am trying to plot P and Q but the matrix dimensions seems to disagree with me.

clc
clf

qmod = @(a) abs((k*exp(-2*(-(a + k)*(a - k))^(1/2))*(a/k - ((-(a + k)*(a - k))^(1/2)*1i)/k)*1i)/(exp(-2*(-(a + k)*(a - k))^(1/2))*(-(a + k)*(a - k))^(1/2) + exp(2*(-(a + k)*(a - k))^(1/2))*(-(a + k)*(a - k))^(1/2) + a*exp(-2*(-(a + k)*(a - k))^(1/2))*1i - a*exp(2*(-(a + k)*(a - k))^(1/2))*1i) + (k*exp(2*(-(a + k)*(a - k))^(1/2))*(a/k + ((-(a + k)*(a - k))^(1/2)*1i)/k))/(exp(-2*(-(a + k)*(a - k))^(1/2))*(-(a + k)*(a - k))^(1/2)*1i + exp(2*(-(a + k)*(a - k))^(1/2))*(-(a + k)*(a - k))^(1/2)*1i - a*exp(-2*(-(a + k)*(a - k))^(1/2)) + a*exp(2*(-(a + k)*(a - k))^(1/2))))^2/abs((k*exp(-2*(-(a + k)*(a - k))^(1/2))*1i)/(exp(-2*(-(a + k)*(a - k))^(1/2))*(-(a + k)*(a - k))^(1/2) + exp(2*(-(a + k)*(a - k))^(1/2))*(-(a + k)*(a - k))^(1/2) + a*exp(-2*(-(a + k)*(a - k))^(1/2))*1i - a*exp(2*(-(a + k)*(a - k))^(1/2))*1i) + (k*exp(2*(-(a + k)*(a - k))^(1/2)))/(a*exp(2*(-(a + k)*(a - k))^(1/2)) - a*exp(-2*(-(a + k)*(a - k))^(1/2)) + exp(-2*(-(a + k)*(a - k))^(1/2))*(-(a + k)*(a - k))^(1/2)*1i + exp(2*(-(a + k)*(a - k))^(1/2))*(-(a + k)*(a - k))^(1/2)*1i))^2
normwave = @(a) 1/(1+(2.*a./31400))
a=linspace(0.1,1);
P=normwave(a);
Q=qmod(a);

[Rik]

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Answer 1

[Rik]

Somewhere in that humongous anonymous function you have made a mistake.

In this case the mistake is that you didn't use array operations, so all those products, powers and divisions are matrix operations.

Try to split qmod over multiple lines is segments that make sense. You could even consider writing the parts as separate anonymous functions. Then make sure to change matrix operations to array operations (replace * by .* etc).

[vipul kumar]

i see that, the only problem is i got that dirty looking function by solving coupled differential equations. I copy-psted it directly.

[vipul kumar]

clc
syms r(z) s(z) a k
ode1 = diff(r) == i*a*r+i*k*s
ode2 = diff(s) == -i*a*s-i*k*r
odes = [ode1 ; ode2]
p = dsolve(odes)
rSol(z) = p.r
sSol(z) = p.s
cond1 = r(-1) == 1;
cond2 = s(1) == 0;
conds = [cond1; cond2];
[rSol(z), sSol(z)] = dsolve(odes,conds)
q(a)=rSol(-1)./sSol(-1);
qmod=(abs(q)).^2

[Rik]

Your definition of normwave was also missing an array operator.

normwave = @(a) 1./(1+(2.*a./31400));
a=linspace(0.1,1);
P=normwave(a);
Q=qmod(a);

function val=qmod(a,k)
%apply values to anonymous function
if nargin==1
    k=1;%this value has to be set somehow
end
% %genarator code:
% syms r(z) s(z) a k
% ode1 = diff(r) == i*a*r+i*k*s;
% ode2 = diff(s) == -i*a*s-i*k*r;
% odes = [ode1 ; ode2];
% p = dsolve(odes);
% rSol(z) = p.r;
% sSol(z) = p.s;
% cond1 = r(-1) == 1;
% cond2 = s(1) == 0;
% conds = [cond1; cond2];
% [rSol(z), sSol(z)] = dsolve(odes,conds);
% q(a)=rSol(-1)./sSol(-1);
% clc,qmod=(abs(q)).^2
qmod_internal = @(a) abs((k*exp(-2*(-(a + k)*(a - k))^(1/2))*(a/k - ...
    ((-(a + k)*(a - k))^(1/2)*1i)/k)*1i)/(exp(-2*(-(a + k)*(a - ...
    k))^(1/2))*(-(a + k)*(a - k))^(1/2) + exp(2*(-(a + k)*(a - ...
    k))^(1/2))*(-(a + k)*(a - k))^(1/2) + a*exp(-2*(-(a + k)*(a - ...
    k))^(1/2))*1i - a*exp(2*(-(a + k)*(a - k))^(1/2))*1i) + ...
    (k*exp(2*(-(a + k)*(a - k))^(1/2))*(a/k + ((-(a + k)*(a - ...
    k))^(1/2)*1i)/k))/(exp(-2*(-(a + k)*(a - k))^(1/2))*(-(a + k)*(a - ...
    k))^(1/2)*1i + exp(2*(-(a + k)*(a - k))^(1/2))*(-(a + k)*(a - ...
    k))^(1/2)*1i - a*exp(-2*(-(a + k)*(a - k))^(1/2)) + a*exp(2*(-(a + ...
    k)*(a - k))^(1/2))))^2/abs((k*exp(-2*(-(a + k)*(a - ...
    k))^(1/2))*1i)/(exp(-2*(-(a + k)*(a - k))^(1/2))*(-(a + k)*(a - ...
    k))^(1/2) + exp(2*(-(a + k)*(a - k))^(1/2))*(-(a + k)*(a - ...
    k))^(1/2) + a*exp(-2*(-(a + k)*(a - k))^(1/2))*1i - a*exp(2*(-(a + ...
    k)*(a - k))^(1/2))*1i) + (k*exp(2*(-(a + k)*(a - ...
    k))^(1/2)))/(a*exp(2*(-(a + k)*(a - k))^(1/2)) - a*exp(-2*(-(a + ...
    k)*(a - k))^(1/2)) + exp(-2*(-(a + k)*(a - k))^(1/2))*(-(a + ...
    k)*(a - k))^(1/2)*1i + exp(2*(-(a + k)*(a - k))^(1/2))*(-(a + ...
    k)*(a - k))^(1/2)*1i))^2;
if isscalar(a)
    val=qmod_internal(a);
else
    val=arrayfun(qmod_internal,a);
end
end

[vipul kumar]

Hey Rik, thank you so much for this. I did not get the correct plot though. Can you suggest a better method of solving coupled differential equations, as dsolve gave me a series solution contaning exponentials.

[Rik]

I have never worked with differential equations in Matlab, so I don't know where to start. I would start with a google search that also includes a generic name for your application. I know there are several functions to do with differential equations, like ode45. It's documentation has a fairly prominent link with the text 'Choose an ODE Solver', so that would seem a good place to start.

Another point is that this solution requires a value for k. I randomly chose 1, just because it worked. It might not actually be the correct value, so you could also have a look into that.

[vipul kumar]

There is one more doubt, using your code how do i plot P vs Q?

[Star Strider]

Use the matlabFunction function to create anonymous functions from the symbolic functions.

For example:

rSoln = matlabFunction(rSol)                                % Create Anonymous Function From Symbolic Function
sSoln = matlabFunction(sSol)                                % Create Anonymous Function From Symbolic Function

and so for the others as well. They are also fully vectorised. You can then use them as you would any other numeric function. (I added the ‘n’ to avoid overwriting the original symbolic expressions. Name them whatever you wish.)

[vipul kumar]

@Star Strider i got that, in that way i would not have to define function handle. Right?

But the problem was with matrix multiplication

[Star Strider]

It defines the function handle for you. (Run those lines and then look at the results in your Command Window.) You only need to provide all the arguments.

Is there still a problelm in the functions produced by matlabFunction? (It specifies array operations, not matrix operations.) If so, it may be necessary to edit those functions to do matrix operations if those are what you want to do. That simply involves removing the dot operators from those operations, so multiplication becomes * rather than .*. You also need to be certain that the matrix sizes are conformable to the operations you want to do.

[vipul kumar]

Yes that editing i did by replacing all '*' by '.*' and rik provided a much shorter method. But i could not obtain a plot P vs Q (ref is in the comments). P.S total noobie to programming.