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Algorithm 1 Bayesian positive source separation algorithm (BPSS) 

for i = 1 , . . . , N$_{MC}$ do % sampling the abundance hyperparameters for p = 1 , . . . , P do Draw λ$_{p}$ from the pdf 

end for % sampling the abundance hyperparameters for p = 1 , . . . , P do Draw γ$_{p}$ from the gamma distribution 

end for % sampling the abundance vectors for p = 1 , . . . , P and r = 1 , . . . , R do Draw a$_{p,r}$ from the pdf 

end for % sampling the noise hyperparameter Draw ψ$_{e}$ from the inverse-gamma distribution 

% sampling the noise variances for p = 1 , . . . , P do Draw σ 2 e ,p from the inverse-gamma distribution 

end for % sampling the source hyperparameters for r = 1 , . . . , R do Draw α$_{r}$ from the pdf 

end for % sampling the source hyperparameters for r = 1 , . . . , R do Draw β$_{r}$ from the gamma distribution 

end for % sampling the source spectrum for r = 1 , . . . , R and l = 1 , . . . , L do Draw s$_{r,l}$ from the pdf 

end for end for 

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Algorithm 2 Fully constrained Bayesian positive source sep- aration algorithm (BPSS2) 

for i = 1 , . . . , N$_{MC}$ do % sampling the abundance vectors for p = 1 , . . . , P do Draw a$_{p}$$_{:}$ from the pdf 

with 

end for % sampling the noise hyperparameter Draw ψ$_{e}$ from the inverse-gamma distribution 

% sampling the noise variances for p = 1 , . . . , P do Draw σ 2 e ,p from the inverse-gamma distribution 

end for % sampling the source hyperparameters for r = 1 , . . . , R do Draw α$_{r}$ from the pdf 

end for % sampling the source hyperparameters for r = 1 , . . . , R do Draw β$_{r}$ from the gamma distribution 

end for % sampling the source spectrum for r = 1 , . . . , R and l = 1 , . . . , L do Draw s$_{r,l}$ from the pdf 

end for end for 

time on an x86 processor architecture, while the changes to the code have been minimal. Furthermore, most dataset come as single precision. 

3) OS Architecture: It is interesting to note that MATLAB c ○ is limited in terms of memory usage (regardless of the size of physical memory). This depends on the Operating System (OS) and on the MATLAB version (see Table II-A3). 

Therefore, a 32-bits LINUX architecture has been chosen. 

4) Parallelization: MATLAB c ○ contains libraries dedicated to automatically parallelize parts of the algorithms on a single computer. BPSS has been run on a 4 -core machine. The underlying matrix libraries already provide a certain level of parallelism depending on the number of available cores. However, in the future, parts of the code could be parallelized 

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