def compare_to_benchmark(self):
""" Are we comparing to a benchmark? """
basename = self.rp.get_param("io.basename")
compare_file = "{}/tests/{}{:04d}".format(self.solver_name, basename,
self.sim.n)
msg.warning("comparing to: {} ".format(compare_file))
try:
sim_bench = io.read(compare_file)
except IOError:
msg.warning("ERROR openning compare file")
return "ERROR openning compare file"
result = compare.compare(self.sim.cc_data, sim_bench.cc_data)
if result == 0:
msg.success("results match benchmark\n")
else:
msg.warning("ERROR: " + compare.errors[result] + "\n")
return result
def compare_to_benchmark(self, rtol):
""" Are we comparing to a benchmark? """
basename = self.rp.get_param("io.basename")
compare_file = "{}/tests/{}{:04d}".format(
self.solver_name, basename, self.sim.n)
msg.warning("comparing to: {} ".format(compare_file))
try:
sim_bench = io.read(compare_file)
except IOError:
msg.warning("ERROR opening compare file")
return "ERROR opening compare file"
result = compare.compare(self.sim.cc_data, sim_bench.cc_data, rtol)
if result == 0:
msg.success("results match benchmark to within relative tolerance of {}\n".format(rtol))
else:
msg.warning("ERROR: " + compare.errors[result] + "\n")
return result
def test_general_poisson_inhomogeneous(N, store_bench=False, comp_bench=False,
make_plot=False, verbose=1):
"""
test the general MG solver. The return value
here is the error compared to the exact solution, UNLESS
comp_bench=True, in which case the return value is the
error compared to the stored benchmark
"""
# test the multigrid solver
nx = N
ny = nx
# create the coefficient variable
g = patch.Grid2d(nx, ny, ng=1)
d = patch.CellCenterData2d(g)
bc_c = patch.BCObject(xlb="neumann", xrb="neumann",
ylb="neumann", yrb="neumann")
d.register_var("alpha", bc_c)
d.register_var("beta", bc_c)
d.register_var("gamma_x", bc_c)
d.register_var("gamma_y", bc_c)
d.create()
a = d.get_var("alpha")
a[:,:] = alpha(g.x2d, g.y2d)
b = d.get_var("beta")
b[:,:] = beta(g.x2d, g.y2d)
gx = d.get_var("gamma_x")
gx[:,:] = gamma_x(g.x2d, g.y2d)
gy = d.get_var("gamma_y")
gy[:,:] = gamma_y(g.x2d, g.y2d)
# create the multigrid object
a = MG.GeneralMG2d(nx, ny,
xl_BC_type="dirichlet", yl_BC_type="dirichlet",
xr_BC_type="dirichlet", yr_BC_type="dirichlet",
xl_BC=xl_func,
yl_BC=yl_func,
coeffs=d,
verbose=verbose, vis=0, true_function=true)
# initialize the solution to 0
a.init_zeros()
# initialize the RHS using the function f
rhs = f(a.x2d, a.y2d)
print( np.min(rhs), np.max(rhs))
a.init_RHS(rhs)
# solve to a relative tolerance of 1.e-10
a.solve(rtol=1.e-10)
# alternately, we can just use smoothing by uncommenting the following
#a.smooth(a.nlevels-1,50000)
# get the solution
v = a.get_solution()
# compute the error from the analytic solution
b = true(a.x2d,a.y2d)
e = v - b
enorm = a.soln_grid.norm(e)
print(" L2 error from true solution = %g\n rel. err from previous cycle = %g\n num. cycles = %d" % \
(enorm, a.relative_error, a.num_cycles))
# plot the solution
if make_plot:
plt.clf()
plt.figure(figsize=(10.0,4.0), dpi=100, facecolor='w')
plt.subplot(121)
plt.imshow(np.transpose(v[a.ilo:a.ihi+1,a.jlo:a.jhi+1]),
interpolation="nearest", origin="lower",
extent=[a.xmin, a.xmax, a.ymin, a.ymax])
plt.xlabel("x")
plt.ylabel("y")
plt.title("nx = {}".format(nx))
plt.colorbar()
plt.subplot(122)
plt.imshow(np.transpose(e[a.ilo:a.ihi+1,a.jlo:a.jhi+1]),
interpolation="nearest", origin="lower",
extent=[a.xmin, a.xmax, a.ymin, a.ymax])
plt.xlabel("x")
plt.ylabel("y")
plt.title("error")
plt.colorbar()
plt.tight_layout()
plt.savefig("mg_general_inhomogeneous_test.png")
# store the output for later comparison
bench = "mg_general_poisson_inhomogeneous"
bench_dir = os.environ["PYRO_HOME"] + "/multigrid/tests/"
my_data = a.get_solution_object()
if store_bench:
my_data.write("{}/{}".format(bench_dir, bench))
# do we do a comparison?
if comp_bench:
compare_file = "{}/{}".format(bench_dir, bench)
msg.warning("comparing to: %s " % (compare_file) )
bench_grid, bench_data = patch.read(compare_file)
result = compare.compare(my_data.grid, my_data,
bench_grid, bench_data)
if result == 0:
msg.success("results match benchmark\n")
else:
msg.warning("ERROR: " + compare.errors[result] + "\n")
return result
# normal return -- error wrt true solution
return enorm
def test_general_poisson_dirichlet(N,
store_bench=False,
comp_bench=False,
make_plot=False,
verbose=1):
"""
test the general MG solver. The return value
here is the error compared to the exact solution, UNLESS
comp_bench=True, in which case the return value is the
error compared to the stored benchmark
"""
# test the multigrid solver
nx = N
ny = nx
# create the coefficient variable
g = patch.Grid2d(nx, ny, ng=1)
d = patch.CellCenterData2d(g)
bc_c = bnd.BC(xlb="neumann", xrb="neumann", ylb="neumann", yrb="neumann")
d.register_var("alpha", bc_c)
d.register_var("beta", bc_c)
d.register_var("gamma_x", bc_c)
d.register_var("gamma_y", bc_c)
d.create()
a = d.get_var("alpha")
a[:, :] = alpha(g.x2d, g.y2d)
b = d.get_var("beta")
b[:, :] = beta(g.x2d, g.y2d)
gx = d.get_var("gamma_x")
gx[:, :] = gamma_x(g.x2d, g.y2d)
gy = d.get_var("gamma_y")
gy[:, :] = gamma_y(g.x2d, g.y2d)
# create the multigrid object
a = MG.GeneralMG2d(nx,
ny,
xl_BC_type="dirichlet",
yl_BC_type="dirichlet",
xr_BC_type="dirichlet",
yr_BC_type="dirichlet",
coeffs=d,
verbose=verbose,
vis=0,
true_function=true)
# initialize the solution to 0
a.init_zeros()
# initialize the RHS using the function f
rhs = f(a.x2d, a.y2d)
a.init_RHS(rhs)
# solve to a relative tolerance of 1.e-11
a.solve(rtol=1.e-11)
# alternately, we can just use smoothing by uncommenting the following
# a.smooth(a.nlevels-1,50000)
# get the solution
v = a.get_solution()
# compute the error from the analytic solution
b = true(a.x2d, a.y2d)
e = v - b
enorm = e.norm()
print(
" L2 error from true solution = %g\n rel. err from previous cycle = %g\n num. cycles = %d"
% (enorm, a.relative_error, a.num_cycles))
# plot the solution
if make_plot:
plt.clf()
plt.figure(figsize=(10.0, 4.0), dpi=100, facecolor='w')
plt.subplot(121)
plt.imshow(np.transpose(v.v()),
interpolation="nearest",
origin="lower",
extent=[a.xmin, a.xmax, a.ymin, a.ymax])
plt.xlabel("x")
plt.ylabel("y")
plt.title("nx = {}".format(nx))
plt.colorbar()
plt.subplot(122)
plt.imshow(np.transpose(e.v()),
interpolation="nearest",
origin="lower",
extent=[a.xmin, a.xmax, a.ymin, a.ymax])
plt.xlabel("x")
plt.ylabel("y")
plt.title("error")
plt.colorbar()
plt.tight_layout()
plt.savefig("mg_general_dirichlet_test.png")
# store the output for later comparison
bench = "mg_general_poisson_dirichlet"
bench_dir = os.environ["PYRO_HOME"] + "/multigrid/tests/"
my_data = a.get_solution_object()
if store_bench:
my_data.write("{}/{}".format(bench_dir, bench))
# do we do a comparison?
if comp_bench:
compare_file = "{}/{}".format(bench_dir, bench)
msg.warning("comparing to: %s " % (compare_file))
bench = io.read(compare_file)
result = compare.compare(my_data, bench)
if result == 0:
msg.success("results match benchmark\n")
else:
msg.warning("ERROR: " + compare.errors[result] + "\n")
return result
# normal return -- error wrt true solution
return enorm
def doit(solver_name, problem_name, param_file,
other_commands=None,
comp_bench=False, make_bench=False):
msg.bold('pyro ...')
tc = profile.TimerCollection()
tm_main = tc.timer("main")
tm_main.begin()
# import desired solver under "solver" namespace
solver = importlib.import_module(solver_name)
#-------------------------------------------------------------------------
# runtime parameters
#-------------------------------------------------------------------------
# parameter defaults
rp = runparams.RuntimeParameters()
rp.load_params("_defaults")
rp.load_params(solver_name + "/_defaults")
# problem-specific runtime parameters
rp.load_params(solver_name + "/problems/_" + problem_name + ".defaults")
# now read in the inputs file
if not os.path.isfile(param_file):
# check if the param file lives in the solver's problems directory
param_file = solver_name + "/problems/" + param_file
if not os.path.isfile(param_file):
msg.fail("ERROR: inputs file does not exist")
rp.load_params(param_file, no_new=1)
# and any commandline overrides
if not other_commands == None:
rp.command_line_params(other_commands)
# write out the inputs.auto
rp.print_paramfile()
#-------------------------------------------------------------------------
# initialization
#-------------------------------------------------------------------------
# initialize the Simulation object -- this will hold the grid and
# data and know about the runtime parameters and which problem we
# are running
sim = solver.Simulation(solver_name, problem_name, rp, timers=tc)
sim.initialize()
sim.preevolve()
#-------------------------------------------------------------------------
# evolve
#-------------------------------------------------------------------------
init_tstep_factor = rp.get_param("driver.init_tstep_factor")
max_dt_change = rp.get_param("driver.max_dt_change")
fix_dt = rp.get_param("driver.fix_dt")
verbose = rp.get_param("driver.verbose")
plt.ion()
sim.cc_data.t = 0.0
# output the 0th data
basename = rp.get_param("io.basename")
sim.cc_data.write("{}{:04d}".format(basename, sim.n))
dovis = rp.get_param("vis.dovis")
if dovis:
plt.figure(num=1, figsize=(8,6), dpi=100, facecolor='w')
sim.dovis()
while not sim.finished():
# fill boundary conditions
sim.cc_data.fill_BC_all()
# get the timestep
if fix_dt > 0.0:
sim.dt = fix_dt
else:
sim.compute_timestep()
if sim.n == 0:
sim.dt = init_tstep_factor*sim.dt
else:
sim.dt = min(max_dt_change*dt_old, sim.dt)
dt_old = sim.dt
if sim.cc_data.t + sim.dt > sim.tmax:
sim.dt = sim.tmax - sim.cc_data.t
# evolve for a single timestep
sim.evolve()
if verbose > 0: print("%5d %10.5f %10.5f" % (sim.n, sim.cc_data.t, sim.dt))
# output
if sim.do_output():
if verbose > 0: msg.warning("outputting...")
basename = rp.get_param("io.basename")
sim.cc_data.write("{}{:04d}".format(basename, sim.n))
# visualization
if dovis:
tm_vis = tc.timer("vis")
tm_vis.begin()
sim.dovis()
store = rp.get_param("vis.store_images")
if store == 1:
basename = rp.get_param("io.basename")
plt.savefig("{}{:04d}.png".format(basename, sim.n))
tm_vis.end()
tm_main.end()
#-------------------------------------------------------------------------
# benchmarks (for regression testing)
#-------------------------------------------------------------------------
# are we comparing to a benchmark?
if comp_bench:
compare_file = solver_name + "/tests/" + basename + "%4.4d" % (sim.n)
msg.warning("comparing to: %s " % (compare_file) )
try: bench_grid, bench_data = patch.read(compare_file)
except:
msg.warning("ERROR openning compare file")
return "ERROR openning compare file"
result = compare.compare(sim.cc_data.grid, sim.cc_data, bench_grid, bench_data)
if result == 0:
msg.success("results match benchmark\n")
else:
msg.warning("ERROR: " + compare.errors[result] + "\n")
# are we storing a benchmark?
if make_bench:
if not os.path.isdir(solver_name + "/tests/"):
try: os.mkdir(solver_name + "/tests/")
except:
msg.fail("ERROR: unable to create the solver's tests/ directory")
bench_file = solver_name + "/tests/" + basename + "%4.4d" % (sim.n)
msg.warning("storing new benchmark: {}\n".format(bench_file))
sim.cc_data.write(bench_file)
#-------------------------------------------------------------------------
# final reports
#-------------------------------------------------------------------------
if verbose > 0: rp.print_unused_params()
if verbose > 0: tc.report()
sim.finalize()
if comp_bench:
return result
else:
return None
def test_poisson_dirichlet(N,
store_bench=False,
comp_bench=False,
make_plot=False,
verbose=1):
# test the multigrid solver
nx = N
ny = nx
# create the multigrid object
a = MG.CellCenterMG2d(nx,
ny,
xl_BC_type="dirichlet",
yl_BC_type="dirichlet",
xr_BC_type="dirichlet",
yr_BC_type="dirichlet",
verbose=verbose)
# initialize the solution to 0
a.init_zeros()
# initialize the RHS using the function f
rhs = f(a.x2d, a.y2d)
a.init_RHS(rhs)
# solve to a relative tolerance of 1.e-11
a.solve(rtol=1.e-11)
# alternately, we can just use smoothing by uncommenting the following
#a.smooth(a.nlevels-1,50000)
# get the solution
v = a.get_solution()
# compute the error from the analytic solution
b = true(a.x2d, a.y2d)
e = v - b
print(" L2 error from true solution = %g\n rel. err from previous cycle = %g\n num. cycles = %d" % \
(e.norm(), a.relative_error, a.num_cycles))
# plot it
if make_plot:
plt.figure(num=1, figsize=(5.0, 5.0), dpi=100, facecolor='w')
plt.imshow(np.transpose(v[a.ilo:a.ihi + 1, a.jlo:a.jhi + 1]),
interpolation="nearest",
origin="lower",
extent=[a.xmin, a.xmax, a.ymin, a.ymax])
plt.xlabel("x")
plt.ylabel("y")
plt.savefig("mg_test.png")
# store the output for later comparison
bench = "mg_poisson_dirichlet"
bench_dir = os.environ["PYRO_HOME"] + "/multigrid/tests/"
my_data = a.get_solution_object()
if store_bench:
my_data.write("{}/{}".format(bench_dir, bench))
# do we do a comparison?
if comp_bench:
compare_file = "{}/{}".format(bench_dir, bench)
msg.warning("comparing to: %s " % (compare_file))
bench_grid, bench_data = patch.read(compare_file)
result = compare.compare(my_data.grid, my_data, bench_grid, bench_data)
if result == 0:
msg.success("results match benchmark\n")
else:
msg.warning("ERROR: " + compare.errors[result] + "\n")
return result
return None
def doit(solver_name, problem_name, param_file,
other_commands=None,
comp_bench=False, reset_bench_on_fail=False, make_bench=False):
"""The main driver to run pyro"""
msg.bold('pyro ...')
tc = profile.TimerCollection()
tm_main = tc.timer("main")
tm_main.begin()
# import desired solver under "solver" namespace
solver = importlib.import_module(solver_name)
#-------------------------------------------------------------------------
# runtime parameters
#-------------------------------------------------------------------------
# parameter defaults
rp = runparams.RuntimeParameters()
rp.load_params("_defaults")
rp.load_params(solver_name + "/_defaults")
# problem-specific runtime parameters
rp.load_params(solver_name + "/problems/_" + problem_name + ".defaults")
# now read in the inputs file
if not os.path.isfile(param_file):
# check if the param file lives in the solver's problems directory
param_file = solver_name + "/problems/" + param_file
if not os.path.isfile(param_file):
msg.fail("ERROR: inputs file does not exist")
rp.load_params(param_file, no_new=1)
# and any commandline overrides
if other_commands is not None:
rp.command_line_params(other_commands)
# write out the inputs.auto
rp.print_paramfile()
#-------------------------------------------------------------------------
# initialization
#-------------------------------------------------------------------------
# initialize the Simulation object -- this will hold the grid and
# data and know about the runtime parameters and which problem we
# are running
sim = solver.Simulation(solver_name, problem_name, rp, timers=tc)
sim.initialize()
sim.preevolve()
#-------------------------------------------------------------------------
# evolve
#-------------------------------------------------------------------------
verbose = rp.get_param("driver.verbose")
plt.ion()
sim.cc_data.t = 0.0
# output the 0th data
basename = rp.get_param("io.basename")
sim.write("{}{:04d}".format(basename, sim.n))
dovis = rp.get_param("vis.dovis")
if dovis:
plt.figure(num=1, figsize=(8, 6), dpi=100, facecolor='w')
sim.dovis()
while not sim.finished():
# fill boundary conditions
sim.cc_data.fill_BC_all()
# get the timestep
sim.compute_timestep()
# evolve for a single timestep
sim.evolve()
if verbose > 0:
print("%5d %10.5f %10.5f" % (sim.n, sim.cc_data.t, sim.dt))
# output
if sim.do_output():
if verbose > 0:
msg.warning("outputting...")
basename = rp.get_param("io.basename")
sim.write("{}{:04d}".format(basename, sim.n))
# visualization
if dovis:
tm_vis = tc.timer("vis")
tm_vis.begin()
sim.dovis()
store = rp.get_param("vis.store_images")
if store == 1:
basename = rp.get_param("io.basename")
plt.savefig("{}{:04d}.png".format(basename, sim.n))
tm_vis.end()
# final output
if verbose > 0:
msg.warning("outputting...")
basename = rp.get_param("io.basename")
sim.write("{}{:04d}".format(basename, sim.n))
tm_main.end()
#-------------------------------------------------------------------------
# benchmarks (for regression testing)
#-------------------------------------------------------------------------
result = 0
# are we comparing to a benchmark?
if comp_bench:
compare_file = "{}/tests/{}{:04d}".format(
solver_name, basename, sim.n)
msg.warning("comparing to: {} ".format(compare_file))
try:
sim_bench = io.read(compare_file)
except:
msg.warning("ERROR openning compare file")
return "ERROR openning compare file"
result = compare.compare(sim.cc_data, sim_bench.cc_data)
if result == 0:
msg.success("results match benchmark\n")
else:
msg.warning("ERROR: " + compare.errors[result] + "\n")
# are we storing a benchmark?
if make_bench or (result != 0 and reset_bench_on_fail):
if not os.path.isdir(solver_name + "/tests/"):
try:
os.mkdir(solver_name + "/tests/")
except:
msg.fail("ERROR: unable to create the solver's tests/ directory")
bench_file = solver_name + "/tests/" + basename + "%4.4d" % (sim.n)
msg.warning("storing new benchmark: {}\n".format(bench_file))
sim.write(bench_file)
#-------------------------------------------------------------------------
# final reports
#-------------------------------------------------------------------------
if verbose > 0:
rp.print_unused_params()
tc.report()
sim.finalize()
if comp_bench:
return result
tm_main.end()
#-----------------------------------------------------------------------------
# benchmarks (for regression testing)
#-----------------------------------------------------------------------------
# are we comparing to a benchmark?
if comp_bench:
compare_file = solver_name + "/tests/" + basename + "%4.4d" % (n)
msg.warning("comparing to: %s " % (compare_file) )
bench_grid, bench_data = patch.read(compare_file)
result = compare.compare(sim.cc_data.grid, sim.cc_data, bench_grid, bench_data)
if result == 0:
msg.success("results match benchmark\n")
else:
msg.fail("ERROR: " + compare.errors[result] + "\n")
# are we storing a benchmark?
if make_bench:
bench_file = solver_name + "/tests/" + basename + "%4.4d" % (n)
msg.warning("storing new benchmark: %s\n " % (bench_file) )
sim.cc_data.write(bench_file)
#-----------------------------------------------------------------------------
# final reports
#-----------------------------------------------------------------------------
rp.print_unused_params()
def test_vc_poisson_periodic(N,
store_bench=False,
comp_bench=False,
make_plot=False,
verbose=1):
"""
test the variable-coefficient MG solver. The return value
here is the error compared to the exact solution, UNLESS
comp_bench=True, in which case the return value is the
error compared to the stored benchmark
"""
# test the multigrid solver
nx = N
ny = nx
# create the coefficient variable
g = patch.Grid2d(nx, ny, ng=1)
d = patch.CellCenterData2d(g)
bc_c = bnd.BC(xlb="periodic",
xrb="periodic",
ylb="periodic",
yrb="periodic")
d.register_var("c", bc_c)
d.create()
c = d.get_var("c")
c[:, :] = alpha(g.x2d, g.y2d)
# check whether the RHS sums to zero (necessary for periodic data)
rhs = f(g.x2d, g.y2d)
print("rhs sum: {}".format(np.sum(rhs[g.ilo:g.ihi + 1, g.jlo:g.jhi + 1])))
# create the multigrid object
a = MG.VarCoeffCCMG2d(nx,
ny,
xl_BC_type="periodic",
yl_BC_type="periodic",
xr_BC_type="periodic",
yr_BC_type="periodic",
coeffs=c,
coeffs_bc=bc_c,
verbose=verbose,
vis=0,
true_function=true)
# initialize the solution to 0
a.init_zeros()
# initialize the RHS using the function f
rhs = f(a.x2d, a.y2d)
a.init_RHS(rhs)
# solve to a relative tolerance of 1.e-11
a.solve(rtol=1.e-11)
# alternately, we can just use smoothing by uncommenting the following
#a.smooth(a.nlevels-1,10000)
# get the solution
v = a.get_solution()
# get the true solution
b = true(a.x2d, a.y2d)
# compute the error from the analytic solution -- note that with
# periodic BCs all around, there is nothing to normalize the
# solution. We subtract off the average of phi from the MG
# solution (we do the same for the true solution to put them on
# the same footing)
e = v - np.sum(v.v()) / (nx * ny) - (
b - np.sum(b[a.ilo:a.ihi + 1, a.jlo:a.jhi + 1]) / (nx * ny))
enorm = e.norm()
print(" L2 error from true solution = %g\n rel. err from previous cycle = %g\n num. cycles = %d" % \
(enorm, a.relative_error, a.num_cycles))
# plot the solution
if make_plot:
plt.clf()
plt.figure(figsize=(10.0, 4.0), dpi=100, facecolor='w')
plt.subplot(121)
plt.imshow(np.transpose(v.v()),
interpolation="nearest",
origin="lower",
extent=[a.xmin, a.xmax, a.ymin, a.ymax])
plt.xlabel("x")
plt.ylabel("y")
plt.title("nx = {}".format(nx))
plt.colorbar()
plt.subplot(122)
plt.imshow(np.transpose(e.v()),
interpolation="nearest",
origin="lower",
extent=[a.xmin, a.xmax, a.ymin, a.ymax])
plt.xlabel("x")
plt.ylabel("y")
plt.title("error")
plt.colorbar()
plt.tight_layout()
plt.savefig("mg_vc_periodic_test.png")
# store the output for later comparison
bench = "mg_vc_poisson_periodic"
bench_dir = os.environ["PYRO_HOME"] + "/multigrid/tests/"
my_data = a.get_solution_object()
if store_bench:
my_data.write("{}/{}".format(bench_dir, bench))
# do we do a comparison?
if comp_bench:
compare_file = "{}/{}".format(bench_dir, bench)
msg.warning("comparing to {}".format(compare_file))
bench_grid, bench_data = patch.read(compare_file)
result = compare.compare(my_data.grid, my_data, bench_grid, bench_data)
if result == 0:
msg.success("results match benchmark\n")
else:
msg.warning("ERROR: {}\n".format(compare.errors[result]))
return result
# normal return -- error wrt true solution
return enorm
def test_poisson_dirichlet(N, store_bench=False, comp_bench=False,
make_plot=False, verbose=1):
# test the multigrid solver
nx = N
ny = nx
# create the multigrid object
a = MG.CellCenterMG2d(nx, ny,
xl_BC_type="dirichlet", yl_BC_type="dirichlet",
xr_BC_type="dirichlet", yr_BC_type="dirichlet",
verbose=verbose)
# initialize the solution to 0
a.init_zeros()
# initialize the RHS using the function f
rhs = f(a.x2d, a.y2d)
a.init_RHS(rhs)
# solve to a relative tolerance of 1.e-11
a.solve(rtol=1.e-11)
# alternately, we can just use smoothing by uncommenting the following
#a.smooth(a.nlevels-1,50000)
# get the solution
v = a.get_solution()
# compute the error from the analytic solution
b = true(a.x2d,a.y2d)
e = v - b
print(" L2 error from true solution = %g\n rel. err from previous cycle = %g\n num. cycles = %d" % \
(a.soln_grid.norm(e), a.relative_error, a.num_cycles))
# plot it
if make_plot:
plt.figure(num=1, figsize=(5.0,5.0), dpi=100, facecolor='w')
plt.imshow(np.transpose(v[a.ilo:a.ihi+1,a.jlo:a.jhi+1]),
interpolation="nearest", origin="lower",
extent=[a.xmin, a.xmax, a.ymin, a.ymax])
plt.xlabel("x")
plt.ylabel("y")
plt.savefig("mg_test.png")
# store the output for later comparison
bench = "mg_poisson_dirichlet"
bench_dir = os.environ["PYRO_HOME"] + "/multigrid/tests/"
my_data = a.get_solution_object()
if store_bench:
my_data.write("{}/{}".format(bench_dir, bench))
# do we do a comparison?
if comp_bench:
compare_file = "{}/{}".format(bench_dir, bench)
msg.warning("comparing to: %s " % (compare_file) )
bench_grid, bench_data = patch.read(compare_file)
result = compare.compare(my_data.grid, my_data, bench_grid, bench_data)
if result == 0:
msg.success("results match benchmark\n")
else:
msg.warning("ERROR: " + compare.errors[result] + "\n")
return result
return None
def test_vc_poisson_periodic(N, store_bench=False, comp_bench=False,
make_plot=False, verbose=1):
"""
test the variable-coefficient MG solver. The return value
here is the error compared to the exact solution, UNLESS
comp_bench=True, in which case the return value is the
error compared to the stored benchmark
"""
# test the multigrid solver
nx = N
ny = nx
# create the coefficient variable
g = patch.Grid2d(nx, ny, ng=1)
d = patch.CellCenterData2d(g)
bc_c = patch.BCObject(xlb="periodic", xrb="periodic",
ylb="periodic", yrb="periodic")
d.register_var("c", bc_c)
d.create()
c = d.get_var("c")
c[:,:] = alpha(g.x2d, g.y2d)
# check whether the RHS sums to zero (necessary for periodic data)
rhs = f(g.x2d, g.y2d)
print("rhs sum: {}".format(np.sum(rhs[g.ilo:g.ihi+1,g.jlo:g.jhi+1])))
# create the multigrid object
a = MG.VarCoeffCCMG2d(nx, ny,
xl_BC_type="periodic", yl_BC_type="periodic",
xr_BC_type="periodic", yr_BC_type="periodic",
coeffs=c, coeffs_bc=bc_c,
verbose=verbose, vis=0, true_function=true)
# initialize the solution to 0
a.init_zeros()
# initialize the RHS using the function f
rhs = f(a.x2d, a.y2d)
a.init_RHS(rhs)
# solve to a relative tolerance of 1.e-11
a.solve(rtol=1.e-11)
# alternately, we can just use smoothing by uncommenting the following
#a.smooth(a.nlevels-1,10000)
# get the solution
v = a.get_solution()
# get the true solution
b = true(a.x2d,a.y2d)
# compute the error from the analytic solution -- note that with
# periodic BCs all around, there is nothing to normalize the
# solution. We subtract off the average of phi from the MG
# solution (we do the same for the true solution to put them on
# the same footing)
e = v - np.sum(v[a.ilo:a.ihi+1,a.jlo:a.jhi+1])/(nx*ny) - (b - np.sum(b[a.ilo:a.ihi+1,a.jlo:a.jhi+1])/(nx*ny))
enorm = a.soln_grid.norm(e)
print(" L2 error from true solution = %g\n rel. err from previous cycle = %g\n num. cycles = %d" % \
(enorm, a.relative_error, a.num_cycles))
# plot the solution
if make_plot:
plt.clf()
plt.figure(figsize=(10.0,4.0), dpi=100, facecolor='w')
plt.subplot(121)
plt.imshow(np.transpose(v[a.ilo:a.ihi+1,a.jlo:a.jhi+1]),
interpolation="nearest", origin="lower",
extent=[a.xmin, a.xmax, a.ymin, a.ymax])
plt.xlabel("x")
plt.ylabel("y")
plt.title("nx = {}".format(nx))
plt.colorbar()
plt.subplot(122)
plt.imshow(np.transpose(e[a.ilo:a.ihi+1,a.jlo:a.jhi+1]),
interpolation="nearest", origin="lower",
extent=[a.xmin, a.xmax, a.ymin, a.ymax])
plt.xlabel("x")
plt.ylabel("y")
plt.title("error")
plt.colorbar()
plt.tight_layout()
plt.savefig("mg_vc_periodic_test.png")
# store the output for later comparison
bench = "mg_vc_poisson_periodic"
bench_dir = os.environ["PYRO_HOME"] + "/multigrid/tests/"
my_data = a.get_solution_object()
if store_bench:
my_data.write("{}/{}".format(bench_dir, bench))
# do we do a comparison?
if comp_bench:
compare_file = "{}/{}".format(bench_dir, bench)
msg.warning("comparing to {}".format(compare_file))
bench_grid, bench_data = patch.read(compare_file)
result = compare.compare(my_data.grid, my_data,
bench_grid, bench_data)
if result == 0:
msg.success("results match benchmark\n")
else:
msg.warning("ERROR: {}\n".format(compare.errors[result]))
return result
# normal return -- error wrt true solution
return enorm
pf.end()
#-----------------------------------------------------------------------------
# benchmarks (for regression testing)
#-----------------------------------------------------------------------------
# are we comparing to a benchmark?
if comp_bench:
compare_file = solverName + "/tests/" + basename + "%4.4d" % (n)
msg.warning("comparing to: %s " % (compare_file) )
bench_grid, bench_data = patch.read(compare_file)
result = compare.compare(my_grid, my_data, bench_grid, bench_data)
if result == 0:
msg.success("results match benchmark\n")
else:
msg.fail("ERROR: " + compare.errors[result] + "\n")
# are we storing a benchmark?
if make_bench:
bench_file = solverName + "/tests/" + basename + "%4.4d" % (n)
msg.warning("storing new benchmark: %s\n " % (bench_file) )
my_data.write(bench_file)
#-----------------------------------------------------------------------------
# final reports
#-----------------------------------------------------------------------------
rp.print_unused_params()