Problem with matrix logarithms, in the complex case

[joao moreira]

Hello,

I tried posting this on the users list, but got no answers, so I'll try
here. Basically, I'm trying to understand why the matrix logarithm is
implemented the way it is (in macros/elem/logm.sci, in scilab 4.1.2), and if
there is some reason for it not calculating in the case described below.

--------

Hi all,

I have an issue with matrix logarithms, in the complex case. Consider
the following matrix :

A=[
    -0.01+0*%i 0.13+0*%i;
     0.00+0*%i 0.08+0*%i;
  ];

Coefficients are real, but I force them to be complex, hoping that
scilab will use a complex logarithm matrix function. But scilab says
"unable to diagonalize!"... I understand that as a real matrix, I
can't calculate its log, but as a complex matrix, why doesn't this
work ?

Using algorithms from Golub, van Loan, "Matrix Computations", I coded
a complex matrix log function, and found logm(A) = L where

L=[
    -4.6051702+3.1415927*%i  3.0036378-4.5378561*%i;
     0.0000000+0.0000000*%i -2.5257286+0.0000000*%i;
  ];

and it's easy to check that exp(log(A)) == log(exp(A)) == A.

I looked in the scilab source, and found that logm is actually a .sci
file that does
.........................
a=a+0*%i;   //Set complex
[s,u,bs]=bdiag(a);
  if maxi(bs)>1 then
    error('logm: unable to diagonalize!');return
  end
.........................

bdiag does block diagonalisation, finds a 2x2 block, and refuses to
continue !... Is this normal ? is there some reason for scilab not
calculating this ?

Maybe I'm missing something obvious, thanks for helping.

Joao


-- 
Joao Moreira (math student)
Paris, France
joao.mrr1 at gmail.com
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