DESCRIPTION
r.covar outputs a covariance/correlation matrix for user-specified
raster map layer(s).  The output can be printed, or saved by redirecting
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 matrix would result in
N real eigen values and N eigen vectors (each composed 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
     1.000000  0.914922  0.889581
     0.914922  1.000000  0.939452
     0.889581  0.939452  1.000000
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>
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"
SEE ALSO
i.pca,
m.eigensystem (Addon),
r.mapcalc,
r.rescale
AUTHOR
Michael Shapiro, U.S. Army Construction Engineering Research Laboratory