def main():
"""Solve Lyapunov Equation SO1 System."""
# read data
m = mmread("@CMAKE_SOURCE_DIR@/tests/data/TripleChain/M_301.mtx").tocsr()
d = mmread("@CMAKE_SOURCE_DIR@/tests/data/TripleChain/D_301.mtx").tocsr()
k = mmread("@CMAKE_SOURCE_DIR@/tests/data/TripleChain/K_301.mtx").tocsr()
# generate rhs
b = np.ones((2 * m.shape[0], 1), dtype=np.double)
# bounds for shift parameters
lowerbound = 1e-8
upperbound = 1e+8
# create options instance
opt = Options()
opt.adi.output = 0
opt.adi.res2_tol = 1e-7
opt.type = MESS_OP_NONE
# create equation
eqn = EquationGLyapSO1(opt, m, d, k, b, lowerbound, upperbound)
# solve equation
z, status = lradi(eqn, opt)
# get residual
res2 = status.res2_norm
res2_0 = status.res2_0
it = status.it
print("it = %d \t rel_res2 = %e\t res2 = %e \n" % (it, res2 / res2_0, res2))
print("Size of Low Rank Solution Factor Z: %d x %d \n"%(z.shape))
print(status)
def main():
"""Demonstrate Callback functionality"""
# read data
a = mmread('@CMAKE_SOURCE_DIR@/tests/data/Rail/A.mtx')
b = mmread('@CMAKE_SOURCE_DIR@/tests/data/Rail/B.mtx')
c = mmread('@CMAKE_SOURCE_DIR@/tests/data/Rail/C.mtx')
e = mmread('@CMAKE_SOURCE_DIR@/tests/data/Rail/E.mtx')
# create options
opt = Options()
opt.nm.output = 0
opt.adi.output = 0
# create instance of MyEquation and solve
opt.type = MESS_OP_NONE
eqn1 = MyEquation(opt, a, e, b, c)
z1, stat1 = lrnm(eqn1, opt)
# create instance of MyEquation and solve
opt.type = MESS_OP_TRANSPOSE
eqn2 = MyEquation(opt, a, e, b, c)
z2, stat2 = lrnm(eqn2, opt)
# print information and compute residual again to make sure that we have everything correct
print("\n")
print("MyEquation: eqn1")
print("Size of Low Rank Solution Factor Z1: %d x %d \n" % (z1.shape))
print(stat1.lrnm_stat())
nrmr1, nrmrhs1, relnrm1 = res2_ric(a, e, b, c, z1, MESS_OP_NONE)
print("check for eqn1:\t rel_res2=%e\t res2=%e\t nrmrhs=%e\n" %
(relnrm1, nrmr1, nrmrhs1))
print("\n")
print(
"--------------------------------------------------------------------------------------"
)
print("\n")
# print information and compute residual again to make sure that we have everything correct
print("MyEquation: eqn2")
print("Size of Low Rank Solution Factor Z2: %d x %d \n" % (z2.shape))
print(stat2.lrnm_stat())
nrmr2, nrmrhs2, relnrm2 = res2_ric(a, e, b, c, z2, MESS_OP_TRANSPOSE)
print("check for eqn1:\t rel_res2=%e\t res2=%e\t nrmrhs=%e\n" %
(relnrm2, nrmr2, nrmrhs2))
def main():
"""Solve Riccati Equation SO1 System equation."""
# read data
m = mmread("@CMAKE_SOURCE_DIR@/tests/data/TripleChain/M_301.mtx").tocsr()
d = mmread("@CMAKE_SOURCE_DIR@/tests/data/TripleChain/D_301.mtx").tocsr()
k = mmread("@CMAKE_SOURCE_DIR@/tests/data/TripleChain/K_301.mtx").tocsr()
# generate rhs
b = np.ones((2 * m.shape[0], 1), dtype=np.double)
c = np.ones((1, m.shape[0]), dtype=np.double)
# bounds for shift parameters
lowerbound = 1e-8
upperbound = 1e+8
# create options instance
opt = Options()
opt.adi.output = 0
opt.nm.output = 0
opt.nm.res2_tol = 1e-6
opt.adi.res2_tol = 1e-10
opt.adi.maxit = 1000
opt.type = MESS_OP_NONE
opt.adi.shifts.paratype = MESS_LRCFADI_PARA_MINMAX
# create equation
eqn = EquationGRiccatiSO1(opt, m, d, k, b, c, lowerbound, upperbound)
# solve equation
z, status = lrnm(eqn, opt)
# get residual
res2 = status.res2_norm
res2_0 = status.res2_0
it = status.it
print("it = %d \t rel_res2 = %e\t res2 = %e \n" %
(it, res2 / res2_0, res2))
print("Size of Low Rank Solution Factor Z: %d x %d \n" % (z.shape))
print(status.lrnm_stat())