To evaluate a 3D Legendre series on the Cartesian product of x, y and z use the polynomial.legendre.leggrid3d() method in Python Numpy. The method returns the values of the three dimensional Chebyshev series at points in the Cartesian product of x, and z. If c has fewer than three dimensions, ones are implicitly appended to its shape to make it 3-D. The shape of the result will be c.shape[3:] + x.shape + y.shape + z.shape.The 1st parameter is x, y, z. The three dimensional series is evaluated at the points in the Cartesian product of x, y and z. If ... Read More

The pandas Series.factorize() method is used to encode the series object as an enumerated type or categorical variable. This method generates the numeric representation of the series data.The output of this Series.factorize() method is a tuple and it has two elements one is indicating codes and another element indicates uniques.Example 1In the following example, we will see how the series.factorize() method encodes the elements of the series object.# importing pandas package import pandas as pd # create a series s = pd.Series({'A':"aa", 'B':"bb", "C":"cc"}) print(s) result = s.factorize() print(result)ExplanationHere the series object is created by using a python ... Read More

To evaluate a 3D Legendre series on the Cartesian product of x, y and z use the polynomial.legendre.leggrid3d() method in Python Numpy. The method returns the values of the three dimensional Chebyshev series at points in the Cartesian product of x, and z. If c has fewer than three dimensions, ones are implicitly appended to its shape to make it 3-D. The shape of the result will be c.shape[3:] + x.shape + y.shape + z.shape.The 1st parameter is x, y, z. The three dimensional series is evaluated at the points in the Cartesian product of x, y and z. If ... Read More

To integrate a Hermite_e series, use the hermite_e.hermeint() method in Python. The 1st parameter, c is an array of Hermite_e 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: 1).The 3rd parameter, k is an integration constant(s). The value of the first integral at lbnd is the first value in the list, the value of the second integral at lbnd is the second value, etc. If k == [] (the default), all ... Read More

If some of the elements in the series object have lists, then we can unnest those list elements into multiple rows of the series object. Unnesting is nothing but exploding the lists into rows.So this transformation can be done easily with the help of the pandas series.explode() method. This method is used to transform list-like elements of a series object into rows, and the index will be duplicated for these rows.The ignore_index is the only parameter for this method and it takes boolean values, False is the default one, and True means the resulting index will be labeled from 0 ... Read More

To differentiate a Hermite_e series, use the hermite_e.hermeder() method in Python. The 1st parameter, c is an array of Hermite_e 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 ... Read More

It is very common to have missing values in a series object, and if you want to compare that type of series objects then the ordinary comparison does not work because nan != nan, In that case, we can use the equals() method. The equals() method considers Nan’s in the same location to be equal.The fundamental operation of the pandas series.equals() method is used to compare two series for equality. it returns True if the two series have the same elements and shape, and returns False if the two series are unequal.Example 1In the following example, two series objects series1 ... Read More

To generate a pseudo Vandermonde matrix of the Hermite polynomial, use the hermite_e.hermevander2d() in Python Numpy. The method returns the pseudo-Vandermonde matrix. The parameter, x, y are an array of point coordinates, all of the same shape. The dtypes will be converted to either float64 or complex128 depending on whether any of the elements are complex. Scalars are converted to 1-D arrays. The parameter, deg is the list of maximum degrees of the form [x_deg, y_deg].StepsAt first, import the required library −import numpy as np from numpy.polynomial import hermite as HCreate arrays of point coordinates, all of the same shape ... Read More

The basic operation of the series.equals() method in the pandas constructor is used to test whether the elements in two series objects are the same or not, and it also compares the shape of the two series object.The equals() method is very similar to the pandas series.eq() method but the difference is it will return a boolean value as a result, whereas the eq() method returns a series object with boolean values.The output boolean value True indicates the elements in two series objects are the same. And it indicates False for unequal elements in series objects.Example 1In the following example, ... Read More

To generate a pseudo Vandermonde matrix of the Hermite_e polynomial, use the hermite_e.hermevander2d() in Python Numpy. The method returns the pseudo-Vandermonde matrix. The parameter, x, y are an array of point coordinates, all of the same shape. The dtypes will be converted to either float64 or complex128 depending on whether any of the elements are complex. Scalars are converted to 1-D arrays. The parameter, deg is the list of maximum degrees of the form [x_deg, y_deg].StepsAt first, import the required library −import numpy as np from numpy.polynomial import hermite as HCreate arrays of point coordinates, all of the same shape ... Read More