How to obtain a no-loop iteration in MATLAB using anonymous functions?

I tried to adapt this base program to my needs, but I am running into an issue. In my particular program I have my function F dependent on other functions. Would you have suggestions on how to incorporate the same idea if the program was modified to include

q = sym('q',[1,10]);
i = 1:10;
M = @(q) tan(q)/(1+sin(7*q))
N = log(M(q))
F = i - 2*q*N == 0;
solq = solve(F,q)

I obtain the same errors in this program that I do in my actual program. I am informed that MATLAB is doing away with the sym('q',...) style argument in favor of 'syms q'. If I use this notation, everything ends up being symbolic, including the answer. I essentially want to solve the equation given in F. The general code works until I include an anonymous function. Is there a way around this?

Answer 1

[Jim Joy]

It appears that the error here is related to how MATLAB is interpreting the multiplication and division used. Since your data is stored as vectors, you need to use "./" and ".*" in place of "/" and "*", if I correctly understand what you are trying to do.

The code below resolves this issue. Note, however, that "solve" returns a numerical solution:

q = sym('q',[1,10]);
i = sym(1:10);
M = tan(q)./(1+sin(7*q))
N = log(M)
F = i - 2*q.*N == 0;
solq = solve(F,q)

Note that solves 10 equations for 10 independent unknowns.

Best Regards,

Jim

[BM]

Jim, thanks for your response. I copied your code into MATLAB, but I receive the following error

Warning: 20 equations in 10 variables. 
> In /usr/local/common/packages64/Matlab_2014a/toolbox/symbolic/symbolic/symengine.p>symengine at 56
  In mupadengine.mupadengine>mupadengine.evalin at 97
  In mupadengine.mupadengine>mupadengine.feval at 150
  In solve at 170
  In untitled3 at 6 
Warning: Explicit solution could not be found. 
> In solve at 179
  In untitled3 at 6 

solq =

[ empty sym ]

Do you know why this error occurs? Also, a numerical solution is fine and expected. I expect 10 different answers, one for each iteration of 'i'. After I get a handle on this, I was going to try to iterate the second variable 'n' in the equation, so that I then have 100 answers. That is, for every iteration of 'n' from 1:10, I would have 10 iterations of 'i' from 1:10. Ultimately, I would be able to like to run the program, and then type in the command window a command with a given 'i'-value and a given 'n'-value and get the solution to my function 'F' corresponding to those values. I hope this clears up what I am trying to ultimately accomplish.

[Jim Joy]

This appears to be due to how MATLAB R2014a parses equations.

If you change the call to "solve" to the form shown below, the warning goes away, and a solution is returned:

>> solq = solve(F)

[BM]

It does solve it now, but the output is now

solq =

     q1: [1x1 sym]
     q2: [1x1 sym]
     q3: [1x1 sym]
     q4: [1x1 sym]
     q5: [1x1 sym]
     q6: [1x1 sym]
     q7: [1x1 sym]
     q8: [1x1 sym]
     q9: [1x1 sym]
    q10: [1x1 sym]

The solutions of F should not be symbolic, as I should have actual values for q1...q10.

[Jim Joy]

The answer is symbolic in the sense that the datatype of the solutions is a MATLAB 'sym'. That being said, the answers are numeric. You can see this by entering the command below:

>> solq.q1
ans =
 - 227.2660704691069869919292425356 + 0.23260362927881213795953027706372i

The solutions are represented using 'vpa' (variable-precision arithmetic), which is the Symbolic Math Toolbox's way of representing numeric values. You can convert to 'double' types using the line of code below:

>> double(sol.q1)
ans =
-2.2727e+02 + 2.3260e-01i

Note that, as the name implies, numbers represented in vpa can have variable amounts of precision. Thus, there may be round-off error when converting to doubles.

[BM]

Jim Joy, thanks a bunch. I was reading up on conversion from symbolic (https://www.mathworks.com/help/symbolic/conversion.html) prior to your answer.

I will pay attention to the MATLAB syntax between versions when I look up info on the site as well! Thanks for the lessons!