def main():
"""Solve a generalized Lyapunov Equation using glyap."""
# generate matrices
n = 100
a = rand(n, n)
e = rand(n, n)
y1 = rand(n, n)
y1 = y1 + y1.T
y2 = rand(n, n)
y2 = y2 + y2.T
# solve standard and generalized Lyapunov Equation
x1, ahat, qa = glyap(a, None, y1, MESS_OP_NONE)
x2, ahat2, ehat2, qa2, qe2 = glyap(a, e, y1, MESS_OP_NONE)
# solve again using schur decomposition
x3 = glyap(a, None, y2, MESS_OP_NONE, ahat, None, qa, None)
x4 = glyap(a, e, y2, MESS_OP_NONE, ahat2, ehat2, qa2, qe2)
# compute residual
res1, _, relres1 = res2_glyap(a, None, y1, x1, MESS_OP_NONE)
res2, _, relres2 = res2_glyap(a, e, y1, x2, MESS_OP_NONE)
res3, _, relres3 = res2_glyap(a, None, y2, x3, MESS_OP_NONE)
res4, _, relres4 = res2_glyap(a, e, y2, x4, MESS_OP_NONE)
print("n = {0:d}".format(n))
print("(1): residual = {0:e}\t rel. residual = {1:e}".format(
res1, relres1))
print("(2): residual = {0:e}\t rel. residual = {1:e}".format(
res2, relres2))
print("(3): residual = {0:e}\t rel. residual = {1:e}".format(
res3, relres3))
print("(4): residual = {0:e}\t rel. residual = {1:e}".format(
res4, relres4))
print("\n")
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