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Evaluate a 3-D Hermite_e series on the Cartesian product of x, y and z in Python
To evaluate a 3-D Hermite_e series on the Cartesian product of x, y and z, use the hermite.hermegrid3d(x, y, z, c) method in Python. The method returns the values of the three 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 3D array of coefficients −
c = np.arange(16).reshape(2,2,4)
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.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 3D array of coefficients
c = np.arange(16).reshape(2,2,4)
# 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.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]]] Dimensions of our Array... 3 Datatype of our Array object... int64 Shape of our Array object... (2, 2, 4) Result... [[[-20. 248.] [-30. 404.]] [[-30. 436.] [-45. 702.]]]
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