Article Categories
- All Categories
-
Data Structure
-
Networking
-
RDBMS
-
Operating System
-
Java
-
MS Excel
-
iOS
-
HTML
-
CSS
-
Android
-
Python
-
C Programming
-
C++
-
C#
-
MongoDB
-
MySQL
-
Javascript
-
PHP
-
Economics & Finance
Programming Articles
Page 195 of 2547
Evaluate a 2D Legendre series at points (x, y) with 3D array of coefficient in Python
To evaluate a 2D Legendre series at points (x, y) with a 3D coefficient array, use the numpy.polynomial.legendre.legval2d() method. This method computes the values of a two-dimensional Legendre series at specified coordinate pairs. Syntax The basic syntax is ? numpy.polynomial.legendre.legval2d(x, y, c) Parameters The function accepts the following parameters ? x, y ? Coordinate arrays where the series is evaluated. Must have the same shape. c ? Array of coefficients where c[i, j] contains the coefficient for the term of multi-degree (i, j). For 3D arrays, additional indices enumerate multiple coefficient ...
Read MoreEvaluate a 2D Legendre series at points (x, y) in Python
To evaluate a 2D Legendre series at points (x, y), use the polynomial.legendre.legval2d() method in NumPy. The method returns the values of the two dimensional Legendre series at points formed from pairs of corresponding values from x and y. Syntax numpy.polynomial.legendre.legval2d(x, y, c) Parameters The function accepts the following parameters: x, y − The two dimensional series is evaluated at the points (x, y), where x and y must have the same shape. If x or y is a list or tuple, it is first converted to an ndarray, otherwise it is ...
Read MoreEvaluate a Legendre series at list of points x in Python
To evaluate a Legendre series at specific points, use the polynomial.legendre.legval() method in NumPy. This function allows you to compute Legendre polynomial values efficiently at single points or arrays of points. Syntax numpy.polynomial.legendre.legval(x, c, tensor=True) Parameters x: Points at which to evaluate the Legendre series. Can be a scalar, list, or array. c: Array of coefficients where c[n] contains the coefficient for the degree-n term. tensor: If True (default), evaluates every coefficient column for every element of x. If False, broadcasts x over coefficient columns. Example Let's evaluate a Legendre ...
Read MoreEvaluate a 3D Legendre series on the Cartesian product of x, y and z with 4d array of coefficient in Python
To evaluate a 3D Legendre series on the Cartesian product of x, y and z, use the polynomial.legendre.leggrid3d() method in Python NumPy. This method evaluates a three-dimensional Legendre series at points in the Cartesian product of x, y, and z coordinates. Syntax numpy.polynomial.legendre.leggrid3d(x, y, z, c) Parameters x, y, z: The coordinates where the series is evaluated. The three-dimensional series is evaluated at points in the Cartesian product of x, y and z. If any parameter is a list or tuple, it is converted to an ndarray. c: Array of coefficients ordered so ...
Read MoreEvaluate a 3D Legendre series on the Cartesian product of x, y and z in Python
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 Legendre series at points in the Cartesian product of x, y, and z coordinates. Syntax numpy.polynomial.legendre.leggrid3d(x, y, z, c) Parameters x, y, z: The three-dimensional series is evaluated at the points in the Cartesian product of x, y and z. If x, y, or z is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and, if ...
Read MoreIntegrate a Hermite_e series in Python
The Hermite_e series integration can be performed using NumPy's hermite_e.hermeint() method. This method integrates a Hermite_e polynomial series and returns the coefficients of the integrated series. Syntax The hermite_e.hermeint() method accepts several parameters ? numpy.polynomial.hermite_e.hermeint(c, m=1, k=[], lbnd=0, scl=1, axis=0) Parameters c ? Array of Hermite_e series coefficients m ? Order of integration (default: 1) k ? Integration constants (default: []) lbnd ? Lower bound of integral (default: 0) scl ? Scalar multiplier (default: 1) axis ? Axis over which integration is performed (default: 0) Basic Integration Example Let's ...
Read MoreDifferentiate a Hermite_e series, set the derivatives and multiply each differentiation by a scalar in Python
To differentiate a Hermite_e series, use the hermite_e.hermeder() method in Python. This function allows you to compute derivatives and apply scalar multiplication to each differentiation step. Syntax numpy.polynomial.hermite_e.hermeder(c, m=1, scl=1, axis=0) Parameters The function accepts the following parameters ? c ? Array of Hermite_e series coefficients. For multidimensional arrays, different axes correspond to different variables m ? Number of derivatives to take (must be non-negative, default: 1) scl ? Scalar multiplier for each differentiation. Final result is multiplied by scl**m (default: 1) axis ? Axis over which the derivative is taken (default: ...
Read MoreGenerate a Pseudo Vandermonde matrix of the Hermite_e polynomial with float array of points coordinates in Python
To generate a pseudo Vandermonde matrix of the Hermite_e polynomial, use the hermite_e.hermevander2d() function in NumPy. This method returns a pseudo-Vandermonde matrix where each row corresponds to a point coordinate and each column represents polynomial basis functions up to specified degrees. Syntax numpy.polynomial.hermite_e.hermevander2d(x, y, deg) Parameters The function accepts the following parameters: x, y: Arrays of point coordinates with the same shape. Data types are converted to float64 or complex128 automatically. deg: List specifying maximum degrees as [x_deg, y_deg]. Complete Example Let's create a complete example demonstrating the generation ...
Read MoreGenerate a Pseudo Vandermonde matrix of the Hermite_e polynomial in Python
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 and y 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]. Syntax numpy.polynomial.hermite_e.hermevander2d(x, y, deg) Parameters The parameters for the hermevander2d() function are ? x, y ? ...
Read MoreConvert a Legendre series to a polynomial in Python
In Python, you can convert a Legendre series to a polynomial using NumPy's polynomial.legendre.leg2poly() method. This function transforms Legendre series coefficients into standard polynomial coefficients. Syntax numpy.polynomial.legendre.leg2poly(c) Parameters: c: 1-D array containing Legendre series coefficients, ordered from lowest to highest degree Returns: 1-D array of equivalent polynomial coefficients ordered from lowest to highest degree. Example Let's convert a Legendre series with coefficients [1, 2, 3, 4, 5] to its polynomial form ? import numpy as np from numpy.polynomial import legendre as L # Create Legendre series coefficients ...
Read More