def solve_lyap_dense(A, E, B, trans=False, options=None):
"""Compute the solution of a Lyapunov equation.
See :func:`pymor.algorithms.lyapunov.solve_lyap_dense` for a
general description.
This function uses `slycot.sb03md` (if `E is None`) and
`slycot.sg03ad` (if `E is not None`), which are based on the
Bartels-Stewart algorithm.
Parameters
----------
A
The operator A as a 2D |NumPy array|.
E
The operator E as a 2D |NumPy array| or `None`.
B
The operator B as a 2D |NumPy array|.
trans
Whether the first operator in the Lyapunov equation is
transposed.
options
The solver options to use (see
:func:`lyap_dense_solver_options`).
Returns
-------
X
Lyapunov equation solution as a |NumPy array|.
"""
_solve_lyap_dense_check_args(A, E, B, trans)
options = _parse_options(options, lyap_dense_solver_options(), 'slycot_bartels-stewart', None, False)
if options['type'] == 'slycot_bartels-stewart':
n = A.shape[0]
C = -B.dot(B.T) if not trans else -B.T.dot(B)
trana = 'T' if not trans else 'N'
dico = 'C'
job = 'B'
if E is None:
U = np.zeros((n, n))
X, scale, sep, ferr, _ = slycot.sb03md(n, C, A, U, dico, job=job, trana=trana)
_solve_check(A.dtype, 'slycot.sb03md', sep, ferr)
else:
fact = 'N'
uplo = 'L'
Q = np.zeros((n, n))
Z = np.zeros((n, n))
_, _, _, _, X, scale, sep, ferr, _, _, _ = slycot.sg03ad(dico, job, fact, trana, uplo,
n, A, E,
Q, Z, C)
_solve_check(A.dtype, 'slycot.sg03ad', sep, ferr)
X /= scale
else:
raise ValueError(f"Unexpected Lyapunov equation solver ({options['type']}).")
return X
def solve_lyap_dense(A, E, B, trans=False, options=None):
"""Compute the solution of a Lyapunov equation.
See :func:`pymor.algorithms.lyapunov.solve_lyap_dense` for a
general description.
This function uses `slycot.sb03md` (if `E is None`) and
`slycot.sg03ad` (if `E is not None`), which are based on the
Bartels-Stewart algorithm.
Parameters
----------
A
The operator A as a 2D |NumPy array|.
E
The operator E as a 2D |NumPy array| or `None`.
B
The operator B as a 2D |NumPy array|.
trans
Whether the first operator in the Lyapunov equation is
transposed.
options
The solver options to use (see
:func:`lyap_dense_solver_options`).
Returns
-------
X
Lyapunov equation solution as a |NumPy array|.
"""
_solve_lyap_dense_check_args(A, E, B, trans)
options = _parse_options(options, lyap_dense_solver_options(), 'slycot_bartels-stewart', None, False)
if options['type'] == 'slycot_bartels-stewart':
n = A.shape[0]
C = -B.dot(B.T) if not trans else -B.T.dot(B)
trana = 'T' if not trans else 'N'
dico = 'C'
job = 'B'
if E is None:
U = np.zeros((n, n))
X, scale, sep, ferr, _ = slycot.sb03md(n, C, A, U, dico, job=job, trana=trana)
_solve_check(A.dtype, 'slycot.sb03md', sep, ferr)
else:
fact = 'N'
uplo = 'L'
Q = np.zeros((n, n))
Z = np.zeros((n, n))
_, _, _, _, X, scale, sep, ferr, _, _, _ = slycot.sg03ad(dico, job, fact, trana, uplo,
n, A, E,
Q, Z, C)
_solve_check(A.dtype, 'slycot.sg03ad', sep, ferr)
X /= scale
else:
raise ValueError(f"Unexpected Lyapunov equation solver ({options['type']}).")
return X
def solve_lyap_dense(A, E, B, trans=False, options=None):
"""Compute the solution of a Lyapunov equation.
See :func:`pymor.algorithms.lyapunov.solve_lyap_dense` for a
general description.
This function uses `scipy.linalg.solve_continuous_lyapunov`, which
is a dense solver for Lyapunov equations with E=I.
.. note::
If E is not `None`, the problem will be reduced to a standard
continuous-time algebraic Lyapunov equation by inverting E.
Parameters
----------
A
The operator A as a 2D |NumPy array|.
E
The operator E as a 2D |NumPy array| or `None`.
B
The operator B as a 2D |NumPy array|.
trans
Whether the first operator in the Lyapunov equation is
transposed.
options
The solver options to use (see
:func:`lyap_dense_solver_options`).
Returns
-------
X
Lyapunov equation solution as a |NumPy array|.
"""
_solve_lyap_dense_check_args(A, E, B, trans)
options = _parse_options(options, lyap_dense_solver_options(), 'scipy',
None, False)
if options['type'] == 'scipy':
if E is not None:
A = solve(E, A) if not trans else solve(E.T, A.T).T
B = solve(E, B) if not trans else solve(E.T, B.T).T
if trans:
A = A.T
B = B.T
X = solve_continuous_lyapunov(A, -B.dot(B.T))
else:
raise ValueError(
f"Unexpected Lyapunov equation solver ({options['type']}).")
return X
def solve_lyap_dense(A, E, B, trans=False, options=None):
"""Compute the solution of a Lyapunov equation.
See :func:`pymor.algorithms.lyapunov.solve_lyap_dense` for a
general description.
This function uses `scipy.linalg.solve_continuous_lyapunov`, which
is a dense solver for Lyapunov equations with E=I.
.. note::
If E is not `None`, the problem will be reduced to a standard
continuous-time algebraic Lyapunov equation by inverting E.
Parameters
----------
A
The operator A as a 2D |NumPy array|.
E
The operator E as a 2D |NumPy array| or `None`.
B
The operator B as a 2D |NumPy array|.
trans
Whether the first operator in the Lyapunov equation is
transposed.
options
The solver options to use (see
:func:`lyap_dense_solver_options`).
Returns
-------
X
Lyapunov equation solution as a |NumPy array|.
"""
_solve_lyap_dense_check_args(A, E, B, trans)
options = _parse_options(options, lyap_dense_solver_options(), 'scipy', None, False)
if options['type'] == 'scipy':
if E is not None:
A = solve(E, A) if not trans else solve(E.T, A.T).T
B = solve(E, B) if not trans else solve(E.T, B.T).T
if trans:
A = A.T
B = B.T
X = solve_continuous_lyapunov(A, -B.dot(B.T))
else:
raise ValueError(f"Unexpected Lyapunov equation solver ({options['type']}).")
return X
def solve_lyap_dense(A, E, B, trans=False, options=None):
"""Compute the solution of a Lyapunov equation.
See :func:`pymor.algorithms.lyapunov.solve_lyap_dense` for a
general description.
This function uses `pymess.glyap`.
Parameters
----------
A
The operator A as a 2D |NumPy array|.
E
The operator E as a 2D |NumPy array| or `None`.
B
The operator B as a 2D |NumPy array|.
trans
Whether the first operator in the Lyapunov equation is
transposed.
options
The solver options to use (see
:func:`lyap_dense_solver_options`).
Returns
-------
X
Lyapunov equation solution as a |NumPy array|.
"""
_solve_lyap_dense_check_args(A, E, B, trans)
options = _parse_options(options, lyap_lrcf_solver_options(),
'pymess_glyap', None, False)
if options['type'] == 'pymess_glyap':
Y = B.dot(B.T) if not trans else B.T.dot(B)
op = pymess.MESS_OP_NONE if not trans else pymess.MESS_OP_TRANSPOSE
X = pymess.glyap(A, E, Y, op=op)[0]
X = np.asarray(X)
else:
raise ValueError(
f'Unexpected Lyapunov equation solver ({options["type"]}).')
return X
def solve_lyap_dense(A, E, B, trans=False, options=None):
"""Compute the solution of a Lyapunov equation.
See :func:`pymor.algorithms.lyapunov.solve_lyap_dense` for a
general description.
This function uses `pymess.glyap`.
Parameters
----------
A
The operator A as a 2D |NumPy array|.
E
The operator E as a 2D |NumPy array| or `None`.
B
The operator B as a 2D |NumPy array|.
trans
Whether the first operator in the Lyapunov equation is
transposed.
options
The solver options to use (see
:func:`lyap_dense_solver_options`).
Returns
-------
X
Lyapunov equation solution as a |NumPy array|.
"""
_solve_lyap_dense_check_args(A, E, B, trans)
options = _parse_options(options, lyap_lrcf_solver_options(), 'pymess_glyap', None, False)
if options['type'] == 'pymess_glyap':
Y = B.dot(B.T) if not trans else B.T.dot(B)
op = pymess.MESS_OP_NONE if not trans else pymess.MESS_OP_TRANSPOSE
X = pymess.glyap(A, E, Y, op=op)[0]
else:
raise ValueError(f'Unexpected Lyapunov equation solver ({options["type"]}).')
return X
