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,...] [required]
- Name of raster map(s)
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.
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.
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.mapcalc
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 values 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.
i.pca,
m.eigensystem (Addon),
r.mapcalc,
r.rescale
Michael Shapiro, U.S. Army Construction Engineering Research Laboratory
SOURCE CODE
Available at:
r.covar source code
(history)
Latest change: Thursday Jan 26 14:10:26 2023 in commit: cdd84c130cea04b204479e2efdc75c742efc4843
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© 2003-2024
GRASS Development Team,
GRASS GIS 8.5.0dev Reference Manual