def main():
"""Solve standard/generalized Riccati equation."""
# read data
e = mmread("@CMAKE_SOURCE_DIR@/tests/data/filter2D/filter2D.E").tocsr()
a = mmread("@CMAKE_SOURCE_DIR@/tests/data/filter2D/filter2D.A").tocsr()
b = mmread("@CMAKE_SOURCE_DIR@/tests/data/filter2D/filter2D.B")
c = mmread("@CMAKE_SOURCE_DIR@/tests/data/filter2D/filter2D.C")
#create opt instance
opt1 = Options()
opt1.nm.output = 1
opt1.adi.output = 0
opt1.nm.res2_tol = 1e-4
opt2 = Options()
opt2.nm.output = 1
opt2.adi.output = 0
opt2.nm.res2_tol = 1e-4
# create standard and generalized equation
eqn1 = EquationGRiccati(opt1, a, None, b, c)
eqn2 = EquationGRiccati(opt2, a, e, b, c)
# solve both equations
z1, stat1 = lrnm(eqn1, opt1)
z2, stat2 = lrnm(eqn2, opt2)
print("Standard Riccati Equation \n")
print("Size of Low Rank Solution Factor Z1: %d x %d \n"%(z1.shape))
print(stat1.lrnm_stat())
print(stat1)
print("Generalized Riccati Equation \n")
print("Size of Low Rank Solution Factor Z2: %d x %d \n"%(z2.shape))
print(stat2.lrnm_stat())
print(stat2)
def main():
"""Solve standard/generalized Lyapunov equation."""
# read data
e = mmread("@CMAKE_SOURCE_DIR@/tests/data/filter2D/filter2D.E").tocsr()
a = mmread("@CMAKE_SOURCE_DIR@/tests/data/filter2D/filter2D.A").tocsr()
b = mmread("@CMAKE_SOURCE_DIR@/tests/data/filter2D/filter2D.B")
# create opt instances
opt1 = Options()
opt1.adi.output = 0
opt1.adi.res2_tol = 1e-6
print(opt1)
opt2 = Options()
opt2.adi.output = 0
opt2.adi.res2_tol = 1e-6
print(opt2)
# create standard and generalized equation
eqn1 = EquationGLyap(opt1, a, None, b)
eqn2 = EquationGLyap(opt2, a, e, b)
# solve both equations
z1, stat1 = lradi(eqn1, opt1)
z2, stat2 = lradi(eqn2, opt2)
print("Standard Lyapunov Equation \n")
print("Size of Low Rank Solution Factor Z1: %d x %d \n" % (z1.shape))
print(stat1)
print("Generalized Lyapunov Equation \n")
print("Size of Low Rank Solution Factor Z2: %d x %d \n" % (z2.shape))
print(stat2)
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():
"""Solve Lyapunov Equation DAE1 System."""
# read data
e11 = mmread("@CMAKE_SOURCE_DIR@/tests/data/bips98_606/E11.mtx").tocsr()
a11 = mmread("@CMAKE_SOURCE_DIR@/tests/data/bips98_606/A11.mtx").tocsr()
a12 = mmread("@CMAKE_SOURCE_DIR@/tests/data/bips98_606/A12.mtx").tocsr()
a21 = mmread("@CMAKE_SOURCE_DIR@/tests/data/bips98_606/A21.mtx").tocsr()
a22 = mmread("@CMAKE_SOURCE_DIR@/tests/data/bips98_606/A22.mtx").tocsr()
b = mmread("@CMAKE_SOURCE_DIR@/tests/data/bips98_606/B.mtx").todense()
b = b / norm(b)
#create opt instance
opt = Options()
opt.adi.output = 0
opt.nm.output = 0
opt.adi.res2_tol = 1e-10
print(opt)
# create equation
eqn = EquationGLyapDAE1(opt, e11, a11, a12, a21, a22, b)
# solve equation
z, status = lradi(eqn, opt)
# get residual
res2 = status.res2_norm
res2_0 = status.res2_0
it = status.it
print("Size of Low Rank Solution Factor Z: %d x %d \n" % (z.shape))
print("it = %d \t rel_res2 = %e\t res2 = %e \n" %
(it, res2 / res2_0, res2))
print(status)
def main():
"""Solve Lyapunov Equation for DAE2 System."""
# read data
m = mmread(
"@CMAKE_SOURCE_DIR@/tests/data/NSE/NSE_RE_100_lvl1_M.mtx").tocsr()
a = mmread(
"@CMAKE_SOURCE_DIR@/tests/data/NSE/NSE_RE_100_lvl1_A.mtx").tocsr()
g = mmread(
"@CMAKE_SOURCE_DIR@/tests/data/NSE/NSE_RE_100_lvl1_G.mtx").tocsr()
b = mmread("@CMAKE_SOURCE_DIR@/tests/data/NSE/NSE_RE_100_lvl1_B.mtx")
delta = -0.02
#create opt instance
opt = Options()
opt.adi.output = 0
opt.nm.output = 0
opt.adi.res2_tol = 1e-5
opt.adi.paratype = MESS_LRCFADI_PARA_ADAPTIVE_V
print(opt)
# create equation
eqn = EquationGLyapDAE2(opt, m, a, g, b, delta, None)
# solve equation
z, status = lradi(eqn, opt)
# get residual
res2 = status.res2_norm
res2_0 = status.res2_0
it = status.it
print("Size of Low Rank Solution Factor Z: %d x %d \n" % (z.shape))
print("it = %d \t rel_res2 = %e\t res2 = %e \n" %
(it, res2 / res2_0, res2))
print(status)
def setUp(self):
"""is called before every test function"""
self.opt = Options()
self.opt.adi.res2_tol = 1e-10
self.opt.adi.maxit = 1000
self.opt.adi.output = 0
self.opt.nm.output = 0
def setUp(self):
"""is called before every test function"""
self.a = mmread(self.amtx).tocsr()
self.b = mmread(self.bmtx)
self.c = mmread(self.cmtx)
self.e = mmread(self.emtx).tocsr()
self.opt = Options()
self.opt.type = MESS_OP_TRANSPOSE
def setUp(self):
"""is called before every test function"""
self.opt = Options()
self.opt.adi.res2_tol = 5e-8
self.opt.adi.output = 0
self.opt.nm.output = 0
self.opt.adi.shifts.paratype = MESS_LRCFADI_PARA_ADAPTIVE_V
self.delta = -0.02
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 setUp(self):
"""is called before every test function"""
self.opt = Options()
self.opt.adi.output = 0
self.opt.nm.output = 0
self.opt.adi.res2_tol = 1e-10
self.a = mmread(self.amtx).tocsr()
self.b = mmread(self.bmtx).todense()
self.e = mmread(self.emtx).tocsr()
def setUp(self):
"""is called before every test function"""
self.opt = Options()
self.opt.adi.res2_tol = 1e-6
self.opt.nm.res2_tol = 5e-1
self.opt.nm.maxit = 30
self.opt.adi.output = 0
self.opt.nm.output = 0
self.delta = -0.02
def setUp(self):
"""is called before every test function"""
self.opt = Options()
self.opt.adi.res2_tol = 1e-7
self.opt.nm.res2_tol = 1e-2
self.opt.adi.output = 0
self.opt.nm.output = 0
self.lowerbound = 1e-8
self.upperbound = 1e+8
self.m = mmread(self.mmtx).tocsr()
self.d = mmread(self.dmtx).tocsr()
self.k = mmread(self.kmtx).tocsr()
def setUp(self):
"""is called before every test function"""
self.opt = Options()
self.opt.adi.res2_tol = 1e-8
self.opt.adi.output = 0
self.opt.nm.output = 0
self.opt.adi.shifts.paratype = MESS_LRCFADI_PARA_MINMAX
self.lowerbound = 1e-8
self.upperbound = 1e+8
self.m = mmread(self.mmtx).tocsr()
self.d = mmread(self.dmtx).tocsr()
self.k = mmread(self.kmtx).tocsr()
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())
def main():
"""Solve Riccati Equation DAE1 System."""
# read data
e11 = mmread("@CMAKE_SOURCE_DIR@/tests/data/bips98_606/E11.mtx").tocsr()
a11 = mmread("@CMAKE_SOURCE_DIR@/tests/data/bips98_606/A11.mtx").tocsr()
a12 = mmread("@CMAKE_SOURCE_DIR@/tests/data/bips98_606/A12.mtx").tocsr()
a21 = mmread("@CMAKE_SOURCE_DIR@/tests/data/bips98_606/A21.mtx").tocsr()
a22 = mmread("@CMAKE_SOURCE_DIR@/tests/data/bips98_606/A22.mtx").tocsr()
#create opt instance
opt = Options()
opt.adi.output = 0
opt.nm.output = 0
opt.nm.res2_tol = 1e-10
# generate some matrices b and c
seed(1111)
if opt.type == MESS_OP_TRANSPOSE:
b = rand(e11.shape[0], 2)
c = rand(2, e11.shape[1] + a22.shape[1])
else:
b = rand(e11.shape[0] + a22.shape[0], 2)
c = rand(2, e11.shape[1])
b = b / norm(b, 'fro')
c = c / norm(c, 'fro')
# create equation
eqn = EquationGRiccatiDAE1(opt, e11, a11, a12, a21, a22, b, c)
# solve equation
z, status = lrnm(eqn, opt)
# get residual
res2 = status.res2_norm
res2_0 = status.res2_0
it = status.it
print("Size of Low Rank Solution Factor Z: %d x %d \n" % (z.shape))
print("it = %d \t rel_res2 = %e\t res2 = %e \n" %
(it, res2 / res2_0, res2))
print(status.lrnm_stat())
