Evaluate a 3-D polynomial on the Cartesian product of x, y, z with 4d array of coefficient in Python

To evaluate a 3-D polynomial on the Cartesian product of x and y, use the polynomial.polygrid3d(x, y, c) method in Python. The method returns the values of the two dimensional polynomial at points in the Cartesian product of x and y.

The 1st parameter, x,y,z are the three dimensional series is evaluated at the points in the Cartesian product of x, y, and z. If x,`y`, or z is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and, if it isn’t an ndarray, it is treated as a scalar.

The 2nd parameter, c is an array of coefficients ordered so that the coefficients for terms of degree i,j are contained in c[i,j]. If c has dimension greater than two the remaining indices enumerate multiple sets of coefficients. If c has fewer than three dimensions, ones are implicitly appended to its shape to make it 3-D. The shape of the result will be c.shape[3:] + x.shape + y.shape + z.shape.

Steps

At first, import the required library −

import numpy as np
from numpy.polynomial.polynomial import polygrid3d

Create a 4d array of coefficients −

c = np.arange(48).reshape(2,2,6,2)

Display the array −

print("Our Array...\n",c)

Check the Dimensions −

print("\nDimensions of our Array...\n",c.ndim)

Get the Datatype −

print("\nDatatype of our Array object...\n",c.dtype)

Get the Shape −

print("\nShape of our Array object...\n",c.shape)

To evaluate a 3-D polynomial on the Cartesian product of x and y, use the polynomial.polygrid3d(x, y, c) method in Python. The method returns the values of the two dimensional polynomial at points in the Cartesian product of x and y −

print("\nResult...\n",polygrid3d([1,2],[1,2],[1,2],c))

Example

import numpy as np
from numpy.polynomial.polynomial import polygrid3d

# Create a 4d array of coefficients
c = np.arange(48).reshape(2,2,6,2)

# Display the array
print("Our Array...\n",c)

# Check the Dimensions
print("\nDimensions of our Array...\n",c.ndim)

# Get the Datatype
print("\nDatatype of our Array object...\n",c.dtype)

# Get the Shape
print("\nShape of our Array object...\n",c.shape)

# To evaluate a 3-D polynomial on the Cartesian product of x and y, use the polynomial.polygrid3d(x, y, c) method in Python
print("\nResult...\n",polygrid3d([1,2],[1,2],[1,2],c))

Output

Our Array...
   [[[[ 0 1]
   [ 2 3]
   [ 4 5]
   [ 6 7]
   [ 8 9]
   [10 11]]

   [[12 13]
   [14 15]
   [16 17]
   [18 19]
   [20 21]
   [22 23]]]


   [[[24 25]
   [26 27]
   [28 29]
   [30 31]
   [32 33]
   [34 35]]

   [[36 37]
   [38 39]
   [40 41]
   [42 43]
   [44 45]
   [46 47]]]]

Dimensions of our Array...
4

Datatype of our Array object...
int64

Shape of our Array object...
(2, 2, 6, 2)

Result...
   [[[[ 552. 6600.]
   [ 900. 10656.]]

   [[ 972. 11412.]
   [ 1566. 18252.]]]


   [[[ 576. 6852.]
   [ 936. 11034.]]

   [[ 1008. 11790.]
   [ 1620. 18819.]]]]