Generate a Vandermonde matrix of the Chebyshev polynomial with float array of points in Python

To generate a Vandermonde matrix of the Chebyshev polynomial, use the chebyshev.chebvander() in Python Numpy. The method returns the Vandermonde matrix. The shape of the returned matrix is x.shape + (deg + 1,), where The last index is the degree of the corresponding Chebyshev polynomial. The dtype will be the same as the converted x.

The parameter, a is 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 chebyshev as C

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 Chebyshev polynomial, use the chebyshev.chebvander() in Python −

print("\nResult...\n",C.chebvander(x, 2))

Example

import numpy as np
from numpy.polynomial import chebyshev as C

# 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 Chebyshev polynomial, use the chebyshev.chebvander() in Python Numpy
print("\nResult...\n",C.chebvander(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 23.5 ]
[ 1. -1.4 2.92]
[ 1. 2.5 11.5 ]]