Module « scipy.linalg »

Fonction solve_continuous_lyapunov - module scipy.linalg

Signature de la fonction solve_continuous_lyapunov

def solve_continuous_lyapunov(a, q) 

Description

solve_continuous_lyapunov.__doc__

    Solves the continuous Lyapunov equation :math:`AX + XA^H = Q`.

    Uses the Bartels-Stewart algorithm to find :math:`X`.

    Parameters
    ----------
    a : array_like
        A square matrix

    q : array_like
        Right-hand side square matrix

    Returns
    -------
    x : ndarray
        Solution to the continuous Lyapunov equation

    See Also
    --------
    solve_discrete_lyapunov : computes the solution to the discrete-time
        Lyapunov equation
    solve_sylvester : computes the solution to the Sylvester equation

    Notes
    -----
    The continuous Lyapunov equation is a special form of the Sylvester
    equation, hence this solver relies on LAPACK routine ?TRSYL.

    .. versionadded:: 0.11.0

    Examples
    --------
    Given `a` and `q` solve for `x`:

    >>> from scipy import linalg
    >>> a = np.array([[-3, -2, 0], [-1, -1, 0], [0, -5, -1]])
    >>> b = np.array([2, 4, -1])
    >>> q = np.eye(3)
    >>> x = linalg.solve_continuous_lyapunov(a, q)
    >>> x
    array([[ -0.75  ,   0.875 ,  -3.75  ],
           [  0.875 ,  -1.375 ,   5.3125],
           [ -3.75  ,   5.3125, -27.0625]])
    >>> np.allclose(a.dot(x) + x.dot(a.T), q)
    True