bartorch.linop.ScaledSum

class bartorch.linop.ScaledSum(shape, axes)

Sum over axes, divided by the square root of how many were summed.

BART’s linop_scaled_sum. The scaling is what makes it well behaved: its normal operator is an orthogonal projection rather than a multiple of one, so its spectral norm is one and pinv() has a closed form – BART solves (A^H A + damp I) x = A^H y here directly, with no iteration.

Sum is the plain sum, which is what a reader usually wants; this is the one to reach for inside a solver, where the conditioning and the exact inverse are worth the factor.

Parameters:

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

• axes (int or tuple of int) – Which axes to sum, as indices into shape.

__init__(shape, axes)

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)
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