## DOTLEFTDIVIDE Element-wise Left-Division Operator

Section: Mathematical Operators

### Usage

Divides two numerical arrays (elementwise) - gets its name from the fact that the divisor is on the left. There are two forms for its use, both with the same general syntax:

      y = a .\ b

where `a` and `b` are `n`-dimensional arrays of numerical type. In the first case, the two arguments are the same size, in which case, the output `y` is the same size as the inputs, and is the element-wise division of `b` by `a`. In the second case, either `a` or `b` is a scalar, in which case `y` is the same size as the larger argument, and is the division of the scalar with each element of the other argument. The type of `y` depends on the types of `a` and `b` using type promotion rules, with one important exception: unlike `C`, integer types are promoted to `double` prior to division.

### Function Internals

There are three formulae for the dot-left-divide operator, depending on the sizes of the three arguments. In the most general case, in which the two arguments are the same size, the output is computed via:

If `a` is a scalar, then the output is computed via

On the other hand, if `b` is a scalar, then the output is computed via

### Examples

Here are some examples of using the dot-left-divide operator. First, a straight-forward usage of the `.\` operator. The first example is straightforward:

    --> 3 .\ 8

    ans =

        2.6667

Note that this is not the same as evaluating `8/3` in `C` - there, the output would be `2`, the result of the integer division. We can also divide complex arguments:

    --> a = 3 + 4*i

    a =

        3.0000 +  4.0000i

    --> b = 5 + 8*i

    b =

        5.0000 +  8.0000i

    --> c = b .\ a

    c =

        0.5281 -  0.0449i

If a `complex` value is divided by a `double`, the result is promoted to `dcomplex`.

    --> b = a .\ 2.0

    b =

        0.2400 -  0.3200i

We can also demonstrate the three forms of the dot-left-divide operator. First the element-wise version:

    --> a = [1,2;3,4]

    a =

     1 2
     3 4

    --> b = [2,3;6,7]

    b =

     2 3
     6 7

    --> c = a .\ b

    c =

        2.0000    1.5000
        2.0000    1.7500

Then the scalar versions

    --> c = a .\ 3

    c =

        3.0000    1.5000
        1.0000    0.7500

    --> c = 3 .\ a

    c =

        0.3333    0.6667
        1.0000    1.3333