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  module fvn_sparse
  use fvn_common
  implicit none
  
  ! Sparse solving
  interface fvn_sparse_solve
      module procedure fvn_zl_sparse_solve,fvn_zi_sparse_solve,fvn_dl_sparse_solve,fvn_di_sparse_solve
  end interface fvn_sparse_solve
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  interface fvn_sparse_det
      module procedure fvn_zl_sparse_det,fvn_zi_sparse_det,fvn_dl_sparse_det,fvn_di_sparse_det
  end interface fvn_sparse_det
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  contains
  !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
  !
  ! SPARSE RESOLUTION
  !
  !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
  ! 
  ! Sparse resolution is done by interfaçing Tim Davi's UMFPACK
  ! http://www.cise.ufl.edu/research/sparse/SuiteSparse/
  ! Used packages from SuiteSparse : AMD,UMFPACK,UFconfig
  !
  ! Solve Ax=B using UMFPACK
  !
  ! Where A is a sparse matrix given in its triplet form 
  ! T -> non zero elements
  ! Ti,Tj -> row and column index (1-based) of the given elt
  ! n : rank of matrix A
  ! nz : number of non zero elts
  !
  ! fvn_*_sparse_solve
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  ! * = zl : double complex + integer(kind=dp_kind)
  ! * = zi : double complex + integer(kind=sp_kind)
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  !
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  subroutine fvn_zl_sparse_solve(n,nz,T,Ti,Tj,B,x,status,det)
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  implicit none
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  integer(kind=dp_kind), intent(in) :: n,nz
  complex(kind=dp_kind),dimension(nz),intent(in) :: T
  integer(kind=dp_kind),dimension(nz),intent(in)  :: Ti,Tj
  complex(kind=dp_kind),dimension(n),intent(in) :: B
  complex(kind=dp_kind),dimension(n),intent(out) :: x
  integer(kind=dp_kind), intent(out) :: status
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  real(kind=dp_kind), dimension(3), optional, intent(out) :: det
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  integer(kind=dp_kind),dimension(:),allocatable :: wTi,wTj
  real(kind=dp_kind),dimension(:),allocatable :: Tx,Tz
  real(kind=dp_kind),dimension(:),allocatable :: Ax,Az
  integer(kind=dp_kind),dimension(:),allocatable :: Ap,Ai
  integer(kind=dp_kind) :: symbolic,numeric
  real(kind=dp_kind),dimension(:),allocatable :: xx,xz,bx,bz
  real(kind=dp_kind),dimension(90) :: info
  real(kind=dp_kind),dimension(20) :: control
  integer(kind=dp_kind) :: sys
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  status=0
  
  ! we use a working copy of Ti and Tj to perform 1-based to 0-based translation
  ! Tx and Tz are the real and imaginary parts of T
  allocate(wTi(nz),wTj(nz))
  allocate(Tx(nz),Tz(nz))
  Tx=dble(T)
  Tz=aimag(T)
  wTi=Ti-1
  wTj=Tj-1
  allocate(Ax(nz),Az(nz))
  allocate(Ap(n+1),Ai(nz))
  
  ! perform the triplet to compressed column form -> Ap,Ai,Ax,Az
  call umfpack_zl_triplet_to_col(n,n,nz,wTi,wTj,Tx,Tz,Ap,Ai,Ax,Az,status)
  ! if status is not zero a problem has occured
  if (status /= 0) then
      write(*,*) "Problem during umfpack_zl_triplet_to_col"
  endif
  
  ! Define defaults control values
  call umfpack_zl_defaults(control)
  
  ! Symbolic analysis
  call umfpack_zl_symbolic(n,n,Ap,Ai,Ax,Az,symbolic, control, info)
  ! info(1) should be zero
  if (info(1) /= 0) then
      write(*,*) "Problem during symbolic analysis"
      status=info(1)
  endif
  
  ! Numerical factorization
  call umfpack_zl_numeric (Ap, Ai, Ax, Az, symbolic, numeric, control, info)
  ! info(1) should be zero
  if (info(1) /= 0) then
      write(*,*) "Problem during numerical factorization"
      status=info(1)
  endif
  
  ! free the C symbolic pointer
  call umfpack_zl_free_symbolic (symbolic)
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  ! if parameter det is present, the determinant of the matrix is calculated
  if (present(det) ) then
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    call umfpack_zl_get_determinant(det(1),det(2),det(3),numeric,info,status)
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    ! info(1) should be zero
    if (info(1) /= 0) then
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        if ( (info(1) < 1) .or. (info(1) >3) ) then ! not a warning
            write(*,*) "Problem during sparse determinant, returned code : ",info(1)
        endif
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        status=info(1)
    endif
  endif
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  allocate(bx(n),bz(n),xx(n),xz(n))
  bx=dble(B)
  bz=aimag(B)
  sys=0
  ! sys may be used to define type of solving -> see umfpack.h
  
  ! Solving
  call umfpack_zl_solve (sys, Ap, Ai, Ax,Az, xx,xz, bx,bz, numeric, control, info)
  ! info(1) should be zero
  if (info(1) /= 0) then
      write(*,*) "Problem during solving"
      status=info(1)
  endif
  
  
  ! free the C numeric pointer
  call umfpack_zl_free_numeric (numeric)
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  x=cmplx(xx,xz,dp_kind)
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  deallocate(bx,bz,xx,xz)
  deallocate(Ax,Az)
  deallocate(Tx,Tz)
  deallocate(wTi,wTj)
  end subroutine
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  subroutine fvn_zi_sparse_solve(n,nz,T,Ti,Tj,B,x,status,det)
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  implicit none
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  integer(kind=sp_kind), intent(in) :: n,nz
  complex(kind=dp_kind),dimension(nz),intent(in) :: T
  integer(kind=sp_kind),dimension(nz),intent(in)  :: Ti,Tj
  complex(kind=dp_kind),dimension(n),intent(in) :: B
  complex(kind=dp_kind),dimension(n),intent(out) :: x
  integer(kind=sp_kind), intent(out) :: status
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  real(kind=dp_kind), dimension(3), optional, intent(out) :: det
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  integer(kind=sp_kind),dimension(:),allocatable :: wTi,wTj
  real(kind=dp_kind),dimension(:),allocatable :: Tx,Tz
  real(kind=dp_kind),dimension(:),allocatable :: Ax,Az
  integer(kind=sp_kind),dimension(:),allocatable :: Ap,Ai
  !integer(kind=dp_kind) :: symbolic,numeric
  integer(kind=sp_kind),dimension(2) :: symbolic,numeric
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  ! As symbolic and numeric are used to store a C pointer, it is necessary to
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  ! still use an integer(kind=dp_kind) for 64bits machines
  ! An other possibility : integer(kind=sp_kind),dimension(2) :: symbolic,numeric
  real(kind=dp_kind),dimension(:),allocatable :: xx,xz,bx,bz
  real(kind=dp_kind),dimension(90) :: info
  real(kind=dp_kind),dimension(20) :: control
  integer(kind=sp_kind) :: sys
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  status=0
  ! we use a working copy of Ti and Tj to perform 1-based to 0-based translation
  ! Tx and Tz are the real and imaginary parts of T
  allocate(wTi(nz),wTj(nz))
  allocate(Tx(nz),Tz(nz))
  Tx=dble(T)
  Tz=aimag(T)
  wTi=Ti-1
  wTj=Tj-1
  allocate(Ax(nz),Az(nz))
  allocate(Ap(n+1),Ai(nz))
  
  ! perform the triplet to compressed column form -> Ap,Ai,Ax,Az
  call umfpack_zi_triplet_to_col(n,n,nz,wTi,wTj,Tx,Tz,Ap,Ai,Ax,Az,status)
  ! if status is not zero a problem has occured
  if (status /= 0) then
      write(*,*) "Problem during umfpack_zl_triplet_to_col"
  endif
  
  ! Define defaults control values
  call umfpack_zi_defaults(control)
  
  ! Symbolic analysis
  call umfpack_zi_symbolic(n,n,Ap,Ai,Ax,Az,symbolic, control, info)
  ! info(1) should be zero
  if (info(1) /= 0) then
      write(*,*) "Problem during symbolic analysis"
      status=info(1)
  endif
  
  ! Numerical factorization
  call umfpack_zi_numeric (Ap, Ai, Ax, Az, symbolic, numeric, control, info)
  ! info(1) should be zero
  if (info(1) /= 0) then
      write(*,*) "Problem during numerical factorization"
      status=info(1)
  endif
  
  ! free the C symbolic pointer
  call umfpack_zi_free_symbolic (symbolic)
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  ! if parameter det is present, the determinant of the matrix is calculated
  if (present(det) ) then
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    call umfpack_zi_get_determinant(det(1),det(2),det(3),numeric,info,status)
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    ! info(1) should be zero
    if (info(1) /= 0) then
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        if ( (info(1) < 1) .or. (info(1) >3) ) then ! not a warning
            write(*,*) "Problem during sparse determinant, returned code : ",info(1)
        endif
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        status=info(1)
    endif
  endif
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  allocate(bx(n),bz(n),xx(n),xz(n))
  bx=dble(B)
  bz=aimag(B)
  sys=0
  ! sys may be used to define type of solving -> see umfpack.h
  
  ! Solving
  call umfpack_zi_solve (sys, Ap, Ai, Ax,Az, xx,xz, bx,bz, numeric, control, info)
  ! info(1) should be zero
  if (info(1) /= 0) then
      write(*,*) "Problem during solving"
      status=info(1)
  endif
  
  ! free the C numeric pointer
  call umfpack_zi_free_numeric (numeric)
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  x=cmplx(xx,xz,dp_kind)
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  deallocate(bx,bz,xx,xz)
  deallocate(Ax,Az)
  deallocate(Tx,Tz)
  deallocate(wTi,wTj)
  end subroutine
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  subroutine fvn_dl_sparse_solve(n,nz,T,Ti,Tj,B,x,status,det)
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  implicit none
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  integer(kind=dp_kind), intent(in) :: n,nz
  real(kind=dp_kind),dimension(nz),intent(in) :: T
  integer(kind=dp_kind),dimension(nz),intent(in)  :: Ti,Tj
  real(kind=dp_kind),dimension(n),intent(in) :: B
  real(kind=dp_kind),dimension(n),intent(out) :: x
  integer(kind=dp_kind), intent(out) :: status
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  real(kind=dp_kind), dimension(2), optional, intent(out) :: det
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  integer(kind=dp_kind),dimension(:),allocatable :: wTi,wTj
  real(kind=dp_kind),dimension(:),allocatable :: A
  integer(kind=dp_kind),dimension(:),allocatable :: Ap,Ai
  !integer(kind=dp_kind) :: symbolic,numeric
  integer(kind=dp_kind) :: symbolic,numeric
  real(kind=dp_kind),dimension(90) :: info
  real(kind=dp_kind),dimension(20) :: control
  integer(kind=dp_kind) :: sys
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  status=0
  ! we use a working copy of Ti and Tj to perform 1-based to 0-based translation
  allocate(wTi(nz),wTj(nz))
  wTi=Ti-1
  wTj=Tj-1
  allocate(A(nz))
  allocate(Ap(n+1),Ai(nz))
  
  ! perform the triplet to compressed column form -> Ap,Ai,Ax,Az
  call umfpack_dl_triplet_to_col(n,n,nz,wTi,wTj,T,Ap,Ai,A,status)
  ! if status is not zero a problem has occured
  if (status /= 0) then
      write(*,*) "Problem during umfpack_dl_triplet_to_col"
  endif
  
  ! Define defaults control values
  call umfpack_dl_defaults(control)
  
  ! Symbolic analysis
  call umfpack_dl_symbolic(n,n,Ap,Ai,A,symbolic, control, info)
  ! info(1) should be zero
  if (info(1) /= 0) then
      write(*,*) "Problem during symbolic analysis"
      status=info(1)
  endif
  
  ! Numerical factorization
  call umfpack_dl_numeric (Ap, Ai, A, symbolic, numeric, control, info)
  ! info(1) should be zero
  if (info(1) /= 0) then
      write(*,*) "Problem during numerical factorization"
      status=info(1)
  endif
  
  ! free the C symbolic pointer
  call umfpack_dl_free_symbolic (symbolic)
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  ! if parameter det is present, the determinant of the matrix is calculated
  if (present(det) ) then
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    call umfpack_dl_get_determinant(det(1),det(2),numeric,info,status)
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    ! info(1) should be zero
    if (info(1) /= 0) then
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        if ( (info(1) < 1) .or. (info(1) >3) ) then ! not a warning
            write(*,*) "Problem during sparse determinant, returned code : ",info(1)
        endif
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        status=info(1)
    endif
  endif
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  sys=0
  ! sys may be used to define type of solving -> see umfpack.h
  
  ! Solving
  call umfpack_dl_solve (sys, Ap, Ai, A, x, B, numeric, control, info)
  ! info(1) should be zero
  if (info(1) /= 0) then
      write(*,*) "Problem during solving"
      status=info(1)
  endif
  
  ! free the C numeric pointer
  call umfpack_dl_free_numeric (numeric)
  
  deallocate(A)
  deallocate(wTi,wTj)
  end subroutine
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  subroutine fvn_di_sparse_solve(n,nz,T,Ti,Tj,B,x,status,det)
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  implicit none
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  integer(kind=sp_kind), intent(in) :: n,nz
  real(kind=dp_kind),dimension(nz),intent(in) :: T
  integer(kind=sp_kind),dimension(nz),intent(in)  :: Ti,Tj
  real(kind=dp_kind),dimension(n),intent(in) :: B
  real(kind=dp_kind),dimension(n),intent(out) :: x
  integer(kind=sp_kind), intent(out) :: status
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  real(kind=dp_kind), dimension(2), optional, intent(out) :: det
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  integer(kind=sp_kind),dimension(:),allocatable :: wTi,wTj
  real(kind=dp_kind),dimension(:),allocatable :: A
  integer(kind=sp_kind),dimension(:),allocatable :: Ap,Ai
  !integer(kind=dp_kind) :: symbolic,numeric
  integer(kind=sp_kind),dimension(2) :: symbolic,numeric
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  ! As symbolic and numeric are used to store a C pointer, it is necessary to
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  ! still use an integer(kind=dp_kind) for 64bits machines
  ! An other possibility : integer(kind=sp_kind),dimension(2) :: symbolic,numeric
  real(kind=dp_kind),dimension(90) :: info
  real(kind=dp_kind),dimension(20) :: control
  integer(kind=sp_kind) :: sys
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  status=0
  ! we use a working copy of Ti and Tj to perform 1-based to 0-based translation
  allocate(wTi(nz),wTj(nz))
  wTi=Ti-1
  wTj=Tj-1
  allocate(A(nz))
  allocate(Ap(n+1),Ai(nz))
  
  ! perform the triplet to compressed column form -> Ap,Ai,Ax,Az
  call umfpack_di_triplet_to_col(n,n,nz,wTi,wTj,T,Ap,Ai,A,status)
  ! if status is not zero a problem has occured
  if (status /= 0) then
      write(*,*) "Problem during umfpack_di_triplet_to_col"
  endif
  
  ! Define defaults control values
  call umfpack_di_defaults(control)
  
  ! Symbolic analysis
  call umfpack_di_symbolic(n,n,Ap,Ai,A,symbolic, control, info)
  ! info(1) should be zero
  if (info(1) /= 0) then
      write(*,*) "Problem during symbolic analysis"
      status=info(1)
  endif
  
  ! Numerical factorization
  call umfpack_di_numeric (Ap, Ai, A, symbolic, numeric, control, info)
  ! info(1) should be zero
  if (info(1) /= 0) then
      write(*,*) "Problem during numerical factorization"
      status=info(1)
  endif
  
  ! free the C symbolic pointer
  call umfpack_di_free_symbolic (symbolic)
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  ! if parameter det is present, the determinant of the matrix is calculated
  if (present(det) ) then
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    call umfpack_di_get_determinant(det(1),det(2),numeric,info,status)
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    ! info(1) should be zero
    if (info(1) /= 0) then
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        if ( (info(1) < 1) .or. (info(1) >3) ) then ! not a warning
            write(*,*) "Problem during sparse determinant, returned code : ",info(1)
        endif
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        status=info(1)
    endif
  endif
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  sys=0
  ! sys may be used to define type of solving -> see umfpack.h
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  ! Solving
  call umfpack_di_solve (sys, Ap, Ai, A, x, B, numeric, control, info)
  ! info(1) should be zero
  if (info(1) /= 0) then
      write(*,*) "Problem during solving"
      status=info(1)
  endif
  
  ! free the C numeric pointer
  call umfpack_di_free_numeric (numeric)
  
  deallocate(A)
  deallocate(wTi,wTj)
  end subroutine
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  !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
  !
  ! SPARSE DETERMINANT
  !
  !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
  subroutine fvn_zl_sparse_det(n,nz,T,Ti,Tj,det,status)
  implicit none
  integer(kind=dp_kind), intent(in) :: n,nz
  complex(kind=dp_kind),dimension(nz),intent(in) :: T
  integer(kind=dp_kind),dimension(nz),intent(in)  :: Ti,Tj
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  real(kind=dp_kind), dimension(3), intent(out) :: det
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  integer(kind=dp_kind), intent(out) :: status
  
  integer(kind=dp_kind),dimension(:),allocatable :: wTi,wTj
  real(kind=dp_kind),dimension(:),allocatable :: Tx,Tz
  real(kind=dp_kind),dimension(:),allocatable :: Ax,Az
  integer(kind=dp_kind),dimension(:),allocatable :: Ap,Ai
  integer(kind=dp_kind) :: symbolic,numeric
  real(kind=dp_kind),dimension(90) :: info
  real(kind=dp_kind),dimension(20) :: control
  real(kind=dp_kind) :: Mx,Mz,Ex
  
  
  status=0
  
  ! we use a working copy of Ti and Tj to perform 1-based to 0-based translation
  ! Tx and Tz are the real and imaginary parts of T
  allocate(wTi(nz),wTj(nz))
  allocate(Tx(nz),Tz(nz))
  Tx=dble(T)
  Tz=aimag(T)
  wTi=Ti-1
  wTj=Tj-1
  allocate(Ax(nz),Az(nz))
  allocate(Ap(n+1),Ai(nz))
  
  ! perform the triplet to compressed column form -> Ap,Ai,Ax,Az
  call umfpack_zl_triplet_to_col(n,n,nz,wTi,wTj,Tx,Tz,Ap,Ai,Ax,Az,status)
  ! if status is not zero a problem has occured
  if (status /= 0) then
      write(*,*) "Problem during umfpack_zl_triplet_to_col"
  endif
  
  ! Define defaults control values
  call umfpack_zl_defaults(control)
  
  ! Symbolic analysis
  call umfpack_zl_symbolic(n,n,Ap,Ai,Ax,Az,symbolic, control, info)
  ! info(1) should be zero
  if (info(1) /= 0) then
      write(*,*) "Problem during symbolic analysis"
      status=info(1)
  endif
  
  ! Numerical factorization
  call umfpack_zl_numeric (Ap, Ai, Ax, Az, symbolic, numeric, control, info)
  ! info(1) should be zero
  if (info(1) /= 0) then
      write(*,*) "Problem during numerical factorization"
      status=info(1)
  endif
  
  ! free the C symbolic pointer
  call umfpack_zl_free_symbolic (symbolic)
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  call umfpack_zl_get_determinant(det(1),det(2),det(3),numeric,info,status)
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  ! info(1) should be zero
  if (info(1) /= 0) then
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        if ( (info(1) < 1) .or. (info(1) >3) ) then ! not a warning
            write(*,*) "Problem during sparse determinant, returned code : ",info(1)
        endif
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      status=info(1)
  endif
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  ! free the C numeric pointer
  call umfpack_zl_free_numeric (numeric)
  
  deallocate(Ax,Az)
  deallocate(Tx,Tz)
  deallocate(wTi,wTj)
  end subroutine
  
  
  subroutine fvn_zi_sparse_det(n,nz,T,Ti,Tj,det,status)
  implicit none
  integer(kind=sp_kind), intent(in) :: n,nz
  complex(kind=dp_kind),dimension(nz),intent(in) :: T
  integer(kind=sp_kind),dimension(nz),intent(in)  :: Ti,Tj
  integer(kind=sp_kind), intent(out) :: status
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  real(kind=dp_kind), dimension(3), intent(out) :: det
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  integer(kind=sp_kind),dimension(:),allocatable :: wTi,wTj
  real(kind=dp_kind),dimension(:),allocatable :: Tx,Tz
  real(kind=dp_kind),dimension(:),allocatable :: Ax,Az
  integer(kind=sp_kind),dimension(:),allocatable :: Ap,Ai
  !integer(kind=dp_kind) :: symbolic,numeric
  integer(kind=sp_kind),dimension(2) :: symbolic,numeric
  ! As symbolic and numeric are used to store a C pointer, it is necessary to
  ! still use an integer(kind=dp_kind) for 64bits machines
  ! An other possibility : integer(kind=sp_kind),dimension(2) :: symbolic,numeric
  real(kind=dp_kind),dimension(90) :: info
  real(kind=dp_kind),dimension(20) :: control
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  status=0
  ! we use a working copy of Ti and Tj to perform 1-based to 0-based translation
  ! Tx and Tz are the real and imaginary parts of T
  allocate(wTi(nz),wTj(nz))
  allocate(Tx(nz),Tz(nz))
  Tx=dble(T)
  Tz=aimag(T)
  wTi=Ti-1
  wTj=Tj-1
  allocate(Ax(nz),Az(nz))
  allocate(Ap(n+1),Ai(nz))
  
  ! perform the triplet to compressed column form -> Ap,Ai,Ax,Az
  call umfpack_zi_triplet_to_col(n,n,nz,wTi,wTj,Tx,Tz,Ap,Ai,Ax,Az,status)
  ! if status is not zero a problem has occured
  if (status /= 0) then
      write(*,*) "Problem during umfpack_zl_triplet_to_col"
  endif
  
  ! Define defaults control values
  call umfpack_zi_defaults(control)
  
  ! Symbolic analysis
  call umfpack_zi_symbolic(n,n,Ap,Ai,Ax,Az,symbolic, control, info)
  ! info(1) should be zero
  if (info(1) /= 0) then
      write(*,*) "Problem during symbolic analysis"
      status=info(1)
  endif
  
  ! Numerical factorization
  call umfpack_zi_numeric (Ap, Ai, Ax, Az, symbolic, numeric, control, info)
  ! info(1) should be zero
  if (info(1) /= 0) then
      write(*,*) "Problem during numerical factorization"
      status=info(1)
  endif
  
  ! free the C symbolic pointer
  call umfpack_zi_free_symbolic (symbolic)
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  call umfpack_zi_get_determinant(det(1),det(2),det(3),numeric,info,status)
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  ! info(1) should be zero
  if (info(1) /= 0) then
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        if ( (info(1) < 1) .or. (info(1) >3) ) then ! not a warning
            write(*,*) "Problem during sparse determinant, returned code : ",info(1)
        endif
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      status=info(1)
  endif
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  ! free the C numeric pointer
  call umfpack_zi_free_numeric (numeric)
  
  deallocate(Ax,Az)
  deallocate(Tx,Tz)
  deallocate(wTi,wTj)
  end subroutine
  
  subroutine fvn_dl_sparse_det(n,nz,T,Ti,Tj,det,status)
  implicit none
  integer(kind=dp_kind), intent(in) :: n,nz
  real(kind=dp_kind),dimension(nz),intent(in) :: T
  integer(kind=dp_kind),dimension(nz),intent(in)  :: Ti,Tj
  integer(kind=dp_kind), intent(out) :: status
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  real(kind=dp_kind), dimension(2), intent(out) :: det
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  integer(kind=dp_kind),dimension(:),allocatable :: wTi,wTj
  real(kind=dp_kind),dimension(:),allocatable :: A
  integer(kind=dp_kind),dimension(:),allocatable :: Ap,Ai
  !integer(kind=dp_kind) :: symbolic,numeric
  integer(kind=dp_kind) :: symbolic,numeric
  real(kind=dp_kind),dimension(90) :: info
  real(kind=dp_kind),dimension(20) :: control
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  status=0
  ! we use a working copy of Ti and Tj to perform 1-based to 0-based translation
  allocate(wTi(nz),wTj(nz))
  wTi=Ti-1
  wTj=Tj-1
  allocate(A(nz))
  allocate(Ap(n+1),Ai(nz))
  
  ! perform the triplet to compressed column form -> Ap,Ai,Ax,Az
  call umfpack_dl_triplet_to_col(n,n,nz,wTi,wTj,T,Ap,Ai,A,status)
  ! if status is not zero a problem has occured
  if (status /= 0) then
      write(*,*) "Problem during umfpack_dl_triplet_to_col"
  endif
  
  ! Define defaults control values
  call umfpack_dl_defaults(control)
  
  ! Symbolic analysis
  call umfpack_dl_symbolic(n,n,Ap,Ai,A,symbolic, control, info)
  ! info(1) should be zero
  if (info(1) /= 0) then
      write(*,*) "Problem during symbolic analysis"
      status=info(1)
  endif
  
  ! Numerical factorization
  call umfpack_dl_numeric (Ap, Ai, A, symbolic, numeric, control, info)
  ! info(1) should be zero
  if (info(1) /= 0) then
      write(*,*) "Problem during numerical factorization"
      status=info(1)
  endif
  
  ! free the C symbolic pointer
  call umfpack_dl_free_symbolic (symbolic)
c64a05f8a   wdaniau   Sparse Determinan... 
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  call umfpack_dl_get_determinant(det(1),det(2),numeric,info,status)
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  ! info(1) should be zero
  if (info(1) /= 0) then
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        if ( (info(1) < 1) .or. (info(1) >3) ) then ! not a warning
            write(*,*) "Problem during sparse determinant, returned code : ",info(1)
        endif
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      status=info(1)
  endif
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  ! free the C numeric pointer
  call umfpack_dl_free_numeric (numeric)
  
  deallocate(A)
  deallocate(wTi,wTj)
  end subroutine
  
  
  subroutine fvn_di_sparse_det(n,nz,T,Ti,Tj,det,status)
  implicit none
  integer(kind=sp_kind), intent(in) :: n,nz
  real(kind=dp_kind),dimension(nz),intent(in) :: T
  integer(kind=sp_kind),dimension(nz),intent(in)  :: Ti,Tj
  integer(kind=sp_kind), intent(out) :: status
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  real(kind=dp_kind), dimension(2), intent(out) :: det
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  integer(kind=sp_kind),dimension(:),allocatable :: wTi,wTj
  real(kind=dp_kind),dimension(:),allocatable :: A
  integer(kind=sp_kind),dimension(:),allocatable :: Ap,Ai
  !integer(kind=dp_kind) :: symbolic,numeric
  integer(kind=sp_kind),dimension(2) :: symbolic,numeric
  ! As symbolic and numeric are used to store a C pointer, it is necessary to
  ! still use an integer(kind=dp_kind) for 64bits machines
  ! An other possibility : integer(kind=sp_kind),dimension(2) :: symbolic,numeric
  real(kind=dp_kind),dimension(90) :: info
  real(kind=dp_kind),dimension(20) :: control
  integer(kind=sp_kind) :: sys
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  status=0
  ! we use a working copy of Ti and Tj to perform 1-based to 0-based translation
  allocate(wTi(nz),wTj(nz))
  wTi=Ti-1
  wTj=Tj-1
  allocate(A(nz))
  allocate(Ap(n+1),Ai(nz))
  
  ! perform the triplet to compressed column form -> Ap,Ai,Ax,Az
  call umfpack_di_triplet_to_col(n,n,nz,wTi,wTj,T,Ap,Ai,A,status)
  ! if status is not zero a problem has occured
  if (status /= 0) then
      write(*,*) "Problem during umfpack_di_triplet_to_col"
  endif
  
  ! Define defaults control values
  call umfpack_di_defaults(control)
  
  ! Symbolic analysis
  call umfpack_di_symbolic(n,n,Ap,Ai,A,symbolic, control, info)
  ! info(1) should be zero
  if (info(1) /= 0) then
      write(*,*) "Problem during symbolic analysis"
      status=info(1)
  endif
  
  ! Numerical factorization
  call umfpack_di_numeric (Ap, Ai, A, symbolic, numeric, control, info)
  ! info(1) should be zero
  if (info(1) /= 0) then
      write(*,*) "Problem during numerical factorization"
      status=info(1)
  endif
  
  
  ! free the C symbolic pointer
  call umfpack_di_free_symbolic (symbolic)
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  call umfpack_di_get_determinant(det(1),det(2),numeric,info,status)
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  ! info(1) should be zero
  if (info(1) /= 0) then
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        if ( (info(1) < 1) .or. (info(1) >3) ) then ! not a warning
            write(*,*) "Problem during sparse determinant, returned code : ",info(1)
        endif
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      status=info(1)
  endif
  
  ! free the C numeric pointer
  call umfpack_di_free_numeric (numeric)
  
  deallocate(A)
  deallocate(wTi,wTj)
  end subroutine
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  end module fvn_sparse