Covariances/Erdas/Grass

GRASS GRASS user
1

From prasad@ghat.inhs.uiuc.edu Wed Apr 28 09:05:57 1993
Date: Wed, 28 Apr 1993 11:00:12 -0500
From: Anantha Prasad <prasad@ghat.inhs.uiuc.edu>
To: lobo@Jasper.Stanford.EDU
Subject: Covariances/Erdas/Grass
Content-Length: 1725

Hi Agus:
Here are the results from Erdas7.5 and grass4.1beta+Splus for your test data:
As you can observe, the covariance matrix reported by Erdas and Grass differ - since this is an extremely small database, the resulting eigenvalues and eigenvectors do not differ much....but in case of large databases they do...resulting in large differences...I will do the covariance matrix by hand and determine which is right...Thanks much for the help. Please keep me informed. Since you must have already done this to test the output from grass, I assume Erdas is not reporting it correctly. Am I right? Let me know. Thanks. Anantha Prasad (prasad@ghat.inhs.uiuc.edu)

NOTE: Erdas (Version 7.5) Covariance Matrix,Eigenvalues & Eigenvectors:
Covariance Matrix:
          1 2 3
   1 338.24 4.59 -32.00
   2 4.59 2016.23 -308.88
   3 -32.00 -308.88 2227.68

      Eigenvalues: Var. %: Total %: Angle: Scale:
   1 2448.82 53.44 53.44 89.59 1
   2 1795.64 39.19 92.63 20.97 1
   3 337.70 7.37 100.00 69.04 1
Eigenvectors:
          1 2 3
       -0.01 -0.01 1.00
       -0.58 0.81 0.00
        0.81 0.58 0.02
****************************************************************
NOTE: Grass4.1beta Covariance Matrix:

352.333333 4.783333 -33.333333
4.783333 2100.243333 -321.750000
-33.333333 -321.750000 2320.500000

NOTE: Splus eigenvalues and eigenvectors:
$eigenvalues:
[1] 2550.8538 1870.4541 351.7687

$eigenvectors:
           [,1] [,2] [,3]
[1,] -0.0136013 0.01019403 0.9998555328
[2,] -0.5811429 -0.81380140 0.0003916771
[3,] 0.8136878 -0.58105366 0.0169929433

ERDAS result is wrong, not by too much but wrong.
r.covar is correct.
Agus