pyfaust.proj.spsymm Class Reference

Functor for the SYMM SP projector. More...

Public Member Functions
def	__init__ (self, shape, k, normalized=True, pos=False)
Public Member Functions inherited from pyfaust.proj.proj_gen
def	__init__ (self, shape)
def	__call__ (self, M)

Public Attributes
	constraint
Public Attributes inherited from pyfaust.proj.proj_gen
	shape

Detailed Description

Functor for the SYMM SP projector.

A, the image matrix of M, is such that A is symmetric and \(k \le \| A \|_0 \le k + 1, \| A\|_F = 1 \) (if normalized == True), assuming that \(\| M \|_0 >= k\).

Examples

>>> from pyfaust.proj import spsymm
>>> from numpy.random import rand, seed
>>> import numpy as np
>>> seed(42) # just for reproducibility
>>> M = np.round(rand(5,5), decimals=2)
>>> M
array([[0.37, 0.95, 0.73, 0.6 , 0.16],
[0.16, 0.06, 0.87, 0.6 , 0.71],
[0.02, 0.97, 0.83, 0.21, 0.18],
[0.18, 0.3 , 0.52, 0.43, 0.29],
[0.61, 0.14, 0.29, 0.37, 0.46]])
>>> p = spsymm(M.shape, 3, normalized=False)
>>> p(M)
array([[0.  , 0.95, 0.  , 0.  , 0.  ],
[0.95, 0.  , 0.97, 0.  , 0.  ],
[0.  , 0.97, 0.  , 0.  , 0.  ],
[0.  , 0.  , 0.  , 0.  , 0.  ],
[0.  , 0.  , 0.  , 0.  , 0.  ]])
>>> np.linalg.norm(p(M) - p(M).T) == 0
True
>>> np.count_nonzero(p(M)) == 4
True

Constructor & Destructor Documentation

__init__()

def pyfaust.proj.spsymm.__init__	(		self,
			shape,
			k,
			normalized = True,
			pos = False
	)

Parameters

shape	(tuple(int,int)) the size of the input matrix.
k	(int) the number of nonzeros of the projection image. The result might be k+1 nonzeros in case of an odd number of nonzeros on the diagonal.
normalized	(bool) True to normalize the projection image according to its Frobenius norm.
pos	(bool) True to skip negative values (replaced by zero) of the matrix to project.

Member Data Documentation

constraint

pyfaust.proj.spsymm.constraint

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The documentation for this class was generated from the following file:

• proj.py