#!/usr/bin/env python
# coding: utf-8

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import numpy as np
import matplotlib.pyplot as plt
get_ipython().run_line_magic('matplotlib', 'inline')

from scipy.interpolate import RegularGridInterpolator


# ## Multilinear Interpolation
# * Use `RegularGridInterpolator` from `scipy.interpolate`
# 
# Do a 3D example, that is, we have some data $f_i = z_i(x_i, y_i, z_i)$

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#-------- define grids in x, y, z

x = np.linspace(0,1,101)
y = np.linspace(0,1,101)
z = np.linspace(0,1,101)

#-------- define the function on the grid

X,Y,Z = np.meshgrid(x,y,z)        # just used for conveninece 
f = np.sin(9*X)*np.sin(9*Y)*Z

#-------- define interpolant and interpolate to "wanted" point xw, yw, zw

finterp = RegularGridInterpolator( (x,y,z), f )

xw = yw = zw = 0.155
f_w = finterp( (xw, yw, zw) )
f_w


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