def show_residual_across_simulation(stats,fname):
extract_stats = grep_stats(stats,type='residual')
maxsteps = 0
maxiter = 0
minres = 0
maxres = -99
for k,v in extract_stats.items():
maxsteps = max(maxsteps,getattr(k,'step'))
maxiter = max(maxiter,getattr(k,'iter'))
minres = min(minres,np.log10(v))
maxres = max(maxres,np.log10(v))
# print(getattr(k,'step'),getattr(k,'iter'),v)
# print(maxsteps,maxiter,minres,maxres)
residual = np.zeros((maxiter,maxsteps+1))
residual[:] = -99
for k,v in extract_stats.items():
step = getattr(k,'step')
iter = getattr(k,'iter')
if iter is not -1:
residual[iter-1,step] = np.log10(v)
# Set up latex stuff and fonts
# rc('text', usetex=True)
# rc('font', **{"sans-serif": ["Arial"], "size": 30})
rc('font', family='serif',size=30)
rc('legend', fontsize='small')
rc('xtick', labelsize='small')
rc('ytick', labelsize='small')
fig, ax = plt.subplots(figsize=(15,10))
cmap = plt.get_cmap('Reds')
plt.pcolor(residual.T, cmap=cmap, vmin=minres, vmax=maxres)
cax = plt.colorbar()
cax.set_label('log10(residual)')
ax.set_xlabel('iteration')
ax.set_ylabel('step')
ax.set_xticks(np.arange(maxiter)+0.5, minor=False)
ax.set_yticks(np.arange(maxsteps+1)+0.5, minor=False)
ax.set_xticklabels(np.arange(maxiter)+1, minor=False)
ax.set_yticklabels(np.arange(maxsteps+1), minor=False)
plt.tight_layout()
plt.savefig(fname, rasterized=True, transparent=True, bbox_inches='tight')
plt.show()
pass
description['transfer_params'] = tparams
# quickly generate block of steps
MS = mp.generate_steps(num_procs,sparams,description)
# setup parameters "in time"
t0 = MS[0].levels[0].prob.t0
dt = 0.5
Tend = 8*dt
# get initial values on finest level
P = MS[0].levels[0].prob
uinit = P.u_exact(t0)
# call main function to get things done...
uend,stats = mp.run_pfasst(MS,u0=uinit,t0=t0,dt=dt,Tend=Tend)
# df.plot(uend.values,interactive=True)
# compute exact solution and compare
uex = P.u_exact(Tend)
print('(classical) error at time %s: %s' %(Tend,abs(uex-uend)/abs(uex)))
uex = df.Expression('sin(a*x[0]) * cos(t)',a=np.pi,t=Tend)
print('(fenics-style) error at time %s: %s' %(Tend,df.errornorm(uex,uend.values)))
extract_stats = grep_stats(stats,iter=-1,type='residual')
sortedlist_stats = sort_stats(extract_stats,sortby='step')
print(extract_stats,sortedlist_stats)
# setup parameters "in time"
t0 = 0
dt = 1/16*np.pi
Tend = 16*dt#np.pi
# get initial values on finest level
P = MS[0].levels[0].prob
uinit = P.u_exact(t0)
print('Init:',uinit.pos.values,uinit.vel.values)
# call main function to get things done...
uend,stats = mp.run_pfasst(MS,u0=uinit,t0=t0,dt=dt,Tend=Tend)
extract_stats = grep_stats(stats,type='energy')
sortedlist_stats = sort_stats(extract_stats,sortby='time')
R0 = np.linalg.norm(uinit.pos.values[:])
H0 = 1/2*np.dot(uinit.vel.values[:],uinit.vel.values[:])+0.02/R0
energy_err = [abs(entry[1]-H0)/H0 for entry in sortedlist_stats]
fig = plt.figure()
plt.plot(energy_err,'bo--')
plt.show()
# rc('text', usetex=True)
# rc('font', family='serif', size=20)
# rc('legend', fontsize='small')
MS = mp.generate_steps(num_procs, sparams, description)
# setup parameters "in time"
t0 = 0
dt = 0.1
Tend = 2
P = MS[0].levels[0].prob
uinit = P.u_exact(t0)
print('Init:', uinit.values)
# call main function to get things done...
uend, stats = mp.run_pfasst_serial(MS, u0=uinit, t0=t0, dt=dt, Tend=Tend)
# get stats and error
extract_stats = grep_stats(stats, type='niter')
sortedlist_stats = sort_stats(extract_stats, sortby='time')
uex = P.u_exact(Tend)
print(
'Error:',
np.linalg.norm(uex.values - uend.values, np.inf) /
np.linalg.norm(uex.values, np.inf))
print('Min/Max/Sum number of iterations: %s/%s/%s' %
(min(entry[1] for entry in sortedlist_stats),
max(entry[1] for entry in sortedlist_stats),
sum(entry[1] for entry in sortedlist_stats)))
description['num_nodes'] = 3
description['sweeper_class'] = imex_1st_order
description['level_params'] = lparams
description['transfer_class'] = mesh_to_mesh_1d
description['transfer_params'] = tparams
# quickly generate block of steps
MS = mp.generate_steps(num_procs, sparams, description)
# setup parameters "in time"
t0 = 0
dt = 0.125
Tend = 4 * dt
# get initial values on finest level
P = MS[0].levels[0].prob
uinit = P.u_exact(t0)
# call main function to get things done...
uend, stats = mp.run_pfasst_serial(MS, u0=uinit, t0=t0, dt=dt, Tend=Tend)
# compute exact solution and compare
uex = P.u_exact(Tend)
print('error at time %s: %s' %
(Tend, np.linalg.norm(uex.values - uend.values, np.inf) /
np.linalg.norm(uex.values, np.inf)))
extract_stats = grep_stats(stats, iter=-1, type='residual')
sortedlist_stats = sort_stats(extract_stats, sortby='step')
print(extract_stats, sortedlist_stats)
# quickly generate block of steps
MS = mp.generate_steps(num_procs,sparams,description)
# setup parameters "in time"
t0 = 0
dt = 0.1
Tend = 2
P = MS[0].levels[0].prob
uinit = P.u_exact(t0)
print('Init:',uinit.values)
# call main function to get things done...
uend,stats = mp.run_pfasst(MS,u0=uinit,t0=t0,dt=dt,Tend=Tend)
# get stats and error
extract_stats = grep_stats(stats,type='niter')
sortedlist_stats = sort_stats(extract_stats,sortby='time')
np.set_printoptions(16)
print('u_end:',uend.values,' at time',Tend)
# this is for Tend = 2.0, computed with 2k time-steps and M=3 (G-Le)
if Tend == 2.0:
uex = np.array([1.7092338721248415, -0.17438654047532 ])
print('Error:',np.linalg.norm(uex-uend.values,np.inf)/np.linalg.norm(uex,np.inf))
plt.show()
# quickly generate block of steps
MS = mp.generate_steps(num_procs,sparams,description)
# setup parameters "in time"
t0 = 0
dt = 0.1
Tend = 4*dt
# get initial values on finest level
P = MS[0].levels[0].prob
uinit = P.u_exact(t0)
# call main function to get things done...
uend,stats = mp.run_pfasst(MS,u0=uinit,t0=t0,dt=dt,Tend=Tend)
# compute exact solution and compare
uex = P.u_exact(Tend)
print('error at time %s: %s' %(Tend,np.linalg.norm(uex.values-uend.values,np.inf)/np.linalg.norm(
uex.values,np.inf)))
# Get residual at last step (being the max of all residuals.. most likely) on the fine level
extract_stats = grep_stats(stats,step=3,level=-1,type='residual')
sortedlist_stats = sort_stats(extract_stats,sortby='iter')[1:] # remove '-1' entry
print(sortedlist_stats)
# Get the error against the analytical solution at the last step
extract_stats = grep_stats(stats,step=3,level=-1,type='error')
sortedlist_stats = sort_stats(extract_stats,sortby='iter')
print(sortedlist_stats)
# setup parameters "in time"
t0 = 0
dt = 1 / 16 * np.pi
Tend = 16 * dt #np.pi
# get initial values on finest level
P = MS[0].levels[0].prob
uinit = P.u_exact(t0)
print('Init:', uinit.pos.values, uinit.vel.values)
# call main function to get things done...
uend, stats = mp.run_pfasst_serial(MS, u0=uinit, t0=t0, dt=dt, Tend=Tend)
extract_stats = grep_stats(stats, type='energy')
sortedlist_stats = sort_stats(extract_stats, sortby='time')
R0 = np.linalg.norm(uinit.pos.values[:])
H0 = 1 / 2 * np.dot(uinit.vel.values[:], uinit.vel.values[:]) + 0.02 / R0
energy_err = [abs(entry[1] - H0) / H0 for entry in sortedlist_stats]
fig = plt.figure()
plt.plot(energy_err, 'bo--')
plt.show()
# rc('text', usetex=True)
# rc('font', family='serif', size=20)
# rc('legend', fontsize='small')
# setup parameters "in time"
t0 = 0
dt = 0.1
Tend = 2
P = MS[0].levels[0].prob
uinit = P.u_exact(t0)
print("Init:", uinit.values)
# call main function to get things done...
uend, stats = mp.run_pfasst(MS, u0=uinit, t0=t0, dt=dt, Tend=Tend)
# get stats and error
extract_stats = grep_stats(stats, type="niter")
sortedlist_stats = sort_stats(extract_stats, sortby="time")
uex = P.u_exact(Tend)
print("Error:", np.linalg.norm(uex.values - uend.values, np.inf) / np.linalg.norm(uex.values, np.inf))
print(
"Min/Max/Sum number of iterations: %s/%s/%s"
% (
min(entry[1] for entry in sortedlist_stats),
max(entry[1] for entry in sortedlist_stats),
sum(entry[1] for entry in sortedlist_stats),
)
)
