t_hmap_frenet Derived Type

type, public, extends(c_hmap) :: t_hmap_frenet


Inherits

type~~t_hmap_frenet~~InheritsGraph type~t_hmap_frenet t_hmap_frenet type~c_hmap c_hmap type~t_hmap_frenet->type~c_hmap

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.
real(kind=wp), public, ALLOCATABLE :: rc(:)

input cosine coefficients of R0 as array (0:n_max) of modes (0,1,...,n_max)*nfp
real(kind=wp), public, ALLOCATABLE :: rs(:)

input sine coefficients of R0 as array (0:n_max) of modes (0,1,...,n_max)*nfp
real(kind=wp), public, ALLOCATABLE :: zc(:)

input cosine coefficients of Z0 as array (0:n_max) of modes (0,1,...,n_max)*nfp
real(kind=wp), public, ALLOCATABLE :: zs(:)

input sine coefficients of Z0 as array (0:n_max) of modes (0,1,...,n_max)*nfp
integer, public, ALLOCATABLE :: Xn(:)

array of mode numbers, local variable =(0,1,...,n_max)*nfp
logical, public :: omnig = .FALSE.

omnigenity. True: sign change of frame at pi/nfp , False: no sign change

Constructor

public interface t_hmap_frenet

  • public function hmap_frenet_init() result(sf)

    initialize the type hmap_frenet, reading from parameterfile and then call init_params

    Arguments

    None

    Return Value type(t_hmap_frenet)

    self

  • public function hmap_frenet_init_params(nfp, n_max, nvisu, Rc, Rs, Zc, Zs, omnig) result(sf)

    initialize the type hmap_frenet with number of elements

    Arguments

    Type IntentOptional Attributes Name
    integer, intent(in) :: nfp

    number of field periods
    integer, intent(in) :: n_max

    maximum mode number of guiding curve
    integer, intent(in) :: nvisu

    number of visualization points per field period (-1: no visualization)
    real(kind=wp), intent(in) :: Rc(0:n_max)

    R cos(-n*zeta) modes of guiding curve, 0..n_max
    real(kind=wp), intent(in) :: Rs(0:n_max)

    R sin(-n*zeta) modes of guiding curve, 0..n_max
    real(kind=wp), intent(in) :: Zc(0:n_max)

    Z cos(-n*zeta) modes of guiding curve, 0..n_max
    real(kind=wp), intent(in) :: Zs(0:n_max)

    Z sin(-n*zeta) modes of guiding curve, 0..n_max
    logical, intent(in) :: omnig

    omnigeneity, gives sign function of Frenet frame. False: sigma=1, True: sigma=+1 for 0<=zeta<=pi/nfp, and -1 for pi/nfp

    Return Value type(t_hmap_frenet)

    self


Finalization Procedures

final :: hmap_frenet_free

  • public subroutine hmap_frenet_free(sf)

    finalize the type hmap_frenet

    Arguments

    Type IntentOptional Attributes Name
    type(t_hmap_frenet), 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 IntentOptional Attributes 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 IntentOptional Attributes 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 IntentOptional Attributes 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 IntentOptional Attributes 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 IntentOptional Attributes 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 IntentOptional Attributes 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_frenet_eval_all

  • public subroutine hmap_frenet_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 IntentOptional Attributes Name
    class(t_hmap_frenet), 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_frenet_eval

  • public function hmap_frenet_eval(sf, q_in) result(x_out)

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

    Arguments

    Type IntentOptional Attributes Name
    class(t_hmap_frenet), intent(in) :: sf
    real(kind=wp), intent(in) :: q_in(3)

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

procedure, public :: eval_aux => hmap_frenet_eval_aux

  • public function hmap_frenet_eval_aux(sf, q1, q2, xv) result(x_out)

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

    Arguments

    Type IntentOptional Attributes Name
    class(t_hmap_frenet), 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_frenet_eval_dxdq

  • public function hmap_frenet_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 IntentOptional Attributes Name
    class(t_hmap_frenet), 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_frenet_eval_dxdq_aux

  • public function hmap_frenet_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 IntentOptional Attributes Name
    class(t_hmap_frenet), 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_frenet_eval_Jh

  • public function hmap_frenet_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 IntentOptional Attributes Name
    class(t_hmap_frenet), intent(in) :: sf
    real(kind=wp), intent(in) :: q_in(3)

    Return Value real(kind=wp)

procedure, public :: eval_Jh_aux => hmap_frenet_eval_Jh_aux

  • public function hmap_frenet_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 IntentOptional Attributes Name
    class(t_hmap_frenet), 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_frenet_eval_Jh_dq

  • public function hmap_frenet_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 IntentOptional Attributes Name
    class(t_hmap_frenet), 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_frenet_eval_Jh_dq_aux

  • public function hmap_frenet_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)

    Read more…

    Arguments

    Type IntentOptional Attributes Name
    class(t_hmap_frenet), 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_frenet_eval_gij

  • public function hmap_frenet_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 of ds and dtheta and 1 for dzeta

    Arguments

    Type IntentOptional Attributes Name
    class(t_hmap_frenet), 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_frenet_eval_gij_aux

  • public function hmap_frenet_eval_gij_aux(sf, qL1, qL2, qL3, q1, q2, qR1, qR2, qR3, xv) 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 of ds and dtheta and 1 for dzeta

    Arguments

    Type IntentOptional Attributes Name
    class(t_hmap_frenet), 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_frenet_eval_gij_dq

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

    evaluate sum_k=1,3 q_vec^k * sum_ij (qL_i d/dq^k(G_ij(q_G)) qR_j) , k=1,2 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 of ds and dtheta and 1 for dzeta

    Arguments

    Type IntentOptional Attributes Name
    class(t_hmap_frenet), 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_frenet_eval_gij_dq_aux

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

    evaluate sum_ij (qL_i d/dq^k(G_ij(q_G)) qR_j) , k=1,2 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 of ds and dtheta and 1 for dzeta

    Read more…

    Arguments

    Type IntentOptional Attributes Name
    class(t_hmap_frenet), 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_frenet_get_dx_dqi

  • public subroutine hmap_frenet_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 IntentOptional Attributes Name
    class(t_hmap_frenet), 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_frenet_get_dx_dqi_aux

  • public subroutine hmap_frenet_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 IntentOptional Attributes Name
    class(t_hmap_frenet), 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_frenet_get_ddx_dqij

  • public subroutine hmap_frenet_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 IntentOptional Attributes Name
    class(t_hmap_frenet), 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_frenet_get_ddx_dqij_aux

  • public subroutine hmap_frenet_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 IntentOptional Attributes Name
    class(t_hmap_frenet), 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_X0 => hmap_frenet_eval_X0_fromRZ

  • public pure subroutine hmap_frenet_eval_X0_fromRZ(sf, zeta, X0, X0p, X0pp, X0ppp, X0p4)

    evaluate curve X0(zeta), position and first three derivatives, from given R0,Z0 Fourier

    Read more…

    Arguments

    Type IntentOptional Attributes Name
    class(t_hmap_frenet), 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) :: X0p(1:3)

    1st derivative in zeta
    real(kind=wp), intent(out) :: X0pp(1:3)

    2nd derivative in zeta
    real(kind=wp), intent(out) :: X0ppp(1:3)

    3rd derivative in zeta
    real(kind=wp), intent(out), optional :: X0p4(1:3)

    4th derivative in zeta

procedure, public :: sigma => hmap_frenet_sigma

  • public function hmap_frenet_sigma(sf, zeta) result(sigma)

    sign function depending on zeta, if omnig=False, sigma=1 if omnig=True, sigma=+1 for 0<=zeta<=pi/nfp, and -1 for pi/nfp

    Arguments

    Type IntentOptional Attributes Name
    class(t_hmap_frenet), intent(in) :: sf
    real(kind=wp), intent(in) :: zeta

    Return Value real(kind=wp)

Source Code

TYPE,EXTENDS(c_hmap) :: t_hmap_frenet
  !---------------------------------------------------------------------------------------------------------------------------------
  LOGICAL  :: initialized=.FALSE.
  !---------------------------------------------------------------------------------------------------------------------------------
  ! parameters for hmap_frenet:
  !curve description
  !INTEGER             :: nfp  !already part of c_hmap. Is overwritten in init
  REAL(wp),ALLOCATABLE :: rc(:)  !! input cosine coefficients of R0 as array (0:n_max) of modes (0,1,...,n_max)*nfp
  REAL(wp),ALLOCATABLE :: rs(:)  !! input   sine coefficients of R0 as array (0:n_max) of modes (0,1,...,n_max)*nfp
  REAL(wp),ALLOCATABLE :: zc(:)  !! input cosine coefficients of Z0 as array (0:n_max) of modes (0,1,...,n_max)*nfp
  REAL(wp),ALLOCATABLE :: zs(:)  !! input   sine coefficients of Z0 as array (0:n_max) of modes (0,1,...,n_max)*nfp
  INTEGER,ALLOCATABLE  :: Xn(:)   !! array of mode numbers,  local variable =(0,1,...,n_max)*nfp
  LOGICAL              :: omnig=.FALSE.   !! omnigenity. True: sign change of frame at pi/nfp , False: no sign change
  !---------------------------------------------------------------------------------------------------------------------------------

  CONTAINS

  FINAL :: hmap_frenet_free
  PROCEDURE :: eval_all        => hmap_frenet_eval_all
  PROCEDURE :: eval            => hmap_frenet_eval
  PROCEDURE :: eval_aux        => hmap_frenet_eval_aux
  PROCEDURE :: eval_dxdq       => hmap_frenet_eval_dxdq
  PROCEDURE :: eval_dxdq_aux   => hmap_frenet_eval_dxdq_aux
  PROCEDURE :: eval_Jh         => hmap_frenet_eval_Jh
  PROCEDURE :: eval_Jh_aux     => hmap_frenet_eval_Jh_aux
  PROCEDURE :: eval_Jh_dq      => hmap_frenet_eval_Jh_dq
  PROCEDURE :: eval_Jh_dq_aux  => hmap_frenet_eval_Jh_dq_aux
  PROCEDURE :: eval_gij        => hmap_frenet_eval_gij
  PROCEDURE :: eval_gij_aux    => hmap_frenet_eval_gij_aux
  PROCEDURE :: eval_gij_dq     => hmap_frenet_eval_gij_dq
  PROCEDURE :: eval_gij_dq_aux => hmap_frenet_eval_gij_dq_aux
  PROCEDURE :: get_dx_dqi       => hmap_frenet_get_dx_dqi
  PROCEDURE :: get_dx_dqi_aux   => hmap_frenet_get_dx_dqi_aux
  PROCEDURE :: get_ddx_dqij     => hmap_frenet_get_ddx_dqij
  PROCEDURE :: get_ddx_dqij_aux => hmap_frenet_get_ddx_dqij_aux

  !---------------------------------------------------------------------------------------------------------------------------------
  ! procedures for hmap_frenet:
  PROCEDURE :: eval_X0       => hmap_frenet_eval_X0_fromRZ
  PROCEDURE :: sigma         => hmap_frenet_sigma
END TYPE t_hmap_frenet