Calculating derivative and integration using matlab - matlab

I am trying to find second derivative of a function, but while initializing my symbols i am getting the following error:
Error using ==> subsindex
Function 'subsindex' is not defined for values of class 'sym'.
The commands I am using are:
syms x a b c L;
u = (a*x(x-L))+(b*x((x^2)-(L^2)))+(c*x((x^3)-(L^3)));
"u" is my function.

I don't know much about MATLAB's symbolic capabilities, but that error is coming from the pieces like
x(x-L)
which MATLAB is interpreting as an indexing operation. Did you mean multiplication there? I.e.
x*(x-L)

Related

Integrating a function on matlab

I have a density function f_N which is defined as follows (K_nu(z) is the modified Bessel function):
I want to compute the following integral for each value of N:
The following is the implementation of the above in matlab.
for N=1:100
syms z
f =#(z) (1/(gamma(N)*sqrt(pi))*(z/2).^(N-0.5).*besselk(0.5-N,z));
g = #(z) f(z).*log(f(z));
val=integral(g,0,Inf);
But when I run the above code, it's always returning NaN for varoious values of N with the following warning:
Warning: Infinite or Not-a-Number value encountered
Can someone suggest a simple way to do this or avoid this issue?
I don't think you are doing what you think you are doing. Your declaration of z as a symbol will get overridden by the function handle definition. That means the integral is not a symbolic one, but a numeric one. So what you simply need to do is to drop the function handle notation "#(z)" and do the integral symbolically...
My guess, without thoroughly analysing this, is that one of the points in you integration domain [0,inf] yields a value f (x)=inf, which would destroy a numeric integration technique, but perhaps not a symbolic one.

MATLAB error when solving simultaneous equations

I am running a MATLAB code which solves a set of non-linear simultaneous equations. The code can be found here. The data input for the code (in excel) can be found here.
I encounter the following error:
Error using sym/subsasgn (line 733)
Indexed assignment to empty SYM objects is supported only in the 0-by-0 case.
Error in Solution (line 69)
x(i,:) = (b(i,1) - b0)./(c(i,1)*x0) + c0/c(i,1);
Does anyone have any idea how I can resolve this?
When declaring a symbolic variable, you have to specify the dimensions, otherwise it's a scalar. Instead of syms x; use sym and set the dimension argument:
x=sym('x',[3,4])
Replace [3,4] with the dimensions you want.

How to differentiate a function w.r.t another symbolic function in MATLAB?

Using the code,
syms x(t)
y=x^2
diff(y,t)
diff(y,x)
I get the following error:
2*D(x)(t)*x(t)
Error using sym/diff (line 26)
All arguments, except for the first one, must not be symbolic functions.
Is there a way to tackle this? Thanks for your time.
I dont know much about the Symbolic Math Toolbox, but taking a derivative wrt to a function does not seem to be supported (at least in a direct fashion) for diff.
You can substitute a variable, compute a derivative, and substitute the function back. Like so:
syms z
subs(diff(subs(y,x,z),z),z,x)
ans(t) = 2*x(t)

fit with lsqcurvefit does not work maybe function maldefined

I am trying to fit function F to experimental data.
x_tem and yd are both vectors of size (12,1). The function should find the best
fitting value y_tau of the function to the experimental data.
I just can't find the mistake - matlab is showing me the error :
Error in lsqcurvefit (line 199)
initVals.F = feval(funfcn_x_xdata{3},xCurrent,XDATA,varargin{:});
Caused by:
Failure in initial user-supplied objective function evaluation. LSQCURVEFIT cannot continue.
The code is:
x_tem=Temp_aero_korrektur(:,1);
yd=Temp_aero_korrektur(:,2);
F = #(y_tau,x_tem)((-1)*((273.15-x_tem)*(273.15-y_tau(1))*8.314* (((17.62*x_tem)/(243.12+x_tem))-((17.62*y_tau(1))/(243.12+y_tau(1)))))/(40714.53));
yd_tau = lsqcurvefit(F,-40,x_tem,yd);
There are two possibilities here. One is that you do actually want to use matrix operations in your objective function (so that, for example, x_tem/x_tem gives a single scalar value using mrdivide). If this is the case then you should be calling lsqcurvefit with the transpose of x_tem
yd_tau = lsqcurvefit(F,-40,x_tem',yd);
The other option is that you actually meant to calculate your objective function on each value of x_tem (so, for example, using x_tem./x_tem to give a vector the same length as x_tem). If this is the case then your objective function should be
F = #(y_tau,x_tem)((-1)*((273.15-x_tem).*(273.15-y_tau(1)).*8.314.* (((17.62*x_tem)./(243.12+x_tem))-((17.62*y_tau(1))/(243.12+y_tau(1)))))/(40714.53))
(See documentation for times and rdivide for element-wise operations)

Partial derivative with Matlab Symbolic Toolbox for Lagrangian equations of motion

I'm trying to derive Lagrangian equations of motion in Matlab using the symbolic toolbox. This involves partial derivatives of a function and your coordinates, but matlab seems to not accept this.
So I would do this in Matlab:
syms t x(t) % t: time, x(t) position dependent on time
m = sym('m'); % mass, a constant parameter
T = m/2*diff(x,t)^2; % kinetic energy
dTdx = diff(T,x);
ddTdxDotdt = diff( diff(T,diff(x,t)), t);
But as soon as I try to differentiate anything in x (or diff(x,t)), Matlab complains:
Error using mupadmex
Error in MuPAD command: The variable is invalid. [stdlib::diff]
Error in sym/diff (line 44)
R = mupadmex('symobj::diff', S.s, x.s, int2str(n));
Does anyone know the proper way of handling this?
Matlab ought to be able to do this as you have it written, but I think that it doesn't like taking derivatives with respect to a symfun. Type whos in the command window and you'll see that x is listed as a symfun while t is just a sym. The help for diff kind of indicates this limitation. It won't event try to take the derivative of a constant with respect to x(t): diff(1,x) "complains" just the same. Unless newer versions of Matlab fix this (I'm on R2012b) I think you only option may be to come up with a scheme using two instances of x.