bartorch.optim.iterators.NormalEquations

class bartorch.optim.iterators.NormalEquations(weight=0.0)

||A x - y||^2 / 2, differentiated through BART’s normal operator.

The gradient is A^H A x - A^H y. Written that way rather than as A^H (A x - y) it is one application of the operator’s own normal, which for an encoding built with toeplitz=True is a convolution with a point spread function rather than a transform and its adjoint. That is the difference the whole encoding was built for, and it would be lost by taking the obvious route.

A^H y does not change during a solve, so it is computed once and kept, keyed by the tensor it came from. A physics that is not one of ours falls back to A_adjoint(A(x) - y).

__init__(weight=0.0)

Initialize internal Module state, shared by both nn.Module and ScriptModule.

Methods

__init__([weight])	Initialize internal Module state, shared by both nn.Module and ScriptModule.
add_module(name, module)	Add a child module to the current module.
apply(fn)	Apply fn recursively to every submodule (as returned by .children()) as well as self.
bfloat16()	Casts all floating point parameters and buffers to bfloat16 datatype.
bregman_prox(x, bregman_potential, *args[, ...])	Calculates the (right) Bregman proximity operator of h` at \(x\), with Bregman potential bregman_potential.
buffers([recurse])	Return an iterator over module buffers.
children()	Return an iterator over immediate children modules.
compile(*args, **kwargs)	Compile this Module's forward using torch.compile().
conjugate(x, *args, **kwargs)	Computes the convex conjugate potential \(h^*(y) = \sup_{x} \langle x, y \rangle - h(x)\).
cpu()	Move all model parameters and buffers to the CPU.
cuda([device])	Move all model parameters and buffers to the GPU.
double()	Casts all floating point parameters and buffers to double datatype.
eval()	Set the module in evaluation mode.
extra_repr()	Return the extra representation of the module.
float()	Casts all floating point parameters and buffers to float datatype.
fn(x, y, physics, *args, **kwargs)	Computes the data fidelity term \(\datafid{x}{y} = \distance{\forw{x}}{y}\).
forward(x, *args, **kwargs)	Computes the value of the potential \(h(x)\).
get_buffer(target)	Return the buffer given by target if it exists, otherwise throw an error.
get_extra_state()	Return any extra state to include in the module's state_dict.
get_parameter(target)	Return the parameter given by target if it exists, otherwise throw an error.
get_submodule(target)	Return the submodule given by target if it exists, otherwise throw an error.
grad(x, y, physics, *args, **kwargs)	Calculates the gradient of the data fidelity term \(\datafidname\) at \(x\).
grad_conj(x, *args, **kwargs)	Calculates the gradient of the convex conjugate potential \(h^*\) at \(x\).
grad_d(u, y, *args, **kwargs)	Computes the gradient \(\nabla_u\distance{u}{y}\), computed in \(u\).
half()	Casts all floating point parameters and buffers to half datatype.
ipu([device])	Move all model parameters and buffers to the IPU.
load_state_dict(state_dict[, strict, assign])	Copy parameters and buffers from state_dict into this module and its descendants.
modules([remove_duplicate])	Return an iterator over all modules in the network.
mtia([device])	Move all model parameters and buffers to the MTIA.
named_buffers([prefix, recurse, ...])	Return an iterator over module buffers, yielding both the name of the buffer as well as the buffer itself.
named_children()	Return an iterator over immediate children modules, yielding both the name of the module as well as the module itself.
named_modules([memo, prefix, remove_duplicate])	Return an iterator over all modules in the network, yielding both the name of the module as well as the module itself.
named_parameters([prefix, recurse, ...])	Return an iterator over module parameters, yielding both the name of the parameter as well as the parameter itself.
normal(x, physics)	A^H A x + lambda x, the operator lsqr builds.
parameters([recurse])	Return an iterator over module parameters.
prox(x, *args[, gamma, stepsize_inter, ...])	Calculates the proximity operator of \(h\) at \(x\).
prox_conjugate(x, *args[, gamma, lamb])	Calculates the proximity operator of the convex conjugate \((\lambda h)^*\) at \(x\), using the Moreau formula.
prox_d(u, y, *args, **kwargs)	Computes the proximity operator \(\operatorname{prox}_{\gamma\distance{\cdot}{y}}(u)\), computed in \(u\).
prox_d_conjugate(u, y, *args, **kwargs)	Computes the proximity operator of the convex conjugate of the distance function \(\distance{u}{y}\).
register_backward_hook(hook)	Register a backward hook on the module.
register_buffer(name, tensor[, persistent])	Add a buffer to the module.
register_forward_hook(hook, *[, prepend, ...])	Register a forward hook on the module.
register_forward_pre_hook(hook, *[, ...])	Register a forward pre-hook on the module.
register_full_backward_hook(hook[, prepend])	Register a backward hook on the module.
register_full_backward_pre_hook(hook[, prepend])	Register a backward pre-hook on the module.
register_load_state_dict_post_hook(hook)	Register a post-hook to be run after module's load_state_dict() is called.
register_load_state_dict_pre_hook(hook)	Register a pre-hook to be run before module's load_state_dict() is called.
register_module(name, module)	Alias for add_module().
register_parameter(name, param)	Add a parameter to the module.
register_state_dict_post_hook(hook)	Register a post-hook for the state_dict() method.
register_state_dict_pre_hook(hook)	Register a pre-hook for the state_dict() method.
requires_grad_([requires_grad])	Change if autograd should record operations on parameters in this module.
set_extra_state(state)	Set extra state contained in the loaded state_dict.
set_submodule(target, module[, strict])	Set the submodule given by target if it exists, otherwise throw an error.
share_memory()	See torch.Tensor.share_memory_().
state_dict(*args[, destination, prefix, ...])	Return a dictionary containing references to the whole state of the module.
to(*args, **kwargs)	Move and/or cast the parameters and buffers.
to_empty(*, device[, recurse])	Move the parameters and buffers to the specified device without copying storage.
train([mode])	Set the module in training mode.
type(dst_type)	Casts all parameters and buffers to dst_type.
xpu([device])	Move all model parameters and buffers to the XPU.
zero_grad([set_to_none])	Reset gradients of all model parameters.

Attributes

T_destination
call_super_init
dump_patches
training