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, 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 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, 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 Chebyshev polynomial, use the chebyshev.chebvander() in Python Numpy print("\nResult...\n",C.chebvander(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. -1.] [ 1. 1. 1.] [ 1. -1. 1.] [ 1. 2. 7.]]