pyfaust.tools Namespace Reference

The pyfaust tools module. More...

Functions
def	omp (y, D, maxiter=None, tol=0, relerr=True, verbose=False)
	Runs the greedy OMP algorithm optimized by Cholesky decomposition. More...

Detailed Description

The pyfaust tools module.

Function Documentation

omp()

def pyfaust.tools.omp	(		y,
			D,
			maxiter = None,
			tol = 0,
			relerr = True,
			verbose = False
	)

Runs the greedy OMP algorithm optimized by Cholesky decomposition.

Parameters

y	the vector to approximate by D@x.
D	the dictionary as a numpy array or a Faust.
maxiter	the maximum number of iterations of the algorithm. By default (None) it's y's dimension: max(y.shape).
tol	the tolerance error to reach for the algorithm to stop. By default, it's zero for not stopping on error criterion.
relerr	the type of error stopping criterion. Default to True to use relative error, otherwise (False) the absolute error is used.
verbose	to enable the verbosity (value to True).

Returns

x the solution of y = D@x (according to the error).

Examples

>>> from pyfaust.tools import omp
>>> from scipy.sparse import random
>>> from pyfaust import rand, seed
>>> import numpy as np
>>> np.random.seed(42) # just for reproducibility
>>> seed(42)
>>> D = rand(1024, 1024)
>>> x0 = random(1024, 1, .01)
>>> y = D @ x0
>>> maxiter = 17
>>> x = omp(y, D, maxiter, tol=10**-16)

Stopping. Exact signal representation found!

>>> # omp() runs at most maxiter iterations until the error tolerance is
>>> # reached