To return the scaled companion matrix of a 1-D array of polynomial coefficients, return the hermite_e.hermecompanion() method in Python Numpy. The basis polynomials are scaled so that the companion matrix is symmetric when c is an Hermite_e basis polynomial. This provides better eigenvalue estimates than the unscaled case and for ... Read More

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 ... Read More

To integrate a Hermite_e series, use the hermite.hermeint() method in Python. The 1st parameter, c is an array of Hermite_e series coefficients. If c is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index. The 2nd parameter, m is an ... Read More

To integrate a Hermite_e series, use the hermite_e.hermeint() method in Python. The 1st parameter, c is an array of Hermite_e series coefficients. If c is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index.The 2nd parameter, m is an order ... Read More

To remove small trailing coefficients from Legendre polynomial, use the legendre.legtrim() method in Python numpy. The method returns a 1-d array with trailing zeros removed. If the resulting series would be empty, a series containing a single zero is returned.The “Small” means “small in absolute value” and is controlled by ... Read More

To get the Least squares fit of Legendre series to data, use the legendre.legfit() method in Python numpy. The method returns the Legendre coefficients ordered from low to high. If y was 2-D, the coefficients for the data in column k of y are in column k.The parameter, x are ... Read More

To return the scaled companion matrix of a 1-D array of Legendre polynomial coefficients, use the legendre.legcompanion() method in Python Numpy. The usual companion matrix of the Legendre polynomials is already symmetric when c is a basis Laguerre polynomial, so no scaling is applied.Returns the scaled Companion matrix of dimensions ... Read More

To integrate a Hermite_e series, use the hermite_e.hermeint() method in Python. The 1st parameter, c is an array of Hermite_e series coefficients. If c is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index.The 2nd parameter, m is an order ... Read More

To integrate a Hermite_e series, use the hermite_e.hermeint() method in Python. The 1st parameter, c is an array of Hermite_e series coefficients. If c is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index. The 2nd parameter, m is an ... Read More

To evaluate a Legendre series at points x, use the polynomial.legendre.legval() method in Python Numpy. The 1st parameter is x. If x is a list or tuple, it is converted to an ndarray, otherwise it is left unchanged and treated as a scalar. In either case, x or its elements ... Read More