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 pseudo- Vandermonde 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 ... Read More

To integrate a Hermite_e series, use the hermite.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

The strings package of Golang has a Replace() function which we can use to replace some characters in a string with a new value. It replaces only a specified "n" occurrences of the substring.In addition to Replace(), there is a ReplaceAll() function that replaces all the occurrences of a given substring with a new value.Syntaxfunc Replace(s, old, new string, n int) stringWhere, s is the given stringold is the string which we want to replacenew is the string which will replace the old stringn represents the number of characters which we want to replace in the given string.ExampleThe following example demonstrates ... 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

To remove small trailing coefficients from Legendre polynomial, use the legendre.legtrim() method in Python numpy. The method returns a 1-d array with trailing zeros removed. If the resulting series would be empty, a series containing a single zero is returned.The “Small” means “small in absolute value” and is controlled by the parameter tol; “trailing” means highest order coefficient(s), e.g., in [0, 1, 1, 0, 0] (which represents 0 + x + x**2 + 0*x**3 + 0*x**4) both the 3-rd and 4-th order coefficients would be “trimmed”. The parameter c is a 1-d array of coefficients, ordered from lowest order to ... Read More

The strings package of Golang provides a Fields() method, which can be used to split a string around one or more instances of consecutive whitespace characters.The Fields() function splits a given string into substrings by removing any space characters, including newlines. And it treats multiple consecutive spaces as a single space.Syntaxfunc Fields(s string) []stringWhere s is the string parameter.ExampleLet us consider the following example −package main import (    "fmt"    "strings" ) func main() {    // Initializing the Strings    string1 := " The Golang Programming Language "    // Display the Strings    fmt.Println("Input String:", string1) ... Read More

The EqualFold() function in Golang is an inbuilt function of strings package which is used to check whether the given strings (UTF-8 strings) are equal. The comparison is not case-sensitive. It accepts two string parameters and returns True if both the strings are equal under Unicode case-folding (i.e., case-insensitive), False otherwise.Syntaxfunc EqualFold(s, t string) boolWhere s and t are strings. It returns a Boolean value.ExampleThe following example demonstrates how to use EqualFold() in a Go program −package main import (    "fmt"    "strings" ) func main() {    // Intializing the Strings    R := "Welcome to Tutorialspoint" ... Read More

To get the Least squares fit of Legendre series to data, use the legendre.legfit() method in Python numpy. The method returns the Legendre coefficients ordered from low to high. If y was 2-D, the coefficients for the data in column k of y are in column k.The parameter, x are the x-coordinates of the M sample (data) points (x[i], y[i]). The parameter, y are the y-coordinates of the sample points. Several sets of sample points sharing the same xcoordinates can be (independently) fit with one call to polyfit by passing in for y a 2-D array that contains one data ... Read More

To return the scaled companion matrix of a 1-D array of Legendre polynomial coefficients, use the legendre.legcompanion() method in Python Numpy. The usual companion matrix of the Legendre polynomials is already symmetric when c is a basis Laguerre polynomial, so no scaling is applied.Returns the scaled Companion matrix of dimensions (deg, deg). The parameter, c is a 1-D array of Legendre series coefficients ordered from low to high degree.StepsAt first, import the required library −import numpy as np from numpy.polynomial import legendre as LCreate a 1D array of coefficients −c = np.array([1, 2, 3, 4, 5])Display the array −print("Our Array...", ... 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