To convert a polynomial to a Chebyshev series, use the chebyshev.poly2cheb() method in Python Numpy. Convert an array representing the coefficients of a polynomial ordered from lowest degree to highest, to an array of the coefficients of the equivalent Chebyshev series, ordered from lowest to highest degree. The method returns a 1-D array containing the coefficients of the equivalent Chebyshev series. The parameter c, is a 1-D array containing the polynomial coefficientsStepsAt first, import the required library −import numpy as np from numpy import polynomial as PCreate an array using the numpy.array() method −c = np.array([1, 2, 3, 4, 5])Display ... Read More

To convert a Chebyshev series to a polynomial, use the chebyshev.cheb2poly() method in Python Numpy. Convert an array representing the coefficients of a Chebyshev series, ordered from lowest degree to highest, to an array of the coefficients of the equivalent polynomial (relative to the “standard” basis) ordered from lowest to highest degree.The method returns a 1-D array containing the coefficients of the equivalent polynomial ordered from lowest order term to highest. The parameter c, is a 1-D array containing the Chebyshev series coefficients, ordered from lowest order term to highest.StepsAt first, import the required library −import numpy as np from ... Read More

To remove small trailing coefficients from Chebyshev polynomial, use the chebyshev.chebtrim() 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 the parameter tol; “trailing” means highest order coefficient(s), e.g., in [0, 1, 1, 0, 0] (which represents 0 + x + x**2 + 0*x**3 + 0*x**4) both the 3-rd and 4-th order coefficients would be “trimmed.” The parameter c is a 1-d array of coefficients, ordered from lowest order to ... 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 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 raise a Hermite series to a power, use the polynomial.hermite.hermpow() method in Python Numpy. The method returns Hermite series of power. Returns the Hermite series c raised to the power pow. The argument c is a sequence of coefficients ordered from low to high. i.e., [1, 2, 3] is the series P_0 + 2*P_1 + 3*P_2.The parameter, c is a 1-D array of Hermite series coefficients ordered from low to high. The parameter, pow is a Power to which the series will be raised. The parameter, maxpower is the maximum power allowed. This is mainly to limit growth of ... Read More

To divide one Hermite series by another, use the polynomial.hermite.hermdiv() method in Python Numpy. The method returns an array of Hermite series coefficients representing the quotient and remainder. Returns the quotient-with-remainder of two Hermite series c1 / c2. The arguments are sequences of coefficients from lowest order “term” to highest, e.g., [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 ... Read More

To multiply one Hermite series to another, use the polynomial.hermite.hermmul() method in Python Numpy. The method returns an array representing the Hermite series of their product. Returns the product of two Hermite series c1 * c2. The arguments are sequences of coefficients, from lowest order “term” to highest, e.g., [1, 2, 3] represents the series P_0 + 2*P_1 + 3*P_2. The parameters 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, 2, 3]) c2 ... Read More

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