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Updates in Lapack Utility #311

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May 18, 2024
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Updates in Lapack Utility #311

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Updates in Lapack Utility
May 17, 2024
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Updates in Lapack
May 17, 2024
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81 changes: 79 additions & 2 deletions src/modules/Lapack/src/GE_EigenValueMethods.F90
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Original file line number Diff line number Diff line change
Expand Up @@ -16,8 +16,85 @@
!

MODULE GE_EigenValueMethods
! USE GlobalData, ONLY: DFP, I4B, LGT
! IMPLICIT NONE
USE GlobalData, ONLY: DFP, DFPC, I4B, LGT
IMPLICIT NONE
CHARACTER(*), PARAMETER :: modName = "GE_EigenValueMethods"
PRIVATE

PUBLIC :: GetEigVals
PUBLIC :: GetEig

!----------------------------------------------------------------------------
! getEigVals
!----------------------------------------------------------------------------

!> author: Shion Shimizu
! date: 2024-05-17
! summary: calculate eigenvalues for real matrix

INTERFACE GetEigVals
MODULE SUBROUTINE deigvals(A, lam)
REAL(DFP), INTENT(IN) :: A(:, :)
COMPLEX(DFPC), INTENT(INOUT) :: lam(:)
END SUBROUTINE deigvals
END INTERFACE GetEigVals

!----------------------------------------------------------------------------
! getEigVals
!----------------------------------------------------------------------------

!> author: Shion Shimizu
! date: 2024-05-17
! summary: calculate eigenvalues for complex matrix

INTERFACE GetEigVals
MODULE SUBROUTINE zeigvals(A, lam)
COMPLEX(DFPC), INTENT(IN) :: A(:, :)
COMPLEX(DFPC), INTENT(INOUT) :: lam(:)
END SUBROUTINE zeigvals
END INTERFACE GetEigVals

!----------------------------------------------------------------------------
! getEig
!----------------------------------------------------------------------------

!> author: Shion Shimizu
! date: 2024-05-17
! summary: calculate eigenvalues and eigenvectors for real matrix

INTERFACE GetEig
MODULE SUBROUTINE deig(A, lam, c)
REAL(DFP), INTENT(IN) :: A(:, :)
COMPLEX(DFPC), INTENT(INOUT) :: lam(:)
! eigenvalues
! should be allocated
COMPLEX(DFPC), INTENT(INOUT) :: c(:, :)
! eigenvectors
! c(i,j) = ith component of jth eigenvec.
! should be allocated
END SUBROUTINE deig
END INTERFACE GetEig

!----------------------------------------------------------------------------
! getEig
!----------------------------------------------------------------------------

!> author: Shion Shimizu
! date: 2024-05-17
! summary: calculate eigenvalues and eigenvectors for complex matrix

INTERFACE GetEig
MODULE SUBROUTINE zeig(A, lam, c)
COMPLEX(DFPC), INTENT(IN) :: A(:, :)
COMPLEX(DFPC), INTENT(INOUT) :: lam(:)
! eigenvalues
! should be allocated
COMPLEX(DFPC), INTENT(INOUT) :: c(:, :)
! eigenvectors
! c(i,j) = ith component of jth eigenvec.
! should be allocated
END SUBROUTINE zeig
END INTERFACE GetEig

!----------------------------------------------------------------------------
! DGEES@EigenValue
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192 changes: 179 additions & 13 deletions src/submodules/Lapack/src/[email protected]
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Expand Up @@ -13,17 +13,183 @@
!
! You should have received a copy of the GNU General Public License
! along with this program. If not, see <https: //www.gnu.org/licenses/>
!

! SUBMODULE(GE_EigenValueMethods) Methods
! ! USE BaseMethod
! ! IMPLICIT NONE
! ! CONTAINS
!
! !----------------------------------------------------------------------------
! ! DGEES
! !----------------------------------------------------------------------------
!
! ! MODULE PROCEDURE dgees_1
! ! END PROCEDURE dgees_1
! END SUBMODULE Methods
! the implementation of deig, zeig, deigvals, and zeigvals are copied from
! linalg.f90 available in https://github.com/certik/fortran-utils
! and are modified to suit the needs of EASIFEM library

SUBMODULE(GE_EigenValueMethods) Methods
USE BaseMethod, ONLY: ErrorMsg, LA_GEEV, stderr, tostring, &
Display
USE AssertUtility
IMPLICIT NONE
COMPLEX(DFPC), PARAMETER :: i_ = (0.0_DFP, 1.0_DFP)
CONTAINS

!----------------------------------------------------------------------------
! getEig
!----------------------------------------------------------------------------

MODULE PROCEDURE deig
! LAPACK variables for DGEEV:
REAL(DFP), ALLOCATABLE :: At(:, :), vl(:, :), vr(:, :), wi(:), &
work(:), wr(:)
INTEGER(I4B) :: info, lda, ldvl, ldvr, lwork, n, i

CHARACTER(*), PARAMETER :: myName = "deig"

lda = SIZE(A(:, 1))
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n = SIZE(A(1, :))
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! CALL Assert(Mat=A, s=[n, n], msg="[ARG ERROR] :: A should be square", &
! file=__FILE__, line=__LINE__, routine=myName)
! CALL Assert(n1=SIZE(lam), n2=n, msg="[ARG ERROR] :: size of lam should be "// &
! "equal to "//tostring(n), file=__FILE__, line=__LINE__, &
! routine=myName)
! CALL Assert(mat=c, s=[n, n], msg="[ARG ERROR] :: shape of c should be"// &
! "the same as one of A", file=__FILE__, line=__LINE__, &
! routine=myName)
ldvl = n
ldvr = n
lwork = 8 * n ! TODO: can this size be optimized? query first?
ALLOCATE (At(lda, n), wr(n), wi(n), vl(ldvl, n), vr(ldvr, n), &
work(lwork))
At = A

CALL LA_GEEV('N', 'V', n, At, lda, wr, wi, vl, ldvl, vr, ldvr, &
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work, lwork, info)
IF (info .NE. 0) CALL GeevErrorMsg(info, n)

lam = wr + i_ * wi
! as DGEEV has a rather complicated way of returning the eigenvectors,
! it is necessary to build the complex array of eigenvectors from
! two real arrays:
DO i = 1, n
IF (wi(i) > 0.0) THEN ! first of two conjugate eigenvalues
c(:, i) = vr(:, i) + i_ * vr(:, i + 1)
ELSEIF (wi(i) < 0.0_DFP) THEN ! second of two conjugate eigenvalues
c(:, i) = vr(:, i - 1) - i_ * vr(:, i)
ELSE
c(:, i) = vr(:, i)
END IF
END DO

END PROCEDURE deig

!----------------------------------------------------------------------------
! getEig
!----------------------------------------------------------------------------

MODULE PROCEDURE zeig
! LAPACK variables:
INTEGER(I4B) :: info, lda, ldvl, ldvr, lwork, n, lrwork
REAL(DFP), ALLOCATABLE :: rwork(:)
COMPLEX(DFPC), ALLOCATABLE :: vl(:, :), vr(:, :), work(:)

CHARACTER(*), PARAMETER :: myName = "zeig"

lda = SIZE(A(:, 1))
n = SIZE(A(1, :))
! CALL Assert(Mat=A, s=[n, n], msg="[ARG ERROR] :: A should be square", &
! file=__FILE__, line=__LINE__, routine=myName)
! CALL Assert(n1=SIZE(lam), n2=n, msg="[ARG ERROR] :: size of lam should be "// &
! "equal to "//tostring(n), file=__FILE__, line=__LINE__, &
! routine=myName)
! CALL Assert(mat=c, s=[n, n], msg="[ARG ERROR] :: shape of c should be"// &
! "the same as one of A", file=__FILE__, line=__LINE__, &
! routine=myName)
ldvl = n
ldvr = n
lwork = 8 * n ! TODO: can this size be optimized? query first?
lrwork = 2 * n
ALLOCATE (vl(ldvl, n), vr(ldvr, n), work(lwork), rwork(lrwork))
c = A
CALL LA_GEEV('N', 'V', n, c, lda, lam, vl, ldvl, vr, ldvr, work, &
lwork, rwork, info)
IF (info .NE. 0) CALL GeevErrorMsg(info, n)
c = vr

END PROCEDURE zeig

!----------------------------------------------------------------------------
! getEigVals
!----------------------------------------------------------------------------

MODULE PROCEDURE deigvals
! LAPACK variables for DGEEV:
REAL(DFP), ALLOCATABLE :: At(:, :), vl(:, :), vr(:, :), wi(:), work(:), wr(:)
INTEGER :: info, lda, ldvl, ldvr, lwork, n

CHARACTER(*), PARAMETER :: myName = "deigvals"

lda = SIZE(A(:, 1))
n = SIZE(A(1, :))
! CALL assert_shape(A, [n, n], "solve", "A")
ldvl = n
ldvr = n
lwork = 8 * n ! TODO: can this size be optimized? query first?
ALLOCATE (At(lda, n), wr(n), wi(n), vl(ldvl, n), &
vr(ldvr, n), work(lwork))
At = A
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CALL LA_GEEV('N', 'N', n, At, lda, wr, wi, vl, ldvl, vr, ldvr, &
work, lwork, info)
IF (info .NE. 0) CALL GeevErrorMsg(info, n)

lam = wr + i_ * wi
END PROCEDURE deigvals

!----------------------------------------------------------------------------
! getEigVals_2
!----------------------------------------------------------------------------

MODULE PROCEDURE zeigvals
! LAPACK variables:
INTEGER :: info, lda, ldvl, ldvr, lwork, n, lrwork
REAL(DFP), ALLOCATABLE :: rwork(:)
COMPLEX(DFPC), ALLOCATABLE :: At(:, :), vl(:, :), vr(:, :), work(:)

CHARACTER(*), PARAMETER :: myName = "zeigvals"

lda = SIZE(A(:, 1))
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n = SIZE(A(1, :))
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! CALL assert_shape(A, [n, n], "solve", "A")
ldvl = n
ldvr = n
lwork = 8 * n ! TODO: can this size be optimized? query first?
lrwork = 2 * n
ALLOCATE (At(lda, n), vl(ldvl, n), vr(ldvr, n), &
work(lwork), rwork(lrwork))
At = A
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Why do you make a copy

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@shishiousan shishiousan May 17, 2024 •
edited
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@vickysharma0812
This is because GEEV destroy the A
I can add optional boolean argument like destroy to switch making copy.

For example

INTERFACE GetEigVals
  MODULE SUBROUTINE deigvals(A, lam, destroy)
    REAL(DFP), INTENT(IN) :: A(:, :)
    COMPLEX(DFPC), INTENT(INOUT) :: lam(:)
    LOGICAL(LGT), OPTIONAL, INTENT(IN) :: destroy
    ! default true
  END SUBROUTINE deigvals
END INTERFACE GetEigVals

How do you think ?

CALL LA_GEEV('N', 'N', n, At, lda, lam, vl, ldvl, vr, ldvr, work, &
lwork, rwork, info)
IF (info .NE. 0) CALL GeevErrorMsg(info, n)

END PROCEDURE zeigvals

!----------------------------------------------------------------------------
! geevErrorMsg
!----------------------------------------------------------------------------

SUBROUTINE GeevErrorMsg(info, n)
INTEGER(I4B), INTENT(IN) :: info, n

CALL Display(info, "LA_GEEV returned info = ")
IF (info .LT. 0) THEN
CALL Display("The "//tostring(-info)//"-th argument "// &
"had an illegal value.")
ELSE
CALL Display("The QR algorithm failed to compute all the")
CALL Display("eigenvalues, and no eigenvectors have been computed;")
CALL Display("elements "//tostring(info + 1)//":"//tostring(n)// &
" of WR and WI contain eigenvalues which converged.")
END IF
CALL ErrorMsg( &
& msg="ERROR IN LA_GEEV", &
& file=__FILE__, &
& line=__LINE__, &
& routine="zeigvals", &
& unitno=stderr)
STOP
END SUBROUTINE GeevErrorMsg

END SUBMODULE Methods