Tutorial: Operators and Ext Module

This tutorial will go through the operators and Ext module. The operators in Owl are implemented using functors. However, you do not need to work with functors directly in order to use the operators.

Basic Operators

The operators have been included in each Ndarray and Matrix module. The following table summarises the operators currently implemented in Owl.

Operator	Example	Operation	Dense/Sparse	Ndarray/Matrix
+	x + y	element-wise add	both	both
-	x - y	element-wise sub	both	both
*	x * y	element-wise mul	both	both
/	x / y	element-wise div	both	both
+$	x +$ a	add scalar	both	both
-$	x -$ a	sub scalar	both	both
*$	x *$ a	mul scalar	both	both
/$	x /$ a	div scalar	both	both
$+	a $+ x	scalar add	both	both
$-	a $- x	scalar sub	both	both
$*	a $* x	scalar mul	both	both
$/	a $/ x	scalar div	both	both
=	x = y	comparison	both	both
!=	x != y	comparison	both	both
<>	x <> y	same as !=	both	both
>	x > y	comparison	both	both
<	x < y	comparison	both	both
>=	x >= y	comparison	both	both
<=	x <= y	comparison	both	both
=.	x =. y	comparison	Dense	both
!=.	x !=. y	comparison	Dense	both
<>.	x <>. y	same as !=.	Dense	both
>.	x >. y	comparison	Dense	both
<.	x <. y	comparison	Dense	both
>=.	x >=. y	comparison	Dense	both
<=.	x <=. y	comparison	Dense	both
**	x ** y	power function	Dense	both
*@	x *@ y	matrix multiply	both	Matrix

There are a list of things worth your attention as below.

• * is for element-wise multiplication; *@ is for matrix multiplication. You can easily understand the reason if you read the source code of Algodiff module. Using * for element-wise multiplication (for matrices) leads to the consistent implementation of algorithmic differentiation.

• +$ has its corresponding operator $+ if we flip the order of parameters. However, be very careful about the operator precedence since OCaml determines the precedence based on the first character of an infix. +$ preserves the precedence whereas $+ does not. Therefore, I do not recommend using $+. If you do use it, please use parentheses to explicitly specify the precedence. The same argument also applies to -$, *$, and /$.

• For comparison operators, e.g. both = and =. compare all the elements in two variables x and y. The difference is that = returns a boolean value whereas =. returns a matrix or ndarray of the same shape and same type as x and y. In the returned result, the value in a given position is 1 if the values of the corresponding position in x and y satisfy the predicate, otherwise it is 0.

Operators are easy to use, here are some examples.

let x = Mat.uniform 5 5;;
let y = Mat.uniform 5 5;;

Mat.(x + y);;
Mat.(x * y);;
Mat.(x ** y);;
Mat.(x *@ y);;

...

(* please compare the returns of the following two examples *)
Mat.(x > y);;
Mat.(x >. y);;

Extension Module