def makeplot(plotfile, variable, outfile):
myg, myd = patch.read(plotfile)
if variable == "vort":
vx = myd.get_var("x-velocity")
vy = myd.get_var("y-velocity")
v = myg.scratch_array()
v[myg.ilo:myg.ihi+1,myg.jlo:myg.jhi+1] = \
0.5*(vy[myg.ilo+1:myg.ihi+2,myg.jlo:myg.jhi+1] -
vy[myg.ilo-1:myg.ihi,myg.jlo:myg.jhi+1])/myg.dx - \
0.5*(vx[myg.ilo:myg.ihi+1,myg.jlo+1:myg.jhi+2] -
vx[myg.ilo:myg.ihi+1,myg.jlo-1:myg.jhi])/myg.dy
else:
v = myd.get_var(variable)
plt.figure(num=1, figsize=(6.0, 6.0), dpi=100, facecolor='w')
plt.imshow(np.transpose(v[myg.ilo:myg.ihi + 1, myg.jlo:myg.jhi + 1]),
interpolation="nearest",
origin="lower",
extent=[myg.xmin, myg.xmax, myg.ymin, myg.ymax])
plt.axis("off")
plt.subplots_adjust(bottom=0.0, top=1.0, left=0.0, right=1.0)
plt.savefig(outfile)
def makeplot(plotfile_name, solver_name, outfile, width, height):
""" plot the data in a plotfile using the solver's vis() method """
_, myd = patch.read(plotfile_name)
solver = importlib.import_module(solver_name)
sim = solver.Simulation(solver_name, None, None)
sim.cc_data = myd
plt.figure(num=1, figsize=(width, height), dpi=100, facecolor='w')
sim.dovis()
if outfile.endswith(".pdf"):
plt.savefig(outfile, bbox_inches="tight")
else:
plt.savefig(outfile)
plt.show()
def makeplot(plotfile, variable, outfile):
myg, myd = patch.read(plotfile)
plt.figure(num=1, figsize=(6.5, 5.25), dpi=100, facecolor='w')
var = myd.get_var(variable)
img = plt.imshow(np.transpose(var.v()),
interpolation="nearest",
origin="lower",
extent=[myg.xmin, myg.xmax, myg.ymin, myg.ymax])
plt.colorbar()
plt.xlabel("x")
plt.ylabel("y")
plt.savefig(outfile, bbox_inches="tight")
plt.show()
optional arguments:
-h, --help show this help message and exit
-o image.png output image name. The extension .png will generate a PNG
file, .eps will generate an EPS file (default: plot.png).
"""
print usage
sys.exit()
if __name__== "__main__":
try: opts, next = getopt.getopt(sys.argv[1:], "o:h")
except getopt.GetoptError:
sys.exit("invalid calling sequence")
outfile = "plot.png"
for o, a in opts:
if o == "-h": usage()
if o == "-o": outfile = a
try: file = next[0]
except: usage()
try: variable = next[1]
except: usage()
myg, myd = patch.read(file)
makeplot(myd, variable, outfile)
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 test_vc_poisson_dirichlet(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="neumann",
xrb="neumann",
ylb="neumann",
yrb="neumann")
d.register_var("c", bc_c)
d.create()
c = d.get_var("c")
c.d[:, :] = alpha(g.x2d, g.y2d)
# create the multigrid object
a = MG.VarCoeffCCMG2d(nx,
ny,
xl_BC_type="dirichlet",
yl_BC_type="dirichlet",
xr_BC_type="dirichlet",
yr_BC_type="dirichlet",
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-1,50000)
# 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_vc_dirichlet_test.png")
# store the output for later comparison
bench = "mg_vc_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
# normal return -- error wrt true solution
return enorm
basename = rp.get_param("io.basename")
pylab.savefig(basename + "%4.4d" % (n) + ".png")
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" % (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)
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_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
if not len(sys.argv) == 3:
print usage
sys.exit(2)
try: file1 = sys.argv[1]
except:
print usage
sys.exit(2)
try: file2 = sys.argv[2]
except:
print usage
sys.exit(2)
myg, myd = patch.read(file1)
myg2, myd2 = patch.read(file2)
U_analytic = myg2.scratch_array()
U_numerical = myg.scratch_array()
# compute total velocity from myd
px = myd.get_var("x-momentum")
py = myd.get_var("y-momentum")
density = myd.get_var("density")
u = px/density
v = py/density
px2 = myd2.get_var("x-momentum")
def process(file):
# read the data and convert to the primitive variables (and velocity
# magnitude)
myg, myd = patch.read(file)
phi_t = myd.get_var("phi")
phi = phi_t[myg.ilo:myg.ihi + 1, myg.jlo:myg.jhi + 1]
# get the problem parameters
t_0 = myd.get_aux("t_0")
phi_0 = myd.get_aux("phi_0")
phi_max = myd.get_aux("phi_max")
k = myd.get_aux("k")
t = myd.t
# radially bin
# see http://code.google.com/p/agpy/source/browse/trunk/agpy/radialprofile.py?r=317
# for inspiration
# first define the bins
rmin = 0
rmax = np.sqrt(myg.xmax**2 + myg.ymax**2)
nbins = np.int(np.sqrt(myg.nx**2 + myg.ny**2))
# bins holds the edges, so there is one more value than actual bin
# bin_centers holds the center value of the bin
bins = np.linspace(rmin, rmax, nbins + 1)
bin_centers = 0.5 * (bins[1:] + bins[:-1])
# radius of each zone
xcenter = 0.5 * (myg.xmin + myg.xmax)
ycenter = 0.5 * (myg.ymin + myg.ymax)
r = np.sqrt(
(myg.x2d[myg.ilo:myg.ihi + 1, myg.jlo:myg.jhi + 1] - xcenter)**2 +
(myg.y2d[myg.ilo:myg.ihi + 1, myg.jlo:myg.jhi + 1] - ycenter)**2)
# bin the radii -- digitize returns an array with the same shape
# as the input array but with elements of the array specifying
# which bin that location belongs to. The value of whichbin will
# be 1 if we are located in the bin defined by bins[0] to bins[1].
# This means that there will be no 0s
whichbin = np.digitize(r.flat, bins)
# bincount counts the number of occurrences of each non-negative
# integer value in whichbin. Each entry in ncount gives the
# number of occurrences of it in whichbin. The length of ncount
# is set by the maximum value in whichbin
ncount = np.bincount(whichbin)
# now bin the associated data
phi_bin = np.zeros(len(ncount) - 1, dtype=np.float64)
for n in range(ncount):
# remember that there are no whichbin == 0, since that
# corresponds to the left edge. So we want whichbin == 1 to
# correspond to the first value of bin_centers
# (bin_centers[0])
phi_bin[n - 1] = np.sum(phi.flat[whichbin == n]) / np.sum(ncount[n])
bin_centers = bin_centers[0:len(ncount) - 1]
# get the analytic solution
phi_exact = gaussian.phi_analytic(bin_centers, t, t_0, k, phi_0, phi_max)
return bin_centers, phi_exact, phi_bin
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
basename = rp.get_param("io.basename")
pylab.savefig(basename + "%4.4d" % (n) + ".png")
pfd.end()
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)
def compare(time,res=512,base='/Users/cgkim/Dropbox/pyro/data/',fileout=False):
if res == 512:
f1='vortex_e1_512%4.4d.pyro' % time
f0='vortex_e0_512%4.4d.pyro' % time
elif res == 256:
f1='vortex_e1_256_%4.4d.pyro' % time
f0='vortex_e0_256_%4.4d.pyro' % time
elif res == 128:
f1='vortex_e1_%4.4d.pyro' % time
f0='vortex_e0_%4.4d.pyro' % time
g1,d1 = patch.read(base+f1)
g0,d0 = patch.read(base+f0)
time=d1.t
w1,gwx1,gwy1 = get_vorticity(g1,d1)
w0,gwx0,gwy0 = get_vorticity(g0,d0)
dw=w1-w0
dgwx=gwx1-gwx0
dgwy=gwy1-gwy0
dgw=np.sqrt(dgwx**2+dgwy**2)
n1=g1.nx/4
n2=g1.nx/4*3
# print dgw.shape
plt.clf()
y2d=g1.y2d[g1.ilo:g1.ihi+1,g1.jlo:g1.jhi+1]
x2d=g1.x2d[g1.ilo:g1.ihi+1,g1.jlo:g1.jhi+1]
idx1=y2d < (-x2d+0.5+0.4*time)
idx2=y2d > (-x2d+1.5-0.4*time)
idx3=y2d > (+x2d+0.6*time)
idx4=y2d < (+x2d-2.0-0.6*time)
dgw[idx1]=0.
dgw[idx2]=0.
dgw[idx3]=0.
dgw[idx4]=0.
upper=y2d > -x2d
lower=y2d < -x2d
# x1,y1= x2d[upper][np.argmax(dgw[upper])],y2d[upper][np.argmax(dgw[upper])]
# x2,y2= x2d[lower][np.argmax(dgw[lower])],y2d[lower][np.argmax(dgw[lower])]
# print x1,y1,x2,y2
# print np.sqrt((x1-x2)**2+(y1-y2)**2),g1.dx
x1,y1= x2d.flatten()[np.argmax(dgw)],y2d.flatten()[np.argmax(dgw)]
nres=np.sqrt((x1-1.0)**2+(y1-0.0)**2)/g1.dx
im=plt.imshow(dgw.T,origin='lower',interpolation='nearest',
extent=[g1.xmin,g1.xmax,g1.ymin,g1.ymax],
norm=LogNorm(vmin=1.e-2,vmax=1.e2))
plt.plot(g1.xr,-g1.xr+0.5+0.4*time,ls=':',color='w')
plt.plot(g1.xr,-g1.xr+1.5-0.4*time,ls=':',color='w')
plt.plot(g1.xr,+g1.xr+0.6*time,ls=':',color='w')
plt.plot(g1.xr,+g1.xr-2.0-0.6*time,ls=':',color='w')
plt.xlim(0,2)
plt.ylim(-1,1)
plt.colorbar(im)
plt.scatter(x1,y1,marker='*')
plt.axhline(0,ls=':')
plt.axvline(1,ls=':')
norm=np.sum(dgw**2*g1.dx*g1.dy)
if fileout:
if time == 0.0:
fp=open('norm_%d.txt' % res,'w')
else:
fp=open('norm_%d.txt' % res,'a')
fp.write("%15.5e %15.5e %15.5e\n" % (time,norm,nres))
fp.close()
print time,norm,nres
return time,norm
def process(file):
# read the data and convert to the primitive variables (and velocity
# magnitude)
myg, myd = patch.read(file)
phi_t = myd.get_var("phi")
phi = phi_t[myg.ilo:myg.ihi+1,myg.jlo:myg.jhi+1]
# get the problem parameters
t_0 = myd.get_aux("t_0")
phi_0 = myd.get_aux("phi_0")
phi_max = myd.get_aux("phi_max")
k = myd.get_aux("k")
t = myd.t
# radially bin
# see http://code.google.com/p/agpy/source/browse/trunk/agpy/radialprofile.py?r=317
# for inspiration
# first define the bins
rmin = 0
rmax = np.sqrt(myg.xmax**2 + myg.ymax**2)
nbins = np.int(np.sqrt(myg.nx**2 + myg.ny**2))
# bins holds the edges, so there is one more value than actual bin
# bin_centers holds the center value of the bin
bins = np.linspace(rmin, rmax, nbins+1)
bin_centers = 0.5*(bins[1:] + bins[:-1])
# radius of each zone
xcenter = 0.5*(myg.xmin + myg.xmax)
ycenter = 0.5*(myg.ymin + myg.ymax)
r = np.sqrt( (myg.x2d[myg.ilo:myg.ihi+1,myg.jlo:myg.jhi+1] - xcenter)**2 +
(myg.y2d[myg.ilo:myg.ihi+1,myg.jlo:myg.jhi+1] - ycenter)**2 )
# bin the radii -- digitize returns an array with the same shape
# as the input array but with elements of the array specifying
# which bin that location belongs to. The value of whichbin will
# be 1 if we are located in the bin defined by bins[0] to bins[1].
# This means that there will be no 0s
whichbin = np.digitize(r.flat, bins)
# bincount counts the number of occurrences of each non-negative
# integer value in whichbin. Each entry in ncount gives the
# number of occurrences of it in whichbin. The length of ncount
# is set by the maximum value in whichbin
ncount = np.bincount(whichbin)
# now bin the associated data
phi_bin = np.zeros(len(ncount)-1, dtype=np.float64)
for n in range(ncount):
# remember that there are no whichbin == 0, since that
# corresponds to the left edge. So we want whichbin == 1 to
# correspond to the first value of bin_centers
# (bin_centers[0])
phi_bin[n-1] = np.sum(phi.flat[whichbin==n])/np.sum(ncount[n])
bin_centers = bin_centers[0:len(ncount)-1]
# get the analytic solution
phi_exact = gaussian.phi_analytic(bin_centers, t, t_0, k, phi_0, phi_max)
return bin_centers, phi_exact, phi_bin
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
print usage
sys.exit()
if __name__ == "__main__":
try:
opts, next = getopt.getopt(sys.argv[1:], "o:h:")
except getopt.GetoptError:
sys.exit("invalid calling sequence")
outfile = "plot.png"
for o, a in opts:
if o == "-h": usage()
if o == "-o": outfile = a
try:
var = next[0]
except:
usage()
try:
file = next[1]
except:
usage()
myg, myd = patch.read(file)
makeplot(myd, var, outfile)
def init_data(my_data, rp):
""" initialize the isothermal atmosphere problem """
msg.bold("initializing the isothermal atmosphere problem...")
# make sure that we are passed a valid patch object
if not isinstance(my_data, patch.CellCenterData2d):
print("ERROR: patch invalid in isothermal.py")
print(my_data.__class__)
sys.exit()
# get the density, momenta, and energy as separate variables
dens = my_data.get_var("density")
xmom = my_data.get_var("x-momentum")
ymom = my_data.get_var("y-momentum")
ener = my_data.get_var("energy")
gamma = rp.get_param("eos.gamma")
grav_const = rp.get_param("compressible.grav")
cs = rp.get_param("isothermal.cs")
eddington_ratio = rp.get_param("isothermal.eddington")
dens1 = rp.get_param("isothermal.dens1")
amp = rp.get_param("isothermal.amp")
nwaves = rp.get_param("isothermal.nwaves")
xmax = rp.get_param("mesh.xmax")
ymax = rp.get_param("mesh.ymax")
if grav_const != 0.0:
scale_height = cs*cs/numpy.abs(grav_const)
else:
scale_height = 0.1
print("scale height:",scale_height)
smallpres = 1.e-10
smalldens = smallpres/(cs**2)
# compute optical depth
kappa = 1.0
c = 1.0
column_density = dens1*scale_height*(1.0-numpy.exp(-ymax))
optical_depth = column_density*kappa
I_0 = (1./numpy.pi)*eddington_ratio*c*numpy.abs(grav_const) \
*column_density/(1.0-numpy.exp(-optical_depth))
my_data.set_aux("surface_brightness", I_0)
my_data.set_aux("speed_of_light", c)
my_data.set_aux("opacity",kappa)
print("optical depth:",optical_depth)
print("surface brightness:",I_0)
# compute Eddington ratio
rad_accel = (numpy.pi*I_0)*kappa/c* \
(1.0-numpy.exp(-optical_depth))/optical_depth \
# mass weighted flux (plane-parallel radiation, constant kappa)
net_accel = rad_accel + grav_const
eddington_ratio = rad_accel/numpy.abs(grav_const)
print("eddington_ratio:",eddington_ratio)
print("net accel:",net_accel)
# initialize the components, remember, that ener here is
# rho*eint + 0.5*rho*v**2, where eint is the specific
# internal energy (erg/g)
xmom.d[:,:] = 0.0
ymom.d[:,:] = 0.0
dens.d[:,:] = 0.0
if rp.get_param('restart.flag') != 0:
# reload simulation state from file
grid,cells = patch.read(rp.get_param('restart.snapshot'))
dens.d[:,:] = cells.get_var('density').d
xmom.d[:,:] = cells.get_var('x-momentum').d
ymom.d[:,:] = cells.get_var('y-momentum').d
ener.d[:,:] = cells.get_var('energy').d
## must set time!!
my_data.t = cells.t
else:
# set the density to be stratified in the y-direction
myg = my_data.grid
p = myg.scratch_array()
dens.d[:,:] = dens1*numpy.exp(-myg.y2d/scale_height)
dens.d[dens.d < smalldens] = smalldens
p.d[:,:] = dens.d * cs**2 / gamma
# set the velocity perturbations
u = 0.
A = amp*numpy.random.rand(dens.d.shape[0],dens.d.shape[1])
# v = A*(1+numpy.cos(nwaves*numpy.pi*myg.x2d/xmax))*0.5
v = A*(numpy.cos(nwaves*numpy.pi*myg.x2d/xmax))*0.5
# set the momenta
xmom.d[:,:] = dens.d * u
ymom.d[:,:] = dens.d * v
# set the energy (P = cs2*dens/gamma)
ener.d[:,:] = p.d[:,:]/(gamma - 1.0) + \
0.5*(xmom.d[:,:]**2 + ymom.d[:,:]**2)/dens.d[:,:]