MATLAB operators as functions

Question

I was just curious that whether all operators in MATLAB are internally implemented as functions? We have equivalent functions for almost all MATLAB operators. plus for +, minus for -, eq for == and transpose for '.

Answer 1

Most operators are represented by functions, yes.

A thorough list is provided on the MathWorks page Implementing Operators for Your Class, reproduced here:

a + b               plus(a,b)         Binary addition
a - b               minus(a,b)        Binary subtraction
-a                  uminus(a)         Unary minus
+a                  uplus(a)          Unary plus
a.*b                times(a,b)        Element-wise multiplication
a*b                 mtimes(a,b)       Matrix multiplication
a./b                rdivide(a,b)      Right element-wise division
a.\b                ldivide(a,b)      Left element-wise division
a/b                 mrdivide(a,b)     Matrix right division
a\b                 mldivide(a,b)     Matrix left division
a.^b                power(a,b)        Element-wise power
a^b                 mpower(a,b)       Matrix power
a < b               lt(a,b)           Less than
a > b               gt(a,b)           Greater than
a <= b              le(a,b)           Less than or equal to
a >= b              ge(a,b)           Greater than or equal to
a ~= b              ne(a,b)           Not equal to
a == b              eq(a,b)           Equality
a & b               and(a,b)          Logical AND
a | b               or(a,b)           Logical OR
~a                  not(a)            Logical NOT
a:d:b               colon(a,d,b)      Colon operator
a:b
colon(a,b)               
a'                  ctranspose(a)     Complex conjugate transpose
a.'                 transpose(a)      Matrix transpose
command line output display(a)        Display method
[a b]               horzcat(a,b,...)  Horizontal concatenation
[a; b]              vertcat(a,b,...)  Vertical concatenation
a(s1,s2,...sn)      subsref(a,s)      Subscripted reference
a(s1,...,sn) = b    subsasgn(a,s,b)   Subscripted assignment
b(a)                subsindex(a)      Subscript index

Another good place to look for a list is actually the documentation for bsxfun, which applies any element-wise function with very powerful virtual data replication.

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Often useful is vertcat. horizontal vs. vertical concatenation with a comma separated list:

>> c = {'a','b'};
>> horzcat(c{:}) % [c{1} c{2}]
ans =
     ab
>> vertcat(c{:}) % [c{1};c{2}]
ans =
    a
    b

---

In addition to many other documented operators with named functions (colon,transpose,etc.), there are a couple undocumented ones that you can access with builtin:

parenthesis

>> x = [4 5 6];
>> builtin('_paren',x,[2 3])  % x([2 3])
ans =
     5     6

curly braces

>> c = {'one','two'};
>> builtin('_brace',c,2)  % c{2}
ans =
two

struct field access (dot)

>> s = struct('f','contents');
>> builtin('_dot',s,'f')  % s.f
ans =
contents

However, note that the proper and supported way to use (), {}, or . is via subsref, subasgn, and subindex, depending on the context.

These builtins refer to the operators described in help paren. Also explore the punctuation listed in help punct.

Answer 2

Yes, that's how MATLAB enables operator overloading, by mapping infix operators to named functions.

The documentation lists (by category) the functions invoked by operators. And more here.