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Evaluate a 3-D Hermite series on the Cartesian product of x, y and z with 4d array of coefficient in Python
To evaluate a 3-D Hermite series on the Cartesian product of x, y and z, use the hermite.hermgrid3d(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 library −
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)To evaluate a 3-D Hermite series on the Cartesian product of x, y and z, use the hermite.hermgrid3d(x, y, z, c) method in Python −
print("\nResult...\n",H.hermgrid3d([1,2],[1,2],[1,2],c))Example
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)
# To evaluate a 3-D Hermite series on the Cartesian product of x, y and z, use the hermite.hermgrid3d(x, y, z, c) method in Python
print("\nResult...\n",H.hermgrid3d([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... [[[[ -8100. 32472.] [-14148. 56976.]] [[-14796. 59832.] [-25740. 104480.]]] [[[ -8343. 33543.] [-14553. 58761.]] [[-15201. 61617.] [-26415. 107455.]]]]
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