# counts¶

## Purpose¶

Counts the numbers of elements of a vector that fall into specified ranges.

## Format¶

c = counts(x, v)
Parameters: x (Nx1 vector) – the numbers to be counted v (Px1 vector) – breakpoints specifying the ranges within which counts are to be made. The vector v MUST be sorted in ascending order. c (Px1 vector) – the counts of the elements of x that fall into the regions: $\begin{split}x \leq v,\\ v < x \leq v,\\ \vdots\\ v[p-1] < x \leq v[p]\end{split}$

## Examples¶

### Basic example¶

Count the number of elements which are in a specific range.

// Original data
x = { 1.5, 3, 5, 4, 1, 3 };

// Break points
v = { 0, 2, 4 };

// Get counts
c = counts(x, v);

    1.5
3       0       0
x = 5   v = 2   c = 2
4       4       3
1
3


### Count integers¶

Count how many times each integer from 1 to 10 is present in a vector.

x = { 9, 8, 9, 9, 6, 8, 6, 7 };

ints = seqa(1, 1, 10);

c = counts(x, ints);

       1      0
2      0
3      0
4      0
ints = 5  c = 0
6      2
7      1
8      2
9      3
10      0


## Remarks¶

If the maximum value of x is greater than the last element (the maximum value) of v, the sum of the elements of the result, c, will be less than $$N$$, the total number of elements in x.

If

    1
2
3
4      4
x = 5  v = 5
6      8
7
8
9


then

    4
c = 1
3


The first category can be a missing value if you need to count missings directly. Also $$+\infty$$ or $$-\infty$$ are allowed as breakpoints. The missing value must be the first breakpoint if it is included as a breakpoint and infinities must be in the proper location depending on their sign. $$-\infty$$ must be in the $$[2, 1]$$ element of the breakpoint vector if there is a missing value as a category as well, otherwise it has to be in the $$[1, 1]$$ element. If $$+\infty$$ is included, it must be the last element of the breakpoint vector.