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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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> |
!! PURPOSE: Generic Spline interpolation routines. These routines |
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> |
!! assume that we are on a uniform grid for precomputation of |
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> |
!! spline parameters. |
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!! |
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!! @author Charles F. Vardeman II |
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< |
!! @version $Id: interpolation.F90,v 1.2 2006-04-14 20:04:31 gezelter Exp $ |
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> |
!! @version $Id: interpolation.F90,v 1.4 2006-04-14 21:49:54 gezelter Exp $ |
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module INTERPOLATION |
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type, public :: cubicSpline |
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private |
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+ |
logical :: isUniform = .false. |
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integer :: np = 0 |
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– |
real(kind=dp) :: dx |
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real(kind=dp) :: dx_i |
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real (kind=dp), pointer,dimension(:) :: x => null() |
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real (kind=dp), pointer,dimension(:,:) :: c => null() |
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end type cubicSpline |
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|
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interface newSpline |
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< |
module procedure newSplineWithoutDerivs |
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< |
module procedure newSplineWithDerivs |
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< |
end interface |
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< |
|
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> |
public :: newSpline |
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public :: deleteSpline |
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< |
|
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> |
public :: lookup_spline |
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> |
public :: lookup_uniform_spline |
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> |
public :: lookup_nonuniform_spline |
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> |
|
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contains |
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+ |
|
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< |
subroutine newSplineWithoutDerivs(cs, x, y, yp1, ypn, boundary) |
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< |
|
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> |
subroutine newSpline(cs, x, y, yp1, ypn, isUniform) |
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> |
|
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!************************************************************************ |
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! |
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< |
! newSplineWithoutDerivs solves for slopes defining a cubic spline. |
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> |
! newSpline solves for slopes defining a cubic spline. |
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! |
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! Discussion: |
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! |
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! Parameters: |
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! |
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! Input, real x(N), the abscissas or X values of |
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! the data points. The entries of TAU are assumed to be |
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> |
! the data points. The entries of x are assumed to be |
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! strictly increasing. |
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! |
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! Input, real y(I), contains the function value at x(I) for |
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! I = 1, N. |
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! |
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! yp1 contains the slope at x(1) and ypn contains |
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! the slope at x(N). |
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! Input, real yp1 contains the slope at x(1) |
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! Input, real ypn contains the slope at x(N) |
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! |
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! On output, the intermediate slopes at x(I) have been |
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! stored in cs%C(2,I), for I = 2 to N-1. |
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! On output, the slopes at x(I) have been stored in |
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> |
! cs%C(2,I), for I = 1 to N. |
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implicit none |
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type (cubicSpline), intent(inout) :: cs |
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real( kind = DP ), intent(in) :: x(:), y(:) |
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real( kind = DP ), intent(in) :: yp1, ypn |
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character(len=*), intent(in) :: boundary |
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> |
logical, intent(in) :: isUniform |
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real( kind = DP ) :: g, divdif1, divdif3, dx |
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integer :: i, alloc_error, np |
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alloc_error = 0 |
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if (cs%np .ne. 0) then |
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< |
call handleWarning("interpolation::newSplineWithoutDerivs", & |
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"Type was already created") |
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> |
call handleWarning("interpolation::newSpline", & |
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> |
"cubicSpline struct was already created") |
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call deleteSpline(cs) |
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end if |
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! make sure the sizes match |
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if (size(x) .ne. size(y)) then |
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< |
call handleError("interpolation::newSplineWithoutDerivs", & |
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> |
np = size(x) |
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> |
|
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> |
if ( size(y) .ne. np ) then |
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> |
call handleError("interpolation::newSpline", & |
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"Array size mismatch") |
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end if |
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|
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np = size(x) |
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> |
|
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cs%np = np |
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+ |
cs%isUniform = isUniform |
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allocate(cs%x(np), stat=alloc_error) |
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if(alloc_error .ne. 0) then |
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< |
call handleError("interpolation::newSplineWithoutDerivs", & |
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> |
call handleError("interpolation::newSpline", & |
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"Error in allocating storage for x") |
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endif |
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|
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allocate(cs%c(4,np), stat=alloc_error) |
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if(alloc_error .ne. 0) then |
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< |
call handleError("interpolation::newSplineWithoutDerivs", & |
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> |
call handleError("interpolation::newSpline", & |
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"Error in allocating storage for c") |
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endif |
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cs%c(1,i) = y(i) |
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enddo |
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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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< |
cs%c(2,1) = yp1 |
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< |
else |
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< |
cs%c(2,1) = 0.0_DP |
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< |
endif |
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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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< |
cs%c(2,1) = ypn |
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< |
else |
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< |
cs%c(2,1) = 0.0_DP |
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< |
endif |
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> |
! Set the first derivative of the function to the second coefficient of |
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> |
! each of the endpoints |
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|
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+ |
cs%c(2,1) = yp1 |
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+ |
cs%c(2,np) = ypn |
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+ |
|
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! |
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! Set up the right hand side of the linear system. |
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! |
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+ |
|
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do i = 2, cs%np - 1 |
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cs%c(2,i) = 3.0_DP * ( & |
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(x(i) - x(i-1)) * (cs%c(1,i+1) - cs%c(1,i)) / (x(i+1) - x(i)) + & |
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(x(i+1) - x(i)) * (cs%c(1,i) - cs%c(1,i-1)) / (x(i) - x(i-1))) |
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– |
end do |
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– |
! |
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– |
! Set the diagonal coefficients. |
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– |
! |
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– |
cs%c(4,1) = 1.0_DP |
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– |
do i = 2, cs%np - 1 |
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– |
cs%c(4,i) = 2.0_DP * ( x(i+1) - x(i-1) ) |
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– |
end do |
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– |
cs%c(4,cs%np) = 1.0_DP |
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– |
! |
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– |
! Set the off-diagonal coefficients. |
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– |
! |
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– |
cs%c(3,1) = 0.0_DP |
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– |
do i = 2, cs%np |
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– |
cs%c(3,i) = x(i) - x(i-1) |
| 192 |
– |
end do |
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– |
! |
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– |
! Forward elimination. |
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– |
! |
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– |
do i = 2, cs%np - 1 |
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– |
g = -cs%c(3,i+1) / cs%c(4,i-1) |
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– |
cs%c(4,i) = cs%c(4,i) + g * cs%c(3,i-1) |
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– |
cs%c(2,i) = cs%c(2,i) + g * cs%c(2,i-1) |
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|
end do |
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– |
! |
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– |
! Back substitution for the interior slopes. |
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– |
! |
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– |
do i = cs%np - 1, 2, -1 |
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– |
cs%c(2,i) = ( cs%c(2,i) - cs%c(3,i) * cs%c(2,i+1) ) / cs%c(4,i) |
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– |
end do |
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– |
! |
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– |
! Now compute the quadratic and cubic coefficients used in the |
| 209 |
– |
! piecewise polynomial representation. |
| 210 |
– |
! |
| 211 |
– |
do i = 1, cs%np - 1 |
| 212 |
– |
dx = x(i+1) - x(i) |
| 213 |
– |
divdif1 = ( cs%c(1,i+1) - cs%c(1,i) ) / dx |
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– |
divdif3 = cs%c(2,i) + cs%c(2,i+1) - 2.0_DP * divdif1 |
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– |
cs%c(3,i) = ( divdif1 - cs%c(2,i) - divdif3 ) / dx |
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– |
cs%c(4,i) = divdif3 / ( dx * dx ) |
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– |
end do |
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|
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– |
cs%c(3,cs%np) = 0.0_DP |
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– |
cs%c(4,cs%np) = 0.0_DP |
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– |
|
| 222 |
– |
cs%dx = dx |
| 223 |
– |
cs%dx_i = 1.0_DP / dx |
| 224 |
– |
return |
| 225 |
– |
end subroutine newSplineWithoutDerivs |
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– |
|
| 227 |
– |
subroutine newSplineWithDerivs(cs, x, y, yp) |
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– |
|
| 229 |
– |
!************************************************************************ |
| 175 |
|
! |
| 231 |
– |
! newSplineWithDerivs |
| 232 |
– |
|
| 233 |
– |
implicit none |
| 234 |
– |
|
| 235 |
– |
type (cubicSpline), intent(inout) :: cs |
| 236 |
– |
real( kind = DP ), intent(in) :: x(:), y(:), yp(:) |
| 237 |
– |
real( kind = DP ) :: g, divdif1, divdif3, dx |
| 238 |
– |
integer :: i, alloc_error, np |
| 239 |
– |
|
| 240 |
– |
alloc_error = 0 |
| 241 |
– |
|
| 242 |
– |
if (cs%np .ne. 0) then |
| 243 |
– |
call handleWarning("interpolation::newSplineWithDerivs", & |
| 244 |
– |
"Type was already created") |
| 245 |
– |
call deleteSpline(cs) |
| 246 |
– |
end if |
| 247 |
– |
|
| 248 |
– |
! make sure the sizes match |
| 249 |
– |
|
| 250 |
– |
if ((size(x) .ne. size(y)).or.(size(x) .ne. size(yp))) then |
| 251 |
– |
call handleError("interpolation::newSplineWithDerivs", & |
| 252 |
– |
"Array size mismatch") |
| 253 |
– |
end if |
| 254 |
– |
|
| 255 |
– |
np = size(x) |
| 256 |
– |
cs%np = np |
| 257 |
– |
|
| 258 |
– |
allocate(cs%x(np), stat=alloc_error) |
| 259 |
– |
if(alloc_error .ne. 0) then |
| 260 |
– |
call handleError("interpolation::newSplineWithDerivs", & |
| 261 |
– |
"Error in allocating storage for x") |
| 262 |
– |
endif |
| 263 |
– |
|
| 264 |
– |
allocate(cs%c(4,np), stat=alloc_error) |
| 265 |
– |
if(alloc_error .ne. 0) then |
| 266 |
– |
call handleError("interpolation::newSplineWithDerivs", & |
| 267 |
– |
"Error in allocating storage for c") |
| 268 |
– |
endif |
| 269 |
– |
|
| 270 |
– |
do i = 1, np |
| 271 |
– |
cs%x(i) = x(i) |
| 272 |
– |
cs%c(1,i) = y(i) |
| 273 |
– |
cs%c(2,i) = yp(i) |
| 274 |
– |
enddo |
| 275 |
– |
! |
| 176 |
|
! Set the diagonal coefficients. |
| 177 |
|
! |
| 178 |
|
cs%c(4,1) = 1.0_DP |
| 216 |
|
cs%c(3,cs%np) = 0.0_DP |
| 217 |
|
cs%c(4,cs%np) = 0.0_DP |
| 218 |
|
|
| 319 |
– |
cs%dx = dx |
| 219 |
|
cs%dx_i = 1.0_DP / dx |
| 220 |
|
|
| 221 |
|
return |
| 222 |
< |
end subroutine newSplineWithDerivs |
| 222 |
> |
end subroutine newSplineWithoutDerivs |
| 223 |
|
|
| 224 |
|
subroutine deleteSpline(this) |
| 225 |
|
|
| 336 |
|
|
| 337 |
|
return |
| 338 |
|
end subroutine lookup_uniform_spline |
| 339 |
+ |
|
| 340 |
+ |
subroutine lookup_spline(cs, xval, yval) |
| 341 |
+ |
|
| 342 |
+ |
type (cubicSpline), intent(in) :: cs |
| 343 |
+ |
real( kind = DP ), intent(inout) :: xval |
| 344 |
+ |
real( kind = DP ), intent(inout) :: yval |
| 345 |
+ |
|
| 346 |
+ |
if (cs%isUniform) then |
| 347 |
+ |
call lookup_uniform_spline(cs, xval, yval) |
| 348 |
+ |
else |
| 349 |
+ |
call lookup_nonuniform_spline(cs, xval, yval) |
| 350 |
+ |
endif |
| 351 |
+ |
|
| 352 |
+ |
return |
| 353 |
+ |
end subroutine lookup_spline |
| 354 |
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|
| 355 |
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end module INTERPOLATION |
