sll_local_solutions Subroutine

public subroutine sll_local_solutions(vll, tau, drpan2, csrc1, slc1sum, mihvy, mihvz, mijvy, mijvz, yif, zif, ncheb, ipan, lmsize, lmsize2, nrmax, nvec, jlk_index, hlk, jlk, hlk2, jlk2, gmatprefactor, cmodesll, lbessel, use_sratrick1)

Calculation of the local irregular solutions

1. Prepare VJLR, VNL, VHLR, which appear in the integrands TAU(K,IPAN) is used instead of TAU(K,IPAN)**2, which directly gives RLL(r) and SLL(r) multiplied with r. TAU is the radial mesh.
2. Prepare the source terms YR, ZR, YI, ZI because of the conventions used by Gonzalez et al, Journal of Computational Physics 134, 134-149 (1997) a factor $\sqrt(E)$ is included in the source terms this factor is removed by the definition of ZSLC1SUM given below $$\begin{equation} vjlr = \kappa J V = \kappa r j V \end{equation}$$ $$\begin{equation} vhlr = \kappa H V = \kappa r h V \end{equation}$$ i.e. prepare terms $\kappa JDV$, $\kappa HDV$ appearing in 5.11, 5.12.

Then determine the local solutions solve the equations $$\begin{equation} SLV \times YRLL=S \end{equation}$$ and $$\begin{equation} SLV \times ZRLL=C \end{equation}$$ and $$\begin{equation} SRV \times YILL=C \end{equation}$$ and $$\begin{equation} SRV \times ZILL=S \end{equation}$$ i.e., solve system $A U=J$, see eq. 5.68.

Arguments

Type	Intent	Optional	Attributes		Name
complex(kind=dp)				::	vll(lmsize*nvec,lmsize*nvec,nrmax)
real(kind=dp)				::	tau(0:ncheb)
real(kind=dp)				::	drpan2
real(kind=dp)				::	csrc1(0:ncheb,0:ncheb)
real(kind=dp)				::	slc1sum(0:ncheb)
complex(kind=dp)				::	mihvy(lmsize,lmsize)
complex(kind=dp)				::	mihvz(lmsize,lmsize)
complex(kind=dp)				::	mijvy(lmsize,lmsize)
complex(kind=dp)				::	mijvz(lmsize,lmsize)
complex(kind=dp)				::	yif(lmsize2,lmsize,0:ncheb)
complex(kind=dp)				::	zif(lmsize2,lmsize,0:ncheb)
integer				::	ncheb
integer				::	ipan
integer				::	lmsize
integer				::	lmsize2
integer				::	nrmax
integer				::	nvec
integer				::	jlk_index(2*lmsize)
complex(kind=dp)				::	hlk(lbessel,nrmax)
complex(kind=dp)				::	jlk(lbessel,nrmax)
complex(kind=dp)				::	hlk2(lbessel,nrmax)
complex(kind=dp)				::	jlk2(lbessel,nrmax)
complex(kind=dp)				::	gmatprefactor
character(len=1)				::	cmodesll
integer				::	lbessel
integer				::	use_sratrick1