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Using quad() for multidimensional integration

From: Vinayak Dutt
Subject: Using quad() for multidimensional integration
Date: Wed, 16 Aug 95 18:52:53 CDT

Hi Octavers:

I am trying to use Octave to do multidimensional integration using the
quadrature method: quad(). I have a triple integral of type:

(TeX Notation)

\int_{x=0}^{R} F(x)  \int_{y=0}^{f(x)} G(y) \int_{0}^{g(y)}  H(z) dz dy dx

I guess, th exact integral does not matter, except that its triple integral.

So I implement this by having the integral function itself involve another
integration using quad() which again involves another integration.

a = quad('func1',x1,x2);

% and

function f2 = func1(x)
  y2 = f(x);
  f2 = F(x)*quad('func2',y1,y2);

% and

function f3 = func2(y)
  z1 = 0;
  z2 = g(y);
  f3 = G(y)*quad('H',z1,z2);

But when I do triple integral this way, I find that first two quadratures are 
evaulated at all. The functions func1 and func2 were evaluated only once. Only
func2 was used to completely evaluate func1 for that single func1 evaluation.
It seems the recursion in quad() is somehow killing the hiher level quad() 

Could this be due to usage of some globals in quad() which make it 

Any comments?

I am using Octave-1.1.1 on SPARC-Solaris2.4 with gcc2.6.3.

 * vinayak dutt
 * ex-graduate student, ultrasound research
 * mayo graduate school, rochester mn
 * e-mail: address@hidden
 *         address@hidden
 *         address@hidden
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