HermiteanToRealFFT(_:axes:descriptor:name:)
Creates a Hermitean-to-real fast Fourier transform operation and returns the result tensor.
Declaration
func HermiteanToRealFFT(_ tensor: MPSGraphTensor, axes: [NSNumber], descriptor: MPSGraphFFTDescriptor, name: String?) -> MPSGraphTensorParameters
- tensor:
A complex-valued input tensor with reduced size (see Discussion). Must have datatype
MPSDataTypeComplexFloat32orMPSDataTypeComplexFloat16. - axes:
An array of numbers that specifies over which axes MPSGraph performs the Fourier transform - all axes must be contained within last four dimensions of the input tensor.
- descriptor:
A descriptor that defines the parameters of the Fourier transform operation - see Mpsgraphfftdescriptor.
- name:
The name for the operation.
Return Value
A valid MPSGraphTensor of type MPSDataTypeFloat32 or MPSDataTypeFloat16 (full size).
Discussion
This operation computes the fast Fourier transform of a complex-valued input tensor according to the following formulae.
output[mu] = scale * sum_nu exp( +/- i * 2Pi * mu * nu / n ) in'[nu], wherein'[nu] = conjugate(in[n - nu]), for the last dimension defined by axes when nu is out of range of the input dimension. 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. With this API MPSGraph treats the input tensor to have only the unique frequencies, which means that the resulting tensor has size (inSize-1)*2 + x in the last dimension defined by axes, where inSize = shape(input)[axis] ( = (n/2)+1 ) is the size of the input tensor in the last transformed dimension and x = 1 when roundToOddHermitean = YES and x = 0 otherwise.