matfaust::tools Namespace Reference

The matfaust tools namespace. More...

Functions
function	omp (y, D, varargin)
	Runs the greedy OMP algorithm optimized by Cholesky decomposition. More...

Detailed Description

The matfaust tools namespace.

Function Documentation

omp()

function matfaust::tools::omp	(	y	,
		D	,
		varargin
	)

Runs the greedy OMP algorithm optimized by Cholesky decomposition.

Usage

    x=omp(y, D) runs the algorithm with the default configuration which is equivalent to x=omp(y, D, 'maxiter', length(y), 'verbose', false).
    x=omp(y, D, 'maxiter', N) stops the algorithm after N iterations.
    x=omp(y, D, 'tol', 10^-16) runs the algoritm until the relative error is lower or equal to 10**-16. This is equivalent to x=omp(y, D, 'tol', 10^-16, 'relerr', true)
    x=omp(y, D, 'maxiter', N, 'tol', 10^-16) runs at most N iterations until the tol precision is reached.
    x=omp(y, D, 'tol', 10^-16, 'relerr', false) runs the algorithm until the absolute error is lower or equal to 10**-16.

Parameters

y	The vector to approximate by D*x.
D	The dictionary as a matrix or a Faust.
'maxiter',number	(optional) To define a maximum number of iterations (by default this length(y)).
'tol',number	(optional) To define the error value used for the relative or absolute error (by default this is 0, for not stopping on any error criterion).
'relerr',true	(optional) To define a stopping criterion based on the relative error (this is the default error).
'relerr',false	(optional) To define a stopping criterion based on the absolute error.
'verbose',true	(optional) To enable the verbosity.
'verbose',false	(optional) To disable the verbosity (this is the default option).

Returns

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

Example:

>> rng(42)
>> F = matfaust.rand(15, 10);
>> x = rand(10, 1)
 
x =
 
    0.3745
    0.9507
    0.7320
    0.5987
    0.1560
    0.1560
    0.0581
    0.8662
    0.6011
    0.7081
 
>> y = F * x;
>> x_ = matfaust.tools.omp(y, F)
Stopping. Exact signal representation found!
 
x_ =
 
    0.3745
    0.9507
    0.7320
    0.5987
    0.1560
    0.1560
    0.0581
    0.8662
    0.6011
    0.7081