Fortran toolkit
Borja Petit
interpolation
subroutine interpolation(pos,wth,xnow,xgrid)
implicit none
real(kind=8), intent(in) :: xnow,xgrid(:)
real(kind=8), intent(out) :: wth
integer , intent(out) :: pos
This subroutine finds the closest point in a given grid and return its position (pos) and the relative distance (wth) such that:
xnow = vec(pos)·wth + vec(pos-1)·(1-wth)
- If
xnow< min(xgrid) the subroutine takes min(xgrid) as the interpolated value ofxnow. - If
xnow> max(xgrid) the subroutine takes max(xgrid) as the interpolated value ofxnow.
The vector xvec should be monotonically increasing/decreasing, so that xgrid(i) > xgrid(i-1) or xgrid(i) < xgrid(i-1) is satisfied for any i.
This subroutine is mainly used by the function interpolate.
Dependencies: error
Example
! vector over which we wan to interpolate
vec = [1,2,3]
! interpolate x = 2.3
call interpolation(pos,wth,2.3,vec)
! output: pos = 3, wth = 0.3
! 2.3 = vec(pos)*wth + vec(pos-1)*(one-wth) = 3*0.3 + 2*0.7
! interpolate x = 0
call interpolation(pos,wth,0,vec)
! since 0 is smaller than min(vec), the subroutine returns the min of vec
! output: pos = 2, wth = 0.0
! 1 = vec(pos)*wth + vec(pos-1)*(one-wth) = 2*0.0 + 1*1.0