bartorch.nlop.Derivative

class bartorch.nlop.Derivative(op, output=0, input=0)

DF/dx_input of one output of a nonlinear operator, as a linear one.

nlop_get_derivative. This is a view: the point is wherever the operator’s last application left it, and it moves with the next one. That is what makes it usable as the inner problem of a Gauss-Newton step, where the linearisation point is the iterate, and what makes it wrong to hold on to across an unrelated evaluation.

Parameters:

• op (NonlinearOperator) – A BART-backed operator. One defined in Python by forward, derivative and adjoint has no handle to take a derivative of; use linearize() for those.

• output (int) – Which output and which input, counted BART’s way.

• input (int) – Which output and which input, counted BART’s way.

__init__(op, output=0, input=0)

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__(op[, output, input])
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