>> brownian_test
26-Feb-2012 15:38:27

BROWNIAN_TEST:
  Demonstrate Mercer's theorem and the KL expansion
  for the brownian kernel.
  Using interval [0.1,5]
  Requested 20 eigenmodes, computed 20

   I       Lambda(I)

   1     3.45483
   2     0.64943
   3    0.258758
   4    0.135725
   5   0.0824771
   6   0.0550316
   7   0.0391826
   8   0.0292598
   9   0.0226592
  10   0.0180569
  11    0.014725
  12   0.0122378
  13   0.0103334
  14  0.00884361
  15  0.00765669
  16  0.00669603
  17  0.00590774
  18  0.00525304
  19  0.00470343
  20  0.00423764

  Frobenius norm of I - Psi' * Psi = 2.8599e-10

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

        S        K(s,s) estimate

         0.1        0.872572
       0.345        0.965866
        0.59        0.975246
       0.835        0.979663
        1.08        0.982363
       1.325        0.983638
        1.57        0.984789
       1.815        0.985879
        2.06        0.986908
       2.305        0.987726
        2.55        0.988027
       2.795        0.988036
        3.04        0.988722
       3.285        0.989658
        3.53        0.989281
       3.775        0.989595
        4.02        0.990768
       4.265        0.989518
        4.51         0.99123
       4.755        0.990975
           5        0.981916

  Index    Cumulative Eigenvalue sum

      1    0.705068
      2    0.837604
      3    0.890412
      4    0.918111
      5    0.934943
      6    0.946174
      7     0.95417
      8    0.960142
      9    0.964766
     10    0.968451
     11    0.971456
     12    0.973954
     13    0.976063
     14    0.977868
     15     0.97943
     16    0.980797
     17    0.982002
     18    0.983074
     19    0.984034
     20    0.984899

BROWNIAN_TEST:
  Normal end of execution.

26-Feb-2012 15:38:36
>>