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Differentiate a Laguerre series in Python
To differentiate a Laguerre series, use the laguerre.lagder() method in Python. The method returns the Laguerre series coefficients c differentiated m times along axis. At each iteration the result is multiplied by scl. The argument c is an array of coefficients from low to high degree along each axis, e.g., [1,2,3] represents the series 1*L_0 + 2*L_1 + 3*L_2 while [[1,2],[1,2]] represents 1*L_0(x)*L_0(y) + 1*L_1(x)*L_0(y) + 2*L_0(x)*L_1(y) + 2*L_1(x)*L_1(y) if axis=0 is x and axis=1 is y.
The 1st parameter, c is an array of Laguerre series coefficients. If c is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index. The 2nd parameter, m is the number of derivatives taken, must be non-negative. (Default: 1)
The 3rd parameter, scl is a scalar. Each differentiation is multiplied by scl. The end result is multiplication by scl**m. This is for use in a linear change of variable. (Default: 1). The 4th parameter, axis is an Axis over which the derivative is taken. (Default: 0).
Steps
At first, import the required library −
import numpy as np from numpy.polynomial import laguerre as L
Create an array of coefficients −
c = np.array([1,2,3,4])
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 differentiate a Laguerre series, use the laguerre.lagder() method in Python −
print("\nResult...\n",L.lagder(c))Example
import numpy as np
from numpy.polynomial import laguerre as L
# Create an array of coefficients
c = np.array([1,2,3,4])
# 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 differentiate a Laguerre series, use the laguerre.lagder() method in Python
print("\nResult...\n",L.lagder(c))Output
Our Array... [1 2 3 4] Dimensions of our Array... 1 Datatype of our Array object... int64 Shape of our Array object... (4,) Result... [-9. -7. -4.]
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