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

Algorithm 4

Parallel optimized matrix multiplication with its transpose algorithm [27].

Input:  Matrix  input

Output:  Matrix  result

(1) for  i  from  0  to  input_Rows

(2)  for  j  from  0  to  input_Columns

(3)     Calculate  Diagonal Value:  result  [i,i]  +=  (input[i,j] × input[i,j]);

(4)  endfor

(5) endfor

(6) c=0,  b=0;

(7) for  i  from  1  to  input_Rows

(8)    repeat

(9)      Calculate Non-Diagonal Value:  result  [i,c]  +=  (input[i,b] × input[c,b]);

(10)       b++;

(11)       if  (b>=input_Columns)

(12)      c++;

(13)      b=0;

(14)      Copy  lower-diagonal  value  to   upper-diagonal  value:

(15)      result  [c-1,i]=  result  [i,c-1];

(16)     endif

(17)   until   (!((c<i)&&(b< input_Columns)))

(18)   endfor

(19)   c=0;

(20)   b=0;