Plot a matrix which has functions

I have these functions (in a script):

fx  = @ (x) exp(-x.^2);
f1x = @ (x) 1/(x.^2+1);
fpx = f1x/int(f1x,x,0,1)

I want to plot a table with {fx,fpx} when {x,0,1}.

How can I do this?

Answer 1

[Walter Roberson]

int() is a routine that applies to symbolic expressions, not to function handles. Do you have access to the Symbolic Toolkit? If not, then you will need to do a numeric integration such as with trapz or quadl

If you are using the symbolic toolbox, you would rewrite all three clauses. If you are not, then your last clause should not be

fpx=f1x/int(f1x,x,0,1)

but rather something like

fpx = @(x) f1x(x) ./ quadl(f1x,0,1)

It should not, however, be something like

fpx = @(x) double(subs(f1x,'x',x)) ./ double(int(f1x,x,0,1))

which is close but has the problem that the "x" in the call to "int" needs to be the symbolic variable to integrate with respect to, and should not be the particular value of x that you are using to evaluate f1x in the numerator. You could, however, use:

fpx = @(x) double(subs(f1x,'x',x)) ./ double(int(f1x,'x',0,1))

Once you have constructed fpx to be a function of x, you could construct your table as

SubDivisons = 250;
xvals = linspace(0,1,SubDivisions) .';
YourTable = [fx(xvals), fpx(xvals)];
plot(xvals, YourTable);

[George]

Hello,i tried these but it gives me errors: Error using ==> mldivide

Matrix dimensions must agree.

Error in ==> @(x)1/(x.^2+1)

Error in ==> quadl at 70

y = feval(f,x,varargin{:}); y = y(:).';

Error in ==> @(x)f1x(x)./quadl(f1x,0,1)

Error in ==> sampling2 at 62

YourTable = [fx(xvals), fpx(xvals)];

I will check tomorrow again.Thanks for the help.

[Walter Roberson]

Change your @(x)1/(x.^2+1)

to

@(x)1./(x.^2+1)

[George]

It worked fine now!Thanks a lot!

[George]

May i ask sth else?

How can i write this : I want to integrate fp(z) with z(0,x).

I tried this :" fpz=@(z) f1x(z) ./ quadl(f1x,0,1)

int(fpz,0,x) "

but it doesn't work.

Answer 2

[Paulo Silva]

disp('Executing the function, please wait')
steps=0.05;
%increase steps to speed up execution, accuracy will be lower
%decrease steps to improve accuracy, you have to wait more time
x=0:steps:1;
fx=inline('exp(-x.^2)');
f1x=inline('1./(x.^2+1)');
fpx=sym(f1x)./int(sym(f1x));
fpx=subs(fpx,'x',x);
fx=subs(fx,'x',x);
Table=[fx;fpx];
plot(fx,fpx)
disp('All done, you can find the result in variable Table')

[Ned Gulley]

Hi Paulo: You might want to just edit your old answer to correct it rather than creating a new answer.

[Paulo Silva]

Hi Ned, I will use the edit next time, thanks.

[George]

Hello, i tried these but it gives me the following error:

Error using ==> sym.sym>tomupad at 2162

Conversion to 'sym' from 'inline' is not possible.

Error in ==> sym.sym>sym.sym at 102

S.s = tomupad(x,'');

Error in ==> test at 61

fpx=sym(f1x)./int(sym(f1x));

[Paulo Silva]

I have no idea about what could be wrong, it's working here in Matlab 2008b (32bits), here's the result http://img254.imageshack.us/img254/5666/46107520.jpg