def template_riccati(self, rhs, para):
"""template to reduce code in the test cases"""
#set some options
self.opt.adi.output = 0
self.opt.adi.res2_tol = 1e-10
self.opt.nm.output = 0
self.opt.nm.res2_tol = 1e-3
# setup equation
if para < 0:
eqn = MyEquation2(self.opt, self.a, self.e, rhs, self.b, self.c)
z, status = lrnm(eqn, self.opt)
else:
eqn2 = MyEquation(self.opt, self.a, self.e, rhs, self.b, self.c)
self.opt.adi.shifts.paratype = para
z, status = lrnm(eqn2, self.opt)
#get res2 from lrnm
res2 = status.res2_norm
res2_0 = status.res2_0
it = status.it
print("it=%d\t rel_res2=%e\t res2=%e\t tol=%e\n" %
(it, res2 / res2_0, res2, self.opt.nm.res2_tol))
self.assertLessEqual(res2 / res2_0, self.opt.nm.res2_tol)
#check norm
nrmr, nrmrhs, relnrm = res2_ric(self.a, self.e, self.b, self.c, z,
self.opt.type)
print("check:\t rel_res2=%e\t res2=%e\t nrmrhs=%e\n" %
(relnrm, nrmr, nrmrhs))
# compare residual, should be roughly the same magnitude
self.assertLessEqual(abs(log10(relnrm) - log10(res2 / res2_0)), 1)
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 template_iss(self):
"""template to reduce code in the test cases"""
a = mmread(self.amtx_iss).todense()
b = mmread(self.bmtx_iss).todense()
e = mmread(self.emtx_iss).todense()
c = mmread(self.cmtx_iss).todense()
z = pymess.care(a, e, b, c)
nrmr, nrmrhs, relnrm = res2_ric(a, e, b, c, z, MESS_OP_TRANSPOSE)
print("res2 = {0:e}\t rel = {1:e}\t res2/rel = {2:e}".format(
nrmr, nrmrhs, relnrm))
self.assertLessEqual(relnrm, self.tol)
def main():
"""Solve standard/generalized Riccati equation."""
# read data
a = mmread("@CMAKE_SOURCE_DIR@/tests/data/filter2D/filter2D.A")
e = mmread("@CMAKE_SOURCE_DIR@/tests/data/filter2D/filter2D.E")
b = mmread("@CMAKE_SOURCE_DIR@/tests/data/filter2D/filter2D.B").todense()
c = mmread("@CMAKE_SOURCE_DIR@/tests/data/filter2D/filter2D.C").todense()
# standard
z = care(a, None, b, c)
# compute residual
_, _, rel = res2_ric(a, None, b, c, z, MESS_OP_TRANSPOSE)
print("standard rel. resisudal=", rel)
# generalized
z = care(a, e, b, c)
# compute residual
_, _, rel = res2_ric(a, e, b, c, z, MESS_OP_TRANSPOSE)
print("generalized rel. resisdual=", rel)
def template_care(self, hase, mf1, mf2):
"""template to reduce code in the test cases"""
a = mf1(mmread(self.amtx_rail).tocsr())
b = mmread(self.bmtx_rail).todense()
e = mf2(mmread(self.emtx_rail).tocsr()) if hase else None
c = mmread(self.cmtx_rail).todense()
#if e is not None:
# print("a={0:s} e={1:s} b={2:s} c={3:s}".format(type(a), type(e), type(b), type(c)))
#else:
# print("a={0:s} b={1:s} c={2:s}".format(type(a), type(b), type(c)))
z = pymess.care(a, e, b, c)
nrmr, nrmrhs, relnrm = res2_ric(a, e, b, c, z, MESS_OP_TRANSPOSE)
print("res2 = {0:e}\t rel = {1:e}\t res2/rel = {2:e}".format(
nrmr, nrmrhs, relnrm))
self.assertLessEqual(relnrm, self.tol)