## DOTTIMES Element-wise Multiplication Operator

Section: Mathematical Operators

### Usage

Multiplies two numerical arrays (elementwise). 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 product of `a` and `b`. 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 product of the scalar with each element of the other argument. The rules for manipulating types has changed in FreeMat 4.0. See `typerules` for more details.

### Function Internals

There are three formulae for the dot-times 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 dottimes operator. First, a straight-forward usage of the `.*` operator. The first example is straightforward:

    --> 3 .* 8

    ans =
     24

Next, we multiply a scalar by a vector of values:

    --> 3.1 .* [2,4,5,6,7]

    ans =
        6.2000   12.4000   15.5000   18.6000   21.7000

With complex values

    --> a = 3 + 4*i

    a =
       3.0000 +  4.0000i

    --> b = a .* 2

    b =
       6.0000 +  8.0000i

Finally, 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  6
     18 28