>> gaussian_test
26-Feb-2012 15:54:03

GAUSSIAN_TEST:
  Demonstrate Mercer's theorem and the KL expansion
  for the gaussian kernel.
  Using interval [0,10]
  Requested 20 eigenmodes, computed 20

   I       Lambda(I)

   1     1.73552
   2     1.62934
   3      1.4668
   4     1.26646
   5     1.04904
   6    0.833937
   7    0.636511
   8    0.466704
   9    0.328932
  10    0.222995
  11    0.145525
  12   0.0914911
  13     0.05546
  14   0.0324419
  15   0.0183285
  16   0.0100092
  17  0.00528784
  18  0.00270456
  19  0.00134023
  20  0.00064393

  Frobenius norm of I - Psi' * Psi = 7.27536e-14

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

        S        K(s,s) estimate

           0        0.999162
         0.5        0.999987
           1        0.999982
         1.5         0.99998
           2        0.999976
         2.5        0.999969
           3        0.999961
         3.5        0.999952
           4        0.999944
         4.5        0.999939
           5        0.999938
         5.5        0.999939
           6        0.999944
         6.5        0.999952
           7        0.999961
         7.5        0.999969
           8        0.999976
         8.5         0.99998
           9        0.999982
         9.5        0.999987
          10        0.999162

  Index    Cumulative Eigenvalue sum

      1    0.173552
      2    0.336486
      3    0.483165
      4    0.609811
      5    0.714715
      6    0.798109
      7     0.86176
      8     0.90843
      9    0.941323
     10    0.963623
     11    0.978175
     12    0.987324
     13     0.99287
     14    0.996115
     15    0.997948
     16    0.998948
     17    0.999477
     18    0.999748
     19    0.999882
     20    0.999946

  Use a fixed number of eigenfunctions = 10
  but vary the correlation length RHOBAR.
  (We used RHOBAR = 1 above.)

  The sum of the eigenvalues, divided by (B-A),
  discloses the relative amount of the total variation
  that is captured by the truncated expansion.

      RHOBAR      VARSUM

           4           1
           2    0.999817
           1    0.963623
         0.5    0.723813
        0.25    0.419045
       0.125     0.21838
      0.0625    0.110905
     0.03125    0.055694
    0.015625   0.0318157
   0.0078125   0.0159484

GAUSSIAN_TEST:
  Normal end of execution.

26-Feb-2012 15:54:59
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