Green's function normalisation constant in wrong place

[ehkropf]

It appears greensC0 (and greensCj) are having the normalisation constant applied only when evaluating the full function, but not the "hat" function. The normalisation should be applied to the hat function always, since this is the BVP solution.

TL;DR: The "hat" function gives the wrong values.

[ehkropf]

This fix breaks skprime as evidenced by running skptests primeBasic/*. It appears this is on points outside unit domain.

Note the commit where the fix lives is not on the master branch. See branch green_normalise.

[ehkropf]

Outer point problem confirmed:

dv = [
  -0.2517+0.3129i
   0.2307-0.4667i];
qv = [
  0.2377
  0.1557];
alpha = -0.31837-0.44082i;

w = skprime(alpha, dv, qv);

% Check against product formula.
L = 6;
wp = skprod(dv, qv, L);
wphat = @(z) wp(z, alpha)./(z - alpha);

zp = 0.4793+0.4828i;
zp = [zp; 1/conj(zp)];

err = wphat(zp) - w.hat(zp);

where

err =

      -1.86885043329532e-06 -  2.52521160475083e-08i
         0.0679702753652227 -      0.47787048749888i

The BVP for 1/conj(alpha) is thus not being formed correctly.

[ehkropf]

Note replacing the parameter in the above example with 1/conj(-0.31837-0.44082i) reinforces this.

[ehkropf]

Fixed with merge commit 903bd65.