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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 1.2 2006-04-14 20:04:31 gezelter Exp $ |
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!! @version $Id: interpolation.F90,v 1.3 2006-04-14 21:06:55 chrisfen Exp $ |
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module INTERPOLATION |
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end type cubicSpline |
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interface newSpline |
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module procedure newSplineWithoutDerivs |
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module procedure newSplineWithDerivs |
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module procedure newSpline |
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end interface |
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public :: deleteSpline |
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contains |
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subroutine newSplineWithoutDerivs(cs, x, y, yp1, ypn, boundary) |
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subroutine newSpline(cs, x, y, yp1, ypn) |
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!************************************************************************ |
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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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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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real( kind = DP ) :: g, divdif1, divdif3, dx |
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integer :: i, alloc_error, np |
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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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cs%c(2,1) = yp1 |
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cs%c(2,np) = ypn |
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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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cs%dx_i = 1.0_DP / dx |
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return |
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end subroutine newSplineWithoutDerivs |
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subroutine newSplineWithDerivs(cs, x, y, yp) |
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!************************************************************************ |
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! |
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! newSplineWithDerivs |
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|
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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(:), yp(:) |
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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::newSplineWithDerivs", & |
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"Type 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)).or.(size(x) .ne. size(yp))) then |
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call handleError("interpolation::newSplineWithDerivs", & |
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"Array size mismatch") |
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end if |
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np = size(x) |
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cs%np = np |
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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::newSplineWithDerivs", & |
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"Error in allocating storage for x") |
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endif |
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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::newSplineWithDerivs", & |
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"Error in allocating storage for c") |
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endif |
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do i = 1, np |
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cs%x(i) = x(i) |
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cs%c(1,i) = y(i) |
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cs%c(2,i) = yp(i) |
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enddo |
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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) |
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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 |
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! piecewise polynomial representation. |
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! |
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do i = 1, cs%np - 1 |
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dx = x(i+1) - x(i) |
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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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cs%c(3,cs%np) = 0.0_DP |
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cs%c(4,cs%np) = 0.0_DP |
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|
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cs%dx = dx |
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cs%dx_i = 1.0_DP / dx |
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return |
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end subroutine newSplineWithDerivs |
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subroutine deleteSpline(this) |
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type(cubicSpline) :: this |
