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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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