[Octave-bug-tracker] [bug #34850] Behaviour of chol(a,'lower')

[Salvatore Filippone]

Follow-up Comment #8, bug #34850 (project octave):

Ok, for complex data the situation is even worse: the current code returns the
transpose of the upper factor instead of the conjugate transpose. Test case:
 b=[0,1,2,3;
> -1,0,1,2;
> -2,-1,0,1;
> -3,-2,-1,0]
b =

   0   1   2   3
  -1   0   1   2
  -2  -1   0   1
  -3  -2  -1   0

octave:5> ca=a+i*b
ca =

   12 +  0i    2 +  1i    3 +  2i    4 +  3i
    2 -  1i   14 +  0i    5 +  1i    3 +  2i
    3 -  2i    5 -  1i   16 +  0i    6 +  1i
    4 -  3i    3 -  2i    6 -  1i   16 +  0i

octave:8> chol(ca)
ans =

   3.46410 + 0.00000i   0.57735 + 0.28868i   0.86603 + 0.57735i   1.15470 +
0.86603i
   0.00000 + 0.00000i   3.68556 + 0.00000i   1.17576 + 0.24872i   0.56527 +
0.49744i
   0.00000 + 0.00000i   0.00000 + 0.00000i   3.67048 + 0.00000i   1.01122 +
0.12870i
   0.00000 + 0.00000i   0.00000 + 0.00000i   0.00000 + 0.00000i   3.50864 +
0.00000i

octave:9> chol(ca,'lower')
ans =

   3.46410 + 0.00000i   0.00000 + 0.00000i   0.00000 + 0.00000i   0.00000 +
0.00000i
   0.57735 + 0.28868i   3.68556 + 0.00000i   0.00000 + 0.00000i   0.00000 +
0.00000i
   0.86603 + 0.57735i   1.17576 + 0.24872i   3.67048 + 0.00000i   0.00000 +
0.00000i
   1.15470 + 0.86603i   0.56527 + 0.49744i   1.01122 + 0.12870i   3.50864 +
0.00000i



whereas Matlab correctly returns 
ca=a+i*b

ca =

  12.0000             2.0000 + 1.0000i   3.0000 + 2.0000i   4.0000 + 3.0000i
   2.0000 - 1.0000i  14.0000             5.0000 + 1.0000i   3.0000 + 2.0000i
   3.0000 - 2.0000i   5.0000 - 1.0000i  16.0000             6.0000 + 1.0000i
   4.0000 - 3.0000i   3.0000 - 2.0000i   6.0000 - 1.0000i  16.0000          

>> chol(ca)

ans =

   3.4641             0.5774 + 0.2887i   0.8660 + 0.5774i   1.1547 + 0.8660i
        0             3.6856             1.1758 + 0.2487i   0.5653 + 0.4974i
        0                  0             3.6705             1.0112 + 0.1287i
        0                  0                  0             3.5086          

>> chol(ca,'lower')

ans =

   3.4641                  0                  0                  0          
   0.5774 - 0.2887i   3.6856                  0                  0          
   0.8660 - 0.5774i   1.1758 - 0.2487i   3.6705                  0          
   1.1547 - 0.8660i   0.5653 - 0.4974i   1.0112 - 0.1287i   3.5086          


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