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Return the scaled companion matrix of a 1-D array of Legendre polynomial coefficients in Python
To return the scaled companion matrix of a 1-D array of Legendre polynomial coefficients, use the legendre.legcompanion() method in Python Numpy. The usual companion matrix of the Legendre polynomials is already symmetric when c is a basis Laguerre polynomial, so no scaling is applied.
Returns the scaled Companion matrix of dimensions (deg, deg). The parameter, c is a 1-D array of Legendre series coefficients ordered from low to high degree.
Steps
At first, import the required library −
import numpy as np from numpy.polynomial import legendre as L
Create a 1D array of coefficients −
c = np.array([1, 2, 3, 4, 5])
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 scaled companion matrix of a 1-D array of Legendre polynomial coefficients, use the legendre.legcompanion() method in Python Numpy. The usual companion matrix of the Legendre polynomials is already symmetric when c is a basis Laguerre polynomial, so no scaling is applied −
print("\nResult...\n",L.legcompanion(c))Example
import numpy as np
from numpy.polynomial import legendre as L
# Create a 1D array of coefficients
c = np.array([1, 2, 3, 4, 5])
# 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 scaled companion matrix of a 1-D array of Legendre polynomial coefficients, use the legendre.legcompanion() method in Python Numpy
print("\nResult...\n",L.legcompanion(c))Output
Our Array... [1 2 3 4 5] Dimensions of our Array... 1 Datatype of our Array object... int64 Shape of our Array object... (5,) Result... [[ 0. 0.57735027 0. -0.30237158] [ 0.57735027 0. 0.51639778 -0.34914862] [ 0. 0.51639778 0. 0.10141851] [ 0. 0. 0.50709255 -0.45714286]]
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