Constructing the Gamma function about chebfun

[aaustin141]

From some of the crazy values for the exponents that we see in the output above, it looks to me like this is another symptom of the same, more general problems we've been having with the singularity detector. If we allow only poles instead of arbitrary singularities or specify the exponents manually everything works just fine:

>> G = chebfun(@gamma, [-4 4], 'blowup', 1, 'splitting', 'on')
G = 
   chebfun column (5 smooth pieces)
       interval       length   endpoint values   endpoint exponents
[      -4,      -3]       37       Inf      Inf         [-1      -1]  
[      -3,      -2]       21      -Inf     -Inf         [-1      -1]  
[      -2,      -1]       20       Inf      Inf         [-1      -1]  
[      -1,2.2e-308]       19      -Inf     -Inf         [-1      -1]  
[2.2e-308,       4]       32       Inf        6         [-1      0] 
Epslevel = 2.350567e-14.  Vscale = 1.200000e+01.  Total length = 129.

>> G = chebfun(@gamma, [-4 -3 -2 -1 0 4], 'exps', [-1 -1 -1 -1 -1 -1 -1 -1 -1 0])
G = 
   chebfun column (5 smooth pieces)
       interval       length   endpoint values   endpoint exponents
[      -4,      -3]       30       Inf      Inf         [-1      -1]  
[      -3,      -2]       29      -Inf     -Inf         [-1      -1]  
[      -2,      -1]       24       Inf      Inf         [-1      -1]  
[      -1,       0]       27      -Inf     -Inf         [-1      -1]  
[       0,       4]       35       Inf        6         [-1      0]  
Epslevel = 8.881784e-16.  Vscale = 1.200000e+01.  Total length = 145.

[nickhale]

Does this suggest we should make "'blowup', 1" be the default setting for 'on'. I believe this was the case for V4.

[aaustin141]

Even if it weren't the case for v4, I think I'd suggest that we do that anyway. Sadly, detection of fractional-order singularities is just too fragile right now to be trusted...

[kuanxu]

I think the problem has been fixed as 'blowup' 1 has been the default for 'on' (introduced by the merge of feature-singfun-misc). As AA tried, gamma is now OK.

>> gam = chebfun('gamma(x)',[-4 4],'blowup','on','splitting','on')
gam = 
   chebfun column (5 smooth pieces)
       interval       length   endpoint values   endpoint exponents
[      -4,      -3]       37       Inf      Inf         [-1      -1]  
[      -3,      -2]       21      -Inf     -Inf         [-1      -1]  
[      -2,      -1]       20       Inf      Inf         [-1      -1]  
[      -1,2.2e-308]       19      -Inf     -Inf         [-1      -1]  
[2.2e-308,       4]       32       Inf        6         [-1      0]  
Epslevel = 2.350567e-14.  Vscale = 1.200000e+01.  Total length = 129.