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generic_contract.f90
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MODULE generic_contract
IMPLICIT NONE
!PRIVATE
!PUBLIC :: tensorcontract
INTERFACE tensorcontract
MODULE PROCEDURE tensorcontract4355
MODULE PROCEDURE tensorcontract4442
MODULE PROCEDURE tensorcontract4444
MODULE PROCEDURE tensorcontract5344
MODULE PROCEDURE tensorcontract5455
END INTERFACE
! INTERFACE neworder
! MODULE PROCEDURE neworder4
! MODULE PROCEDURE neworder5
! MODULE PROCEDURE neworder3
! END INTERFACE neworder
CONTAINS
FUNCTION neworder(Order)
! get the correct order for permutation
IMPLICIT NONE
INTEGER :: n
INTEGER, DIMENSION(:) :: Order
INTEGER, DIMENSION(SIZE(Order)) :: neworder
INTEGER, DIMENSION(SIZE(Order)) :: tmpOrder
INTEGER :: i
tmpOrder = Order
Do i = 1, SIZE(Order)
neworder(i) = MINLOC(tmpOrder, dim=1)
tmpOrder(MINLOC(tmpOrder)) = 1000
END DO
END FUNCTION neworder
SUBROUTINE tensorcontract4355 ( A, B, ash, ain, bsh, bin, ABorder, squeeze, error, outT)
!
! Purpose:
! Contract tensor A and B.
! A and B are tensor of ranks as specified in the function name.
! The function name should be understood in the following way:
! tensorcontract4444 means contract two rank 4 tensors ('44')
! into an intermediate rank 4 tensor ('4') and the final result is
! a rank 4 tensor ('4').
! ash and bsh are the ranks of the tensor A and B.
! ain and bin are the common index in A and B respectively.
! ABorder gives the contracted tensor sequence.
! squeeze specifis the new shape of the contracted tensor.
! For example, A(x,y,i,m,n,p), B(a,i,m,b,c); if we want to contract the
! common index i and m then we need to have ain=(3,4) and bin=(2,3);
! after the contraction, we will get the intermediate tensor T(xynp,abc);
! in order to get T(x,a,y,b,n,p,c), we need to set ABorder=(1,5,2,6,3,4,7);
! it usually works in the following way:
! T(xynp,abc):
! x y n p a b c
! 1 2 3 4 5 6 7
! T(x,a,y,b,n,p,c)
! x a y b n p c
! 1 5 2 6 3 4 7 ! This is just ABorder
!
! If squeeze=(3,2,2), then one will squeeze the first 3(xay) index,
! the middle 2(bn), and the last 2(pc) index to form a rank 3 tensor.
! error is the error flag.
! error = 0: no error
! error = 1: The input arrays and ranks are not consistent.
! error = 2: The contracted index is not equal.
!
! In order to get functions for other ranks, one will have to change
! the declaration of the following variables:
! A
! B
! Anew
! Bnew
! outT
! T
! Ssize
! and some others as marked in the template file 'contract.tmpl'.
!
! The code can be generated by 'Cheetah' template engine for differet
! input and output ranks. See the python file 'contract_gen.py' for details.
USE set_precisions
USE useful_functions
IMPLICIT NONE
! Data dictionary: declare calling parameter types & definitions
REAL(kind=DBL), INTENT(IN), DIMENSION(:,:,:,:) :: A ! Input array A
REAL(kind=DBL), INTENT(IN), DIMENSION(:,:,:) :: B ! Input array B
INTEGER, INTENT(IN) :: ash ! Rank of A
INTEGER, INTENT(IN), DIMENSION(:) :: ain ! Contraction index
INTEGER, INTENT(IN) :: bsh ! Rank of B
INTEGER, INTENT(IN), DIMENSION(:) :: bin ! Contraction index
INTEGER, INTENT(IN), DIMENSION(:), OPTIONAL :: ABorder ! Opt input
INTEGER, INTENT(IN), DIMENSION(:), OPTIONAL :: squeeze ! Opt input
INTEGER, INTENT(OUT) :: error ! Error flag
REAL(kind=DBL), INTENT(OUT), DIMENSION(:,:,:,:,:) :: outT ! Output
! Data dictionary: declare local variable types & definitions
INTEGER, DIMENSION(ash) :: indexA ! Index array A
INTEGER, DIMENSION(bsh) :: indexB ! Index array B
INTEGER, DIMENSION(ash - SIZE(ain)) :: Aother ! Index not contracted in A
INTEGER, DIMENSION(bsh - SIZE(bin)) :: Bother ! Index not contracted in B
INTEGER :: Nain, Nbin ! # of index contracted
LOGICAL :: flagA, flagB ! Flags for permutation
REAL(kind=DBL), ALLOCATABLE, DIMENSION(:,:,:,:) :: Anew ! Copy of A
REAL(kind=DBL), ALLOCATABLE, DIMENSION(:,:,:) :: Bnew ! Copy of B
REAL(kind=DBL), ALLOCATABLE, DIMENSION(:,:,:,:,:) :: T ! Intermediate one
INTEGER, DIMENSION(ash) :: Asize ! Size of Anew
INTEGER, DIMENSION(bsh) :: Bsize ! Size of Bnew
INTEGER, DIMENSION(SIZE(ain)) :: SefAsize ! Self dimension
INTEGER, DIMENSION(SIZE(bin)) :: SefBsize ! Self dimension
INTEGER, DIMENSION(ash - SIZE(ain)) :: Asize1 ! Other dimension
INTEGER, DIMENSION(bsh - SIZE(bin)) :: Bsize1 ! Other dimension
INTEGER :: i, k
INTEGER :: Num
INTEGER, DIMENSION(ash + bsh - SIZE(ain) - SIZE(bin) ) :: Tsize
INTEGER, DIMENSION(SIZE(SHAPE(T))) :: OrderSize
INTEGER, DIMENSION(5) :: Ssize
INTEGER :: istat
! Check the consistency of the tensor rank
errorif: IF ( ash /= SIZE(SHAPE(A)) .OR. bsh /= SIZE(SHAPE(B)) ) THEN
error = 1
WRITE(*,*) 'The input arrays and ranks are not consistent.'
ELSE errorif
error = 0
END IF errorif
indexA = (/ (i, i=1,ash) /) ! index array A
indexB = (/ (i, i=1,bsh) /) ! index array B
Aother = setdiff( indexA, ain) ! index not contracted in A
Bother = setdiff( indexB, bin) ! index not contracted in B
Nain = SIZE(ain) ! # of index contracted
Nbin = SIZE(bin) ! # of index contracted
flagA = ALL( indexA(ash - Nain + 1: ash) == ain)
flagB = ALL( indexB(: Nbin) == bin)
ALLOCATE ( Anew( SIZE(A,Aother(1)),&
SIZE(A,Aother(2)),&
SIZE(A,Aother(3)),&
SIZE(A,ain(1)) ) , STAT=istat) ! replace
! permute A only when necessary
ifAllocatedA: IF ( ALLOCATED(Anew) ) THEN
ifA: IF ( .NOT. flagA ) THEN ! Anew(...i)
!Anew = RESHAPE( A, SHAPE(A), ORDER = (/ Aother, ain /) )
Anew = RESHAPE( A, SHAPE(A), ORDER = neworder( (/ Aother, ain /) ) )
! equivalent to permute
ELSE ifA
Anew = A
END IF ifA
ELSE ifAllocatedA
WRITE(*,*) 'Warning-Array Anew not allocated!'
END IF ifAllocatedA
ALLOCATE ( Bnew( SIZE(B,bin(1)),&
SIZE(B,Bother(1)),&
SIZE(B,Bother(2)) ) , STAT=istat) ! replace
! permute B only when necessary
ifAllocatedB: IF ( ALLOCATED(Bnew) ) THEN
ifB: IF ( .NOT. flagB ) THEN ! Bnew(i...)
!Bnew = RESHAPE( B, SHAPE(B), ORDER = (/ bin, Bother /) )
Bnew = RESHAPE( B, SHAPE(B), ORDER = neworder( (/ bin, Bother /) ) )
! equivalent to permute
ELSE ifB
Bnew = B
END IF ifB
ELSE ifAllocatedB
WRITE(*,*) 'Warning-Array Bnew not allocated!'
END IF ifAllocatedB
Asize = UBOUND(Anew) ! size of Anew
Bsize = UBOUND(Bnew) ! size of Bnew
SefAsize = Asize( ash - Nain + 1 : ash ) ! self dimension
SefBsize = Bsize( 1 : Nbin ) ! self dimension
Asize1 = Asize( 1 : ash - Nain ) ! other dimension
Bsize1 = Bsize( Nbin + 1 : bsh ) ! other dimension
! contract Anew(aaa, i) and Bnew(i, bbbb) to T(aaa, bbbb)
Tsize = (/ Asize1, Bsize1 /) ! size of T
prodAB: IF ( PRODUCT(SefAsize) == PRODUCT(SefBsize) ) THEN
ABorderif: IF ( PRESENT( ABorder) ) THEN
OrderSize = Tsize(ABorder)
ALLOCATE(T( Tsize(1),&
Tsize(2),&
Tsize(3),&
Tsize(4),&
Tsize(5) ),&
STAT=istat) ! allocate T
ifAllocatedT: IF ( ALLOCATED(T) ) THEN
T = RESHAPE( MATMUL( & ! contract and reshape T
RESHAPE( Anew, SHAPE = (/ PRODUCT(Asize1), PRODUCT(SefAsize) /) ), &
RESHAPE( Bnew, SHAPE = (/ PRODUCT(SefBsize), PRODUCT(Bsize1) /) ) &
), SHAPE(T), ORDER = neworder( ABorder ) )
ELSE ifAllocatedT
WRITE(*,*) 'Warning-Array T not allocated!'
END IF ifAllocatedT
ELSE ABorderif
OrderSize = Tsize
ALLOCATE(T( Tsize(1),&
Tsize(2),&
Tsize(3),&
Tsize(4),&
Tsize(5) ),&
STAT=istat) ! replace
ifAllocatedT2: IF ( ALLOCATED(T) ) THEN
T = RESHAPE( MATMUL( &
RESHAPE( Anew, SHAPE = (/ PRODUCT(Asize1), PRODUCT(SefAsize) /) ), &
RESHAPE( Bnew, SHAPE = (/ PRODUCT(SefBsize), PRODUCT(Bsize1) /) ) &
), SHAPE(T) )
ELSE ifAllocatedT2
WRITE(*,*) 'Warning-Array T not allocated!'
END IF ifAllocatedT2
END IF ABorderif
DEALLOCATE(Anew, STAT=istat)
DEALLOCATE(Bnew, STAT=istat)
ELSE prodAB
error = 2
WRITE(*,*) 'The contracted index is not equal.'
END IF prodAB
! if optional arguments 'ABorder' and 'squeeze' are present
IF ( PRESENT(ABorder) .AND. PRESENT(squeeze) ) THEN
Num = SIZE(squeeze)
!Tsize = (/ Asize1, Bsize1 /)
!OrderSize = Tsize(ABorder)
k = 1
DO i = 1, Num
Ssize( i ) = PRODUCT( OrderSize( k: k + squeeze(i) -1 ) )
k = k + squeeze(i)
END DO
END IF
outT = T
DEALLOCATE(T, STAT = istat)
END SUBROUTINE tensorcontract4355
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
SUBROUTINE tensorcontract4442 ( A, B, ash, ain, bsh, bin, ABorder, squeeze, error, outT)
!
! Purpose:
! Contract tensor A and B.
! A and B are tensor of ranks as specified in the function name.
! The function name should be understood in the following way:
! tensorcontract4444 means contract two rank 4 tensors ('44')
! into an intermediate rank 4 tensor ('4') and the final result is
! a rank 4 tensor ('4').
! ash and bsh are the ranks of the tensor A and B.
! ain and bin are the common index in A and B respectively.
! ABorder gives the contracted tensor sequence.
! squeeze specifis the new shape of the contracted tensor.
! For example, A(x,y,i,m,n,p), B(a,i,m,b,c); if we want to contract the
! common index i and m then we need to have ain=(3,4) and bin=(2,3);
! after the contraction, we will get the intermediate tensor T(xynp,abc);
! in order to get T(x,a,y,b,n,p,c), we need to set ABorder=(1,5,2,6,3,4,7);
! it usually works in the following way:
! T(xynp,abc):
! x y n p a b c
! 1 2 3 4 5 6 7
! T(x,a,y,b,n,p,c)
! x a y b n p c
! 1 5 2 6 3 4 7 ! This is just ABorder
!
! If squeeze=(3,2,2), then one will squeeze the first 3(xay) index,
! the middle 2(bn), and the last 2(pc) index to form a rank 3 tensor.
! error is the error flag.
! error = 0: no error
! error = 1: The input arrays and ranks are not consistent.
! error = 2: The contracted index is not equal.
!
! In order to get functions for other ranks, one will have to change
! the declaration of the following variables:
! A
! B
! Anew
! Bnew
! outT
! T
! Ssize
! and some others as marked in the template file 'contract.tmpl'.
!
! The code can be generated by 'Cheetah' template engine for differet
! input and output ranks. See the python file 'contract_gen.py' for details.
USE set_precisions
USE useful_functions
IMPLICIT NONE
! Data dictionary: declare calling parameter types & definitions
REAL(kind=DBL), INTENT(IN), DIMENSION(:,:,:,:) :: A ! Input array A
REAL(kind=DBL), INTENT(IN), DIMENSION(:,:,:,:) :: B ! Input array B
INTEGER, INTENT(IN) :: ash ! Rank of A
INTEGER, INTENT(IN), DIMENSION(:) :: ain ! Contraction index
INTEGER, INTENT(IN) :: bsh ! Rank of B
INTEGER, INTENT(IN), DIMENSION(:) :: bin ! Contraction index
INTEGER, INTENT(IN), DIMENSION(:), OPTIONAL :: ABorder ! Opt input
INTEGER, INTENT(IN), DIMENSION(:), OPTIONAL :: squeeze ! Opt input
INTEGER, INTENT(OUT) :: error ! Error flag
REAL(kind=DBL), INTENT(OUT), DIMENSION(:,:) :: outT ! Output
! Data dictionary: declare local variable types & definitions
INTEGER, DIMENSION(ash) :: indexA ! Index array A
INTEGER, DIMENSION(bsh) :: indexB ! Index array B
INTEGER, DIMENSION(ash - SIZE(ain)) :: Aother ! Index not contracted in A
INTEGER, DIMENSION(bsh - SIZE(bin)) :: Bother ! Index not contracted in B
INTEGER :: Nain, Nbin ! # of index contracted
LOGICAL :: flagA, flagB ! Flags for permutation
REAL(kind=DBL), ALLOCATABLE, DIMENSION(:,:,:,:) :: Anew ! Copy of A
REAL(kind=DBL), ALLOCATABLE, DIMENSION(:,:,:,:) :: Bnew ! Copy of B
REAL(kind=DBL), ALLOCATABLE, DIMENSION(:,:,:,:) :: T ! Intermediate one
INTEGER, DIMENSION(ash) :: Asize ! Size of Anew
INTEGER, DIMENSION(bsh) :: Bsize ! Size of Bnew
INTEGER, DIMENSION(SIZE(ain)) :: SefAsize ! Self dimension
INTEGER, DIMENSION(SIZE(bin)) :: SefBsize ! Self dimension
INTEGER, DIMENSION(ash - SIZE(ain)) :: Asize1 ! Other dimension
INTEGER, DIMENSION(bsh - SIZE(bin)) :: Bsize1 ! Other dimension
INTEGER :: i, k
INTEGER :: Num
INTEGER, DIMENSION(ash + bsh - SIZE(ain) - SIZE(bin) ) :: Tsize
INTEGER, DIMENSION(SIZE(SHAPE(T))) :: OrderSize
INTEGER, DIMENSION(2) :: Ssize
INTEGER :: istat
! Check the consistency of the tensor rank
errorif: IF ( ash /= SIZE(SHAPE(A)) .OR. bsh /= SIZE(SHAPE(B)) ) THEN
error = 1
WRITE(*,*) 'The input arrays and ranks are not consistent.'
ELSE errorif
error = 0
END IF errorif
indexA = (/ (i, i=1,ash) /) ! index array A
indexB = (/ (i, i=1,bsh) /) ! index array B
Aother = setdiff( indexA, ain) ! index not contracted in A
Bother = setdiff( indexB, bin) ! index not contracted in B
Nain = SIZE(ain) ! # of index contracted
Nbin = SIZE(bin) ! # of index contracted
flagA = ALL( indexA(ash - Nain + 1: ash) == ain)
flagB = ALL( indexB(: Nbin) == bin)
ALLOCATE ( Anew( SIZE(A,Aother(1)),&
SIZE(A,Aother(2)),&
SIZE(A,ain(1)),&
SIZE(A,ain(2)) ) , STAT=istat) ! replace
! permute A only when necessary
ifAllocatedA: IF ( ALLOCATED(Anew) ) THEN
ifA: IF ( .NOT. flagA ) THEN ! Anew(...i)
!Anew = RESHAPE( A, SHAPE(A), ORDER = (/ Aother, ain /) )
Anew = RESHAPE( A, SHAPE(A), ORDER = neworder( (/ Aother, ain /) ) )
! equivalent to permute
ELSE ifA
Anew = A
END IF ifA
ELSE ifAllocatedA
WRITE(*,*) 'Warning-Array Anew not allocated!'
END IF ifAllocatedA
ALLOCATE ( Bnew( SIZE(B,bin(1)),&
SIZE(B,bin(2)),&
SIZE(B,Bother(1)),&
SIZE(B,Bother(2)) ) , STAT=istat) ! replace
! permute B only when necessary
ifAllocatedB: IF ( ALLOCATED(Bnew) ) THEN
ifB: IF ( .NOT. flagB ) THEN ! Bnew(i...)
!Bnew = RESHAPE( B, SHAPE(B), ORDER = (/ bin, Bother /) )
Bnew = RESHAPE( B, SHAPE(B), ORDER = neworder( (/ bin, Bother /) ) )
! equivalent to permute
ELSE ifB
Bnew = B
END IF ifB
ELSE ifAllocatedB
WRITE(*,*) 'Warning-Array Bnew not allocated!'
END IF ifAllocatedB
Asize = UBOUND(Anew) ! size of Anew
Bsize = UBOUND(Bnew) ! size of Bnew
SefAsize = Asize( ash - Nain + 1 : ash ) ! self dimension
SefBsize = Bsize( 1 : Nbin ) ! self dimension
Asize1 = Asize( 1 : ash - Nain ) ! other dimension
Bsize1 = Bsize( Nbin + 1 : bsh ) ! other dimension
! contract Anew(aaa, i) and Bnew(i, bbbb) to T(aaa, bbbb)
Tsize = (/ Asize1, Bsize1 /) ! size of T
prodAB: IF ( PRODUCT(SefAsize) == PRODUCT(SefBsize) ) THEN
ABorderif: IF ( PRESENT( ABorder) ) THEN
OrderSize = Tsize(ABorder)
ALLOCATE(T( Tsize(1),&
Tsize(2),&
Tsize(3),&
Tsize(4) ),&
STAT=istat) ! allocate T
ifAllocatedT: IF ( ALLOCATED(T) ) THEN
T = RESHAPE( MATMUL( & ! contract and reshape T
RESHAPE( Anew, SHAPE = (/ PRODUCT(Asize1), PRODUCT(SefAsize) /) ), &
RESHAPE( Bnew, SHAPE = (/ PRODUCT(SefBsize), PRODUCT(Bsize1) /) ) &
), SHAPE(T), ORDER = neworder( ABorder ) )
ELSE ifAllocatedT
WRITE(*,*) 'Warning-Array T not allocated!'
END IF ifAllocatedT
ELSE ABorderif
OrderSize = Tsize
ALLOCATE(T( Tsize(1),&
Tsize(2),&
Tsize(3),&
Tsize(4) ),&
STAT=istat) ! replace
ifAllocatedT2: IF ( ALLOCATED(T) ) THEN
T = RESHAPE( MATMUL( &
RESHAPE( Anew, SHAPE = (/ PRODUCT(Asize1), PRODUCT(SefAsize) /) ), &
RESHAPE( Bnew, SHAPE = (/ PRODUCT(SefBsize), PRODUCT(Bsize1) /) ) &
), SHAPE(T) )
ELSE ifAllocatedT2
WRITE(*,*) 'Warning-Array T not allocated!'
END IF ifAllocatedT2
END IF ABorderif
DEALLOCATE(Anew, STAT=istat)
DEALLOCATE(Bnew, STAT=istat)
ELSE prodAB
error = 2
WRITE(*,*) 'The contracted index is not equal.'
END IF prodAB
! if optional arguments 'ABorder' and 'squeeze' are present
IF ( PRESENT(ABorder) .AND. PRESENT(squeeze) ) THEN
Num = SIZE(squeeze)
!Tsize = (/ Asize1, Bsize1 /)
!OrderSize = Tsize(ABorder)
k = 1
DO i = 1, Num
Ssize( i ) = PRODUCT( OrderSize( k: k + squeeze(i) -1 ) )
k = k + squeeze(i)
END DO
outT = RESHAPE( T, Ssize )
END IF
DEALLOCATE(T, STAT = istat)
END SUBROUTINE tensorcontract4442
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
SUBROUTINE tensorcontract4444 ( A, B, ash, ain, bsh, bin, ABorder, squeeze, error, outT)
!
! Purpose:
! Contract tensor A and B.
! A and B are tensor of ranks as specified in the function name.
! The function name should be understood in the following way:
! tensorcontract4444 means contract two rank 4 tensors ('44')
! into an intermediate rank 4 tensor ('4') and the final result is
! a rank 4 tensor ('4').
! ash and bsh are the ranks of the tensor A and B.
! ain and bin are the common index in A and B respectively.
! ABorder gives the contracted tensor sequence.
! squeeze specifis the new shape of the contracted tensor.
! For example, A(x,y,i,m,n,p), B(a,i,m,b,c); if we want to contract the
! common index i and m then we need to have ain=(3,4) and bin=(2,3);
! after the contraction, we will get the intermediate tensor T(xynp,abc);
! in order to get T(x,a,y,b,n,p,c), we need to set ABorder=(1,5,2,6,3,4,7);
! it usually works in the following way:
! T(xynp,abc):
! x y n p a b c
! 1 2 3 4 5 6 7
! T(x,a,y,b,n,p,c)
! x a y b n p c
! 1 5 2 6 3 4 7 ! This is just ABorder
!
! If squeeze=(3,2,2), then one will squeeze the first 3(xay) index,
! the middle 2(bn), and the last 2(pc) index to form a rank 3 tensor.
! error is the error flag.
! error = 0: no error
! error = 1: The input arrays and ranks are not consistent.
! error = 2: The contracted index is not equal.
!
! In order to get functions for other ranks, one will have to change
! the declaration of the following variables:
! A
! B
! Anew
! Bnew
! outT
! T
! Ssize
! and some others as marked in the template file 'contract.tmpl'.
!
! The code can be generated by 'Cheetah' template engine for differet
! input and output ranks. See the python file 'contract_gen.py' for details.
USE set_precisions
USE useful_functions
IMPLICIT NONE
! Data dictionary: declare calling parameter types & definitions
REAL(kind=DBL), INTENT(IN), DIMENSION(:,:,:,:) :: A ! Input array A
REAL(kind=DBL), INTENT(IN), DIMENSION(:,:,:,:) :: B ! Input array B
INTEGER, INTENT(IN) :: ash ! Rank of A
INTEGER, INTENT(IN), DIMENSION(:) :: ain ! Contraction index
INTEGER, INTENT(IN) :: bsh ! Rank of B
INTEGER, INTENT(IN), DIMENSION(:) :: bin ! Contraction index
INTEGER, INTENT(IN), DIMENSION(:), OPTIONAL :: ABorder ! Opt input
INTEGER, INTENT(IN), DIMENSION(:), OPTIONAL :: squeeze ! Opt input
INTEGER, INTENT(OUT) :: error ! Error flag
REAL(kind=DBL), INTENT(OUT), DIMENSION(:,:,:,:) :: outT ! Output
! Data dictionary: declare local variable types & definitions
INTEGER, DIMENSION(ash) :: indexA ! Index array A
INTEGER, DIMENSION(bsh) :: indexB ! Index array B
INTEGER, DIMENSION(ash - SIZE(ain)) :: Aother ! Index not contracted in A
INTEGER, DIMENSION(bsh - SIZE(bin)) :: Bother ! Index not contracted in B
INTEGER :: Nain, Nbin ! # of index contracted
LOGICAL :: flagA, flagB ! Flags for permutation
REAL(kind=DBL), ALLOCATABLE, DIMENSION(:,:,:,:) :: Anew ! Copy of A
REAL(kind=DBL), ALLOCATABLE, DIMENSION(:,:,:,:) :: Bnew ! Copy of B
REAL(kind=DBL), ALLOCATABLE, DIMENSION(:,:,:,:) :: T ! Intermediate one
INTEGER, DIMENSION(ash) :: Asize ! Size of Anew
INTEGER, DIMENSION(bsh) :: Bsize ! Size of Bnew
INTEGER, DIMENSION(SIZE(ain)) :: SefAsize ! Self dimension
INTEGER, DIMENSION(SIZE(bin)) :: SefBsize ! Self dimension
INTEGER, DIMENSION(ash - SIZE(ain)) :: Asize1 ! Other dimension
INTEGER, DIMENSION(bsh - SIZE(bin)) :: Bsize1 ! Other dimension
INTEGER :: i, k
INTEGER :: Num
INTEGER, DIMENSION(ash + bsh - SIZE(ain) - SIZE(bin) ) :: Tsize
INTEGER, DIMENSION(SIZE(SHAPE(T))) :: OrderSize
INTEGER, DIMENSION(4) :: Ssize
INTEGER :: istat
! Check the consistency of the tensor rank
errorif: IF ( ash /= SIZE(SHAPE(A)) .OR. bsh /= SIZE(SHAPE(B)) ) THEN
error = 1
WRITE(*,*) 'The input arrays and ranks are not consistent.'
ELSE errorif
error = 0
END IF errorif
indexA = (/ (i, i=1,ash) /) ! index array A
indexB = (/ (i, i=1,bsh) /) ! index array B
Aother = setdiff( indexA, ain) ! index not contracted in A
Bother = setdiff( indexB, bin) ! index not contracted in B
Nain = SIZE(ain) ! # of index contracted
Nbin = SIZE(bin) ! # of index contracted
flagA = ALL( indexA(ash - Nain + 1: ash) == ain)
flagB = ALL( indexB(: Nbin) == bin)
ALLOCATE ( Anew( SIZE(A,Aother(1)),&
SIZE(A,Aother(2)),&
SIZE(A,ain(1)),&
SIZE(A,ain(2)) ) , STAT=istat) ! replace
! permute A only when necessary
ifAllocatedA: IF ( ALLOCATED(Anew) ) THEN
ifA: IF ( .NOT. flagA ) THEN ! Anew(...i)
!Anew = RESHAPE( A, SHAPE(A), ORDER = (/ Aother, ain /) )
Anew = RESHAPE( A, SHAPE(A), ORDER = neworder( (/ Aother, ain /) ) )
! equivalent to permute
ELSE ifA
Anew = A
END IF ifA
ELSE ifAllocatedA
WRITE(*,*) 'Warning-Array Anew not allocated!'
END IF ifAllocatedA
ALLOCATE ( Bnew( SIZE(B,bin(1)),&
SIZE(B,bin(2)),&
SIZE(B,Bother(1)),&
SIZE(B,Bother(2)) ) , STAT=istat) ! replace
! permute B only when necessary
ifAllocatedB: IF ( ALLOCATED(Bnew) ) THEN
ifB: IF ( .NOT. flagB ) THEN ! Bnew(i...)
!Bnew = RESHAPE( B, SHAPE(B), ORDER = (/ bin, Bother /) )
Bnew = RESHAPE( B, SHAPE(B), ORDER = neworder( (/ bin, Bother /) ) )
! equivalent to permute
ELSE ifB
Bnew = B
END IF ifB
ELSE ifAllocatedB
WRITE(*,*) 'Warning-Array Bnew not allocated!'
END IF ifAllocatedB
Asize = UBOUND(Anew) ! size of Anew
Bsize = UBOUND(Bnew) ! size of Bnew
SefAsize = Asize( ash - Nain + 1 : ash ) ! self dimension
SefBsize = Bsize( 1 : Nbin ) ! self dimension
Asize1 = Asize( 1 : ash - Nain ) ! other dimension
Bsize1 = Bsize( Nbin + 1 : bsh ) ! other dimension
! contract Anew(aaa, i) and Bnew(i, bbbb) to T(aaa, bbbb)
Tsize = (/ Asize1, Bsize1 /) ! size of T
prodAB: IF ( PRODUCT(SefAsize) == PRODUCT(SefBsize) ) THEN
ABorderif: IF ( PRESENT( ABorder) ) THEN
OrderSize = Tsize(ABorder)
ALLOCATE(T( Tsize(1),&
Tsize(2),&
Tsize(3),&
Tsize(4) ),&
STAT=istat) ! allocate T
ifAllocatedT: IF ( ALLOCATED(T) ) THEN
T = RESHAPE( MATMUL( & ! contract and reshape T
RESHAPE( Anew, SHAPE = (/ PRODUCT(Asize1), PRODUCT(SefAsize) /) ), &
RESHAPE( Bnew, SHAPE = (/ PRODUCT(SefBsize), PRODUCT(Bsize1) /) ) &
), SHAPE(T), ORDER = neworder( ABorder ) )
ELSE ifAllocatedT
WRITE(*,*) 'Warning-Array T not allocated!'
END IF ifAllocatedT
ELSE ABorderif
OrderSize = Tsize
ALLOCATE(T( Tsize(1),&
Tsize(2),&
Tsize(3),&
Tsize(4) ),&
STAT=istat) ! replace
ifAllocatedT2: IF ( ALLOCATED(T) ) THEN
T = RESHAPE( MATMUL( &
RESHAPE( Anew, SHAPE = (/ PRODUCT(Asize1), PRODUCT(SefAsize) /) ), &
RESHAPE( Bnew, SHAPE = (/ PRODUCT(SefBsize), PRODUCT(Bsize1) /) ) &
), SHAPE(T) )
ELSE ifAllocatedT2
WRITE(*,*) 'Warning-Array T not allocated!'
END IF ifAllocatedT2
END IF ABorderif
DEALLOCATE(Anew, STAT=istat)
DEALLOCATE(Bnew, STAT=istat)
ELSE prodAB
error = 2
WRITE(*,*) 'The contracted index is not equal.'
END IF prodAB
! if optional arguments 'ABorder' and 'squeeze' are present
IF ( PRESENT(ABorder) .AND. PRESENT(squeeze) ) THEN
Num = SIZE(squeeze)
!Tsize = (/ Asize1, Bsize1 /)
!OrderSize = Tsize(ABorder)
k = 1
DO i = 1, Num
Ssize( i ) = PRODUCT( OrderSize( k: k + squeeze(i) -1 ) )
k = k + squeeze(i)
END DO
END IF
outT = T
DEALLOCATE(T, STAT = istat)
END SUBROUTINE tensorcontract4444
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
SUBROUTINE tensorcontract5344 ( A, B, ash, ain, bsh, bin, ABorder, squeeze, error, outT)
!
! Purpose:
! Contract tensor A and B.
! A and B are tensor of ranks as specified in the function name.
! The function name should be understood in the following way:
! tensorcontract4444 means contract two rank 4 tensors ('44')
! into an intermediate rank 4 tensor ('4') and the final result is
! a rank 4 tensor ('4').
! ash and bsh are the ranks of the tensor A and B.
! ain and bin are the common index in A and B respectively.
! ABorder gives the contracted tensor sequence.
! squeeze specifis the new shape of the contracted tensor.
! For example, A(x,y,i,m,n,p), B(a,i,m,b,c); if we want to contract the
! common index i and m then we need to have ain=(3,4) and bin=(2,3);
! after the contraction, we will get the intermediate tensor T(xynp,abc);
! in order to get T(x,a,y,b,n,p,c), we need to set ABorder=(1,5,2,6,3,4,7);
! it usually works in the following way:
! T(xynp,abc):
! x y n p a b c
! 1 2 3 4 5 6 7
! T(x,a,y,b,n,p,c)
! x a y b n p c
! 1 5 2 6 3 4 7 ! This is just ABorder
!
! If squeeze=(3,2,2), then one will squeeze the first 3(xay) index,
! the middle 2(bn), and the last 2(pc) index to form a rank 3 tensor.
! error is the error flag.
! error = 0: no error
! error = 1: The input arrays and ranks are not consistent.
! error = 2: The contracted index is not equal.
!
! In order to get functions for other ranks, one will have to change
! the declaration of the following variables:
! A
! B
! Anew
! Bnew
! outT
! T
! Ssize
! and some others as marked in the template file 'contract.tmpl'.
!
! The code can be generated by 'Cheetah' template engine for differet
! input and output ranks. See the python file 'contract_gen.py' for details.
USE set_precisions
USE useful_functions
IMPLICIT NONE
! Data dictionary: declare calling parameter types & definitions
REAL(kind=DBL), INTENT(IN), DIMENSION(:,:,:,:,:) :: A ! Input array A
REAL(kind=DBL), INTENT(IN), DIMENSION(:,:,:) :: B ! Input array B
INTEGER, INTENT(IN) :: ash ! Rank of A
INTEGER, INTENT(IN), DIMENSION(:) :: ain ! Contraction index
INTEGER, INTENT(IN) :: bsh ! Rank of B
INTEGER, INTENT(IN), DIMENSION(:) :: bin ! Contraction index
INTEGER, INTENT(IN), DIMENSION(:), OPTIONAL :: ABorder ! Opt input
INTEGER, INTENT(IN), DIMENSION(:), OPTIONAL :: squeeze ! Opt input
INTEGER, INTENT(OUT) :: error ! Error flag
REAL(kind=DBL), INTENT(OUT), DIMENSION(:,:,:,:) :: outT ! Output
! Data dictionary: declare local variable types & definitions
INTEGER, DIMENSION(ash) :: indexA ! Index array A
INTEGER, DIMENSION(bsh) :: indexB ! Index array B
INTEGER, DIMENSION(ash - SIZE(ain)) :: Aother ! Index not contracted in A
INTEGER, DIMENSION(bsh - SIZE(bin)) :: Bother ! Index not contracted in B
INTEGER :: Nain, Nbin ! # of index contracted
LOGICAL :: flagA, flagB ! Flags for permutation
REAL(kind=DBL), ALLOCATABLE, DIMENSION(:,:,:,:,:) :: Anew ! Copy of A
REAL(kind=DBL), ALLOCATABLE, DIMENSION(:,:,:) :: Bnew ! Copy of B
REAL(kind=DBL), ALLOCATABLE, DIMENSION(:,:,:,:) :: T ! Intermediate one
INTEGER, DIMENSION(ash) :: Asize ! Size of Anew
INTEGER, DIMENSION(bsh) :: Bsize ! Size of Bnew
INTEGER, DIMENSION(SIZE(ain)) :: SefAsize ! Self dimension
INTEGER, DIMENSION(SIZE(bin)) :: SefBsize ! Self dimension
INTEGER, DIMENSION(ash - SIZE(ain)) :: Asize1 ! Other dimension
INTEGER, DIMENSION(bsh - SIZE(bin)) :: Bsize1 ! Other dimension
INTEGER :: i, k
INTEGER :: Num
INTEGER, DIMENSION(ash + bsh - SIZE(ain) - SIZE(bin) ) :: Tsize
INTEGER, DIMENSION(SIZE(SHAPE(T))) :: OrderSize
INTEGER, DIMENSION(4) :: Ssize
INTEGER :: istat
! Check the consistency of the tensor rank
errorif: IF ( ash /= SIZE(SHAPE(A)) .OR. bsh /= SIZE(SHAPE(B)) ) THEN
error = 1
WRITE(*,*) 'The input arrays and ranks are not consistent.'
ELSE errorif
error = 0
END IF errorif
indexA = (/ (i, i=1,ash) /) ! index array A
indexB = (/ (i, i=1,bsh) /) ! index array B
Aother = setdiff( indexA, ain) ! index not contracted in A
Bother = setdiff( indexB, bin) ! index not contracted in B
Nain = SIZE(ain) ! # of index contracted
Nbin = SIZE(bin) ! # of index contracted
flagA = ALL( indexA(ash - Nain + 1: ash) == ain)
flagB = ALL( indexB(: Nbin) == bin)
ALLOCATE ( Anew( SIZE(A,Aother(1)),&
SIZE(A,Aother(2)),&
SIZE(A,Aother(3)),&
SIZE(A,ain(1)),&
SIZE(A,ain(2)) ) , STAT=istat) ! replace
! permute A only when necessary
ifAllocatedA: IF ( ALLOCATED(Anew) ) THEN
ifA: IF ( .NOT. flagA ) THEN ! Anew(...i)
!Anew = RESHAPE( A, SHAPE(A), ORDER = (/ Aother, ain /) )
Anew = RESHAPE( A, SHAPE(A), ORDER = neworder( (/ Aother, ain /) ) )
! equivalent to permute
ELSE ifA
Anew = A
END IF ifA
ELSE ifAllocatedA
WRITE(*,*) 'Warning-Array Anew not allocated!'
END IF ifAllocatedA
ALLOCATE ( Bnew( SIZE(B,bin(1)),&
SIZE(B,bin(2)),&
SIZE(B,Bother(1)) ) , STAT=istat) ! replace
! permute B only when necessary
ifAllocatedB: IF ( ALLOCATED(Bnew) ) THEN
ifB: IF ( .NOT. flagB ) THEN ! Bnew(i...)
!Bnew = RESHAPE( B, SHAPE(B), ORDER = (/ bin, Bother /) )
Bnew = RESHAPE( B, SHAPE(B), ORDER = neworder( (/ bin, Bother /) ) )
! equivalent to permute
ELSE ifB
Bnew = B
END IF ifB
ELSE ifAllocatedB
WRITE(*,*) 'Warning-Array Bnew not allocated!'
END IF ifAllocatedB
Asize = UBOUND(Anew) ! size of Anew
Bsize = UBOUND(Bnew) ! size of Bnew
SefAsize = Asize( ash - Nain + 1 : ash ) ! self dimension
SefBsize = Bsize( 1 : Nbin ) ! self dimension
Asize1 = Asize( 1 : ash - Nain ) ! other dimension
Bsize1 = Bsize( Nbin + 1 : bsh ) ! other dimension
! contract Anew(aaa, i) and Bnew(i, bbbb) to T(aaa, bbbb)
Tsize = (/ Asize1, Bsize1 /) ! size of T
prodAB: IF ( PRODUCT(SefAsize) == PRODUCT(SefBsize) ) THEN
ABorderif: IF ( PRESENT( ABorder) ) THEN
OrderSize = Tsize(ABorder)
ALLOCATE(T( Tsize(1),&
Tsize(2),&
Tsize(3),&
Tsize(4) ),&
STAT=istat) ! allocate T
ifAllocatedT: IF ( ALLOCATED(T) ) THEN
T = RESHAPE( MATMUL( & ! contract and reshape T
RESHAPE( Anew, SHAPE = (/ PRODUCT(Asize1), PRODUCT(SefAsize) /) ), &
RESHAPE( Bnew, SHAPE = (/ PRODUCT(SefBsize), PRODUCT(Bsize1) /) ) &
), SHAPE(T), ORDER = neworder( ABorder ) )
ELSE ifAllocatedT
WRITE(*,*) 'Warning-Array T not allocated!'
END IF ifAllocatedT
ELSE ABorderif
OrderSize = Tsize
ALLOCATE(T( Tsize(1),&
Tsize(2),&
Tsize(3),&
Tsize(4) ),&
STAT=istat) ! replace
ifAllocatedT2: IF ( ALLOCATED(T) ) THEN
T = RESHAPE( MATMUL( &
RESHAPE( Anew, SHAPE = (/ PRODUCT(Asize1), PRODUCT(SefAsize) /) ), &
RESHAPE( Bnew, SHAPE = (/ PRODUCT(SefBsize), PRODUCT(Bsize1) /) ) &
), SHAPE(T) )
ELSE ifAllocatedT2
WRITE(*,*) 'Warning-Array T not allocated!'
END IF ifAllocatedT2
END IF ABorderif
DEALLOCATE(Anew, STAT=istat)
DEALLOCATE(Bnew, STAT=istat)
ELSE prodAB
error = 2
WRITE(*,*) 'The contracted index is not equal.'
END IF prodAB
! if optional arguments 'ABorder' and 'squeeze' are present
IF ( PRESENT(ABorder) .AND. PRESENT(squeeze) ) THEN
Num = SIZE(squeeze)
!Tsize = (/ Asize1, Bsize1 /)
!OrderSize = Tsize(ABorder)
k = 1
DO i = 1, Num
Ssize( i ) = PRODUCT( OrderSize( k: k + squeeze(i) -1 ) )
k = k + squeeze(i)
END DO
END IF
outT = T
DEALLOCATE(T, STAT = istat)
END SUBROUTINE tensorcontract5344
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
SUBROUTINE tensorcontract5455 ( A, B, ash, ain, bsh, bin, ABorder, squeeze, error, outT)
!
! Purpose:
! Contract tensor A and B.
! A and B are tensor of ranks as specified in the function name.
! The function name should be understood in the following way:
! tensorcontract4444 means contract two rank 4 tensors ('44')
! into an intermediate rank 4 tensor ('4') and the final result is
! a rank 4 tensor ('4').
! ash and bsh are the ranks of the tensor A and B.
! ain and bin are the common index in A and B respectively.
! ABorder gives the contracted tensor sequence.
! squeeze specifis the new shape of the contracted tensor.
! For example, A(x,y,i,m,n,p), B(a,i,m,b,c); if we want to contract the
! common index i and m then we need to have ain=(3,4) and bin=(2,3);
! after the contraction, we will get the intermediate tensor T(xynp,abc);
! in order to get T(x,a,y,b,n,p,c), we need to set ABorder=(1,5,2,6,3,4,7);
! it usually works in the following way:
! T(xynp,abc):
! x y n p a b c
! 1 2 3 4 5 6 7
! T(x,a,y,b,n,p,c)
! x a y b n p c
! 1 5 2 6 3 4 7 ! This is just ABorder
!
! If squeeze=(3,2,2), then one will squeeze the first 3(xay) index,
! the middle 2(bn), and the last 2(pc) index to form a rank 3 tensor.
! error is the error flag.
! error = 0: no error
! error = 1: The input arrays and ranks are not consistent.
! error = 2: The contracted index is not equal.
!
! In order to get functions for other ranks, one will have to change
! the declaration of the following variables:
! A
! B
! Anew
! Bnew
! outT
! T
! Ssize
! and some others as marked in the template file 'contract.tmpl'.
!
! The code can be generated by 'Cheetah' template engine for differet
! input and output ranks. See the python file 'contract_gen.py' for details.
USE set_precisions
USE useful_functions
IMPLICIT NONE
! Data dictionary: declare calling parameter types & definitions
REAL(kind=DBL), INTENT(IN), DIMENSION(:,:,:,:,:) :: A ! Input array A
REAL(kind=DBL), INTENT(IN), DIMENSION(:,:,:,:) :: B ! Input array B
INTEGER, INTENT(IN) :: ash ! Rank of A
INTEGER, INTENT(IN), DIMENSION(:) :: ain ! Contraction index
INTEGER, INTENT(IN) :: bsh ! Rank of B
INTEGER, INTENT(IN), DIMENSION(:) :: bin ! Contraction index
INTEGER, INTENT(IN), DIMENSION(:), OPTIONAL :: ABorder ! Opt input
INTEGER, INTENT(IN), DIMENSION(:), OPTIONAL :: squeeze ! Opt input
INTEGER, INTENT(OUT) :: error ! Error flag
REAL(kind=DBL), INTENT(OUT), DIMENSION(:,:,:,:,:) :: outT ! Output
! Data dictionary: declare local variable types & definitions
INTEGER, DIMENSION(ash) :: indexA ! Index array A
INTEGER, DIMENSION(bsh) :: indexB ! Index array B
INTEGER, DIMENSION(ash - SIZE(ain)) :: Aother ! Index not contracted in A
INTEGER, DIMENSION(bsh - SIZE(bin)) :: Bother ! Index not contracted in B
INTEGER :: Nain, Nbin ! # of index contracted
LOGICAL :: flagA, flagB ! Flags for permutation
REAL(kind=DBL), ALLOCATABLE, DIMENSION(:,:,:,:,:) :: Anew ! Copy of A
REAL(kind=DBL), ALLOCATABLE, DIMENSION(:,:,:,:) :: Bnew ! Copy of B
REAL(kind=DBL), ALLOCATABLE, DIMENSION(:,:,:,:,:) :: T ! Intermediate one
INTEGER, DIMENSION(ash) :: Asize ! Size of Anew
INTEGER, DIMENSION(bsh) :: Bsize ! Size of Bnew
INTEGER, DIMENSION(SIZE(ain)) :: SefAsize ! Self dimension
INTEGER, DIMENSION(SIZE(bin)) :: SefBsize ! Self dimension
INTEGER, DIMENSION(ash - SIZE(ain)) :: Asize1 ! Other dimension
INTEGER, DIMENSION(bsh - SIZE(bin)) :: Bsize1 ! Other dimension
INTEGER :: i, k
INTEGER :: Num
INTEGER, DIMENSION(ash + bsh - SIZE(ain) - SIZE(bin) ) :: Tsize
INTEGER, DIMENSION(SIZE(SHAPE(T))) :: OrderSize
INTEGER, DIMENSION(5) :: Ssize
INTEGER :: istat
! Check the consistency of the tensor rank
errorif: IF ( ash /= SIZE(SHAPE(A)) .OR. bsh /= SIZE(SHAPE(B)) ) THEN
error = 1
WRITE(*,*) 'The input arrays and ranks are not consistent.'
ELSE errorif
error = 0
END IF errorif
indexA = (/ (i, i=1,ash) /) ! index array A
indexB = (/ (i, i=1,bsh) /) ! index array B
Aother = setdiff( indexA, ain) ! index not contracted in A
Bother = setdiff( indexB, bin) ! index not contracted in B
Nain = SIZE(ain) ! # of index contracted
Nbin = SIZE(bin) ! # of index contracted
flagA = ALL( indexA(ash - Nain + 1: ash) == ain)
flagB = ALL( indexB(: Nbin) == bin)
ALLOCATE ( Anew( SIZE(A,Aother(1)),&
SIZE(A,Aother(2)),&
SIZE(A,Aother(3)),&
SIZE(A,ain(1)),&
SIZE(A,ain(2)) ) , STAT=istat) ! replace
! permute A only when necessary
ifAllocatedA: IF ( ALLOCATED(Anew) ) THEN
ifA: IF ( .NOT. flagA ) THEN ! Anew(...i)
!Anew = RESHAPE( A, SHAPE(A), ORDER = (/ Aother, ain /) )
Anew = RESHAPE( A, SHAPE(A), ORDER = neworder( (/ Aother, ain /) ) )
! equivalent to permute
ELSE ifA
Anew = A
END IF ifA
ELSE ifAllocatedA
WRITE(*,*) 'Warning-Array Anew not allocated!'
END IF ifAllocatedA
ALLOCATE ( Bnew( SIZE(B,bin(1)),&
SIZE(B,bin(2)),&
SIZE(B,Bother(1)),&
SIZE(B,Bother(2)) ) , STAT=istat) ! replace
! permute B only when necessary
ifAllocatedB: IF ( ALLOCATED(Bnew) ) THEN
ifB: IF ( .NOT. flagB ) THEN ! Bnew(i...)
!Bnew = RESHAPE( B, SHAPE(B), ORDER = (/ bin, Bother /) )
Bnew = RESHAPE( B, SHAPE(B), ORDER = neworder( (/ bin, Bother /) ) )
! equivalent to permute