var

---
description: Guidelines for var
globs: **/*
---


 Usage

Computes the variance of an array along a given dimension.
The general syntax for its use is

    y = var(x,d)

where x is an n-dimensions array of numerical type. The
output is of the same numerical type as the input. The
argument d is optional, and denotes the dimension along
which to take the variance. The output y is the same size as
x, except that it is singular along the mean direction. So,
for example, if x is a 3 x 3 x 4 array, and we compute the
mean along dimension d=2, then the output is of size 3 x 1 x
4.


 Internals

The output is computed via
 \[ y(m_1,\ldots,m_{d-1},1,m_{d+1},\ldots,m_{p}) = \frac{1}
{N-1} \sum_{k=1}^{N} \left(x(m_1,\ldots,m_{d-1},k,m_
{d+1},\ldots,m_{p}) - \bar{x}\right)^2, \]
where
 \[ \bar{x} = \frac{1}{N} \sum_{k=1}^{N} x(m_1,\ldots,m_{d-
1},k,m_{d+1},\ldots,m_{p}) \]
If d is omitted, then the mean is taken along the first non-
singleton dimension of x.


 Example

The following piece of code demonstrates various uses of the
var function

  --> A = [5,1,3;3,2,1;0,3,1]

  A =
   5 1 3
   3 2 1
   0 3 1

We start by calling var without a dimension argument, in
which case it defaults to the first nonsingular dimension
(in this case, along the columns or d = 1).

  --> var(A)

  ans =
      6.3333    1.0000    1.3333

Next, we take the variance along the rows.

  --> var(A,2)

  ans =
      4.0000
      1.0000
      2.3333


* FreeMat_Documentation
* Elementary_Functions
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