Evaluate a 2-D Hermite series on the Cartesian product of x and y 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 2D array of coefficients −

c = np.arange(4).reshape(2,2) 

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 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 2D array of coefficients c = np.arange(4).reshape(2,2) # 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 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]] Dimensions of our Array... 2 Datatype of our Array object... int64 Shape of our Array object... (2, 2) Result... [[18. 32.] [34. 60.]]