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Evaluate a 2-D Hermite series on the Cartesian product of x and y with 3d array of coefficient in Python
To evaluate a 2-D Hermite series on the Cartesian product of x and y, use the hermite.hermgrid2d(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 parameters are x, y. The two dimensional series is evaluated at the points in the Cartesian product of x and y. If x or y 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 two dimensions, ones are implicitly appended to its shape to make it 2-D. The shape of the result will be c.shape[2:] + x.shape.
Steps
At first, import the required library −
import numpy as np from numpy.polynomial import hermite as H
Create a 3d array of coefficients −
c = np.arange(24).reshape(2,2,6)
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 2-D Hermite series on the Cartesian product of x and y, use the hermite.hermgrid2d(x, y, c) method in Python −
print("\nResult...\n",H.hermgrid2d([1,2],[1,2], c))
Example
import numpy as np from numpy.polynomial import hermite as H # Create a 3d array of coefficients c = np.arange(24).reshape(2,2,6) # 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 2-D Hermite series on the Cartesian product of x and y, use the hermite.hermgrid2d(x, y, c) method in Python print("\nResult...\n",H.hermgrid2d([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]]] Dimensions of our Array... 3 Datatype of our Array object... int64 Shape of our Array object... (2, 2, 6) Result... [[[108. 192.] [204. 360.]] [[117. 207.] [219. 385.]] [[126. 222.] [234. 410.]] [[135. 237.] [249. 435.]] [[144. 252.] [264. 460.]] [[153. 267.] [279. 485.]]]