Return the companion matrix of a 1-D array of polynomial coefficients in Python



To return the companion matrix of a 1-D array of polynomial coefficients, return the polynomial.polycompanion() method in Python Numpy. The companion matrix for power series cannot be made symmetric by scaling the basis, so this function differs from those for the orthogonal polynomials. The method returns the Companion matrix of dimensions (deg, deg). The parameter, c is a 1-D array of polynomial coefficients ordered from low to high degree.

Steps

At first, import the required libraries −

import numpy as np
from numpy.polynomial.polynomial import polycompanion

Create a 1D array of coefficients −

c = np.array([1, 2, 3])

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 return the companion matrix of a 1-D array of polynomial coefficients, return the polynomial.polycompanion() method −

print("\nResult...\n",polycompanion(c))

Example

import numpy as np
from numpy.polynomial.polynomial import polycompanion

# Create a 1D array of coefficients
c = np.array([1, 2, 3])

# 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 return the companion matrix of a 1-D array of polynomial coefficients, return the polynomial.polycompanion() method in Python Numpy
print("\nResult...\n",polycompanion(c))

Output

Our Array...
[1 2 3]

Dimensions of our Array...
1

Datatype of our Array object...
int64

Shape of our Array object...
(3,)

Result...
[[ 0. -0.33333333]
[ 1. -0.66666667]]

Advertisements