Integrals

Integrals

[Przemyslaw Sliwa]

Sorry,

I see that it has been formatted a bit different than expected. I mean the integral from -INF to INF over f(x)dx.

Thanks

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Re: Integrals

[Stewart V. Wright]

G'day Przemyslaw,

* Przemyslaw Sliwa <przemyslaw.sliwa@db.com> [050106 11:37]:
> Sorry,
> 
> I see that it has been formatted a bit different than expected. I mean the integral from -INF to INF over f(x)dx.
> 

RTFM [1].  Look for "Numerical Integration".  Read a bit further.
Find the section "QAGI adaptive integration on infinite intervals".

Does this help?


Cheers,

S.


[1] http://www.gnu.org/software/gsl/manual/gsl-ref_16.html#SEC248

Re: Integrals

[Axel Hutt]

Przemyslaw Sliwa wrote:

>Can you tell me how you got this?
>
>I have not worked with complex valued functions. Thanks
>
>Przemyslaw
>  
>
>
oh, maybe I was wrong, since I have interpreted the 1 as an i. If the 
exponent is real, means
\phi, k and f are real functions, then the expression is purely 
imaginary and the real part is zero.
Maybe you pass some more information about these functions.

Axel

Re: Integrals

[Przemyslaw Sliwa]

Thanks for this,

One additional question would be how to calculate the integral of a real part of a function:

exp(- 1 \phi \ln(k) f(x, v, T; \phi))
---------------------------------------------
                 i\phi

I used the LaTeX notation. Can anyone help me with this?

Thanks

Przemyslaw




                                                                                                                                                                          
                      Axel Hutt                                                                                                                                           
                      <Axel.Hutt@physik.hu        To:       Przemyslaw Sliwa/DMGCON/DMG UK/DeuBa@DMG UK                                                                   
                      -berlin.de>                 cc:       gsl-discuss@sources.redhat.com                                                                                
                                                  Subject:  Re: Integrals                                                                                                 
                      01/06/2005 05:37 PM                                                                                                                                 
                                                                                                                                                                          
                                                                                                                                                                          




Przemyslaw Sliwa wrote:

>All,
>                                                INF
>                                                 /
>I would like to know if it is possible to calculate the integral of type  I f(x)dx using gsl. If yes can someone explain me how it is done?
>                                                /
>                                                       -INF
>
>Thank you for help,
>
>Pshemek
>
>
>
you may take a look at

http://sources.redhat.com/gsl/ref/gsl-ref_16.html#SEC254

Hope that helps.


Axel







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Re: Integrals

[Axel Vogt]

As nobody takes it ... just take the real part using GSL_REAL.

I guess phi is your integration variable and looking at your
adress/signature some thoughts: this is for option pricing by
applying Fourier inversion for characteristic functions f, no?

In this case the integration is over the whole positive reals
with oscillating integrand, may be non-constant periodics and
sometimes weird damping, the singularity in 0 is removable.
If you want to cover extreme sitautions as well you wish to
be very careful, even with adaptive schemes

If you not need extremly exact values you can use FFT (fast
Fourier transform) with interpolation on the grid. This has
the advantage that for (v,T fixed) you get all values for
your strike k within 1 FFT (but a notational orgy and worth
only for repeated use).

But that's just a thought ... and if i guessed wrong then
just take it as comment that you Q is somewhat vague.

Axel

Przemyslaw Sliwa wrote:
> 
> Thanks for this,
> 
> One additional question would be how to calculate the integral of a real part of a function:
> 
> exp(- 1 \phi \ln(k) f(x, v, T; \phi))
> ---------------------------------------------
>                  i\phi
> 
> I used the LaTeX notation. Can anyone help me with this?
> 
> Thanks
> 
> Przemyslaw
> 
> 
>                       Axel Hutt
>                       <Axel.Hutt@physik.hu        To:       Przemyslaw Sliwa/DMGCON/DMG UK/DeuBa@DMG UK
>                       -berlin.de>                 cc:       gsl-discuss@sources.redhat.com
>                                                   Subject:  Re: Integrals
>                       01/06/2005 05:37 PM
> 
> 
> 
> Przemyslaw Sliwa wrote:
> 
> >All,
> >                                                INF
> >                                                 /
> >I would like to know if it is possible to calculate the integral of type  I f(x)dx using gsl. If yes can someone explain me how it is done?
> >                                                /
> >                                                       -INF
> >
> >Thank you for help,
> >
> >Pshemek
> >
> >
> >
> you may take a look at
> 
> http://sources.redhat.com/gsl/ref/gsl-ref_16.html#SEC254
> 
> Hope that helps.
> 
> Axel
> 
> --
> 
> This e-mail may contain confidential and/or privileged information. If you are not the intended recipient (or have received this e-mail in error) please notify the sender immediately and destroy this e-mail. Any unauthorized copying, disclosure or distribution of the material in this e-mail is strictly forbidden.

Re: Integrals

[Axel Hutt]

Przemyslaw Sliwa wrote:

>Thanks for this,
>
>One additional question would be how to calculate the integral of a real part of a function:
>
>exp(- 1 \phi \ln(k) f(x, v, T; \phi))
>---------------------------------------------
>                 i\phi
>
>I used the LaTeX notation. Can anyone help me with this?
>  
>
well, the real part would be

-sin(\phi \ln(k) f(x))/\phi

and this might be solvable by the mentioned function. Did you try it 
with *gsl_integration_qagi ?

*Axel

Re: Integrals

[Brian Gough]

Przemyslaw Sliwa writes:
 > One additional question would be how to calculate the integral of a real part of a function:

Just a reminder for the new year,

This list isn't the right place to ask "homework" questions which
don't have any connection to GSL.

Thanks

-- 
Brian Gough

Integrals

[Przemyslaw Sliwa]

All,
                                                INF
                                                 /
I would like to know if it is possible to calculate the integral of type  I f(x)dx using gsl. If yes can someone explain me how it is done?
                                                /
                                                       -INF

Thank you for help,

Pshemek


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Re: Integrals

[Axel Hutt]

Przemyslaw Sliwa wrote:

>All,
>                                                INF
>                                                 /
>I would like to know if it is possible to calculate the integral of type  I f(x)dx using gsl. If yes can someone explain me how it is done?
>                                                /
>                                                       -INF
>
>Thank you for help,
>
>Pshemek
>
>  
>
you may take a look at

http://sources.redhat.com/gsl/ref/gsl-ref_16.html#SEC254

Hope that helps.


Axel

Re: Integrals

[Jerome BENOIT]

Hello,

in this case, the general idea is to split your domain in three parts:
SUM(-infinity,+infinity)=SUM(-infinity,a)+SUM(a,b)+SUM(b,+infinity),
with -infinity < a < b < +infinity .
Then, by figuring out an appropriate changement of variable,
you may be able to reduce your three integrals into three finite integrals
to which you can easily apply the function exposed in the Chapter "Numerical Integration".

hth,
Jerome

Przemyslaw Sliwa wrote:
> All,
>                                                 INF
>                                                  /
> I would like to know if it is possible to calculate the integral of type  I f(x)dx using gsl. If yes can someone explain me how it is done?
>                                                 /
>                                                        -INF
> 
> Thank you for help,
> 
> Pshemek
> 
> 
> --
> 
> This e-mail may contain confidential and/or privileged information. If you are not the intended recipient (or have received this e-mail in error) please notify the sender immediately and destroy this e-mail. Any unauthorized copying, disclosure or distribution of the material in this e-mail is strictly forbidden.
> 
> 
>