Subroutine that generates a 2D Gaussian distribution in an elliptic torus as the initial spatial condition of a given particle species in the simulation.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| type(KORC_PARAMS), | intent(inout) | :: | params | Core KORC simulation parameters. |
||
| type(SPECIES), | intent(inout) | :: | spp | An instance of the derived type SPECIES containing all the parameters and simulation variables of the different species in the simulation. |
||
| type(FIELDS), | intent(in) | :: | F | An instance of the KORC derived type FIELDS. |
subroutine MH_psi(params,spp,F)
!! @note Subroutine that generates a 2D Gaussian distribution in an
!! elliptic torus as the initial spatial condition of a given particle
!! species in the simulation. @endnote
TYPE(KORC_PARAMS), INTENT(INOUT) :: params
!! Core KORC simulation parameters.
TYPE(SPECIES), INTENT(INOUT) :: spp
!! An instance of the derived type SPECIES containing all the parameters
!! and simulation variables of the different species in the simulation.
TYPE(FIELDS), INTENT(IN) :: F
!! An instance of the KORC derived type FIELDS.
REAL(rp), DIMENSION(:), ALLOCATABLE :: R_samples,X_samples,Y_samples
!! Major radial location of all samples
REAL(rp), DIMENSION(:), ALLOCATABLE :: PHI_samples
!! Azimuithal angle of all samples
REAL(rp), DIMENSION(:), ALLOCATABLE :: Z_samples
!! Vertical location of all samples
REAL(rp) :: min_R,max_R
REAL(rp) :: min_Z,max_Z
REAL(rp) :: R_buffer
!! Previous sample of R location
REAL(rp) :: Z_buffer
!! Previous sample of Z location
REAL(rp) :: R_test
!! Present sample of R location
REAL(rp) :: Z_test
!! Present sample of Z location
REAL(rp) :: psi_max,psi_max_buff
REAL(rp) :: PSIp_lim,PSIP0,PSIN,PSIN0,PSIN1,sigma,psi0,psi1
REAL(rp) :: rand_unif
!! Uniform random variable [0,1]
REAL(rp) :: ratio
!! MH selection criteria
INTEGER :: nsamples
!! Total number of samples to be distributed over all mpi processes
INTEGER :: ii
!! Sample iterator.
INTEGER :: mpierr
!! mpi error indicator
LOGICAL :: accepted
INTEGER,DIMENSION(33) :: seed=(/1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1/)
if (params%mpi_params%rank.EQ.0_idef) then
write(6,*) '*** START SAMPLING ***'
end if
nsamples = spp%ppp*params%mpi_params%nmpi
psi_max = spp%psi_max
psi_max_buff = spp%psi_max*2._rp
params%GC_coords=.TRUE.
PSIp_lim=F%PSIp_lim
PSIp0=F%PSIP_min
min_R=minval(F%X%R)
max_R=maxval(F%X%R)
min_Z=minval(F%X%Z)
max_Z=maxval(F%X%Z)
sigma=spp%sigmaR*params%cpp%length
!write(6,*) min_R,max_R
!write(6,*) min_Z,max_Z
if (params%mpi_params%rank.EQ.0_idef) then
ALLOCATE(R_samples(nsamples))
ALLOCATE(X_samples(nsamples))
ALLOCATE(Y_samples(nsamples))
! Number of samples to distribute among all MPI processes
ALLOCATE(PHI_samples(nsamples))
! Number of samples to distribute among all MPI processes
ALLOCATE(Z_samples(nsamples))
! Number of samples to distribute among all MPI processes
! Transient !
R_buffer = spp%Ro
Z_buffer = spp%Zo
if (.not.params%SameRandSeed) then
call init_random_seed()
else
call random_seed(put=seed)
end if
accepted=.false.
ii=1_idef
do while (ii .LE. 1000_idef)
if (modulo(ii,100).eq.0) then
write(6,'("Burn: ",I10)') ii
end if
!R_test = R_buffer + random_norm(0.0_rp,spp%dR)
!R_test = R_buffer + get_random_mkl_N(0.0_rp,spp%dR)
R_test = R_buffer + get_random_N()*spp%dR
!Z_test = Z_buffer + random_norm(0.0_rp,spp%dZ)
!Z_test = Z_buffer + get_random_mkl_N(0.0_rp,spp%dZ)
Z_test = Z_buffer + get_random_N()*spp%dZ
do while ((R_test.GT.max_R).OR.(R_test .LT. min_R))
!eta_test = eta_buffer + random_norm(0.0_rp,spp%dth)
!eta_test = eta_buffer + get_random_mkl_N(0.0_rp,spp%dth)
R_test = R_buffer + get_random_N()*spp%dR
end do
do while ((Z_test.GT.max_Z).OR.(Z_test .LT. min_Z))
!eta_test = eta_buffer + random_norm(0.0_rp,spp%dth)
!eta_test = eta_buffer + get_random_mkl_N(0.0_rp,spp%dth)
Z_test = Z_buffer + get_random_N()*spp%dZ
end do
! initialize 2D gaussian argument and distribution function, or
! copy from previous sample
if (ii==1) then
spp%vars%Y(1,1)=R_buffer
spp%vars%Y(1,2)=0
spp%vars%Y(1,3)=Z_buffer
!write(6,*) 'R',R_buffer
!write(6,*) 'Z',Z_buffer
call get_fields(params,spp%vars,F)
psi0=spp%vars%PSI_P(1)
PSIN0=(psi0-PSIp0)/(PSIp_lim-PSIp0)
end if
if (accepted) then
PSIN0=PSIN1
end if
! psi1=PSI_ROT_exp(R_test,spp%Ro,spp%sigmaR,Z_test,spp%Zo, &
! spp%sigmaZ,theta_rad)
spp%vars%Y(1,1)=R_test
spp%vars%Y(1,2)=0._rp
spp%vars%Y(1,3)=Z_test
call get_fields(params,spp%vars,F)
psi1=spp%vars%PSI_P(1)
PSIN1=(psi1-PSIp0)/(PSIp_lim-PSIp0)
!write(6,*) 'R',R_test
!write(6,*) 'Z',Z_test
!write(6,*) 'PSIlim',PSIp_lim
!write(6,*) 'PSI0',PSIp0
!write(6,*) 'PSI1',psi1
!write(6,*) 'PSI0',psi0
!write(6,*) 'PSIN1',PSIN1
!write(6,*) 'PSIN0',PSIN0
! Calculate acceptance ratio for MH algorithm. fRE function
! incorporates p^2 factor of spherical coordinate Jacobian
! for velocity phase space, factors of sin(pitch angle) for velocity
! phase space and cylindrical coordinate Jacobian R for spatial
! phase space incorporated here.
ratio = indicator(PSIN1,psi_max)* &
R_test*EXP(-PSIN1/sigma)/ &
(R_buffer*EXP(-PSIN0/sigma))
! ratio = f1*sin(deg2rad(eta_test))/(f0*sin(deg2rad(eta_buffer)))
accepted=.false.
if (ratio .GE. 1.0_rp) then
accepted=.true.
R_buffer = R_test
Z_buffer = Z_test
ii = ii + 1_idef
else
! call RANDOM_NUMBER(rand_unif)
! if (rand_unif .LT. ratio) then
!if (get_random_mkl_U() .LT. ratio) then
if (get_random_U() .LT. ratio) then
accepted=.true.
R_buffer = R_test
Z_buffer = Z_test
ii = ii + 1_idef
end if
end if
end do
! Transient !
ii=1_idef
do while (ii .LE. nsamples)
! write(6,'("sample:",I15)') ii
if (modulo(ii,nsamples/10).eq.0) then
write(6,'("Sample: ",I10)') ii
end if
!R_test = R_buffer + random_norm(0.0_rp,spp%dR)
!R_test = R_buffer + get_random_mkl_N(0.0_rp,spp%dR)
R_test = R_buffer + get_random_N()*spp%dR
!Z_test = Z_buffer + random_norm(0.0_rp,spp%dZ)
!Z_test = Z_buffer + get_random_mkl_N(0.0_rp,spp%dZ)
Z_test = Z_buffer + get_random_N()*spp%dZ
do while ((R_test.GT.max_R).OR.(R_test .LT. min_R))
!eta_test = eta_buffer + random_norm(0.0_rp,spp%dth)
!eta_test = eta_buffer + get_random_mkl_N(0.0_rp,spp%dth)
R_test = R_buffer + get_random_N()*spp%dR
end do
do while ((Z_test.GT.max_Z).OR.(Z_test .LT. min_Z))
!eta_test = eta_buffer + random_norm(0.0_rp,spp%dth)
!eta_test = eta_buffer + get_random_mkl_N(0.0_rp,spp%dth)
Z_test = Z_buffer + get_random_N()*spp%dZ
end do
if (accepted) then
PSIN0=PSIN1
end if
! psi1=PSI_ROT_exp(R_test,spp%Ro,spp%sigmaR,Z_test,spp%Zo, &
! spp%sigmaZ,theta_rad)
spp%vars%Y(1,1)=R_test
spp%vars%Y(1,2)=0
spp%vars%Y(1,3)=Z_test
call get_fields(params,spp%vars,F)
psi1=spp%vars%PSI_P(1)
PSIN1=(psi1-PSIp0)/(PSIp_lim-PSIp0)
!write(6,*) 'R',R_test
!write(6,*) 'Z',Z_test
!write(6,*) 'PSIlim',PSIp_lim
!write(6,*) 'PSI0',PSIp0
!write(6,*) 'PSI1',psi1
!write(6,*) 'PSI0',psi0
!write(6,*) 'PSIN1',PSIN1
!write(6,*) 'PSIN0',PSIN0
ratio = indicator(PSIN1,psi_max_buff)* &
R_test*EXP(-PSIN1/sigma)/ &
(R_buffer*EXP(-PSIN0/sigma))
! ratio = f1*sin(deg2rad(eta_test))/(f0*sin(deg2rad(eta_buffer)))
accepted=.false.
if (ratio .GE. 1.0_rp) then
accepted=.true.
R_buffer = R_test
Z_buffer = Z_test
else
!call RANDOM_NUMBER(rand_unif)
!if (rand_unif .LT. ratio) then
!if (get_random_mkl_U() .LT. ratio) then
if (get_random_U() .LT. ratio) then
accepted=.true.
R_buffer = R_test
Z_buffer = Z_test
end if
end if
! write(6,'("R: ",E17.10)') R_buffer
! write(6,'("Z: ",E17.10)') Z_buffer
! Only accept sample if it is within desired boundary, but
! add to MC above if within buffer. This helps make the boundary
! more defined.
IF ((INT(indicator(PSIN1,psi_max)).EQ.1).AND. &
ACCEPTED) THEN
R_samples(ii) = R_buffer
Z_samples(ii) = Z_buffer
! write(6,*) 'RS',R_buffer
! Sample phi location uniformly
!call RANDOM_NUMBER(rand_unif)
!PHI_samples(ii) = 2.0_rp*C_PI*rand_unif
!PHI_samples(ii) = 2.0_rp*C_PI*get_random_mkl_U()
PHI_samples(ii) = 2.0_rp*C_PI*get_random_U()
ii = ii + 1_idef
END IF
end do
! if (minval(R_samples(:)).lt.1._rp/params%cpp%length) stop 'error with sample'
! write(6,'("R_sample: ",E17.10)') R_samples(:)*params%cpp%length
X_samples=R_samples*cos(PHI_samples)
Y_samples=R_samples*sin(PHI_samples)
! write(6,*) 'R_samples',R_samples
! write(6,*) 'PHI_samples',PHI_samples
! write(6,*) 'Z_samples',Z_samples
! write(6,*) 'G_samples',G_samples
! write(6,*) 'eta_samples',eta_samples
end if
params%GC_coords=.FALSE.
call MPI_BARRIER(MPI_COMM_WORLD,mpierr)
CALL MPI_SCATTER(X_samples,spp%ppp,MPI_REAL8, &
spp%vars%X(:,1),spp%ppp,MPI_REAL8,0,MPI_COMM_WORLD,mpierr)
CALL MPI_SCATTER(Y_samples,spp%ppp,MPI_REAL8, &
spp%vars%X(:,2),spp%ppp,MPI_REAL8,0,MPI_COMM_WORLD,mpierr)
CALL MPI_SCATTER(Z_samples,spp%ppp,MPI_REAL8, &
spp%vars%X(:,3),spp%ppp,MPI_REAL8,0,MPI_COMM_WORLD,mpierr)
call MPI_BARRIER(MPI_COMM_WORLD,mpierr)
if (params%orbit_model(1:2).eq.'GC') call cart_to_cyl(spp%vars%X,spp%vars%Y)
if (params%mpi_params%rank.EQ.0_idef) then
DEALLOCATE(R_samples)
DEALLOCATE(X_samples)
DEALLOCATE(Y_samples)
DEALLOCATE(Z_samples)
DEALLOCATE(PHI_samples)
end if
end subroutine MH_psi