# FreeBSD Manual Pages

```r.covar(1)		    GRASS GIS User's Manual		    r.covar(1)

NAME
r.covar	 -  Outputs a covariance/correlation matrix for	user-specified
raster map layer(s).

KEYWORDS
raster, statistics

SYNOPSIS
r.covar
r.covar --help
r.covar	[-r]  map=name[,name,...]   [--help]   [--verbose]   [--quiet]
[--ui]

Flags:
-r
Print correlation matrix

--help
Print usage summary

--verbose
Verbose module output

--quiet
Quiet module	output

--ui
Force launching GUI dialog

Parameters:
map=name[,name,...]A [required]
Name	of raster map(s)

DESCRIPTION
r.covar	outputs	 a  covariance/correlation  matrix  for	user-specified
raster map layer(s).  The output	can be printed,	or saved by  redirect-
ing output into a file.

The output is an	N x N symmetric	covariance (correlation) matrix, where
N is the	number of raster map layers specified on the command line.

NOTES
This module can be used as the first step  of  a	 principle  components
transformation.	 The  covariance  matrix  would	be input into a	system
which determines	eigen values and eigen vectors.	An NxN covariance  ma-
trix would result in N real eigen values	and N eigen vectors (each com-
posed of	N real numbers).

The module m.eigensystem	in GRASS GIS Addons can	be compiled  and  used
to generate the eigen values and	vectors.

EXAMPLE
For example,
g.region	raster=layer.1 -p
r.covar -r map=layer.1,layer.2,layer.3
would produce a 3x3 matrix (values are example only):
1.000000  0.914922	0.889581
0.914922  1.000000	0.939452
0.889581  0.939452	1.000000
In  the above example, the eigen	values and corresponding eigen vectors
for the covariance matrix are:
component   eigen value		     eigen vector
1	   1159.745202	 <0.691002  0.720528  0.480511>
2	      5.970541	 <0.711939 -0.635820 -0.070394>
3	    146.503197	 <0.226584  0.347470 -0.846873>
The component corresponding to each vector can be produced using	r.map-
calc as follows:
r.mapcalc "pc.1 = 0.691002*layer.1 + 0.720528*layer.2 + 0.480511*layer.3"
r.mapcalc "pc.2 = 0.711939*layer.1 - 0.635820*layer.2 - 0.070394*layer.3"
r.mapcalc "pc.3 = 0.226584*layer.1 + 0.347470*layer.2 - 0.846873*layer.3"
Note  that  based  on the relative sizes	of the eigen values, pc.1 will
contain about 88% of the	variance in the	data set,  pc.2	 will  contain
about  1%  of the variance in the data set, and pc.3 will contain about
11% of the variance in the data set.  Also, note	that the range of val-
ues  produced in	pc.1, pc.2, and	pc.3 will not (in general) be the same
as those	for layer.1, layer.2, and layer.3.  It	may  be	 necessary  to
rescale	pc.1,  pc.2  and pc.3 to the desired range (e.g. 0-255).  This
can be done with	r.rescale.

AUTHOR
Michael Shapiro,	U.S. Army Construction Engineering Research Laboratory

SOURCE CODE
Available at: r.covar source code (history)

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A(C) 2003-2020 GRASS Development	Team, GRASS GIS	7.8.4 Reference	Manual

GRASS 7.8.4							    r.covar(1)
```

NAME | KEYWORDS | SYNOPSIS | DESCRIPTION | NOTES | EXAMPLE | SEE ALSO | AUTHOR | SOURCE CODE

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