| 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 1.1 2006-04-14 19:57:04 gezelter Exp $ |
| 51 |
> |
!! @version $Id: interpolation.F90,v 1.6 2006-04-17 21:49:12 gezelter Exp $ |
| 52 |
|
|
| 53 |
|
|
| 54 |
< |
module INTERPOLATION |
| 54 |
> |
module interpolation |
| 55 |
|
use definitions |
| 56 |
|
use status |
| 57 |
|
implicit none |
| 60 |
|
character(len = statusMsgSize) :: errMSG |
| 61 |
|
|
| 62 |
|
type, public :: cubicSpline |
| 63 |
< |
private |
| 63 |
> |
logical :: isUniform = .false. |
| 64 |
|
integer :: np = 0 |
| 64 |
– |
real(kind=dp) :: dx |
| 65 |
|
real(kind=dp) :: dx_i |
| 66 |
|
real (kind=dp), pointer,dimension(:) :: x => null() |
| 67 |
< |
real (kind=dp), pointer,dimension(4,:) :: c => null() |
| 67 |
> |
real (kind=dp), pointer,dimension(:,:) :: c => null() |
| 68 |
|
end type cubicSpline |
| 69 |
|
|
| 70 |
< |
interface splineLookup |
| 71 |
< |
module procedure multiSplint |
| 72 |
< |
module procedure splintd |
| 73 |
< |
module procedure splintd1 |
| 74 |
< |
module procedure splintd2 |
| 75 |
< |
end interface |
| 76 |
< |
|
| 77 |
< |
interface newSpline |
| 78 |
< |
module procedure newSplineWithoutDerivs |
| 79 |
< |
module procedure newSplineWithDerivs |
| 80 |
< |
end interface |
| 81 |
< |
|
| 70 |
> |
public :: newSpline |
| 71 |
|
public :: deleteSpline |
| 72 |
< |
|
| 72 |
> |
public :: lookupSpline |
| 73 |
> |
public :: lookupUniformSpline |
| 74 |
> |
public :: lookupNonuniformSpline |
| 75 |
> |
public :: lookupUniformSpline1d |
| 76 |
> |
|
| 77 |
|
contains |
| 78 |
+ |
|
| 79 |
|
|
| 80 |
< |
|
| 81 |
< |
subroutine newSplineWithoutDerivs(cs, x, y, yp1, ypn, boundary) |
| 88 |
< |
|
| 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 |
|
! |
| 98 |
|
! Parameters: |
| 99 |
|
! |
| 100 |
|
! Input, real x(N), the abscissas or X values of |
| 101 |
< |
! the data points. The entries of TAU are assumed to be |
| 101 |
> |
! the data points. The entries of x are assumed to be |
| 102 |
|
! strictly increasing. |
| 103 |
|
! |
| 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 |
< |
character(len=*), intent(in) :: boundary |
| 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 |
< |
|
| 144 |
< |
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 |
|
|
| 156 |
|
cs%c(1,i) = y(i) |
| 157 |
|
enddo |
| 158 |
|
|
| 159 |
< |
if ((boundary.eq.'l').or.(boundary.eq.'L').or. & |
| 160 |
< |
(boundary.eq.'b').or.(boundary.eq.'B')) then |
| 166 |
< |
cs%c(2,1) = yp1 |
| 167 |
< |
else |
| 168 |
< |
cs%c(2,1) = 0.0_DP |
| 169 |
< |
endif |
| 170 |
< |
if ((boundary.eq.'u').or.(boundary.eq.'U').or. & |
| 171 |
< |
(boundary.eq.'b').or.(boundary.eq.'B')) then |
| 172 |
< |
cs%c(2,1) = ypn |
| 173 |
< |
else |
| 174 |
< |
cs%c(2,1) = 0.0_DP |
| 175 |
< |
endif |
| 159 |
> |
! Set the first derivative of the function to the second coefficient of |
| 160 |
> |
! each of the endpoints |
| 161 |
|
|
| 162 |
+ |
cs%c(2,1) = yp1 |
| 163 |
+ |
cs%c(2,np) = ypn |
| 164 |
+ |
|
| 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 |
| 185 |
– |
! |
| 186 |
– |
! Set the diagonal coefficients. |
| 187 |
– |
! |
| 188 |
– |
cs%c(4,1) = 1.0_DP |
| 189 |
– |
do i = 2, cs%np - 1 |
| 190 |
– |
cs%c(4,i) = 2.0_DP * ( x(i+1) - x(i-1) ) |
| 191 |
– |
end do |
| 192 |
– |
cs%c(4,n) = 1.0_DP |
| 193 |
– |
! |
| 194 |
– |
! Set the off-diagonal coefficients. |
| 195 |
– |
! |
| 196 |
– |
cs%c(3,1) = 0.0_DP |
| 197 |
– |
do i = 2, cs%np |
| 198 |
– |
cs%c(3,i) = x(i) - x(i-1) |
| 199 |
– |
end do |
| 200 |
– |
! |
| 201 |
– |
! Forward elimination. |
| 202 |
– |
! |
| 203 |
– |
do i = 2, cs%np - 1 |
| 204 |
– |
g = -cs%c(3,i+1) / cs%c(4,i-1) |
| 205 |
– |
cs%c(4,i) = cs%c(4,i) + g * cs%c(3,i-1) |
| 206 |
– |
cs%c(2,i) = cs%c(2,i) + g * cs%c(2,i-1) |
| 207 |
– |
end do |
| 208 |
– |
! |
| 209 |
– |
! Back substitution for the interior slopes. |
| 210 |
– |
! |
| 211 |
– |
do i = cs%np - 1, 2, -1 |
| 212 |
– |
cs%c(2,i) = ( cs%c(2,i) - cs%c(3,i) * cs%c(2,i+1) ) / cs%c(4,i) |
| 213 |
– |
end do |
| 214 |
– |
! |
| 215 |
– |
! Now compute the quadratic and cubic coefficients used in the |
| 216 |
– |
! piecewise polynomial representation. |
| 217 |
– |
! |
| 218 |
– |
do i = 1, cs%np - 1 |
| 219 |
– |
dx = x(i+1) - x(i) |
| 220 |
– |
divdif1 = ( cs%c(1,i+1) - cs%c(1,i) ) / dx |
| 221 |
– |
divdif3 = cs%c(2,i) + cs%c(2,i+1) - 2.0_DP * divdif1 |
| 222 |
– |
cs%c(3,i) = ( divdif1 - cs%c(2,i) - divdif3 ) / dx |
| 223 |
– |
cs%c(4,i) = divdif3 / ( dx * dx ) |
| 224 |
– |
end do |
| 225 |
– |
|
| 226 |
– |
cs%c(3,np) = 0.0_DP |
| 227 |
– |
cs%c(4,np) = 0.0_DP |
| 228 |
– |
|
| 229 |
– |
cs%dx = dx |
| 230 |
– |
cs%dxi = 1.0_DP / dx |
| 231 |
– |
return |
| 232 |
– |
end subroutine newSplineWithoutDerivs |
| 233 |
– |
|
| 234 |
– |
subroutine newSplineWithDerivs(cs, x, y, yp) |
| 174 |
|
|
| 236 |
– |
!************************************************************************ |
| 175 |
|
! |
| 238 |
– |
! newSplineWithDerivs |
| 239 |
– |
|
| 240 |
– |
implicit none |
| 241 |
– |
|
| 242 |
– |
type (cubicSpline), intent(inout) :: cs |
| 243 |
– |
real( kind = DP ), intent(in) :: x(:), y(:), yp(:) |
| 244 |
– |
real( kind = DP ) :: g, divdif1, divdif3, dx |
| 245 |
– |
integer :: i, alloc_error, np |
| 246 |
– |
|
| 247 |
– |
alloc_error = 0 |
| 248 |
– |
|
| 249 |
– |
if (cs%np .ne. 0) then |
| 250 |
– |
call handleWarning("interpolation::newSplineWithDerivs", & |
| 251 |
– |
"Type was already created") |
| 252 |
– |
call deleteSpline(cs) |
| 253 |
– |
end if |
| 254 |
– |
|
| 255 |
– |
! make sure the sizes match |
| 256 |
– |
|
| 257 |
– |
if ((size(x) .ne. size(y)).or.(size(x) .ne. size(yp))) then |
| 258 |
– |
call handleError("interpolation::newSplineWithDerivs", & |
| 259 |
– |
"Array size mismatch") |
| 260 |
– |
end if |
| 261 |
– |
|
| 262 |
– |
np = size(x) |
| 263 |
– |
cs%np = np |
| 264 |
– |
|
| 265 |
– |
allocate(cs%x(np), stat=alloc_error) |
| 266 |
– |
if(alloc_error .ne. 0) then |
| 267 |
– |
call handleError("interpolation::newSplineWithDerivs", & |
| 268 |
– |
"Error in allocating storage for x") |
| 269 |
– |
endif |
| 270 |
– |
|
| 271 |
– |
allocate(cs%c(4,np), stat=alloc_error) |
| 272 |
– |
if(alloc_error .ne. 0) then |
| 273 |
– |
call handleError("interpolation::newSplineWithDerivs", & |
| 274 |
– |
"Error in allocating storage for c") |
| 275 |
– |
endif |
| 276 |
– |
|
| 277 |
– |
do i = 1, np |
| 278 |
– |
cs%x(i) = x(i) |
| 279 |
– |
cs%c(1,i) = y(i) |
| 280 |
– |
cs%c(2,i) = yp(i) |
| 281 |
– |
enddo |
| 282 |
– |
! |
| 176 |
|
! Set the diagonal coefficients. |
| 177 |
|
! |
| 178 |
|
cs%c(4,1) = 1.0_DP |
| 179 |
|
do i = 2, cs%np - 1 |
| 180 |
|
cs%c(4,i) = 2.0_DP * ( x(i+1) - x(i-1) ) |
| 181 |
|
end do |
| 182 |
< |
cs%c(4,n) = 1.0_DP |
| 182 |
> |
cs%c(4,cs%np) = 1.0_DP |
| 183 |
|
! |
| 184 |
|
! Set the off-diagonal coefficients. |
| 185 |
|
! |
| 213 |
|
cs%c(4,i) = divdif3 / ( dx * dx ) |
| 214 |
|
end do |
| 215 |
|
|
| 216 |
< |
cs%c(3,np) = 0.0_DP |
| 217 |
< |
cs%c(4,np) = 0.0_DP |
| 216 |
> |
cs%c(3,cs%np) = 0.0_DP |
| 217 |
> |
cs%c(4,cs%np) = 0.0_DP |
| 218 |
|
|
| 219 |
< |
cs%dx = dx |
| 327 |
< |
cs%dxi = 1.0_DP / dx |
| 219 |
> |
cs%dx_i = 1.0_DP / dx |
| 220 |
|
|
| 221 |
|
return |
| 222 |
< |
end subroutine newSplineWithoutDerivs |
| 222 |
> |
end subroutine newSpline |
| 223 |
|
|
| 224 |
|
subroutine deleteSpline(this) |
| 225 |
|
|
| 238 |
|
|
| 239 |
|
end subroutine deleteSpline |
| 240 |
|
|
| 241 |
< |
subroutine lookup_nonuniform_spline(cs, xval, yval) |
| 241 |
> |
subroutine lookupNonuniformSpline(cs, xval, yval) |
| 242 |
|
|
| 243 |
|
!************************************************************************* |
| 244 |
|
! |
| 245 |
< |
! lookup_nonuniform_spline evaluates a piecewise cubic Hermite interpolant. |
| 245 |
> |
! lookupNonuniformSpline evaluates a piecewise cubic Hermite interpolant. |
| 246 |
|
! |
| 247 |
|
! Discussion: |
| 248 |
|
! |
| 267 |
|
type (cubicSpline), intent(in) :: cs |
| 268 |
|
real( kind = DP ), intent(in) :: xval |
| 269 |
|
real( kind = DP ), intent(out) :: yval |
| 270 |
+ |
real( kind = DP ) :: dx |
| 271 |
|
integer :: i, j |
| 272 |
|
! |
| 273 |
|
! Find the interval J = [ cs%x(J), cs%x(J+1) ] that contains |
| 291 |
|
yval = cs%c(1,j) + dx * ( cs%c(2,j) + dx * ( cs%c(3,j) + dx * cs%c(4,j) ) ) |
| 292 |
|
|
| 293 |
|
return |
| 294 |
< |
end subroutine lookup_nonuniform_spline |
| 294 |
> |
end subroutine lookupNonuniformSpline |
| 295 |
|
|
| 296 |
< |
subroutine lookup_uniform_spline(cs, xval, yval) |
| 296 |
> |
subroutine lookupUniformSpline(cs, xval, yval) |
| 297 |
|
|
| 298 |
|
!************************************************************************* |
| 299 |
|
! |
| 300 |
< |
! lookup_uniform_spline evaluates a piecewise cubic Hermite interpolant. |
| 300 |
> |
! lookupUniformSpline evaluates a piecewise cubic Hermite interpolant. |
| 301 |
|
! |
| 302 |
|
! Discussion: |
| 303 |
|
! |
| 322 |
|
type (cubicSpline), intent(in) :: cs |
| 323 |
|
real( kind = DP ), intent(in) :: xval |
| 324 |
|
real( kind = DP ), intent(out) :: yval |
| 325 |
+ |
real( kind = DP ) :: a, b, c, d, dx |
| 326 |
|
integer :: i, j |
| 327 |
|
! |
| 328 |
|
! Find the interval J = [ cs%x(J), cs%x(J+1) ] that contains |
| 329 |
|
! or is nearest to xval. |
| 330 |
|
|
| 331 |
< |
j = MAX(1, MIN(cs%np, idint((xval-cs%x(1)) * cs%dxi) + 1)) |
| 331 |
> |
j = MAX(1, MIN(cs%np, idint((xval-cs%x(1)) * cs%dx_i) + 1)) |
| 332 |
|
|
| 333 |
|
dx = xval - cs%x(j) |
| 334 |
|
|
| 335 |
< |
yval = cs%c(1,j) + dx * ( cs%c(2,j) + dx * ( cs%c(3,j) + dx * cs%c(4,j) ) ) |
| 335 |
> |
a = cs%c(1,j) |
| 336 |
> |
b = cs%c(2,j) |
| 337 |
> |
c = cs%c(3,j) |
| 338 |
> |
d = cs%c(4,j) |
| 339 |
> |
|
| 340 |
> |
yval = c + dx * d |
| 341 |
> |
yval = b + dx * yval |
| 342 |
> |
yval = a + dx * yval |
| 343 |
|
|
| 344 |
|
return |
| 345 |
< |
end subroutine lookup_uniform_spline |
| 345 |
> |
end subroutine lookupUniformSpline |
| 346 |
> |
|
| 347 |
> |
subroutine lookupUniformSpline1d(cs, xval, yval, dydx) |
| 348 |
> |
|
| 349 |
> |
implicit none |
| 350 |
> |
|
| 351 |
> |
type (cubicSpline), intent(in) :: cs |
| 352 |
> |
real( kind = DP ), intent(in) :: xval |
| 353 |
> |
real( kind = DP ), intent(out) :: yval, dydx |
| 354 |
> |
real( kind = DP ) :: a, b, c, d, dx |
| 355 |
> |
integer :: i, j |
| 356 |
> |
|
| 357 |
> |
! Find the interval J = [ cs%x(J), cs%x(J+1) ] that contains |
| 358 |
> |
! or is nearest to xval. |
| 359 |
> |
|
| 360 |
> |
j = MAX(1, MIN(cs%np, idint((xval-cs%x(1)) * cs%dx_i) + 1)) |
| 361 |
> |
|
| 362 |
> |
dx = xval - cs%x(j) |
| 363 |
> |
|
| 364 |
> |
a = cs%c(1,j) |
| 365 |
> |
b = cs%c(2,j) |
| 366 |
> |
c = cs%c(3,j) |
| 367 |
> |
d = cs%c(4,j) |
| 368 |
> |
|
| 369 |
> |
yval = c + dx * d |
| 370 |
> |
yval = b + dx * yval |
| 371 |
> |
yval = a + dx * yval |
| 372 |
> |
|
| 373 |
> |
dydx = 2.0d0 * c + 3.0d0 * d * dx |
| 374 |
> |
dydx = b + dx * dydx |
| 375 |
> |
|
| 376 |
> |
return |
| 377 |
> |
end subroutine lookupUniformSpline1d |
| 378 |
> |
|
| 379 |
> |
subroutine lookupSpline(cs, xval, yval) |
| 380 |
> |
|
| 381 |
> |
type (cubicSpline), intent(in) :: cs |
| 382 |
> |
real( kind = DP ), intent(inout) :: xval |
| 383 |
> |
real( kind = DP ), intent(inout) :: yval |
| 384 |
> |
|
| 385 |
> |
if (cs%isUniform) then |
| 386 |
> |
call lookupUniformSpline(cs, xval, yval) |
| 387 |
> |
else |
| 388 |
> |
call lookupNonuniformSpline(cs, xval, yval) |
| 389 |
> |
endif |
| 390 |
> |
|
| 391 |
> |
return |
| 392 |
> |
end subroutine lookupSpline |
| 393 |
|
|
| 394 |
< |
end module INTERPOLATION |
| 394 |
> |
end module interpolation |
