MATLAB集成的匿名函数

Question

I wanted to ask how can I can write this in MATLAB.

I want to integrate fp(z) with z(0,x) . I tried this :

fpz=@(z) f1x(z) ./ quadl(f1x(z),0,1);

sol=int(fpz,0,x)  --> i also tried sol=quadl(fpz,0,x)
y=solve('y=sol',x)

xf=@ (y) y ;   -->this is the function i want

where f1x=@ (x) 1 ./(x.^2+1) and fpx = @(x) f1x(x) ./ quadl(f1x,0,1);

but it doesn't work.

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Hello,thanks for helping. The problem is that i want an analytically solution and i can't get one. I want f1x to give me " 1/x^2+1" , fpx "4/pi*(1+x^2) and fpz "4ArcTan(x)/pi", instead of giving me "f1x=@ 1./(x^2+1)".. With the code you send me ,still the same problem. I managed to come into this :

f1x=@ (x) 1 ./(x.^2+1) fpx = @(x) f1x(x) ./ quadl(f1x,0,1) f2z=@ (z) 1 ./(z.^2+1); fpz=@(z) fpx(z) ./ quadl(f2z,0,1) sol=int(fpz(z),z,0,x) y=solve(subs('y=sol'),x) xf=@ (y) y

The "sol" and "y=" gives me analytically answer but it is wrong because i assume f1x and fpx,fpz doesn't return into analytically expressions.

Answer 1

0 Your definition of fpz doesn't make any sense; as Marcin already said, you're trying to integrate something that isn't a function. This shouldn't be a problem for your alternative version with f2z. I think the code in the original question should have had just f1x rather than f1x(z) in the first line.

1 Your revised version with f2z has a different problem: now in fpz you aren't actually providing the function with an argument.

The following code seems to be the kind of thing you had in mind, and works fine for me (in MATLAB R2008a, as it happens, but none of this should be different in other versions):

f1x = @(x) 1 ./ (x.^2+1);
fpx = @(x) f1x(x) ./ quadl(f1x,0,1);
fpz = @(z) fpx(z) ./ quadl(fpx,0,1);

Now evaluating fpz(3), for instance, spins for about half a second (on my old slow laptop computer) and returns 0.1273.

So I think the problems you've been having with integration of anonymous functions are just a matter of not being quite careful enough to distinguish between the function itself and a particular value of the function.

You have some further questions about the "solve" and "int" functions in the Symbolic Math Toolbox. You should take the following with a pinch of salt because I don't have that toolbox and am relying on the online documentation for it.

3 You're feeding the names of functions you've defined in MATLAB to the Symbolic Math Toolbox functions. I don't think that is supposed to work; "int" and "solve" expect explicit algebraic expressions, not MATLAB functions. (And, further, your functions all use numerical integration -- quad, quadl, etc. -- and there's no possible way that the symbolic functions can do anything useful with that.)

Finally: When you're asking questions of this sort, it's helpful if rather than "it doesn't work" you say how it doesn't work. For instance, your most recent comment is much more useful ("it gives me ..." followed by the actual output you get from MATLAB).