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Generate a Vandermonde matrix of the Hermite_e polynomial with float array of points in Python
To generate a Vandermonde matrix of the Hermite_e polynomial, use the hermite_e.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_e as H
Create an array −
x = np.array([0, 3.5, -1.4, 2.5])
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 generate a Vandermonde matrix of the Hermite_e polynomial, use the hermite_e.hermvander() method −
print("\nResult...\n",H.hermevander(x, 2))Example
import numpy as np
from numpy.polynomial import hermite_e as H
# Create an array
x = np.array([0, 3.5, -1.4, 2.5])
# 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_e polynomial, use the hermite_e.hermvander() in Python Numpy
print("\nResult...\n",H.hermevander(x, 2))Output
Our Array... [ 0. 3.5 -1.4 2.5] Dimensions of our Array... 1 Datatype of our Array object... float64 Shape of our Array object... (4,) Result... [[ 1. 0. -1. ] [ 1. 3.5 11.25] [ 1. -1.4 0.96] [ 1. 2.5 5.25]]
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