-  3.41.0
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
pa 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.


The documentation for this class was generated from the following file:
pyfaust.seed
def seed(s)
(Re)Initializes the pyfaust pseudo-random generator.
Definition: __init__.py:5334
pyfaust.rand
def rand(num_rows, num_cols, num_factors=None, dim_sizes=None, density=None, fac_type='sparse', per_row=True, dev='cpu', dtype='float64', field=None, seed=0)
Generates a random Faust.
Definition: __init__.py:5016
pyfaust.factparams
The module for the parameterization of FAuST's algorithms (Palm4MSA and Hierarchical Factorization)....
Definition: factparams.py:1