) .gt. ax) h = p1*xl
! first three points are
! xl+h, xl-h, xl
rt = xl+h
call deflated_work(errcode)
if (errcode == 1) then
exit icloop
end if
z0 = fprt
y0 = frt
x0 = rt
rt = xl-h
call deflated_work(errcode)
if (errcode == 1) then
exit icloop
end if
z1 = fprt
y1 = frt
h = xl-rt
d = h/(rt-x0)
rt = xl
call deflated_work(errcode)
if (errcode == 1) then
exit icloop
end if
z2 = fprt
y2 = frt
! begin main algorithm
iloop: do
dd = one + d
t1 = z0*d*d
t2 = z1*dd*dd
xx = z2*dd
t3 = z2*d
bi = t1-t2+xx+t3
den = bi*bi-four*(xx*t1-t3*(t2-xx))
! use denominator of maximum amplitude
t1 = cdsqrt(den)
qz = rhun*max(cdabs(bi),cdabs(t1))
t2 = bi + t1
tpq = cdabs(t2)+qz
if (tpq .eq. qz) t2 = zero
t3 = bi - t1
tpq = cdabs(t3) + qz
if (tpq .eq. qz) t3 = zero
den = t2
qz = cdabs(t3)-cdabs(t2)
if (qz .gt. rzero) den = t3
! test for zero denominator
if (cdabs(den) .eq. rzero) then
call trans_rt()
call deflated_work(errcode)
if (errcode == 1) then
exit icloop
end if
z2 = fprt
y2 = frt
cycle iloop
end if
d = -xx/den
d = d+d
h = d*h
rt = rt + h
! check convergence of the first kind
if (cdabs(h) .le. eps1*max(cdabs(rt),ax)) then
if (ic .ne. 0) then
exit icloop
end if
ic = 1
z0 = y1
z1 = y2
z2 = f(rt)
xl = rt
ick = ick+1
if (ick .le. ickmax) then
cycle iloop
end if
! warning error, itmax = maximum
jk = itmax + jk
ier = 33
end if
if (ic .ne. 0) then
cycle icloop
end if
call deflated_work(errcode)
if (errcode == 1) then
exit icloop
end if
do while ( (cdabs(fprt)-cdabs(z2)*rten) .ge. rzero)
! take remedial action to induce
! convergence
d = d*p5
h = h*p5
rt = rt-h
call deflated_work(errcode)
if (errcode == 1) then
exit icloop
end if
end do
z0 = z1
z1 = z2
z2 = fprt
y0 = y1
y1 = y2
y2 = frt
end do iloop
end do icloop
x(l) = rt
infer(l) = jk
l = l+1
end do rloop
contains
subroutine trans_rt()
tem = rten*eps1
if (cdabs(rt) .gt. ax) tem = tem*rt
rt = rt+tem
d = (h+tem)*d/h
h = h+tem
end subroutine trans_rt
subroutine deflated_work(errcode)
! errcode=0 => no errors
! errcode=1 => jk>itmax or convergence of second kind achieved
integer :: errcode,flag
flag=1
loop1: do while(flag==1)
errcode=0
jk = jk+1
if (jk .gt. itmax) then
ier=33
errcode=1
return
end if
frt = f(rt)
fprt = frt
if (l /= 1) then
lm1 = l-1
do i=1,lm1
tem = rt - x(i)
if (cdabs(tem) .eq. rzero) then
!if (ic .ne. 0) go to 15 !! ?? possible?
call trans_rt()
cycle loop1
end if
fprt = fprt/tem
end do
end if
flag=0
end do loop1
if (cdabs(fprt) .le. eps .and. cdabs(frt) .le. eps) then
errcode=1
return
end if
end subroutine deflated_work
end subroutine
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
! Integration
!
! Only double precision coded atm
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
subroutine fvn_d_gauss_legendre(n,qx,qw)
!
! This routine compute the n Gauss Legendre abscissas and weights
! Adapted from Numerical Recipes routine gauleg
!
! n (in) : number of points
! qx(out) : abscissas
! qw(out) : weights
!
implicit none
double precision,parameter :: pi=3.141592653589793d0
integer, intent(in) :: n
double precision, intent(out) :: qx(n),qw(n)
integer :: m,i,j
double precision :: z,z1,p1,p2,p3,pp
m=(n+1)/2
do i=1,m
z=cos(pi*(dble(i)-0.25d0)/(dble(n)+0.5d0))
iloop: do
p1=1.d0
p2=0.d0
do j=1,n
p3=p2
p2=p1
p1=((2.d0*dble(j)-1.d0)*z*p2-(dble(j)-1.d0)*p3)/dble(j)
end do
pp=dble(n)*(z*p1-p2)/(z*z-1.d0)
z1=z
z=z1-p1/pp
if (dabs(z-z1)<=epsilon(z)) then
exit iloop
end if
end do iloop
qx(i)=-z
qx(n+1-i)=z
qw(i)=2.d0/((1.d0-z*z)*pp*pp)
qw(n+1-i)=qw(i)
end do
end subroutine
subroutine fvn_d_gl_integ(f,a,b,n,res)
!
! This is a simple non adaptative integration routine
! using n gauss legendre abscissas and weights
!
! f(in) : the function to integrate
! a(in) : lower bound
! b(in) : higher bound
! n(in) : number of gauss legendre pairs
! res(out): the evaluation of the integral
!
double precision,external :: f
double precision, intent(in) :: a,b
integer, intent(in):: n
double precision, intent(out) :: res
double precision, allocatable :: qx(:),qw(:)
double precision :: xm,xr
integer :: i
! First compute n gauss legendre abs and weight
allocate(qx(n))
allocate(qw(n))
call fvn_d_gauss_legendre(n,qx,qw)
xm=0.5d0*(b+a)
xr=0.5d0*(b-a)
res=0.d0
do i=1,n
res=res+qw(i)*f(xm+xr*qx(i))
end do
res=xr*res
deallocate(qw)
deallocate(qx)
end subroutine
!!!!!!!!!!!!!!!!!!!!!!!!
!
! Simple and double adaptative Gauss Kronrod integration based on
! a modified version of quadpack ( http://www.netlib.org/quadpack
!
! Common parameters :
!
! key (in)
! epsabs
! epsrel
!
!
!!!!!!!!!!!!!!!!!!!!!!!!
subroutine fvn_d_integ_1_gk(f,a,b,epsabs,epsrel,key,res,abserr,ier,limit)
!
! Evaluate the integral of function f(x) between a and b
!
! f(in) : the function
! a(in) : lower bound
! b(in) : higher bound
! epsabs(in) : desired absolute error
! epsrel(in) : desired relative error
! key(in) : gauss kronrod rule
! 1: 7 - 15 points
! 2: 10 - 21 points
! 3: 15 - 31 points
! 4: 20 - 41 points
! 5: 25 - 51 points
! 6: 30 - 61 points
!
! limit(in) : maximum number of subintervals in the partition of the
! given integration interval (a,b). A value of 500 will give the same
! behaviour as the imsl routine dqdag
!
! res(out) : estimated integral value
! abserr(out) : estimated absolute error
! ier(out) : error flag from quadpack routines
! 0 : no error
! 1 : maximum number of subdivisions allowed
! has been achieved. one can allow more
! subdivisions by increasing the value of
! limit (and taking the according dimension
! adjustments into account). however, if
! this yield no improvement it is advised
! to analyze the integrand in order to
! determine the integration difficulaties.
! if the position of a local difficulty can
! be determined (i.e.singularity,
! discontinuity within the interval) one
! will probably gain from splitting up the
! interval at this point and calling the
! integrator on the subranges. if possible,
! an appropriate special-purpose integrator
! should be used which is designed for
! handling the type of difficulty involved.
! 2 : the occurrence of roundoff error is
! detected, which prevents the requested
! tolerance from being achieved.
! 3 : extremely bad integrand behaviour occurs
! at some points of the integration
! interval.
! 6 : the input is invalid, because
! (epsabs.le.0 and
! epsrel.lt.max(50*rel.mach.acc.,0.5d-28))
! or limit.lt.1 or lenw.lt.limit*4.
! result, abserr, neval, last are set
! to zero.
! except when lenw is invalid, iwork(1),
! work(limit*2+1) and work(limit*3+1) are
! set to zero, work(1) is set to a and
! work(limit+1) to b.
implicit none
double precision, external :: f
double precision, intent(in) :: a,b,epsabs,epsrel
integer, intent(in) :: key
integer, intent(in) :: limit
double precision, intent(out) :: res,abserr
integer, intent(out) :: ier
double precision, allocatable :: work(:)
integer, allocatable :: iwork(:)
integer :: lenw,neval,last
! imsl value for limit is 500
lenw=limit*4
allocate(iwork(limit))
allocate(work(lenw))
call dqag(f,a,b,epsabs,epsrel,key,res,abserr,neval,ier,limit,lenw,last,iwork,work)
deallocate(work)
deallocate(iwork)
end subroutine
subroutine fvn_d_integ_2_gk(f,a,b,g,h,epsabs,epsrel,key,res,abserr,ier,limit)
!
! Evaluate the double integral of function f(x,y) for x between a and b and y between g(x) and h(x)
!
! f(in) : the function
! a(in) : lower bound
! b(in) : higher bound
! g(in) : external function describing lower bound for y
! h(in) : external function describing higher bound for y
! epsabs(in) : desired absolute error
! epsrel(in) : desired relative error
! key(in) : gauss kronrod rule
! 1: 7 - 15 points
! 2: 10 - 21 points
! 3: 15 - 31 points
! 4: 20 - 41 points
! 5: 25 - 51 points
! 6: 30 - 61 points
!
! limit(in) : maximum number of subintervals in the partition of the
! given integration interval (a,b). A value of 500 will give the same
! behaviour as the imsl routine dqdag
!
! res(out) : estimated integral value
! abserr(out) : estimated absolute error
! ier(out) : error flag from quadpack routines
! 0 : no error
! 1 : maximum number of subdivisions allowed
! has been achieved. one can allow more
! subdivisions by increasing the value of
! limit (and taking the according dimension
! adjustments into account). however, if
! this yield no improvement it is advised
! to analyze the integrand in order to
! determine the integration difficulaties.
! if the position of a local difficulty can
! be determined (i.e.singularity,
! discontinuity within the interval) one
! will probably gain from splitting up the
! interval at this point and calling the
! integrator on the subranges. if possible,
! an appropriate special-purpose integrator
! should be used which is designed for
! handling the type of difficulty involved.
! 2 : the occurrence of roundoff error is
! detected, which prevents the requested
! tolerance from being achieved.
! 3 : extremely bad integrand behaviour occurs
! at some points of the integration
! interval.
! 6 : the input is invalid, because
! (epsabs.le.0 and
! epsrel.lt.max(50*rel.mach.acc.,0.5d-28))
! or limit.lt.1 or lenw.lt.limit*4.
! result, abserr, neval, last are set
! to zero.
! except when lenw is invalid, iwork(1),
! work(limit*2+1) and work(limit*3+1) are
! set to zero, work(1) is set to a and
! work(limit+1) to b.
implicit none
double precision, external:: f,g,h
double precision, intent(in) :: a,b,epsabs,epsrel
integer, intent(in) :: key,limit
integer, intent(out) :: ier
double precision, intent(out) :: res,abserr
double precision, allocatable :: work(:)
integer, allocatable :: iwork(:)
integer :: lenw,neval,last
! imsl value for limit is 500
lenw=limit*4
allocate(work(lenw))
allocate(iwork(limit))
call dqag_2d_outer(f,a,b,g,h,epsabs,epsrel,key,res,abserr,neval,ier,limit,lenw,last,iwork,work)
deallocate(iwork)
deallocate(work)
end subroutine
subroutine fvn_d_integ_2_inner_gk(f,x,a,b,epsabs,epsrel,key,res,abserr,ier,limit)
!
! Evaluate the single integral of function f(x,y) for y between a and b with a
! given x value
!
! This function is used for the evaluation of the double integral fvn_d_integ_2_gk
!
! f(in) : the function
! x(in) : x
! a(in) : lower bound
! b(in) : higher bound
! epsabs(in) : desired absolute error
! epsrel(in) : desired relative error
! key(in) : gauss kronrod rule
! 1: 7 - 15 points
! 2: 10 - 21 points
! 3: 15 - 31 points
! 4: 20 - 41 points
! 5: 25 - 51 points
! 6: 30 - 61 points
!
! limit(in) : maximum number of subintervals in the partition of the
! given integration interval (a,b). A value of 500 will give the same
! behaviour as the imsl routine dqdag
!
! res(out) : estimated integral value
! abserr(out) : estimated absolute error
! ier(out) : error flag from quadpack routines
! 0 : no error
! 1 : maximum number of subdivisions allowed
! has been achieved. one can allow more
! subdivisions by increasing the value of
! limit (and taking the according dimension
! adjustments into account). however, if
! this yield no improvement it is advised
! to analyze the integrand in order to
! determine the integration difficulaties.
! if the position of a local difficulty can
! be determined (i.e.singularity,
! discontinuity within the interval) one
! will probably gain from splitting up the
! interval at this point and calling the
! integrator on the subranges. if possible,
! an appropriate special-purpose integrator
! should be used which is designed for
! handling the type of difficulty involved.
! 2 : the occurrence of roundoff error is
! detected, which prevents the requested
! tolerance from being achieved.
! 3 : extremely bad integrand behaviour occurs
! at some points of the integration
! interval.
! 6 : the input is invalid, because
! (epsabs.le.0 and
! epsrel.lt.max(50*rel.mach.acc.,0.5d-28))
! or limit.lt.1 or lenw.lt.limit*4.
! result, abserr, neval, last are set
! to zero.
! except when lenw is invalid, iwork(1),
! work(limit*2+1) and work(limit*3+1) are
! set to zero, work(1) is set to a and
! work(limit+1) to b.
implicit none
double precision, external:: f
double precision, intent(in) :: x,a,b,epsabs,epsrel
integer, intent(in) :: key,limit
integer, intent(out) :: ier
double precision, intent(out) :: res,abserr
double precision, allocatable :: work(:)
integer, allocatable :: iwork(:)
integer :: lenw,neval,last
! imsl value for limit is 500
lenw=limit*4
allocate(work(lenw))
allocate(iwork(limit))
call dqag_2d_inner(f,x,a,b,epsabs,epsrel,key,res,abserr,neval,ier,limit,lenw,last,iwork,work)
deallocate(iwork)
deallocate(work)
end subroutine
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Include the modified quadpack files
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
include "fvn_quadpack/dqag_2d_inner.f"
include "fvn_quadpack/dqk15_2d_inner.f"
include "fvn_quadpack/dqk31_2d_outer.f"
include "fvn_quadpack/d1mach.f"
include "fvn_quadpack/dqk31_2d_inner.f"
include "fvn_quadpack/dqage.f"
include "fvn_quadpack/dqk15.f"
include "fvn_quadpack/dqk21.f"
include "fvn_quadpack/dqk31.f"
include "fvn_quadpack/dqk41.f"
include "fvn_quadpack/dqk51.f"
include "fvn_quadpack/dqk61.f"
include "fvn_quadpack/dqk41_2d_outer.f"
include "fvn_quadpack/dqk41_2d_inner.f"
include "fvn_quadpack/dqag_2d_outer.f"
include "fvn_quadpack/dqpsrt.f"
include "fvn_quadpack/dqag.f"
include "fvn_quadpack/dqage_2d_outer.f"
include "fvn_quadpack/dqage_2d_inner.f"
include "fvn_quadpack/dqk51_2d_outer.f"
include "fvn_quadpack/dqk51_2d_inner.f"
include "fvn_quadpack/dqk61_2d_outer.f"
include "fvn_quadpack/dqk21_2d_outer.f"
include "fvn_quadpack/dqk61_2d_inner.f"
include "fvn_quadpack/dqk21_2d_inner.f"
include "fvn_quadpack/dqk15_2d_outer.f"
end module fvn
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