DOTLEFTDIVIDE Element-wise Left-Division Operator

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