Differentiate a Chebyshev series, set the derivatives and multiply each differentiation by a scalar in Python

To differentiate a Chebyshev series, use the polynomial.chebder() method in Python Numpy. The method returns the Chebyshev series of the derivative. Returns the Chebyshev 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*T_0 + 2*T_1 + 3*T_2 while [[1,2],[1,2]] represents 1*T_0(x)*T_0(y) + 1*T_1(x)*T_0(y) + 2*T_0(x)*T_1(y) + 2*T_1(x)*T_1(y) if axis=0 is x and axis=1 is y.

The 1st parameter is c, an array of Chebyshev 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 is m, Number of derivatives taken, must be non-negative. (Default: 1). The 3rd parameter is scl, i.e. 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 is axis i.e. an axis over which the derivative is taken. (Default: 0).

Steps

At first, import the required libraries −

import numpy as np
from numpy.polynomial import chebyshev as C

Create an array of Chebyshev series coefficients −

c = np.array([1,2,3,4])

Display the coefficient array −

print("Our coefficient 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 Chebyshev series, use the polynomial.chebder() method in Python Numpy. The method returns the Chebyshev series of the derivative −

print("\nResult...\n",C.chebder(c, 2, scl = -1))

Example

import numpy as np
from numpy.polynomial import chebyshev as C

# Create an array of Chebyshev series coefficients
c = np.array([1,2,3,4])

# Display the coefficient array
print("Our coefficient 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 Chebyshev series, use the polynomial.chebder() method in Python Numpy.
print("\nResult...\n",C.chebder(c, 2, scl = -1))

Output

Our coefficient Array...
[1 2 3 4]

Dimensions of our Array...
1

Datatype of our Array object...
int64

Shape of our Array object...
(4,)

Result...
[12. 96.]