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Fonction poly - module numpy.matlib

Signature de la fonction poly

def poly(seq_of_zeros) 

Description

poly.__doc__

    Find the coefficients of a polynomial with the given sequence of roots.

    .. note::
       This forms part of the old polynomial API. Since version 1.4, the
       new polynomial API defined in `numpy.polynomial` is preferred.
       A summary of the differences can be found in the
       :doc:`transition guide </reference/routines.polynomials>`.

    Returns the coefficients of the polynomial whose leading coefficient
    is one for the given sequence of zeros (multiple roots must be included
    in the sequence as many times as their multiplicity; see Examples).
    A square matrix (or array, which will be treated as a matrix) can also
    be given, in which case the coefficients of the characteristic polynomial
    of the matrix are returned.

    Parameters
    ----------
    seq_of_zeros : array_like, shape (N,) or (N, N)
        A sequence of polynomial roots, or a square array or matrix object.

    Returns
    -------
    c : ndarray
        1D array of polynomial coefficients from highest to lowest degree:

        ``c[0] * x**(N) + c[1] * x**(N-1) + ... + c[N-1] * x + c[N]``
        where c[0] always equals 1.

    Raises
    ------
    ValueError
        If input is the wrong shape (the input must be a 1-D or square
        2-D array).

    See Also
    --------
    polyval : Compute polynomial values.
    roots : Return the roots of a polynomial.
    polyfit : Least squares polynomial fit.
    poly1d : A one-dimensional polynomial class.

    Notes
    -----
    Specifying the roots of a polynomial still leaves one degree of
    freedom, typically represented by an undetermined leading
    coefficient. [1]_ In the case of this function, that coefficient -
    the first one in the returned array - is always taken as one. (If
    for some reason you have one other point, the only automatic way
    presently to leverage that information is to use ``polyfit``.)

    The characteristic polynomial, :math:`p_a(t)`, of an `n`-by-`n`
    matrix **A** is given by

        :math:`p_a(t) = \mathrm{det}(t\, \mathbf{I} - \mathbf{A})`,

    where **I** is the `n`-by-`n` identity matrix. [2]_

    References
    ----------
    .. [1] M. Sullivan and M. Sullivan, III, "Algebra and Trignometry,
       Enhanced With Graphing Utilities," Prentice-Hall, pg. 318, 1996.

    .. [2] G. Strang, "Linear Algebra and Its Applications, 2nd Edition,"
       Academic Press, pg. 182, 1980.

    Examples
    --------
    Given a sequence of a polynomial's zeros:

    >>> np.poly((0, 0, 0)) # Multiple root example
    array([1., 0., 0., 0.])

    The line above represents z**3 + 0*z**2 + 0*z + 0.

    >>> np.poly((-1./2, 0, 1./2))
    array([ 1.  ,  0.  , -0.25,  0.  ])

    The line above represents z**3 - z/4

    >>> np.poly((np.random.random(1)[0], 0, np.random.random(1)[0]))
    array([ 1.        , -0.77086955,  0.08618131,  0.        ]) # random

    Given a square array object:

    >>> P = np.array([[0, 1./3], [-1./2, 0]])
    >>> np.poly(P)
    array([1.        , 0.        , 0.16666667])

    Note how in all cases the leading coefficient is always 1.