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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.

SEE ALSO
	i.pca, m.eigensystem (Addon), r.mapcalc, r.rescale

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

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

       Main index | Raster index | Topics index	| Keywords index  |  Graphical
       index | Full index

       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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