To return the scaled companion matrix of a 1-D array of polynomial coefficients, return the chebyshev.chebcompanion() method in Python Numpy. The basis polynomials are scaled so that the companion matrix is symmetric when c is a Chebyshev basis polynomial. This provides better eigenvalue estimates than the unscaled case and for basis polynomials the eigenvalues are guaranteed to be real if numpy.linalg.eigvalsh is used to obtain them. The method returns the Scaled companion matrix of dimensions (deg, deg). The parameter, c is a 1-D array of Chebyshev series coefficients ordered from low to high degree.StepsAt first, import the required library −import ... Read More

To differentiate a polynomial, use the polynomial.polyder() method in Python Numpy. Return the polynomial coefficients c differentiated m times along axis. At each iteration the result is multiplied by scl (the scaling factor is for use in a linear change of variable). The argument c is an array of coefficients from low to high degree along each axis, e.g., [1, 2, 3] represents the polynomial 1 + 2*x + 3*x**2 while [[1, 2], [1, 2]] represents 1 + 1*x + 2*y + 2*x*y if axis=0 is x and axis=1 is y. The method returns the Polynomial coefficients of the derivative.The ... Read More

To differentiate a polynomial, use the polynomial.polyder() method in Python Numpy. Return the polynomial coefficients c differentiated m times along axis. At each iteration the result is multiplied by scl (the scaling factor is for use in a linear change of variable). The argument c is an array of coefficients from low to high degree along each axis, e.g., [1, 2, 3] represents the polynomial 1 + 2*x + 3*x**2 while [[1, 2], [1, 2]] represents 1 + 1*x + 2*y + 2*x*y if axis=0 is x and axis=1 is y.The method returns the Polynomial coefficients of the derivative. The ... Read More

To generate a pseudo Vandermonde matrix of the Chebyshev polynomial and x, y, z sample points, use the chebyshev.chebvander() in Python Numpy. The method returns the pseudo-Vandermonde matrix of degrees deg and sample points (x, y, z).The parameter, x, y, z are the 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].StepsAt first, import the required library −import numpy as ... Read More

To generate a Pseudo-Vandermonde matrix of given degree, use the polynomial.polyvander2() in Python Numpy. The method returns the pseudo-Vandermonde matrix of degrees deg and sample points (x, y). The parameter, x and y, are the 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].StepsAt first, import the required library −import numpy as np from numpy.polynomial.polynomial import polyvander2dCreate arrays of point coordinates, ... Read More

To differentiate a Chebyshev series, use the polynomial.chebder() method in Python Numpy. The method returns the Chebyshev series of the derivative. Returns the Chebyshev series coefficients c differentiated m times along axis. At each iteration the result is multiplied by scl. The argument c is an array of coefficients from low to high degree along each axis, e.g., [1, 2, 3] represents the series 1*T_0 + 2*T_1 + 3*T_2 while [[1, 2], [1, 2]] represents 1*T_0(x)*T_0(y) + 1*T_1(x)*T_0(y) + 2*T_0(x)*T_1(y) + 2*T_1(x)*T_1(y) if axis=0 is x and axis=1 is y.The 1st parameter is c, an array of Chebyshev series coefficients. ... Read More

To differentiate a Chebyshev series, use the polynomial.chebder() method in Python Numpy. The method returns the Chebyshev series of the derivative. Returns the Chebyshev series coefficients c differentiated m times along axis. At each iteration the result is multiplied by scl. The argument c is an array of coefficients from low to high degree along each axis, e.g., [1, 2, 3] represents the series 1*T_0 + 2*T_1 + 3*T_2 while [[1, 2], [1, 2]] represents 1*T_0(x)*T_0(y) + 1*T_1(x)*T_0(y) + 2*T_0(x)*T_1(y) + 2*T_1(x)*T_1(y) if axis=0 is x and axis=1 is y.The 1st parameter is c, an array of Chebyshev series coefficients. ... Read More

To generate a Pseudo-Vandermonde matrix of given degree, use the polynomial.polyvander2() in Python Numpy. The method returns the pseudo-Vandermonde matrix of degrees deg and sample points (x, y).The parameter, x and y, are the 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].StepsAt first, import the required library −import numpy as np from numpy.polynomial.polynomial import polyvander2dCreate arrays of point coordinates, all ... Read More

To evaluate a Hermite series at points x, use the hermite.hermval() method in Python Numpy. The 1st parameter, 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 must support addition and multiplication with themselves and with the elements of c.The 2nd parameter, C, an array of coefficients ordered so that the coefficients for terms of degree n are contained in c[n]. If c is multidimensional the remaining indices enumerate multiple polynomials. In the two dimensional case the coefficients ... Read More

To subtract one Hermite series to another, use the polynomial.hermite.hermsub() method in Python Numpy. The method returns an array representing the Hermite series of their difference. Returns the difference of two Hermite series c1 - c2. The sequences of coefficients are from lowest order term to highest, i.e., [1, 2, 3] represents the series P_0 + 2*P_1 + 3*P_2. The parameters c1 and c2 are 1-D arrays of Hermite series coefficients ordered from low to high.StepsAt first, import the required library −import numpy as np from numpy.polynomial import hermite as HCreate 1-D arrays of Hermite series coefficients −c1 = np.array([1, ... Read More