hmap_frenet_test Subroutine

public subroutine hmap_frenet_test(sf)

Uses

  • proc~~hmap_frenet_test~~UsesGraph proc~hmap_frenet_test hmap_frenet_test module~modgvec_globals MODgvec_Globals proc~hmap_frenet_test->module~modgvec_globals iso_fortran_env iso_fortran_env module~modgvec_globals->iso_fortran_env

test hmap_frenet - evaluation of the map

TEST G_ij TEST dJh_dqk with FD TEST dG_ij_dqk with FD

Arguments

Type IntentOptional Attributes Name
class(t_hmap_frenet), intent(inout) :: sf

self

Calls

proc~~hmap_frenet_test~~CallsGraph proc~hmap_frenet_test hmap_frenet_test proc~hmap_frenet_eval t_hmap_frenet%hmap_frenet_eval proc~hmap_frenet_test->proc~hmap_frenet_eval proc~hmap_frenet_eval_all t_hmap_frenet%hmap_frenet_eval_all proc~hmap_frenet_test->proc~hmap_frenet_eval_all proc~hmap_frenet_eval_dxdq t_hmap_frenet%hmap_frenet_eval_dxdq proc~hmap_frenet_test->proc~hmap_frenet_eval_dxdq proc~hmap_frenet_eval_gij t_hmap_frenet%hmap_frenet_eval_gij proc~hmap_frenet_test->proc~hmap_frenet_eval_gij proc~hmap_frenet_eval_gij_dq t_hmap_frenet%hmap_frenet_eval_gij_dq proc~hmap_frenet_test->proc~hmap_frenet_eval_gij_dq proc~hmap_frenet_eval_jh t_hmap_frenet%hmap_frenet_eval_Jh proc~hmap_frenet_test->proc~hmap_frenet_eval_jh proc~hmap_frenet_eval_jh_dq t_hmap_frenet%hmap_frenet_eval_Jh_dq proc~hmap_frenet_test->proc~hmap_frenet_eval_jh_dq proc~hmap_frenet_get_ddx_dqij t_hmap_frenet%hmap_frenet_get_ddx_dqij proc~hmap_frenet_test->proc~hmap_frenet_get_ddx_dqij proc~hmap_frenet_get_dx_dqi t_hmap_frenet%hmap_frenet_get_dx_dqi proc~hmap_frenet_test->proc~hmap_frenet_get_dx_dqi proc~hmap_frenet_init_aux hmap_frenet_init_aux proc~hmap_frenet_test->proc~hmap_frenet_init_aux swrite swrite proc~hmap_frenet_test->swrite interface~cross CROSS proc~hmap_frenet_eval->interface~cross proc~hmap_frenet_eval_x0_fromrz t_hmap_frenet%hmap_frenet_eval_X0_fromRZ proc~hmap_frenet_eval->proc~hmap_frenet_eval_x0_fromrz proc~hmap_frenet_sigma t_hmap_frenet%hmap_frenet_sigma proc~hmap_frenet_eval->proc~hmap_frenet_sigma proc~hmap_frenet_eval_all_e hmap_frenet_eval_all_e proc~hmap_frenet_eval_all->proc~hmap_frenet_eval_all_e proc~hmap_frenet_eval_dxdq->interface~cross proc~hmap_frenet_eval_dxdq->proc~hmap_frenet_eval_x0_fromrz proc~hmap_frenet_eval_dxdq->proc~hmap_frenet_sigma proc~hmap_frenet_eval_gij->interface~cross proc~hmap_frenet_eval_gij->proc~hmap_frenet_eval_x0_fromrz proc~hmap_frenet_eval_gij->proc~hmap_frenet_sigma proc~hmap_frenet_eval_gij_dq->interface~cross proc~hmap_frenet_eval_gij_dq->proc~hmap_frenet_eval_x0_fromrz proc~hmap_frenet_eval_gij_dq->proc~hmap_frenet_sigma proc~hmap_frenet_eval_jh->interface~cross proc~hmap_frenet_eval_jh->proc~hmap_frenet_eval_x0_fromrz proc~hmap_frenet_eval_jh->proc~hmap_frenet_sigma proc~hmap_frenet_eval_jh_dq->interface~cross proc~hmap_frenet_eval_jh_dq->proc~hmap_frenet_eval_x0_fromrz proc~hmap_frenet_eval_jh_dq->proc~hmap_frenet_sigma proc~hmap_frenet_get_ddx_dqij->interface~cross proc~hmap_frenet_get_ddx_dqij->proc~hmap_frenet_eval_x0_fromrz proc~hmap_frenet_get_ddx_dqij->proc~hmap_frenet_sigma proc~hmap_frenet_get_dx_dqi->interface~cross proc~hmap_frenet_get_dx_dqi->proc~hmap_frenet_eval_x0_fromrz proc~hmap_frenet_get_dx_dqi->proc~hmap_frenet_sigma proc~hmap_frenet_init_aux->interface~cross proc~hmap_frenet_init_aux->proc~hmap_frenet_eval_x0_fromrz proc~hmap_frenet_init_aux->proc~hmap_frenet_sigma interface~cross->interface~cross proc~eval_fourier1d eval_fourier1d proc~hmap_frenet_eval_x0_fromrz->proc~eval_fourier1d

Called by

proc~~hmap_frenet_test~~CalledByGraph proc~hmap_frenet_test hmap_frenet_test proc~hmap_frenet_init_params hmap_frenet_init_params proc~hmap_frenet_init_params->proc~hmap_frenet_test interface~t_hmap_frenet t_hmap_frenet interface~t_hmap_frenet->proc~hmap_frenet_init_params proc~hmap_frenet_init hmap_frenet_init interface~t_hmap_frenet->proc~hmap_frenet_init proc~hmap_frenet_init->proc~hmap_frenet_init_params

Source Code

SUBROUTINE hmap_frenet_test( sf )
USE MODgvec_GLobals, ONLY: UNIT_stdOut,testdbg,testlevel,nfailedMsg,nTestCalled,testUnit
IMPLICIT NONE
!-----------------------------------------------------------------------------------------------------------------------------------
! INPUT VARIABLES
  CLASS(t_hmap_frenet), INTENT(INOUT) :: sf  !!self
!-----------------------------------------------------------------------------------------------------------------------------------
! OUTPUT VARIABLES
!-----------------------------------------------------------------------------------------------------------------------------------
! LOCAL VARIABLES
  INTEGER            :: iTest,idir,jdir,kdir,qdir,izeta,i,j,k,ndims(1:3),ijk(3)
  INTEGER,PARAMETER  :: nzeta=5
  INTEGER,PARAMETER  :: ns=2
  INTEGER,PARAMETER  :: nthet=3
  REAL(wp)           :: refreal,checkreal,x(3),q_in(3),q_test(3,3),x_eps(3),dxdq(3),gij,gij_eps,Jh_0,Jh_eps
  REAL(wp),ALLOCATABLE :: zeta(:)
  REAL(wp)           :: qloc(3),q_thet(3),q_zeta(3)
  REAL(wp)           :: dxdq_eps(3),dx_dqi(3,3),ddx_dqij(3,3,3)
  REAL(wp),ALLOCATABLE,DIMENSION(:,:,:) :: 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
  REAL(wp),PARAMETER :: realtol=1.0E-11_wp
  REAL(wp),PARAMETER :: epsFD=1.0e-8
  REAL(wp),PARAMETER :: realtolFD=1.0e-4
  CHARACTER(LEN=10)  :: fail
  REAL(wp)           :: R0, Z0
  TYPE(t_hmap_frenet_auxvar),ALLOCATABLE :: xv(:)
!===================================================================================================================================
  test_called=.TRUE. ! to prevent infinite loop in this routine
  IF(testlevel.LE.0) RETURN
  IF(testdbg) THEN
     Fail=" DEBUG  !!"
  ELSE
     Fail=" FAILED !!"
  END IF
  nTestCalled=nTestCalled+1
  SWRITE(UNIT_stdOut,'(A,I4,A)')'>>>>>>>>> RUN hmap_frenet TEST ID',nTestCalled,'    >>>>>>>>>'
  IF(testlevel.GE.1)THEN

    !evaluate on the axis q1=q2=0
    iTest=101 ; IF(testdbg)WRITE(*,*)'iTest=',iTest
    q_in=(/0.0_wp, 0.0_wp, 0.335_wp*PI/)
    R0 = SUM(sf%rc(:)*COS(sf%Xn(:)*q_in(3)) + sf%rs(:)*SIN(sf%Xn(:)*q_in(3)))
    Z0 = SUM(sf%zc(:)*COS(sf%Xn(:)*q_in(3)) + sf%zs(:)*SIN(sf%Xn(:)*q_in(3)))
    x = sf%eval(q_in )
    checkreal=SUM((x-(/R0*COS(q_in(3)),R0*SIN(q_in(3)),Z0/))**2)
    refreal = 0.0_wp

    IF(testdbg.OR.(.NOT.( ABS(checkreal-refreal).LT. realtol))) THEN
       nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(A,2(I4,A))') &
            '\n!! hmap_frenet TEST ID',nTestCalled ,': TEST ',iTest,Fail
       nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(2(A,E11.3))') &
     '\n =>  should be ', refreal,' : |y-eval_map(x)|^2= ', checkreal
    END IF !TEST

    q_test(1,:)=(/1.0_wp, 0.0_wp, 0.0_wp/)
    q_test(2,:)=(/0.0_wp, 1.0_wp, 0.0_wp/)
    q_test(3,:)=(/0.0_wp, 0.0_wp, 1.0_wp/)
    DO qdir=1,3
      !check dx/dq^i with FD
      iTest=101+qdir ; IF(testdbg)WRITE(*,*)'iTest=',iTest
      q_in=(/0.0_wp, 0.0_wp, 0.335_wp*PI/)
      x = sf%eval(q_in )
      x_eps = sf%eval(q_in+epsFD*q_test(qdir,:))
      dxdq = sf%eval_dxdq(q_in,q_test(qdir,:))
      checkreal=SQRT(SUM((dxdq - (x_eps-x)/epsFD)**2)/SUM(x*x))
      refreal = 0.0_wp

      IF(testdbg.OR.(.NOT.( ABS(checkreal-refreal).LT. realtolFD))) THEN
         nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(A,2(I4,A))') &
              '\n!! hmap_frenet TEST ID',nTestCalled ,': TEST ',iTest,Fail
         nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(2(A,E11.3),(A,I3))') &
       '\n =>  should be <',realtolFD,' : |dxdqFD-eval_dxdq|= ', checkreal,", dq=",qdir
      END IF !TEST
    END DO

    !! TEST G_ij
    DO idir=1,3; DO jdir=idir,3
      iTest=iTest+1 ; IF(testdbg)WRITE(*,*)'iTest=',iTest
      checkreal= SUM(sf%eval_dxdq(q_in,q_test(idir,:))*sf%eval_dxdq(q_in,q_test(jdir,:)))
      refreal  =sf%eval_gij(q_test(idir,:),q_in,q_test(jdir,:))
      IF(testdbg.OR.(.NOT.( ABS(checkreal-refreal).LT. realtol))) THEN
         nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(A,2(I4,A))') &
              '\n!! hmap_frenet TEST ID',nTestCalled ,': TEST ',iTest,Fail
         nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(2(A,E11.3),2(A,I3))') &
       '\n =>  should be ', refreal,' : sum|Gij-eval_gij|= ', checkreal,', i=',idir,', j=',jdir
      END IF !TEST
    END DO; END DO
    !! TEST dJh_dqk with FD
    DO qdir=1,3
      iTest=iTest+1; IF(testdbg)WRITE(*,*)'iTest=',iTest
      Jh_0    = sf%eval_Jh(   q_in                     )
      Jh_eps  = sf%eval_Jh(   q_in+epsFD*q_test(qdir,:))
      refreal = sf%eval_Jh_dq(q_in                     ,q_test(qdir,:))
      checkreal=(Jh_eps-Jh_0)/epsFD-refreal
      refreal=0.0_wp
      IF(testdbg.OR.(.NOT.( ABS(checkreal-refreal).LT. realtolFD))) THEN
         nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(A,2(I4,A))') &
              '\n!! hmap_frenet TEST ID',nTestCalled ,': TEST ',iTest,Fail
         nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(2(A,E11.3),(A,I3))') &
       '\n =>  should be <', realtolFD,' : |dJh_dqFD-eval_Jh_dq|= ', checkreal,', dq=',qdir
      END IF !TEST
    END DO !qdir
    !! TEST dG_ij_dqk with FD
    DO qdir=1,3
    DO idir=1,3; DO jdir=1,3
      iTest=iTest+1; IF(testdbg)WRITE(*,*)'iTest=',iTest
      gij     = sf%eval_gij(   q_test(idir,:),q_in                     ,q_test(jdir,:))
      gij_eps = sf%eval_gij(   q_test(idir,:),q_in+epsFD*q_test(qdir,:),q_test(jdir,:))
      refreal = sf%eval_gij_dq(q_test(idir,:),q_in                     ,q_test(jdir,:),q_test(qdir,:))
      checkreal=(gij_eps-gij)/epsFD-refreal
      refreal=0.0_wp
      IF(testdbg.OR.(.NOT.( ABS(checkreal-refreal).LT. realtolFD))) THEN
         nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(A,2(I4,A))') &
              '\n!! hmap_frenet TEST ID',nTestCalled ,': TEST ',iTest,Fail
         nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(2(A,E11.3),3(A,I3))') &
       '\n =>  should be <', realtolFD,' : |dGij_dqFD-eval_gij_dq|= ', checkreal,', i=',idir,', j=',jdir,', dq=',qdir
      END IF !TEST
    END DO; END DO
    END DO !qdir

    CALL sf%get_dx_dqi(q_in,dx_dqi(1,:),dx_dqi(2,:),dx_dqi(3,:))
    DO qdir=1,3
      !check dx/dq^i with FD
      iTest=10+qdir ; IF(testdbg)WRITE(*,*)'iTest=',iTest
      dxdq = sf%eval_dxdq(q_in,q_test(qdir,:))
      checkreal=SUM(ABS(dxdq-dx_dqi(qdir,:)))
      refreal=0.0_wp
      IF(testdbg.OR.(.NOT.( ABS(checkreal-refreal).LT. realtol))) THEN
         nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(A,2(I4,A))') &
              '\n!! hmap_frenet TEST ID',nTestCalled ,': TEST ',iTest,Fail
         nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(2(A,E11.3),(A,I3))') &
       '\n =>  should be ', refreal,' : |dxdq-eval_dxdq|= ', checkreal,", dq=",qdir
      END IF !TEST
    END DO !qdir
    CALL sf%get_ddx_dqij(q_in,ddx_dqij(1,1,:),ddx_dqij(1,2,:),ddx_dqij(1,3,:), &
                              ddx_dqij(2,2,:),ddx_dqij(2,3,:),ddx_dqij(3,3,:))
    ddx_dqij(2,1,:)=ddx_dqij(1,2,:)
    ddx_dqij(3,1,:)=ddx_dqij(1,3,:)
    ddx_dqij(3,2,:)=ddx_dqij(2,3,:)
    DO qdir=1,3
      dxdq = sf%eval_dxdq(q_in,q_test(qdir,:))
      DO idir=1,3
        iTest=20+idir+3*(qdir-1) ; IF(testdbg)WRITE(*,*)'iTest=',iTest
        dxdq_eps = sf%eval_dxdq(q_in+epsFD*q_test(idir,:),q_test(qdir,:))
        checkreal=SUM(ABS( (dxdq_eps-dxdq)/epsFD-ddx_dqij(qdir,idir,:)))
        refreal=0.0_wp
        IF(testdbg.OR.(.NOT.( ABS(checkreal-refreal).LT. realtolFD))) THEN
           nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(A,2(I4,A))') &
                '\n!! hmap_frenet TEST ID',nTestCalled ,': TEST ',iTest,Fail
           nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(2(A,E11.3),2(A,I3))') &
         '\n =>  should be <', realtolFD,' : |ddx_dqijFD-eval_ddx_dqij|= ', checkreal,", dqi=",qdir,", dqj=",idir
        END IF !TEST
      END DO !idir
    END DO !qdir

 END IF !testlevel >=1
 IF (testlevel .GE. 2) THEN
  DO idir=1,3
    SELECT CASE(idir)
    CASE(1)
      jdir=2; kdir=3
    CASE(2)
      jdir=1; kdir=3
    CASE(3)
      jdir=1; kdir=2
    END SELECT
    ndims(idir)=nzeta+idir
    ndims(jdir)=ns
    ndims(kdir)=nthet
    ALLOCATE(zeta(ndims(idir)),xv(ndims(idir)))
    DO izeta=1,ndims(idir)
      zeta(izeta)=0.333_wp+REAL(izeta-1,wp)/REAL(ndims(idir)-1,wp)*0.221_wp
      xv(izeta)=hmap_frenet_init_aux(sf,zeta(izeta),.TRUE.)
    END DO
    ALLOCATE(q1(ndims(1),ndims(2),ndims(3)))
    ALLOCATE(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, &
             mold=q1)
    !assign somewhat randomly
    DO k=1,ndims(3); DO j=1,ndims(2); DO i=1,ndims(1)
      q1(i,j,k) = 0.11_wp -0.22_wp *REAL((i+j)*k,wp)/REAL((ndims(idir)+ndims(jdir))*ndims(kdir),wp)
      q2(i,j,k) = 0.15_wp -0.231_wp*REAL((i+k)*j,wp)/REAL((ndims(idir)+ndims(kdir))*ndims(jdir),wp)
      dX1_dt(i,j,k)=-0.1_wp  +0.211_wp*REAL((i+2*j)*k,wp)/REAL((ndims(idir)+2*ndims(jdir))*ndims(kdir),wp)
      dX2_dt(i,j,k)= 0.231_wp-0.116_wp*REAL((2*i+k)*j,wp)/REAL((2*ndims(idir)+ndims(kdir))*ndims(jdir),wp)
      dX1_dz(i,j,k)=-0.024_wp+0.013_wp*REAL((3*i+2*j)*k,wp)/REAL((3*ndims(idir)+2*ndims(jdir))*ndims(kdir),wp)
      dX2_dz(i,j,k)=-0.06_wp +0.031_wp*REAL((2*k+3*k)*i,wp)/REAL((2*ndims(kdir)+3*ndims(kdir))*ndims(idir),wp)
    END DO; END DO; END DO
    CALL sf%eval_all(ndims,idir,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)
    DO k=1,ndims(3); DO j=1,ndims(2); DO i=1,ndims(1)
      ijk=(/i,j,k/)
      izeta=ijk(idir)
      qloc=(/q1(i,j,k),q2(i,j,k),zeta(izeta)/)
      q_thet=(/dX1_dt(i,j,k),dX2_dt(i,j,k),0.0_wp/)
      q_zeta=(/dX1_dz(i,j,k),dX2_dz(i,j,k),1.0_wp/)
      Jh(i,j,k)       =Jh(i,j,k)       - sf%eval_Jh(qloc)
      g_tt(i,j,k)     =g_tt(i,j,k)     - sf%eval_gij(q_thet,qloc,q_thet)
      g_tz(i,j,k)     =g_tz(i,j,k)     - sf%eval_gij(q_thet,qloc,q_zeta)
      g_zz(i,j,k)     =g_zz(i,j,k)     - sf%eval_gij(q_zeta,qloc,q_zeta)
      Jh_dq1(i,j,k)   =Jh_dq1(i,j,k)   - sf%eval_Jh_dq(qloc,(/1.0_wp,0.0_wp,0.0_wp/))
      Jh_dq2(i,j,k)   =Jh_dq2(i,j,k)   - sf%eval_Jh_dq(qloc,(/0.0_wp,1.0_wp,0.0_wp/))
      g_tt_dq1(i,j,k) =g_tt_dq1(i,j,k) - sf%eval_gij_dq(q_thet,qloc,q_thet,(/1.0_wp,0.0_wp,0.0_wp/))
      g_tt_dq2(i,j,k) =g_tt_dq2(i,j,k) - sf%eval_gij_dq(q_thet,qloc,q_thet,(/0.0_wp,1.0_wp,0.0_wp/))
      g_tz_dq1(i,j,k) =g_tz_dq1(i,j,k) - sf%eval_gij_dq(q_thet,qloc,q_zeta,(/1.0_wp,0.0_wp,0.0_wp/))
      g_tz_dq2(i,j,k) =g_tz_dq2(i,j,k) - sf%eval_gij_dq(q_thet,qloc,q_zeta,(/0.0_wp,1.0_wp,0.0_wp/))
      g_zz_dq1(i,j,k) =g_zz_dq1(i,j,k) - sf%eval_gij_dq(q_zeta,qloc,q_zeta,(/1.0_wp,0.0_wp,0.0_wp/))
      g_zz_dq2(i,j,k) =g_zz_dq2(i,j,k) - sf%eval_gij_dq(q_zeta,qloc,q_zeta,(/0.0_wp,1.0_wp,0.0_wp/))
      g_t1(i,j,k)     =g_t1(i,j,k)     - sf%eval_gij(q_thet,qloc,(/1.0_wp,0.0_wp,0.0_wp/))
      g_t2(i,j,k)     =g_t2(i,j,k)     - sf%eval_gij(q_thet,qloc,(/0.0_wp,1.0_wp,0.0_wp/))
      g_z1(i,j,k)     =g_z1(i,j,k)     - sf%eval_gij(q_zeta,qloc,(/1.0_wp,0.0_wp,0.0_wp/))
      g_z2(i,j,k)     =g_z2(i,j,k)     - sf%eval_gij(q_zeta,qloc,(/0.0_wp,1.0_wp,0.0_wp/))
      Gh11(i,j,k)     =Gh11(i,j,k)     - sf%eval_gij((/1.0_wp,0.0_wp,0.0_wp/),qloc,(/1.0_wp,0.0_wp,0.0_wp/))
      Gh22(i,j,k)     =Gh22(i,j,k)     - sf%eval_gij((/0.0_wp,1.0_wp,0.0_wp/),qloc,(/0.0_wp,1.0_wp,0.0_wp/))
    END DO; END DO; END DO

    iTest=201+20*idir ; IF(testdbg)WRITE(*,*)'iTest=',iTest
    checkreal=SUM(ABS(Jh))/REAL(PRODUCT(ndims),wp)
    refreal=0.0_wp
    IF(testdbg.OR.(.NOT.( ABS(checkreal-refreal).LT. realtol))) THEN
      nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(A,2(I4,A))') &
           '\n!! hmap_frenet TEST ID',nTestCalled ,': TEST ',iTest,Fail
      nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(2(A,E11.3),A,I4)') &
    '\n =>  should be ', refreal,' : |sum(|Jh_all-eval_Jh(xall)|)|= ', checkreal, " ,idir=",idir
    END IF

    iTest=202+20*idir ; IF(testdbg)WRITE(*,*)'iTest=',iTest
    checkreal=SUM(ABS(g_tt))/REAL(PRODUCT(ndims),wp)
    refreal=0.0_wp
    IF(testdbg.OR.(.NOT.( ABS(checkreal-refreal).LT. realtol))) THEN
      nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(A,2(I4,A))') &
           '\n!! hmap_frenet TEST ID',nTestCalled ,': TEST ',iTest,Fail
      nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(2(A,E11.3),A,I4)') &
    '\n =>  should be ', refreal,' : |sum(|g_tt_all-eval_g_tt(xall)|)|= ', checkreal, " ,idir=",idir
    END IF

    iTest=203+20*idir ; IF(testdbg)WRITE(*,*)'iTest=',iTest
    checkreal=SUM(ABS(g_tz))/REAL(PRODUCT(ndims),wp)
    refreal=0.0_wp
    IF(testdbg.OR.(.NOT.( ABS(checkreal-refreal).LT. realtol))) THEN
      nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(A,2(I4,A))') &
           '\n!! hmap_frenet TEST ID',nTestCalled ,': TEST ',iTest,Fail
      nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(2(A,E11.3),A,I4)') &
    '\n =>  should be ', refreal,' : |sum(|g_tz_all-eval_g_tz(xall)|)|= ', checkreal, " ,idir=",idir
    END IF

    iTest=203+20*idir ; IF(testdbg)WRITE(*,*)'iTest=',iTest
    checkreal=SUM(ABS(g_zz))/REAL(PRODUCT(ndims),wp)
    refreal=0.0_wp
    IF(testdbg.OR.(.NOT.( ABS(checkreal-refreal).LT. realtol))) THEN
      nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(A,2(I4,A))') &
           '\n!! hmap_frenet TEST ID',nTestCalled ,': TEST ',iTest,Fail
      nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(2(A,E11.3),A,I4)') &
    '\n =>  should be ', refreal,' : |sum(|g_zz_all-eval_g_zz(xall)|)|= ', checkreal, " ,idir=",idir
    END IF

    iTest=204+20*idir ; IF(testdbg)WRITE(*,*)'iTest=',iTest
    checkreal=SUM(ABS(Jh_dq1))/REAL(PRODUCT(ndims),wp)
    refreal=0.0_wp
    IF(testdbg.OR.(.NOT.( ABS(checkreal-refreal).LT. realtol))) THEN
      nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(A,2(I4,A))') &
           '\n!! hmap_frenet TEST ID',nTestCalled ,': TEST ',iTest,Fail
      nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(2(A,E11.3),A,I4)') &
    '\n =>  should be ', refreal,' : |sum(|Jh_dq1_all-eval_Jh_dq1(xall)|)|= ', checkreal, " ,idir=",idir
    END IF

    iTest=205+20*idir ; IF(testdbg)WRITE(*,*)'iTest=',iTest
    checkreal=SUM(ABS(Jh_dq2))/REAL(PRODUCT(ndims),wp)
    refreal=0.0_wp
    IF(testdbg.OR.(.NOT.( ABS(checkreal-refreal).LT. realtol))) THEN
      nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(A,2(I4,A))') &
           '\n!! hmap_frenet TEST ID',nTestCalled ,': TEST ',iTest,Fail
      nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(2(A,E11.3),A,I4)') &
    '\n =>  should be ', refreal,' : |sum(|Jh_dq2_all-eval_Jh_dq2(xall)|)|= ', checkreal, " ,idir=",idir
    END IF

    iTest=206+20*idir ; IF(testdbg)WRITE(*,*)'iTest=',iTest
    checkreal=SUM(ABS(g_tt_dq1))/REAL(PRODUCT(ndims),wp)
    refreal=0.0_wp
    IF(testdbg.OR.(.NOT.( ABS(checkreal-refreal).LT. realtol))) THEN
      nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(A,2(I4,A))') &
           '\n!! hmap_frenet TEST ID',nTestCalled ,': TEST ',iTest,Fail
      nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(2(A,E11.3),A,I4)') &
    '\n =>  should be ', refreal,' : |sum(|g_tt_dq1_all-eval_g_tt_dq1(xall)|)|= ', checkreal, " ,idir=",idir
    END IF

    iTest=207+20*idir ; IF(testdbg)WRITE(*,*)'iTest=',iTest
    checkreal=SUM(ABS(g_tz_dq1))/REAL(PRODUCT(ndims),wp)
    refreal=0.0_wp
    IF(testdbg.OR.(.NOT.( ABS(checkreal-refreal).LT. realtol))) THEN
      nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(A,2(I4,A))') &
           '\n!! hmap_frenet TEST ID',nTestCalled ,': TEST ',iTest,Fail
      nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(2(A,E11.3),A,I4)') &
    '\n =>  should be ', refreal,' : |sum(|g_tz_dq1_all-eval_g_tz_dq1(xall)|)|= ', checkreal, " ,idir=",idir
    END IF

    iTest=208+20*idir ; IF(testdbg)WRITE(*,*)'iTest=',iTest
    checkreal=SUM(ABS(g_zz_dq1))/REAL(PRODUCT(ndims),wp)
    refreal=0.0_wp
    IF(testdbg.OR.(.NOT.( ABS(checkreal-refreal).LT. realtol))) THEN
      nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(A,2(I4,A))') &
           '\n!! hmap_frenet TEST ID',nTestCalled ,': TEST ',iTest,Fail
      nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(2(A,E11.3),A,I4)') &
    '\n =>  should be ', refreal,' : |sum(|g_zz_dq1_all-eval_g_zz_dq1(xall)|)|= ', checkreal, " ,idir=",idir
    END IF

    iTest=209+20*idir ; IF(testdbg)WRITE(*,*)'iTest=',iTest
    checkreal=SUM(ABS(g_tt_dq2))/REAL(PRODUCT(ndims),wp)
    refreal=0.0_wp
    IF(testdbg.OR.(.NOT.( ABS(checkreal-refreal).LT. realtol))) THEN
      nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(A,2(I4,A))') &
           '\n!! hmap_frenet TEST ID',nTestCalled ,': TEST ',iTest,Fail
      nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(2(A,E11.3),A,I4)') &
    '\n =>  should be ', refreal,' : |sum(|g_tt_dq2_all-eval_g_tt_dq2(xall)|)|= ', checkreal, " ,idir=",idir
    END IF

    iTest=210+20*idir ; IF(testdbg)WRITE(*,*)'iTest=',iTest
    checkreal=SUM(ABS(g_tz_dq2))/REAL(PRODUCT(ndims),wp)
    refreal=0.0_wp
    IF(testdbg.OR.(.NOT.( ABS(checkreal-refreal).LT. realtol))) THEN
      nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(A,2(I4,A))') &
           '\n!! hmap_frenet TEST ID',nTestCalled ,': TEST ',iTest,Fail
      nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(2(A,E11.3),A,I4)') &
    '\n =>  should be ', refreal,' : |sum(|g_tz_dq2_all-eval_g_tz_dq2(xall)|)|= ', checkreal, " ,idir=",idir
    END IF

    iTest=211+20*idir ; IF(testdbg)WRITE(*,*)'iTest=',iTest
    checkreal=SUM(ABS(g_zz_dq2))/REAL(PRODUCT(ndims),wp)
    refreal=0.0_wp
    IF(testdbg.OR.(.NOT.( ABS(checkreal-refreal).LT. realtol))) THEN
      nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(A,2(I4,A))') &
           '\n!! hmap_frenet TEST ID',nTestCalled ,': TEST ',iTest,Fail
      nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(2(A,E11.3),A,I4)') &
    '\n =>  should be ', refreal,' : |sum(|g_zz_dq2_all-eval_g_zz_dq2(xall)|)|= ', checkreal, " ,idir=",idir
    END IF

    iTest=212+20*idir ; IF(testdbg)WRITE(*,*)'iTest=',iTest
    checkreal=SUM(ABS(g_t1))/REAL(PRODUCT(ndims),wp)
    refreal=0.0_wp
    IF(testdbg.OR.(.NOT.( ABS(checkreal-refreal).LT. realtol))) THEN
      nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(A,2(I4,A))') &
           '\n!! hmap_frenet TEST ID',nTestCalled ,': TEST ',iTest,Fail
      nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(2(A,E11.3),A,I4)') &
    '\n =>  should be ', refreal,' : |sum(|g_t1_all-eval_g_t1(xall)|)|= ', checkreal, " ,idir=",idir
    END IF

    iTest=213+20*idir ; IF(testdbg)WRITE(*,*)'iTest=',iTest
    checkreal=SUM(ABS(g_t2))/REAL(PRODUCT(ndims),wp)
    refreal=0.0_wp
    IF(testdbg.OR.(.NOT.( ABS(checkreal-refreal).LT. realtol))) THEN
      nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(A,2(I4,A))') &
           '\n!! hmap_frenet TEST ID',nTestCalled ,': TEST ',iTest,Fail
      nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(2(A,E11.3),A,I4)') &
    '\n =>  should be ', refreal,' : |sum(|g_t2_all-eval_g_t2(xall)|)|= ', checkreal, " ,idir=",idir
    END IF

    iTest=214+20*idir ; IF(testdbg)WRITE(*,*)'iTest=',iTest
    checkreal=SUM(ABS(g_z1))/REAL(PRODUCT(ndims),wp)
    refreal=0.0_wp
    IF(testdbg.OR.(.NOT.( ABS(checkreal-refreal).LT. realtol))) THEN
      nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(A,2(I4,A))') &
           '\n!! hmap_frenet TEST ID',nTestCalled ,': TEST ',iTest,Fail
      nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(2(A,E11.3),A,I4)') &
    '\n =>  should be ', refreal,' : |sum(|g_z1_all-eval_g_z1(xall)|)|= ', checkreal, " ,idir=",idir
    END IF

    iTest=215+20*idir ; IF(testdbg)WRITE(*,*)'iTest=',iTest
    checkreal=SUM(ABS(g_z2))/REAL(PRODUCT(ndims),wp)
    refreal=0.0_wp
    IF(testdbg.OR.(.NOT.( ABS(checkreal-refreal).LT. realtol))) THEN
      nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(A,2(I4,A))') &
           '\n!! hmap_frenet TEST ID',nTestCalled ,': TEST ',iTest,Fail
      nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(2(A,E11.3),A,I4)') &
    '\n =>  should be ', refreal,' : |sum(|g_z2_all-eval_g_z2(xall)|)|= ', checkreal, " ,idir=",idir
    END IF

    iTest=216+20*idir ; IF(testdbg)WRITE(*,*)'iTest=',iTest
    checkreal=SUM(ABS(Gh11))/REAL(PRODUCT(ndims),wp)
    refreal=0.0_wp
    IF(testdbg.OR.(.NOT.( ABS(checkreal-refreal).LT. realtol))) THEN
      nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(A,2(I4,A))') &
           '\n!! hmap_frenet TEST ID',nTestCalled ,': TEST ',iTest,Fail
      nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(2(A,E11.3),A,I4)') &
    '\n =>  should be ', refreal,' : |sum(|Gh11_all-eval_Gh11(xall)|)|= ', checkreal, " ,idir=",idir
    END IF

    iTest=217+20*idir ; IF(testdbg)WRITE(*,*)'iTest=',iTest
    checkreal=SUM(ABS(Gh22))/REAL(PRODUCT(ndims),wp)
    refreal=0.0_wp
    IF(testdbg.OR.(.NOT.( ABS(checkreal-refreal).LT. realtol))) THEN
      nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(A,2(I4,A))') &
           '\n!! hmap_frenet TEST ID',nTestCalled ,': TEST ',iTest,Fail
      nfailedMsg=nfailedMsg+1 ; WRITE(testUnit,'(2(A,E11.3),A,I4)') &
    '\n =>  should be ', refreal,' : |sum(|Gh22_all-eval_Gh22(xall)|)|= ', checkreal, " ,idir=",idir
    END IF

    DEALLOCATE(zeta,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)
    DEALLOCATE(xv)
  END DO !idir
END IF

 test_called=.FALSE. ! to prevent infinite loop in this routine


END SUBROUTINE hmap_frenet_test