numpy.polynomial.chebyshev.chebvander(x, deg) [source] Pseudo-Vandermonde matrix of given degree. Returns the pseudo-Vandermonde matrix of degree deg and sample points x. The pseudo-Vandermonde matrix is defined by where 0 <= i <= deg. The leading indices of V index the elements of x and the last index is the degree of the Chebyshev polynomial. If c is a 1-D array of coefficients of length n + 1 and V is the matrix V = chebvander(x, n), then np.dot(V, c) and chebval(x, c) are the s

numpy.polynomial.chebyshev.chebval3d(x, y, z, c) [source] Evaluate a 3-D Chebyshev series at points (x, y, z). This function returns the values: The parameters x, y, and z are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars and they must have the same shape after conversion. In either case, either x, y, and z or their elements must support multiplication and addition both with themselves and with the elements of c. If c has fewer than 3 dim

numpy.polynomial.chebyshev.chebval2d(x, y, c) [source] Evaluate a 2-D Chebyshev series at points (x, y). This function returns the values: The parameters x and y are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars and they must have the same shape after conversion. In either case, either x and y or their elements must support multiplication and addition both with themselves and with the elements of c. If c is a 1-D array a one is implicitly

numpy.polynomial.chebyshev.chebval(x, c, tensor=True) [source] Evaluate a Chebyshev series at points x. If c is of length n + 1, this function returns the value: The parameter x is converted to an array only if it is a tuple or a list, otherwise it is treated as a scalar. In either case, either x or its elements must support multiplication and addition both with themselves and with the elements of c. If c is a 1-D array, then p(x) will have the same shape as x. If c is multidimensional,

numpy.polynomial.chebyshev.chebtrim(c, tol=0) [source] Remove ?small? ?trailing? coefficients from a polynomial. ?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.? Parameters: c : array_like 1-d array of coefficients, ordered from lowest order to highest. tol : number, optional

numpy.polynomial.chebyshev.chebsub(c1, c2) [source] Subtract one Chebyshev series from another. Returns the difference of two Chebyshev series c1 - c2. The sequences of coefficients are from lowest order term to highest, i.e., [1,2,3] represents the series T_0 + 2*T_1 + 3*T_2. Parameters: c1, c2 : array_like 1-D arrays of Chebyshev series coefficients ordered from low to high. Returns: out : ndarray Of Chebyshev series coefficients representing their difference. See also chebadd, c

numpy.polynomial.chebyshev.chebroots(c) [source] Compute the roots of a Chebyshev series. Return the roots (a.k.a. ?zeros?) of the polynomial Parameters: c : 1-D array_like 1-D array of coefficients. Returns: out : ndarray Array of the roots of the series. If all the roots are real, then out is also real, otherwise it is complex. See also polyroots, legroots, lagroots, hermroots, hermeroots Notes The root estimates are obtained as the eigenvalues of the companion matrix, Roots

numpy.polynomial.chebyshev.chebpow(c, pow, maxpower=16) [source] Raise a Chebyshev series to a power. Returns the Chebyshev 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 T_0 + 2*T_1 + 3*T_2. Parameters: c : array_like 1-D array of Chebyshev series coefficients ordered from low to high. pow : integer Power to which the series will be raised maxpower : integer, optional Maximum power allowed. This is

numpy.polynomial.chebyshev.chebone = array([1])

numpy.polynomial.chebyshev.chebmulx(c) [source] Multiply a Chebyshev series by x. Multiply the polynomial c by x, where x is the independent variable. Parameters: c : array_like 1-D array of Chebyshev series coefficients ordered from low to high. Returns: out : ndarray Array representing the result of the multiplication. Notes New in version 1.5.0.