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 202 of 2547
Generate a Pseudo Vandermonde matrix of the Hermite polynomial in Python
To generate a pseudo Vandermonde matrix of the Hermite polynomial, use the hermite.hermvander2d() method in Python NumPy. This method returns a 2D pseudo-Vandermonde matrix where each row corresponds to a point and each column represents a basis function. The parameter x, 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 a list of maximum degrees of the form [x_deg, y_deg]. Syntax numpy.polynomial.hermite.hermvander2d(x, y, deg) ...
Read MoreGenerate a Vandermonde matrix of the Hermite polynomial with complex array of points in Python
To generate a Vandermonde matrix of the Hermite polynomial with complex array points, use the hermite.hermvander() function in Python NumPy. This method returns the pseudo-Vandermonde matrix where each row corresponds to an evaluation point and each column represents a different degree of the Hermite polynomial. The returned matrix has shape x.shape + (deg + 1, ), where the last index corresponds to the degree of the Hermite polynomial. The dtype will match the converted input array. Parameters x − Array of points. Converts to float64 or complex128 depending on whether elements are complex. Scalar inputs are ...
Read MoreIntegrate a Hermite series over axis 1 in Python
To integrate a Hermite series over a specific axis, use the hermite.hermint() method in Python. This function integrates Hermite series coefficients along the specified axis, which is useful for multidimensional polynomial operations. Parameters The hermite.hermint() method accepts the following parameters: c: Array of Hermite series coefficients. For multidimensional arrays, different axes correspond to different variables m: Order of integration (must be positive, default: 1) k: Integration constant(s) (default: []) lbnd: Lower bound of the integral (default: 0) scl: Scalar multiplier applied after each integration (default: 1) axis: Axis over which the integral is taken ...
Read MoreIntegrate a Hermite series over specific axis in Python
To integrate a Hermite series, use the hermite.hermint() method in Python. This method integrates Hermite series coefficients over a specified axis, making it useful for polynomial integration in scientific computing. Syntax numpy.polynomial.hermite.hermint(c, m=1, k=[], lbnd=0, scl=1, axis=0) Parameters Parameter Description Default c Array of Hermite series coefficients Required m Order of integration (must be positive) 1 k Integration constant(s) [] (zero) lbnd Lower bound of the integral 0 scl Scalar multiplier after each integration 1 axis Axis over which integration ...
Read MoreEvaluate a 3-D Laguerre series on the Cartesian product of x, y and z with 4d array of coefficient in Python
To evaluate a 3-D Laguerre series on the Cartesian product of x, y and z, use the polynomial.laguerre.laggrid3d() method in Python. The method returns the values of the three-dimensional Laguerre series at points in the Cartesian product of x, y and z. If the coefficient array c has fewer than three 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 + y.shape + z.shape. Syntax numpy.polynomial.laguerre.laggrid3d(x, y, z, c) Parameters x, y, z − The three-dimensional series is evaluated at ...
Read MoreEvaluate a 3-D Laguerre series on the Cartesian product of x, y and z in Python
To evaluate a 3-D Laguerre series on the Cartesian product of x, y and z, use the polynomial.laguerre.laggrid3d() method in Python. The method returns the values of the three-dimensional Laguerre series at points in the Cartesian product of x, y and z. Syntax numpy.polynomial.laguerre.laggrid3d(x, y, z, c) Parameters The function takes the following parameters: x, y, z: Arrays of coordinates where the series is evaluated. If a list or tuple, it's converted to ndarray. Scalars are treated as 0-D arrays. c: Array of coefficients ordered so that coefficients for terms of degree ...
Read MoreGenerate a Hermite series with given complex roots in Python
To generate a Hermite series with given complex roots, use the hermite.hermfromroots() method in Python NumPy. The method returns a 1-D array of coefficients. If all roots are real then out is a real array, if some of the roots are complex, then out is complex even if all the coefficients in the result are real. Syntax numpy.polynomial.hermite.hermfromroots(roots) Parameters roots − A sequence containing the roots of the Hermite polynomial. Example with Complex Roots Let's create a Hermite series with complex roots using imaginary unit j ? from numpy.polynomial import ...
Read MoreGenerate a Vandermonde matrix of the Laguerre polynomial with complex array of points in Python
To generate a pseudo Vandermonde matrix of the Laguerre polynomial with complex points, use the laguerre.lagvander() function from NumPy. This function returns a matrix where each row contains the evaluated Laguerre polynomials of different degrees at a specific point. Syntax numpy.polynomial.laguerre.lagvander(x, deg) Parameters The function accepts the following parameters − x − Array of points. The dtype is converted to float64 or complex128 depending on whether any elements are complex deg − Degree of the resulting matrix Return Value Returns a pseudo-Vandermonde matrix with shape x.shape + (deg + ...
Read MoreEvaluate a 2-D Hermite series at points (x,y) with 3D array of coefficient in Python
To evaluate a 2D Hermite series at points (x, y), use the hermite.hermval2d() method in NumPy. This method returns the values of the two-dimensional polynomial at points formed with pairs of corresponding values from x and y. The first parameter consists of x and y coordinates. 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 left unchanged and if it isn't an ndarray it is treated as a scalar. ...
Read MoreIntegrate a Hermite series and set the Integration constant in Python
To integrate a Hermite series, use the hermite.hermint() method in Python. This method integrates a Hermite series and allows you to set integration constants. Syntax numpy.polynomial.hermite.hermint(c, m=1, k=[], lbnd=0, scl=1, axis=0) Parameters The method accepts the following parameters − c − Array of Hermite series coefficients. For multidimensional arrays, different axes correspond to different variables m − Order of integration (must be positive, default: 1) k − Integration constant(s). If empty list (default), all constants are zero. For m=1, can be a scalar lbnd − Lower bound of the integral (default: 0) ...
Read More