1r.covar(1)                    Grass User's Manual                   r.covar(1)
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NAME

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

10       raster, statistics
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SYNOPSIS

13       r.covar
14       r.covar --help
15       r.covar  [-r]  map=name[,name,...]   [--help]   [--verbose]   [--quiet]
16       [--ui]
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18   Flags:
19       -r
20           Print correlation matrix
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22       --help
23           Print usage summary
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25       --verbose
26           Verbose module output
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28       --quiet
29           Quiet module output
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31       --ui
32           Force launching GUI dialog
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34   Parameters:
35       map=name[,name,...] [required]
36           Name of raster map(s)
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DESCRIPTION

39       r.covar  outputs  a  covariance/correlation  matrix  for user-specified
40       raster map layer(s).  The output can be printed, or saved by  redirect‐
41       ing output into a file.
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43       The output is an N x N symmetric covariance (correlation) matrix, where
44       N is the number of raster map layers specified on the command line.
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NOTES

47       This module can be used as the first step  of  a  principle  components
48       transformation.   The  covariance  matrix  would be input into a system
49       which determines eigen values and  eigen  vectors.  An  NxN  covariance
50       matrix  would  result  in N real eigen values and N eigen vectors (each
51       composed of N real numbers).
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53       The module m.eigensystem in GRASS GIS Addons can be compiled  and  used
54       to generate the eigen values and vectors.
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EXAMPLE

57       For example,
58       g.region raster=layer.1 -p
59       r.covar -r map=layer.1,layer.2,layer.3
60       would produce a 3x3 matrix (values are example only):
61            1.000000  0.914922  0.889581
62            0.914922  1.000000  0.939452
63            0.889581  0.939452  1.000000
64       In  the above example, the eigen values and corresponding eigen vectors
65       for the covariance matrix are:
66       component   eigen value               eigen vector
67           1       1159.745202   <0.691002  0.720528  0.480511>
68           2          5.970541   <0.711939 -0.635820 -0.070394>
69           3        146.503197   <0.226584  0.347470 -0.846873>
70       The component corresponding to each vector can be produced using r.map‐
71       calc as follows:
72       r.mapcalc "pc.1 = 0.691002*layer.1 + 0.720528*layer.2 + 0.480511*layer.3"
73       r.mapcalc "pc.2 = 0.711939*layer.1 - 0.635820*layer.2 - 0.070394*layer.3"
74       r.mapcalc "pc.3 = 0.226584*layer.1 + 0.347470*layer.2 - 0.846873*layer.3"
75       Note  that  based  on the relative sizes of the eigen values, pc.1 will
76       contain about 88% of the variance in the data set,  pc.2  will  contain
77       about  1%  of the variance in the data set, and pc.3 will contain about
78       11% of the variance in the data set.  Also, note that the range of val‐
79       ues  produced in pc.1, pc.2, and pc.3 will not (in general) be the same
80       as those for layer.1, layer.2, and layer.3.  It  may  be  necessary  to
81       rescale  pc.1,  pc.2  and pc.3 to the desired range (e.g. 0-255).  This
82       can be done with r.rescale.
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SEE ALSO

85        i.pca, m.eigensystem (Addon), r.mapcalc, r.rescale
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AUTHOR

88       Michael Shapiro, U.S. Army Construction Engineering Research Laboratory
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SOURCE CODE

91       Available at: r.covar source code (history)
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93       Main index | Raster index | Topics index | Keywords index  |  Graphical
94       index | Full index
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96       © 2003-2019 GRASS Development Team, GRASS GIS 7.8.2 Reference Manual
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100GRASS 7.8.2                                                         r.covar(1)
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