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c
c
c ###################################################
c ## COPYRIGHT (C) 1990 by Jay William Ponder ##
c ## All Rights Reserved ##
c ###################################################
c
c ################################################################
c ## ##
c ## subroutine image -- compute the minimum image distance ##
c ## ##
c ################################################################
c
c
c "image" takes the components of pairwise distance between
c two points in a periodic box and converts to the components
c of the minimum image distance
c
c literature reference:
c
c U. K. Deiters, "Efficient Coding of the Minimum Image Convention",
c Zeitschrift fur Physikalische Chemie, 227, 345-352 (2013)
c
c note the "do while" clause below can be written using the "nint"
c intrinsic, and the two forms give equivalent values:
c
c do while (abs(xr) .gt. xbox2)
c xr = xr - sign(xbox,xr) vs. xr = xr - xbox*nint(xr/xbox)
c end do
c
c which one is faster depends upon specific machine and compiler
c combinations, and other implementations are also possible
c
c
subroutine image (xr,yr,zr)
use boxes
use cell
use math
implicit none
real*8 xr,yr,zr
real*8 corr
c
c
c for orthogonal lattice, find the desired image directly
c
if (orthogonal) then
do while (abs(xr) .gt. xcell2)
xr = xr - sign(xcell,xr)
end do
do while (abs(yr) .gt. ycell2)
yr = yr - sign(ycell,yr)
end do
do while (abs(zr) .gt. zcell2)
zr = zr - sign(zcell,zr)
end do
c
c for monoclinic lattice, convert x and z to fractional,
c find desired image, then translate back to Cartesian
c
else if (monoclinic) then
zr = zr / beta_sin
xr = xr - zr*beta_cos
do while (abs(xr) .gt. xcell2)
xr = xr - sign(xcell,xr)
end do
do while (abs(yr) .gt. ycell2)
yr = yr - sign(ycell,yr)
end do
do while (abs(zr) .gt. zcell2)
zr = zr - sign(zcell,zr)
end do
xr = xr + zr*beta_cos
zr = zr * beta_sin
c
c for triclinic lattice, convert to fractional coordinates,
c find image, then translate fractional back to Cartesian
c
else if (triclinic) then
zr = zr / gamma_term
yr = (yr - zr*beta_term) / gamma_sin
xr = xr - yr*gamma_cos - zr*beta_cos
do while (abs(xr) .gt. xcell2)
xr = xr - sign(xcell,xr)
end do
do while (abs(yr) .gt. ycell2)
yr = yr - sign(ycell,yr)
end do
do while (abs(zr) .gt. zcell2)
zr = zr - sign(zcell,zr)
end do
xr = xr + yr*gamma_cos + zr*beta_cos
yr = yr*gamma_sin + zr*beta_term
zr = zr * gamma_term
c
c for truncated octahedron, remove the corner pieces
c
else if (octahedron) then
do while (abs(xr) .gt. xbox2)
xr = xr - sign(xbox,xr)
end do
do while (abs(yr) .gt. ybox2)
yr = yr - sign(ybox,yr)
end do
do while (abs(zr) .gt. zbox2)
zr = zr - sign(zbox,zr)
end do
if (abs(xr)+abs(yr)+abs(zr) .gt. box34) then
xr = xr - sign(xbox2,xr)
yr = yr - sign(ybox2,yr)
zr = zr - sign(zbox2,zr)
end if
c
c for rhombic dodecahedron, align along the x- and y-axes
c
else if (dodecadron) then
do while (abs(xr) .gt. xbox2)
xr = xr - sign(xbox,xr)
end do
do while (abs(yr) .gt. ybox2)
yr = yr - sign(ybox,yr)
end do
zr = zr - root2*zbox*nint(zr/(zbox*root2))
corr = xbox2 * int(abs(xr/xbox)+abs(yr/ybox)
& +abs(root2*zr/zbox))
xr = xr - sign(corr,xr)
yr = yr - sign(corr,yr)
zr = zr - sign(corr,zr)*root2
end if
return
end
c
c
c ###############################################################
c ## ##
c ## subroutine imager -- replicate minimum image distance ##
c ## ##
c ###############################################################
c
c
c "imager" takes the components of pairwise distance between
c two points in the same or neighboring periodic boxes and
c converts to the components of the minimum image distance
c
c
subroutine imager (xr,yr,zr,i)
use boxes
use cell
use math
implicit none
integer i
real*8 xr,yr,zr
real*8 xmove,ymove,zmove
real*8 corr
c
c
c set the distance to translate along each cell axis
c
xmove = icell(1,i) * xbox
ymove = icell(2,i) * ybox
zmove = icell(3,i) * zbox
c
c for orthogonal lattice, find the desired image directly
c
if (orthogonal) then
xr = xr + xmove
do while (abs(xr) .gt. xcell2)
xr = xr - sign(xcell,xr)
end do
yr = yr + ymove
do while (abs(yr) .gt. ycell2)
yr = yr - sign(ycell,yr)
end do
zr = zr + zmove
do while (abs(zr) .gt. zcell2)
zr = zr - sign(zcell,zr)
end do
c
c for monoclinic lattice, convert x and z to fractional,
c find desired image, then translate back to Cartesian
c
else if (monoclinic) then
zr = zr / beta_sin
xr = xr - zr*beta_cos
xr = xr + xmove
do while (abs(xr) .gt. xcell2)
xr = xr - sign(xcell,xr)
end do
yr = yr + ymove
do while (abs(yr) .gt. ycell2)
yr = yr - sign(ycell,yr)
end do
zr = zr + zmove
do while (abs(zr) .gt. zcell2)
zr = zr - sign(zcell,zr)
end do
xr = xr + zr*beta_cos
zr = zr * beta_sin
c
c for triclinic lattice, convert to fractional coordinates,
c find image, then translate fractional back to Cartesian
c
else if (triclinic) then
zr = zr / gamma_term
yr = (yr - zr*beta_term) / gamma_sin
xr = xr - yr*gamma_cos - zr*beta_cos
xr = xr + xmove
do while (abs(xr) .gt. xcell2)
xr = xr - sign(xcell,xr)
end do
yr = yr + ymove
do while (abs(yr) .gt. ycell2)
yr = yr - sign(ycell,yr)
end do
zr = zr + zmove
do while (abs(zr) .gt. zcell2)
zr = zr - sign(zcell,zr)
end do
xr = xr + yr*gamma_cos + zr*beta_cos
yr = yr*gamma_sin + zr*beta_term
zr = zr * gamma_term
c
c for truncated octahedron, remove the corner pieces
c
else if (octahedron) then
do while (abs(xr) .gt. xbox2)
xr = xr - sign(xbox,xr)
end do
do while (abs(yr) .gt. ybox2)
yr = yr - sign(ybox,yr)
end do
do while (abs(zr) .gt. zbox2)
zr = zr - sign(zbox,zr)
end do
if (abs(xr)+abs(yr)+abs(zr) .gt. box34) then
xr = xr - sign(xbox2,xr)
yr = yr - sign(ybox2,yr)
zr = zr - sign(zbox2,zr)
end if
c
c for rhombic dodecahedron, align along the x- and y-axes
c
else if (dodecadron) then
do while (abs(xr) .gt. xbox2)
xr = xr - sign(xbox,xr)
end do
do while (abs(yr) .gt. ybox2)
yr = yr - sign(ybox,yr)
end do
zr = zr - root2*zbox*nint(zr/(zbox*root2))
corr = xbox2 * int(abs(xr/xbox)+abs(yr/ybox)
& +abs(root2*zr/zbox))
xr = xr - sign(corr,xr)
yr = yr - sign(corr,yr)
zr = zr - sign(corr,zr)*root2
end if
return
end
c
c
c ###########################################################
c ## ##
c ## subroutine imagen -- fast minimum image magnitude ##
c ## ##
c ###########################################################
c
c
c "imagen" takes the components of pairwise distance between
c two points and converts to the components of the minimum
c image distance
c
c note this is a fast version for use in computing the 3D
c distance during neighbor list construction
c
c
subroutine imagen (xr,yr,zr)
use boxes
use math
implicit none
real*8 xr,yr,zr
real*8 corr
c
c
c for orthogonal lattice, find the desired image directly
c
if (orthogonal) then
xr = xr - xbox*nint(xr/xbox)
yr = yr - ybox*nint(yr/ybox)
zr = zr - zbox*nint(zr/zbox)
c
c for monoclinic lattice, convert x and z to fractional,
c find desired image, then translate back to Cartesian
c
else if (monoclinic) then
zr = zr / beta_sin
xr = xr - zr*beta_cos
xr = xr - xbox*nint(xr/xbox)
yr = yr - ybox*nint(yr/ybox)
zr = zr - zbox*nint(zr/zbox)
xr = xr + zr*beta_cos
zr = zr * beta_sin
c
c for triclinic lattice, convert to fractional coordinates,
c find image, then translate fractional back to Cartesian
c
else if (triclinic) then
zr = zr / gamma_term
yr = (yr - zr*beta_term) / gamma_sin
xr = xr - yr*gamma_cos - zr*beta_cos
xr = xr - xbox*nint(xr/xbox)
yr = yr - ybox*nint(yr/ybox)
zr = zr - zbox*nint(zr/zbox)
xr = xr + yr*gamma_cos + zr*beta_cos
yr = yr*gamma_sin + zr*beta_term
zr = zr * gamma_term
c
c for truncated octahedron, remove the corner pieces
c
else if (octahedron) then
xr = xr - xbox*nint(xr/xbox)
yr = yr - ybox*nint(yr/ybox)
zr = zr - zbox*nint(zr/zbox)
if (abs(xr)+abs(yr)+abs(zr) .gt. box34) then
xr = xr - sign(xbox2,xr)
yr = yr - sign(ybox2,yr)
zr = zr - sign(zbox2,zr)
end if
c
c for rhombic dodecahedron, align along the x- and y-axes
c
else if (dodecadron) then
xr = xr - xbox*nint(xr/xbox)
yr = yr - ybox*nint(yr/ybox)
zr = zr - root2*zbox*nint(zr/(zbox*root2))
corr = xbox2 * int(abs(xr/xbox)+abs(yr/ybox)
& +abs(root2*zr/zbox))
xr = xr - sign(corr,xr)
yr = yr - sign(corr,yr)
zr = zr - sign(corr,zr)*root2
end if
return
end