Note: This addon document is for an older version of GRASS GIS that will be discontinued soon. You should upgrade your GRASS GIS installation, and read the current addon manual page.

3 462.876649 480.411218 281.758307 480.411218 513.015646 278.914813 281.758307 278.914813 336.326645

The output will be K groups of lines; each group will have the format:

E real part imaginary part relative importance V real part imaginary part ... K lines ... N real part imaginary part ... K lines ... W real part imaginary part ... K lines ...The

For the example input matrix above, the output would be:

E 1159.7452017844 0.0000000000 88.38 V 0.6910021591 0.0000000000 V 0.7205280412 0.0000000000 V 0.4805108400 0.0000000000 N 0.6236808478 0.0000000000 N 0.6503301526 0.0000000000 N 0.4336967751 0.0000000000 W 21.2394712045 0.0000000000 W 22.1470141296 0.0000000000 W 14.7695575384 0.0000000000 E 5.9705414972 0.0000000000 0.45 V 0.7119385973 0.0000000000 V -0.6358200627 0.0000000000 V -0.0703936743 0.0000000000 N 0.7438340890 0.0000000000 N -0.6643053754 0.0000000000 N -0.0735473745 0.0000000000 W 1.8175356507 0.0000000000 W -1.6232096923 0.0000000000 W -0.1797107407 0.0000000000 E 146.5031967184 0.0000000000 11.16 V 0.2265837636 0.0000000000 V 0.3474697082 0.0000000000 V -0.8468727535 0.0000000000 N 0.2402770238 0.0000000000 N 0.3684685345 0.0000000000 N -0.8980522763 0.0000000000 W 2.9082771721 0.0000000000 W 4.4598880523 0.0000000000 W -10.8698904856 0.0000000000

In general, the solution to the eigen system results in complex numbers (with both real and imaginary parts). However, in the example above, since the input matrix is symmetric (i.e., inverting the rows and columns gives the same matrix) the eigen system has only real values (i.e., the imaginary part is zero). This fact makes it possible to use eigen vectors to perform principle component transformation of data sets. The covariance or correlation matrix of any data set is symmetric and thus has only real eigen values and vectors.

(echo 3; r.covar map.1,map.2,map.3 | grep -v "N = ") | m.eigensystem

Then, using the W vector, new maps are created:

r.mapcalc "pc.1 = 21.2395*map.1 + 22.1470*map.2 + 14.7696*map.3" r.mapcalc "pc.2 = 2.9083*map.1 + 4.4599*map.2 - 10.8699*map.3" r.mapcalc "pc.3 = 1.8175*map.1 - 1.6232*map.2 - 0.1797*map.3"

The equivalent *i.pca* command is:

i.pca in=spot.ms.1,spot.ms.2,spot.ms.3 out=spot_pca

r.covar

r.mapcalc

r.rescale

The interface was coded by Michael Shapiro, U.S.Army Construction Engineering Research Laboratory

Available at: m.eigensystem source code (history)

Latest change: Mon Jun 28 07:54:09 2021 in commit: 1cfc0af029a35a5d6c7dae5ca7204d0eb85dbc55

Note: This addon document is for an older version of GRASS GIS that will be discontinued soon. You should upgrade your GRASS GIS installation, and read the current addon manual page.

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