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 :
Python3
# importing numpy module and polyval3d functionimport numpy as npfrom numpy.polynomial.polynomial import polyval3d# creating an 4d array of coefficients 'C' # using numpyC = 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 :
Python3
# importing numpy module and polyval3d functionimport numpy as npfrom 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.]]
