Collaboration diagram for Trigonometric factors:

Variables
real, dimension(:,:), allocatable	allglobal::cosi
	some precomputed cosines

real, dimension(:,:), allocatable	allglobal::sini
	some precomputed sines

real, dimension(:), allocatable	allglobal::gteta
	something related to \(\sqrt g\) and \(\theta\) ?

real, dimension(:), allocatable	allglobal::gzeta
	something related to \(\sqrt g\) and \(\zeta\) ?

real, dimension(:), allocatable	allglobal::ajk
	definition of coordinate axis

real, dimension(:,:,:,:), allocatable	allglobal::dradr
	derivatives of coordinate axis

real, dimension(:,:,:,:), allocatable	allglobal::dradz
	derivatives of coordinate axis

real, dimension(:,:,:,:), allocatable	allglobal::dzadr
	derivatives of coordinate axis

real, dimension(:,:,:,:), allocatable	allglobal::dzadz
	derivatives of coordinate axis

real, dimension(:,:,:), allocatable	allglobal::drodr
	derivatives of coordinate axis

real, dimension(:,:,:), allocatable	allglobal::drodz
	derivatives of coordinate axis

real, dimension(:,:,:), allocatable	allglobal::dzodr
	derivatives of coordinate axis

real, dimension(:,:,:), allocatable	allglobal::dzodz
	derivatives of coordinate axis

integer, dimension(:,:), allocatable	allglobal::djkp
	for calculating cylindrical volume

integer, dimension(:,:), allocatable	allglobal::djkm
	for calculating cylindrical volume

Detailed Description

To facilitate construction of the metric integrals, various trigonometric identities are exploited.
The following are used for volume integrals (see volume() ):
\begin{eqnarray} a_{i,j,k} &=& 4 \; m_k \oint\!\!\!\oint \!d\theta d\zeta \,\,\, \cos(\alpha_i)\cos(\alpha_j)\cos(\alpha_k) /(2\pi)^2 , \\ b_{i,j,k} &=& 4 \; m_j \oint\!\!\!\oint \!d\theta d\zeta \,\,\, \cos(\alpha_i)\sin(\alpha_j)\sin(\alpha_k) /(2\pi)^2 , \end{eqnarray}

Variables