Evaluate a 3-D polynomial at points (x, y, z) with 4D array of coefficient using NumPy in Python

In this article, we will look at how to evaluate a 3-dimensional polynomial at points (x, y, z) with a 4D array of coefficients using NumPy in Python.

polynomial.polyval3d method 

We are using polynomial.polyval3d() function present in the NumPy module of python for the evaluation purpose of a 3-dimensional polynomial at points x, y, and z.Here at points x, y, and z, the 3-dimensional series is being evaluated if x, y, and z have a similar shape, if either from x, y, and z is a list or a tuple then before evaluation it is going to be converted to an nd-array else it is kept as it is. Also if it is not an nd-array, it will be treated as a scalar. Another parameter 'C' is present which is an ordered array of coefficients with multi-degree terms i, j, k present in C[i, j, k]. 

Syntax : polyval3d(x, y, z, C)

Parameters: 

• x, y, z : The three-dimensional series is analyzed at the array-like points.
• C :  It is an sorted array of coefficients organised so that the coefficient of the term of multi-degree i,j,k is contained in c[i,j,k].

Returns: the multidimensional polynomial values on the points formed with the triples of the corresponding values from x, y and z.

Example 1 :

# importing numpy module and polyval3d function
import numpy as np
from numpy.polynomial.polynomial import polyval3d

# creating an 4d array of coefficients 'C' 
# using numpy
C = np.arange(24).reshape(2,2,3,2)

# Now using polyval3d function we are 
# evaluating the 3D polynomial at points
# (x,y,z)
print(polyval3d([2,1],[1,2],[2,3], C))

Output :

[[ 582. 1032.]
 [ 624. 1110.]]

Example 2 :

# importing numpy module and polyval3d function
import numpy as np
from numpy.polynomial.polynomial import polyval3d

# creating an 4d array of coefficients 'C'
C = np.arange(72).reshape(3,2,6,2)

# Now using polyval3d function evaluate 
# the 3D polynomial at points (x,y,z)
x = [4,1]
y = [1,2]
z = [2,3]

print("The result of evaluation by polyval3d function is : \n",
      polyval3d(x, y, z, C))

Output :

The result of evaluation by polyval3d function is : 
 [[146412. 134370.]
 [149058. 137646.]]