integration

integration

[Francisco J Molina]

I am using  gsl_integration_qagi to integrate a function similar to a
Gaussian ( it is always positive and tends to zero as x tends to +/-
infinity.

Since this function is never 0, I wonder if it is possible to modify the
source code to use a 60-point Gauss-Kronrod rule of QAGS?

Re: integration

[Brian Gough]

Francisco J Molina writes:
 > I am using  gsl_integration_qagi to integrate a function similar to a
 > Gaussian ( it is always positive and tends to zero as x tends to +/-
 > infinity.
 > 
 > Since this function is never 0, I wonder if it is possible to modify the
 > source code to use a 60-point Gauss-Kronrod rule of QAGS?

The integration rule is fixed at compile time, but if you copy the
file integration/qags.c and its #include's into your application you
can modify the reference to the integration rule and override the
version in the library.

Brian

integration

[Francisco J Molina]

I am using  gsl_integration_qagi to integrate a function similar to a
Gaussian ( it is always positive and tends to zero as x tends to +/-
infinity.

Since this function is never 0, I wonder if it is possible to modify the
source code to use a 60-point Gauss-Kronrod rule of QAGS?

Re: integration

[Brian Gough]

Francisco J Molina writes:
 > I am using  gsl_integration_qagi to integrate a function similar to a
 > Gaussian ( it is always positive and tends to zero as x tends to +/-
 > infinity.
 > 
 > Since this function is never 0, I wonder if it is possible to modify the
 > source code to use a 60-point Gauss-Kronrod rule of QAGS?

The integration rule is fixed at compile time, but if you copy the
file integration/qags.c and its #include's into your application you
can modify the reference to the integration rule and override the
version in the library.

Brian

Re: integration

[Gert Van den Eynde]

On Wednesday 20 August 2003 13:07, Brian Gough wrote:
> The only thing I can contribute here is that all of the quadpack
> routines assume smooth functions.  Apart from that, I don't know much
> about integro-differential equations.

A small addendum: QUADPACK (the original FORTRAN code) allows functions with 
end-point singularities (routine DQAGS(E)). You would do that anyway when 
integrating a function with singularties: locate the singularities and split 
up the integration interval accordingly. With the routine DQAGP(E) you can 
even provide information on the kind of singularty.I suppose the GSL routine 
is the C translation of DQAGS. Of course, the function inside the integration 
boundaries should be smooth (numerical integration is for a big part based on 
the approximation of the function by orthogonal polynomials). 

For an overview of all original QUADPACK routines, have a look here 

http://netlib.org/quadpack/doc


Hope this helps,

gert

Re: integration

[Brian Gough]

Axel Hutt writes:
 > I apply the GSL-routine qag and related for the integration part in
 > integro-differential equations. The routines are okay, but quite
 > slow for rather non-smooth data (like random initial values).  Does
 > anybody also apply GSL-routines for integration for
 > integro-differential equations and if yes, which routines do you
 > apply?  I also try some hand-made Taylor-expansion-routines, which
 > however show less stable behaviour.

The only thing I can contribute here is that all of the quadpack
routines assume smooth functions.  Apart from that, I don't know much
about integro-differential equations.

integration

[Axel Hutt]

Dear all,

I apply the GSL-routine qag and related for the integration
part in integro-differential equations. The routines are okay,
but quite slow for rather non-smooth data (like random initial
values).
Does anybody also apply GSL-routines for integration for
integro-differential equations and if yes, which routines do you
apply?
I also try some hand-made Taylor-expansion-routines, which however
show less stable behaviour.


Axel

Re: integration

[Brian Gough]

Good point, Aric, we should start with the straightforward methods. If
you'd like to write something along those lines that would be really
useful.

Brian

Aric Hagberg wrote:
> 
> DASSL is quite a complicated piece of software.  To properly
> implement an ODE solver like that - actually I believe that does
> differential+algebraic equations too - we need things
> like nonlinear equation solvers, finite differencing,
> linear equation solvers, etc.
> 
> It is certainly possible to write an ODE solver for GSL
> right now using Runge-Kutta or some other explicit method without
> needing those things.
> 
> Aric

Re: integration

[Aric Hagberg]

DASSL is quite a complicated piece of software.  To properly
implement an ODE solver like that - actually I believe that does 
differential+algebraic equations too - we need things 
like nonlinear equation solvers, finite differencing, 
linear equation solvers, etc.

It is certainly possible to write an ODE solver for GSL
right now using Runge-Kutta or some other explicit method without
needing those things. 

Aric

Re: integration

[Brian Gough]

Hi,
I am working on a C implementation of QUADPACK for the integration (i.e.
quadrature) section. We haven't done any work on an ODE solvers
directory yet but something like DASSL is a candidate for that.
regards
Brian Gough

integration

[David J. Dooling]

Hello, I stumbled across the GSL today and started looking through the
manual.  In the manual there were sections for integration, but they
contained no text.  Therefore, I was wondering if anyone could answer
a couple questions.

What sorts of integration capabilities does the GSL plan to implement?
I would guess you are planning on implementing simple integration
schemes for functions, e. g., Runge-Kutta and slightly more
sophisticated techniques, and a brief look at the code suggests this
is accurate.

Are there any plans to implement more robust differential equation
solvers capable of solving systems of ODE's, stiff ODE's, or
differential/algebraic equations (like DASSL)?

Thanks.

DAVID.
~~~~~~
d-dooling@nwu.edu
David J. Dooling
Dept. of Chemical Engineering
Northwestern University
http://winnie.chem-eng.nwu.edu/students/dooling.html