ivan@154: function [x] = generate_vector(N, K, ensemble, sigma, p)
ivan@154: % =========================================================================
ivan@154: %                       Sparse vector generator
ivan@154: % =========================================================================
ivan@154: % INPUT ARGUMENTS:
ivan@154: % N                         Size of sparse vector.
ivan@154: % K                         Sparsity of vector.
ivan@154: % ensemble                  Ensemble type of measurement matrix. Possible
ivan@154: %                           values are:
ivan@154: %                           -'Gaussian': K non-zero elements of the sparse vector
ivan@154: %                           are drawn from normal distribution N(0,1).
ivan@154: %                           -'sGaussian': K non-zero elements of the sparse vector
ivan@154: %                           are drawn from normal distribution N(0,sigma^2).
ivan@154: %                           -'Bernoulli': K non-zero elements of the sparse vector
ivan@154: %                           are drawn from Bernoulli distribution (1/2,1/2).
ivan@154: %                           -'pBernoulli': K non-zero elements of the sparse vector
ivan@154: %                           are drawn from Bernoulli distribution (p,1-p).
ivan@154: % sigma                     Standard deviation of Gaussian distribution.
ivan@154: % p                         Parameter of Bernoulli distribution.
ivan@154: % =========================================================================
ivan@154: % OUTPUT ARGUMENTS:
ivan@154: % x                     K-sparse vector.
ivan@154: % =========================================================================
ivan@154: % 01/04/2011, by Anastasios Kyrillidis. anastasios.kyrillidis@epfl.ch, EPFL.
ivan@154: % =========================================================================
ivan@154: 
ivan@154: if nargin < 3
ivan@154:     ensemble = 'Gaussian';
ivan@154: end;
ivan@154: 
ivan@154: if nargin < 4
ivan@154:     sigma = 1;
ivan@154:     p = 0.5; 
ivan@154: end;
ivan@154: 
ivan@154: x = zeros(N,1);
ivan@154: rand_indices = randperm(N);
ivan@154: 
ivan@154: switch ensemble
ivan@154:     case 'Gaussian'
ivan@154:         x(rand_indices(1:K)) = randn(K,1);         % Standard normal distribution ~ N(0,1)
ivan@154:     case 'sGaussian'
ivan@154:         x(rand_indices(1:K)) = sigma*randn(K,1);    % Normal distribution ~ N(0,sigma^2)
ivan@154:     case 'Uniform'
ivan@154:         x(rand_indices(1:K)) = rand(K,1);           % Uniform [0,1] distribution
ivan@154:     case 'Bernoulli'
ivan@154:         x(rand_indices(1:K)) = (-1).^round(rand(K,1));     % Bernoulli ~ (1/2, 1/2) distribution
ivan@154:     case 'pBernoulli'
ivan@154:         x(rand_indices(1:K)) = (-1).^(rand(K,1) > p);   % Bernoulli ~ (p, 1-p) distribution     
ivan@154: end;
ivan@154: 
ivan@154: x = x/norm(x);