Symmetrize STRIDE Δ matrices

[d-burg]

The procedure outlined in sym.f follows the procedure written by Fitzpatrick through equation (16) (see: Benchmark.pdf). On this first pass and as far as I can tell, I've implemented all GPEC equilibrium quantities, integrals, and matrix multiplies correctly – however, the resulting matrices do not yet follow the desired symmetry properties.

One question for now: does this look like I'm calculating the J(psi_N) contour integral correctly? I'm also not totally sure about the need for jac in this case.

GPEC/stride/sym.f

Lines 148 to 165 in 4568a5c

	! Calculate J(psi_N) contour integral
	dtheta = twopi / real(mthsurf)
	DO itheta=0,mthsurf
	CALL bicube_eval(rzphi,psilim,theta(itheta),1)
	rfac=SQRT(rzphi%f(1))
	angle=twopi*(theta(itheta)+rzphi%f(2))
	r(itheta)=ro+rfac*COS(angle)
	z(itheta)=zo+rfac*SIN(angle)
	jac=rzphi%f(4)
	w(1,1)=(1+rzphi%fy(2))*twopi**2*rfac*r(itheta)/jac
	w(1,2)=-rzphi%fy(1)*pi*r(itheta)/(rfac*jac)
	delpsi=SQRT(w(1,1)**2+w(1,2)**2)
	J(ising)=J(ising)+
	$ (1.0/(delpsi**2))*(dtheta/twopi)!/jac !DB !!
	ENDDO

And in the meantime, I'll continue checking through the rest of the algebra (f_S, f_L, etc) for any issues.

[logan-nc]

Your J does indeed look to be the theta integral of 1/(delpsi)^2, which is what Richard defines it as here,

What do you think @parkjk ?

[logan-nc]

Any progress here @d-burg?

[d-burg]

Any progress here @d-burg?

I think I have a shot if I can set up the psi_tor spline correctly! I'll return to it this week @logan-nc

[logan-nc]

Status @d-burg?

[logan-nc]

@d-burg this seems to have gone stale. Let's get it merged or closed as part of your current PR push

[d-burg]

@logan-nc should we keep this on the backburner? With my latest changes to this branch (and without TJ's Fitzpatrick-specific flux coordinate "r") I still haven't been able to get the outputs looking correct. However, given how well the STRIDE and TJ Δ' values align, and how close the growth rates are on circular equilibria, I'm not sure if we need this symmetrization? This might be a good question for a future meeting with Dylan or Richard, if we can catch him at MHDW.

[logan-nc]

Sounds good @d-burg. change the pr status from "open" to "draft" please. if/when you come back to it you can change it back