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!! |
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!! Copyright (c) 2006 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. Acknowledgement of the program authors must be made in any |
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!! publication of scientific results based in part on use of the |
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!! program. An acceptable form of acknowledgement is citation of |
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!! the article in which the program was described (Matthew |
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!! A. Meineke, Charles F. Vardeman II, Teng Lin, Christopher |
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!! J. Fennell and J. Daniel Gezelter, "OOPSE: An Object-Oriented |
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!! Parallel Simulation Engine for Molecular Dynamics," |
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!! J. Comput. Chem. 26, pp. 252-271 (2005)) |
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!! |
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!! 2. 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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!! 3. 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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!! |
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!! interpolation.F90 |
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!! |
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!! Created by Charles F. Vardeman II on 03 Apr 2006. |
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!! |
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!! PURPOSE: Generic Spline interplelation routines. These routines assume that we are on a uniform grid for |
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!! precomputation of spline parameters. |
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!! |
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!! @author Charles F. Vardeman II |
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!! @version $Id: interpolation.F90,v 1.1 2006-04-12 21:15:17 chuckv Exp $ |
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|
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|
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module INTERPOLATION |
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use definitions |
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use status |
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implicit none |
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PRIVATE |
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|
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character(len = statusMsgSize) :: errMSG |
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|
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type, public :: splineType |
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private |
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integer :: npoints = 0 |
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real(kind=dp) :: delta_x |
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real(kind=dp) :: range |
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real(kind=dp) :: range_inv |
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real (kind=dp), pointer,dimension(:) :: xa => null() |
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real (kind=dp), pointer,dimension(:) :: ya => null() |
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real (kind=dp), pointer,dimension(:) :: yppa => null() |
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end type splineType |
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|
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type, public :: multiSplineType |
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private |
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integer :: npoints = 0 |
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integer :: nfuncs = 0 |
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|
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integer :: npoints = 0 |
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real(kind=dp) :: delta_x |
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real(kind=dp) :: range |
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real(kind=dp) :: range_inv |
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real (kind=dp), pointer,dimension(:) :: xa => null() |
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real (kind=dp), pointer,dimension(:,:) :: ya => null() |
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real (kind=dp), pointer,dimension(:,:) :: yppa => null() |
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end type splineType |
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|
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|
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interface splineLookup |
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module procedure multiSplint |
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module procedure splintd |
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module procedure splintd1 |
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module procedure splintd2 |
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end interface |
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|
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public :: splint |
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public :: newSpline |
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public :: newMultiSpline |
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public :: deleteSpline |
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public :: deleteMultiSpline |
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|
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|
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contains |
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|
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!! mySpline is pointer to spline type, nx number of data points, |
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!! xa tabulated x values and ya respective values for xa, yp1 |
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!! is value for derivative at first point and ypn is value |
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!! for derivative at point n. |
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subroutine newSpline(thisSpline,nx, xa, ya, yp1, ypn, boundary) |
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|
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! yp1 and ypn are the first derivatives of y at the two endpoints |
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! if boundary is 'L' the lower derivative is used |
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! if boundary is 'U' the upper derivative is used |
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! if boundary is 'B' then both derivatives are used |
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! if boundary is anything else, then both derivatives are assumed to be 0 |
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|
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|
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type (splineType), intent(inout) :: thisSpline |
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|
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|
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real( kind = DP ), pointer, dimension(:) :: xa |
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real( kind = DP ), pointer, dimension(:) :: ya |
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real( kind = DP ), dimension(size(xa)) :: u |
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real( kind = DP ) :: yp1,ypn,un,qn,sig,p |
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character(len=*) :: boundary |
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integer :: nx, i, k, max_array_size |
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integer :: alloc_error |
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|
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alloc_error = 0 |
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|
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if (thisSpline%npoints/=0) then |
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call handleWarning("INTERPOLATION:newSpline",& |
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"Type has already been created") |
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call deleteSpline(thisSpline) |
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end if |
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|
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|
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! make sure the sizes match |
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if ((nx /= size(xa)) .or. (nx /= size(ya))) then |
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call handleWarning("INTERPOLATION:newSpline","Array size mismatch") |
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end if |
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|
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|
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thisSpline%npoints = nx |
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allocate(thisSpline%yppa(nx),stat=alloc_error) |
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if(alloc_error .ne. 0) call handleWarning("INTERPOLATION:newSpline",& |
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"Error in allocating storage for yppa") |
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|
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thisSpline%xa => xa |
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thisSpline%ya => ya |
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|
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|
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|
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|
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if ((boundary.eq.'l').or.(boundary.eq.'L').or. & |
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(boundary.eq.'b').or.(boundary.eq.'B')) then |
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thisSpline%yppa(1) = -0.5E0_DP |
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u(1) = (3.0E0_DP/(xa(2)-xa(1)))*((ya(2)-& |
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ya(1))/(xa(2)-xa(1))-yp1) |
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else |
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thisSpline%yppa(1) = 0.0E0_DP |
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u(1) = 0.0E0_DP |
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endif |
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|
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do i = 2, nx - 1 |
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sig = (thisSpline%xa(i) - thisSpline%xa(i-1)) / (thisSpline%xa(i+1) - thisSpline%xa(i-1)) |
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p = sig * thisSpline%yppa(i-1) + 2.0E0_DP |
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thisSpline%yppa(i) = (sig - 1.0E0_DP) / p |
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u(i) = (6.0E0_DP*((thisSpline%ya(i+1)-thisSpline%ya(i))/(thisSpline%xa(i+1)-thisSpline%xa(i)) - & |
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(thisSpline%ya(i)-thisSpline%ya(i-1))/(thisSpline%xa(i)-thisSpline%xa(i-1)))/ & |
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(thisSpline%xa(i+1)-thisSpline%xa(i-1)) - sig * u(i-1))/p |
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enddo |
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|
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if ((boundary.eq.'u').or.(boundary.eq.'U').or. & |
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(boundary.eq.'b').or.(boundary.eq.'B')) then |
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qn = 0.5E0_DP |
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un = (3.0E0_DP/(thisSpline%xa(nx)-thisSpline%xa(nx-1)))* & |
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(ypn-(thisSpline%ya(nx)-thisSpline%ya(nx-1))/(thisSpline%xa(nx)-thisSpline%xa(nx-1))) |
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else |
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qn = 0.0E0_DP |
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un = 0.0E0_DP |
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endif |
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|
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thisSpline%yppa(nx)=(un-qn*u(nx-1))/(qn*thisSpline%yppa(nx-1)+1.0E0_DP) |
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|
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do k = nx-1, 1, -1 |
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thisSpline%yppa(k)=thisSpline%yppa(k)*thisSpline%yppa(k+1)+u(k) |
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enddo |
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|
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end subroutine newSpline |
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|
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subroutine deleteSpline(thisSpline) |
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type(splineType) :: thisSpline |
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|
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|
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|
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if(associated(thisSpline%xa)) then |
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deallocate(thisSpline%xa) |
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thisSpline%xa => null() |
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end if |
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if(associated(thisSpline%ya)) then |
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deallocate(thisSpline%ya) |
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thisSpline%ya => null() |
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end if |
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if(associated(thisSpline%yppa)) then |
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deallocate(thisSpline%yppa) |
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thisSpline%yppa => null() |
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end if |
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|
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thisSpline%npoints=0 |
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|
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end subroutine deleteSpline |
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|
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subroutine splintd2(thisSpline, x, y, dy, d2y) |
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type(splineType) :: thisSpline |
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real( kind = DP ), intent(in) :: x |
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real( kind = DP ), intent(out) :: y,dy,d2y |
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|
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|
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real( kind = DP ) :: del, h, a, b, c, d |
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integer :: j |
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|
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! this spline code assumes that the x points are equally spaced |
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! do not attempt to use this code if they are not. |
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|
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|
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! find the closest point with a value below our own: |
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j = FLOOR(real((thisSpline%npoints-1),kind=dp) * & |
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(x - thisSpline%xa(1)) / (thisSpline%xa(thisSpline%npoints) - thisSpline%xa(1))) + 1 |
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|
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! check to make sure we're inside the spline range: |
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if ((j.gt.thisSpline%npoints).or.(j.lt.1)) then |
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write(errMSG,*) "EAM_splint: x is outside bounds of spline: ",x,j |
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call handleError("INTERPOLATION::SPLINT2d",errMSG) |
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endif |
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! check to make sure we haven't screwed up the calculation of j: |
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if ((x.lt.thisSpline%xa(j)).or.(x.gt.thisSpline%xa(j+1))) then |
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if (j.ne.thisSpline%npoints) then |
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write(errMSG,*) "EAM_splint:",x," x is outside bounding range" |
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call handleError("INTERPOLATION::SPLINT2d",errMSG) |
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endif |
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endif |
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|
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del = thisSpline%xa(j+1) - x |
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h = thisSpline%xa(j+1) - thisSpline%xa(j) |
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|
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a = del / h |
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b = 1.0E0_DP - a |
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c = a*(a*a - 1.0E0_DP)*h*h/6.0E0_DP |
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d = b*(b*b - 1.0E0_DP)*h*h/6.0E0_DP |
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|
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y = a*thisSpline%ya(j) + b*thisSpline%ya(j+1) + c*thisSpline%yppa(j) + d*thisSpline%yppa(j+1) |
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|
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dy = (thisSpline%ya(j+1)-thisSpline%ya(j))/h & |
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- (3.0E0_DP*a*a - 1.0E0_DP)*h*thisSpline%yppa(j)/6.0E0_DP & |
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+ (3.0E0_DP*b*b - 1.0E0_DP)*h*thisSpline%yppa(j+1)/6.0E0_DP |
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|
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|
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d2y = a*thisSpline%yppa(j) + b*thisSpline%yppa(j+1) |
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|
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|
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end subroutine splintd2 |
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subroutine splintd1(thisSpline, x, y, dy) |
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type(splineType) :: thisSpline |
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real( kind = DP ), intent(in) :: x |
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real( kind = DP ), intent(out) :: y,dy |
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|
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|
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real( kind = DP ) :: del, h, a, b, c, d |
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integer :: j |
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|
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! this spline code assumes that the x points are equally spaced |
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! do not attempt to use this code if they are not. |
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|
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|
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! find the closest point with a value below our own: |
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j = FLOOR(real((thisSpline%npoints-1),kind=dp) *& |
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(x - thisSpline%xa(1)) / (thisSpline%xa(thisSpline%npoints) - thisSpline%xa(1))) + 1 |
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|
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! check to make sure we're inside the spline range: |
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if ((j.gt.thisSpline%npoints).or.(j.lt.1)) then |
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write(errMSG,*) "EAM_splint: x is outside bounds of spline: ",x,j |
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call handleError("INTERPOLATION::SPLINT2d",errMSG) |
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endif |
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! check to make sure we haven't screwed up the calculation of j: |
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if ((x.lt.thisSpline%xa(j)).or.(x.gt.thisSpline%xa(j+1))) then |
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if (j.ne.thisSpline%npoints) then |
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write(errMSG,*) "EAM_splint:",x," x is outside bounding range" |
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call handleError("INTERPOLATION::SPLINT2d",errMSG) |
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endif |
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endif |
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|
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del = thisSpline%xa(j+1) - x |
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h = thisSpline%xa(j+1) - thisSpline%xa(j) |
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|
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a = del / h |
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b = 1.0E0_DP - a |
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c = a*(a*a - 1.0E0_DP)*h*h/6.0E0_DP |
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d = b*(b*b - 1.0E0_DP)*h*h/6.0E0_DP |
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|
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y = a*thisSpline%ya(j) + b*thisSpline%ya(j+1) + c*thisSpline%yppa(j) + d*thisSpline%yppa(j+1) |
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|
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dy = (thisSpline%ya(j+1)-thisSpline%ya(j))/h & |
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- (3.0E0_DP*a*a - 1.0E0_DP)*h*thisSpline%yppa(j)/6.0E0_DP & |
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+ (3.0E0_DP*b*b - 1.0E0_DP)*h*thisSpline%yppa(j+1)/6.0E0_DP |
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|
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|
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|
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|
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|
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end subroutine splintd1 |
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subroutine splintd(thisSpline, x, y) |
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type(splineType) :: thisSpline |
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real( kind = DP ), intent(in) :: x |
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real( kind = DP ), intent(out) :: y |
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|
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|
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real( kind = DP ) :: del, h, a, b, c, d |
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integer :: j |
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|
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! this spline code assumes that the x points are equally spaced |
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! do not attempt to use this code if they are not. |
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|
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|
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! find the closest point with a value below our own: |
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j = FLOOR(real((thisSpline%npoints-1),kind=dp) * & |
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(x - thisSpline%xa(1)) / (thisSpline%xa(thisSpline%npoints) - thisSpline%xa(1))) + 1 |
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|
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! check to make sure we're inside the spline range: |
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if ((j.gt.thisSpline%npoints).or.(j.lt.1)) then |
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write(errMSG,*) "EAM_splint: x is outside bounds of spline: ",x,j |
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call handleError("INTERPOLATION::SPLINT2d",errMSG) |
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endif |
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! check to make sure we haven't screwed up the calculation of j: |
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if ((x.lt.thisSpline%xa(j)).or.(x.gt.thisSpline%xa(j+1))) then |
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if (j.ne.thisSpline%npoints) then |
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write(errMSG,*) "EAM_splint:",x," x is outside bounding range" |
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call handleError("INTERPOLATION::SPLINT2d",errMSG) |
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endif |
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endif |
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|
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del = thisSpline%xa(j+1) - x |
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h = thisSpline%xa(j+1) - thisSpline%xa(j) |
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|
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a = del / h |
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b = 1.0E0_DP - a |
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c = a*(a*a - 1.0E0_DP)*h*h/6.0E0_DP |
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d = b*(b*b - 1.0E0_DP)*h*h/6.0E0_DP |
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|
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y = a*thisSpline%ya(j) + b*thisSpline%ya(j+1) + c*thisSpline%yppa(j) + d*thisSpline%yppa(j+1) |
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|
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end subroutine splintd |
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|
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|
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end module INTERPOLATION |
