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Multiply one Legendre series to another in Python
To multiply one Legendre series from another, use the polynomial.legendre.legmul() method in Python Numpy. The method returns an array representing the Legendre series of their product. Returns the multiplication of two Legendre series c1 * c2. The arguments are sequences of coefficients ordered from lowest order term to highest, i.e., [1,2,3] represents the series P_0 + 2*P_1 + 3*P_2. The parameters c1 and c2 are 1-D arrays of Legendre series coefficients ordered from low to high.
Steps
At first, import the required library −
import numpy as np from numpy.polynomial import laguerre as L
Create 1-D arrays of Legendre series coefficients −
c1 = np.array([2,3,4]) c2 = np.array([4,3,2])
Display the arrays of coefficients −
print("Array1...\n",c1)
print("\nArray2...\n",c2)Display the datatype −
print("\nArray1 datatype...\n",c1.dtype)
print("\nArray2 datatype...\n",c2.dtype)Check the Dimensions of both the arrays −
print("\nDimensions of Array1...\n",c1.ndim)
print("\nDimensions of Array2...\n",c2.ndim)Check the Shape of both the arrays −
print("\nShape of Array1...\n",c1.shape)
print("\nShape of Array2...\n",c2.shape)To multiply one Legendre series from another, use the polynomial.legendre.legmul() method in Python Numpy −
print("\nResult (product)....\n",L.legmul(c1, c2))Example
import numpy as np
from numpy.polynomial import legendre as L
# Create 1-D arrays of Legendre series coefficients
c1 = np.array([2,3,4])
c2 = np.array([4,3,2])
# Display the arrays of coefficients
print("Array1...\n",c1)
print("\nArray2...\n",c2)
# Display the datatype
print("\nArray1 datatype...\n",c1.dtype)
print("\nArray2 datatype...\n",c2.dtype)
# Check the Dimensions of both the arrays
print("\nDimensions of Array1...\n",c1.ndim)
print("\nDimensions of Array2...\n",c2.ndim)
# Check the Shape of both the arrays
print("\nShape of Array1...\n",c1.shape)
print("\nShape of Array2...\n",c2.shape)
# To multiply one Legendre series from another, use the polynomial.legendre.legmul() method in Python Numpy
# The method returns an array representing the Legendre series of their product.
print("\nResult (product)....\n",L.legmul(c1, c2))Output
Array1... [2 3 4] Array2... [4 3 2] Array1 datatype... int64 Array2 datatype... int64 Dimensions of Array1... 1 Dimensions of Array2... 1 Shape of Array1... (3,) Shape of Array2... (3,) Result (product).... [12.6 25.2 28.28571429 10.8 4.11428571]
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