General function in symbolic toolbox

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dominik 2014-5-20

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回答： Martin Ahrnbom 2020-6-16

Is it possible in the matlab symbolic toolbox to define general functions, i.e. to define functions only as a general mapping from agruments to output without defining the functional form?

E.g. I would like to define f(x). Then id like to use f(x) in a number of symbolic operations. E.g.

syms x y; 
%define general function
Equation=f(x)+y;
Grad=gradient(Equation,[x, y])

Now for grad id like to get Grad = [ derivative(f(x),x) , y ]

Then id be able to youse matlabFunction to create a matlab function from that, replacing all references to f(x) by the relevant functional form.

(I could of course assume this functional form from the beginning but then id have to rerun the code for every change in f(x) and in my application it would also be too slow since matlab would subsitute out f(x) everytime its used.)

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Star Strider 2014-5-20

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编辑：Star Strider 2014-5-20

在 MATLAB Online 中打开

Beginning with R2012a, it has been possible to define functions in the Symbolic Math Toolbox the way you would normally define functions:

syms t x y
f(x) = x^2 + 2*x + 1
g(t) = 10*exp(-t)
h(x,t) = x^2 - t^2
r1 = f(pi)
r2 = g(5)
r3 = h(3,5)
gradh = gradient(h)
grh = matlabFunction(gradh)

All give the expected numeric and symbolic results.

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Cedric 2014-5-20

编辑：Cedric 2014-5-20

+1 -> 1500!

Star Strider 2014-5-20

编辑：Star Strider 2014-5-20

THANK YOU, CEDRIC!!

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dominik 2014-5-20

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Hi Thanks for the answer, it seems I havent expressed my question clearly.

In what you propose you define the function explicitly. E.g. f(x) = x^2; Then derivative(f(x)) evaluates to 2*x; This is exactly what i do NOT want to do. Since the function and the operations with the functions are so complex that it makes matlab infeasibly slow.

I want to keep the function as a placeholder only. As if it was a constant, only when deriving treat it as a general function of its arguments (and apply the chain rule). something like f(x)=f(x); Then derivative(f(x),x) evaluates to d_f(x); where f(x) and d_f(x) are unknown functions, all we know is the latter is the derivative of the former

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dominik 2014-5-20

编辑：dominik 2014-5-20

Not sure if i understand your last comment.

Let me describe exactly what im trying to do.

I have to solve an equation system numerically. To do so i want to provide derivatives to the solver. These derivatives I want to calculate symbolically to avoid mistakes.

So first i define my equation syste in the symbolic toolbox. Equ1=G1(x,f(x)), Equ2=G2(x,f(x)) etc where x is a vector and G are functions whose functional form i type down, e.g. Equ1=G1(x,f(x))=x(1)+x(2)^2/f(x)

Then i find the derivatives Grad1=Jacobian(E1,x), Grad2=Jacobian(E2,x) etc.

Then i use matlabfunction to create a function with the outputs [Equ1 Equ2...] and [Grad1 Grad2 ...]

Now the tricky bit is the f(x). If f(x) was a easy function -say log(x(1))- it wouldnt be a problem. I'd define a either symbolic function f=symfun(x(1),x) or equivalently define f=log(x(1)); Matlab would subsitute out f and provide me the gradients.

Yet my f is a function of many lines, it is recursive (hence not very suitable for he toolbox) and furthermore it contains max mins and if conditions(hence cant be written in the toolbox), so i cant just define f. Thats why i would like matlab to simply write f wherever f appears and to write d_f whenever it has to derive f. Once i have the matlabfunction code i can then replace f and d_f using the complicated (but fast since recursive) external function.