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### CORRELATE

CORRELATE

The CORRELATE function computes the linear Pearson correlation coefficient of two vectors or the correlation matrix of an m x n array. Alternatively, this function computes the covariance of two vectors or the covariance matrix of an m x n array.

This routine is written in the IDL language. Its source code can be found in the file correlate.pro in the lib subdirectory of the IDL distribution.

## Examples

Define the data vectors.

`X = [65,63,67,64,68,62,70,66,68,67,69,71]Y = [68,66,68,65,69,66,68,65,71,67,68,70]`

Compute the linear Pearson correlation coefficient of x and y. The result should be 0.702652:

`PRINT, CORRELATE(X, Y)`

IDL prints:

`0.702652`

Compute the covariance of x and y. The result should be 3.66667.

`PRINT, CORRELATE(X, Y, /COVARIANCE)`

IDL prints:

`3.66667`

Define an array with x and y as its columns.

`A = TRANSPOSE([[X],[Y]])`

Compute the correlation matrix.

`PRINT, CORRELATE(A)`

IDL prints:

`  1.00000    0.702652`
`  0.702652   1.00000`

## Syntax

Result = CORRELATE( X [, Y] [, /COVARIANCE] [, /DOUBLE] )

## Return Value

If vectors of unequal lengths are specified, the longer vector is truncated to the length of the shorter vector and a single correlation coefficient is returned. If an m x n array is specified, the result will be an m x m array of linear Pearson correlation coefficients, with the element i,j corresponding to correlation of the ith and jth columns of the input array.

## Arguments

### X

A vector or an m x n array. X can be integer, single-, or double-precision floating-point.

### Y

An integer, single-, or double-precision floating-point vector. If X is an m x n array, Y should not be supplied.

## Keywords

### COVARIANCE

Set this keyword to compute the sample covariance rather than the correlation coefficient.

### DOUBLE

Set this keyword to force the computation to be done in double-precision arithmetic.

## Version History

 Pre 4.0 Introduced

## Resources and References

J. Neter, W. Wasserman, G.A. Whitmore, Applied Statistics (Third Edition), Allyn and Bacon (ISBN 0-205-10328-6).