Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Economics & Finance
To compute the roots of a Hermite series, use the hermite.hermroots() method in Python NumPy. The method returns an array of the roots of the series. If all the roots are real, then the output is also real, otherwise it is complex. The parameter c is a 1-D array of coefficients. The root estimates are obtained as the eigenvalues of the companion matrix. Roots far from the origin of the complex plane may have large errors due to the numerical instability of the series for such values. Roots with multiplicity greater than 1 will also show larger errors as ... Read More
To evaluate a Laguerre series at multi-dimensional array of points x, use the polynomial.laguerre.lagval() method in Python NumPy. This function allows you to evaluate Laguerre polynomials efficiently across multiple dimensions. Function Parameters The lagval() function accepts three parameters: x: The evaluation points. If x is a list or tuple, it is converted to an ndarray. The elements must support addition and multiplication operations. c: Array of coefficients where c[n] contains coefficients for terms of degree n. For multidimensional arrays, remaining indices enumerate multiple polynomials. tensor: Boolean parameter (default True). When True, evaluates every column of coefficients ... Read More
To evaluate a Laguerre series at array of points x, use the polynomial.laguerre.lagval() method in Python NumPy. This method evaluates a Laguerre polynomial series at given points using the coefficients and evaluation points you provide. Syntax The lagval() method has the following syntax: numpy.polynomial.laguerre.lagval(x, c, tensor=True) Parameters x − Array of points at which to evaluate the polynomial. If x is a list or tuple, it is converted to an ndarray. Elements must support addition and multiplication with coefficient elements. c − Array of coefficients ordered so that coefficients for terms of ... Read More
To evaluate a Laguerre series at points x, use the polynomial.laguerre.lagval() method in Python NumPy. This function broadcasts evaluation points over coefficient columns when tensor=False. Syntax numpy.polynomial.laguerre.lagval(x, c, tensor=True) Parameters The function accepts three parameters ? x − Array of points at which to evaluate the series. Can be scalar, list, or array c − Array of coefficients ordered so that coefficients for degree n are in c[n]. For multidimensional arrays, remaining indices enumerate multiple polynomials tensor − If True (default), extends coefficient shape. If False, broadcasts x over coefficient columns ... Read More
To integrate a Laguerre series, use the laguerre.lagint() method in Python. The method returns the Laguerre 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. Syntax numpy.polynomial.laguerre.lagint(c, m=1, k=[], lbnd=0, scl=1, axis=0) Parameters c − Array of Laguerre series coefficients. If c is multidimensional, different axes correspond to different variables m − Order of integration, must be positive (Default: 1) k − Integration ... Read More
The Laguerre polynomial integration in Python can be performed using NumPy's laguerre.lagint() method. This function integrates Laguerre series coefficients along a specified axis, allowing for flexible multi-dimensional operations. Syntax numpy.polynomial.laguerre.lagint(c, m=1, k=[], lbnd=0, scl=1, axis=0) Parameters The function accepts the following parameters: c − Array of Laguerre series coefficients m − Order of integration (default: 1) k − Integration constant(s) (default: []) lbnd − Lower bound of integral (default: 0) scl − Scaling factor (default: 1) axis − Axis over which integration is performed (default: 0) Basic Integration Example ... Read More
To generate a Vandermonde matrix of the Laguerre polynomial, use the laguerre.lagvander() method in NumPy. This function returns a pseudo-Vandermonde matrix where each row contains the Laguerre polynomial values evaluated at a specific point. The Laguerre polynomials are orthogonal polynomials used in mathematical analysis and physics. The Vandermonde matrix has shape x.shape + (deg + 1, ), where the last index corresponds to the polynomial degree. Syntax numpy.polynomial.laguerre.lagvander(x, deg) Parameters x: Array of points. Converted to float64 or complex128 depending on element types. Scalar values are converted to 1-D arrays. deg: Degree ... Read More
To generate a pseudo Vandermonde matrix of the Laguerre polynomial, use the laguerre.lagvander() function in Python NumPy. The method returns the pseudo-Vandermonde matrix with shape x.shape + (deg + 1, ), where the last index corresponds to the degree of the Laguerre polynomial. The dtype will match the converted x array. The parameter x is an array of points, converted to float64 or complex128 depending on whether elements are complex. If x is scalar, it converts to a 1-D array. The parameter deg specifies the degree of the resulting matrix. Syntax numpy.polynomial.laguerre.lagvander(x, deg) Parameters ... Read More
To compute the roots of a Laguerre series, use the laguerre.lagroots() method in Python NumPy. The method returns an array of the roots of the series. If all the roots are real, then output is also real, otherwise it is complex. The root estimates are obtained as the eigenvalues of the companion matrix. Roots far from the origin of the complex plane may have large errors due to the numerical instability of the series for such values. Roots with multiplicity greater than 1 will also show larger errors as the value of the series near such points is relatively ... Read More
To compute the roots of a Laguerre series, use the laguerre.lagroots() method in Python NumPy. The method returns an array of the roots of the series. If all the roots are real, then the output is also real, otherwise it is complex. The root estimates are obtained as the eigenvalues of the companion matrix. Roots far from the origin of the complex plane may have large errors due to the numerical instability of the series for such values. Roots with multiplicity greater than 1 will also show larger errors as the value of the series near such points is ... Read More