>> besselj_test

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

   I       Lambda(I)

   1     3.17066
   2     2.88271
   3     2.07275
   4     1.56348
   5    0.289208
   6   0.0202783
   7  0.000885653
   8  2.81715e-05
   9  6.86275e-07
  10  1.3217e-08

  Frobenius norm of I - Psi' * Psi = 1.20173e-10

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

        S        K(s,s) estimate

           0               1
         0.5               1
           1               1
         1.5               1
           2               1
         2.5               1
           3               1
         3.5               1
           4               1
         4.5               1
           5               1
         5.5               1
           6               1
         6.5               1
           7               1
         7.5               1
           8               1
         8.5               1
           9               1
         9.5               1
          10               1

  Index    Cumulative Eigenvalue sum

      1    0.317066
      2    0.605336
      3    0.812612
      4     0.96896
      5    0.997881
      6    0.999909
      7    0.999997
      8           1
      9           1
     10           1

  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

           1           1
         0.5    0.999978
        0.25    0.805957
       0.125    0.546661
      0.0625    0.379695
     0.03125    0.266238
    0.015625    0.187491
   0.0078125    0.132309
??? Error using ==> linop.eigs>value at 237
No convergence with 1025 points. Check sigma, or ask for fewer modes.

Error in ==> linop.eigs>@(x)value(x) at 155
    chebfun( @(x) value(x), dom, settings);

Error in ==> getfun>@(x)op(x) at 31
g = fun(@(x) op(x), interval, pref, scl);

Error in ==> growfun at 250
                g = set(g,'vals',op(xvals));

Error in ==> fun.fun at 228
    [g,ish] = growfun(op,g,pref);

Error in ==> getfun at 31
g = fun(@(x) op(x), interval, pref, scl);

Error in ==> auto at 32
     [funs,hpy,scl] = getfun(op,ends,pref,scl);

Error in ==> ctor_adapt at 128
            [fs,es,scl] = auto(op,es,scl,pref);

Error in ==> chebfun.chebfun at 243
    f = ctor_adapt(f,argin{:},pref);        % adaptive call

Error in ==> linop.eigs at 155
    chebfun( @(x) value(x), dom, settings);

Error in ==> besselj_test at 215
    lambda_vec = eigs ( F, eigen_use, 'lm' );
 
>>