Matlab: How to plot the function $P(x)$ versus $x$, where $P(x)=\int_0^\infty f(y)W(x,y)dy$?

In Matlab:

How to plot the function versus x, where

?

I have obtaind the an array of N values for through some (long) numerical calculation, for an array of N values y.

The function has an analytic expression: .

My question is how to plot , which is a function of x defined by this integral over another function of y?

(The ``∞" is not the problem, of course this can just be set to some large constant, e.g., or , maybe?)

*To emphasize: I know how this can be done using a loop for each value of x : for every x, I can calculate P(x)=trapz(y,f(y)W(x,y)) (~not written in Matlab code).

But, can this be done without a loop?

[Torsten]

You can use "arrayfun", but in principle, it's the same as a loop.

[Image Analyst]

Can't you use meshgrid or griddata

[x, y] = meshgrid(xRange, yRange);

etc.

[Walter Roberson]

trapz() can operate on 2d arrays.

[Erez]

@Torsten @Image Analyst@Walter Roberson Guys, thanks for all the ideas, can you show please how to implemet them? -- I haven't been able to understand how to do it myself from the comments :) Maybe it is simple.. but not to me ;)

[Torsten]

Follow Walter Roberson's hint :

y = (0:10:100).';
x = 3:6;
W = exp(-x.^2./y);
f = @(y)y.^2;
fy = repmat(f(y),1,numel(x));
result = trapz(y,fy.*W)

result = 1×4

1.0e+05 * 2.9353 2.6553 2.3400 2.0112

Can you take it from here ?

Answer 1

[David Hill]

y=1:.01:5;
x=0:.01:7;
[X,Y]=meshgrid(x,y);
W=exp(-X.^2./Y);
f=y.^2;%as an example
I=trapz(W.*f')/.01;%each column of I is the integral at each corresponding x value

[Walter Roberson]

You should be using the two-input version of trapz(). Possibly add in the dimension number too.

[Erez]

@Walter Roberson Very sorry for the long delay. Walter, can you explain pls?

[Walter Roberson]

See Torston's version at https://www.mathworks.com/matlabcentral/answers/1738095-matlab-how-to-plot-the-function-p-x-versus-x-where-p-x-int_0-infty-f-y-w-x-y-dy#comment_2212745