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interpolate

function interpolate(x1,x2,...,xn,y1,y2,...,yn,mat) result(xi)
  implicit none
  real(kind=8) :: x1    , x2    , ... , xn
  real(kind=8) :: y1(:) , y2(:) , ... , yn(:)   
  real(kind=8) :: mat(:,:,...,:)

This function returns the linearly interpolated value of an n-dimensional function, with n < 7. The variables x1, x2, …, xn are the values of the variables to be interpolated over their coresponding grids y1, y2, …., yn, and mat is an n-dimensional array with the results.

Internal dependencies: error, interpolation

Note: interpolate is an interface that calls specific functions depending on the dimension of mat. These functions are interpolate1d, interpolate2d, …, interpolate6d.

Example

We have a 2-dimensional array mat whose (i,j)-element is the value of some function func evaluated at the i-element of the vector xgrid, and the j-element of the vector ygrid:

do i=1,nx
  do j=1,ny
    mat(i,j) = func(xgrid(i),ygrid(j))
  end do
end do

Then, we can interpolate the value of func at (x0,y0) as:

func0 = interpolate(x0,y0,xgrid,ygrid,mat)

If the array mat is 3-dimensional, we can interpolate the value of func at (x0,y0,z0) as

func0 = interpolate(x0,y0,z0,xgrid,ygrid,zgrid,mat)