| 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. These routines |
| 47 |
> |
!! assume that we are on a uniform grid for precomputation of |
| 48 |
> |
!! spline parameters. |
| 49 |
|
!! |
| 50 |
|
!! @author Charles F. Vardeman II |
| 51 |
< |
!! @version $Id: interpolation.F90,v 1.3 2006-04-14 21:06:55 chrisfen Exp $ |
| 51 |
> |
!! @version $Id: interpolation.F90,v 1.4 2006-04-14 21:49:54 gezelter Exp $ |
| 52 |
|
|
| 53 |
|
|
| 54 |
|
module INTERPOLATION |
| 61 |
|
|
| 62 |
|
type, public :: cubicSpline |
| 63 |
|
private |
| 64 |
+ |
logical :: isUniform = .false. |
| 65 |
|
integer :: np = 0 |
| 64 |
– |
real(kind=dp) :: dx |
| 66 |
|
real(kind=dp) :: dx_i |
| 67 |
|
real (kind=dp), pointer,dimension(:) :: x => null() |
| 68 |
|
real (kind=dp), pointer,dimension(:,:) :: c => null() |
| 69 |
|
end type cubicSpline |
| 70 |
|
|
| 71 |
< |
interface newSpline |
| 71 |
< |
module procedure newSpline |
| 72 |
< |
end interface |
| 73 |
< |
|
| 71 |
> |
public :: newSpline |
| 72 |
|
public :: deleteSpline |
| 73 |
< |
|
| 73 |
> |
public :: lookup_spline |
| 74 |
> |
public :: lookup_uniform_spline |
| 75 |
> |
public :: lookup_nonuniform_spline |
| 76 |
> |
|
| 77 |
|
contains |
| 78 |
+ |
|
| 79 |
|
|
| 80 |
< |
|
| 81 |
< |
subroutine newSpline(cs, x, y, yp1, ypn) |
| 80 |
< |
|
| 80 |
> |
subroutine newSpline(cs, x, y, yp1, ypn, isUniform) |
| 81 |
> |
|
| 82 |
|
!************************************************************************ |
| 83 |
|
! |
| 84 |
< |
! newSplineWithoutDerivs solves for slopes defining a cubic spline. |
| 84 |
> |
! newSpline solves for slopes defining a cubic spline. |
| 85 |
|
! |
| 86 |
|
! Discussion: |
| 87 |
|
! |
| 104 |
|
! Input, real y(I), contains the function value at x(I) for |
| 105 |
|
! I = 1, N. |
| 106 |
|
! |
| 107 |
< |
! yp1 contains the slope at x(1) and ypn contains |
| 108 |
< |
! the slope at x(N). |
| 107 |
> |
! Input, real yp1 contains the slope at x(1) |
| 108 |
> |
! Input, real ypn contains the slope at x(N) |
| 109 |
|
! |
| 110 |
< |
! On output, the intermediate slopes at x(I) have been |
| 111 |
< |
! stored in cs%C(2,I), for I = 2 to N-1. |
| 110 |
> |
! On output, the slopes at x(I) have been stored in |
| 111 |
> |
! cs%C(2,I), for I = 1 to N. |
| 112 |
|
|
| 113 |
|
implicit none |
| 114 |
|
|
| 115 |
|
type (cubicSpline), intent(inout) :: cs |
| 116 |
|
real( kind = DP ), intent(in) :: x(:), y(:) |
| 117 |
|
real( kind = DP ), intent(in) :: yp1, ypn |
| 118 |
+ |
logical, intent(in) :: isUniform |
| 119 |
|
real( kind = DP ) :: g, divdif1, divdif3, dx |
| 120 |
|
integer :: i, alloc_error, np |
| 121 |
|
|
| 122 |
|
alloc_error = 0 |
| 123 |
|
|
| 124 |
|
if (cs%np .ne. 0) then |
| 125 |
< |
call handleWarning("interpolation::newSplineWithoutDerivs", & |
| 126 |
< |
"Type was already created") |
| 125 |
> |
call handleWarning("interpolation::newSpline", & |
| 126 |
> |
"cubicSpline struct was already created") |
| 127 |
|
call deleteSpline(cs) |
| 128 |
|
end if |
| 129 |
|
|
| 130 |
|
! make sure the sizes match |
| 131 |
|
|
| 132 |
< |
if (size(x) .ne. size(y)) then |
| 133 |
< |
call handleError("interpolation::newSplineWithoutDerivs", & |
| 132 |
> |
np = size(x) |
| 133 |
> |
|
| 134 |
> |
if ( size(y) .ne. np ) then |
| 135 |
> |
call handleError("interpolation::newSpline", & |
| 136 |
|
"Array size mismatch") |
| 137 |
|
end if |
| 138 |
< |
|
| 135 |
< |
np = size(x) |
| 138 |
> |
|
| 139 |
|
cs%np = np |
| 140 |
+ |
cs%isUniform = isUniform |
| 141 |
|
|
| 142 |
|
allocate(cs%x(np), stat=alloc_error) |
| 143 |
|
if(alloc_error .ne. 0) then |
| 144 |
< |
call handleError("interpolation::newSplineWithoutDerivs", & |
| 144 |
> |
call handleError("interpolation::newSpline", & |
| 145 |
|
"Error in allocating storage for x") |
| 146 |
|
endif |
| 147 |
|
|
| 148 |
|
allocate(cs%c(4,np), stat=alloc_error) |
| 149 |
|
if(alloc_error .ne. 0) then |
| 150 |
< |
call handleError("interpolation::newSplineWithoutDerivs", & |
| 150 |
> |
call handleError("interpolation::newSpline", & |
| 151 |
|
"Error in allocating storage for c") |
| 152 |
|
endif |
| 153 |
|
|
| 162 |
|
cs%c(2,1) = yp1 |
| 163 |
|
cs%c(2,np) = ypn |
| 164 |
|
|
| 161 |
– |
|
| 165 |
|
! |
| 166 |
|
! Set up the right hand side of the linear system. |
| 167 |
|
! |
| 168 |
+ |
|
| 169 |
|
do i = 2, cs%np - 1 |
| 170 |
|
cs%c(2,i) = 3.0_DP * ( & |
| 171 |
|
(x(i) - x(i-1)) * (cs%c(1,i+1) - cs%c(1,i)) / (x(i+1) - x(i)) + & |
| 172 |
|
(x(i+1) - x(i)) * (cs%c(1,i) - cs%c(1,i-1)) / (x(i) - x(i-1))) |
| 173 |
|
end do |
| 174 |
+ |
|
| 175 |
|
! |
| 176 |
|
! Set the diagonal coefficients. |
| 177 |
|
! |
| 216 |
|
cs%c(3,cs%np) = 0.0_DP |
| 217 |
|
cs%c(4,cs%np) = 0.0_DP |
| 218 |
|
|
| 214 |
– |
cs%dx = dx |
| 219 |
|
cs%dx_i = 1.0_DP / dx |
| 220 |
+ |
|
| 221 |
|
return |
| 222 |
|
end subroutine newSplineWithoutDerivs |
| 223 |
|
|
| 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 |
|
|
| 355 |
|
end module INTERPOLATION |
