Re: problem with acos

[zampala]

>
> | I need to calculate the inverse cosine of this matrix (2x2, complex
> values):
> | 
> | P =
> | 
> | 9.9422e-01 - 0.0000e+00i 8.9732e+08 - 0.0000e+00i
> | -1.0151e+00 + 0.0000e+00i 3.0910e+05 - 0.0000e+00i
> | 
> | octave:97> acos(P)
> | ans =
> | 
> | 0.10755 - 0.00000i NaN + Infi
> | 3.14159 - 0.17368i 0.00000 + 13.33457i
> | 
> | octave:98> acos(P(1,2))
> | ans = NaN + Infi
>
> Apparently your matrix P has some small imaginary components.  Try
>
>   format long
>   P
>
> so that they will be displayed.

I tried that, but still a long series of zero. However,
octave:39> isreal(P(1,2))
ans = 0
octave:40>

meaning that the imaginary component is small but not zero.

>
> When you write it this way, you are setting the imaginary part to
> exactly 0.  

Yeah, the best fix I could think of is to set to zero imaginary or real
parts smaller than, say, 1e-5.

> What do you expect the value of
> acos (X) to be when X is real and outside the range [-1,1]?  What do
> you expect it to be when X is complex, and there is a large real part
> and a small imaginary part?

Actually I don't know what to expect from the acos output.
The problem is indeed with a complex number made of big real and small
imaginary component - performed a quick test.
Could anyone confirm this? Does it make any mathematical sense?

Any better fix that I could use?
Going down to the C library level is beyond my skills

mirko
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