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In order to obtain maximum performance in FFTW, you should store your
data in arrays that have been specially aligned in memory (see SIMD alignment and fftw_malloc). Enforcing alignment also permits you to
safely use the new-array execute functions (see New-array Execute Functions) to apply a given plan to more than one pair of in/out
arrays. Unfortunately, standard Fortran arrays do *not* provide
any alignment guarantees. The *only* way to allocate aligned
memory in standard Fortran is to allocate it with an external C
function, like the `fftw_alloc_real`

and
`fftw_alloc_complex`

functions. Fortunately, Fortran 2003 provides
a simple way to associate such allocated memory with a standard Fortran
array pointer that you can then use normally.

We therefore recommend allocating all your input/output arrays using the following technique:

- Declare a
`pointer`

,`arr`

, to your array of the desired type and dimensions. For example,`real(C_DOUBLE), pointer :: a(:,:)`

for a 2d real array, or`complex(C_DOUBLE_COMPLEX), pointer :: a(:,:,:)`

for a 3d complex array. - The number of elements to allocate must be an
`integer(C_SIZE_T)`

. You can either declare a variable of this type, e.g.`integer(C_SIZE_T) :: sz`

, to store the number of elements to allocate, or you can use the`int(..., C_SIZE_T)`

intrinsic function. e.g. set`sz = L * M * N`

or use`int(L * M * N, C_SIZE_T)`

for an L × M × N array. - Declare a
`type(C_PTR) :: p`

to hold the return value from FFTW's allocation routine. Set`p = fftw_alloc_real(sz)`

for a real array, or`p = fftw_alloc_complex(sz)`

for a complex array. - Associate your pointer
`arr`

with the allocated memory`p`

using the standard`c_f_pointer`

subroutine:`call c_f_pointer(p, arr, [...dimensions...])`

, where`[...dimensions...])`

are an array of the dimensions of the array (in the usual Fortran order). e.g.`call c_f_pointer(p, arr, [L,M,N])`

for an L × M × N array. (Alternatively, you can omit the dimensions argument if you specified the shape explicitly when declaring`arr`

.) You can now use`arr`

as a usual multidimensional array. - When you are done using the array, deallocate the memory by
`call fftw_free(p)`

on`p`

.

For example, here is how we would allocate an L × M 2d real array:

real(C_DOUBLE), pointer :: arr(:,:) type(C_PTR) :: p p = fftw_alloc_real(int(L * M, C_SIZE_T)) call c_f_pointer(p, arr, [L,M])...use arr and arr(i,j) as usual...call fftw_free(p)

and here is an L × M × N 3d complex array:

complex(C_DOUBLE_COMPLEX), pointer :: arr(:,:,:) type(C_PTR) :: p p = fftw_alloc_complex(int(L * M * N, C_SIZE_T)) call c_f_pointer(p, arr, [L,M,N])...use arr and arr(i,j,k) as usual...call fftw_free(p)

See Reversing array dimensions for an example allocating a single array and associating both real and complex array pointers with it, for in-place real-to-complex transforms.