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cholesky.f90
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#if defined(__CUDA)
module cholesky
use cudafor
use cublas
use cusolverDn
logical, save :: cusolver_init=.false.
type(cusolverDnHandle):: handle_cusolver
integer, device :: devInfo_d
integer :: istat
complex(8), parameter:: cone=cmplx( 1.0d+0, 0.0d+0 ), czero=cmplx( 0.0D+0, 0.0D+0 )
real(8) , parameter:: one=1.0d+0, zero=0.0D+0
! Generic interfaces for compute:
! Cholesky factorization:
! dpotrf(double precision) and zpotrf( double complex matrix)
! Inverse of a triangular matrix:
! dtrtri(double precision) and ztrtri( double complex matrix)
! For the TRTRI routines, only the path used by Quantum-Espresso ( Lower, non-unit)
! is implemented on GPU.
! The CPU routines will be in the BLAS library, we are just specifying the interface
! to dispatch to the CPU or GPU based on the properties of the matrix A
interface dpotrf
subroutine dpotrf( uplo, n, A, lda, info )
use kinds, only : dp
character:: uplo
integer:: n, lda,info
real(dp):: A(lda,*)
end subroutine dpotrf
module procedure dpotrf_gpu
end interface dpotrf
interface zpotrf
subroutine zpotrf( uplo, n, A, lda, info )
use kinds, only : dp
character:: uplo
integer :: n, lda,info
complex(dp):: A(lda,*)
end subroutine zpotrf
module procedure zpotrf_gpu
end interface zpotrf
interface dtrtri
subroutine dtrtri( uplo, diag, n, A, lda, info )
use kinds, only : dp
character:: uplo, diag
integer:: n, lda, info
real(dp):: A(lda,*)
end subroutine dtrtri
module procedure dtrtri_gpu
end interface dtrtri
interface ztrtri
subroutine ztrtri( uplo, diag, n, A, lda, info )
use kinds, only : dp
character:: uplo, diag
integer :: n, lda,info
complex(dp):: A(lda,*)
end subroutine ztrtri
module procedure ztrtri_gpu
end interface ztrtri
contains
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
SUBROUTINE dpotrf_gpu( uplo, n, A, lda, info )
use kinds, only : dp
implicit none
character:: UPLO
integer :: n,lda,info
real(dp), intent(inout), device:: A(lda,*)
!
! given a matrix A, returns the Cholesky decomposition of A
! for cholesky matrices
!
real(dp), device:: work(1)
integer :: lwork=1
logical:: upper
logical,external:: lsame
if (.not. cusolver_init) then
istat = cusolverDnCreate(handle_cusolver)
if (istat /= CUSOLVER_STATUS_SUCCESS) write(*,*) 'cusolver handle creation failed'
end if
info = -1
upper = lsame( uplo, 'U' )
if(upper) then
istat= cusolverDnDpotrf(handle_cusolver, CUBLAS_FILL_MODE_UPPER, n, A, lda, work, lwork, devInfo_d)
else
istat= cusolverDnDpotrf(handle_cusolver, CUBLAS_FILL_MODE_LOWER, n, A, lda, work, lwork, devInfo_d)
endif
info=devInfo_d
END SUBROUTINE dpotrf_gpu
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
SUBROUTINE zpotrf_gpu( uplo, n, A, lda, info )
use kinds, only : dp
implicit none
character:: UPLO
integer :: n,lda,info
complex(dp), intent(inout), device:: A(lda,*)
!
! given a matrix A, returns the Cholesky decomposition of A
! for cholesky matrices
!
complex(dp), device:: work(1)
integer :: lwork=1
logical:: upper
logical,external:: lsame
if (.not. cusolver_init) then
istat = cusolverDnCreate(handle_cusolver)
if (istat /= CUSOLVER_STATUS_SUCCESS) write(*,*) 'cusolver handle creation failed'
end if
info = -1
upper = lsame( uplo, 'U' )
if(upper) then
istat= cusolverDnZpotrf(handle_cusolver, CUBLAS_FILL_MODE_UPPER, n, A, lda, work, lwork, devInfo_d)
else
istat= cusolverDnZpotrf(handle_cusolver, CUBLAS_FILL_MODE_LOWER, n, A, lda, work, lwork, devInfo_d)
endif
info=devInfo_d
END SUBROUTINE zpotrf_gpu
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! The two following routines are the GPU implementation of the ZTRTRI LAPACK routine.
! This routine computes the inverse of a complex lower non-unit triangular matrix.
! This is the unblocked code that operates on a block 32x32
attributes(global) subroutine ztrti2_gpu(n,a,lda)
use cudafor
implicit none
integer, value :: n,lda
complex(8),device :: a(lda,*)
complex(8),shared :: a_s(32,32)
complex(8) :: cv
integer :: tx,ty,tl,i,j,ii
if (n == 0 ) return
tx=threadIdx%x
ty=threadIdx%y
! Linear id of the thread (tx,ty)
tl=tx+ blockDim%x*(ty-1)
! Load a_d in shared memory
if (tx <= n .and. ty <= n) then
a_s(tx,ty)=a(tx,ty)
endif
call syncthreads()
! Compute all the diagonal elements
if (tl <=n ) a_s(tl,tl)=cone/a_s(tl,tl)
call syncthreads()
! For each column working backward
do i=n-1,1,-1
if ( tl >i .and. tl <= n) then
cv=czero
do j= i+1,tl
cv = cv + a_s(j , i ) * a_s(tl ,j)
end do
end if
! call syncthreads()
if ( tl >i .and. tl <= n) then
a_s(tl,i)=-cv*a_s(i,i)
end if
! call syncthreads()
end do
call syncthreads()
! Write back to global memory
if (tx <= n .and. ty <= n) then
a(tx,ty)=a_s(tx,ty)
endif
end subroutine ztrti2_gpu
! This routine computes the inverse of a complex lower non-unit triangular matrix.
! This is the blocked code that operates on a generic size matrix
subroutine ztrtri_gpu(uplo, diag, n, a, lda, info )
use cublas
implicit none
character :: uplo, diag
integer :: lda, n, info,sizeb
complex(8),device:: a( lda, * )
logical:: nounit, upper, supported
logical, external:: lsame
integer:: nb,nn,j,jb
type(dim3):: threads
if (n == 0 ) return
upper = lsame( uplo, 'U' )
nounit = lsame( diag, 'N' )
IF( .not.upper .and. .not.lsame( uplo, 'L' ) ) THEN
info = -1
else if( .not.nounit .and. .not.lsame( diag, 'u' ) ) then
info = -2
else if( n.lt.0 ) theN
info = -3
else if( lda.lt.max( 1, n ) ) theN
info = -5
end iF
! Check if this is a supported configuratio, lower non unit triangular
supported=(.not.upper) .and. nounit
if ( .not.supported) then
print *," Only L and no-unit implemented on GPU", upper,nounit
info=-6
return
endif
! Block size for zttri2 on GPU is 32
nb=32
threads=dim3(32,32,1)
if( nb .ge. n ) then
! If the problem size is smaller than block size, call directly unblocked code
call ztrti2_gpu<<<1,threads>>>( n, a, lda )
else
! Use blocked code
!
! Compute inverse of lower triangular matrix
!
nn = ( ( n-1 ) / nb )*nb + 1
do j = nn, 1, -nb
jb = min( nb, n-j+1 )
if( j+jb.le.n ) then
!
! Compute rows j+jb:n of current block column
!
call ztrmm( 'Left', 'Lower', 'No transpose', diag, &
n-j-jb+1, jb, cone, a( j+jb, j+jb ), lda, &
a( j+jb, j ), lda )
call ztrsm( 'Right', 'Lower', 'No transpose', diag, &
n-j-jb+1, jb, -cone, a( j, j ), lda, &
a( j+jb, j ), lda )
end if
!
! Compute inverse of current diagonal block
!
call ztrti2_gpu<<<1,threads>>>( jb, a( j, j ), lda )
end do
endif
end subroutine ztrtri_gpu
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! The two following routines are the GPU implementation of the ZTRTRI LAPACK routine.
! This routine computes the inverse of a double precision lower non-unit triangular matrix.
! This is the unblocked code that operates on a block 32x32
attributes(global) subroutine dtrti2_gpu(n,a,lda)
use cudafor
implicit none
integer, value :: n,lda
real(8),device :: a(lda,*)
real(8),shared :: a_s(32,32)
real(8) :: cv
integer :: tx,ty,tl,i,j,ii
if (n == 0 ) return
tx=threadIdx%x
ty=threadIdx%y
! Linear id of the thread (tx,ty)
tl=tx+ blockDim%x*(ty-1)
! Load a_d in shared memory
if (tx <= n .and. ty <= n) then
a_s(tx,ty)=a(tx,ty)
endif
call syncthreads()
! Compute all the diagonal elements
if (tl <=n ) a_s(tl,tl)=one/a_s(tl,tl)
call syncthreads()
! For each column working backward
do i=n-1,1,-1
if ( tl >i .and. tl <= n) then
cv=zero
do j= i+1,tl
cv = cv + a_s(j , i ) * a_s(tl ,j)
end do
end if
! call syncthreads()
if ( tl >i .and. tl <= n) then
a_s(tl,i)=-cv*a_s(i,i)
end if
! call syncthreads()
end do
call syncthreads()
! Write back to global memory
if (tx <= n .and. ty <= n) then
a(tx,ty)=a_s(tx,ty)
endif
end subroutine dtrti2_gpu
! This routine computes the inverse of a complex lower non-unit triangular matrix.
! This is the blocked code that operates on a generic size matrix
subroutine dtrtri_gpu(uplo, diag, n, a, lda, info )
use cublas
implicit none
character :: uplo, diag
integer :: lda, n, info,sizeb
real(8),device:: a( lda, * )
logical:: nounit, upper
logical, external:: lsame
integer:: nb,nn,j,jb
type(dim3):: threads
if (n == 0 ) return
upper = lsame( uplo, 'U' )
nounit = lsame( diag, 'N' )
IF( .not.upper .and. .not.lsame( uplo, 'L' ) ) THEN
info = -1
else if( .not.nounit .and. .not.lsame( diag, 'u' ) ) then
info = -2
else if( n.lt.0 ) theN
info = -3
else if( lda.lt.max( 1, n ) ) theN
info = -5
end iF
if (.not. upper .or. .not.nounit ) then
print *," Only L no unit implemented on GPU"
endif
! Block size for dttri2 on GPU is 32
nb=32
threads=dim3(32,32,1)
if( nb .ge. n ) then
! If the problem size is smaller than block size, call directly unblocked code
call dtrti2_gpu<<<1,threads>>>( n, a, lda )
else
! Use blocked code
!
! Compute inverse of lower triangular matrix
!
nn = ( ( n-1 ) / nb )*nb + 1
do j = nn, 1, -nb
jb = min( nb, n-j+1 )
if( j+jb.le.n ) then
!
! Compute rows j+jb:n of current block column
!
call dtrmm( 'Left', 'Lower', 'No transpose', diag, &
n-j-jb+1, jb, one, a( j+jb, j+jb ), lda, &
a( j+jb, j ), lda )
call dtrsm( 'Right', 'Lower', 'No transpose', diag, &
n-j-jb+1, jb, -one, a( j, j ), lda, &
a( j+jb, j ), lda )
end if
!
! Compute inverse of current diagonal block
!
call dtrti2_gpu<<<1,threads>>>( jb, a( j, j ), lda )
end do
endif
end subroutine dtrtri_gpu
end module
#endif