Fortran Wiki
interpolation

PCHIP method

Below is a function that interpolates an array using a Piecewise Cubic Hermitian Interpolator. The required external methods are provided by the PCHIP module.

  function interpolate(x, y, p) result(r)
    !! This function constructs a piecewise cubic Hermitian interpolation of an array y(x) based on discrete numerical data,
    !! and evaluates the interpolation at points p. Note that the mesh spacing of x does not necessarily have to be uniform.
    real(wp), intent(in)  :: x(:)         !! Variable x
    real(wp), intent(in)  :: y(size(x))   !! Function y(x)
    real(wp), intent(in)  :: p(:)         !! Interpolation domain p
    real(wp)              :: r(size(p))   !! Interpolation result y(p)

    real(wp)              :: d(size(x))
    integer               :: err

    ! Create a PCHIP interpolation of the input data
    call dpchez(size(x), x, y, d, .false., 0, 0, err)

    ! Extract the interpolated data at provided points
    call dpchfe(size(x), x, y, d, 1, .false., size(p), p, r, err)
  end function