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|
! Copyright (C) 2005 Barbara Ercolano
!
! Version 2.02
module pathIntegration_mod
use common_mod
use interpolation_mod
use vector_mod
contains
! This subroutine performs the integration of opacities from a position
! aVec to the edge of the nebula in the arbitrary direction uHat
subroutine integratePathTau(grid, aVec, uHat, freq, nTau, absTau, lambda)
implicit none
type(grid_type), intent(in) :: grid(*) ! grid
type(vector), intent(in) :: uHat ! direction vector
type(vector), intent(in) :: aVec ! starting position vector
integer, intent(out) :: nTau ! actual size of opacity and length arrays
real, intent(in) :: freq ! the frequency [Hz]
real, intent(out), &
& dimension(maxTau) :: absTau ! absorption optical depth
real, intent(out), &
& dimension(maxTau) :: lambda ! distance array
! local variables
type(vector) :: rVec ! position vector
type(vector) :: vHat ! direction vector
integer :: freqP ! frequency index
integer :: i ! counter
integer :: xP, yP, zP ! x, y, and z axis indeces
integer, parameter :: nl = 4 ! defines the size of the distance increment
real :: dlSmall ! distance increment
if (nGrids>1) then
print*, 'integratePathTau: tau integration routine still not developed for multiple grids... returning '
return
end if
! locate the input frequency in the frequency array
call locate(nuArray(1:nbins), freq, freqP)
if (freqP<=0 .or. freqP>nbins) then
print*, "! integratePathTau: out of bounds frequency ", freqP, freq, nuArray(1), nuArray(nbins)
print*, nuArray
stop
end if
! locate the starting position in the cartesian grid
call locate(grid(1)%xAxis, aVec%x, xP)
if ( xP < grid(1)%nx ) then
if ( aVec%x >= (grid(1)%xAxis(xP)+ &
& grid(1)%xAxis(xP+1))/2. ) xP = xP+1
end if
call locate(grid(1)%yAxis, aVec%y, yP)
if ( yP < grid(1)%ny ) then
if ( aVec%y >= (grid(1)%yAxis(yP)+ &
& grid(1)%yAxis(yP+1))/2. ) yP = yP+1
end if
call locate(grid(1)%zAxis, aVec%z, zP)
if ( zP < grid(1)%nz ) then
if ( aVec%z >= (grid(1)%zAxis(zP)+ &
& grid(1)%zAxis(zP+1))/2. ) zP = zP+1
end if
! check that the input position is not outside the grid
if ( (xP <= 0).or.(xP > grid(1)%nx) ) then
print*, "! integratePathTau: starting position in x is outside the grid",xP,yP,zP
stop
else if ( (yP <= 0).or.(yP > grid(1)%ny) ) then
print*, "! integratePathTau: starting position in y is outside the grid",xP,yP,zP
stop
else if ( (zP <= 0).or.(zP > grid(1)%nz) ) then
print*, "! integratePathTau: starting position in z is outside the grid",xP,yP,zP
stop
end if
! define dlSmall
dlSmall = dl(1)
! initialize the optical depth arrays
absTau = 0.
lambda = 0.
! initialize nTau
nTau = 1
! initialize direction vactor
vHat = uHat
! the first optical depth are all zero (as displacement is zero)
! these have already been set to zero in the initialization of the arrays
! so add the first displacements vector (dlSmall*vHat)
rVec = aVec + dlSmall*vHat
! execute this loop until the edge of the grid is reached
do i = 1, maxTau
! check if the path is still within the ionized region
if (rVec%x > grid(1)%xAxis(grid(1)%nx)) exit
if (rVec%y > grid(1)%yAxis(grid(1)%ny)) exit
if (rVec%z > grid(1)%zAxis(grid(1)%nz)) exit
if ( sqrt( (rvec%x/1.e10)**2 + (rvec%y/1.e10)**2 + (rvec%z/1.e10)**2)*1.e10 >= R_out &
& .and. R_out > 0.) exit
if (lgSymmetricXYZ) then
if( rVec%x < grid(1)%xAxis(1) ) then
vHat%x = -vHat%x
rVec%x = -rVec%x
call locate(grid(1)%xAxis, rVec%x, xP)
end if
if( rVec%y < grid(1)%yAxis(1) ) then
vHat%y = -vHat%y
rVec%y = -rVec%y
call locate(grid(1)%yAxis, rVec%y, yP)
end if
if( rVec%z < grid(1)%zAxis(1) ) then
vHat%z = -vHat%z
rVec%z = -rVec%z
call locate(grid(1)%zAxis, rVec%z, zP)
end if
end if
! x-axis
if (xP < grid(1)%nx) then
if ( rVec%x > (grid(1)%xAxis(xP)+grid(1)%xAxis(xP+1))/2. ) then
xP = xP + 1
end if
else if (xP == grid(1)%nx) then
if ( rVec%x > grid(1)%xAxis(xP) ) exit
end if
if (xP > 1) then
if ( rVec%x < (grid(1)%xAxis(xP)+grid(1)%xAxis(xP-1))/2. ) then
xP = xP - 1
end if
end if
! y-axis
if (yP < grid(1)%ny) then
if ( rVec%y > (grid(1)%yAxis(yP)+grid(1)%yAxis(yP+1))/2. ) then
yP = yP + 1
end if
else if (yP == grid(1)%ny) then
if (rVec%y > grid(1)%yAxis(yP)) exit
end if
if (yP > 1) then
if ( rVec%y < (grid(1)%yAxis(yP)+grid(1)%yAxis(yP-1))/2. ) then
yP = yP - 1
end if
end if
! z-axis
if (zP < grid(1)%nz) then
if ( rVec%z > (grid(1)%zAxis(zP)+grid(1)%zAxis(zP+1))/2. ) then
zP = zP + 1
end if
else if (zP == grid(1)%nz) then
if (rVec%z > grid(1)%zAxis(zP)) exit
end if
if (zP > 1) then
if ( rVec%z < (grid(1)%zAxis(zP)+grid(1)%zAxis(zP-1))/2. ) then
zP = zP - 1
end if
end if
if (.not.lgSymmetricXYZ) then
if ((xP < 1) .or. (zP < 1) .or. (yP < 1)) exit
end if
! check if there's any symmetries and if the path must be reflected
if (lgSymmetricXYZ) then
if (xP<1) then
vHat%x=-vHat%x
rVec%x=-rVec%x
call locate(grid(1)%xAxis, rVec%x, xP)
if (xP < grid(1)%nx) then
if ( rVec%x > (grid(1)%xAxis(xP)+grid(1)%xAxis(xP+1))/2. ) xP = xP + 1
else if (xP == grid(1)%nx) then
if (rVec%x > grid(1)%xAxis(xP)) exit
end if
end if
if (yP<1) then
vHat%y=-vHat%y
rVec%y=-rVec%y
call locate(grid(1)%yAxis, rVec%y, yP)
if (yP < grid(1)%ny) then
if ( rVec%y > (grid(1)%yAxis(yP)+grid(1)%yAxis(yP+1))/2. ) yP = yP + 1
else if (yP == grid(1)%ny) then
if (rVec%y > grid(1)%yAxis(yP)) exit
end if
end if
if (zP<1) then
vHat%z=-vHat%z
rVec%z=-rVec%z
call locate(grid(1)%zAxis, rVec%z, zP)
if (zP < grid(1)%nz) then
if ( rVec%z > (grid(1)%zAxis(zP)+grid(1)%zAxis(zP+1))/2. ) zP = zP + 1
else if (zP == grid(1)%nz) then
if (rVec%z > grid(1)%zAxis(zP)) exit
end if
end if
end if
! increment nTau
nTau = nTau + 1
! this should never happen (as the loop is stopped at maxTau anyway)
! just a sanity check
if (nTau > maxTau) then
print*, "! integratePathTau: tau arrays are full", xP,yP,zP
exit
end if
! add the delta optical depths
absTau(nTau) = absTau(nTau-1) + grid(1)%opacity(grid(1)%active(xP,yP,zP),freqP)*dlSmall
lambda(nTau) = lambda(nTau-1) + dlSmall
! increment position by adding the displacements vector (dlSmall*vHat)
rVec = rVec + dlSmall*vHat
end do
end subroutine integratePathTau
! This subroutine performs the integration of opacities from a position
! aVec to the edge of the nebula in the arbitrary direction uHat
subroutine integratePathTauNu(grid, aVec, uHat, freqP, absTau)
implicit none
type(grid_type), intent(in) :: grid(*) ! grid
type(vector), intent(in) :: uHat ! direction vector
type(vector), intent(in) :: aVec ! starting position vector
real, intent(out) :: absTau ! extinction optical depth
! local variables
type(vector) :: rVec ! position vector
type(vector) :: vHat ! direction vector
integer, intent(in) :: freqP ! the frequency index
integer :: i ! counter
integer :: xP, yP, zP ! x, y, and z axis indeces
real :: dlSmall ! distance increment
if (nGrids>1) then
print*, 'integratePathTau: tau integration routine still not developed for multiple grids... returning '
return
end if
! locate the starting position in the cartesian grid
call locate(grid(1)%xAxis, aVec%x, xP)
if ( xP < grid(1)%nx ) then
if ( aVec%x >= (grid(1)%xAxis(xP)+ &
& grid(1)%xAxis(xP+1))/2. ) xP = xP+1
end if
call locate(grid(1)%yAxis, aVec%y, yP)
if ( yP < grid(1)%ny ) then
if ( aVec%y >= (grid(1)%yAxis(yP)+ &
& grid(1)%yAxis(yP+1))/2. ) yP = yP+1
end if
call locate(grid(1)%zAxis, aVec%z, zP)
if ( zP < grid(1)%nz ) then
if ( aVec%z >= (grid(1)%zAxis(zP)+ &
& grid(1)%zAxis(zP+1))/2. ) zP = zP+1
end if
! check that the input position is not outside the grid
if ( (xP <= 0).or.(xP > grid(1)%nx) ) then
print*, "! integratePathTau: starting position in x is outside the grid",xP,yP,zP
stop
else if ( (yP <= 0).or.(yP > grid(1)%ny) ) then
print*, "! integratePathTau: starting position in y is outside the grid",xP,yP,zP
stop
else if ( (zP <= 0).or.(zP > grid(1)%nz) ) then
print*, "! integratePathTau: starting position in z is outside the grid",xP,yP,zP
stop
end if
dlSmall = 0.
if (uHat%x > 0.) then
! find linear increment
dlSmall = abs(grid(1)%xAxis(2) - grid(1)%xAxis(1))
do i = 2, grid(1)%nx-1
dlSmall = min(dlSmall, abs(grid(1)%xAxis(i+1)-grid(1)%xAxis(i)) )
end do
end if
if (uHat%y > 0.) then
if (dlSmall <= 0.) then
! find linear increment
dlSmall = abs(grid(1)%yAxis(2) - grid(1)%yAxis(1))
do i = 2, grid(1)%ny-1
dlSmall = min(dlSmall, abs(grid(1)%yAxis(i+1)-grid(1)%yAxis(i)) )
end do
else
! find linear increment
do i = 1, grid(1)%ny-1
dlSmall = min(dlSmall, abs(grid(1)%yAxis(i+1)-grid(1)%yAxis(i)) )
end do
end if
end if
if (uHat%z > 0.) then
if (dlSmall <= 0.) then
! find linear increment
dlSmall = abs(grid(1)%zAxis(2) - grid(1)%zAxis(1))
do i = 2, grid(1)%nz-1
dlSmall = min(dlSmall, abs(grid(1)%zAxis(i+1)-grid(1)%zAxis(i)) )
end do
else
! find linear increment
do i = 1, grid(1)%nz-1
dlSmall = min(dlSmall, abs(grid(1)%zAxis(i+1)-grid(1)%zAxis(i)) )
end do
end if
end if
dlSmall = dlSmall/2.
! initialize the optical depth arrays
absTau = 0.
! initialize direction vector
vHat = uHat
! the first optical depth are all zero (as displacement is zero)
! these have already been set to zero in the initialization of the arrays
! so add the first displacements vector (dlSmall*vHat)
rVec = aVec + dlSmall*vHat
! execute this loop until the edge of the grid is reached
do i = 1, maxTau
! check if the path is still within the ionized region
if (rVec%x > grid(1)%xAxis(grid(1)%nx)) exit
if (rVec%y > grid(1)%yAxis(grid(1)%ny)) exit
if (rVec%z > grid(1)%zAxis(grid(1)%nz)) exit
if ( sqrt( (rvec%x/1.e10)**2 + (rvec%y/1.e10)**2 + (rvec%z/1.e10)**2)*1.e10 >= R_out &
& .and. R_out > 0.) exit
if (lgSymmetricXYZ) then
if( rVec%x < grid(1)%xAxis(1) ) then
vHat%x = -vHat%x
rVec%x = -rVec%x
call locate(grid(1)%xAxis, rVec%x, xP)
end if
if( rVec%y < grid(1)%yAxis(1) ) then
vHat%y = -vHat%y
rVec%y = -rVec%y
call locate(grid(1)%yAxis, rVec%y, yP)
end if
if( rVec%z < grid(1)%zAxis(1) ) then
vHat%z = -vHat%z
rVec%z = -rVec%z
call locate(grid(1)%zAxis, rVec%z, zP)
end if
end if
! x-axis
if (xP < grid(1)%nx) then
if ( rVec%x > (grid(1)%xAxis(xP)+grid(1)%xAxis(xP+1))/2. ) then
xP = xP + 1
end if
else if (xP == grid(1)%nx) then
if ( rVec%x > grid(1)%xAxis(xP) ) exit
end if
if (xP > 1) then
if ( rVec%x < (grid(1)%xAxis(xP)+grid(1)%xAxis(xP-1))/2. ) then
xP = xP - 1
end if
end if
! y-axis
if (yP < grid(1)%ny) then
if ( rVec%y > (grid(1)%yAxis(yP)+grid(1)%yAxis(yP+1))/2. ) then
yP = yP + 1
end if
else if (yP == grid(1)%ny) then
if (rVec%y > grid(1)%yAxis(yP)) exit
end if
if (yP > 1) then
if ( rVec%y < (grid(1)%yAxis(yP)+grid(1)%yAxis(yP-1))/2. ) then
yP = yP - 1
end if
end if
! z-axis
if (zP < grid(1)%nz) then
if ( rVec%z > (grid(1)%zAxis(zP)+grid(1)%zAxis(zP+1))/2. ) then
zP = zP + 1
end if
else if (zP == grid(1)%nz) then
if (rVec%z > grid(1)%zAxis(zP)) exit
end if
if (zP > 1) then
if ( rVec%z < (grid(1)%zAxis(zP)+grid(1)%zAxis(zP-1))/2. ) then
zP = zP - 1
end if
end if
if (.not.lgSymmetricXYZ) then
if ((xP < 1) .or. (zP < 1) .or. (yP < 1)) exit
end if
! check if there's any symmetries and if the path must be reflected
if (lgSymmetricXYZ) then
if (xP<1) then
vHat%x=-vHat%x
rVec%x=-rVec%x
call locate(grid(1)%xAxis, rVec%x, xP)
if (xP < grid(1)%nx) then
if ( rVec%x > (grid(1)%xAxis(xP)+grid(1)%xAxis(xP+1))/2. ) xP = xP + 1
else if (xP == grid(1)%nx) then
if (rVec%x > grid(1)%xAxis(xP)) exit
end if
end if
if (yP<1) then
vHat%y=-vHat%y
rVec%y=-rVec%y
call locate(grid(1)%yAxis, rVec%y, yP)
if (yP < grid(1)%ny) then
if ( rVec%y > (grid(1)%yAxis(yP)+grid(1)%yAxis(yP+1))/2. ) yP = yP + 1
else if (yP == grid(1)%ny) then
if (rVec%y > grid(1)%yAxis(yP)) exit
end if
end if
if (zP<1) then
vHat%z=-vHat%z
rVec%z=-rVec%z
call locate(grid(1)%zAxis, rVec%z, zP)
if (zP < grid(1)%nz) then
if ( rVec%z > (grid(1)%zAxis(zP)+grid(1)%zAxis(zP+1))/2. ) zP = zP + 1
else if (zP == grid(1)%nz) then
if (rVec%z > grid(1)%zAxis(zP)) exit
end if
end if
end if
! add the delta optical depths
absTau = absTau + grid(1)%opacity(grid(1)%active(xP,yP,zP),freqP)*dlSmall
! increment position by adding the displacements vector (dlSmall*vHat)
rVec = rVec + dlSmall*vHat
end do
end subroutine integratePathTauNu
end module pathIntegration_mod
|
