Transposition

This is an option that allows for the result of a high-dimensional transform to be presented in a transposed manner. The default setting is DFTI_NONE and can be set to DFTI_ALLOW. Similar to that of scrambled order, sometimes in higher dimension transform, performance can be gained if the result is delivered in a transposed manner. FFT interface offers an option for the output be returned in a transposed form if performance gain is possible. Since the generic stride specification is naturally suited for representation of transposition, this option allows the strides for the output to be possibly different from those originally specified by the user. Consider an example where a two-dimensional result

Y_j₁,_j₂, 0 ≤ j_i < n_i,

is expected. Originally the user specified that the result be distributed in the (flat) array Y in with generic strides L₁ = 1 and L₂ = n₁. With the transposition option, the computation may actually return the result into Y with stride L₁ = n₂ and L₂ = 1. These strides can be obtained from an appropriate inquiry function. Note also that in dimension 3 and above, transposition means an arbitrary permutation of the dimension.