t_hmap_axisNB

type, public, extends(c_hmap) :: t_hmap_axisNB

Inherits

Help

Components

Type	Visibility	Attributes		Name		Initial
integer,	public		::	which_hmap			points to hmap (1: MHD3D)
integer,	public		::	nfp	=	-1	number of field periods used in hmap. If =-1, its not used
integer,	public		::	n_max	=	0	maximum number of toroidal modes needed to describe hmap. Used for estimating the number of integration points.
logical,	public		::	initialized	=	.FALSE.
integer,	public		::	nzeta	=	0	number of points in zeta direction of the input axis
integer,	public		::	sgn_rot			sign of rotation around Z axis, either +1 or -1: positive means that from one field period to the next, xyz rotate counterclockwise around the Z-axis (right hand rule), negative then clockwise.
real(kind=wp),	public,	ALLOCATABLE	::	zeta(:)			zeta positions in one field period (1:nzeta), on 'half' grid: zeta(i)=(i-0.5)/nzeta*(2pi/nfp)
real(kind=wp),	public,	ALLOCATABLE	::	xyz(:,:)			cartesian coordinates of the axis for a full turn, (1:NFPnzeta,1:3), zeta is on 'half' grid: zeta(i)=(i-0.5)/(NFPnzeta)*(2pi)
real(kind=wp),	public,	ALLOCATABLE	::	Nxyz(:,:)			"normal" vector of axis frame in cartesian coordinates for a full turn (1:NFP*nzeta,1:3). NOT ASSUMED TO BE ORTHOGONAL to tangent of curve
real(kind=wp),	public,	ALLOCATABLE	::	Bxyz(:,:)			"Bi-normal" vector of axis frame in cartesian coordinates for a full turn (1:NFP*nzeta,1:3). NOT ASSUMED TO BE ORTHOGONAL to tangent of curve or Nxyz
real(kind=wp),	public,	ALLOCATABLE	::	xyz_hat_modes(:,:)			fourier modes of xhat,yhat,zhat on one field period, x=cos(zeta)xhat-sgn_rotsin(zeta)yhat, y=sin(zeta)xhat+sgn_rotcos(zeta)yhat, z=zhat
real(kind=wp),	public,	ALLOCATABLE	::	Nxyz_hat_modes(:,:)			1d fourier modes of Nxyz, one field period
real(kind=wp),	public,	ALLOCATABLE	::	Bxyz_hat_modes(:,:)			1d fourier modes of Bxyz, one field period
character(len=1024),	public		::	ncfile	=	" "	name of netcdf file with axis information
type(t_fBase),	public		::	fb_hat			container for 1d fourier base of xhat
class(t_ncfile),	public,	ALLOCATABLE	::	nc			container for netcdf-file

Constructor

public interface t_hmap_axisNB

public function hmap_axisNB_init() result(sf)

initialize the type hmap_axisNB, reading from parameterfile and call init_params

Arguments
None
Return Value type(t_hmap_axisNB)

self

public function hmap_axisNB_init_params(ncfile, nvisu) result(sf)

initialize the type hmap_axisNB and read "G-frame" from netcdf

transform from full period cartesian coordinates to one-field period "hat" cartesian coordinates, by rotating around the zaxis with the local angle zeta, with the sign given by which direction xyz(zeta=0) rotates to xyz(zeta=2pi/nfp) INVERSION OF: x=cos(zeta)xhat - sgn_rotsin(zeta)yhat, y=cos(zeta)yhat + sgn_rotsin(zeta)xhat, z <=> zhat ==> xhat=cos(zeta)x+sgn_rotsin(zeta)y, yhat=cos(zeta)y-sgn_rotsin(zeta)x, check that all points on full period are the same in the xhat,yhat,zhat coordinates NOTE THIS FUNCTION IS USING sinz=sin(zeta),cosz=cos(zeta) and sgn_rot computed above!!!!

Arguments

Type	Intent	Optional	Attributes		Name
character(len=*),	intent(in)			::	ncfile	netcdf file containing the group "axis" from which to read the G-frame
integer,	intent(in)			::	nvisu	number of visualization points for G-Frame per field period, -1: no visualization

Return Value type(t_hmap_axisNB)

self

Finalization Procedures

final :: hmap_axisNB_free

public subroutine hmap_axisNB_free(sf)

finalize the type hmap_axisNB

Arguments

Type	Intent	Optional	Attributes		Name
type(t_hmap_axisNB),	intent(inout)			::	sf	self

Type-Bound Procedures

procedure, public :: eval_aux_all => hmap_eval_aux_all

public function hmap_eval_aux_all(sf, np, q1_in, q2_in, xv) result(xyz)

call %eval_aux on 1d array of points of size np, using auxiliary variable array of same size

Arguments

Type	Intent		Name
class(c_hmap),	intent(in)	::	sf
integer,	intent(in)	::	np
real(kind=wp),	intent(in)	::	q1_in(1:np)
real(kind=wp),	intent(in)	::	q2_in(1:np)
class(c_hmap_auxvar),	intent(in)	::	xv(1:np)

Return Value real(kind=wp), (1:3,1:np)

procedure, public :: eval_dxdq_aux_all => hmap_eval_dxdq_aux_all

public function hmap_eval_dxdq_aux_all(sf, np, q1, q2, q1_vec, q2_vec, q3_vec, xv) result(dxdq_qvec)

call %eval_dxdq_aux on 1d array of points of size np, using auxiliary variable array of same size

Arguments

Type	Intent		Name
class(c_hmap),	intent(in)	::	sf
integer,	intent(in)	::	np
real(kind=wp),	intent(in)	::	q1(1:np)
real(kind=wp),	intent(in)	::	q2(1:np)
real(kind=wp),	intent(in)	::	q1_vec(1:np)
real(kind=wp),	intent(in)	::	q2_vec(1:np)
real(kind=wp),	intent(in)	::	q3_vec(1:np)
class(c_hmap_auxvar),	intent(in)	::	xv(1:np)

Return Value real(kind=wp), (1:3,1:np)

procedure, public :: eval_Jh_aux_all => hmap_eval_Jh_aux_all

public function hmap_eval_Jh_aux_all(sf, np, q1, q2, xv) result(Jh)

call %eval_Jh_aux on 1d array of points of size np, using auxiliary variable array of same size

Arguments

Type	Intent		Name
class(c_hmap),	intent(in)	::	sf
integer,	intent(in)	::	np
real(kind=wp),	intent(in)	::	q1(1:np)
real(kind=wp),	intent(in)	::	q2(1:np)
class(c_hmap_auxvar),	intent(in)	::	xv(1:np)

Return Value real(kind=wp), (1:np)

procedure, public :: eval_Jh_dq_aux_all => hmap_eval_Jh_dq_aux_all

public function hmap_eval_Jh_dq_aux_all(sf, np, q1, q2, q1_vec, q2_vec, q3_vec, xv) result(Jh_dq)

call %eval_Jh_dq1_aux on 1d array of points of size np, using auxiliary variable array of same size

Arguments

Type	Intent		Name
class(c_hmap),	intent(in)	::	sf
integer,	intent(in)	::	np
real(kind=wp),	intent(in)	::	q1(1:np)
real(kind=wp),	intent(in)	::	q2(1:np)
real(kind=wp),	intent(in)	::	q1_vec(1:np)
real(kind=wp),	intent(in)	::	q2_vec(1:np)
real(kind=wp),	intent(in)	::	q3_vec(1:np)
class(c_hmap_auxvar),	intent(in)	::	xv(1:np)

Return Value real(kind=wp), (1:np)

procedure, public :: eval_gij_aux_all => hmap_eval_gij_aux_all

public function hmap_eval_gij_aux_all(sf, np, qL1, qL2, qL3, q1, q2, qR1, qR2, qR3, xv) result(g_ab)

Arguments

Type	Intent		Name
class(c_hmap),	intent(in)	::	sf
integer,	intent(in)	::	np
real(kind=wp),	intent(in)	::	qL1(1:np)
real(kind=wp),	intent(in)	::	qL2(1:np)
real(kind=wp),	intent(in)	::	qL3(1:np)
real(kind=wp),	intent(in)	::	q1(1:np)
real(kind=wp),	intent(in)	::	q2(1:np)
real(kind=wp),	intent(in)	::	qR1(1:np)
real(kind=wp),	intent(in)	::	qR2(1:np)
real(kind=wp),	intent(in)	::	qR3(1:np)
class(c_hmap_auxvar),	intent(in)	::	xv(1:np)

Return Value real(kind=wp), (1:np)

procedure, public :: eval_gij_dq_aux_all => hmap_eval_gij_dq_aux_all

public function hmap_eval_gij_dq_aux_all(sf, np, qL1, qL2, qL3, q1, q2, qR1, qR2, qR3, q1_vec, q2_vec, q3_vec, xv) result(g_ab_dq)

Arguments

Type	Intent		Name
class(c_hmap),	intent(in)	::	sf
integer,	intent(in)	::	np
real(kind=wp),	intent(in)	::	qL1(1:np)
real(kind=wp),	intent(in)	::	qL2(1:np)
real(kind=wp),	intent(in)	::	qL3(1:np)
real(kind=wp),	intent(in)	::	q1(1:np)
real(kind=wp),	intent(in)	::	q2(1:np)
real(kind=wp),	intent(in)	::	qR1(1:np)
real(kind=wp),	intent(in)	::	qR2(1:np)
real(kind=wp),	intent(in)	::	qR3(1:np)
real(kind=wp),	intent(in)	::	q1_vec(1:np)
real(kind=wp),	intent(in)	::	q2_vec(1:np)
real(kind=wp),	intent(in)	::	q3_vec(1:np)
class(c_hmap_auxvar),	intent(in)	::	xv(1:np)

Return Value real(kind=wp), (1:np)

procedure, public :: eval_all => hmap_axisNB_eval_all

public subroutine hmap_axisNB_eval_all(sf, ndims, dim_zeta, xv, q1, q2, dX1_dt, dX2_dt, dX1_dz, dX2_dz, Jh, g_tt, g_tz, g_zz, Jh_dq1, g_tt_dq1, g_tz_dq1, g_zz_dq1, Jh_dq2, g_tt_dq2, g_tz_dq2, g_zz_dq2, g_t1, g_t2, g_z1, g_z2, Gh11, Gh22)

evaluate all metrics necessary for optimizer

Arguments

Type	Intent	Attributes		Name
class(t_hmap_axisNB),	intent(in)		::	sf
integer,	intent(in)		::	ndims(3)	3D dimensions of input arrays
integer,	intent(in)		::	dim_zeta	which dimension is zeta dependent
class(c_hmap_auxvar),	intent(in)		::	xv(ndims(dim_zeta))	zeta point positions
real(kind=wp),	intent(in),	DIMENSION(ndims(1),ndims(2),ndims(3))	::	q1
real(kind=wp),	intent(in),	DIMENSION(ndims(1),ndims(2),ndims(3))	::	q2
real(kind=wp),	intent(in),	DIMENSION(ndims(1),ndims(2),ndims(3))	::	dX1_dt
real(kind=wp),	intent(in),	DIMENSION(ndims(1),ndims(2),ndims(3))	::	dX2_dt
real(kind=wp),	intent(in),	DIMENSION(ndims(1),ndims(2),ndims(3))	::	dX1_dz
real(kind=wp),	intent(in),	DIMENSION(ndims(1),ndims(2),ndims(3))	::	dX2_dz
real(kind=wp),	intent(out),	DIMENSION(ndims(1),ndims(2),ndims(3))	::	Jh
real(kind=wp),	intent(out),	DIMENSION(ndims(1),ndims(2),ndims(3))	::	g_tt
real(kind=wp),	intent(out),	DIMENSION(ndims(1),ndims(2),ndims(3))	::	g_tz
real(kind=wp),	intent(out),	DIMENSION(ndims(1),ndims(2),ndims(3))	::	g_zz
real(kind=wp),	intent(out),	DIMENSION(ndims(1),ndims(2),ndims(3))	::	Jh_dq1
real(kind=wp),	intent(out),	DIMENSION(ndims(1),ndims(2),ndims(3))	::	g_tt_dq1
real(kind=wp),	intent(out),	DIMENSION(ndims(1),ndims(2),ndims(3))	::	g_tz_dq1
real(kind=wp),	intent(out),	DIMENSION(ndims(1),ndims(2),ndims(3))	::	g_zz_dq1
real(kind=wp),	intent(out),	DIMENSION(ndims(1),ndims(2),ndims(3))	::	Jh_dq2
real(kind=wp),	intent(out),	DIMENSION(ndims(1),ndims(2),ndims(3))	::	g_tt_dq2
real(kind=wp),	intent(out),	DIMENSION(ndims(1),ndims(2),ndims(3))	::	g_tz_dq2
real(kind=wp),	intent(out),	DIMENSION(ndims(1),ndims(2),ndims(3))	::	g_zz_dq2
real(kind=wp),	intent(out),	DIMENSION(ndims(1),ndims(2),ndims(3))	::	g_t1
real(kind=wp),	intent(out),	DIMENSION(ndims(1),ndims(2),ndims(3))	::	g_t2
real(kind=wp),	intent(out),	DIMENSION(ndims(1),ndims(2),ndims(3))	::	g_z1
real(kind=wp),	intent(out),	DIMENSION(ndims(1),ndims(2),ndims(3))	::	g_z2
real(kind=wp),	intent(out),	DIMENSION(ndims(1),ndims(2),ndims(3))	::	Gh11
real(kind=wp),	intent(out),	DIMENSION(ndims(1),ndims(2),ndims(3))	::	Gh22

procedure, public :: eval => hmap_axisNB_eval

public function hmap_axisNB_eval(sf, q_in) result(x_out)

evaluate the mapping h (q1,q2,zeta) -> (x,y,z)

Arguments

Type	Intent	Optional	Attributes		Name
class(t_hmap_axisNB),	intent(in)			::	sf
real(kind=wp),	intent(in)			::	q_in(3)

Return Value real(kind=wp), (3)

procedure, public :: eval_aux => hmap_axisNB_eval_aux

public function hmap_axisNB_eval_aux(sf, q1, q2, xv) result(x_out)

evaluate the mapping h (q1,q2,zeta) -> (x,y,z)

Arguments

Type	Intent		Name
class(t_hmap_axisNB),	intent(in)	::	sf
real(kind=wp),	intent(in)	::	q1
real(kind=wp),	intent(in)	::	q2
class(c_hmap_auxvar),	intent(in)	::	xv

Return Value real(kind=wp), (3)

procedure, public :: eval_dxdq => hmap_axisNB_eval_dxdq

public function hmap_axisNB_eval_dxdq(sf, q_in, q_vec) result(dxdq_qvec)

evaluate total derivative of the mapping sum k=1,3 (dx(1:3)/dq^k) q_vec^k, where dx(1:3)/dq^k, k=1,2,3 is evaluated at q_in=(X^1,X^2,zeta) ,

Arguments

Type	Intent		Name
class(t_hmap_axisNB),	intent(in)	::	sf
real(kind=wp),	intent(in)	::	q_in(3)
real(kind=wp),	intent(in)	::	q_vec(3)

Return Value real(kind=wp), (3)

procedure, public :: eval_dxdq_aux => hmap_axisNB_eval_dxdq_aux

public function hmap_axisNB_eval_dxdq_aux(sf, q1, q2, q1_vec, q2_vec, q3_vec, xv) result(dxdq_qvec)

evaluate total derivative of the mapping sum k=1,3 (dx(1:3)/dq^k) q_vec^k, where dx(1:3)/dq^k, k=1,2,3 is evaluated at q_in=(X^1,X^2,zeta) ,

Arguments

Type	Intent		Name
class(t_hmap_axisNB),	intent(in)	::	sf
real(kind=wp),	intent(in)	::	q1
real(kind=wp),	intent(in)	::	q2
real(kind=wp),	intent(in)	::	q1_vec
real(kind=wp),	intent(in)	::	q2_vec
real(kind=wp),	intent(in)	::	q3_vec
class(c_hmap_auxvar),	intent(in)	::	xv

Return Value real(kind=wp), (3)

procedure, public :: eval_Jh => hmap_axisNB_eval_Jh

public function hmap_axisNB_eval_Jh(sf, q_in) result(Jh)

evaluate Jacobian of mapping h: J_h=sqrt(det(G)) at q=(q^1,q^2,zeta)

Arguments

Type	Intent	Optional	Attributes		Name
class(t_hmap_axisNB),	intent(in)			::	sf
real(kind=wp),	intent(in)			::	q_in(3)

Return Value real(kind=wp)

procedure, public :: eval_Jh_aux => hmap_axisNB_eval_Jh_aux

public function hmap_axisNB_eval_Jh_aux(sf, q1, q2, xv) result(Jh)

evaluate Jacobian of mapping h: J_h=sqrt(det(G)) at q=(q^1,q^2,zeta)

Arguments

Type	Intent		Name
class(t_hmap_axisNB),	intent(in)	::	sf
real(kind=wp),	intent(in)	::	q1
real(kind=wp),	intent(in)	::	q2
class(c_hmap_auxvar),	intent(in)	::	xv

Return Value real(kind=wp)

procedure, public :: eval_Jh_dq => hmap_axisNB_eval_Jh_dq

public function hmap_axisNB_eval_Jh_dq(sf, q_in, q_vec) result(Jh_dq)

evaluate derivative of Jacobian of mapping h: sum_k q_vec^k dJ_h/dq^k, k=1,2,3 at q=(q^1,q^2,zeta)

Arguments

Type	Intent		Name
class(t_hmap_axisNB),	intent(in)	::	sf
real(kind=wp),	intent(in)	::	q_in(3)
real(kind=wp),	intent(in)	::	q_vec(3)

Return Value real(kind=wp)

procedure, public :: eval_Jh_dq_aux => hmap_axisNB_eval_Jh_dq_aux

public function hmap_axisNB_eval_Jh_dq_aux(sf, q1, q2, q1_vec, q2_vec, q3_vec, xv) result(Jh_dq)

evaluate derivative of Jacobian of mapping h: sum_k q_vec^k dJ_h/dq^k, k=1,2,3 at q=(q^1,q^2,zeta)

Arguments

Type	Intent		Name
class(t_hmap_axisNB),	intent(in)	::	sf
real(kind=wp),	intent(in)	::	q1
real(kind=wp),	intent(in)	::	q2
real(kind=wp),	intent(in)	::	q1_vec
real(kind=wp),	intent(in)	::	q2_vec
real(kind=wp),	intent(in)	::	q3_vec
class(c_hmap_auxvar),	intent(in)	::	xv

Return Value real(kind=wp)

procedure, public :: eval_gij => hmap_axisNB_eval_gij

public function hmap_axisNB_eval_gij(sf, qL_in, q_G, qR_in) result(g_ab)

evaluate sum_ij (qL_i (G_ij(q_G)) qR_j) ,, where qL=(dX^1/dalpha,dX^2/dalpha ,dzeta/dalpha) and qR=(dX^1/dbeta,dX^2/dbeta ,dzeta/dbeta) and dzeta_dalpha then known to be either 0.0 for ds and dtheta and 1.0 for dzeta

Arguments

Type	Intent		Name
class(t_hmap_axisNB),	intent(in)	::	sf
real(kind=wp),	intent(in)	::	qL_in(3)
real(kind=wp),	intent(in)	::	q_G(3)
real(kind=wp),	intent(in)	::	qR_in(3)

Return Value real(kind=wp)

procedure, public :: eval_gij_aux => hmap_axisNB_eval_gij_aux

public function hmap_axisNB_eval_gij_aux(sf, qL1, qL2, qL3, q1, q2, qR1, qR2, qR3, xv) result(g_ab)

Arguments

Type	Intent		Name
class(t_hmap_axisNB),	intent(in)	::	sf
real(kind=wp),	intent(in)	::	qL1
real(kind=wp),	intent(in)	::	qL2
real(kind=wp),	intent(in)	::	qL3
real(kind=wp),	intent(in)	::	q1
real(kind=wp),	intent(in)	::	q2
real(kind=wp),	intent(in)	::	qR1
real(kind=wp),	intent(in)	::	qR2
real(kind=wp),	intent(in)	::	qR3
class(c_hmap_auxvar),	intent(in)	::	xv

Return Value real(kind=wp)

procedure, public :: eval_gij_dq => hmap_axisNB_eval_gij_dq

public function hmap_axisNB_eval_gij_dq(sf, qL_in, q_G, qR_in, q_vec) result(g_ab_dq)

evaluate sum_k q_vec^k * sum_ij (qL_i d/dq^k(G_ij(q_G)) qR_j) , k=1,2,3 where qL=(dX^1/dalpha,dX^2/dalpha [,dzeta/dalpha]) and qR=(dX^1/dbeta,dX^2/dbeta [,dzeta/dbeta]) and where qL=(dX^1/dalpha,dX^2/dalpha ,dzeta/dalpha) and qR=(dX^1/dbeta,dX^2/dbeta ,dzeta/dbeta) and dzeta_dalpha then known to be either 0.0 for ds and dtheta and 1.0 for dzeta

Arguments

Type	Intent		Name
class(t_hmap_axisNB),	intent(in)	::	sf
real(kind=wp),	intent(in)	::	qL_in(3)
real(kind=wp),	intent(in)	::	q_G(3)
real(kind=wp),	intent(in)	::	qR_in(3)
real(kind=wp),	intent(in)	::	q_vec(3)

Return Value real(kind=wp)

procedure, public :: eval_gij_dq_aux => hmap_axisNB_eval_gij_dq_aux

public function hmap_axisNB_eval_gij_dq_aux(sf, qL1, qL2, qL3, q1, q2, qR1, qR2, qR3, q1_vec, q2_vec, q3_vec, xv) result(g_ab_dq)

Arguments

Type	Intent		Name
class(t_hmap_axisNB),	intent(in)	::	sf
real(kind=wp),	intent(in)	::	qL1
real(kind=wp),	intent(in)	::	qL2
real(kind=wp),	intent(in)	::	qL3
real(kind=wp),	intent(in)	::	q1
real(kind=wp),	intent(in)	::	q2
real(kind=wp),	intent(in)	::	qR1
real(kind=wp),	intent(in)	::	qR2
real(kind=wp),	intent(in)	::	qR3
real(kind=wp),	intent(in)	::	q1_vec
real(kind=wp),	intent(in)	::	q2_vec
real(kind=wp),	intent(in)	::	q3_vec
class(c_hmap_auxvar),	intent(in)	::	xv

Return Value real(kind=wp)

procedure, public :: get_dx_dqi => hmap_axisNB_get_dx_dqi

public subroutine hmap_axisNB_get_dx_dqi(sf, q_in, dx_dq1, dx_dq2, dx_dq3)

evaluate all first derivatives dx(1:3)/dq^i, i=1,2,3 , at q_in=(X^1,X^2,zeta),

Arguments

Type	Intent	Attributes		Name
class(t_hmap_axisNB),	intent(in)		::	sf
real(kind=wp),	intent(in)		::	q_in(3)
real(kind=wp),	intent(out),	DIMENSION(3)	::	dx_dq1
real(kind=wp),	intent(out),	DIMENSION(3)	::	dx_dq2
real(kind=wp),	intent(out),	DIMENSION(3)	::	dx_dq3

procedure, public :: get_dx_dqi_aux => hmap_axisNB_get_dx_dqi_aux

public subroutine hmap_axisNB_get_dx_dqi_aux(sf, q1, q2, xv, dx_dq1, dx_dq2, dx_dq3)

evaluate all first derivatives dx(1:3)/dq^i, i=1,2,3 , at q_in=(X^1,X^2,zeta),

Arguments

Type	Intent	Attributes		Name
class(t_hmap_axisNB),	intent(in)		::	sf
real(kind=wp),	intent(in)		::	q1
real(kind=wp),	intent(in)		::	q2
class(c_hmap_auxvar),	intent(in)		::	xv
real(kind=wp),	intent(out),	DIMENSION(3)	::	dx_dq1
real(kind=wp),	intent(out),	DIMENSION(3)	::	dx_dq2
real(kind=wp),	intent(out),	DIMENSION(3)	::	dx_dq3

procedure, public :: get_ddx_dqij => hmap_axisNB_get_ddx_dqij

public subroutine hmap_axisNB_get_ddx_dqij(sf, q_in, ddx_dq11, ddx_dq12, ddx_dq13, ddx_dq22, ddx_dq23, ddx_dq33)

evaluate all second derivatives d^2x(1:3)/(dq^i dq^j), i,j=1,2,3 is evaluated at q_in=(X^1,X^2,zeta),

Arguments

Type	Intent	Attributes		Name
class(t_hmap_axisNB),	intent(in)		::	sf
real(kind=wp),	intent(in)		::	q_in(3)
real(kind=wp),	intent(out),	DIMENSION(3)	::	ddx_dq11
real(kind=wp),	intent(out),	DIMENSION(3)	::	ddx_dq12
real(kind=wp),	intent(out),	DIMENSION(3)	::	ddx_dq13
real(kind=wp),	intent(out),	DIMENSION(3)	::	ddx_dq22
real(kind=wp),	intent(out),	DIMENSION(3)	::	ddx_dq23
real(kind=wp),	intent(out),	DIMENSION(3)	::	ddx_dq33

procedure, public :: get_ddx_dqij_aux => hmap_axisNB_get_ddx_dqij_aux

public subroutine hmap_axisNB_get_ddx_dqij_aux(sf, q1, q2, xv, ddx_dq11, ddx_dq12, ddx_dq13, ddx_dq22, ddx_dq23, ddx_dq33)

evaluate all second derivatives d^2x(1:3)/(dq^i dq^j), i,j=1,2,3 is evaluated at q_in=(X^1,X^2,zeta),

Arguments

Type	Intent	Attributes		Name
class(t_hmap_axisNB),	intent(in)		::	sf
real(kind=wp),	intent(in)		::	q1
real(kind=wp),	intent(in)		::	q2
class(c_hmap_auxvar),	intent(in)		::	xv
real(kind=wp),	intent(out),	DIMENSION(3)	::	ddx_dq11
real(kind=wp),	intent(out),	DIMENSION(3)	::	ddx_dq12
real(kind=wp),	intent(out),	DIMENSION(3)	::	ddx_dq13
real(kind=wp),	intent(out),	DIMENSION(3)	::	ddx_dq22
real(kind=wp),	intent(out),	DIMENSION(3)	::	ddx_dq23
real(kind=wp),	intent(out),	DIMENSION(3)	::	ddx_dq33

procedure, public :: eval_TNB => hmap_axisNB_eval_TNB_hat

public subroutine hmap_axisNB_eval_TNB_hat(sf, zeta, X0, T, N, B, Np, Bp, Tp, Npp, Bpp)

evaluate curve X0(zeta), and T=X0',N,B,N',B', using the fourier series of X0_hat,N_hat and B_hat and transform from "hat" coordinates to cartesian coordinates: x=xhatcos(zeta)-sgn_rotyhatsin(zeta), y=yhatcos(zeta)+sgn_rotsin(zeta)xhat, z=zhat

Arguments

Type	Intent	Optional		Name
class(t_hmap_axisNB),	intent(in)		::	sf
real(kind=wp),	intent(in)		::	zeta	position along closed curve parametrized in [0,2pi]
real(kind=wp),	intent(out)		::	X0(1:3)	curve position in cartesian coordinates
real(kind=wp),	intent(out)		::	T(1:3)	tangent X0'
real(kind=wp),	intent(out)		::	N(1:3)	Normal
real(kind=wp),	intent(out)		::	B(1:3)	bi-Normal
real(kind=wp),	intent(out)		::	Np(1:3)	derivative of Normal in zeta (N')
real(kind=wp),	intent(out)		::	Bp(1:3)	derivative of bi-Normal in zeta (B')
real(kind=wp),	intent(out),	optional	::	Tp(1:3)	derivative of tangent in zeta (X0'')
real(kind=wp),	intent(out),	optional	::	Npp(1:3)	2nd derivative of Normal in zeta (N'')
real(kind=wp),	intent(out),	optional	::	Bpp(1:3)	2nd derivative of bi-Normal in zeta (B'')

Source Code

TYPE,EXTENDS(c_hmap) :: t_hmap_axisNB
  !---------------------------------------------------------------------------------------------------------------------------------
  LOGICAL  :: initialized=.FALSE.
  !---------------------------------------------------------------------------------------------------------------------------------
  ! parameters for hmap_axisNB:
  !INTEGER              :: nfp   !! already part of c_hmap. Is overwritten in init!
  !curve description
  INTEGER              :: nzeta=0       !! number of points in zeta direction of the input axis
  INTEGER              :: sgn_rot       !! sign of rotation around Z axis,  either +1 or -1: positive means that from one field period to the next,
                                        !! xyz rotate counterclockwise around the Z-axis (right hand rule), negative then clockwise.
  REAL(wp),ALLOCATABLE :: zeta(:)       !! zeta positions in one field period (1:nzeta),  on 'half' grid: zeta(i)=(i-0.5)/nzeta*(2pi/nfp)
  REAL(wp),ALLOCATABLE :: xyz(:,:)      !! cartesian coordinates of the axis for a full turn, (1:NFP*nzeta,1:3), zeta is on 'half' grid: zeta(i)=(i-0.5)/(NFP*nzeta)*(2pi)
  REAL(wp),ALLOCATABLE :: Nxyz(:,:)     !! "normal" vector of axis frame in cartesian coordinates for a full turn (1:NFP*nzeta,1:3). NOT ASSUMED TO BE ORTHOGONAL to tangent of curve
  REAL(wp),ALLOCATABLE :: Bxyz(:,:)      !! "Bi-normal" vector of axis frame in cartesian coordinates for a full turn (1:NFP*nzeta,1:3). NOT ASSUMED TO BE ORTHOGONAL to tangent of curve or Nxyz
  !fourier modes
  REAL(wp),ALLOCATABLE :: xyz_hat_modes(:,:)   !! fourier modes of xhat,yhat,zhat on one field period,
                                               !! x=cos(zeta)xhat-sgn_rot*sin(zeta)yhat,
                                               !! y=sin(zeta)xhat+sgn_rot*cos(zeta)yhat, z=zhat
  REAL(wp),ALLOCATABLE :: Nxyz_hat_modes(:,:)   !! 1d fourier modes of Nxyz, one field period
  REAL(wp),ALLOCATABLE :: Bxyz_hat_modes(:,:)   !! 1d fourier modes of Bxyz, one field period

  CHARACTER(LEN=1024)   :: ncfile=" " !! name of netcdf file with axis information
  !---------------------------------------------------------------------------------------------------------------------------------
  TYPE(t_fbase)        :: fb_hat  !! container for 1d fourier base of xhat
  CLASS(t_ncfile),ALLOCATABLE  :: nc  !! container for netcdf-file


  CONTAINS

  FINAL     :: hmap_axisNB_free
  PROCEDURE :: eval_all        => hmap_axisNB_eval_all
  PROCEDURE :: eval            => hmap_axisNB_eval
  PROCEDURE :: eval_aux        => hmap_axisNB_eval_aux
  PROCEDURE :: eval_dxdq       => hmap_axisNB_eval_dxdq
  PROCEDURE :: eval_dxdq_aux   => hmap_axisNB_eval_dxdq_aux
  PROCEDURE :: eval_Jh         => hmap_axisNB_eval_Jh
  PROCEDURE :: eval_Jh_aux     => hmap_axisNB_eval_Jh_aux
  PROCEDURE :: eval_Jh_dq      => hmap_axisNB_eval_Jh_dq
  PROCEDURE :: eval_Jh_dq_aux  => hmap_axisNB_eval_Jh_dq_aux
  PROCEDURE :: eval_gij        => hmap_axisNB_eval_gij
  PROCEDURE :: eval_gij_aux    => hmap_axisNB_eval_gij_aux
  PROCEDURE :: eval_gij_dq     => hmap_axisNB_eval_gij_dq
  PROCEDURE :: eval_gij_dq_aux => hmap_axisNB_eval_gij_dq_aux
  PROCEDURE :: get_dx_dqi       => hmap_axisNB_get_dx_dqi
  PROCEDURE :: get_dx_dqi_aux   => hmap_axisNB_get_dx_dqi_aux
  PROCEDURE :: get_ddx_dqij     => hmap_axisNB_get_ddx_dqij
  PROCEDURE :: get_ddx_dqij_aux => hmap_axisNB_get_ddx_dqij_aux

  !---------------------------------------------------------------------------------------------------------------------------------
  ! procedures for hmap_axisNB:
  PROCEDURE :: eval_TNB         => hmap_axisNB_eval_TNB_hat

END TYPE t_hmap_axisNB

t_hmap_axisNB Derived Type

Contents

Variables

Constructor

Finalization Procedures

Type-Bound Procedures

Source Code

type, public, extends(c_hmap) :: t_hmap_axisNB

Inherits

Components

Constructor

public interface t_hmap_axisNB

public function hmap_axisNB_init() result(sf)

Arguments

Return Value type(t_hmap_axisNB)

public function hmap_axisNB_init_params(ncfile, nvisu) result(sf)

Arguments

Return Value type(t_hmap_axisNB)

Finalization Procedures

final :: hmap_axisNB_free

public subroutine hmap_axisNB_free(sf)

Arguments

Type-Bound Procedures

procedure, public :: eval_aux_all => hmap_eval_aux_all

public function hmap_eval_aux_all(sf, np, q1_in, q2_in, xv) result(xyz)

Arguments

Return Value real(kind=wp), (1:3,1:np)

procedure, public :: eval_dxdq_aux_all => hmap_eval_dxdq_aux_all

public function hmap_eval_dxdq_aux_all(sf, np, q1, q2, q1_vec, q2_vec, q3_vec, xv) result(dxdq_qvec)

Arguments

Return Value real(kind=wp), (1:3,1:np)

procedure, public :: eval_Jh_aux_all => hmap_eval_Jh_aux_all

public function hmap_eval_Jh_aux_all(sf, np, q1, q2, xv) result(Jh)

Arguments

Return Value real(kind=wp), (1:np)

procedure, public :: eval_Jh_dq_aux_all => hmap_eval_Jh_dq_aux_all

public function hmap_eval_Jh_dq_aux_all(sf, np, q1, q2, q1_vec, q2_vec, q3_vec, xv) result(Jh_dq)

Arguments

Return Value real(kind=wp), (1:np)

procedure, public :: eval_gij_aux_all => hmap_eval_gij_aux_all

public function hmap_eval_gij_aux_all(sf, np, qL1, qL2, qL3, q1, q2, qR1, qR2, qR3, xv) result(g_ab)

Arguments

Return Value real(kind=wp), (1:np)

procedure, public :: eval_gij_dq_aux_all => hmap_eval_gij_dq_aux_all

public function hmap_eval_gij_dq_aux_all(sf, np, qL1, qL2, qL3, q1, q2, qR1, qR2, qR3, q1_vec, q2_vec, q3_vec, xv) result(g_ab_dq)

Arguments

Return Value real(kind=wp), (1:np)

procedure, public :: eval_all => hmap_axisNB_eval_all

public subroutine hmap_axisNB_eval_all(sf, ndims, dim_zeta, xv, q1, q2, dX1_dt, dX2_dt, dX1_dz, dX2_dz, Jh, g_tt, g_tz, g_zz, Jh_dq1, g_tt_dq1, g_tz_dq1, g_zz_dq1, Jh_dq2, g_tt_dq2, g_tz_dq2, g_zz_dq2, g_t1, g_t2, g_z1, g_z2, Gh11, Gh22)

Arguments

procedure, public :: eval => hmap_axisNB_eval

public function hmap_axisNB_eval(sf, q_in) result(x_out)

Arguments

Return Value real(kind=wp), (3)

procedure, public :: eval_aux => hmap_axisNB_eval_aux

public function hmap_axisNB_eval_aux(sf, q1, q2, xv) result(x_out)

Arguments

Return Value real(kind=wp), (3)

procedure, public :: eval_dxdq => hmap_axisNB_eval_dxdq

public function hmap_axisNB_eval_dxdq(sf, q_in, q_vec) result(dxdq_qvec)

Arguments

Return Value real(kind=wp), (3)

procedure, public :: eval_dxdq_aux => hmap_axisNB_eval_dxdq_aux

public function hmap_axisNB_eval_dxdq_aux(sf, q1, q2, q1_vec, q2_vec, q3_vec, xv) result(dxdq_qvec)

Arguments

Return Value real(kind=wp), (3)

procedure, public :: eval_Jh => hmap_axisNB_eval_Jh

public function hmap_axisNB_eval_Jh(sf, q_in) result(Jh)

Arguments

Return Value real(kind=wp)

procedure, public :: eval_Jh_aux => hmap_axisNB_eval_Jh_aux

public function hmap_axisNB_eval_Jh_aux(sf, q1, q2, xv) result(Jh)

Arguments

Return Value real(kind=wp)

procedure, public :: eval_Jh_dq => hmap_axisNB_eval_Jh_dq

public function hmap_axisNB_eval_Jh_dq(sf, q_in, q_vec) result(Jh_dq)

Arguments

Return Value real(kind=wp)

procedure, public :: eval_Jh_dq_aux => hmap_axisNB_eval_Jh_dq_aux

public function hmap_axisNB_eval_Jh_dq_aux(sf, q1, q2, q1_vec, q2_vec, q3_vec, xv) result(Jh_dq)