MATLAB: Generation of symbolic vector of functions

symbolicSymbolic Math Toolbox

I need to define a lot of symbolic variables for DAE solver.

Instead of using

sym f1(t) f2(t) % up to arbitrary fN(t)

i would prefer something like this

sym('f_%d(t)',[1 N])

or similar. But it seems that use of parenthes is not allowed. Is possible to generate programatically such vectors?

Best Answer

syms("f_" + (1:N) + "(t)")

The output cannot be assigned to anything.

syms() must be used for this, not sym()

str2sym() will not work for this purpose, and instead will effectively give you back variable names that just happen to include '(' 't' ')' characters but which are not functions.

There is an alternative involving aarrayfun of a symfun call and 'uniform', 0

Related Solutions

MATLAB: How to convert strings to symbolic expressions without sym()

y = evalin(symengine, 'x+1')

which does the same thing as

y = sym('x+1')

except that going through sym() has more overhead for this situation and will give you the warning.

Caution: when you use

syms x
sym('x+1')

then the x of the second version does not necessarily refer to the same thing that the first one refers to. For example if you had used

syms x y
x = y + 2
sym('x+1')

then you will not get y + 3

MATLAB: Symbolic differentiation with respect to first derivative

https://www.mathworks.com/help/symbolic/functionalderivative.html is the only available tool provided by Mathworks.

However, this is not going to do what you want:

syms x(t); dx = diff(x); eqn = dx - 2;
>> diff(eqn,dx)
Error using sym/diff (line 26)
Arguments, except for the first, must not be symbolic functions.

(which is a misleading error message that I will file a bug about.)

Note that if you would to have

eqn = x - 2
diff(eqn, x)

the result would be 1, not -2 . -2 is constant with respect to x(t) or diff(x,t) so it is going to vanish in the derivative.

It is tempting to use something like https://www.mathworks.com/help/symbolic/odetovectorfield.html to substitute the derivative with a symbol that you can then differentiate with respect to. However, drivatives are not independent of the original function, and you can arrive at wrong answers if you do this. I have posted examples in the past demonstrating that differentiating with one function with respect to another by processes like this give incorrect solutions (but that was a while ago and might be a bit tricky to locate now.) You cannot generally differentiate with respect to a function using normal calculus: you need The Calculus of Variations, which MATLAB does not implement.

Best Answer

Related Solutions

MATLAB: How to convert strings to symbolic expressions without sym()

MATLAB: Symbolic differentiation with respect to first derivative

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