How do I set default values for functions parameters in MATLAB?

There isn't a direct way to do this like you've attempted.

The usual approach is to use "varargs" and check against the number of arguments. Something like:

function f(arg1, arg2, arg3)

  if nargin < 3
    arg3 =   'some default'
  end

end

There are a few fancier things you can do with isempty, etc., and you might want to look at MATLAB central for some packages that bundle these sorts of things.

You might have a look at varargin, nargchk, etc. They're useful functions for this sort of thing. varargs allow you to leave a variable number of final arguments, but this doesn't get you around the problem of default values for some/all of them.

I've used the inputParser object to deal with setting default options. MATLAB won't accept the Python-like format you specified in the question, but you should be able to call the function like this:

wave(a, b, n, k, T, f, flag, 'fTrue', inline('0'))

After you define the wave function like this:

function wave(a, b, n, k, T, f, flag, varargin)

    i_p = inputParser;
    i_p.FunctionName = 'WAVE';

    i_p.addRequired('a', @isnumeric);
    i_p.addRequired('b', @isnumeric);
    i_p.addRequired('n', @isnumeric);
    i_p.addRequired('k', @isnumeric);
    i_p.addRequired('T', @isnumeric);
    i_p.addRequired('f', @isnumeric);
    i_p.addRequired('flag', @isnumeric);
    i_p.addOptional('ftrue', inline('0'), 1);

    i_p.parse(a, b, n, k, T, f, flag, varargin{:});

Now the values passed into the function are available through i_p.Results. Also, I wasn't sure how to validate that the parameter passed in for ftrue was actually an inline function, so I left the validator blank.

Yes, it might be really nice to have the capability to do as you have written. But it is not possible in MATLAB. Many of my utilities that allow defaults for the arguments tend to be written with explicit checks in the beginning like this:

if (nargin<3) or isempty(myParameterName)
  MyParameterName = defaultValue;
elseif (.... tests for non-validity of the value actually provided ...)
  error('The sky is falling!')
end

Ok, so I would generally apply a better, more descriptive error message. See that the check for an empty variable allows the user to pass in an empty pair of brackets, [], as a placeholder for a variable that will take on its default value. The author must still supply the code to replace that empty argument with its default value though.

My utilities that are more sophisticated, with many parameters, all of which have default arguments, will often use a property/value pair interface for default arguments. This basic paradigm is seen in the handle graphics tools in MATLAB, as well as in optimset, odeset, etc.

As a means to work with these property/value pairs, you will need to learn about varargin, as a way of inputting a fully variable number of arguments to a function. I wrote (and posted) a utility to work with such property/value pairs, parse_pv_pairs.m. It helps you to convert property/value pairs into a MATLAB structure. It also enables you to supply default values for each parameter. Converting an unwieldy list of parameters into a structure is a very nice way to pass them around in MATLAB.

I've found that the parseArgs function can be very helpful.

Here's its documentation:

Helper function for parsing varargin. Makes it easy to write functions that take arguments like this: subaxis(4,2,1,'spacing',0,'marginleft',.1,'H','pt',.1)

ArgStruct=parseArgs(varargin,ArgStruct[,FlagtypeParams[,Aliases]])

• ArgStruct is the structure full of named arguments with default values.
• Flagtype params is params that don't require a value. (the value will be set to 1 if it is present)
• Aliases can be used to map one argument-name to several argstruct fields

example usage:

function parseargtest(varargin)

%define the acceptable named arguments and assign default values
Args=struct('Holdaxis',0, ...
'SpacingVertical',0.05,'SpacingHorizontal',0.05, ...
'PaddingLeft',0,'PaddingRight',0,'PaddingTop',0,'PaddingBottom',0, ...
'MarginLeft',.1,'MarginRight',.1,'MarginTop',.1,'MarginBottom',.1, ...
'rows',[],'cols',[]);

%The capital letters define abrreviations.
% Eg. parseargtest('spacingvertical',0) is equivalent to parseargtest('sv',0)

Args=parseArgs(varargin,Args, ... 
% fill the arg-struct with values entered by the user, e.g.
% {'Holdaxis'}, ... %this argument has no value (flag-type)
% {'Spacing' {'sh','sv'}; 'Padding' {'pl','pr','pt','pb'}; 'Margin' {'ml','mr','mt','mb'}});

disp(Args)

"True" default arguments (i.e. defaults via a purpose-built language feature rather than parsing functions or hand-rolled code) were introduced in 2019b with the arguments block.

As a simplified example, consider the following function:

function myFun(a,b,c)
    arguments
        a
        b
        c = 0
    end
    disp([a b c])
end

c is an optional input with a default value of 0. Inputs a and b have no defaults defined making them required inputs.

myFun may now be called with or without passing a value for c, with the default value of c=0 being used if no value is provided.

>> myFun(1,2)
     1     2     0

>> myFun(1,2,3)
     1     2     3

This is more or less lifted from the MATLAB manual; I've only got passing experience...

function my_output = wave ( a, b, n, k, T, f, flag, varargin )
  optargin = numel(varargin);
  fTrue = inline('0');
  if optargin > 0
    fTrue = varargin{1};
  end
  % code ...
end

Matlab doesn't provide a mechanism for this, but you can construct one in userland code that's terser than inputParser or "if nargin < 1..." sequences.

function varargout = getargs(args, defaults)
%GETARGS Parse function arguments, with defaults
%
% args is varargin from the caller. By convention, a [] means "use default".
% defaults (optional) is a cell vector of corresponding default values

if nargin < 2;  defaults = {}; end

varargout = cell(1, nargout);
for i = 1:nargout
    if numel(args) >= i && ~isequal(args{i}, [])
        varargout{i} = args{i};
    elseif numel(defaults) >= i
        varargout{i} = defaults{i};
    end
end

Then you can call it in your functions like this:

function y = foo(varargin)
%FOO 
%
% y = foo(a, b, c, d, e, f, g)

[a, b,  c,       d, e, f, g] = getargs(varargin,...
{1, 14, 'dfltc'});

The formatting is a convention that lets you read down from parameter names to their default values. You can extend your getargs() with optional parameter type specifications (for error detection or implicit conversion) and argument count ranges.

There are two drawbacks to this approach. First, it's slow, so you don't want to use it for functions that are called in loops. Second, Matlab's function help - the autocompletion hints on the command line - don't work for varargin functions. But it is pretty convenient.

I like to do this in a somewhat more object-oriented way.

Before calling wave(), save some of your arguments within a struct, e.g. one called parameters:

parameters.flag = 42;
parameters.fTrue = 1;
wave(a, b, n, k, T, f, parameters);

Within the wave function then check, whether the struct parameters contains a field called 'flag' and if so, if its value is non empty. Then assign it either a default value you define before, or the value given as an argument in the parameters struct:

function output = wave(a, b, n, k, T, f, parameters)
  flagDefault = 18;
  fTrueDefault = 0;
  if (isfield(parameters,'flag') == 0 || isempty(parameters.flag)), flag=flagDefault;else flag=parameters.flag; end
  if (isfield(parameter, 'fTrue') == 0 || isempty(parameters.fTrue)), fTrue=fTrueDefault;else fTrue=parameters.fTrue; end
  ...
end

This makes it easier to handle large numbers of arguments, because it does not depend on the order of the given arguments. That said, it is also helpful if you have to add more arguments later, because you don't have to change the functions signature to do so.