To generate a Legendre series, use the polynomial.legendre.legfromroots() method in Python. The method returns a 1-D array of coefficients. If all roots are real then out is a real array, if some of the roots are complex, then out is complex even if all the coefficients in the result are real. The parameter roots are the sequence containing the roots.StepsAt first, import the required library −import numpy as np from numpy.polynomial import legendre as LTo generate a Legendre series, use the polynomial.legendre.legfromroots() method in Python −print("Result...", L.legfromroots((-1, 0, 1)))Get the datatype −print("Type...", L.legfromroots((-1, 0, 1)).dtype)Get the shape −print("Shape...", L.legfromroots((-1, 0, ... Read More

The pandas series constructor has an apply() which accepts any user-defined function that applies to the values of the given series object.In the same way, we can apply an anonymous function over a pandas series object. We can use this apply() method on both the pandas data structures DataFrame and Series. It Performs element-wise transformations and returns a new series object as a result.Example 1# import pandas package import pandas as pd import numpy as np # create a pandas series s = pd.Series(np.random.randint(10, 20, 5)) print(s) # Applying an anonymous function result = s.apply(lambda x: x**2) print('Output ... Read More

To integrate a Legendre series, use the polynomial.legendre.legint() method in Python. The method returns the Legendre series coefficients c integrated m times from lbnd along axis. At each iteration the resulting series is multiplied by scl and an integration constant, k, is added. The scaling factor is for use in a linear change of variable.The 1st parameter, c is an array of Legendre 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 an order of integration, must be positive. (Default: ... Read More

To generate a pseudo Vandermonde matrix of the Legendre polynomial, use the polynomial.legvander() method in Python Numpy. The method returns the pseudo-Vandermonde matrix. The shape of the returned matrix is x.shape + (deg + 1, ), where The last index is the degree of the corresponding Legendre polynomial. The dtype will be the same as the converted x.The parameter, x returns an Array of points. The dtype is converted to float64 or complex128 depending on whether any of the elements are complex. If x is scalar it is converted to a 1-D array. The parameter, deg is the degree of ... Read More

To generate a pseudo Vandermonde matrix of the Legendre polynomial, use the polynomial.legvander() method in Python NumpyThe method returns the pseudo-Vandermonde matrix. The shape of the returned matrix is x.shape + (deg + 1, ), where The last index is the degree of the corresponding Legendre polynomial. The dtype will be the same as the converted x.The parameter, x returns an Array of points. The dtype is converted to float64 or complex128 depending on whether any of the elements are complex. If x is scalar it is converted to a 1-D array. The parameter, deg is the degree of the ... Read More

The apply() method in pandas Series is used to call our function on a series object. By using this apply() method we can apply our own function on our series object.The apply() method is very similar to some other pandas series methods like agg() and map(). Here the difference is we can apply a function on values of the given series object.Example 1# import pandas package import pandas as pd # create a pandas series s = pd.Series([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) print(s) # Applying a function result = s.apply(type) print('Output of apply ... Read More

To compute the roots of a Legendre series, use the polynomial.legendre.lagroots() method in Python. The method returns an array of the roots of the series. If all the roots are real, then out is also real, otherwise it is complex. The parameter c is a 1-D array of coefficients.StepsAt first, import the required library −from numpy.polynomial import legendre as LCompute the roots of a Legendre series −j = complex(0, 1) print("Result...", L.legroots((-j, j)))Get the datatype −print("Type...", L.legroots((-j, j)).dtype)Get the shape −print("Shape...", L.legroots((-j, j)).shape)Examplefrom numpy.polynomial import legendre as L # To compute the roots of a Legendre series, use the ... Read More

The basic operation of pandas.Series.append() method is used to concatenate a series with another series. And it will return a new series with resultant elements.This append() method has some parameters like to_append, ignore_index, and verify_integrity to concatenate two pandas series objects.Example 1# import the required packages import pandas as pd import numpy as np series1 = pd.Series(np.random.randint(1, 100, 5)) print(series1) series2 = pd.Series(np.random.randint(1, 100, 4)) print(series2) # apply append method on series result = series1.append(series2) print("Resultant series: ", result)ExplanationIn the following example, we have appended a pandas series object “series1” with another series object “series2”. we ... Read More

To compute the roots of a Legendre series, use the polynomial.legendre.legroots() method in Python. The method returns an array of the roots of the series. If all the roots are real, then out is also real, otherwise it is complex. The parameter c is a 1-D array of coefficients.StepsAt first, import the required library −from numpy.polynomial import legendre as LTo compute the roots of a Legendre series, use the polynomial.legendre.legroots() method in Python −print("Result...", L.legroots((0, 1, 2)))Get the datatype −print("Type...", L.legroots((0, 1, 2)).dtype)Get the shape −print("Shape...", L.legroots((0, 1, 2)).shape) Examplefrom numpy.polynomial import legendre as L # To compute the ... Read More

To generate a Legendre series, use the polynomial.legendre.legfromroots() method in Python. The method returns a 1-D array of coefficients. If all roots are real then out is a real array, if some of the roots are complex, then out is complex even if all the coefficients in the result are real. The parameter roots are the sequence containing the roots.StepsAt first, import the required library −from numpy.polynomial import legendre as LGenerate a Legendre series using the polynomial.legendre.legfromroots() method in Python −j = complex(0, 1) print("Result...", L.legfromroots((-j, j)))Get the datatype −print("Type...", L.legfromroots((-j, j)).dtype)Get the shape −print("Shape...", L.legfromroots((-j, j)).shape)Examplefrom numpy.polynomial import legendre ... Read More