symbolic derivative with constant output

Hi everyone,

I am working on a code requiring the definition of an anonymous function that is the derivative of another anonymous function specified at runtime. The use of matlabFunction is straightforward in most cases, and the resulting anonymous function can be used as the original function.

>> syms t
>> x = @(t)sin(t);
>> dxdt = matlabFunction(diff(x(t)))

dxdt =

  function_handle with value:

    @(t)cos(t)

>> dxdt(10)

ans =

   -0.8391

However, it could happen that the original anonimous function can be linear or constant. In this case matlabFunction creates an output that does not accepts inputs:

>> syms t
>> x = @(t)10*t;
>> dxdt = matlabFunction(diff(x(t)))

dxdt =

  function_handle with value:

    @()1.0e1

>> dxdt(10)
Error using symengine>@()1.0e1
Too many input arguments.

How can I define the derivative of an anonymous function such that the output in the last case is usable with one input for any input? In the previous case I would like to have something like:

dxdt = @(t)10;

Thanks in advance

Fabio

[madhan ravi]

why do you need the function handle with t for anyways for your last case?

[Fabio Freschi]

Because the code is rather general and the derivative is used later in the algorithm.

Since I don't have the control of the input function x(t), I would like to have a comprehensive implementation that covers also the latter case

[madhan ravi]

you can like use nargin() to check the number of the inputs in a function and can create an if condition to process your data further according to the number of inputs

Answer 1

[Walter Roberson]

matlabFunction(diff(x(t),t), 'vars', t)

The result would permit one input argument. However, it would return a scalar output no matter what the size of the input. So what you can do is

temp = diff(x(t),t);
if isempty(symvar(temp))
    tempdxdt = matlabFunction(temp, 'vars', t);   %when the value is a constant, the generated function returns a scalar no matter what size of t is
    dxdt = @(t) ones(size(t)) * tempdxdt(t);
else
    dxdt = matlabFunction(temp, 'vars', t);
end