fastFourierTransform(_:axesTensor:descriptor:name:)

Declaration

func fastFourierTransform(_ tensor: MPSGraphTensor, axesTensor: MPSGraphTensor, descriptor: MPSGraphFFTDescriptor, name: String?) -> MPSGraphTensor

Parameters

• tensor:

  A complex or real-valued input tensor.

• axesTensor:

  A tensor of rank one containing the axes over which MPSGraph performs the transformation. See Fastfouriertransform(_:axes:descriptor:name:).

• descriptor:

  A descriptor that defines the parameters of the Fourier transform operation - see Mpsgraphfftdescriptor.

• name:

  The name for the operation.

Return Value

A valid complex-valued MPSGraphTensor of the same shape as tensor.

Discussion

This operation computes the fast Fourier transform of the input tensor according to the following formulae.

    output[mu] = scale * sum_nu exp( +/- i * 2Pi * mu * nu / n ) input[nu], where

scale = 1 for scaling_mode = none, scale = 1/V_f for scaling_mode = size, scale = 1/sqrt(V_f) for scaling_mode = unitary, where V_f is the volume of the transformation defined by the dimensions included in axes (V_f = prod_{i \in axes} shape(input)[i]) (see scalingMode), + is selected in +/- when inverse is specified, otherwise - is used and the sum is done separately over each dimension in axes and n is the dimension length of that axis.