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Package parsimony :: Package functions :: Package multiblock :: Module losses :: Class MultiblockNesterovFunctionWrapper
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Class MultiblockNesterovFunctionWrapper

source code

                        object --+            
                                 |            
               properties.Function --+        
                                     |        
          properties.CompositeFunction --+    
                                         |    
                            object --+   |    
                                     |   |    
                   properties.Gradient --+    
                                         |    
                            object --+   |    
                                     |   |    
                   properties.StepSize --+    
                                         |    
                            object --+   |    
                                     |   |    
           properties.ProximalOperator --+    
                                         |    
                 MultiblockFunctionWrapper --+
                                             |
                            object --+       |
                                     |       |
                   properties.Gradient --+   |
                                         |   |
                            object --+   |   |
                                     |   |   |
properties.LipschitzContinuousGradient --+   |
                                         |   |
                            object --+   |   |
                                     |   |   |
                properties.Eigenvalues --+   |
                                         |   |
                            object --+   |   |
                                     |   |   |
           properties.ProximalOperator --+   |
                                         |   |
               properties.NesterovFunction --+
                                             |
                                object --+   |
                                         |   |
                   properties.Continuation --+
                                             |
                                            MultiblockNesterovFunctionWrapper
Instance Methods [hide private]
 
__init__(self, function, w, index)
x.__init__(...) initializes x; see help(type(x)) for signature		 source code
 
get_params(self, *args) source code
 
fmu(self, beta, mu=None)
Returns the smoothed function value.		 source code
 
phi(self, alpha, beta)
Function value with known alpha.		 source code
 
get_mu(self)
Returns the regularisation constant for the smoothing.		 source code
 
set_mu(self, mu)
Sets the regularisation constant for the smoothing.		 source code
 
alpha(self, beta)
Dual variable of the Nesterov function.		 source code
 
A(self)
Linear operator of the Nesterov function.		 source code
 
Aa(self, alpha)
Compute A'*alpha.		 source code
 
project(self, alpha)
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)
Compute a "good" value of mu with respect to the given beta.		 source code
 
mu_opt(self, eps)
The optimal value of mu given epsilon.		 source code
 
eps_opt(self, mu)
The optimal value of epsilon given mu.		 source code
 
eps_max(self, mu)
The maximum value of epsilon.		 source code
 
mu_max(self, eps)
The maximum value of mu.		 source code

Inherited from MultiblockFunctionWrapper: f, grad, prox, step

Inherited from properties.Function: reset, set_params

Inherited from properties.NesterovFunction: L, lA, lambda_max

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]

Inherited from MultiblockFunctionWrapper: __abstractmethods__

Inherited from MultiblockFunctionWrapper (private): _abc_negative_cache_version

Inherited from properties.CompositeFunction: __metaclass__

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

Properties [hide private]

Inherited from object: __class__

Method Details [hide private]

__init__(self, function, w, index)
(Constructor)

source code 

x.__init__(...) initializes x; see help(type(x)) for signature

Overrides: object.__init__
(inherited documentation)

get_params(self, *args)

source code 
Overrides: properties.Function.get_params

fmu(self, beta, mu=None)

source code  
Returns the smoothed function value.

From the interface "NesterovFunction".

Parameters
----------
beta : Numpy array. A weight vector.

mu : Non-negative float. The regularisation constant for the smoothing.
Overrides: properties.NesterovFunction.fmu

phi(self, alpha, beta)

source code 

Function value with known alpha.

From the interface "NesterovFunction".

Overrides: properties.NesterovFunction.phi

get_mu(self)

source code 

Returns the regularisation constant for the smoothing.

From the interface "NesterovFunction".

Overrides: properties.NesterovFunction.get_mu

set_mu(self, mu)

source code  
Sets the regularisation constant for the smoothing.

From the interface "NesterovFunction".

Parameters
----------
mu : Non-negative float. The regularisation constant for the smoothing
        to use from now on.

Returns
-------
old_mu : Non-negative float. The old regularisation constant for the
        smoothing that was overwritten and no longer is used.
Overrides: properties.NesterovFunction.set_mu

alpha(self, beta)

source code  
Dual variable of the Nesterov function.

From the interface "NesterovFunction".

Parameters
----------
beta : Numpy array (p-by-1). The variable for which to compute the dual
        variable alpha.
Overrides: properties.NesterovFunction.alpha

A(self)

source code 

Linear operator of the Nesterov function.

From the interface "NesterovFunction".

Overrides: properties.NesterovFunction.A

Aa(self, alpha)

source code  
Compute A'*alpha.

From the interface "NesterovFunction".

Parameters
----------
alpha : Numpy array (x-by-1). The dual variable alpha.
Overrides: properties.NesterovFunction.Aa

project(self, alpha)

source code  
Projection onto the compact space of the Nesterov function.

From the interface "NesterovFunction".

Parameters
----------
alpha : Numpy array (x-by-1). The not-yet-projected dual variable
        alpha.
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  
Compute a "good" value of mu with respect to the given beta.

From the interface "NesterovFunction".

Parameters
----------
beta : Numpy array (p-by-1). The primal variable at which to compute a
        feasible value of mu.
Overrides: properties.NesterovFunction.estimate_mu

mu_opt(self, eps)

source code  
The optimal value of mu given epsilon.

Parameters
----------
eps : Positive float. The desired precision.

Returns
-------
mu : Positive float. The optimal regularisation parameter.

From the interface "Continuation".
Overrides: properties.Continuation.mu_opt

eps_opt(self, mu)

source code  
The optimal value of epsilon given mu.

Parameters
----------
mu : Positive float. The regularisation constant of the smoothing.

Returns
-------
eps : Positive float. The optimal precision.

From the interface "Continuation".
Overrides: properties.Continuation.eps_opt

eps_max(self, mu)

source code  
The maximum value of epsilon.

From the interface "Continuation".

Parameters
----------
mu : Positive float. The regularisation constant of the smoothing.

Returns
-------
eps : Positive float. The upper limit, the maximum, precision.
Overrides: properties.Continuation.eps_max

mu_max(self, eps)

source code  
The maximum value of mu.

From the interface "Continuation".

Parameters
----------
eps : Positive float. The maximum precision of the smoothing.

Returns
-------
mu : Positive float. The upper limit, the maximum, of the
        regularisation constant of the smoothing.
Overrides: properties.Continuation.mu_max

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