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!! |
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!! Copyright (c) 2005 The University of Notre Dame. All Rights Reserved. |
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!! |
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!! The University of Notre Dame grants you ("Licensee") a |
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!! non-exclusive, royalty free, license to use, modify and |
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!! redistribute this software in source and binary code form, provided |
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!! that the following conditions are met: |
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!! |
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!! 1. Redistributions of source code must retain the above copyright |
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!! notice, this list of conditions and the following disclaimer. |
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!! |
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!! 2. Redistributions in binary form must reproduce the above copyright |
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!! notice, this list of conditions and the following disclaimer in the |
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!! documentation and/or other materials provided with the |
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!! distribution. |
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!! |
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!! This software is provided "AS IS," without a warranty of any |
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!! kind. All express or implied conditions, representations and |
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!! warranties, including any implied warranty of merchantability, |
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!! fitness for a particular purpose or non-infringement, are hereby |
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!! excluded. The University of Notre Dame and its licensors shall not |
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!! be liable for any damages suffered by licensee as a result of |
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!! using, modifying or distributing the software or its |
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!! derivatives. In no event will the University of Notre Dame or its |
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!! licensors be liable for any lost revenue, profit or data, or for |
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!! direct, indirect, special, consequential, incidental or punitive |
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!! damages, however caused and regardless of the theory of liability, |
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!! arising out of the use of or inability to use software, even if the |
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!! University of Notre Dame has been advised of the possibility of |
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!! such damages. |
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!! |
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!! SUPPORT OPEN SCIENCE! If you use OpenMD or its source code in your |
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!! research, please cite the appropriate papers when you publish your |
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!! work. Good starting points are: |
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!! |
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!! [1] Meineke, et al., J. Comp. Chem. 26, 252-271 (2005). |
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!! [2] Fennell & Gezelter, J. Chem. Phys. 124, 234104 (2006). |
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!! [3] Sun, Lin & Gezelter, J. Chem. Phys. 128, 24107 (2008). |
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!! [4] Vardeman & Gezelter, in progress (2009). |
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!! |
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|
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|
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module shapes |
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|
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use force_globals |
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use definitions |
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use atype_module |
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use vector_class |
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use simulation |
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use status |
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use lj |
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implicit none |
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|
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PRIVATE |
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#define __FORTRAN90 |
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#include "UseTheForce/DarkSide/fInteractionMap.h" |
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INTEGER, PARAMETER:: CHEBYSHEV_TN = 1 |
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INTEGER, PARAMETER:: CHEBYSHEV_UN = 2 |
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INTEGER, PARAMETER:: LAGUERRE = 3 |
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INTEGER, PARAMETER:: HERMITE = 4 |
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INTEGER, PARAMETER:: SH_COS = 0 |
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INTEGER, PARAMETER:: SH_SIN = 1 |
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|
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logical, save :: haveShapeMap = .false. |
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|
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public :: do_shape_pair |
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public :: newShapeType |
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public :: complete_Shape_FF |
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public :: destroyShapeTypes |
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public :: getShapeCut |
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|
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type, private :: Shape |
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integer :: atid |
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integer :: nContactFuncs |
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integer :: nRangeFuncs |
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integer :: nStrengthFuncs |
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integer :: bigL |
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integer :: bigM |
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integer, pointer, dimension(:) :: ContactFuncLValue => null() |
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integer, pointer, dimension(:) :: ContactFuncMValue => null() |
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integer, pointer, dimension(:) :: ContactFunctionType => null() |
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real(kind=dp), pointer, dimension(:) :: ContactFuncCoefficient => null() |
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integer, pointer, dimension(:) :: RangeFuncLValue => null() |
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integer, pointer, dimension(:) :: RangeFuncMValue => null() |
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integer, pointer, dimension(:) :: RangeFunctionType => null() |
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real(kind=dp), pointer, dimension(:) :: RangeFuncCoefficient => null() |
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integer, pointer, dimension(:) :: StrengthFuncLValue => null() |
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integer, pointer, dimension(:) :: StrengthFuncMValue => null() |
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integer, pointer, dimension(:) :: StrengthFunctionType => null() |
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real(kind=dp), pointer, dimension(:) :: StrengthFuncCoefficient => null() |
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logical :: isLJ |
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real ( kind = dp ) :: epsilon |
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real ( kind = dp ) :: sigma |
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end type Shape |
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|
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type, private :: ShapeList |
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integer :: n_shapes = 0 |
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integer :: currentShape = 0 |
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type(Shape), pointer :: Shapes(:) => null() |
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integer, pointer :: atidToShape(:) => null() |
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end type ShapeList |
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|
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type(ShapeList), save :: ShapeMap |
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|
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integer :: lmax |
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|
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contains |
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|
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subroutine newShapeType(nContactFuncs, ContactFuncLValue, & |
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ContactFuncMValue, ContactFunctionType, ContactFuncCoefficient, & |
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nRangeFuncs, RangeFuncLValue, RangeFuncMValue, RangeFunctionType, & |
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RangeFuncCoefficient, nStrengthFuncs, StrengthFuncLValue, & |
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StrengthFuncMValue, StrengthFunctionType, StrengthFuncCoefficient, & |
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c_ident, status) |
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|
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integer :: nContactFuncs |
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integer :: nRangeFuncs |
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integer :: nStrengthFuncs |
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integer :: shape_ident |
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integer :: status |
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integer :: c_ident |
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integer :: myATID |
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integer :: bigL |
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integer :: bigM |
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integer :: j, me, nShapeTypes, nLJTypes, ntypes, current, alloc_stat |
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integer, pointer :: MatchList(:) => null() |
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|
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integer, dimension(nContactFuncs) :: ContactFuncLValue |
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integer, dimension(nContactFuncs) :: ContactFuncMValue |
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integer, dimension(nContactFuncs) :: ContactFunctionType |
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real(kind=dp), dimension(nContactFuncs) :: ContactFuncCoefficient |
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integer, dimension(nRangeFuncs) :: RangeFuncLValue |
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integer, dimension(nRangeFuncs) :: RangeFuncMValue |
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integer, dimension(nRangeFuncs) :: RangeFunctionType |
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real(kind=dp), dimension(nRangeFuncs) :: RangeFuncCoefficient |
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integer, dimension(nStrengthFuncs) :: StrengthFuncLValue |
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integer, dimension(nStrengthFuncs) :: StrengthFuncMValue |
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integer, dimension(nStrengthFuncs) :: StrengthFunctionType |
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real(kind=dp), dimension(nStrengthFuncs) :: StrengthFuncCoefficient |
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|
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status = 0 |
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! check to see if this is the first time into this routine... |
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if (.not.associated(ShapeMap%Shapes)) then |
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|
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call getMatchingElementList(atypes, "is_Shape", .true., & |
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nShapeTypes, MatchList) |
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|
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call getMatchingElementList(atypes, "is_LennardJones", .true., & |
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nLJTypes, MatchList) |
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|
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ShapeMap%n_shapes = nShapeTypes + nLJTypes |
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|
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allocate(ShapeMap%Shapes(nShapeTypes + nLJTypes)) |
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|
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ntypes = getSize(atypes) |
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|
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allocate(ShapeMap%atidToShape(ntypes)) |
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end if |
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|
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ShapeMap%currentShape = ShapeMap%currentShape + 1 |
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current = ShapeMap%currentShape |
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|
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call allocateShape(nContactFuncs, nRangeFuncs, nStrengthFuncs, & |
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ShapeMap%Shapes(current), stat=alloc_stat) |
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if (alloc_stat .ne. 0) then |
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status = -1 |
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return |
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endif |
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|
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myATID = getFirstMatchingElement(atypes, "c_ident", c_ident) |
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|
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ShapeMap%atidToShape(myATID) = current |
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ShapeMap%Shapes(current)%atid = myATID |
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ShapeMap%Shapes(current)%nContactFuncs = nContactFuncs |
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ShapeMap%Shapes(current)%nRangeFuncs = nRangeFuncs |
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ShapeMap%Shapes(current)%nStrengthFuncs = nStrengthFuncs |
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ShapeMap%Shapes(current)%ContactFuncLValue = ContactFuncLValue |
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ShapeMap%Shapes(current)%ContactFuncMValue = ContactFuncMValue |
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ShapeMap%Shapes(current)%ContactFunctionType = ContactFunctionType |
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ShapeMap%Shapes(current)%ContactFuncCoefficient = ContactFuncCoefficient |
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ShapeMap%Shapes(current)%RangeFuncLValue = RangeFuncLValue |
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ShapeMap%Shapes(current)%RangeFuncMValue = RangeFuncMValue |
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ShapeMap%Shapes(current)%RangeFunctionType = RangeFunctionType |
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ShapeMap%Shapes(current)%RangeFuncCoefficient = RangeFuncCoefficient |
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ShapeMap%Shapes(current)%StrengthFuncLValue = StrengthFuncLValue |
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ShapeMap%Shapes(current)%StrengthFuncMValue = StrengthFuncMValue |
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ShapeMap%Shapes(current)%StrengthFunctionType = StrengthFunctionType |
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ShapeMap%Shapes(current)%StrengthFuncCoefficient = StrengthFuncCoefficient |
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|
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bigL = -1 |
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bigM = -1 |
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|
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do j = 1, ShapeMap%Shapes(current)%nContactFuncs |
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if (ShapeMap%Shapes(current)%ContactFuncLValue(j) .gt. bigL) then |
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bigL = ShapeMap%Shapes(current)%ContactFuncLValue(j) |
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endif |
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if (ShapeMap%Shapes(current)%ContactFuncMValue(j) .gt. bigM) then |
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bigM = ShapeMap%Shapes(current)%ContactFuncMValue(j) |
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endif |
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enddo |
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do j = 1, ShapeMap%Shapes(current)%nRangeFuncs |
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if (ShapeMap%Shapes(current)%RangeFuncLValue(j) .gt. bigL) then |
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bigL = ShapeMap%Shapes(current)%RangeFuncLValue(j) |
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endif |
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if (ShapeMap%Shapes(current)%RangeFuncMValue(j) .gt. bigM) then |
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bigM = ShapeMap%Shapes(current)%RangeFuncMValue(j) |
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endif |
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enddo |
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do j = 1, ShapeMap%Shapes(current)%nStrengthFuncs |
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if (ShapeMap%Shapes(current)%StrengthFuncLValue(j) .gt. bigL) then |
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bigL = ShapeMap%Shapes(current)%StrengthFuncLValue(j) |
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endif |
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if (ShapeMap%Shapes(current)%StrengthFuncMValue(j) .gt. bigM) then |
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bigM = ShapeMap%Shapes(current)%StrengthFuncMValue(j) |
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endif |
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enddo |
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|
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ShapeMap%Shapes(current)%bigL = bigL |
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ShapeMap%Shapes(current)%bigM = bigM |
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|
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end subroutine newShapeType |
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|
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subroutine allocateShape(nContactFuncs, nRangeFuncs, nStrengthFuncs, & |
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myShape, stat) |
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|
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integer, intent(in) :: nContactFuncs, nRangeFuncs, nStrengthFuncs |
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type(Shape), intent(inout) :: myShape |
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integer, intent(out) :: stat |
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integer :: alloc_stat |
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|
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stat = 0 |
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if (associated(myShape%contactFuncLValue)) then |
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deallocate(myShape%contactFuncLValue) |
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endif |
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allocate(myShape%contactFuncLValue(nContactFuncs), stat = alloc_stat) |
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if (alloc_stat .ne. 0) then |
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stat = -1 |
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return |
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endif |
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if (associated(myShape%contactFuncMValue)) then |
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deallocate(myShape%contactFuncMValue) |
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endif |
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allocate(myShape%contactFuncMValue(nContactFuncs), stat = alloc_stat) |
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if (alloc_stat .ne. 0) then |
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stat = -1 |
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return |
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endif |
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if (associated(myShape%contactFunctionType)) then |
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deallocate(myShape%contactFunctionType) |
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endif |
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allocate(myShape%contactFunctionType(nContactFuncs), stat = alloc_stat) |
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if (alloc_stat .ne. 0) then |
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stat = -1 |
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return |
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endif |
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if (associated(myShape%contactFuncCoefficient)) then |
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deallocate(myShape%contactFuncCoefficient) |
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endif |
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allocate(myShape%contactFuncCoefficient(nContactFuncs), stat = alloc_stat) |
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if (alloc_stat .ne. 0) then |
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stat = -1 |
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return |
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endif |
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|
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if (associated(myShape%rangeFuncLValue)) then |
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deallocate(myShape%rangeFuncLValue) |
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endif |
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allocate(myShape%rangeFuncLValue(nRangeFuncs), stat = alloc_stat) |
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if (alloc_stat .ne. 0) then |
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stat = -1 |
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return |
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endif |
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if (associated(myShape%rangeFuncMValue)) then |
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deallocate(myShape%rangeFuncMValue) |
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endif |
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allocate(myShape%rangeFuncMValue(nRangeFuncs), stat = alloc_stat) |
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if (alloc_stat .ne. 0) then |
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stat = -1 |
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return |
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endif |
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if (associated(myShape%rangeFunctionType)) then |
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deallocate(myShape%rangeFunctionType) |
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endif |
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allocate(myShape%rangeFunctionType(nRangeFuncs), stat = alloc_stat) |
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if (alloc_stat .ne. 0) then |
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stat = -1 |
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return |
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endif |
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if (associated(myShape%rangeFuncCoefficient)) then |
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deallocate(myShape%rangeFuncCoefficient) |
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endif |
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allocate(myShape%rangeFuncCoefficient(nRangeFuncs), stat = alloc_stat) |
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if (alloc_stat .ne. 0) then |
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stat = -1 |
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return |
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endif |
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|
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if (associated(myShape%strengthFuncLValue)) then |
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deallocate(myShape%strengthFuncLValue) |
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endif |
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allocate(myShape%strengthFuncLValue(nStrengthFuncs), stat = alloc_stat) |
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if (alloc_stat .ne. 0) then |
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stat = -1 |
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return |
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endif |
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if (associated(myShape%strengthFuncMValue)) then |
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deallocate(myShape%strengthFuncMValue) |
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endif |
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allocate(myShape%strengthFuncMValue(nStrengthFuncs), stat = alloc_stat) |
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if (alloc_stat .ne. 0) then |
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stat = -1 |
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return |
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endif |
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if (associated(myShape%strengthFunctionType)) then |
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deallocate(myShape%strengthFunctionType) |
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endif |
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allocate(myShape%strengthFunctionType(nStrengthFuncs), stat = alloc_stat) |
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if (alloc_stat .ne. 0) then |
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stat = -1 |
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return |
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endif |
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if (associated(myShape%strengthFuncCoefficient)) then |
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deallocate(myShape%strengthFuncCoefficient) |
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endif |
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allocate(myShape%strengthFuncCoefficient(nStrengthFuncs), stat=alloc_stat) |
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if (alloc_stat .ne. 0) then |
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stat = -1 |
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return |
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endif |
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|
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return |
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|
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end subroutine allocateShape |
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|
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subroutine complete_Shape_FF(status) |
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integer :: status |
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integer :: i, j, l, m, lm, function_type |
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real(kind=dp) :: thisDP, sigma |
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integer :: alloc_stat, iTheta, iPhi, nSteps, nAtypes, myATID, current |
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logical :: thisProperty |
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|
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status = 0 |
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if (ShapeMap%currentShape == 0) then |
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call handleError("init_Shape_FF", "No members in ShapeMap") |
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status = -1 |
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return |
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end if |
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|
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nAtypes = getSize(atypes) |
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|
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if (nAtypes == 0) then |
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status = -1 |
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return |
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end if |
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|
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! atypes comes from c side |
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do i = 1, nAtypes |
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|
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myATID = getFirstMatchingElement(atypes, 'c_ident', i) |
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call getElementProperty(atypes, myATID, "is_LennardJones", thisProperty) |
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|
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if (thisProperty) then |
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ShapeMap%currentShape = ShapeMap%currentShape + 1 |
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current = ShapeMap%currentShape |
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|
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ShapeMap%atidToShape(myATID) = current |
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ShapeMap%Shapes(current)%atid = myATID |
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|
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ShapeMap%Shapes(current)%isLJ = .true. |
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|
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ShapeMap%Shapes(current)%epsilon = getEpsilon(myATID) |
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ShapeMap%Shapes(current)%sigma = getSigma(myATID) |
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|
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endif |
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|
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end do |
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|
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haveShapeMap = .true. |
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|
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! do i = 1, ShapeMap%n_shapes |
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! write(*,*) 'i = ', i, ' isLJ = ', ShapeMap%Shapes(i)%isLJ |
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! end do |
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|
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end subroutine complete_Shape_FF |
| 385 |
|
| 386 |
function getShapeCut(atomID) result(cutValue) |
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integer, intent(in) :: atomID |
| 388 |
real(kind=dp) :: cutValue, whoopdedoo |
| 389 |
|
| 390 |
!! this is just a placeholder for a cutoff value, hopefully we'll |
| 391 |
!! develop a method to calculate a sensible value |
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whoopdedoo = 9.0_dp |
| 393 |
|
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cutValue = whoopdedoo |
| 395 |
|
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end function getShapeCut |
| 397 |
|
| 398 |
subroutine do_shape_pair(atid1, atid2, d, rij, r2, sw, & |
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vpair, fpair, pot, A1, A2, f1, t1, t2) |
| 400 |
|
| 401 |
INTEGER, PARAMETER:: LMAX = 64 |
| 402 |
INTEGER, PARAMETER:: MMAX = 64 |
| 403 |
|
| 404 |
integer, intent(in) :: atid1, atid2 |
| 405 |
real (kind=dp), intent(inout) :: rij, r2 |
| 406 |
real (kind=dp), dimension(3), intent(in) :: d |
| 407 |
real (kind=dp), dimension(3), intent(inout) :: fpair |
| 408 |
real (kind=dp) :: pot, vpair, sw, dswdr |
| 409 |
real (kind=dp), dimension(9) :: A1, A2 |
| 410 |
real (kind=dp), dimension(3) :: f1 |
| 411 |
real (kind=dp), dimension(3) :: t1, t2 |
| 412 |
|
| 413 |
real (kind=dp) :: r3, r5, rt2, rt3, rt5, rt6, rt11, rt12, rt126 |
| 414 |
integer :: st1, st2 |
| 415 |
integer :: l, m, lm, id1, id2, localError, function_type |
| 416 |
real (kind=dp) :: sigma_i, s_i, eps_i, sigma_j, s_j, eps_j |
| 417 |
real (kind=dp) :: coeff |
| 418 |
real (kind=dp) :: pot_temp |
| 419 |
|
| 420 |
real (kind=dp) :: dsigmaidx, dsigmaidy, dsigmaidz |
| 421 |
real (kind=dp) :: dsigmaidux, dsigmaiduy, dsigmaiduz |
| 422 |
real (kind=dp) :: dsigmajdx, dsigmajdy, dsigmajdz |
| 423 |
real (kind=dp) :: dsigmajdux, dsigmajduy, dsigmajduz |
| 424 |
|
| 425 |
real (kind=dp) :: dsidx, dsidy, dsidz |
| 426 |
real (kind=dp) :: dsidux, dsiduy, dsiduz |
| 427 |
real (kind=dp) :: dsjdx, dsjdy, dsjdz |
| 428 |
real (kind=dp) :: dsjdux, dsjduy, dsjduz |
| 429 |
|
| 430 |
real (kind=dp) :: depsidx, depsidy, depsidz |
| 431 |
real (kind=dp) :: depsidux, depsiduy, depsiduz |
| 432 |
real (kind=dp) :: depsjdx, depsjdy, depsjdz |
| 433 |
real (kind=dp) :: depsjdux, depsjduy, depsjduz |
| 434 |
|
| 435 |
real (kind=dp) :: xi, yi, zi, xj, yj, zj, xi2, yi2, zi2, xj2, yj2, zj2 |
| 436 |
|
| 437 |
real (kind=dp) :: sti2, stj2 |
| 438 |
|
| 439 |
real (kind=dp) :: proji, proji3, projj, projj3 |
| 440 |
real (kind=dp) :: cti, ctj, cpi, cpj, spi, spj |
| 441 |
real (kind=dp) :: Phunc, sigma, s, eps, rtdenom, rt |
| 442 |
|
| 443 |
real (kind=dp) :: dctidx, dctidy, dctidz |
| 444 |
real (kind=dp) :: dctidux, dctiduy, dctiduz |
| 445 |
real (kind=dp) :: dctjdx, dctjdy, dctjdz |
| 446 |
real (kind=dp) :: dctjdux, dctjduy, dctjduz |
| 447 |
|
| 448 |
real (kind=dp) :: dcpidx, dcpidy, dcpidz |
| 449 |
real (kind=dp) :: dcpidux, dcpiduy, dcpiduz |
| 450 |
real (kind=dp) :: dcpjdx, dcpjdy, dcpjdz |
| 451 |
real (kind=dp) :: dcpjdux, dcpjduy, dcpjduz |
| 452 |
|
| 453 |
real (kind=dp) :: dspidx, dspidy, dspidz |
| 454 |
real (kind=dp) :: dspidux, dspiduy, dspiduz |
| 455 |
real (kind=dp) :: dspjdx, dspjdy, dspjdz |
| 456 |
real (kind=dp) :: dspjdux, dspjduy, dspjduz |
| 457 |
|
| 458 |
real (kind=dp) :: dPhuncdX, dPhuncdY, dPhuncdZ |
| 459 |
real (kind=dp) :: dPhuncdUx, dPhuncdUy, dPhuncdUz |
| 460 |
|
| 461 |
real (kind=dp) :: dsigmadxi, dsigmadyi, dsigmadzi |
| 462 |
real (kind=dp) :: dsigmaduxi, dsigmaduyi, dsigmaduzi |
| 463 |
real (kind=dp) :: dsigmadxj, dsigmadyj, dsigmadzj |
| 464 |
real (kind=dp) :: dsigmaduxj, dsigmaduyj, dsigmaduzj |
| 465 |
|
| 466 |
real (kind=dp) :: dsdxi, dsdyi, dsdzi |
| 467 |
real (kind=dp) :: dsduxi, dsduyi, dsduzi |
| 468 |
real (kind=dp) :: dsdxj, dsdyj, dsdzj |
| 469 |
real (kind=dp) :: dsduxj, dsduyj, dsduzj |
| 470 |
|
| 471 |
real (kind=dp) :: depsdxi, depsdyi, depsdzi |
| 472 |
real (kind=dp) :: depsduxi, depsduyi, depsduzi |
| 473 |
real (kind=dp) :: depsdxj, depsdyj, depsdzj |
| 474 |
real (kind=dp) :: depsduxj, depsduyj, depsduzj |
| 475 |
|
| 476 |
real (kind=dp) :: drtdxi, drtdyi, drtdzi |
| 477 |
real (kind=dp) :: drtduxi, drtduyi, drtduzi |
| 478 |
real (kind=dp) :: drtdxj, drtdyj, drtdzj |
| 479 |
real (kind=dp) :: drtduxj, drtduyj, drtduzj |
| 480 |
|
| 481 |
real (kind=dp) :: drdxi, drdyi, drdzi |
| 482 |
real (kind=dp) :: drduxi, drduyi, drduzi |
| 483 |
real (kind=dp) :: drdxj, drdyj, drdzj |
| 484 |
real (kind=dp) :: drduxj, drduyj, drduzj |
| 485 |
|
| 486 |
real (kind=dp) :: dvdxi, dvdyi, dvdzi |
| 487 |
real (kind=dp) :: dvduxi, dvduyi, dvduzi |
| 488 |
real (kind=dp) :: dvdxj, dvdyj, dvdzj |
| 489 |
real (kind=dp) :: dvduxj, dvduyj, dvduzj |
| 490 |
|
| 491 |
real (kind=dp) :: fxi, fyi, fzi, fxj, fyj, fzj |
| 492 |
real (kind=dp) :: txi, tyi, tzi, txj, tyj, tzj |
| 493 |
real (kind=dp) :: fxii, fyii, fzii, fxij, fyij, fzij |
| 494 |
real (kind=dp) :: fxji, fyji, fzji, fxjj, fyjj, fzjj |
| 495 |
real (kind=dp) :: fxradial, fyradial, fzradial |
| 496 |
|
| 497 |
real (kind=dp) :: xihat, yihat, zihat, xjhat, yjhat, zjhat |
| 498 |
|
| 499 |
real (kind=dp) :: plm_i(0:LMAX,0:MMAX), dlm_i(0:LMAX,0:MMAX) |
| 500 |
real (kind=dp) :: plm_j(0:LMAX,0:MMAX), dlm_j(0:LMAX,0:MMAX) |
| 501 |
real (kind=dp) :: tm_i(0:MMAX), dtm_i(0:MMAX), um_i(0:MMAX), dum_i(0:MMAX) |
| 502 |
real (kind=dp) :: tm_j(0:MMAX), dtm_j(0:MMAX), um_j(0:MMAX), dum_j(0:MMAX) |
| 503 |
|
| 504 |
if (.not.haveShapeMap) then |
| 505 |
call handleError("calc_shape", "NO SHAPEMAP!!!!") |
| 506 |
return |
| 507 |
endif |
| 508 |
|
| 509 |
!! We assume that the rotation matrices have already been calculated |
| 510 |
!! and placed in the A array. |
| 511 |
r3 = r2*rij |
| 512 |
r5 = r3*r2 |
| 513 |
|
| 514 |
drdxi = -d(1) / rij |
| 515 |
drdyi = -d(2) / rij |
| 516 |
drdzi = -d(3) / rij |
| 517 |
drduxi = 0.0_dp |
| 518 |
drduyi = 0.0_dp |
| 519 |
drduzi = 0.0_dp |
| 520 |
|
| 521 |
drdxj = d(1) / rij |
| 522 |
drdyj = d(2) / rij |
| 523 |
drdzj = d(3) / rij |
| 524 |
drduxj = 0.0_dp |
| 525 |
drduyj = 0.0_dp |
| 526 |
drduzj = 0.0_dp |
| 527 |
|
| 528 |
! use the atid to find the shape type (st) for each atom: |
| 529 |
st1 = ShapeMap%atidToShape(atid1) |
| 530 |
st2 = ShapeMap%atidToShape(atid2) |
| 531 |
|
| 532 |
if (ShapeMap%Shapes(st1)%isLJ) then |
| 533 |
|
| 534 |
sigma_i = ShapeMap%Shapes(st1)%sigma |
| 535 |
s_i = ShapeMap%Shapes(st1)%sigma |
| 536 |
eps_i = ShapeMap%Shapes(st1)%epsilon |
| 537 |
dsigmaidx = 0.0_dp |
| 538 |
dsigmaidy = 0.0_dp |
| 539 |
dsigmaidz = 0.0_dp |
| 540 |
dsigmaidux = 0.0_dp |
| 541 |
dsigmaiduy = 0.0_dp |
| 542 |
dsigmaiduz = 0.0_dp |
| 543 |
dsidx = 0.0_dp |
| 544 |
dsidy = 0.0_dp |
| 545 |
dsidz = 0.0_dp |
| 546 |
dsidux = 0.0_dp |
| 547 |
dsiduy = 0.0_dp |
| 548 |
dsiduz = 0.0_dp |
| 549 |
depsidx = 0.0_dp |
| 550 |
depsidy = 0.0_dp |
| 551 |
depsidz = 0.0_dp |
| 552 |
depsidux = 0.0_dp |
| 553 |
depsiduy = 0.0_dp |
| 554 |
depsiduz = 0.0_dp |
| 555 |
else |
| 556 |
|
| 557 |
! rotate the inter-particle separation into the two different |
| 558 |
! body-fixed coordinate systems: |
| 559 |
|
| 560 |
xi = A1(1)*d(1) + A1(2)*d(2) + A1(3)*d(3) |
| 561 |
yi = A1(4)*d(1) + A1(5)*d(2) + A1(6)*d(3) |
| 562 |
zi = A1(7)*d(1) + A1(8)*d(2) + A1(9)*d(3) |
| 563 |
|
| 564 |
xihat = xi / rij |
| 565 |
yihat = yi / rij |
| 566 |
zihat = zi / rij |
| 567 |
xi2 = xi*xi |
| 568 |
yi2 = yi*yi |
| 569 |
zi2 = zi*zi |
| 570 |
cti = zi / rij |
| 571 |
|
| 572 |
if (cti .gt. 1.0_dp) cti = 1.0_dp |
| 573 |
if (cti .lt. -1.0_dp) cti = -1.0_dp |
| 574 |
|
| 575 |
dctidx = - zi * xi / r3 |
| 576 |
dctidy = - zi * yi / r3 |
| 577 |
dctidz = 1.0_dp / rij - zi2 / r3 |
| 578 |
dctidux = yi / rij ! - (zi * xi2) / r3 |
| 579 |
dctiduy = -xi / rij !- (zi * yi2) / r3 |
| 580 |
dctiduz = 0.0_dp !zi / rij - (zi2 * zi) / r3 |
| 581 |
|
| 582 |
! this is an attempt to try to truncate the singularity when |
| 583 |
! sin(theta) is near 0.0: |
| 584 |
|
| 585 |
sti2 = 1.0_dp - cti*cti |
| 586 |
if (abs(sti2) .lt. 1.0e-12_dp) then |
| 587 |
proji = sqrt(rij * 1.0e-12_dp) |
| 588 |
dcpidx = 1.0_dp / proji |
| 589 |
dcpidy = 0.0_dp |
| 590 |
dcpidux = xi / proji |
| 591 |
dcpiduy = 0.0_dp |
| 592 |
dspidx = 0.0_dp |
| 593 |
dspidy = 1.0_dp / proji |
| 594 |
dspidux = 0.0_dp |
| 595 |
dspiduy = yi / proji |
| 596 |
else |
| 597 |
proji = sqrt(xi2 + yi2) |
| 598 |
proji3 = proji*proji*proji |
| 599 |
dcpidx = 1.0_dp / proji - xi2 / proji3 |
| 600 |
dcpidy = - xi * yi / proji3 |
| 601 |
dcpidux = xi / proji - (xi2 * xi) / proji3 |
| 602 |
dcpiduy = - (xi * yi2) / proji3 |
| 603 |
dspidx = - xi * yi / proji3 |
| 604 |
dspidy = 1.0_dp / proji - yi2 / proji3 |
| 605 |
dspidux = - (yi * xi2) / proji3 |
| 606 |
dspiduy = yi / proji - (yi2 * yi) / proji3 |
| 607 |
endif |
| 608 |
|
| 609 |
cpi = xi / proji |
| 610 |
dcpidz = 0.0_dp |
| 611 |
dcpiduz = 0.0_dp |
| 612 |
|
| 613 |
spi = yi / proji |
| 614 |
dspidz = 0.0_dp |
| 615 |
dspiduz = 0.0_dp |
| 616 |
|
| 617 |
call Associated_Legendre(cti, ShapeMap%Shapes(st1)%bigM, & |
| 618 |
ShapeMap%Shapes(st1)%bigL, LMAX, & |
| 619 |
plm_i, dlm_i) |
| 620 |
|
| 621 |
call Orthogonal_Polynomial(cpi, ShapeMap%Shapes(st1)%bigM, MMAX, & |
| 622 |
CHEBYSHEV_TN, tm_i, dtm_i) |
| 623 |
call Orthogonal_Polynomial(cpi, ShapeMap%Shapes(st1)%bigM, MMAX, & |
| 624 |
CHEBYSHEV_UN, um_i, dum_i) |
| 625 |
|
| 626 |
sigma_i = 0.0_dp |
| 627 |
s_i = 0.0_dp |
| 628 |
eps_i = 0.0_dp |
| 629 |
dsigmaidx = 0.0_dp |
| 630 |
dsigmaidy = 0.0_dp |
| 631 |
dsigmaidz = 0.0_dp |
| 632 |
dsigmaidux = 0.0_dp |
| 633 |
dsigmaiduy = 0.0_dp |
| 634 |
dsigmaiduz = 0.0_dp |
| 635 |
dsidx = 0.0_dp |
| 636 |
dsidy = 0.0_dp |
| 637 |
dsidz = 0.0_dp |
| 638 |
dsidux = 0.0_dp |
| 639 |
dsiduy = 0.0_dp |
| 640 |
dsiduz = 0.0_dp |
| 641 |
depsidx = 0.0_dp |
| 642 |
depsidy = 0.0_dp |
| 643 |
depsidz = 0.0_dp |
| 644 |
depsidux = 0.0_dp |
| 645 |
depsiduy = 0.0_dp |
| 646 |
depsiduz = 0.0_dp |
| 647 |
|
| 648 |
do lm = 1, ShapeMap%Shapes(st1)%nContactFuncs |
| 649 |
l = ShapeMap%Shapes(st1)%ContactFuncLValue(lm) |
| 650 |
m = ShapeMap%Shapes(st1)%ContactFuncMValue(lm) |
| 651 |
coeff = ShapeMap%Shapes(st1)%ContactFuncCoefficient(lm) |
| 652 |
function_type = ShapeMap%Shapes(st1)%ContactFunctionType(lm) |
| 653 |
|
| 654 |
if ((function_type .eq. SH_COS).or.(m.eq.0)) then |
| 655 |
Phunc = coeff * tm_i(m) |
| 656 |
dPhuncdX = coeff * dtm_i(m) * dcpidx |
| 657 |
dPhuncdY = coeff * dtm_i(m) * dcpidy |
| 658 |
dPhuncdZ = coeff * dtm_i(m) * dcpidz |
| 659 |
dPhuncdUx = coeff * dtm_i(m) * dcpidux |
| 660 |
dPhuncdUy = coeff * dtm_i(m) * dcpiduy |
| 661 |
dPhuncdUz = coeff * dtm_i(m) * dcpiduz |
| 662 |
else |
| 663 |
Phunc = coeff * spi * um_i(m-1) |
| 664 |
dPhuncdX = coeff * (spi * dum_i(m-1) * dcpidx + dspidx *um_i(m-1)) |
| 665 |
dPhuncdY = coeff * (spi * dum_i(m-1) * dcpidy + dspidy *um_i(m-1)) |
| 666 |
dPhuncdZ = coeff * (spi * dum_i(m-1) * dcpidz + dspidz *um_i(m-1)) |
| 667 |
dPhuncdUx = coeff*(spi * dum_i(m-1)*dcpidux + dspidux *um_i(m-1)) |
| 668 |
dPhuncdUy = coeff*(spi * dum_i(m-1)*dcpiduy + dspiduy *um_i(m-1)) |
| 669 |
dPhuncdUz = coeff*(spi * dum_i(m-1)*dcpiduz + dspiduz *um_i(m-1)) |
| 670 |
endif |
| 671 |
|
| 672 |
sigma_i = sigma_i + plm_i(m,l)*Phunc |
| 673 |
!!$ write(*,*) 'dsigmaidux = ', dsigmaidux |
| 674 |
!!$ write(*,*) 'Phunc = ', Phunc |
| 675 |
dsigmaidx = dsigmaidx + plm_i(m,l)*dPhuncdX + & |
| 676 |
Phunc * dlm_i(m,l) * dctidx |
| 677 |
dsigmaidy = dsigmaidy + plm_i(m,l)*dPhuncdY + & |
| 678 |
Phunc * dlm_i(m,l) * dctidy |
| 679 |
dsigmaidz = dsigmaidz + plm_i(m,l)*dPhuncdZ + & |
| 680 |
Phunc * dlm_i(m,l) * dctidz |
| 681 |
dsigmaidux = dsigmaidux + plm_i(m,l)* dPhuncdUx + & |
| 682 |
Phunc * dlm_i(m,l) * dctidux |
| 683 |
dsigmaiduy = dsigmaiduy + plm_i(m,l)* dPhuncdUy + & |
| 684 |
Phunc * dlm_i(m,l) * dctiduy |
| 685 |
dsigmaiduz = dsigmaiduz + plm_i(m,l)* dPhuncdUz + & |
| 686 |
Phunc * dlm_i(m,l) * dctiduz |
| 687 |
!!$ write(*,*) 'dsigmaidux = ', dsigmaidux, '; dPhuncdUx = ', dPhuncdUx, & |
| 688 |
!!$ '; dctidux = ', dctidux, '; plm_i(m,l) = ', plm_i(m,l), & |
| 689 |
!!$ '; dlm_i(m,l) = ', dlm_i(m,l), '; m = ', m, '; l = ', l |
| 690 |
end do |
| 691 |
|
| 692 |
do lm = 1, ShapeMap%Shapes(st1)%nRangeFuncs |
| 693 |
l = ShapeMap%Shapes(st1)%RangeFuncLValue(lm) |
| 694 |
m = ShapeMap%Shapes(st1)%RangeFuncMValue(lm) |
| 695 |
coeff = ShapeMap%Shapes(st1)%RangeFuncCoefficient(lm) |
| 696 |
function_type = ShapeMap%Shapes(st1)%RangeFunctionType(lm) |
| 697 |
|
| 698 |
if ((function_type .eq. SH_COS).or.(m.eq.0)) then |
| 699 |
Phunc = coeff * tm_i(m) |
| 700 |
dPhuncdX = coeff * dtm_i(m) * dcpidx |
| 701 |
dPhuncdY = coeff * dtm_i(m) * dcpidy |
| 702 |
dPhuncdZ = coeff * dtm_i(m) * dcpidz |
| 703 |
dPhuncdUx = coeff * dtm_i(m) * dcpidux |
| 704 |
dPhuncdUy = coeff * dtm_i(m) * dcpiduy |
| 705 |
dPhuncdUz = coeff * dtm_i(m) * dcpiduz |
| 706 |
else |
| 707 |
Phunc = coeff * spi * um_i(m-1) |
| 708 |
dPhuncdX = coeff * (spi * dum_i(m-1) * dcpidx + dspidx *um_i(m-1)) |
| 709 |
dPhuncdY = coeff * (spi * dum_i(m-1) * dcpidy + dspidy *um_i(m-1)) |
| 710 |
dPhuncdZ = coeff * (spi * dum_i(m-1) * dcpidz + dspidz *um_i(m-1)) |
| 711 |
dPhuncdUx = coeff*(spi * dum_i(m-1)*dcpidux + dspidux *um_i(m-1)) |
| 712 |
dPhuncdUy = coeff*(spi * dum_i(m-1)*dcpiduy + dspiduy *um_i(m-1)) |
| 713 |
dPhuncdUz = coeff*(spi * dum_i(m-1)*dcpiduz + dspiduz *um_i(m-1)) |
| 714 |
endif |
| 715 |
|
| 716 |
s_i = s_i + plm_i(m,l)*Phunc |
| 717 |
|
| 718 |
dsidx = dsidx + plm_i(m,l)*dPhuncdX + & |
| 719 |
Phunc * dlm_i(m,l) * dctidx |
| 720 |
dsidy = dsidy + plm_i(m,l)*dPhuncdY + & |
| 721 |
Phunc * dlm_i(m,l) * dctidy |
| 722 |
dsidz = dsidz + plm_i(m,l)*dPhuncdZ + & |
| 723 |
Phunc * dlm_i(m,l) * dctidz |
| 724 |
|
| 725 |
dsidux = dsidux + plm_i(m,l)* dPhuncdUx + & |
| 726 |
Phunc * dlm_i(m,l) * dctidux |
| 727 |
dsiduy = dsiduy + plm_i(m,l)* dPhuncdUy + & |
| 728 |
Phunc * dlm_i(m,l) * dctiduy |
| 729 |
dsiduz = dsiduz + plm_i(m,l)* dPhuncdUz + & |
| 730 |
Phunc * dlm_i(m,l) * dctiduz |
| 731 |
|
| 732 |
end do |
| 733 |
|
| 734 |
do lm = 1, ShapeMap%Shapes(st1)%nStrengthFuncs |
| 735 |
l = ShapeMap%Shapes(st1)%StrengthFuncLValue(lm) |
| 736 |
m = ShapeMap%Shapes(st1)%StrengthFuncMValue(lm) |
| 737 |
coeff = ShapeMap%Shapes(st1)%StrengthFuncCoefficient(lm) |
| 738 |
function_type = ShapeMap%Shapes(st1)%StrengthFunctionType(lm) |
| 739 |
|
| 740 |
if ((function_type .eq. SH_COS).or.(m.eq.0)) then |
| 741 |
Phunc = coeff * tm_i(m) |
| 742 |
dPhuncdX = coeff * dtm_i(m) * dcpidx |
| 743 |
dPhuncdY = coeff * dtm_i(m) * dcpidy |
| 744 |
dPhuncdZ = coeff * dtm_i(m) * dcpidz |
| 745 |
dPhuncdUx = coeff * dtm_i(m) * dcpidux |
| 746 |
dPhuncdUy = coeff * dtm_i(m) * dcpiduy |
| 747 |
dPhuncdUz = coeff * dtm_i(m) * dcpiduz |
| 748 |
else |
| 749 |
Phunc = coeff * spi * um_i(m-1) |
| 750 |
dPhuncdX = coeff * (spi * dum_i(m-1) * dcpidx + dspidx *um_i(m-1)) |
| 751 |
dPhuncdY = coeff * (spi * dum_i(m-1) * dcpidy + dspidy *um_i(m-1)) |
| 752 |
dPhuncdZ = coeff * (spi * dum_i(m-1) * dcpidz + dspidz *um_i(m-1)) |
| 753 |
dPhuncdUx = coeff*(spi * dum_i(m-1)*dcpidux + dspidux *um_i(m-1)) |
| 754 |
dPhuncdUy = coeff*(spi * dum_i(m-1)*dcpiduy + dspiduy *um_i(m-1)) |
| 755 |
dPhuncdUz = coeff*(spi * dum_i(m-1)*dcpiduz + dspiduz *um_i(m-1)) |
| 756 |
endif |
| 757 |
|
| 758 |
eps_i = eps_i + plm_i(m,l)*Phunc |
| 759 |
|
| 760 |
depsidx = depsidx + plm_i(m,l)*dPhuncdX + & |
| 761 |
Phunc * dlm_i(m,l) * dctidx |
| 762 |
depsidy = depsidy + plm_i(m,l)*dPhuncdY + & |
| 763 |
Phunc * dlm_i(m,l) * dctidy |
| 764 |
depsidz = depsidz + plm_i(m,l)*dPhuncdZ + & |
| 765 |
Phunc * dlm_i(m,l) * dctidz |
| 766 |
|
| 767 |
depsidux = depsidux + plm_i(m,l)* dPhuncdUx + & |
| 768 |
Phunc * dlm_i(m,l) * dctidux |
| 769 |
depsiduy = depsiduy + plm_i(m,l)* dPhuncdUy + & |
| 770 |
Phunc * dlm_i(m,l) * dctiduy |
| 771 |
depsiduz = depsiduz + plm_i(m,l)* dPhuncdUz + & |
| 772 |
Phunc * dlm_i(m,l) * dctiduz |
| 773 |
|
| 774 |
end do |
| 775 |
|
| 776 |
endif |
| 777 |
|
| 778 |
! now do j: |
| 779 |
|
| 780 |
if (ShapeMap%Shapes(st2)%isLJ) then |
| 781 |
sigma_j = ShapeMap%Shapes(st2)%sigma |
| 782 |
s_j = ShapeMap%Shapes(st2)%sigma |
| 783 |
eps_j = ShapeMap%Shapes(st2)%epsilon |
| 784 |
dsigmajdx = 0.0_dp |
| 785 |
dsigmajdy = 0.0_dp |
| 786 |
dsigmajdz = 0.0_dp |
| 787 |
dsigmajdux = 0.0_dp |
| 788 |
dsigmajduy = 0.0_dp |
| 789 |
dsigmajduz = 0.0_dp |
| 790 |
dsjdx = 0.0_dp |
| 791 |
dsjdy = 0.0_dp |
| 792 |
dsjdz = 0.0_dp |
| 793 |
dsjdux = 0.0_dp |
| 794 |
dsjduy = 0.0_dp |
| 795 |
dsjduz = 0.0_dp |
| 796 |
depsjdx = 0.0_dp |
| 797 |
depsjdy = 0.0_dp |
| 798 |
depsjdz = 0.0_dp |
| 799 |
depsjdux = 0.0_dp |
| 800 |
depsjduy = 0.0_dp |
| 801 |
depsjduz = 0.0_dp |
| 802 |
else |
| 803 |
|
| 804 |
! rotate the inter-particle separation into the two different |
| 805 |
! body-fixed coordinate systems: |
| 806 |
! negative sign because this is the vector from j to i: |
| 807 |
|
| 808 |
xj = -(A2(1)*d(1) + A2(2)*d(2) + A2(3)*d(3)) |
| 809 |
yj = -(A2(4)*d(1) + A2(5)*d(2) + A2(6)*d(3)) |
| 810 |
zj = -(A2(7)*d(1) + A2(8)*d(2) + A2(9)*d(3)) |
| 811 |
|
| 812 |
xjhat = xj / rij |
| 813 |
yjhat = yj / rij |
| 814 |
zjhat = zj / rij |
| 815 |
xj2 = xj*xj |
| 816 |
yj2 = yj*yj |
| 817 |
zj2 = zj*zj |
| 818 |
ctj = zj / rij |
| 819 |
|
| 820 |
if (ctj .gt. 1.0_dp) ctj = 1.0_dp |
| 821 |
if (ctj .lt. -1.0_dp) ctj = -1.0_dp |
| 822 |
|
| 823 |
dctjdx = - zj * xj / r3 |
| 824 |
dctjdy = - zj * yj / r3 |
| 825 |
dctjdz = 1.0_dp / rij - zj2 / r3 |
| 826 |
dctjdux = yj / rij !- (zi * xj2) / r3 |
| 827 |
dctjduy = -xj / rij !- (zj * yj2) / r3 |
| 828 |
dctjduz = 0.0_dp !zj / rij - (zj2 * zj) / r3 |
| 829 |
|
| 830 |
! this is an attempt to try to truncate the singularity when |
| 831 |
! sin(theta) is near 0.0: |
| 832 |
|
| 833 |
stj2 = 1.0_dp - ctj*ctj |
| 834 |
if (abs(stj2) .lt. 1.0e-12_dp) then |
| 835 |
projj = sqrt(rij * 1.0e-12_dp) |
| 836 |
dcpjdx = 1.0_dp / projj |
| 837 |
dcpjdy = 0.0_dp |
| 838 |
dcpjdux = xj / projj |
| 839 |
dcpjduy = 0.0_dp |
| 840 |
dspjdx = 0.0_dp |
| 841 |
dspjdy = 1.0_dp / projj |
| 842 |
dspjdux = 0.0_dp |
| 843 |
dspjduy = yj / projj |
| 844 |
else |
| 845 |
projj = sqrt(xj2 + yj2) |
| 846 |
projj3 = projj*projj*projj |
| 847 |
dcpjdx = 1.0_dp / projj - xj2 / projj3 |
| 848 |
dcpjdy = - xj * yj / projj3 |
| 849 |
dcpjdux = xj / projj - (xj2 * xj) / projj3 |
| 850 |
dcpjduy = - (xj * yj2) / projj3 |
| 851 |
dspjdx = - xj * yj / projj3 |
| 852 |
dspjdy = 1.0_dp / projj - yj2 / projj3 |
| 853 |
dspjdux = - (yj * xj2) / projj3 |
| 854 |
dspjduy = yj / projj - (yj2 * yj) / projj3 |
| 855 |
endif |
| 856 |
|
| 857 |
cpj = xj / projj |
| 858 |
dcpjdz = 0.0_dp |
| 859 |
dcpjduz = 0.0_dp |
| 860 |
|
| 861 |
spj = yj / projj |
| 862 |
dspjdz = 0.0_dp |
| 863 |
dspjduz = 0.0_dp |
| 864 |
|
| 865 |
|
| 866 |
! write(*,*) 'dcpdu = ' ,dcpidux, dcpiduy, dcpiduz |
| 867 |
! write(*,*) 'dcpdu = ' ,dcpjdux, dcpjduy, dcpjduz |
| 868 |
call Associated_Legendre(ctj, ShapeMap%Shapes(st2)%bigM, & |
| 869 |
ShapeMap%Shapes(st2)%bigL, LMAX, & |
| 870 |
plm_j, dlm_j) |
| 871 |
|
| 872 |
call Orthogonal_Polynomial(cpj, ShapeMap%Shapes(st2)%bigM, MMAX, & |
| 873 |
CHEBYSHEV_TN, tm_j, dtm_j) |
| 874 |
call Orthogonal_Polynomial(cpj, ShapeMap%Shapes(st2)%bigM, MMAX, & |
| 875 |
CHEBYSHEV_UN, um_j, dum_j) |
| 876 |
|
| 877 |
sigma_j = 0.0_dp |
| 878 |
s_j = 0.0_dp |
| 879 |
eps_j = 0.0_dp |
| 880 |
dsigmajdx = 0.0_dp |
| 881 |
dsigmajdy = 0.0_dp |
| 882 |
dsigmajdz = 0.0_dp |
| 883 |
dsigmajdux = 0.0_dp |
| 884 |
dsigmajduy = 0.0_dp |
| 885 |
dsigmajduz = 0.0_dp |
| 886 |
dsjdx = 0.0_dp |
| 887 |
dsjdy = 0.0_dp |
| 888 |
dsjdz = 0.0_dp |
| 889 |
dsjdux = 0.0_dp |
| 890 |
dsjduy = 0.0_dp |
| 891 |
dsjduz = 0.0_dp |
| 892 |
depsjdx = 0.0_dp |
| 893 |
depsjdy = 0.0_dp |
| 894 |
depsjdz = 0.0_dp |
| 895 |
depsjdux = 0.0_dp |
| 896 |
depsjduy = 0.0_dp |
| 897 |
depsjduz = 0.0_dp |
| 898 |
|
| 899 |
do lm = 1, ShapeMap%Shapes(st2)%nContactFuncs |
| 900 |
l = ShapeMap%Shapes(st2)%ContactFuncLValue(lm) |
| 901 |
m = ShapeMap%Shapes(st2)%ContactFuncMValue(lm) |
| 902 |
coeff = ShapeMap%Shapes(st2)%ContactFuncCoefficient(lm) |
| 903 |
function_type = ShapeMap%Shapes(st2)%ContactFunctionType(lm) |
| 904 |
|
| 905 |
if ((function_type .eq. SH_COS).or.(m.eq.0)) then |
| 906 |
Phunc = coeff * tm_j(m) |
| 907 |
dPhuncdX = coeff * dtm_j(m) * dcpjdx |
| 908 |
dPhuncdY = coeff * dtm_j(m) * dcpjdy |
| 909 |
dPhuncdZ = coeff * dtm_j(m) * dcpjdz |
| 910 |
dPhuncdUx = coeff * dtm_j(m) * dcpjdux |
| 911 |
dPhuncdUy = coeff * dtm_j(m) * dcpjduy |
| 912 |
dPhuncdUz = coeff * dtm_j(m) * dcpjduz |
| 913 |
else |
| 914 |
Phunc = coeff * spj * um_j(m-1) |
| 915 |
dPhuncdX = coeff * (spj * dum_j(m-1) * dcpjdx + dspjdx *um_j(m-1)) |
| 916 |
dPhuncdY = coeff * (spj * dum_j(m-1) * dcpjdy + dspjdy *um_j(m-1)) |
| 917 |
dPhuncdZ = coeff * (spj * dum_j(m-1) * dcpjdz + dspjdz *um_j(m-1)) |
| 918 |
dPhuncdUx = coeff*(spj * dum_j(m-1)*dcpjdux + dspjdux *um_j(m-1)) |
| 919 |
dPhuncdUy = coeff*(spj * dum_j(m-1)*dcpjduy + dspjduy *um_j(m-1)) |
| 920 |
dPhuncdUz = coeff*(spj * dum_j(m-1)*dcpjduz + dspjduz *um_j(m-1)) |
| 921 |
endif |
| 922 |
|
| 923 |
sigma_j = sigma_j + plm_j(m,l)*Phunc |
| 924 |
|
| 925 |
dsigmajdx = dsigmajdx + plm_j(m,l)*dPhuncdX + & |
| 926 |
Phunc * dlm_j(m,l) * dctjdx |
| 927 |
dsigmajdy = dsigmajdy + plm_j(m,l)*dPhuncdY + & |
| 928 |
Phunc * dlm_j(m,l) * dctjdy |
| 929 |
dsigmajdz = dsigmajdz + plm_j(m,l)*dPhuncdZ + & |
| 930 |
Phunc * dlm_j(m,l) * dctjdz |
| 931 |
|
| 932 |
dsigmajdux = dsigmajdux + plm_j(m,l)* dPhuncdUx + & |
| 933 |
Phunc * dlm_j(m,l) * dctjdux |
| 934 |
dsigmajduy = dsigmajduy + plm_j(m,l)* dPhuncdUy + & |
| 935 |
Phunc * dlm_j(m,l) * dctjduy |
| 936 |
dsigmajduz = dsigmajduz + plm_j(m,l)* dPhuncdUz + & |
| 937 |
Phunc * dlm_j(m,l) * dctjduz |
| 938 |
|
| 939 |
end do |
| 940 |
|
| 941 |
do lm = 1, ShapeMap%Shapes(st2)%nRangeFuncs |
| 942 |
l = ShapeMap%Shapes(st2)%RangeFuncLValue(lm) |
| 943 |
m = ShapeMap%Shapes(st2)%RangeFuncMValue(lm) |
| 944 |
coeff = ShapeMap%Shapes(st2)%RangeFuncCoefficient(lm) |
| 945 |
function_type = ShapeMap%Shapes(st2)%RangeFunctionType(lm) |
| 946 |
|
| 947 |
if ((function_type .eq. SH_COS).or.(m.eq.0)) then |
| 948 |
Phunc = coeff * tm_j(m) |
| 949 |
dPhuncdX = coeff * dtm_j(m) * dcpjdx |
| 950 |
dPhuncdY = coeff * dtm_j(m) * dcpjdy |
| 951 |
dPhuncdZ = coeff * dtm_j(m) * dcpjdz |
| 952 |
dPhuncdUx = coeff * dtm_j(m) * dcpjdux |
| 953 |
dPhuncdUy = coeff * dtm_j(m) * dcpjduy |
| 954 |
dPhuncdUz = coeff * dtm_j(m) * dcpjduz |
| 955 |
else |
| 956 |
Phunc = coeff * spj * um_j(m-1) |
| 957 |
dPhuncdX = coeff * (spj * dum_j(m-1) * dcpjdx + dspjdx *um_j(m-1)) |
| 958 |
dPhuncdY = coeff * (spj * dum_j(m-1) * dcpjdy + dspjdy *um_j(m-1)) |
| 959 |
dPhuncdZ = coeff * (spj * dum_j(m-1) * dcpjdz + dspjdz *um_j(m-1)) |
| 960 |
dPhuncdUx = coeff*(spj * dum_j(m-1)*dcpjdux + dspjdux *um_j(m-1)) |
| 961 |
dPhuncdUy = coeff*(spj * dum_j(m-1)*dcpjduy + dspjduy *um_j(m-1)) |
| 962 |
dPhuncdUz = coeff*(spj * dum_j(m-1)*dcpjduz + dspjduz *um_j(m-1)) |
| 963 |
endif |
| 964 |
|
| 965 |
s_j = s_j + plm_j(m,l)*Phunc |
| 966 |
|
| 967 |
dsjdx = dsjdx + plm_j(m,l)*dPhuncdX + & |
| 968 |
Phunc * dlm_j(m,l) * dctjdx |
| 969 |
dsjdy = dsjdy + plm_j(m,l)*dPhuncdY + & |
| 970 |
Phunc * dlm_j(m,l) * dctjdy |
| 971 |
dsjdz = dsjdz + plm_j(m,l)*dPhuncdZ + & |
| 972 |
Phunc * dlm_j(m,l) * dctjdz |
| 973 |
|
| 974 |
dsjdux = dsjdux + plm_j(m,l)* dPhuncdUx + & |
| 975 |
Phunc * dlm_j(m,l) * dctjdux |
| 976 |
dsjduy = dsjduy + plm_j(m,l)* dPhuncdUy + & |
| 977 |
Phunc * dlm_j(m,l) * dctjduy |
| 978 |
dsjduz = dsjduz + plm_j(m,l)* dPhuncdUz + & |
| 979 |
Phunc * dlm_j(m,l) * dctjduz |
| 980 |
|
| 981 |
end do |
| 982 |
|
| 983 |
do lm = 1, ShapeMap%Shapes(st2)%nStrengthFuncs |
| 984 |
l = ShapeMap%Shapes(st2)%StrengthFuncLValue(lm) |
| 985 |
m = ShapeMap%Shapes(st2)%StrengthFuncMValue(lm) |
| 986 |
coeff = ShapeMap%Shapes(st2)%StrengthFuncCoefficient(lm) |
| 987 |
function_type = ShapeMap%Shapes(st2)%StrengthFunctionType(lm) |
| 988 |
|
| 989 |
if ((function_type .eq. SH_COS).or.(m.eq.0)) then |
| 990 |
Phunc = coeff * tm_j(m) |
| 991 |
dPhuncdX = coeff * dtm_j(m) * dcpjdx |
| 992 |
dPhuncdY = coeff * dtm_j(m) * dcpjdy |
| 993 |
dPhuncdZ = coeff * dtm_j(m) * dcpjdz |
| 994 |
dPhuncdUz = coeff * dtm_j(m) * dcpjdux |
| 995 |
dPhuncdUy = coeff * dtm_j(m) * dcpjduy |
| 996 |
dPhuncdUz = coeff * dtm_j(m) * dcpjduz |
| 997 |
else |
| 998 |
Phunc = coeff * spj * um_j(m-1) |
| 999 |
dPhuncdX = coeff * (spj * dum_j(m-1) * dcpjdx + dspjdx *um_j(m-1)) |
| 1000 |
dPhuncdY = coeff * (spj * dum_j(m-1) * dcpjdy + dspjdy *um_j(m-1)) |
| 1001 |
dPhuncdZ = coeff * (spj * dum_j(m-1) * dcpjdz + dspjdz *um_j(m-1)) |
| 1002 |
dPhuncdUx = coeff*(spj * dum_j(m-1)*dcpjdux + dspjdux *um_j(m-1)) |
| 1003 |
dPhuncdUy = coeff*(spj * dum_j(m-1)*dcpjduy + dspjduy *um_j(m-1)) |
| 1004 |
dPhuncdUz = coeff*(spj * dum_j(m-1)*dcpjduz + dspjduz *um_j(m-1)) |
| 1005 |
endif |
| 1006 |
|
| 1007 |
! write(*,*) 'l,m = ', l, m, coeff, dPhuncdUx, dPhuncdUy, dPhuncdUz |
| 1008 |
|
| 1009 |
eps_j = eps_j + plm_j(m,l)*Phunc |
| 1010 |
|
| 1011 |
depsjdx = depsjdx + plm_j(m,l)*dPhuncdX + & |
| 1012 |
Phunc * dlm_j(m,l) * dctjdx |
| 1013 |
depsjdy = depsjdy + plm_j(m,l)*dPhuncdY + & |
| 1014 |
Phunc * dlm_j(m,l) * dctjdy |
| 1015 |
depsjdz = depsjdz + plm_j(m,l)*dPhuncdZ + & |
| 1016 |
Phunc * dlm_j(m,l) * dctjdz |
| 1017 |
|
| 1018 |
depsjdux = depsjdux + plm_j(m,l)* dPhuncdUx + & |
| 1019 |
Phunc * dlm_j(m,l) * dctjdux |
| 1020 |
depsjduy = depsjduy + plm_j(m,l)* dPhuncdUy + & |
| 1021 |
Phunc * dlm_j(m,l) * dctjduy |
| 1022 |
depsjduz = depsjduz + plm_j(m,l)* dPhuncdUz + & |
| 1023 |
Phunc * dlm_j(m,l) * dctjduz |
| 1024 |
|
| 1025 |
end do |
| 1026 |
|
| 1027 |
endif |
| 1028 |
|
| 1029 |
! phew, now let's assemble the potential energy: |
| 1030 |
|
| 1031 |
sigma = 0.5*(sigma_i + sigma_j) |
| 1032 |
! write(*,*) sigma_i, ' = sigma_i; ', sigma_j, ' = sigma_j' |
| 1033 |
dsigmadxi = 0.5*dsigmaidx |
| 1034 |
dsigmadyi = 0.5*dsigmaidy |
| 1035 |
dsigmadzi = 0.5*dsigmaidz |
| 1036 |
dsigmaduxi = 0.5*dsigmaidux |
| 1037 |
dsigmaduyi = 0.5*dsigmaiduy |
| 1038 |
dsigmaduzi = 0.5*dsigmaiduz |
| 1039 |
|
| 1040 |
dsigmadxj = 0.5*dsigmajdx |
| 1041 |
dsigmadyj = 0.5*dsigmajdy |
| 1042 |
dsigmadzj = 0.5*dsigmajdz |
| 1043 |
dsigmaduxj = 0.5*dsigmajdux |
| 1044 |
dsigmaduyj = 0.5*dsigmajduy |
| 1045 |
dsigmaduzj = 0.5*dsigmajduz |
| 1046 |
|
| 1047 |
s = 0.5*(s_i + s_j) |
| 1048 |
|
| 1049 |
dsdxi = 0.5*dsidx |
| 1050 |
dsdyi = 0.5*dsidy |
| 1051 |
dsdzi = 0.5*dsidz |
| 1052 |
dsduxi = 0.5*dsidux |
| 1053 |
dsduyi = 0.5*dsiduy |
| 1054 |
dsduzi = 0.5*dsiduz |
| 1055 |
|
| 1056 |
dsdxj = 0.5*dsjdx |
| 1057 |
dsdyj = 0.5*dsjdy |
| 1058 |
dsdzj = 0.5*dsjdz |
| 1059 |
dsduxj = 0.5*dsjdux |
| 1060 |
dsduyj = 0.5*dsjduy |
| 1061 |
dsduzj = 0.5*dsjduz |
| 1062 |
|
| 1063 |
eps = sqrt(eps_i * eps_j) |
| 1064 |
!!$ write(*,*) 'dsidu = ', dsidux, dsiduy, dsiduz |
| 1065 |
!!$ write(*,*) 'dsigidu = ', dsigmaidux, dsigmaiduy, dsigmaiduz |
| 1066 |
!!$ write(*,*) sigma_j, ' is sigma j; ', s_j, ' is s j; ', eps_j, ' is eps j' |
| 1067 |
depsdxi = eps_j * depsidx / (2.0_dp * eps) |
| 1068 |
depsdyi = eps_j * depsidy / (2.0_dp * eps) |
| 1069 |
depsdzi = eps_j * depsidz / (2.0_dp * eps) |
| 1070 |
depsduxi = eps_j * depsidux / (2.0_dp * eps) |
| 1071 |
depsduyi = eps_j * depsiduy / (2.0_dp * eps) |
| 1072 |
depsduzi = eps_j * depsiduz / (2.0_dp * eps) |
| 1073 |
|
| 1074 |
depsdxj = eps_i * depsjdx / (2.0_dp * eps) |
| 1075 |
depsdyj = eps_i * depsjdy / (2.0_dp * eps) |
| 1076 |
depsdzj = eps_i * depsjdz / (2.0_dp * eps) |
| 1077 |
depsduxj = eps_i * depsjdux / (2.0_dp * eps) |
| 1078 |
depsduyj = eps_i * depsjduy / (2.0_dp * eps) |
| 1079 |
depsduzj = eps_i * depsjduz / (2.0_dp * eps) |
| 1080 |
|
| 1081 |
!!$ write(*,*) 'depsidu = ', depsidux, depsiduy, depsiduz |
| 1082 |
|
| 1083 |
!!$ write(*,*) 'depsjdu = ', depsjdux, depsjduy, depsjduz |
| 1084 |
!!$ write(*,*) 'depsduj = ', depsduxj, depsduyj, depsduzj |
| 1085 |
!!$ |
| 1086 |
!!$ write(*,*) 's, sig, eps = ', s, sigma, eps |
| 1087 |
|
| 1088 |
rtdenom = rij-sigma+s |
| 1089 |
rt = s / rtdenom |
| 1090 |
|
| 1091 |
drtdxi = (dsdxi - rt * (drdxi - dsigmadxi + dsdxi)) / rtdenom |
| 1092 |
drtdyi = (dsdyi - rt * (drdyi - dsigmadyi + dsdyi)) / rtdenom |
| 1093 |
drtdzi = (dsdzi - rt * (drdzi - dsigmadzi + dsdzi)) / rtdenom |
| 1094 |
drtduxi = (dsduxi - rt * (drduxi - dsigmaduxi + dsduxi)) / rtdenom |
| 1095 |
drtduyi = (dsduyi - rt * (drduyi - dsigmaduyi + dsduyi)) / rtdenom |
| 1096 |
drtduzi = (dsduzi - rt * (drduzi - dsigmaduzi + dsduzi)) / rtdenom |
| 1097 |
drtdxj = (dsdxj - rt * (drdxj - dsigmadxj + dsdxj)) / rtdenom |
| 1098 |
drtdyj = (dsdyj - rt * (drdyj - dsigmadyj + dsdyj)) / rtdenom |
| 1099 |
drtdzj = (dsdzj - rt * (drdzj - dsigmadzj + dsdzj)) / rtdenom |
| 1100 |
drtduxj = (dsduxj - rt * (drduxj - dsigmaduxj + dsduxj)) / rtdenom |
| 1101 |
drtduyj = (dsduyj - rt * (drduyj - dsigmaduyj + dsduyj)) / rtdenom |
| 1102 |
drtduzj = (dsduzj - rt * (drduzj - dsigmaduzj + dsduzj)) / rtdenom |
| 1103 |
|
| 1104 |
!!$ write(*,*) 'drtd_i = ', drtdxi, drtdyi, drtdzi |
| 1105 |
!!$ write(*,*) 'drtdu_j = ', drtduxj, drtduyj, drtduzj |
| 1106 |
|
| 1107 |
rt2 = rt*rt |
| 1108 |
rt3 = rt2*rt |
| 1109 |
rt5 = rt2*rt3 |
| 1110 |
rt6 = rt3*rt3 |
| 1111 |
rt11 = rt5*rt6 |
| 1112 |
rt12 = rt6*rt6 |
| 1113 |
rt126 = rt12 - rt6 |
| 1114 |
|
| 1115 |
pot_temp = 4.0_dp * eps * rt126 |
| 1116 |
|
| 1117 |
vpair = vpair + pot_temp |
| 1118 |
|
| 1119 |
pot = pot + pot_temp*sw |
| 1120 |
|
| 1121 |
!!$ write(*,*) 'drtdu, depsdu = ', drtduxi, depsduxi |
| 1122 |
|
| 1123 |
dvdxi = 24.0_dp*eps*(2.0_dp*rt11 - rt5)*drtdxi + 4.0_dp*depsdxi*rt126 |
| 1124 |
dvdyi = 24.0_dp*eps*(2.0_dp*rt11 - rt5)*drtdyi + 4.0_dp*depsdyi*rt126 |
| 1125 |
dvdzi = 24.0_dp*eps*(2.0_dp*rt11 - rt5)*drtdzi + 4.0_dp*depsdzi*rt126 |
| 1126 |
dvduxi = 24.0_dp*eps*(2.0_dp*rt11 - rt5)*drtduxi + 4.0_dp*depsduxi*rt126 |
| 1127 |
dvduyi = 24.0_dp*eps*(2.0_dp*rt11 - rt5)*drtduyi + 4.0_dp*depsduyi*rt126 |
| 1128 |
dvduzi = 24.0_dp*eps*(2.0_dp*rt11 - rt5)*drtduzi + 4.0_dp*depsduzi*rt126 |
| 1129 |
|
| 1130 |
dvdxj = 24.0_dp*eps*(2.0_dp*rt11 - rt5)*drtdxj + 4.0_dp*depsdxj*rt126 |
| 1131 |
dvdyj = 24.0_dp*eps*(2.0_dp*rt11 - rt5)*drtdyj + 4.0_dp*depsdyj*rt126 |
| 1132 |
dvdzj = 24.0_dp*eps*(2.0_dp*rt11 - rt5)*drtdzj + 4.0_dp*depsdzj*rt126 |
| 1133 |
dvduxj = 24.0_dp*eps*(2.0_dp*rt11 - rt5)*drtduxj + 4.0_dp*depsduxj*rt126 |
| 1134 |
dvduyj = 24.0_dp*eps*(2.0_dp*rt11 - rt5)*drtduyj + 4.0_dp*depsduyj*rt126 |
| 1135 |
dvduzj = 24.0_dp*eps*(2.0_dp*rt11 - rt5)*drtduzj + 4.0_dp*depsduzj*rt126 |
| 1136 |
!!$ write(*,*) 'drtduxi = ', drtduxi, ' depsduxi = ', depsduxi |
| 1137 |
! do the torques first since they are easy: |
| 1138 |
! remember that these are still in the body fixed axes |
| 1139 |
|
| 1140 |
txi = 0.0_dp |
| 1141 |
tyi = 0.0_dp |
| 1142 |
tzi = 0.0_dp |
| 1143 |
|
| 1144 |
txj = 0.0_dp |
| 1145 |
tyj = 0.0_dp |
| 1146 |
tzj = 0.0_dp |
| 1147 |
|
| 1148 |
txi = (dvduyi - dvduzi) * sw |
| 1149 |
tyi = (dvduzi - dvduxi) * sw |
| 1150 |
tzi = (dvduxi - dvduyi) * sw |
| 1151 |
|
| 1152 |
txj = (dvduyj - dvduzj) * sw |
| 1153 |
tyj = (dvduzj - dvduxj) * sw |
| 1154 |
tzj = (dvduxj - dvduyj) * sw |
| 1155 |
|
| 1156 |
!!$ txi = dvduxi * sw |
| 1157 |
!!$ tyi = dvduyi * sw |
| 1158 |
!!$ tzi = dvduzi * sw |
| 1159 |
!!$ |
| 1160 |
!!$ txj = dvduxj * sw |
| 1161 |
!!$ tyj = dvduyj * sw |
| 1162 |
!!$ tzj = dvduzj * sw |
| 1163 |
|
| 1164 |
write(*,*) 't1 = ', txi, tyi, tzi |
| 1165 |
write(*,*) 't2 = ', txj, tyj, tzj |
| 1166 |
|
| 1167 |
! go back to lab frame using transpose of rotation matrix: |
| 1168 |
|
| 1169 |
t1(1) = t1(1) + a1(1)*txi + a1(4)*tyi + a1(7)*tzi |
| 1170 |
t1(2) = t1(2) + a1(2)*txi + a1(5)*tyi + a1(8)*tzi |
| 1171 |
t1(3) = t1(3) + a1(3)*txi + a1(6)*tyi + a1(9)*tzi |
| 1172 |
|
| 1173 |
t2(1) = t2(1) + a2(1)*txj + a2(4)*tyj + a2(7)*tzj |
| 1174 |
t2(2) = t2(2) + a2(2)*txj + a2(5)*tyj + a2(8)*tzj |
| 1175 |
t2(3) = t2(3) + a2(3)*txj + a2(6)*tyj + a2(9)*tzj |
| 1176 |
|
| 1177 |
! Now, on to the forces: |
| 1178 |
|
| 1179 |
! first rotate the i terms back into the lab frame: |
| 1180 |
|
| 1181 |
fxi = -dvdxi * sw |
| 1182 |
fyi = -dvdyi * sw |
| 1183 |
fzi = -dvdzi * sw |
| 1184 |
|
| 1185 |
fxj = -dvdxj * sw |
| 1186 |
fyj = -dvdyj * sw |
| 1187 |
fzj = -dvdzj * sw |
| 1188 |
|
| 1189 |
fxii = a1(1)*fxi + a1(4)*fyi + a1(7)*fzi |
| 1190 |
fyii = a1(2)*fxi + a1(5)*fyi + a1(8)*fzi |
| 1191 |
fzii = a1(3)*fxi + a1(6)*fyi + a1(9)*fzi |
| 1192 |
|
| 1193 |
fxjj = a2(1)*fxj + a2(4)*fyj + a2(7)*fzj |
| 1194 |
fyjj = a2(2)*fxj + a2(5)*fyj + a2(8)*fzj |
| 1195 |
fzjj = a2(3)*fxj + a2(6)*fyj + a2(9)*fzj |
| 1196 |
|
| 1197 |
fxij = -fxii |
| 1198 |
fyij = -fyii |
| 1199 |
fzij = -fzii |
| 1200 |
|
| 1201 |
fxji = -fxjj |
| 1202 |
fyji = -fyjj |
| 1203 |
fzji = -fzjj |
| 1204 |
|
| 1205 |
fxradial = (fxii + fxji) |
| 1206 |
fyradial = (fyii + fyji) |
| 1207 |
fzradial = (fzii + fzji) |
| 1208 |
!!$ write(*,*) fxradial, ' is fxrad; ', fyradial, ' is fyrad; ', fzradial, 'is fzrad' |
| 1209 |
|
| 1210 |
f1(1) = f1(1) + fxradial |
| 1211 |
f1(2) = f1(2) + fxradial |
| 1212 |
f1(3) = f1(3) + fxradial |
| 1213 |
|
| 1214 |
end subroutine do_shape_pair |
| 1215 |
|
| 1216 |
SUBROUTINE Associated_Legendre(x, l, m, lmax, plm, dlm) |
| 1217 |
|
| 1218 |
! Purpose: Compute the associated Legendre functions |
| 1219 |
! Plm(x) and their derivatives Plm'(x) |
| 1220 |
! Input : x --- Argument of Plm(x) |
| 1221 |
! l --- Order of Plm(x), l = 0,1,2,...,n |
| 1222 |
! m --- Degree of Plm(x), m = 0,1,2,...,N |
| 1223 |
! lmax --- Physical dimension of PLM and DLM |
| 1224 |
! Output: PLM(l,m) --- Plm(x) |
| 1225 |
! DLM(l,m) --- Plm'(x) |
| 1226 |
! |
| 1227 |
! adapted from the routines in |
| 1228 |
! COMPUTATION OF SPECIAL FUNCTIONS by Shanjie Zhang and Jianming Jin |
| 1229 |
! ISBN 0-471-11963-6 |
| 1230 |
! |
| 1231 |
! The original Fortran77 codes can be found here: |
| 1232 |
! http://iris-lee3.ece.uiuc.edu/~jjin/routines/routines.html |
| 1233 |
|
| 1234 |
real (kind=dp), intent(in) :: x |
| 1235 |
integer, intent(in) :: l, m, lmax |
| 1236 |
real (kind=dp), dimension(0:lmax,0:m), intent(out) :: PLM, DLM |
| 1237 |
integer :: i, j, ls |
| 1238 |
real (kind=dp) :: xq, xs |
| 1239 |
|
| 1240 |
! zero out both arrays: |
| 1241 |
DO I = 0, m |
| 1242 |
DO J = 0, l |
| 1243 |
PLM(J,I) = 0.0_dp |
| 1244 |
DLM(J,I) = 0.0_dp |
| 1245 |
end DO |
| 1246 |
end DO |
| 1247 |
|
| 1248 |
! start with 0,0: |
| 1249 |
PLM(0,0) = 1.0_DP |
| 1250 |
|
| 1251 |
! x = +/- 1 functions are easy: |
| 1252 |
IF (abs(X).EQ.1.0_DP) THEN |
| 1253 |
DO I = 1, m |
| 1254 |
PLM(0, I) = X**I |
| 1255 |
DLM(0, I) = 0.5_DP*I*(I+1.0_DP)*X**(I+1) |
| 1256 |
end DO |
| 1257 |
DO J = 1, m |
| 1258 |
DO I = 1, l |
| 1259 |
IF (I.EQ.1) THEN |
| 1260 |
DLM(I, J) = 1.0D+300 |
| 1261 |
ELSE IF (I.EQ.2) THEN |
| 1262 |
DLM(I, J) = -0.25_DP*(J+2)*(J+1)*J*(J-1)*X**(J+1) |
| 1263 |
ENDIF |
| 1264 |
end DO |
| 1265 |
end DO |
| 1266 |
RETURN |
| 1267 |
ENDIF |
| 1268 |
|
| 1269 |
LS = 1 |
| 1270 |
IF (abs(X).GT.1.0_DP) LS = -1 |
| 1271 |
XQ = sqrt(LS*(1.0_DP-X*X)) |
| 1272 |
XS = LS*(1.0_DP-X*X) |
| 1273 |
|
| 1274 |
DO I = 1, l |
| 1275 |
PLM(I, I) = -LS*(2.0_DP*I-1.0_DP)*XQ*PLM(I-1, I-1) |
| 1276 |
enddo |
| 1277 |
|
| 1278 |
DO I = 0, l |
| 1279 |
PLM(I, I+1)=(2.0_DP*I+1.0_DP)*X*PLM(I, I) |
| 1280 |
enddo |
| 1281 |
|
| 1282 |
DO I = 0, l |
| 1283 |
DO J = I+2, m |
| 1284 |
PLM(I, J)=((2.0_DP*J-1.0_DP)*X*PLM(I,J-1) - & |
| 1285 |
(I+J-1.0_DP)*PLM(I,J-2))/(J-I) |
| 1286 |
end DO |
| 1287 |
end DO |
| 1288 |
|
| 1289 |
DLM(0, 0)=0.0_DP |
| 1290 |
DO J = 1, m |
| 1291 |
DLM(0, J)=LS*J*(PLM(0,J-1)-X*PLM(0,J))/XS |
| 1292 |
end DO |
| 1293 |
|
| 1294 |
DO I = 1, l |
| 1295 |
DO J = I, m |
| 1296 |
DLM(I,J) = LS*I*X*PLM(I, J)/XS + (J+I)*(J-I+1.0_DP)/XQ*PLM(I-1, J) |
| 1297 |
end DO |
| 1298 |
end DO |
| 1299 |
|
| 1300 |
RETURN |
| 1301 |
END SUBROUTINE Associated_Legendre |
| 1302 |
|
| 1303 |
|
| 1304 |
subroutine Orthogonal_Polynomial(x, m, mmax, function_type, pl, dpl) |
| 1305 |
|
| 1306 |
! Purpose: Compute orthogonal polynomials: Tn(x) or Un(x), |
| 1307 |
! or Ln(x) or Hn(x), and their derivatives |
| 1308 |
! Input : function_type --- Function code |
| 1309 |
! =1 for Chebyshev polynomial Tn(x) |
| 1310 |
! =2 for Chebyshev polynomial Un(x) |
| 1311 |
! =3 for Laguerre polynomial Ln(x) |
| 1312 |
! =4 for Hermite polynomial Hn(x) |
| 1313 |
! n --- Order of orthogonal polynomials |
| 1314 |
! x --- Argument of orthogonal polynomials |
| 1315 |
! Output: PL(n) --- Tn(x) or Un(x) or Ln(x) or Hn(x) |
| 1316 |
! DPL(n)--- Tn'(x) or Un'(x) or Ln'(x) or Hn'(x) |
| 1317 |
! |
| 1318 |
! adapted from the routines in |
| 1319 |
! COMPUTATION OF SPECIAL FUNCTIONS by Shanjie Zhang and Jianming Jin |
| 1320 |
! ISBN 0-471-11963-6 |
| 1321 |
! |
| 1322 |
! The original Fortran77 codes can be found here: |
| 1323 |
! http://iris-lee3.ece.uiuc.edu/~jjin/routines/routines.html |
| 1324 |
|
| 1325 |
real(kind=dp), intent(in) :: x |
| 1326 |
integer, intent(in):: m, mmax |
| 1327 |
integer, intent(in):: function_type |
| 1328 |
real(kind=dp), dimension(0:mmax), intent(inout) :: pl, dpl |
| 1329 |
|
| 1330 |
real(kind=dp) :: a, b, c, y0, y1, dy0, dy1, yn, dyn |
| 1331 |
integer :: k |
| 1332 |
|
| 1333 |
A = 2.0_DP |
| 1334 |
B = 0.0_DP |
| 1335 |
C = 1.0_DP |
| 1336 |
Y0 = 1.0_DP |
| 1337 |
Y1 = 2.0_DP*X |
| 1338 |
DY0 = 0.0_DP |
| 1339 |
DY1 = 2.0_DP |
| 1340 |
PL(0) = 1.0_DP |
| 1341 |
PL(1) = 2.0_DP*X |
| 1342 |
DPL(0) = 0.0_DP |
| 1343 |
DPL(1) = 2.0_DP |
| 1344 |
IF (function_type.EQ.CHEBYSHEV_TN) THEN |
| 1345 |
Y1 = X |
| 1346 |
DY1 = 1.0_DP |
| 1347 |
PL(1) = X |
| 1348 |
DPL(1) = 1.0_DP |
| 1349 |
ELSE IF (function_type.EQ.LAGUERRE) THEN |
| 1350 |
Y1 = 1.0_DP-X |
| 1351 |
DY1 = -1.0_DP |
| 1352 |
PL(1) = 1.0_DP-X |
| 1353 |
DPL(1) = -1.0_DP |
| 1354 |
ENDIF |
| 1355 |
DO K = 2, m |
| 1356 |
IF (function_type.EQ.LAGUERRE) THEN |
| 1357 |
A = -1.0_DP/K |
| 1358 |
B = 2.0_DP+A |
| 1359 |
C = 1.0_DP+A |
| 1360 |
ELSE IF (function_type.EQ.HERMITE) THEN |
| 1361 |
C = 2.0_DP*(K-1.0_DP) |
| 1362 |
ENDIF |
| 1363 |
YN = (A*X+B)*Y1-C*Y0 |
| 1364 |
DYN = A*Y1+(A*X+B)*DY1-C*DY0 |
| 1365 |
PL(K) = YN |
| 1366 |
DPL(K) = DYN |
| 1367 |
Y0 = Y1 |
| 1368 |
Y1 = YN |
| 1369 |
DY0 = DY1 |
| 1370 |
DY1 = DYN |
| 1371 |
end DO |
| 1372 |
|
| 1373 |
|
| 1374 |
RETURN |
| 1375 |
|
| 1376 |
end subroutine Orthogonal_Polynomial |
| 1377 |
|
| 1378 |
subroutine deallocateShapes(this) |
| 1379 |
type(Shape), pointer :: this |
| 1380 |
|
| 1381 |
if (associated( this%ContactFuncLValue)) then |
| 1382 |
deallocate(this%ContactFuncLValue) |
| 1383 |
this%ContactFuncLValue => null() |
| 1384 |
end if |
| 1385 |
|
| 1386 |
if (associated( this%ContactFuncMValue)) then |
| 1387 |
deallocate( this%ContactFuncMValue) |
| 1388 |
this%ContactFuncMValue => null() |
| 1389 |
end if |
| 1390 |
if (associated( this%ContactFunctionType)) then |
| 1391 |
deallocate(this%ContactFunctionType) |
| 1392 |
this%ContactFunctionType => null() |
| 1393 |
end if |
| 1394 |
|
| 1395 |
if (associated( this%ContactFuncCoefficient)) then |
| 1396 |
deallocate(this%ContactFuncCoefficient) |
| 1397 |
this%ContactFuncCoefficient => null() |
| 1398 |
end if |
| 1399 |
|
| 1400 |
if (associated( this%RangeFuncLValue)) then |
| 1401 |
deallocate(this%RangeFuncLValue) |
| 1402 |
this%RangeFuncLValue => null() |
| 1403 |
end if |
| 1404 |
if (associated( this%RangeFuncMValue)) then |
| 1405 |
deallocate( this%RangeFuncMValue) |
| 1406 |
this%RangeFuncMValue => null() |
| 1407 |
end if |
| 1408 |
|
| 1409 |
if (associated( this%RangeFunctionType)) then |
| 1410 |
deallocate( this%RangeFunctionType) |
| 1411 |
this%RangeFunctionType => null() |
| 1412 |
end if |
| 1413 |
if (associated( this%RangeFuncCoefficient)) then |
| 1414 |
deallocate(this%RangeFuncCoefficient) |
| 1415 |
this%RangeFuncCoefficient => null() |
| 1416 |
end if |
| 1417 |
|
| 1418 |
if (associated( this%StrengthFuncLValue)) then |
| 1419 |
deallocate(this%StrengthFuncLValue) |
| 1420 |
this%StrengthFuncLValue => null() |
| 1421 |
end if |
| 1422 |
|
| 1423 |
if (associated( this%StrengthFuncMValue )) then |
| 1424 |
deallocate(this%StrengthFuncMValue) |
| 1425 |
this%StrengthFuncMValue => null() |
| 1426 |
end if |
| 1427 |
|
| 1428 |
if(associated( this%StrengthFunctionType)) then |
| 1429 |
deallocate(this%StrengthFunctionType) |
| 1430 |
this%StrengthFunctionType => null() |
| 1431 |
end if |
| 1432 |
if (associated( this%StrengthFuncCoefficient )) then |
| 1433 |
deallocate(this%StrengthFuncCoefficient) |
| 1434 |
this%StrengthFuncCoefficient => null() |
| 1435 |
end if |
| 1436 |
end subroutine deallocateShapes |
| 1437 |
|
| 1438 |
subroutine destroyShapeTypes |
| 1439 |
integer :: i |
| 1440 |
type(Shape), pointer :: thisShape |
| 1441 |
|
| 1442 |
! First walk through and kill the shape |
| 1443 |
do i = 1,ShapeMap%n_shapes |
| 1444 |
thisShape => ShapeMap%Shapes(i) |
| 1445 |
call deallocateShapes(thisShape) |
| 1446 |
end do |
| 1447 |
|
| 1448 |
! set shape map to starting values |
| 1449 |
ShapeMap%n_shapes = 0 |
| 1450 |
ShapeMap%currentShape = 0 |
| 1451 |
|
| 1452 |
if (associated(ShapeMap%Shapes)) then |
| 1453 |
deallocate(ShapeMap%Shapes) |
| 1454 |
ShapeMap%Shapes => null() |
| 1455 |
end if |
| 1456 |
|
| 1457 |
if (associated(ShapeMap%atidToShape)) then |
| 1458 |
deallocate(ShapeMap%atidToShape) |
| 1459 |
ShapeMap%atidToShape => null() |
| 1460 |
end if |
| 1461 |
|
| 1462 |
|
| 1463 |
end subroutine destroyShapeTypes |
| 1464 |
|
| 1465 |
|
| 1466 |
end module shapes |
