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>> matern_test ( )
04-Nov-2012 10:49:34

matern_TEST:
  Demonstrate Mercer's theorem and the KL expansion
  for the matern kernel.
  Using interval [0,1]
  Requested 20 eigenmodes, computed 20

   I       Lambda(I)

   1    0.823995
   2    0.150008
   3   0.0213663
   4  0.00354483
   5  0.000760505
   6  0.000207016
   7  6.83611e-05
   8  2.62758e-05
   9  1.13807e-05
  10  5.4212e-06
  11  2.7889e-06
  12  1.52834e-06
  13  8.82843e-07
  14  5.33173e-07
  15  3.34472e-07
  16  2.16821e-07
  17  1.44631e-07
  18  9.89302e-08
  19  6.91918e-08
  20  4.93611e-08

  Frobenius norm of I - Psi' * Psi = 1.25724e-08

  Truncated estimate of K(s,s) = 1 for S in the interval.

        S        K(s,s) estimate

           0        0.999999
        0.05               1
         0.1               1
        0.15               1
         0.2               1
        0.25               1
         0.3               1
        0.35               1
         0.4               1
        0.45               1
         0.5               1
        0.55               1
         0.6               1
        0.65               1
         0.7               1
        0.75               1
         0.8               1
        0.85               1
         0.9               1
        0.95               1
           1        0.999999

  Index    Cumulative Eigenvalue sum

      1    0.823995
      2    0.974003
      3    0.995369
      4    0.998914
      5    0.999675
      6    0.999882
      7     0.99995
      8    0.999976
      9    0.999988
     10    0.999993
     11    0.999996
     12    0.999998
     13    0.999998
     14    0.999999
     15    0.999999
     16    0.999999
     17           1
     18           1
     19           1
     20           1

MATERN_TEST:
  Normal end of execution.

04-Nov-2012 10:49:43
>>