| 6 |
|
!! redistribute this software in source and binary code form, provided |
| 7 |
|
!! that the following conditions are met: |
| 8 |
|
!! |
| 9 |
< |
!! 1. Acknowledgement of the program authors must be made in any |
| 10 |
< |
!! publication of scientific results based in part on use of the |
| 11 |
< |
!! program. An acceptable form of acknowledgement is citation of |
| 12 |
< |
!! the article in which the program was described (Matthew |
| 13 |
< |
!! A. Meineke, Charles F. Vardeman II, Teng Lin, Christopher |
| 14 |
< |
!! J. Fennell and J. Daniel Gezelter, "OOPSE: An Object-Oriented |
| 15 |
< |
!! Parallel Simulation Engine for Molecular Dynamics," |
| 16 |
< |
!! J. Comput. Chem. 26, pp. 252-271 (2005)) |
| 17 |
< |
!! |
| 18 |
< |
!! 2. Redistributions of source code must retain the above copyright |
| 9 |
> |
!! 1. Redistributions of source code must retain the above copyright |
| 10 |
|
!! notice, this list of conditions and the following disclaimer. |
| 11 |
|
!! |
| 12 |
< |
!! 3. Redistributions in binary form must reproduce the above copyright |
| 12 |
> |
!! 2. Redistributions in binary form must reproduce the above copyright |
| 13 |
|
!! notice, this list of conditions and the following disclaimer in the |
| 14 |
|
!! documentation and/or other materials provided with the |
| 15 |
|
!! distribution. |
| 29 |
|
!! University of Notre Dame has been advised of the possibility of |
| 30 |
|
!! such damages. |
| 31 |
|
!! |
| 32 |
+ |
!! SUPPORT OPEN SCIENCE! If you use OpenMD or its source code in your |
| 33 |
+ |
!! research, please cite the appropriate papers when you publish your |
| 34 |
+ |
!! work. Good starting points are: |
| 35 |
+ |
!! |
| 36 |
+ |
!! [1] Meineke, et al., J. Comp. Chem. 26, 252-271 (2005). |
| 37 |
+ |
!! [2] Fennell & Gezelter, J. Chem. Phys. 124, 234104 (2006). |
| 38 |
+ |
!! [3] Sun, Lin & Gezelter, J. Chem. Phys. 128, 24107 (2008). |
| 39 |
+ |
!! [4] Vardeman & Gezelter, in progress (2009). |
| 40 |
|
!! |
| 41 |
+ |
!! |
| 42 |
|
!! interpolation.F90 |
| 43 |
|
!! |
| 44 |
|
!! Created by Charles F. Vardeman II on 03 Apr 2006. |
| 45 |
|
!! |
| 46 |
< |
!! PURPOSE: Generic Spline interplelation routines. These routines assume that we are on a uniform grid for |
| 47 |
< |
!! precomputation of spline parameters. |
| 46 |
> |
!! PURPOSE: Generic Spline interpolation routines. |
| 47 |
|
!! |
| 48 |
|
!! @author Charles F. Vardeman II |
| 49 |
< |
!! @version $Id: interpolation.F90,v 1.3 2006-04-14 21:06:55 chrisfen Exp $ |
| 49 |
> |
!! @version $Id: interpolation.F90,v 1.10 2009-11-25 20:02:05 gezelter Exp $ |
| 50 |
|
|
| 51 |
|
|
| 52 |
< |
module INTERPOLATION |
| 52 |
> |
module interpolation |
| 53 |
|
use definitions |
| 54 |
|
use status |
| 55 |
|
implicit none |
| 56 |
|
PRIVATE |
| 57 |
|
|
| 59 |
– |
character(len = statusMsgSize) :: errMSG |
| 60 |
– |
|
| 58 |
|
type, public :: cubicSpline |
| 59 |
< |
private |
| 60 |
< |
integer :: np = 0 |
| 64 |
< |
real(kind=dp) :: dx |
| 59 |
> |
logical :: isUniform = .false. |
| 60 |
> |
integer :: n = 0 |
| 61 |
|
real(kind=dp) :: dx_i |
| 62 |
|
real (kind=dp), pointer,dimension(:) :: x => null() |
| 63 |
< |
real (kind=dp), pointer,dimension(:,:) :: c => null() |
| 63 |
> |
real (kind=dp), pointer,dimension(:) :: y => null() |
| 64 |
> |
real (kind=dp), pointer,dimension(:) :: b => null() |
| 65 |
> |
real (kind=dp), pointer,dimension(:) :: c => null() |
| 66 |
> |
real (kind=dp), pointer,dimension(:) :: d => null() |
| 67 |
|
end type cubicSpline |
| 68 |
|
|
| 69 |
< |
interface newSpline |
| 71 |
< |
module procedure newSpline |
| 72 |
< |
end interface |
| 73 |
< |
|
| 69 |
> |
public :: newSpline |
| 70 |
|
public :: deleteSpline |
| 71 |
< |
|
| 71 |
> |
public :: lookupSpline |
| 72 |
> |
public :: lookupUniformSpline |
| 73 |
> |
public :: lookupNonuniformSpline |
| 74 |
> |
public :: lookupUniformSpline1d |
| 75 |
> |
|
| 76 |
|
contains |
| 77 |
+ |
|
| 78 |
|
|
| 79 |
< |
|
| 80 |
< |
subroutine newSpline(cs, x, y, yp1, ypn) |
| 80 |
< |
|
| 81 |
< |
!************************************************************************ |
| 82 |
< |
! |
| 83 |
< |
! newSplineWithoutDerivs solves for slopes defining a cubic spline. |
| 84 |
< |
! |
| 85 |
< |
! Discussion: |
| 86 |
< |
! |
| 87 |
< |
! A tridiagonal linear system for the unknown slopes S(I) of |
| 88 |
< |
! F at x(I), I=1,..., N, is generated and then solved by Gauss |
| 89 |
< |
! elimination, with S(I) ending up in cs%C(2,I), for all I. |
| 90 |
< |
! |
| 91 |
< |
! Reference: |
| 92 |
< |
! |
| 93 |
< |
! Carl DeBoor, |
| 94 |
< |
! A Practical Guide to Splines, |
| 95 |
< |
! Springer Verlag. |
| 96 |
< |
! |
| 97 |
< |
! Parameters: |
| 98 |
< |
! |
| 99 |
< |
! Input, real x(N), the abscissas or X values of |
| 100 |
< |
! the data points. The entries of x are assumed to be |
| 101 |
< |
! strictly increasing. |
| 102 |
< |
! |
| 103 |
< |
! Input, real y(I), contains the function value at x(I) for |
| 104 |
< |
! I = 1, N. |
| 105 |
< |
! |
| 106 |
< |
! yp1 contains the slope at x(1) and ypn contains |
| 107 |
< |
! the slope at x(N). |
| 108 |
< |
! |
| 109 |
< |
! On output, the intermediate slopes at x(I) have been |
| 110 |
< |
! stored in cs%C(2,I), for I = 2 to N-1. |
| 111 |
< |
|
| 79 |
> |
subroutine newSpline(cs, x, y, isUniform) |
| 80 |
> |
|
| 81 |
|
implicit none |
| 82 |
|
|
| 83 |
|
type (cubicSpline), intent(inout) :: cs |
| 84 |
|
real( kind = DP ), intent(in) :: x(:), y(:) |
| 85 |
< |
real( kind = DP ), intent(in) :: yp1, ypn |
| 86 |
< |
real( kind = DP ) :: g, divdif1, divdif3, dx |
| 118 |
< |
integer :: i, alloc_error, np |
| 85 |
> |
real( kind = DP ) :: fp1, fpn, p |
| 86 |
> |
REAL( KIND = DP), DIMENSION(size(x)-1) :: diff_y, H |
| 87 |
|
|
| 88 |
+ |
logical, intent(in) :: isUniform |
| 89 |
+ |
integer :: i, alloc_error, n, k |
| 90 |
+ |
|
| 91 |
|
alloc_error = 0 |
| 92 |
|
|
| 93 |
< |
if (cs%np .ne. 0) then |
| 94 |
< |
call handleWarning("interpolation::newSplineWithoutDerivs", & |
| 95 |
< |
"Type was already created") |
| 93 |
> |
if (cs%n .ne. 0) then |
| 94 |
> |
call handleWarning("interpolation::newSpline", & |
| 95 |
> |
"cubicSpline struct was already created") |
| 96 |
|
call deleteSpline(cs) |
| 97 |
|
end if |
| 98 |
|
|
| 99 |
|
! make sure the sizes match |
| 100 |
|
|
| 101 |
< |
if (size(x) .ne. size(y)) then |
| 102 |
< |
call handleError("interpolation::newSplineWithoutDerivs", & |
| 101 |
> |
n = size(x) |
| 102 |
> |
|
| 103 |
> |
if ( size(y) .ne. size(x) ) then |
| 104 |
> |
call handleError("interpolation::newSpline", & |
| 105 |
|
"Array size mismatch") |
| 106 |
|
end if |
| 107 |
+ |
|
| 108 |
+ |
cs%n = n |
| 109 |
+ |
cs%isUniform = isUniform |
| 110 |
|
|
| 111 |
< |
np = size(x) |
| 136 |
< |
cs%np = np |
| 137 |
< |
|
| 138 |
< |
allocate(cs%x(np), stat=alloc_error) |
| 111 |
> |
allocate(cs%x(n), stat=alloc_error) |
| 112 |
|
if(alloc_error .ne. 0) then |
| 113 |
< |
call handleError("interpolation::newSplineWithoutDerivs", & |
| 113 |
> |
call handleError("interpolation::newSpline", & |
| 114 |
|
"Error in allocating storage for x") |
| 115 |
|
endif |
| 116 |
|
|
| 117 |
< |
allocate(cs%c(4,np), stat=alloc_error) |
| 117 |
> |
allocate(cs%y(n), stat=alloc_error) |
| 118 |
|
if(alloc_error .ne. 0) then |
| 119 |
< |
call handleError("interpolation::newSplineWithoutDerivs", & |
| 119 |
> |
call handleError("interpolation::newSpline", & |
| 120 |
> |
"Error in allocating storage for y") |
| 121 |
> |
endif |
| 122 |
> |
|
| 123 |
> |
allocate(cs%b(n), stat=alloc_error) |
| 124 |
> |
if(alloc_error .ne. 0) then |
| 125 |
> |
call handleError("interpolation::newSpline", & |
| 126 |
> |
"Error in allocating storage for b") |
| 127 |
> |
endif |
| 128 |
> |
|
| 129 |
> |
allocate(cs%c(n), stat=alloc_error) |
| 130 |
> |
if(alloc_error .ne. 0) then |
| 131 |
> |
call handleError("interpolation::newSpline", & |
| 132 |
|
"Error in allocating storage for c") |
| 133 |
|
endif |
| 134 |
< |
|
| 135 |
< |
do i = 1, np |
| 134 |
> |
|
| 135 |
> |
allocate(cs%d(n), stat=alloc_error) |
| 136 |
> |
if(alloc_error .ne. 0) then |
| 137 |
> |
call handleError("interpolation::newSpline", & |
| 138 |
> |
"Error in allocating storage for d") |
| 139 |
> |
endif |
| 140 |
> |
|
| 141 |
> |
! make sure we are monotinically increasing in x: |
| 142 |
> |
|
| 143 |
> |
h = diff(x) |
| 144 |
> |
if (any(h <= 0)) then |
| 145 |
> |
call handleError("interpolation::newSpline", & |
| 146 |
> |
"Negative dx interval found") |
| 147 |
> |
end if |
| 148 |
> |
|
| 149 |
> |
! load x and y values into the cubicSpline structure: |
| 150 |
> |
|
| 151 |
> |
do i = 1, n |
| 152 |
|
cs%x(i) = x(i) |
| 153 |
< |
cs%c(1,i) = y(i) |
| 154 |
< |
enddo |
| 153 |
> |
cs%y(i) = y(i) |
| 154 |
> |
end do |
| 155 |
|
|
| 156 |
< |
! Set the first derivative of the function to the second coefficient of |
| 157 |
< |
! each of the endpoints |
| 156 |
> |
! Calculate coefficients for the tridiagonal system: store |
| 157 |
> |
! sub-diagonal in B, diagonal in D, difference quotient in C. |
| 158 |
|
|
| 159 |
< |
cs%c(2,1) = yp1 |
| 160 |
< |
cs%c(2,np) = ypn |
| 161 |
< |
|
| 159 |
> |
cs%b(1:n-1) = h |
| 160 |
> |
diff_y = diff(y) |
| 161 |
> |
cs%c(1:n-1) = diff_y / h |
| 162 |
|
|
| 163 |
< |
! |
| 164 |
< |
! Set up the right hand side of the linear system. |
| 165 |
< |
! |
| 166 |
< |
do i = 2, cs%np - 1 |
| 167 |
< |
cs%c(2,i) = 3.0_DP * ( & |
| 168 |
< |
(x(i) - x(i-1)) * (cs%c(1,i+1) - cs%c(1,i)) / (x(i+1) - x(i)) + & |
| 169 |
< |
(x(i+1) - x(i)) * (cs%c(1,i) - cs%c(1,i-1)) / (x(i) - x(i-1))) |
| 163 |
> |
if (n == 2) then |
| 164 |
> |
! Assume the derivatives at both endpoints are zero |
| 165 |
> |
! another assumption could be made to have a linear interpolant |
| 166 |
> |
! between the two points. In that case, the b coefficients |
| 167 |
> |
! below would be diff_y(1)/h(1) and the c and d coefficients would |
| 168 |
> |
! both be zero. |
| 169 |
> |
cs%b(1) = 0.0_dp |
| 170 |
> |
cs%c(1) = -3.0_dp * (diff_y(1)/h(1))**2 |
| 171 |
> |
cs%d(1) = -2.0_dp * (diff_y(1)/h(1))**3 |
| 172 |
> |
cs%b(2) = cs%b(1) |
| 173 |
> |
cs%c(2) = 0.0_dp |
| 174 |
> |
cs%d(2) = 0.0_dp |
| 175 |
> |
cs%dx_i = 1.0_dp / h(1) |
| 176 |
> |
return |
| 177 |
> |
end if |
| 178 |
> |
|
| 179 |
> |
cs%d(1) = 2.0_dp * cs%b(1) |
| 180 |
> |
do i = 2, n-1 |
| 181 |
> |
cs%d(i) = 2.0_dp * (cs%b(i) + cs%b(i-1)) |
| 182 |
|
end do |
| 183 |
< |
! |
| 184 |
< |
! Set the diagonal coefficients. |
| 185 |
< |
! |
| 186 |
< |
cs%c(4,1) = 1.0_DP |
| 187 |
< |
do i = 2, cs%np - 1 |
| 188 |
< |
cs%c(4,i) = 2.0_DP * ( x(i+1) - x(i-1) ) |
| 189 |
< |
end do |
| 190 |
< |
cs%c(4,cs%np) = 1.0_DP |
| 191 |
< |
! |
| 192 |
< |
! Set the off-diagonal coefficients. |
| 193 |
< |
! |
| 194 |
< |
cs%c(3,1) = 0.0_DP |
| 195 |
< |
do i = 2, cs%np |
| 196 |
< |
cs%c(3,i) = x(i) - x(i-1) |
| 197 |
< |
end do |
| 198 |
< |
! |
| 199 |
< |
! Forward elimination. |
| 200 |
< |
! |
| 201 |
< |
do i = 2, cs%np - 1 |
| 202 |
< |
g = -cs%c(3,i+1) / cs%c(4,i-1) |
| 203 |
< |
cs%c(4,i) = cs%c(4,i) + g * cs%c(3,i-1) |
| 204 |
< |
cs%c(2,i) = cs%c(2,i) + g * cs%c(2,i-1) |
| 183 |
> |
cs%d(n) = 2.0_dp * cs%b(n-1) |
| 184 |
> |
|
| 185 |
> |
! Calculate estimates for the end slopes using polynomials |
| 186 |
> |
! that interpolate the data nearest the end. |
| 187 |
> |
|
| 188 |
> |
fp1 = cs%c(1) - cs%b(1)*(cs%c(2) - cs%c(1))/(cs%b(1) + cs%b(2)) |
| 189 |
> |
if (n > 3) then |
| 190 |
> |
fp1 = fp1 + cs%b(1)*((cs%b(1) + cs%b(2))*(cs%c(3) - cs%c(2))/ & |
| 191 |
> |
(cs%b(2) + cs%b(3)) - cs%c(2) + cs%c(1))/(x(4) - x(1)) |
| 192 |
> |
end if |
| 193 |
> |
|
| 194 |
> |
fpn = cs%c(n-1) + cs%b(n-1)*(cs%c(n-1) - cs%c(n-2))/(cs%b(n-2) + cs%b(n-1)) |
| 195 |
> |
if (n > 3) then |
| 196 |
> |
fpn = fpn + cs%b(n-1)*(cs%c(n-1) - cs%c(n-2) - (cs%b(n-2) + cs%b(n-1))* & |
| 197 |
> |
(cs%c(n-2) - cs%c(n-3))/(cs%b(n-2) + cs%b(n-3)))/(x(n) - x(n-3)) |
| 198 |
> |
end if |
| 199 |
> |
|
| 200 |
> |
! Calculate the right hand side and store it in C. |
| 201 |
> |
|
| 202 |
> |
cs%c(n) = 3.0_dp * (fpn - cs%c(n-1)) |
| 203 |
> |
do i = n-1,2,-1 |
| 204 |
> |
cs%c(i) = 3.0_dp * (cs%c(i) - cs%c(i-1)) |
| 205 |
|
end do |
| 206 |
< |
! |
| 207 |
< |
! Back substitution for the interior slopes. |
| 208 |
< |
! |
| 209 |
< |
do i = cs%np - 1, 2, -1 |
| 210 |
< |
cs%c(2,i) = ( cs%c(2,i) - cs%c(3,i) * cs%c(2,i+1) ) / cs%c(4,i) |
| 206 |
> |
cs%c(1) = 3.0_dp * (cs%c(1) - fp1) |
| 207 |
> |
|
| 208 |
> |
! Solve the tridiagonal system. |
| 209 |
> |
|
| 210 |
> |
do k = 2, n |
| 211 |
> |
p = cs%b(k-1) / cs%d(k-1) |
| 212 |
> |
cs%d(k) = cs%d(k) - p*cs%b(k-1) |
| 213 |
> |
cs%c(k) = cs%c(k) - p*cs%c(k-1) |
| 214 |
|
end do |
| 215 |
< |
! |
| 216 |
< |
! Now compute the quadratic and cubic coefficients used in the |
| 217 |
< |
! piecewise polynomial representation. |
| 202 |
< |
! |
| 203 |
< |
do i = 1, cs%np - 1 |
| 204 |
< |
dx = x(i+1) - x(i) |
| 205 |
< |
divdif1 = ( cs%c(1,i+1) - cs%c(1,i) ) / dx |
| 206 |
< |
divdif3 = cs%c(2,i) + cs%c(2,i+1) - 2.0_DP * divdif1 |
| 207 |
< |
cs%c(3,i) = ( divdif1 - cs%c(2,i) - divdif3 ) / dx |
| 208 |
< |
cs%c(4,i) = divdif3 / ( dx * dx ) |
| 215 |
> |
cs%c(n) = cs%c(n) / cs%d(n) |
| 216 |
> |
do k = n-1, 1, -1 |
| 217 |
> |
cs%c(k) = (cs%c(k) - cs%b(k) * cs%c(k+1)) / cs%d(k) |
| 218 |
|
end do |
| 219 |
|
|
| 220 |
< |
cs%c(3,cs%np) = 0.0_DP |
| 212 |
< |
cs%c(4,cs%np) = 0.0_DP |
| 220 |
> |
! Calculate the coefficients defining the spline. |
| 221 |
|
|
| 222 |
< |
cs%dx = dx |
| 223 |
< |
cs%dx_i = 1.0_DP / dx |
| 224 |
< |
return |
| 217 |
< |
end subroutine newSplineWithoutDerivs |
| 222 |
> |
cs%d(1:n-1) = diff(cs%c) / (3.0_dp * h) |
| 223 |
> |
cs%b(1:n-1) = diff_y / h - h * (cs%c(1:n-1) + h * cs%d(1:n-1)) |
| 224 |
> |
cs%b(n) = cs%b(n-1) + h(n-1) * (2.0_dp*cs%c(n-1) + h(n-1)*3.0_dp*cs%d(n-1)) |
| 225 |
|
|
| 226 |
+ |
if (isUniform) then |
| 227 |
+ |
cs%dx_i = 1.0_dp / (x(2) - x(1)) |
| 228 |
+ |
endif |
| 229 |
+ |
|
| 230 |
+ |
return |
| 231 |
+ |
|
| 232 |
+ |
contains |
| 233 |
+ |
|
| 234 |
+ |
function diff(v) |
| 235 |
+ |
! Auxiliary function to compute the forward difference |
| 236 |
+ |
! of data stored in a vector v. |
| 237 |
+ |
|
| 238 |
+ |
implicit none |
| 239 |
+ |
real (kind = dp), dimension(:), intent(in) :: v |
| 240 |
+ |
real (kind = dp), dimension(size(v)-1) :: diff |
| 241 |
+ |
|
| 242 |
+ |
integer :: n |
| 243 |
+ |
|
| 244 |
+ |
n = size(v) |
| 245 |
+ |
diff = v(2:n) - v(1:n-1) |
| 246 |
+ |
return |
| 247 |
+ |
end function diff |
| 248 |
+ |
|
| 249 |
+ |
end subroutine newSpline |
| 250 |
+ |
|
| 251 |
|
subroutine deleteSpline(this) |
| 252 |
|
|
| 253 |
|
type(cubicSpline) :: this |
| 254 |
|
|
| 255 |
< |
if(associated(this%x)) then |
| 256 |
< |
deallocate(this%x) |
| 257 |
< |
this%x => null() |
| 255 |
> |
if(associated(this%d)) then |
| 256 |
> |
deallocate(this%d) |
| 257 |
> |
this%d => null() |
| 258 |
|
end if |
| 259 |
|
if(associated(this%c)) then |
| 260 |
|
deallocate(this%c) |
| 261 |
|
this%c => null() |
| 262 |
|
end if |
| 263 |
+ |
if(associated(this%b)) then |
| 264 |
+ |
deallocate(this%b) |
| 265 |
+ |
this%b => null() |
| 266 |
+ |
end if |
| 267 |
+ |
if(associated(this%y)) then |
| 268 |
+ |
deallocate(this%y) |
| 269 |
+ |
this%y => null() |
| 270 |
+ |
end if |
| 271 |
+ |
if(associated(this%x)) then |
| 272 |
+ |
deallocate(this%x) |
| 273 |
+ |
this%x => null() |
| 274 |
+ |
end if |
| 275 |
|
|
| 276 |
< |
this%np = 0 |
| 276 |
> |
this%n = 0 |
| 277 |
|
|
| 278 |
|
end subroutine deleteSpline |
| 279 |
|
|
| 280 |
< |
subroutine lookup_nonuniform_spline(cs, xval, yval) |
| 280 |
> |
subroutine lookupNonuniformSpline(cs, xval, yval) |
| 281 |
|
|
| 238 |
– |
!************************************************************************* |
| 239 |
– |
! |
| 240 |
– |
! lookup_nonuniform_spline evaluates a piecewise cubic Hermite interpolant. |
| 241 |
– |
! |
| 242 |
– |
! Discussion: |
| 243 |
– |
! |
| 244 |
– |
! newSpline must be called first, to set up the |
| 245 |
– |
! spline data from the raw function and derivative data. |
| 246 |
– |
! |
| 247 |
– |
! Modified: |
| 248 |
– |
! |
| 249 |
– |
! 06 April 1999 |
| 250 |
– |
! |
| 251 |
– |
! Reference: |
| 252 |
– |
! |
| 253 |
– |
! Conte and de Boor, |
| 254 |
– |
! Algorithm PCUBIC, |
| 255 |
– |
! Elementary Numerical Analysis, |
| 256 |
– |
! 1973, page 234. |
| 257 |
– |
! |
| 258 |
– |
! Parameters: |
| 259 |
– |
! |
| 282 |
|
implicit none |
| 283 |
|
|
| 284 |
|
type (cubicSpline), intent(in) :: cs |
| 285 |
|
real( kind = DP ), intent(in) :: xval |
| 286 |
|
real( kind = DP ), intent(out) :: yval |
| 287 |
< |
real( kind = DP ) :: dx |
| 287 |
> |
real( kind = DP ) :: dx |
| 288 |
|
integer :: i, j |
| 289 |
|
! |
| 290 |
|
! Find the interval J = [ cs%x(J), cs%x(J+1) ] that contains |
| 291 |
|
! or is nearest to xval. |
| 292 |
|
! |
| 293 |
< |
j = cs%np - 1 |
| 293 |
> |
j = cs%n - 1 |
| 294 |
|
|
| 295 |
< |
do i = 1, cs%np - 2 |
| 295 |
> |
do i = 0, cs%n - 2 |
| 296 |
|
|
| 297 |
|
if ( xval < cs%x(i+1) ) then |
| 298 |
|
j = i |
| 304 |
|
! Evaluate the cubic polynomial. |
| 305 |
|
! |
| 306 |
|
dx = xval - cs%x(j) |
| 307 |
< |
|
| 286 |
< |
yval = cs%c(1,j) + dx * ( cs%c(2,j) + dx * ( cs%c(3,j) + dx * cs%c(4,j) ) ) |
| 307 |
> |
yval = cs%y(j) + dx*(cs%b(j) + dx*(cs%c(j) + dx*cs%d(j))) |
| 308 |
|
|
| 309 |
|
return |
| 310 |
< |
end subroutine lookup_nonuniform_spline |
| 310 |
> |
end subroutine lookupNonuniformSpline |
| 311 |
|
|
| 312 |
< |
subroutine lookup_uniform_spline(cs, xval, yval) |
| 312 |
> |
subroutine lookupUniformSpline(cs, xval, yval) |
| 313 |
|
|
| 293 |
– |
!************************************************************************* |
| 294 |
– |
! |
| 295 |
– |
! lookup_uniform_spline evaluates a piecewise cubic Hermite interpolant. |
| 296 |
– |
! |
| 297 |
– |
! Discussion: |
| 298 |
– |
! |
| 299 |
– |
! newSpline must be called first, to set up the |
| 300 |
– |
! spline data from the raw function and derivative data. |
| 301 |
– |
! |
| 302 |
– |
! Modified: |
| 303 |
– |
! |
| 304 |
– |
! 06 April 1999 |
| 305 |
– |
! |
| 306 |
– |
! Reference: |
| 307 |
– |
! |
| 308 |
– |
! Conte and de Boor, |
| 309 |
– |
! Algorithm PCUBIC, |
| 310 |
– |
! Elementary Numerical Analysis, |
| 311 |
– |
! 1973, page 234. |
| 312 |
– |
! |
| 313 |
– |
! Parameters: |
| 314 |
– |
! |
| 314 |
|
implicit none |
| 315 |
|
|
| 316 |
|
type (cubicSpline), intent(in) :: cs |
| 317 |
|
real( kind = DP ), intent(in) :: xval |
| 318 |
|
real( kind = DP ), intent(out) :: yval |
| 319 |
< |
real( kind = DP ) :: dx |
| 319 |
> |
real( kind = DP ) :: dx |
| 320 |
|
integer :: i, j |
| 321 |
|
! |
| 322 |
|
! Find the interval J = [ cs%x(J), cs%x(J+1) ] that contains |
| 323 |
|
! or is nearest to xval. |
| 324 |
+ |
|
| 325 |
+ |
j = MAX(1, MIN(cs%n-1, int((xval-cs%x(1)) * cs%dx_i) + 1)) |
| 326 |
+ |
|
| 327 |
+ |
dx = xval - cs%x(j) |
| 328 |
+ |
yval = cs%y(j) + dx*(cs%b(j) + dx*(cs%c(j) + dx*cs%d(j))) |
| 329 |
+ |
|
| 330 |
+ |
return |
| 331 |
+ |
end subroutine lookupUniformSpline |
| 332 |
|
|
| 333 |
< |
j = MAX(1, MIN(cs%np, idint((xval-cs%x(1)) * cs%dx_i) + 1)) |
| 333 |
> |
subroutine lookupUniformSpline1d(cs, xval, yval, dydx) |
| 334 |
> |
|
| 335 |
> |
implicit none |
| 336 |
|
|
| 337 |
+ |
type (cubicSpline), intent(in) :: cs |
| 338 |
+ |
real( kind = DP ), intent(in) :: xval |
| 339 |
+ |
real( kind = DP ), intent(out) :: yval, dydx |
| 340 |
+ |
real( kind = DP ) :: dx |
| 341 |
+ |
integer :: i, j |
| 342 |
+ |
|
| 343 |
+ |
! Find the interval J = [ cs%x(J), cs%x(J+1) ] that contains |
| 344 |
+ |
! or is nearest to xval. |
| 345 |
+ |
|
| 346 |
+ |
|
| 347 |
+ |
j = MAX(1, MIN(cs%n-1, int((xval-cs%x(1)) * cs%dx_i) + 1)) |
| 348 |
+ |
|
| 349 |
|
dx = xval - cs%x(j) |
| 350 |
+ |
yval = cs%y(j) + dx*(cs%b(j) + dx*(cs%c(j) + dx*cs%d(j))) |
| 351 |
|
|
| 352 |
< |
yval = cs%c(1,j) + dx * ( cs%c(2,j) + dx * ( cs%c(3,j) + dx * cs%c(4,j) ) ) |
| 352 |
> |
dydx = cs%b(j) + dx*(2.0_dp * cs%c(j) + 3.0_dp * dx * cs%d(j)) |
| 353 |
> |
|
| 354 |
> |
return |
| 355 |
> |
end subroutine lookupUniformSpline1d |
| 356 |
> |
|
| 357 |
> |
subroutine lookupSpline(cs, xval, yval) |
| 358 |
> |
|
| 359 |
> |
type (cubicSpline), intent(in) :: cs |
| 360 |
> |
real( kind = DP ), intent(inout) :: xval |
| 361 |
> |
real( kind = DP ), intent(inout) :: yval |
| 362 |
|
|
| 363 |
+ |
if (cs%isUniform) then |
| 364 |
+ |
call lookupUniformSpline(cs, xval, yval) |
| 365 |
+ |
else |
| 366 |
+ |
call lookupNonuniformSpline(cs, xval, yval) |
| 367 |
+ |
endif |
| 368 |
+ |
|
| 369 |
|
return |
| 370 |
< |
end subroutine lookup_uniform_spline |
| 370 |
> |
end subroutine lookupSpline |
| 371 |
|
|
| 372 |
< |
end module INTERPOLATION |
| 372 |
> |
end module interpolation |
