irfft#

Perform an N-D complex-to-real (C2R) FFT on the provided complex operand. The direction is implicitly inverse.

Parameters:

operand – A tensor (ndarray-like object). The currently supported types are numpy.ndarray, cupy.ndarray, and torch.Tensor.
axes – The dimensions along which the FFT is performed. axes[-1] is the ‘last transformed’ axis for rffts. Currently, it is required that the axes are contiguous and include the first or the last dimension. Only up to 3D FFTs are supported.
options – Specify options for the FFT as a FFTOptions object. Alternatively, a dict containing the parameters for the FFTOptions constructor can also be provided. If not specified, the value will be set to the default-constructed FFTOptions object.
execution – Specify execution space options for the FFT as a ExecutionCUDA or ExecutionCPU object. Alternatively, a string (‘cuda’ or ‘cpu’), or a dict with the ‘name’ key set to ‘cpu’ or ‘cuda’ and optional parameters relevant to the given execution space. If not specified, the execution space will be selected to match operand’s storage (in GPU or host memory), and the corresponding ExecutionCUDA or ExecutionCPU object will be default-constructed.
prolog – Provide device-callable function in LTO-IR format to use as load-callback as an object of type DeviceCallable. Alternatively, a dict containing the parameters for the DeviceCallable constructor can also be provided. The default is no prolog. Currently, callbacks are supported only with CUDA execution.
epilog – Provide device-callable function in LTO-IR format to use as store-callback as an object of type DeviceCallable. Alternatively, a dict containing the parameters for the DeviceCallable constructor can also be provided. The default is no epilog. Currently, callbacks are supported only with CUDA execution.
stream – Provide the CUDA stream to use for executing the operation. Acceptable inputs include cudaStream_t (as Python int), cupy.cuda.Stream, and torch.cuda.Stream. If a stream is not provided, the current stream from the operand package will be used.

Returns:

A real tensor that remains on the same device and belongs to the same package as the input operand. The extent of the last transformed axis in the result will be (operand.shape[axes[-1]] - 1) * 2 if FFTOptions.last_axis_parity is even, or operand.shape[axes[-1]] * 2 - 1 if FFTOptions.last_axis_parity is odd.

See also

fft(), ifft(), FFT.

Examples

>>> import cupy as cp
>>> import nvmath

Create a 3-D symmetric complex128 ndarray on the GPU:

>>> shape = 512, 768, 256
>>> a = nvmath.fft.rfft(cp.random.rand(*shape, dtype=cp.float64))

Perform a 3-D C2R FFT using the irfft() wrapper. The result r is a CuPy float64 ndarray:

>>> r = nvmath.fft.irfft(a)
>>> r.dtype
dtype('float64')

Notes

This function performs an inverse C2R N-D FFT, which is similar to irfftn but different from irfft in various numerical packages.
This function is a convenience wrapper around FFT and and is specifically meant for single use. The same computation can be performed with the stateful API by setting FFTOptions.fft_type to 'C2R' and passing the argument direction='inverse' when calling FFT.execute().
The input to this function must be Hermitian-symmetric, otherwise the result is undefined. While the symmetry requirement is partially captured by the different extents in the last transformed dimension between the input and result, there are additional constraints. As a specific example, 1-D transforms require the first element (and the last element, if the extent is even) of the input to be purely real-valued. In addition, if the input to irfft was generated using an R2C FFT with an odd last axis size, FFTOptions.last_axis_parity must be set to odd to recover the original signal.
For more details, please refer to C2R example and odd C2R example.