Contraction

This generic function performs contraction of tensors.

The contraction method contracts the multi-dimension arrays.

The general syntax is given below:

ans = CONTRACTION(a1, a2)

where,

a1 and a2 can be a Fortran array of rank 1, 2, 3, and 4.

Let's employ the following notation:

r0 rank-0 scalar
r1 rank-1 vector
r2 rank-2 matrix
r3 rank-3
r4 rank-4

Then, the following table explains this operator.

a1	a2	ans
`r1`	`r1`	`r0`
`r1`	`r2`	`r1`
`r1`	`r3`	`r2`
`r1`	`r4`	`r3`
`r2`	`r1`	`r1`
`r2`	`r2`	`r0`
`r2`	`r3`	`r1`
`r2`	`r4`	`r2`
`r3`	`r1`	`r2`
`r3`	`r2`	`r1`
`r3`	`r3`	`r0`
`r3`	`r4`	`r1`
`r4`	`r1`	`r3`
`r4`	`r2`	`r2`
`r4`	`r3`	`r1`
`r4`	`r4`	`r0`

Interface 1

܀ Interface
️܀ See example
↢

INTERFACE
  MODULE PURE FUNCTION Contraction(a1, a2) RESULT(ans)
    REAL(DFP), INTENT(IN) :: a1(:, :, :, :)
    REAL(DFP), INTENT(IN) :: a2(:)
    REAL(DFP) :: ans(size(a1, 1), size(a1, 2), size(a1, 3))
  END FUNCTION
END INTERFACE

Interface 2

܀ Interface
️܀ See example
↢

INTERFACE
  MODULE PURE FUNCTION Contraction(a1, a2) RESULT(ans)
    REAL(DFP), INTENT(IN) :: a1(:, :, :, :)
    REAL(DFP), INTENT(IN) :: a2(:,:)
    REAL(DFP) :: ans(size(a1, 1), size(a1, 2))
  END FUNCTION
END INTERFACE

Interface 3

܀ Interface
️܀ See example
↢

 INTERFACE
  MODULE PURE FUNCTION Contraction(a1, a2) RESULT(ans)
    REAL(DFP), INTENT(IN) :: a1(:, :, :, :)
    REAL(DFP), INTENT(IN) :: a2(:, :, :)
    REAL(DFP) :: ans(size(a1, 1))
  END FUNCTION
END INTERFACE

Interface 4

܀ Interface
️܀ See example
↢

INTERFACE
  MODULE PURE FUNCTION Contraction(a1, a2) RESULT(ans)
    REAL(DFP), INTENT(IN) :: a1(:, :, :, :)
    REAL(DFP), INTENT(IN) :: a2(:, :, :, :)
    REAL(DFP) :: ans
  END FUNCTION
END INTERFACE

Interface 5

܀ Interface
️܀ See example
↢

 INTERFACE
  MODULE PURE FUNCTION Contraction(a1, a2) RESULT(ans)
    REAL(DFP), INTENT(IN) :: a1(:, :, :)
    REAL(DFP), INTENT(IN) :: a2(:)
    REAL(DFP) :: ans(size(a1, 1), size(a1, 2))
  END FUNCTION
END INTERFACE

Interface 6

܀ Interface
️܀ See example
↢

 INTERFACE
  MODULE PURE FUNCTION Contraction(a1, a2) RESULT(ans)
    REAL(DFP), INTENT(IN) :: a1(:, :, :)
    REAL(DFP), INTENT(IN) :: a2(:, :)
    REAL(DFP) :: ans(size(a1, 1))
  END FUNCTION
END INTERFACE

Interface 7

܀ Interface
️܀ See example
↢

 INTERFACE
  MODULE PURE FUNCTION Contraction(a1, a2) RESULT(ans)
    REAL(DFP), INTENT(IN) :: a1(:,:,:)
    REAL(DFP), INTENT(IN) :: a2(:, :, :)
    REAL(DFP) :: ans
  END FUNCTION
END INTERFACE

Interface 8

܀ Interface
️܀ See example
↢

 INTERFACE
  MODULE PURE FUNCTION Contraction(a1, a2) RESULT(ans)
    REAL(DFP), INTENT(IN) :: a1(:,:,:)
    REAL(DFP), INTENT(IN) :: a2(:, :, :, :)
    REAL(DFP) :: ans(size(a2,4))
  END FUNCTION
END INTERFACE

Interface 9

܀ Interface
️܀ See example
↢

 INTERFACE
  MODULE PURE FUNCTION Contraction(a1, a2) RESULT(ans)
    REAL(DFP), INTENT(IN) :: a1(:, :)
    REAL(DFP), INTENT(IN) :: a2(:)
    REAL(DFP) :: ans(size(a1, 1))
  END FUNCTION
END INTERFACE

Interface 10

܀ Interface
️܀ See example
↢

 INTERFACE
  MODULE PURE FUNCTION Contraction(a1, a2) RESULT(ans)
    REAL(DFP), INTENT(IN) :: a1(:, :)
    REAL(DFP), INTENT(IN) :: a2(:, :)
    REAL(DFP) :: ans
  END FUNCTION
END INTERFACE

Interface 11

܀ Interface
️܀ See example
↢

 INTERFACE
  MODULE PURE FUNCTION Contraction(a1, a2) RESULT(ans)
    REAL(DFP), INTENT(IN) :: a1(:,:)
    REAL(DFP), INTENT(IN) :: a2(:, :, :)
    REAL(DFP) :: ans(size(a2,3))
  END FUNCTION
END INTERFACE

Interface 12

܀ Interface
️܀ See example
↢

 INTERFACE
  MODULE PURE FUNCTION Contraction(a1, a2) RESULT(ans)
    REAL(DFP), INTENT(IN) :: a1(:,:)
    REAL(DFP), INTENT(IN) :: a2(:, :, :, :)
    REAL(DFP) :: ans(size(a2,3), size(a2,4))
  END FUNCTION
END INTERFACE

Interface 13

܀ Interface
️܀ See example
↢

 INTERFACE
  MODULE PURE FUNCTION Contraction(a1, a2) RESULT(ans)
    REAL(DFP), INTENT(IN) :: a1(:)
    REAL(DFP), INTENT(IN) :: a2(:)
    REAL(DFP) :: ans
  END FUNCTION
END INTERFACE

Interface 14

܀ Interface
️܀ See example
↢

 INTERFACE
  MODULE PURE FUNCTION Contraction(a1, a2) RESULT(ans)
    REAL(DFP), INTENT(IN) :: a1(:)
    REAL(DFP), INTENT(IN) :: a2(:, :)
    REAL(DFP) :: ans(size(a2,2))
  END FUNCTION
END INTERFACE

Interface 15

܀ Interface
️܀ See example
↢

 INTERFACE
  MODULE PURE FUNCTION Contraction(a1, a2) RESULT(ans)
    REAL(DFP), INTENT(IN) :: a1(:)
    REAL(DFP), INTENT(IN) :: a2(:, :, :)
    REAL(DFP) :: ans(size(a2,2), size(a2,3))
  END FUNCTION
END INTERFACE

Interface 16

܀ Interface
️܀ See example
↢

 INTERFACE
  MODULE PURE FUNCTION Contraction(a1, a2) RESULT(ans)
    REAL(DFP), INTENT(IN) :: a1(:)
    REAL(DFP), INTENT(IN) :: a2(:, :, :, :)
    REAL(DFP) :: ans(size(a2,2), size(a2,3), size(a2,4))
  END FUNCTION
END INTERFACE

Contraction

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