Re: expm1 & log1p

[Jaroslav Hajek]

On Tue, Mar 18, 2008 at 4:26 PM, David Bateman
<address@hidden> wrote:
> David Bateman wrote:
>  > Jaroslav Hajek wrote:
>  >
>  >>> Also the matlab
>  >>>  functions accept complex arguments whereas your version seems to be
>  >>>  limited to real arguments
>  >>>
>  >>>
>  >>>
>  >> I missed that. Apparently there are only real versions in GNU C
>  >> library. I'll try to make
>  >> a complex version using the real version.
>  >>
>  >>
>  >>
>  >>
>  >
>  > Complex expm1 (const Complex& x)
>  > {
>  >     double xr = x.real ();
>  >     Complex xc = Complex (0., x.imag ());
>  >     return exp (xc) * expm1 (xr);
>  > }
>  >
>  > D.
>  >
>  >
>  >
>  Opps
>
>
>  Complex expm1 (const Complex& x)
>  {
>   return ((exp (Complex (0., x.imag ())) + 1.0) * expm1 (x.real ()));
>
>
> }
>

that does not seem to work, I'm afraid.

(exp(i*y)+1) * (exp(x)-1) = exp(x+i*y) -1 + (exp(x)-exp(i*y))

A possible formula is using complex sine

exp(z)-1 = -exp(z/2) * 2*i*sin(i*z/2)

or work the real and imag parts separately

exp(x+i*y)-1 = u+v+u*v + i*sin(y), with
u = exp(x)-1, v = cos(y)-1 = 2*sin(y/2)^2.

I'd say the second option is better.


>  D.
>
>
>  --
>  David Bateman                                address@hidden
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>
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>



-- 
RNDr. Jaroslav Hajek
computing expert
Aeronautical Research and Test Institute (VZLU)
Prague, Czech Republic
url: www.highegg.matfyz.cz