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

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To evaluate a 3-D Hermite_e series on the Cartesian product of x, y and z, use the hermite_e.hermegrid3d(x, y, z, c) method in Python. The method returns the values of the two dimensional polynomial at points in the Cartesian product of x, y and z.

The parameters are x, y, z. 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 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 libraries −

import numpy as np
from numpy.polynomial import hermite_e 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)

To evaluate a 3-D Hermite_e series on the Cartesian product of x, y and z, use the hermite_e.hermegrid3d(x, y, z, c) method in Python −

print("\nResult...\n",H.hermegrid3d([1,2],[1,2],[1,2],c))

Example

import numpy as np
from numpy.polynomial import hermite_e 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)

# To evaluate a 3-D Hermite_e series on the Cartesian product of x, y and z, use the hermite_e.hermegrid3d(x, y, z, c) method in Python
print("\nResult...\n",H.hermegrid3d([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...
[[[[ 424. -1848.]
  [ 684. -2952.]]

[[ 732. -3132.]
 [ 1170. -4968.]]]


[[[ 440. -1908.]
  [ 708. -3042.]]

[[ 756. -3222.]
 [ 1206. -5103.]]]]
raja
Updated on 28-Feb-2022 11:27:52

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