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Generate a Vandermonde matrix of the Hermite polynomial in Python
To generate a Vandermonde matrix of the Hermite polynomial, use the hermite.hermvander() in Python Numpy. The method returns the pseudo-Vandermonde matrix. The shape of the returned matrix is x.shape + (deg + 1,), where The last index is the degree of the corresponding Hermite polynomial. The dtype will be the same as the converted x.
The parameter, x returns an Array of points. The dtype is converted to float64 or complex128 depending on whether any of the elements are complex. If x is scalar it is converted to a 1-D array. The parameter, deg is the degree of the resulting matrix.
Steps
At first, import the required library −
import numpy as np from numpy.polynomial import hermite as H
Create an array −
x = np.array([0, 1, -1, 2])
Display the array −
print("Our Array...\n",x)To generate a Vandermonde matrix of the Hermite polynomial, use the hermite.hermvander() in Python Numpy −
print("\nResult...\n",H.hermvander(x, 2))Example
import numpy as np
from numpy.polynomial import hermite as H
# Create an array
x = np.array([0, 1, -1, 2])
# Display the array
print("Our Array...\n",x)
# Check the Dimensions
print("\nDimensions of our Array...\n",x.ndim)
# Get the Datatype
print("\nDatatype of our Array object...\n",x.dtype)
# Get the Shape
print("\nShape of our Array object...\n",x.shape)
# To generate a Vandermonde matrix of the Hermite polynomial, use the hermite.hermvander() in Python Numpy
print("\nResult...\n",H.hermvander(x, 2))Output
Our Array... [ 0 1 -1 2] Dimensions of our Array... 1 Datatype of our Array object... int64 Shape of our Array object... (4,) Result... [[ 1. 0. -2.] [ 1. 2. 2.] [ 1. -2. 2.] [ 1. 4. 14.]]
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