bartorch.linop.FFT

class bartorch.linop.FFT(shape, axes, inverse=False, centred=True, **kwargs)

BART’s unitary Fourier transform along axes, centred by default.

Parameters:

• shape (tuple of int) – The shape it transforms, C order.

• axes (int or tuple of int) – Which axes to transform, as indices into shape; negative indices count from the end.

• inverse (bool) – Transform the other way.

• centred (bool) – Put the zero frequency in the middle, which is BART’s fftc.

Examples

>>> F = FFT((8, 16), axes=(-1, -2))
>>> F(x).shape
torch.Size([8, 16])

__init__(shape, axes, inverse=False, centred=True, **kwargs)

Methods

A(x, **kwargs)	A x, under deepinv's name.
A_adjoint(y, **kwargs)	A^H y, under deepinv's name, recorded for autograd.
A_adjoint_A(x, **kwargs)	A^H A x, under deepinv's name, recorded for autograd.
A_dagger(y, **kwargs)	The pseudo-inverse, under deepinv's name.
__init__(shape, axes[, inverse, centred])
adjoint(y[, out])	A^H y, without recording for autograd.
cogram()	A A^H as an operator.
conj()	conj(A): conjugate the input, apply, conjugate the output.
forward(x[, out])	A x, without recording for autograd.
gram()	A^H A as an operator.
normal(x[, out])	A^H A x.
opnorm()	The spectral norm, by BART's power iteration on A^H A.
pinv(y[, damp])	(A^H A + damp I)^-1 A^H y, the damped least-squares solution.
to_nonlinear()	The same operator as a NonlinearOperator.

Attributes

H	A^H, from BART's own adjoint constructor.
T	A^T, the adjoint without the conjugation, as conj(A).H.
codim_rank	How many axes the codomain has.
codim_shape	The codomain, under pyxu's name for it; the same as oshape.
codim_size	How many elements the codomain holds.
device
dim_rank	How many axes the domain has.
dim_shape	The domain, under pyxu's name for it; the same as ishape.
dim_size	How many elements the domain holds.
ishape
oshape