atoms

Module: atoms

Inheritance diagram for regreg.atoms:

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Classes

affine_atom

class regreg.atoms.affine_atom(atom_obj, atransform)

Bases: object

Given a seminorm on \(\mathbb{R}^p\), i.e. \(\beta \mapsto h_K(\beta)\) this class creates a new seminorm that evaluates \(h_K(D\beta+\alpha)\)

This class does not have a prox, but its dual does. The prox of the dual is

\[\text{minimize} \frac{1}{2} \|y-x\|^2_2 + x^T\alpha \ \text{s.t.} \ x \in \lambda K\]

__init__(atom_obj, atransform)

Initialize self. See help(type(self)) for accurate signature.

property dual

latexify(var=None, idx='')

Return a LaTeX representation of an object.

>>> from regreg.api import l1norm
>>> penalty = l1norm(10, lagrange=0.9)
>>> penalty.latexify(var=r'\gamma') 
'\\lambda_{} \\|\\gamma\\|_1'

Parameters

var : string

Argument of the functions

idx : string

Optional subscript index.

Returns

L : string

A LaTeX representation of the atom.

nonsmooth_objective(arg, check_feasibility=False)

Return self.atom.seminorm(self.linear_transform.linear_map(x))

objective_vars = {'linear': 'X'}

smoothed(smoothing_quadratic)

Add quadratic smoothing term

atom

class regreg.atoms.atom(shape, offset=None, quadratic=None, initial=None)

Bases: regreg.problems.composite.nonsmooth

A class that defines the API for support functions.

__init__(shape, offset=None, quadratic=None, initial=None)

Initialize self. See help(type(self)) for accurate signature.

apply_offset(x)

If self.offset is not None, return x-self.offset, else return x.

property conjugate

The conjugate of an atom.

property dual

get_conjugate()

get_dual()

get_offset()

get_quadratic()

Get the quadratic part of the composite.

latexify(var=None, idx='')

property linear_transform

The linear transform applied before a penalty is computed. Defaults to regreg.affine.identity

>>> from regreg.api import l1norm
>>> penalty = l1norm(30, lagrange=3.4)
>>> type(penalty.linear_transform)
<class 'regreg.affine.identity'>

nonsmooth_objective(arg, check_feasibility=False)

objective(x, check_feasibility=False)

objective_template = 'f(%(var)s)'

objective_vars = {'dualklass': 'dualnorm', 'klass': 'norm', 'offset': '\\alpha', 'shape': 'p', 'var': '\\beta'}

property offset

proximal(proxq, prox_control=None)

proximal_optimum(quadratic)

proximal_step(quadratic, prox_control=None)

Compute the proximal optimization

Parameters

prox_control: [None, dict]

If not None, then a dictionary of parameters for the prox procedure

property quadratic

Quadratic part of the object, instance of regreg.identity_quadratic.identity_quadratic.

set_offset(value)

set_quadratic(quadratic)

Set the quadratic part of the composite.

smooth_objective(x, mode='both', check_feasibility=False)

The zero function.

smoothed(smoothing_quadratic)

Add quadratic smoothing term

solve(quadratic=None, return_optimum=False, **fit_args)

tol = 1e-05