bartorch.optim.iterators.ADMMIteration

class bartorch.optim.iterators.ADMMIteration(terms, image_shape, biases=None, **kwargs)

BART’s alternating direction method of multipliers, one step of it.

admm.c’s admm, which solves

min_x 0.5 ||A x - y||^2 + sum_j f_j(G_j x - b_j)

for arbitrary convex f_j. Each step solves for x by conjugate gradients on A^H A + rho sum_j G_j^H G_j, warm-started from the iterate before it, then updates each term’s split variable and dual:

rhs = A^H y + rho sum_j G_j^H (z_j - u_j + b_j)
x   = cg(rhs, from x)
w_j = alpha G_j x + (1 - alpha) (z_j + b_j) + u_j - b_j
z_j = prox_j(w_j, lambda / rho)
u_j = w_j - z_j

with alpha = 1.6, BART’s over-relaxation, and Boyd’s primal and dual residuals deciding when to stop and – with dynamic_rho – how rho moves.

The inner solve is BART’s own conjugate gradients over an operator whose normal is the one above, so the encoding is asked for its normal: a Toeplitz encoding stays one inside every step.

Parameters:

• terms (sequence of Regularizer) – The f_j, each with the transform and bias it carries.

• image_shape (tuple of int) – What the terms are configured for.

• biases (sequence of tensor, optional) – The b_j, each of its term’s transformed shape.

Notes

maxiter is a budget on applications of the normal operator rather than a count of outer steps, which is BART’s rule and a surprising one: admm breaks when nr_invokes > maxiter, and nr_invokes counts conjugate-gradient iterations across the whole run. Thirty with ten inner iterations is about five outer steps, not thirty.

__init__(terms, image_shape, biases=None, **kwargs)

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

Methods

__init__(terms, image_shape[, biases])	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.
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().
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.
forward(X, cur_data_fidelity, cur_prior, ...)	General form of a single iteration of splitting algorithms for minimizing \(F = f + \lambda \regname\), alternating between a step on \(f\) and a step on \(\regname\).
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.
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.
parameters([recurse])	Return an iterator over module parameters.
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.
relaxation_step(u, v, beta)	Performs a relaxation step of the form \(\beta u + (1-\beta) v\).
requires_grad_([requires_grad])	Change if autograd should record operations on parameters in this module.
restart()	Forget the budget already spent, for a fresh run.
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