bartorch.linop.Matrix

class bartorch.linop.Matrix(matrix, oshape, ishape)

Multiplication by a matrix along one axis, BART’s linop_matrix.

The matrix is an array like any other: it contracts the axis the domain and the codomain differ along and broadcasts over the axes it has only one of, so one operator can carry a different matrix per slice.

Parameters:

• matrix (tensor) – The matrix, with the domain’s size along the axis it contracts and the codomain’s along the axis it produces.

• oshape (tuple of int) – Codomain and domain, C order, with the same number of axes.

• ishape (tuple of int) – Codomain and domain, C order, with the same number of axes.

Examples

A basis of k functions over t samples, applied along the first axis of (t, y, x):

>>> B = Matrix(basis, (k, y, x), (t, y, x))

__init__(matrix, oshape, ishape)

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__(matrix, oshape, ishape)
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