How to define a piecewise anonymous function

Hello everyone,

the example code

syms x
continuous_function = x^2+x;
matlabFunction(continuous_function,'Vars',x)

gives me the anonymous function

 @(x)x+x.^2

I would like a similar result for piecewise functions. However, the code

syms x
piecewise_function = piecewise( 0<x<1, x, 'otherwiseVal', 0 );
matlabFunction(piecewise_function,'Vars',x)

does not work.

Thanks for any help!

Answer 1

[Star Strider]

You need to use ‘logical indexing’:

piecewise_function = @(x) (x.^2+x) .* ((0<x) & (x<1));

x = linspace(-1, 2);
figure
plot(x, piecewise_function(x))

producing:

[Stephan]

Thank you!

Do I understand you correctly that there is no function that converts

piecewise_function = piecewise( 0<x<1, x^2+x, 'otherwiseVal', 0 );

to

@(x) (x.^2+x) .* ((0<x) & (x<1))

[Star Strider]

Yes.

This code:

syms x
piecewise_function = piecewise( 0<x<1, x^2+x, 'otherwiseVal', 0 );
matlabFunction(piecewise_function)

throws this error:

Error using symengine
Unable to generate code for piecewise for use in anonymous functions.

(and some others).

The construction I use here appears to be the only way. Various such expressions can be combined in one function to create piecewise functions across various intervals, for example:

piecewise_function = @(x) (x.^2+x) .* ((0<x) & (x<1)) + (x+sqrt(x)).*((x>=1) & (x<1.5));

So all is not lost.

[Stephan]

Thank you for this useful remark!

[Star Strider]

As always, my pleasure!

[ElPerroVerde]

THANK YOU SO MUCH!!!!!!!!!!!! I've been looking for something like this for months!!!

[Star Strider]

ElPerroVerde — My pleasure!

A Vote would be appreciated!

.

[Roy Goodman]

How can we modify this to take the value NaN outside the interval [0 1]?

[Roy Goodman]

MATLAB Copilot returns code that fails!

[Torsten]

piecewise_function = @(x) (x.^2+x) + 0./((0<=x) & (x<=1));
x = linspace(-1, 2);
figure
plot(x, piecewise_function(x))

[Walter Roberson]

syms x
f = piecewise((0<=x) & (x<=1),x.^2+x,nan)

f = 

piecewise_function = matlabFunction(f, 'file', 'test_piecewise.m')

piecewise_function = function_handle with value:
    @test_piecewise

dbtype test_piecewise

1     function f = test_piecewise(x)
2     %TEST_PIECEWISE
3     %    F = TEST_PIECEWISE(X)
4     
5     %    This function was generated by the Symbolic Math Toolbox version 25.2.
6     %    29-Oct-2025 22:14:42
7     
8     t2 = ((0.0 <= x) & (x <= 1.0));
9     if ~all(cellfun(@isscalar,{t2}))
10        error(message('symbolic:sym:matlabFunction:ConditionsMustBeScalar'));
11    end
12    if (t2)
13        f = x+x.^2;
14    else
15        f = NaN;
16    end
17    end

x = linspace(-1, 2);
plot(x, arrayfun(piecewise_function, x))
xline([-1 2])

●

[Roy Goodman]

Thanks!

Answer 2

[Walter Roberson]

If you use matlabFunction with 'file' option, then it will convert piecewise() into if/else in the generated code.

Note: because it uses if/else instead of logical indexing, the generated code will not be vectorized on that variable.