How to create a local function during the code run

Hello, everyone!

I have a question about opportunity of creating local functions during the code run.

For example I have this code:

function diffprobe
x0=[1 1];
for i=1:2
    a=strcat('@odeEvent', num2str(i));
    str = str2func(a);
    options(i)=odeset('Events', str, 'RelTol',1e-9,'AbsTol',1e-9);
    [~,~,TE,XE,IE]=ode45(@System, [0 inf],x0, options(i));
end

function [value, isterminal, direction]=odeEvent1(~,x)
value=[x(1)];
isterminal=[1];
direction=0;

function [value, isterminal, direction]=odeEvent2(~,x)
value=[x(2)];
isterminal=[1];
direction=0;


function RPF=System(~,x)
RPF=[x(2);...
    -x(2)-1];

It is work right, but i have an interest to somehow create local functions odeEvent1 and odeEvent2 during the cycle, because of I need to generalize the method on high order systems so the cycle might go not from 1 to 2, but from 1 to n, and obviously I don't want to rewrite the code every time, when I try the new system.

Answer 1

[Ameer Hamza]

Dynamically creating a function name is not a recommended coding practice. Following shows how to do such a thing more efficiently

function diffprobe
x0=[1 1];
for i=1:2
    options(i)=odeset('Events', @(t,x) odeEvent(t,x,i), 'RelTol',1e-9,'AbsTol',1e-9);
    [~,~,TE,XE,IE]=ode45(@System, [0 inf],x0, options(i));
end

function [value, isterminal, direction]=odeEvent(~,x,i)
value=[x(i)];
isterminal=[1];
direction=0;

function RPF=System(~,x)
RPF=[x(2);...
    -x(2)-1];

[Ivan Khomich]

O, very thanks.

It turned out to be very easy, but when I tried this myself I use this notation:

options(i)=odeset('Events', @(t,x,i) odeEvent, 'RelTol',1e-9,'AbsTol',1e-9);

and got the errors.

So, it turns out that @(a,b,...z) is the variables that go the solver, and odeEvent(t,x,i) - is the variables that go to the function odeEvent, right?

[Ameer Hamza]

Yes, @(t,x) is the requirement of the solver(), whereas odeEvent(t,x,i) shows how you pass the solver variables to your odeEvent functions. You can read the documentation related to anonymous functions to see in detail what is happening here.

[Steven Lord]

What Ivan Khomich wrote:

options(i)=odeset('Events', @(t,x,i) odeEvent, 'RelTol',1e-9,'AbsTol',1e-9);

ode45 will call the anonymous function stored in the Events option with two inputs (that is what it is documented to do) and so the variable named i will be undefined. The anonymous function will call odeEvent with zero inputs.

What Ameer Hamza wrote:

options(i)=odeset('Events', @(t,x) odeEvent(t,x,i), 'RelTol',1e-9,'AbsTol',1e-9);

ode45 will call the anonymous function stored in the Events option with two inputs. The anonymous function will call odeEvent with three inputs, the two passed into it by ode45 and one the anonymous function "remembered" because that variable existed when the anonymous function was created.