!--------------------------------------------------------------------------------------------------!
!   CP2K: A general program to perform molecular dynamics simulations                              !
!   Copyright (C) 2000 - 2018  CP2K developers group                                               !
!--------------------------------------------------------------------------------------------------!

! **************************************************************************************************
!> \brief various cholesky decomposition related routines
!> \par History
!>      09.2002 created [fawzi]
!> \author Fawzi Mohamed
! **************************************************************************************************
MODULE cp_fm_cholesky
   USE cp_blacs_env,                    ONLY: cp_blacs_env_type
   USE cp_fm_types,                     ONLY: cp_fm_type
   USE cp_log_handling,                 ONLY: cp_to_string
   USE kinds,                           ONLY: dp,&
                                              sp
#include "../base/base_uses.f90"

   IMPLICIT NONE
   PRIVATE

   LOGICAL, PRIVATE, PARAMETER :: debug_this_module = .TRUE.
   CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'cp_fm_cholesky'

   PUBLIC :: cp_fm_cholesky_decompose, cp_fm_cholesky_invert, &
             cp_fm_cholesky_reduce, cp_fm_cholesky_restore

!***
CONTAINS

! **************************************************************************************************
!> \brief used to replace a symmetric positive def. matrix M with its cholesky
!>      decomposition U: M = U^T * U, with U upper triangular
!> \param matrix the matrix to replace with its cholesky decomposition
!> \param n the number of row (and columns) of the matrix &
!>        (defaults to the min(size(matrix)))
!> \param info_out ...
!> \par History
!>      05.2002 created [JVdV]
!>      12.2002 updated, added n optional parm [fawzi]
!> \author Joost
! **************************************************************************************************
   SUBROUTINE cp_fm_cholesky_decompose(matrix, n, info_out)
      TYPE(cp_fm_type), POINTER                :: matrix
      INTEGER, INTENT(in), OPTIONAL            :: n
      INTEGER, INTENT(out), OPTIONAL           :: info_out

      CHARACTER(len=*), PARAMETER :: routineN = 'cp_fm_cholesky_decompose', &
                                     routineP = moduleN//':'//routineN

      INTEGER                                  :: handle, info, my_n
      REAL(KIND=dp), DIMENSION(:, :), POINTER  :: a
      REAL(KIND=sp), DIMENSION(:, :), POINTER  :: a_sp
#if defined(__SCALAPACK)
      INTEGER, DIMENSION(9)                    :: desca
#endif

      CALL timeset(routineN, handle)

      my_n = MIN(matrix%matrix_struct%nrow_global, &
                 matrix%matrix_struct%ncol_global)
      IF (PRESENT(n)) THEN
         CPASSERT(n <= my_n)
         my_n = n
      END IF

      a => matrix%local_data
      a_sp => matrix%local_data_sp

#if defined(__SCALAPACK)
      desca(:) = matrix%matrix_struct%descriptor(:)

      IF (matrix%use_sp) THEN
         CALL pspotrf('U', my_n, a_sp(1, 1), 1, 1, desca, info)
      ELSE
         CALL pdpotrf('U', my_n, a(1, 1), 1, 1, desca, info)
      ENDIF

#else

      IF (matrix%use_sp) THEN
         CALL spotrf('U', my_n, a_sp(1, 1), SIZE(a_sp, 1), info)
      ELSE
         CALL dpotrf('U', my_n, a(1, 1), SIZE(a, 1), info)
      ENDIF

#endif

      IF (PRESENT(info_out)) THEN
         info_out = info
      ELSE
         IF (info /= 0) &
            CALL cp_abort(__LOCATION__, &
                          "Cholesky decompose failed: the matrix is not positive definite or ill-conditioned.")
      END IF

      CALL timestop(handle)

   END SUBROUTINE cp_fm_cholesky_decompose

! **************************************************************************************************
!> \brief used to replace the cholesky decomposition by the inverse
!> \param matrix the matrix to invert (must be an upper triangular matrix)
!> \param n size of the matrix to invert (defaults to the min(size(matrix)))
!> \param info_out ...
!> \par History
!>      05.2002 created [JVdV]
!> \author Joost VandeVondele
! **************************************************************************************************
   SUBROUTINE cp_fm_cholesky_invert(matrix, n, info_out)
      TYPE(cp_fm_type), POINTER                 :: matrix
      INTEGER, INTENT(in), OPTIONAL             :: n
      INTEGER, INTENT(OUT), OPTIONAL            :: info_out

      CHARACTER(len=*), PARAMETER :: routineN = 'cp_fm_cholesky_invert', &
                                     routineP = moduleN//':'//routineN
      REAL(KIND=dp), DIMENSION(:, :), POINTER  :: a
      REAL(KIND=sp), DIMENSION(:, :), POINTER  :: a_sp
      INTEGER                                   :: info, handle
      INTEGER                                   :: my_n
#if defined(__SCALAPACK)
      INTEGER, DIMENSION(9)                     :: desca
#endif

      CALL timeset(routineN, handle)

      my_n = MIN(matrix%matrix_struct%nrow_global, &
                 matrix%matrix_struct%ncol_global)
      IF (PRESENT(n)) THEN
         CPASSERT(n <= my_n)
         my_n = n
      END IF

      a => matrix%local_data
      a_sp => matrix%local_data_sp

#if defined(__SCALAPACK)

      desca(:) = matrix%matrix_struct%descriptor(:)

      IF (matrix%use_sp) THEN
         CALL pspotri('U', my_n, a_sp(1, 1), 1, 1, desca, info)
      ELSE
         CALL pdpotri('U', my_n, a(1, 1), 1, 1, desca, info)
      ENDIF

#else

      IF (matrix%use_sp) THEN
         CALL spotri('U', my_n, a_sp(1, 1), SIZE(a_sp, 1), info)
      ELSE
         CALL dpotri('U', my_n, a(1, 1), SIZE(a, 1), info)
      ENDIF

#endif

      IF (PRESENT(info_out)) THEN
         info_out = info
      ELSE
         IF (info /= 0) &
            CPABORT("Cholesky invert failed: the matrix is not positive definite or ill-conditioned.")
      END IF

      CALL timestop(handle)

   END SUBROUTINE cp_fm_cholesky_invert

! **************************************************************************************************
!> \brief reduce a matrix pencil A,B to normal form
!>      B has to be cholesky decomposed with  cp_fm_cholesky_decompose
!>      before calling this routine
!>      A,B -> inv(U^T)*A*inv(U),1
!>      (AX=BX -> inv(U^T)*A*inv(U)*U*X=U*X hence evecs U*X)
!> \param matrix the symmetric matrix A
!> \param matrixb the cholesky decomposition of matrix B
!> \param itype ...
!> \par History
!>      05.2002 created [JVdV]
!> \author Joost VandeVondele
! **************************************************************************************************
   SUBROUTINE cp_fm_cholesky_reduce(matrix, matrixb, itype)
      TYPE(cp_fm_type), POINTER           :: matrix, matrixb
      INTEGER, OPTIONAL                   :: itype

      CHARACTER(len=*), PARAMETER :: routineN = 'cp_fm_cholesky_reduce', &
                                     routineP = moduleN//':'//routineN
      REAL(KIND=dp), DIMENSION(:, :), POINTER  :: a, b
      INTEGER                                   :: info, handle
      INTEGER                                   :: n, my_itype
#if defined(__SCALAPACK)
      REAL(KIND=dp)                             :: scale
      INTEGER, DIMENSION(9)                     :: desca, descb
#endif

      CALL timeset(routineN, handle)

      n = matrix%matrix_struct%nrow_global

      my_itype = 1
      IF (PRESENT(itype)) my_itype = itype

      a => matrix%local_data
      b => matrixb%local_data

#if defined(__SCALAPACK)

      desca(:) = matrix%matrix_struct%descriptor(:)
      descb(:) = matrixb%matrix_struct%descriptor(:)

      CALL pdsygst(my_itype, 'U', n, a(1, 1), 1, 1, desca, b(1, 1), 1, 1, descb, scale, info)

      ! this is supposed to be one in current version of lapack
      ! if not, eigenvalues have to be scaled by this number
      IF (scale /= 1.0_dp) &
         CPABORT("scale not equal 1 (scale="//cp_to_string(scale)//")")
#else

      CALL dsygst(my_itype, 'U', n, a(1, 1), n, b(1, 1), n, info)

#endif

      CPASSERT(info == 0)

      CALL timestop(handle)

   END SUBROUTINE cp_fm_cholesky_reduce

!
! op can be "SOLVE" (out = U^-1 * in ) or "MULTIPLY"   (out = U * in )
! pos can be "LEFT" or "RIGHT" (U at the left or at the right)
!
! DEPRECATED, see cp_fm_basic_linalg:cp_fm_triangular_multiply
!
! **************************************************************************************************
!> \brief ...
!> \param matrix ...
!> \param neig ...
!> \param matrixb ...
!> \param matrixout ...
!> \param op ...
!> \param pos ...
!> \param transa ...
! **************************************************************************************************
   SUBROUTINE cp_fm_cholesky_restore(matrix, neig, matrixb, matrixout, op, pos, transa)
      TYPE(cp_fm_type), POINTER          :: matrix, matrixb, matrixout
      INTEGER, INTENT(IN)                         :: neig
      CHARACTER(LEN=*), INTENT(IN)        :: op
      CHARACTER(LEN=*), INTENT(IN), OPTIONAL :: pos
      CHARACTER(LEN=*), INTENT(IN), OPTIONAL :: transa

      CHARACTER(len=*), PARAMETER :: routineN = 'cp_fm_cholesky_restore', &
                                     routineP = moduleN//':'//routineN
      REAL(KIND=dp), DIMENSION(:, :), POINTER         :: a, b, out
      REAL(KIND=sp), DIMENSION(:, :), POINTER         :: a_sp, b_sp, out_sp
      INTEGER                                   :: itype, handle
      INTEGER                                   :: n
      REAL(KIND=dp)                           :: alpha
      INTEGER                                   :: myprow, mypcol
      TYPE(cp_blacs_env_type), POINTER          :: context
      CHARACTER                                 :: chol_pos, chol_transa
#if defined(__SCALAPACK)
      INTEGER                                   :: i
      INTEGER, DIMENSION(9)                     :: desca, descb, descout
#endif

      CALL timeset(routineN, handle)

      context => matrix%matrix_struct%context
      myprow = context%mepos(1)
      mypcol = context%mepos(2)
      n = matrix%matrix_struct%nrow_global
      itype = 1
      IF (op /= "SOLVE" .AND. op /= "MULTIPLY") &
         CPABORT("wrong argument op")

      IF (PRESENT(pos)) THEN
         SELECT CASE (pos)
         CASE ("LEFT")
            chol_pos = 'L'
         CASE ("RIGHT")
            chol_pos = 'R'
         CASE DEFAULT
            CPABORT("wrong argument pos")
         END SELECT
      ELSE
         chol_pos = 'L'
      ENDIF

      chol_transa = 'N'
      IF (PRESENT(transa)) chol_transa = transa

      IF ((matrix%use_sp .NEQV. matrixb%use_sp) .OR. (matrix%use_sp .NEQV. matrixout%use_sp)) &
         CPABORT("not the same precision")

      ! notice b is the cholesky guy
      a => matrix%local_data
      b => matrixb%local_data
      out => matrixout%local_data
      a_sp => matrix%local_data_sp
      b_sp => matrixb%local_data_sp
      out_sp => matrixout%local_data_sp

#if defined(__SCALAPACK)

      desca(:) = matrix%matrix_struct%descriptor(:)
      descb(:) = matrixb%matrix_struct%descriptor(:)
      descout(:) = matrixout%matrix_struct%descriptor(:)
      alpha = 1.0_dp
      DO i = 1, neig
         IF (matrix%use_sp) THEN
            CALL pscopy(n, a_sp(1, 1), 1, i, desca, 1, out_sp(1, 1), 1, i, descout, 1)
         ELSE
            CALL pdcopy(n, a(1, 1), 1, i, desca, 1, out(1, 1), 1, i, descout, 1)
         ENDIF
      ENDDO
      IF (op .EQ. "SOLVE") THEN
         IF (matrix%use_sp) THEN
            CALL pstrsm(chol_pos, 'U', chol_transa, 'N', n, neig, REAL(alpha, sp), b_sp(1, 1), 1, 1, descb, &
                        out_sp(1, 1), 1, 1, descout)
         ELSE
            CALL pdtrsm(chol_pos, 'U', chol_transa, 'N', n, neig, alpha, b(1, 1), 1, 1, descb, out(1, 1), 1, 1, descout)
         ENDIF
      ELSE
         IF (matrix%use_sp) THEN
            CALL pstrmm(chol_pos, 'U', chol_transa, 'N', n, neig, REAL(alpha, sp), b_sp(1, 1), 1, 1, descb, &
                        out_sp(1, 1), 1, 1, descout)
         ELSE
            CALL pdtrmm(chol_pos, 'U', chol_transa, 'N', n, neig, alpha, b(1, 1), 1, 1, descb, out(1, 1), 1, 1, descout)
         ENDIF
      ENDIF
#else

      alpha = 1.0_dp
      IF (matrix%use_sp) THEN
         CALL scopy(neig*n, a_sp(1, 1), 1, out_sp(1, 1), 1)
      ELSE
         CALL dcopy(neig*n, a(1, 1), 1, out(1, 1), 1)
      ENDIF
      IF (op .EQ. "SOLVE") THEN
         IF (matrix%use_sp) THEN
            CALL strsm(chol_pos, 'U', chol_transa, 'N', n, neig, REAL(alpha, sp), b_sp(1, 1), SIZE(b_sp, 1), out_sp(1, 1), n)
         ELSE
            CALL dtrsm(chol_pos, 'U', chol_transa, 'N', n, neig, alpha, b(1, 1), SIZE(b, 1), out(1, 1), n)
         ENDIF
      ELSE
         IF (matrix%use_sp) THEN
            CALL strmm(chol_pos, 'U', chol_transa, 'N', n, neig, REAL(alpha, sp), b_sp(1, 1), n, out_sp(1, 1), n)
         ELSE
            CALL dtrmm(chol_pos, 'U', chol_transa, 'N', n, neig, alpha, b(1, 1), n, out(1, 1), n)
         ENDIF
      ENDIF

#endif

      CALL timestop(handle)

   END SUBROUTINE cp_fm_cholesky_restore

END MODULE cp_fm_cholesky
