To multiply the Hermite_e series by x, where x is the independent variable, use the polynomial.hermite.hermemulx() method in Python Numpy. The method returns an array representing the result of the multiplication. The parameter, c is a 1-D array of Hermite_e series coefficients ordered from low to high.StepsAt first, import the required library −import numpy as np from numpy.polynomial import hermite_e as HCreate an array −c = np.array([1, 2, 3])Display the array −print("Our Array...", c)Check the Dimensions −print("Dimensions of our Array...", c.ndim)Get the Datatype −print("Datatype of our Array object...", c.dtype)Get the Shape −print("Shape of our Array object...", c.shape)To multiply the Hermite_e ... Read More

To subtract one Hermite_e series to another, use the polynomial.hermite.hermesub() method in Python Numpy. The method returns an array representing the Hermite_e series of their difference. Returns the difference of two Hermite_e series c1 - c2. The sequences of coefficients are from lowest order term to highest, i.e., [1, 2, 3] represents the series P_0 + 2*P_1 + 3*P_2. The parameters c1 and c2 are 1-D arrays of Hermite_e series coefficients ordered from low to high.StepsAt first, import the required library −import numpy as np from numpy.polynomial import hermite_e as HCreate 1-D arrays of Hermite_e series coefficients −c1 = np.array([1, ... Read More

To add one Hermite_e series to another, use the polynomial.hermite.heremadd() method in Python Numpy. The method returns an array representing the Hermite_e series of their sum. Returns the sum of two Hermite_e series c1 + c2. The arguments are sequences of coefficients ordered from lowest order term to highest, i.e., [1, 2, 3] represents the series P_0 + 2*P_1 + 3*P_2. The parameters c1 and c2 are 1-D arrays of Hermite_e series coefficients ordered from low to high.StepsAt first, import the required library −import numpy as np from numpy.polynomial import hermite_e as HCreate 1-D arrays of Hermite_e series coefficients −c1 ... Read More

To convert a polynomial to a Legendre series, use the legendre.poly2lag() method in Python Numpy. Convert an array representing the coefficients of a polynomial ordered from lowest degree to highest, to an array of the coefficients of the equivalent Legendre series, ordered from lowest to highest degree. The method returns a 1-D array containing the coefficients of the equivalent Legendre series. The parameter pol, is a 1-D array containing the polynomial coefficientsStepsAt first, import the required library −import numpy as np from numpy.polynomial import legendre as LCreate an array using the numpy.array() method −c = np.array([1, 2, 3, 4, 5])Display ... Read More

Freedom of Information − Freedom of Information (FOI) is a concept that broadly define the principle that individuals and the public at-large have the right to access information that is relevant to their interests.The United Nations identifies freedom of information as a basic human right. The UN argues that FOI provides that governments can be held accountable by providing institutional transparency, and as such, it is essential for the maintenance of the Rule of Law inside a jurisdiction.Freedom of information define a citizen's right to access information that is influence by the state. In some countries, this freedom is provided ... Read More

To generate a pseudo Vandermonde matrix of the Legendre polynomial with x, y, z sample points, use the legendre.legvander3d() method in Python Numpy. Returns the pseudo-Vandermonde matrix of degrees deg and sample points (x, y, z).The parameters, 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 a list of maximum degrees of the form [x_deg, y_deg, z_deg].StepsAt first, import the required library −import numpy as np from ... 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 is ... Read More

To evaluate a 2D Legendre series on the Cartesian product of x and y, use the polynomial.legendre.leggrid2d() method in Python Numpy. The method returns the values of the two dimensional Chebyshev series at points in the Cartesian product of x and y. If c has fewer than two dimensions, ones are implicitly appended to its shape to make it 2-D. The shape of the result will be c.shape[2:] + x.shape + y.shape.The 1st parameter is x, y. The two dimensional series is evaluated at the points in the Cartesian product of x and y. If x or y is a ... Read More

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