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Generate a Vandermonde matrix of given degree with complex array of points in Python
To generate a Vandermonde matrix of given degree, use the polynomial.polyvander() 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 power of x. 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 libraries −
import numpy as np from numpy.polynomial.polynomial import polyvander
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 given degree, use the polynomial.polyvander() in Python Numpy −
print("\nResult...\n",polyvander(x, 2))Example
import numpy as np
from numpy.polynomial.polynomial import polyvander
# 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 given degree, use the polynomial.polyvander() in Python Numpy
print("\nResult...\n",polyvander(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 0.-8.j] [ 1.+0.j -1.+2.j -3.-4.j] [ 1.+0.j 0.+2.j -4.+0.j] [ 1.+0.j 1.+2.j -3.+4.j] [ 1.+0.j 2.+2.j 0.+8.j]]
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