Evaluate a 3-D polynomial at points (x, y, z) with 4D array of coefficient using NumPy in Python
Last Updated :
10 Jan, 2023
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
import numpy as np
from numpy.polynomial.polynomial import polyval3d
C = np.arange( 24 ).reshape( 2 , 2 , 3 , 2 )
print (polyval3d([ 2 , 1 ],[ 1 , 2 ],[ 2 , 3 ], C))
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Output :
[[ 582. 1032.]
[ 624. 1110.]]
Example 2 :
Python3
import numpy as np
from numpy.polynomial.polynomial import polyval3d
C = np.arange( 72 ).reshape( 3 , 2 , 6 , 2 )
x = [ 4 , 1 ]
y = [ 1 , 2 ]
z = [ 2 , 3 ]
print ( "The result of evaluation by polyval3d function is : \n" ,
polyval3d(x, y, z, C))
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Output :
The result of evaluation by polyval3d function is :
[[146412. 134370.]
[149058. 137646.]]
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