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Page 189 of 2547
Evaluate a 3D Legendre series at points (x,y,z) with 2D array of coefficient in Python
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 the coefficient array c has fewer than 3 dimensions, ones are implicitly appended to its shape to make it 3D. The shape of the result will be c.shape[3:] + x.shape. Syntax numpy.polynomial.legendre.legval3d(x, y, z, c) Parameters x, y, z: The three dimensional series is evaluated at the points (x, y, z), where ...
Read MoreGenerate a Pseudo Vandermonde matrix of the Hermite_e polynomial and x, y, z floating array of points in Python
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]. Syntax numpy.polynomial.hermite_e.hermevander3d(x, y, z, deg) Parameters x, y, z: Arrays of ...
Read MoreGenerate a Pseudo Vandermonde matrix of the Legendre polynomial and x, y floating array of points in Python
To generate a pseudo Vandermonde matrix of the Legendre polynomial, use the legendre.legvander2d() method in Python NumPy. This method creates a 2D pseudo-Vandermonde matrix where each row corresponds to a point coordinate and columns represent different polynomial degrees. The pseudo-Vandermonde matrix evaluates Legendre polynomials at given points for all degree combinations up to specified maximum degrees. The returned matrix shape is x.shape + (deg[0] + 1) * (deg[1] + 1), where the last dimension contains polynomial evaluations. Syntax numpy.polynomial.legendre.legvander2d(x, y, deg) Parameters The function accepts the following parameters: x, y − ...
Read MoreGenerate a Pseudo Vandermonde matrix of the Legendre polynomial and x, y array of points in Python
To generate a pseudo Vandermonde matrix of the Legendre polynomial, use the legendre.legvander2d() method in NumPy. This method creates a 2D pseudo-Vandermonde matrix where each column represents evaluations of Legendre polynomial basis functions at given coordinate points. The method returns a matrix with shape x.shape + (deg + 1, ), where the last index corresponds to the degree of the Legendre polynomial. The parameters x and y are arrays of point coordinates with the same shape, and deg is a list specifying maximum degrees as [x_deg, y_deg]. Basic Example Let's create coordinate arrays and generate the pseudo ...
Read MoreGenerate a Vandermonde matrix of the Legendre polynomial with complex array of points in Python
To generate a pseudo Vandermonde matrix of the Legendre polynomial with complex points, use the polynomial.legvander() method in NumPy. This method returns a matrix where each row represents the evaluation of Legendre polynomials at a given point, with columns corresponding to different polynomial degrees. The returned matrix has shape x.shape + (deg + 1, ), where the last index represents the degree of the corresponding Legendre polynomial. The data type matches the input array after conversion to float64 or complex128. Syntax numpy.polynomial.legendre.legvander(x, deg) Parameters x − Array of points. Scalar values are ...
Read MoreEvaluate a Hermite_e series at points x and the shape of the coefficient array extended for each dimension of x in Python
To evaluate a Hermite_e series at points x, use the hermite_e.hermeval() method in Python NumPy. This function allows you to evaluate Hermite_e polynomials at specific points and control how the coefficient array is handled for different dimensions. Parameters The hermeval() method accepts three key 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 coefficients for terms of degree n are in c[n]. For multidimensional arrays, remaining indices enumerate multiple polynomials. tensor: Boolean parameter controlling ...
Read MoreEvaluate a Hermite_e series at points x when coefficients are multi-dimensional in Python
To evaluate a Hermite_e series at points x with multi-dimensional coefficients, use the hermite_e.hermeval() method in Python NumPy. This function allows you to evaluate multiple Hermite_e polynomials simultaneously when coefficients are stored in a multi-dimensional array. Parameters The hermeval() function takes three main parameters ? x − Evaluation points. Can be a scalar, list, or array. Must support addition and multiplication operations. c − Coefficient array where c[n] contains coefficients for degree n terms. For multi-dimensional arrays, additional dimensions represent multiple polynomials. tensor − Boolean flag (default True). When True, evaluates each column of coefficients for ...
Read MoreEvaluate a Hermite_e series at points x in Python
To evaluate a Hermite_e series at points x, use the hermite_e.hermeval() method in Python NumPy. This function computes the value of a Hermite_e polynomial series at specified points using the provided coefficients. Syntax numpy.polynomial.hermite_e.hermeval(x, c, tensor=True) Parameters The hermeval() function accepts the following parameters ? x: Array of points at which to evaluate the series. Can be a scalar, list, tuple, or ndarray c: Array of coefficients ordered so that coefficients for terms of degree n are in c[n] tensor: Boolean flag (default True) controlling how multidimensional coefficients are handled ...
Read MoreGenerate a Legendre series with given roots in Python
To generate a Legendre series with specified roots, use the polynomial.legendre.legfromroots() method in Python. This method returns a 1-D array of Legendre polynomial coefficients. If all roots are real, the output is a real array. If some roots are complex, the output is complex even if all resulting coefficients are real. Syntax numpy.polynomial.legendre.legfromroots(roots) Parameters roots: Array-like sequence containing the roots of the polynomial. Example Let's create a Legendre series with roots at -1, 0, and 1 ? import numpy as np from numpy.polynomial import legendre as L # Generate ...
Read MoreIntegrate a Legendre series over axis 0 in Python
To integrate a Legendre series, use the polynomial.legendre.legint() method in Python. The method returns the Legendre 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.legendre.legint(c, m=1, k=[], lbnd=0, scl=1, axis=0) Parameters The function accepts the following parameters ? c ? An array of Legendre series coefficients. If c is multidimensional, different axes correspond to different variables. m ? Order of ...
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