Generating a Numeric Sequence :: Data Structures (Programming)

Programming

Generating a Numeric Sequence

Because numeric sequences can often be useful in constructing and indexing into matrices and arrays, MATLAB provides a special operator to assist in creating them.

This section covers

The Colon Operator

The colon operator (first:last) generates a 1-by-n matrix (or vector) of sequential numbers from the first value to the last. The default sequence is made up of incremental values, each 1 greater than the previous one:

A = 10:15
A =
    10    11    12    13    14    15

The numeric sequence does not have to be made up of positive integers. It can include negative numbers and fractional numbers as well:

A = -2.5:2.5
A =
   -2.5000   -1.5000   -0.5000    0.5000    1.5000    2.5000

By default, MATLAB always increments by exactly 1 when creating the sequence, even if the ending value is not an integral distance from the start:

A = 1:6.3
A =
     1     2     3     4     5     6

Also, the default series generated by the colon operator always increments rather than decrementing. The operation shown in this example attempts to increment from 9 to 1 and thus MATLAB returns an empty matrix:

```
A = 9:1
A =
   Empty matrix: 1-by-0
```

The next section explains how to generate a nondefault numeric series.

Using the Colon Operator with a Step Value

To generate a series that does not use the default of incrementing by 1, specify an additional value with the colon operator (first:step:last). In between the starting and ending value is a step value that tells MATLAB how much to increment (or decrement, if step is negative) between each number it generates.

To generate a series of numbers from 10 to 50, incrementing by 5, use

A = 10:5:50
A =
    10    15    20    25    30    35    40    45    50

You can increment by noninteger values. This example increments by 0.2:

A = 3:0.2:3.8
A =
    3.0000    3.2000    3.4000    3.6000    3.8000

To create a sequence with a decrementing interval, specify a negative step value:

A = 9:-1:1
A =
    9    8    7    6    5    4    3    2    1

Matrix Concatenation Functions Combining Unlike Data Types