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Package parsimony :: Package functions :: Package nesterov :: Module tv :: Class TotalVariation
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Class TotalVariation

source code

                            object --+        
                                     |        
                   properties.Gradient --+    
                                         |    
                            object --+   |    
                                     |   |    
properties.LipschitzContinuousGradient --+    
                                         |    
                            object --+   |    
                                     |   |    
                properties.Eigenvalues --+    
                                         |    
                            object --+   |    
                                     |   |    
           properties.ProximalOperator --+    
                                         |    
               properties.NesterovFunction --+
                                             |
                                object --+   |
                                         |   |
                        properties.Penalty --+
                                             |
                                object --+   |
                                         |   |
                     properties.Constraint --+
                                             |
                                            TotalVariation

The smoothed Total variation (TV) function

    f(beta) = l * (TV(beta) - c),

where TV(beta) is the smoothed total variation function. The constrained
version has the form

    TV(beta) <= c.
Instance Methods [hide private]
 
__init__(self, l, c=0.0, A=None, mu=0.0, penalty_start=0)
Parameters ---------- l : Non-negative float.		 source code
 
reset(self) source code
 
f(self, beta)
Function value.		 source code
 
phi(self, alpha, beta)
Function value with known alpha.		 source code
 
feasible(self, beta)
Feasibility of the constraint.		 source code
 
L(self)
Lipschitz constant of the gradient.		 source code
 
lambda_max(self)
Largest eigenvalue of the corresponding covariance matrix.		 source code
 
project(self, a)
Projection onto the compact space of the Nesterov function.		 source code
 
M(self)
The maximum value of the regularisation of the dual variable.		 source code
 
estimate_mu(self, beta)
Computes a "good" value of mu with respect to the given beta.		 source code

Inherited from properties.NesterovFunction: A, Aa, alpha, fmu, get_mu, grad, lA, prox, set_mu

Inherited from properties.Gradient: approx_grad

Inherited from properties.LipschitzContinuousGradient: approx_L

Inherited from properties.Eigenvalues: lambda_min

Inherited from object: __delattr__, __format__, __getattribute__, __hash__, __new__, __reduce__, __reduce_ex__, __repr__, __setattr__, __sizeof__, __str__, __subclasshook__

Class Variables [hide private]
  __abstractmethods__ = frozenset([])

Inherited from properties.NesterovFunction: __metaclass__

Inherited from properties.Gradient (private): _abc_cache, _abc_negative_cache, _abc_negative_cache_version, _abc_registry

Properties [hide private]

Inherited from object: __class__

Method Details [hide private]

__init__(self, l, c=0.0, A=None, mu=0.0, penalty_start=0)
(Constructor)

source code  

Parameters
----------
l : Non-negative float. The Lagrange multiplier, or regularisation
        constant, of the function.

c : Float. The limit of the constraint. The function is feasible if
        TV(beta) <= c. The default value is c=0, i.e. the default is a
        regularisation formulation.

A : Numpy array (usually sparse). The linear operator for the Nesterov
        formulation. May not be None!

mu : Non-negative float. The regularisation constant for the smoothing.

penalty_start : Non-negative integer. The number of columns, variables
        etc., to exempt from penalisation. Equivalently, the first
        index to be penalised. Default is 0, all columns are included.
Overrides: object.__init__

phi(self, alpha, beta)

source code 

Function value with known alpha.

From the interface "NesterovFunction".

Overrides: properties.NesterovFunction.phi

feasible(self, beta)

source code 

Feasibility of the constraint.

From the interface "Constraint".

Overrides: properties.Constraint.feasible

L(self)

source code 

Lipschitz constant of the gradient.

From the interface "LipschitzContinuousGradient".

Overrides: properties.LipschitzContinuousGradient.L

lambda_max(self)

source code 

Largest eigenvalue of the corresponding covariance matrix.

From the interface "Eigenvalues".

Overrides: properties.Eigenvalues.lambda_max

project(self, a)

source code 

Projection onto the compact space of the Nesterov function.

From the interface "NesterovFunction".

Overrides: properties.NesterovFunction.project

M(self)

source code  
The maximum value of the regularisation of the dual variable. We
have

    M = max_{alpha in K} 0.5*|alpha|²_2.

From the interface "NesterovFunction".
Overrides: properties.NesterovFunction.M

estimate_mu(self, beta)

source code 

Computes a "good" value of mu with respect to the given beta.

From the interface "NesterovFunction".

Overrides: properties.NesterovFunction.estimate_mu

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