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+% Author : F. Yahaya
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+% Date: 06/09/2018
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+% Contact: farouk.yahaya@univ-littoral.fr
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+
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+% clear all variables
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+% First, initialize the random number generator to make the results in each
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+% test repeatable.
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+% using a seed of 1 rng(1)
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+% Goal: Generate synthetic data of sizes: [m,n]=500, 5000,10000.
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+% For each of the aforementioned matrix size, a total of 40 tests are made
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+% with noise of approximately 30db.
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+
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+
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+% <Parameters>
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+% Total_Tests: Number of desired tests.
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+% X : Input data matrix (m x n)
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+% r : Target low-rank
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+% nu : Security rank
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+% mat_size : Give a name to your matrix size for easier identification of output
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+
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+% Wtheo, Htheo : Simulation of theoretical matrix Wtheo,Htheo
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+% Vtheo : simulation of theoretical data matrix Vtheo
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+% N : simulating noise matrice N
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+% X = Xtheo+N : simulating data matrix X
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+% Winit,Hinit : Matrix initialisation
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+% SNR : Signal to Noise Ratio
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+% compressionLevel : Compression Level, Default=20. See: Mariano
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+% Tepper and Guillermo Sapiro, Compressed Nonnegative
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+% Matrix Factorization is Fast and Accurate, 2015.
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+
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+clear
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+clc
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+rng(1)
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+
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+Total_Tests =40;
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+
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+for i =1:Total_Tests
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+ mat_size='500x500'; % this is just for naming. To change matrix size, change the values for m and n accordingly.
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+
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+ m = 500; n = 500;
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+ r = 15;
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+ nu=10;
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+
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+ rng(i)
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+
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+ Wtheo = 10*rand(m,r);
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+ Htheo = 10*rand(r,n);
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+
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+ Vtheo = Wtheo*Htheo;
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+
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+ rng(200+i)
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+ Winit = rand(m,r);
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+ Hinit = rand(r,n);
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+
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+ compressionLevel = 20;
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+
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+ rng(300+i)
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+ N = 12*randn(m,n); % To reproduce similar results, please keep SNR close to 30db
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+ SNR = snr(Vtheo,N);
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+ X=Vtheo+N;
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+
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+ save( ['synthetic_data/data_',mat_size,'_',int2str(i),'.mat'] ,'X','SNR','N' ,'Wtheo' , 'Htheo' , 'Winit' , 'Hinit' , 'Vtheo','compressionLevel','nu','r' )
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+
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+
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+end
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+disp(['matrix size ', '( ',mat_size,' )', ' : all ',int2str(Total_Tests), ' data simulations ', ' completed!' ]);
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+
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+
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