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([-2.+2.j, -1.+2.j, 0.+2.j, 1.+2.j, 2.+2.j])
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() −
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([-2.+2.j, -1.+2.j, 0.+2.j, 1.+2.j, 2.+2.j])
# 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
# 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
print("\nResult...\n",C.chebvander(x, 2))Output
Our Array... [-2.+2.j -1.+2.j 0.+2.j 1.+2.j 2.+2.j] Dimensions of our Array... 1 Datatype of our Array object... complex128 Shape of our Array object... (5,) Result... [[ 1. +0.j -2. +2.j -1.-16.j] [ 1. +0.j -1. +2.j -7. -8.j] [ 1. +0.j 0. +2.j -9. +0.j] [ 1. +0.j 1. +2.j -7. +8.j] [ 1. +0.j 2. +2.j -1.+16.j]]