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scipy.linalg.

# solve_continuous_lyapunov

scipy.linalg.solve_continuous_lyapunov(a, q)

  Solves the continuous Lyapunov equation \(AX + XA^H = Q\).

  Uses the Bartels-Stewart algorithm to find \(X\).

  The documentation is written assuming array arguments are of specified “core” shapes. However, array argument(s) of this function may have additional “batch” dimensions prepended to the core shape. In this case, the array is treated as a batch of lower-dimensional slices; see Batched Linear Operations for details.

  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.

  Added in version 0.11.0.

  Examples

  Given a and q solve for x:

      >>> import numpy as np
      >>> 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