pyfaust.factparams.ParamsHierarchicalRectMat Class Reference

The simplified parameterization class for factorizing a rectangular matrix with the hierarchical factorization algorithm (pyfaust.fact.hierarchical). More...

Public Member Functions
def	__init__ (self, m, n, j, k, s, rho=0.8, P=1.4)
	Constructor for the specialized parameterization used for example in the pyfaust.demo.bsl (brain souce localization). More...
Public Member Functions inherited from pyfaust.factparams.ParamsHierarchical
def	__init__ (self, fact_constraints, res_constraints, stop_crit1, stop_crit2, is_update_way_R2L=False, init_lambda=1.0, step_size=10.0 **-16, constant_step_size=False, is_fact_side_left=False, is_verbose=False, factor_format='dynamic', packing_RL=True, no_normalization=False, no_lambda=False, norm2_max_iter=100, norm2_threshold=1e-6, grad_calc_opt_mode=ParamsFact.EXTERNAL_OPT, **kwargs)
	Constructor. More...
def	are_constraints_consistent (self, M)
	This method verifies that the constraints are shape-consistent to the matrix/array M to factorize and with each other. More...
def	__repr__ (self)
	Returns object representation. More...
Public Member Functions inherited from pyfaust.factparams.ParamsFact
def	__init__ (self, num_facts, is_update_way_R2L, init_lambda, constraints, step_size, constant_step_size, is_verbose, factor_format='dynamic', packing_RL=True, no_normalization=False, no_lambda=False, norm2_max_iter=100, norm2_threshold=1e-6, grad_calc_opt_mode=EXTERNAL_OPT, **kwargs)

Static Public Member Functions
def	createParams (M, p)
	Static member function to create a ParamsHierarchicalRectMat instance by a simplified parameterization expression. More...
Static Public Member Functions inherited from pyfaust.factparams.ParamsFact
def	factor_format_str2int (factor_format)
def	factor_format_int2str (factor_format)
def	get_constraints (projs)
	Returns a python list of constraints from the projs which is a ConstralintList or a list/tuple that can be a mix of ConstraintGeneric or pyfaust.proj.proj_gen. More...

Additional Inherited Members
Public Attributes inherited from pyfaust.factparams.ParamsFact
	step_size
	constant_step_size
	norm2_max_iter
	norm2_threshold
	factor_format
	packing_RL
	no_normalization
	no_lambda
	use_MHTP

Detailed Description

The simplified parameterization class for factorizing a rectangular matrix with the hierarchical factorization algorithm (pyfaust.fact.hierarchical).

The parameters m and n are the dimensions of the input matrix.

See also

pyfaust.fact.hierarchical, pyfaust.demo.bsl, ParamsHierarchicalRectMat.__init__

Constructor & Destructor Documentation

__init__()

def pyfaust.factparams.ParamsHierarchicalRectMat.__init__	(		self,
			m,
			n,
			j,
			k,
			s,
			rho = 0.8,
			P = 1.4
	)

Constructor for the specialized parameterization used for example in the pyfaust.demo.bsl (brain souce localization).

For a better understanding you might refer to [1].

The figure below describes the sparsity of each factor of the Faust you'll obtain using pyfaust.fact.hierarchical with a ParamsHierarchicalRectMat instance.

The resulting Faust.nnz_sum is: \(\lceil P m^2 \rho^{j-2} \rceil + (j-2) s m + k n\)

Parameters

m	(int) the number of rows of the input matrix.
n	(int) the number of columns of the input matrix.
j	(int) the total number of factors.
k	(int) the integer sparsity per column (SPCOL, pyfaust.proj.spcol) applied to the rightmost factor (index j-1) of shape (m, n).
s	(int) s*m is the integer sparsity targeted (SP, pyfaust.proj.sp) for all the factors from the second (index 1) to index j-2. These factors are square of order n.
rho	(float) defines the integer sparsity (SP, pyfaust.proj.sp) of the i-th residual (i=0:j-2): ceil(P*m**2*rho**i).
P	(float) defines the integer sparsity of the i-th residual (i=0:j-2): ceil(P*m**2*rho**i).

Examples

>>> from pyfaust.factparams import ParamsHierarchicalRectMat
>>> # set p1 with m, n, j, k parameters
>>> p1 = ParamsHierarchicalRectMat(32, 128, 8, 4, 2)
>>> # now with additional optional rho and P
>>> p2 =  ParamsHierarchicalRectMat(32, 128, 8, 4, 2, rho=.7, P=1.5)

[1] Le Magoarou L. and Gribonval R., "Flexible multi-layer sparse approximations of matrices and applications", Journal of Selected Topics in Signal Processing, 2016. [https://hal.archives-ouvertes.fr/hal-01167948v1]

Member Function Documentation

createParams()

def pyfaust.factparams.ParamsHierarchicalRectMat.createParams (   M,   p  )

static

Static member function to create a ParamsHierarchicalRectMat instance by a simplified parameterization expression.

Parameters

p	a list of the form ['rectmat', j, k, s] or [['rectmat', num_facts, k, s], {'rho': rho, 'P': P}] to create a parameter instance with the parameters j, k, s and optionally rho and P (see the class constructor ParamsHierarchicalRectMat.__init__ for their definitions).

Examples

>>> from pyfaust.factparams import ParamsHierarchicalRectMat
>>> from numpy.random import rand, seed
>>> seed(42) # just for reproducibility
>>> num_facts = 9
>>> k = 10
>>> s = 8
>>> p = ParamsHierarchicalRectMat.createParams(rand(256, 1024), ['rectmat', num_facts, k, s])
>>> rho = 1.2
>>> P = 1.5
>>> p2 = ParamsHierarchicalRectMat.createParams(rand(256, 1024), [['rectmat', num_facts, k, s], {'rho': rho, 'P': P}])

Reimplemented in pyfaust.factparams.ParamsHierarchicalRectMatNoResCons.

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

• factparams.py