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Numpy Articles
Page 9 of 81
Evaluate 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 ...
Read MoreGenerate a Vandermonde matrix of the Legendre polynomial with float array of points in Python
A Vandermonde matrix of the Legendre polynomial is useful for polynomial fitting and interpolation. NumPy provides the legvander() method to generate this matrix efficiently with float array points. Syntax numpy.polynomial.legendre.legvander(x, deg) Parameters x − Array of points. Converted to float64 or complex128 depending on element types deg − Degree of the resulting matrix. Must be non-negative integer Return Value Returns the pseudo-Vandermonde matrix with shape x.shape + (deg + 1, ). The last index corresponds to the degree of the Legendre polynomial. Example Generate a Vandermonde matrix of ...
Read MoreGenerate a Vandermonde matrix of the Legendre series in Python
To generate a pseudo Vandermonde matrix of the Legendre polynomial, use the polynomial.legvander() method in NumPy. This function creates a matrix where each row represents the Legendre polynomial evaluated at a specific point. The method returns the pseudo-Vandermonde matrix with shape x.shape + (deg + 1, ), where the last index corresponds to the degree of the Legendre polynomial. The dtype matches the converted input array x. Syntax numpy.polynomial.legendre.legvander(x, deg) Parameters The function accepts the following parameters: x − Array of points. Converted to float64 or complex128 depending on complexity. Scalars ...
Read MoreCompute the roots of a Legendre series with given complex roots in Python
To compute the roots of a Legendre series with complex coefficients, use the polynomial.legendre.legroots() method in Python. The method returns an array containing the roots of the series. If all roots are real, the output is real; otherwise it returns complex values. Syntax numpy.polynomial.legendre.legroots(c) Parameters The parameter c is a 1-D array of Legendre series coefficients ordered from low to high degree. Example Let's compute the roots of a Legendre series with complex coefficients ? from numpy.polynomial import legendre as L # Define complex unit j = complex(0, 1) ...
Read MoreCompute the roots of a Legendre series in Python
To compute the roots of a Legendre series, use the polynomial.legendre.legroots() method in Python. 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. Syntax numpy.polynomial.legendre.legroots(c) Where c is a 1-D array of Legendre series coefficients ordered from low to high degree. Example Let's compute the roots of a Legendre series with coefficients (0, 1, 2) − from numpy.polynomial import legendre as L # ...
Read MoreGenerate a Legendre series with given complex roots in Python
To generate a Legendre series from complex roots in Python, use the polynomial.legendre.legfromroots() method from NumPy. This method returns a 1-D array of coefficients representing the Legendre polynomial. When complex roots are provided, the output array will be of complex type even if the resulting coefficients are real numbers. Syntax numpy.polynomial.legendre.legfromroots(roots) Parameters roots − A sequence containing the roots of the polynomial. Return Value Returns a 1-D array of Legendre series coefficients ordered from low to high degree. Example Let's generate a Legendre series with complex roots -j and j ...
Read MoreEvaluate a Hermite_e series at points x broadcast over the columns of the coefficient in Python
To evaluate a Hermite_e series at points x broadcast over the columns of coefficients, use the hermite_e.hermeval() method in NumPy. This function allows you to evaluate multiple polynomials simultaneously with different broadcasting behaviors. Syntax numpy.polynomial.hermite_e.hermeval(x, c, tensor=True) Parameters The function accepts three parameters: x − Points at which to evaluate the series. Can be a scalar, list, or array. c − Array of coefficients where coefficients for degree n are in c[n]. For multidimensional arrays, columns represent different polynomials. tensor − Boolean flag controlling broadcasting behavior. When False, x is broadcast over ...
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