PEM-PCA: A Parallel Expectation-Maximization PCA Face Recognition Architecture

Algorithm 5

Parallel matrix determinant and cofactor computation.

Input:  Matrix  input

Output:  Double  detVal,  Matrix  cofactor

(1)   if  matrixSize=2  then

(2)   detVal  =  𝑖𝑛𝑝𝑢𝑡[0,0]×𝑖𝑛𝑝𝑢𝑡[1,1]−(𝑖𝑛𝑝𝑢𝑡[0,1]×𝑖𝑛𝑝𝑢𝑡[1,0]);

(3)   result 𝑖,𝑗=(−1)^𝑖+𝑗×𝑑𝑒𝑡𝑒𝑟𝑚𝑖𝑛𝑎𝑛𝑡𝑐𝑟𝑒𝑎𝑡𝑒𝑆𝑢𝑏𝑀𝑎𝑡𝑟𝑖𝑥𝑟𝑒𝑠𝑢𝑙𝑡𝑖,𝑗;

(4)   return  detVal,  cofactor;

(5)   else

(6)   parallel  for  i  from  0  to  dimension

(7)          for  j  from  0  to  columns

(8)        detVal=detVal+𝑖𝑛𝑝𝑢𝑡[0,𝑖]×𝑑𝑒𝑡𝑒𝑟𝑚𝑖𝑛𝑎𝑛𝑡𝑐𝑟𝑒𝑎𝑡𝑒𝑆𝑢𝑏𝑀𝑎𝑡𝑟𝑖𝑥𝑖𝑛𝑝𝑢𝑡,0,𝑖×(−1)^𝑖+𝑗

(9)        result 𝑖,𝑗=(−1)^𝑖+𝑗×𝑑𝑒𝑡𝑒𝑟𝑚𝑖𝑛𝑎𝑛𝑡𝑐𝑟𝑒𝑎𝑡𝑒𝑆𝑢𝑏𝑀𝑎𝑡𝑟𝑖𝑥𝑟𝑒𝑠𝑢𝑙𝑡𝑖,𝑗;

(10)         endfor

(11)   endfor

(12)   return  detVal;

(13)  endif