Question

Say I have a 3D array, A(1:3,1:4,1:5), and I only want to deal with part of it, e.g.:

real :: A(1:3,1:4,1:5), B(1:5,1:2)
real, allocatable :: C(:,:)

allocate(C(size(A,1),size(B,2)))
C = matmul(A(1:3,1,1:5),B)

Fortran seems fine with that. However, if I needed to deal with the transpose, then the transpose function in Fortran gets confused, e.g.:

real :: A(1:3,1:4,1:5), B(1:3,1:2)
real, allocatable :: C(:,:)

allocate(C(size(A,3),size(B,2)))
C = matmul(transpose(A(1:3,1,1:5)),B)

How can I swap dimensions around in an array with Fortran? For example, I have A(3,4,5); is there a function/command that takes this and gives me A(5,4,3) or A(4,3,5) or any arrangement I could wish for? Without, of course, doing something like copying A to a dummy array with the dimensions in the order required. I’m looking for a simple one line elegant way.

Thank you.

Answer 1

You don’t have a problem with TRANSPOSE. It is working just fine for the sample code you provided. The problem is that your arrays are not compatible for matrix multiplication. From Fortran 2008 Standard draft:

Case (i): If MATRIX A has shape [n, m] and MATRIX B has shape [m, k],
the result has shape [n, k].

In your case:

C = matmul(transpose(A(1:3,1,1:5)),B)

Here, transpose(A(1:3,1,1:5)) is a 5×3 matrix, and B is 2×5. Thus, these two matrices are non-comformable for MATMUL. I am wondering how you did not catch on this since compilers give a clear error message:

gfortran 4.1.2:

In file matrix.f90:13

C = matmul(transpose(A(:,1,:)),B)
          1
Error: different shape on dimension 2 for argument 'matrix_a' and dimension 1 for argument 'matrix_b' at (1) for intrinsic matmul

ifort 12.0.2.137:

matrix.f90(13): error #6241: The shapes of the arguments are inconsistent or nonconformable.   [MATMUL]
C = matmul(transpose(A(:,1,:)),B)
----^
compilation aborted for matrix.f90 (code 1)

pgf90 10.6-0 compiles but produces a run-time error:

0: MATMUL: nonconforming array shapes

For reshaping arrays in Fortran, you can use intrinsic function RESHAPE. From Fortran 2008 Standard draft:

13.7.140 RESHAPE (SOURCE, SHAPE [, PAD, ORDER])

1 Description. Construct an array of an arbitrary shape.

2 Class. Transformational
function.

3 Arguments. SOURCE shall be an array of any type. If PAD is
absent or of size zero, the size of SOURCE shall be greater
than or equal to PRODUCT (SHAPE). The size of the result is the product of the values of the
elements of SHAPE. SHAPE shall be a rank-one integer array. SIZE (x), where x is the actual argument corresponding to
SHAPE, shall be a constant expression whose value is positive and less than 16. It shall not have
an element whose value is negative. PAD (optional) shall be an array of the same type and type parameters as SOURCE. ORDER (optional)
shall be of type integer, shall have the same shape as SHAPE, and its
value shall be a permutation of (1, 2, . . . , n), where n is the size
of SHAPE. If absent, it is as if it were present with value (1, 2, . .
. , n).

4 Result Characteristics. The result is an array of shape
SHAPE (that is, SHAPE (RESHAPE (SOURCE, SHAPE, PAD, ORDER)) is equal
to SHAPE) with the same type and type parameters as SOURCE.

5 Result
Value. The elements of the result, taken in permuted subscript order
ORDER (1), . . . , ORDER (n), are those of SOURCE in normal array
element order followed if necessary by those of PAD in array element
order, followed if necessary by additional copies of PAD in array
element order.