To multiply the Hermite series by x, where x is the independent variable, use the polynomial.hermite.hermmulx() method in Python Numpy. The method returns an array representing the result of the multiplication. The parameter, c is a 1-D array 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 an array −c = np.array([1, 2, 3])Display the array −print("Our Array...", c)Check the Dimensions −print("Dimensions of our Array...", c.ndim)Get the Datatype −print("Datatype of our Array object...", c.dtype)Get the Shape −print("Shape of our Array object...", c.shape)To multiply the Hermite ... Read More

To get the least-squares fit of Chebyshev series to data, use the chebyshev.chebfit() in Python Numpy. The method returns the Chebyshev 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 the x-coordinates of the M sample (data) points (x[i], y[i]).The parameter, y are the y-coordinates of the sample points. Several sets of sample points sharing the same x-coordinates can be (independently) fit with one call to polyfit by passing in for y a 2-D array that contains one data set per ... Read More

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