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To evaluate a 3D Legendre series at points x, y, z use the polynomial.legendre.legval3d() method in Python Numpy. The method returns the values of the multidimensional polynomial on points formed with triples of corresponding values from x, y, and z.If c has fewer than 3 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. The 1st parameter is x, y, z. The three dimensional series is evaluated at the points (x, y, z), where x, y, and z must have the same shape. If any of x, ... Read More
To generate a pseudo Vandermonde matrix of the Hermite_e polynomial and x, y, z sample points, use the hermite_e.hermevander3d() in Python Numpy. The method returns the pseudoVandermonde matrix. The parameter, x, y, z are arrays 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, z_deg].StepsAt first, import the required library −import numpy as np from numpy.polynomial import hermite_e as HCreate arrays of ... Read More
To generate a pseudo Vandermonde matrix of the Legendre polynomial, use the legendre.legvander2d() 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, y is 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 ... Read More
In the pandas series constructor, there is a method called argmax() which is used to get the position of maximum value over the series data.The pandas series is a single-dimensional data structure object with row index values. By using row index values we can access the data.The argmax() method in the pandas series is used to get the positional index of the maximum value of the series object. The output of the argmax method is an integer value, which refers to the position where the largest value exists.Example 1# import pandas package import pandas as pd import numpy as np ... Read More
The pandas.Series constructor have an attribute called is_unique. which is used to check whether the data present in the pandas series object is unique or not. As we know, the pandas series object is a single-dimensional data structure, which stores any type of data with label representation.By using the “is_unque” attribute we can check if all data present in the series object holds unique values or not. And it returns a boolean value as an output.It returns “True” if the data present in the given series object is unique, otherwise, it will return “False”.Example 1import pandas as pd # ... Read More
To generate a pseudo Vandermonde matrix of the Legendre polynomial, use the legendre.legvander2d() 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, y is 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 ... 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 check if the data present in the series is monotonically decreasing or not, we can use the is_monotonic_decreasing property of the pandas Series constructor.The monotonically decreasing data is nothing but continuously decreasing values. And the attribute “is_monotonic_decreasing” is used to verify that the data in a given series object is always decreasing or not. And this attribute returns a boolean value as an output.Example 1import pandas as pd # create a series s = pd.Series([100, 57, 23, 10, 5]) print(s) print("Is monotonically decreasing: ", s.is_monotonic_decreasing)ExplanationHere, we initialized a Series with a python list of integer values ... Read More
To evaluate a Hermite_e series at points x, use the hermite.hermeval() method in Python Numpy. The 1st parameter, x, if x is a list or tuple, it is converted to an ndarray, otherwise it is left unchanged and treated as a scalar. In either case, x or its elements must support addition and multiplication with themselves and with the elements of c.The 2nd parameter, C, an array of coefficients ordered so that the coefficients for terms of degree n are contained in c[n]. If c is multidimensional the remaining indices enumerate multiple polynomials. In the two dimensional case the coefficients ... Read More
To evaluate a Hermite_e series at points x, use the hermite.hermeval() method in Python Numpy. The 1st parameter, x, if x is a list or tuple, it is converted to an ndarray, otherwise it is left unchanged and treated as a scalar. In either case, x or its elements must support addition and multiplication with themselves and with the elements of c.The 2nd parameter, C, an array of coefficients ordered so that the coefficients for terms of degree n are contained in c[n]. If c is multidimensional the remaining indices enumerate multiple polynomials. In the two dimensional case the coefficients ... Read More