Prev: PsychToolBox
Next: Assignment within State (syntax error in Stateflow)
From: Ravi on 21 Jun 2010 11:37
Sure ! Let us know how it worked out.

Ravi

"Zim " <abraham_john_love(a)yahoo.com> wrote in message <hvn8sg$9ne$1(a)fred.mathworks.com>...
> Thanks a lot ravi..
>
> "Ravi " <soni_romi(a)yahoo.com.thisisjunkremoveit> wrote in message <hvmg1d$30q$1(a)fred.mathworks.com>...
> > Hi JA,
> >
> > Yes John is correct - dblquad (and most integration functions) can only integrate over a rectangular region (fixed limits).
> >
> > You will have to transform your curvilinear problem to a rectangular problem.
> >
> > integral[f(x,y)*dx*dy] = integral[|J|* f(x(u,v),y(u,v)*du*dv]
> >
> > |J|=absolute value of Jacobian determinant J
> >
> > J=del(x)/del(u)*del(y)/del(v) - del(x)/del(v)*del(y)/del(u)
> >
> > LH integral is your original integral with variable limits.
> >
> > RH integral is the transformed integral with fixed limits which u can use with dblquad.
> >
> >
> > If your region is an ellipse, use the following transformation
> >
> > x=a*v*cos(u)
> >
> > y=b*v*sin(u)
> >
> > a,b=semi major/minor axis of ellipse
> >
> > This will give Jacobian J=a*b*v
> >
> > And the integration limits as
> > 0<=u<=2*pi
> > 0<=v<=1
> >
> > Now you can use dblquad !
> >
> > Ravi
> >
> >
> > "Zim " <abraham_john_love(a)yahoo.com> wrote in message <hvlfb4$i7b$1(a)fred.mathworks.com>...
> > > Hi Everyone
> > > I am trying to integrate a region which sort of ellispe. I am using dblquad to do so where inner limits are function of outer limits as follows. But I am getting error that x1 is undefined @dblquad
> > > (const = constant)
> > >
> > > F = @(x1,x2)((1 ./ (2 .* pi .* const .* const)) .* (exp((-0.5) .* ((((x1 - const).^ 2) ./ const ) + (((x2 - const) .^ 2) ./ const )))));
> > > dblquad(F,x_L,x_H,y1,y2)
> > >
> > >
> > > y1 = (-const - (sqrt((const .^ 2 ) - (4 .* const .* ((cont .* (x1 .^ 2)) + (const .* x1) + const))))) ./ (2 .* C);
> > >
> > > y2 = (-const - (sqrt((const .^ 2 ) + (4 .* const .* ((cont .* (x1 .^ 2)) + (const .* x1) + const))))) ./ (2 .* const);
> > >
> > > thanks in advance,
> > > JA
From: Ravi on 21 Jun 2010 12:16
Hi JA,

If you do not want to transform your problem, you can define a dummy rectangular domain that includes the true domain. Simply assign the integrand function as zero outside the true domain.

So create a nested function "dblquad_fnc" to pass to dblquad.

function [y]=dblquad_fnc(x)

for i=1:length(x)
gx= enter your equation for region, such as ellipse

if (gx<=0)
% Inside domain
y=enter your equation for integrand f(x)
else
% Outside domain
y=0
end
end

end


Now you can use dblquad directly on your original problem.

However, this may increase run time as the integration points will often lie outside the true domain.

So I think if transformation is not too difficult, it is recommended.

Ravi


"Zim " <abraham_john_love(a)yahoo.com> wrote in message <hvlfb4$i7b$1(a)fred.mathworks.com>...
> Hi Everyone
> I am trying to integrate a region which sort of ellispe. I am using dblquad to do so where inner limits are function of outer limits as follows. But I am getting error that x1 is undefined @dblquad
> (const = constant)
>
> F = @(x1,x2)((1 ./ (2 .* pi .* const .* const)) .* (exp((-0.5) .* ((((x1 - const).^ 2) ./ const ) + (((x2 - const) .^ 2) ./ const )))));
> dblquad(F,x_L,x_H,y1,y2)
>
>
> y1 = (-const - (sqrt((const .^ 2 ) - (4 .* const .* ((cont .* (x1 .^ 2)) + (const .* x1) + const))))) ./ (2 .* C);
>
> y2 = (-const - (sqrt((const .^ 2 ) + (4 .* const .* ((cont .* (x1 .^ 2)) + (const .* x1) + const))))) ./ (2 .* const);
>
> thanks in advance,
> JA
From: Steven Lord on 22 Jun 2010 14:47

"Zim " <abraham_john_love(a)yahoo.com> wrote in message
news:hvlfb4$i7b$1(a)fred.mathworks.com...
> Hi Everyone
> I am trying to integrate a region which sort of ellispe. I am using
> dblquad to do so where inner limits are function of outer limits as
> follows. But I am getting error that x1 is undefined @dblquad

Look at QUAD2D.

--
Steve Lord
slord(a)mathworks.com
comp.soft-sys.matlab (CSSM) FAQ: http://matlabwiki.mathworks.com/MATLAB_FAQ
To contact Technical Support use the Contact Us link on
http://www.mathworks.com


First  |  Prev  | 
Pages: 1 2
Prev: PsychToolBox
Next: Assignment within State (syntax error in Stateflow)