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

To evaluate a 3D Hermite series at points (x, y, z), use the hermite.hermval3d() method in Python NumPy. The method returns the values of the multidimensional polynomial on points formed with triples of corresponding values from x, y, and z.

Syntax

hermite.hermval3d(x, y, z, c)

Parameters

The function takes the following parameters ?

• x, y, z ? The coordinates where the series is evaluated. Must have the same shape. Lists or tuples are converted to ndarrays
• c ? Array of coefficients ordered so that the coefficient of term of multi-degree i,j,k is contained in c[i,j,k]. If c has dimension greater than 3, the remaining indices enumerate multiple sets of coefficients

Example

Let's create a 4D array of coefficients and evaluate the Hermite series at specific points ?

import numpy as np
from numpy.polynomial import hermite as H

# 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)

# Evaluate 3D Hermite series at points (x, y, z)
print("\nResult...\n", H.hermval3d([1, 2], [1, 2], [1, 2], c))

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...
[[ -8100. 104480.]
 [ -8343. 107455.]]

How It Works

The hermval3d() method evaluates a 3D Hermite polynomial series using the coefficient array. The fourth dimension in our coefficient array allows for multiple polynomial evaluations simultaneously. Each evaluation point (1,1,1) and (2,2,2) produces results for both sets of coefficients, resulting in a 2×2 output array.

Conclusion

The hermite.hermval3d() method efficiently evaluates 3D Hermite series at specified coordinate points. Use 4D coefficient arrays to evaluate multiple polynomial sets simultaneously at the same points.