def errors(dir, time_l, xy_lim):
for time in time_l:
# reading the model output
var_model = reading_modeloutput(dir, time)
var_model["x_range"] = np.arange(-xy_lim+var_model["dx"]/2., xy_lim, var_model["dx"])
assert(var_model["x_range"].shape[0] == var_model["h"].shape[0]), "domain size differs from model output shape"
var_model["y_range"] = np.arange(-xy_lim+var_model["dy"]/2., xy_lim, var_model["dx"])
assert(var_model["y_range"].shape[0] == var_model["h"].shape[1]), "domainsize differs from model output shape"
# calculating the analytical solution
lamb = eq.d2_lambda_evol(time)
h_an = eq.d2_height_plane(lamb, var_model["x_range"], var_model["y_range"])
# calculating the errors of the drop depth, eq. 25 and 26 from the paper
h_diff = var_model["h"] - h_an
points_nr = var_model["h"].shape[0] * var_model["h"].shape[1]
delh_inf = abs(h_diff).max()
delh_2 = 1./time * ((h_diff**2).sum() / points_nr )**0.5
# outputing general info
if time == time_l[0]:
file = open(dir + "_stats.txt", "w")
fstring = (
"dx = {dx:.4f}\n"
"dy = {dy:.4f}\n"
"dt = {dt:.4f}\n"
"number of points in the domain = {npoints}\n"
"L_inf = max|h_m-h_an|\n"
"L_2 = sqrt(sum(h_m-h_an)^2 / N) / time\n\n"
)
file.write(fstring.format(
dx = var_model["dx"],
dy = var_model["dy"],
dt = var_model["dt"],
npoints = points_nr
)
)
# outputting error statistics
fstring = (
"time = {time:.4f}\n"
"max(h_an) = {max_h_an:.7f}\n"
"max(h_num) = {max_h_num:.7f}\n"
"L_inf = {L_inf:.7f}\n"
"L_2 = {L_2:.7f}\n"
"max(px_num) = {max_px_num:.7f}\n"
"max(py_num) = {max_py_num:.7f}\n\n"
)
file.write(fstring.format(
time = time,
max_h_an = h_an.max(),
max_h_num = var_model["h"].max(),
L_inf = delh_inf,
L_2 = delh_2,
max_px_num = var_model["qx"].max(),
max_py_num = var_model["qy"].max()
)
)
file.close()
def errors(dir, time_l, xy_lim):
for time in time_l:
# reading the model output
var_model = reading_modeloutput(dir, time)
var_model["x_range"] = np.arange(-xy_lim + var_model["dx"] / 2.,
xy_lim, var_model["dx"])
assert (var_model["x_range"].shape[0] == var_model["h"].shape[0]
), "domain size differs from model output shape"
var_model["y_range"] = np.arange(-xy_lim + var_model["dy"] / 2.,
xy_lim, var_model["dx"])
assert (var_model["y_range"].shape[0] == var_model["h"].shape[1]
), "domainsize differs from model output shape"
# calculating the analytical solution
lamb = eq.d2_lambda_evol(time)
h_an = eq.d2_height_plane(lamb, var_model["x_range"],
var_model["y_range"])
# calculating the errors of the drop depth, eq. 25 and 26 from the paper
h_diff = var_model["h"] - h_an
points_nr = var_model["h"].shape[0] * var_model["h"].shape[1]
delh_inf = abs(h_diff).max()
delh_2 = 1. / time * ((h_diff**2).sum() / points_nr)**0.5
# outputing general info
if time == time_l[0]:
file = open(dir + "_stats.txt", "w")
fstring = (
"dx = {dx:.4f}\n"
"dy = {dy:.4f}\n"
"dt = {dt:.4f}\n"
"number of points in the domain = {npoints}\n"
"L_inf = max|h_m-h_an|\n"
"L_2 = sqrt(sum(h_m-h_an)^2 / N) / time\n\n"
)
file.write(
fstring.format(dx=var_model["dx"],
dy=var_model["dy"],
dt=var_model["dt"],
npoints=points_nr))
# outputting error statistics
fstring = ("time = {time:.4f}\n"
"max(h_an) = {max_h_an:.7f}\n"
"max(h_num) = {max_h_num:.7f}\n"
"L_inf = {L_inf:.7f}\n"
"L_2 = {L_2:.7f}\n"
"max(px_num) = {max_px_num:.7f}\n"
"max(py_num) = {max_py_num:.7f}\n\n")
file.write(
fstring.format(time=time,
max_h_an=h_an.max(),
max_h_num=var_model["h"].max(),
L_inf=delh_inf,
L_2=delh_2,
max_px_num=var_model["qx"].max(),
max_py_num=var_model["qy"].max()))
file.close()
def analytic_fig(ax, x_lim, time_l=[0,1,2,3], nxy=320):
x_range = np.linspace(-x_lim, x_lim, nxy)
y_range = np.zeros(nxy)
oznacz = ['k', 'b', 'c', 'y', 'g', 'm', 'r']
for it, time in enumerate(time_l):
lamb = eq.d2_lambda_evol(time)
h = eq.d2_height(lamb, x_range, y_range)
v = eq.d2_velocity(lamb, x_range, y_range)
ax.plot(x_range, h, oznacz[it])
ax.plot(x_range, v, oznacz[it]+ "--")
ps.ticks_changes(ax)
def analytic_fig(ax, x_lim, time_l=[0, 1, 2, 3], nxy=320):
x_range = np.linspace(-x_lim, x_lim, nxy)
y_range = np.zeros(nxy)
oznacz = ['k', 'b', 'c', 'y', 'g', 'm', 'r']
for it, time in enumerate(time_l):
lamb = eq.d2_lambda_evol(time)
h = eq.d2_height(lamb, x_range, y_range)
v = eq.d2_velocity(lamb, x_range, y_range)
ax.plot(x_range, h, oznacz[it])
ax.plot(x_range, v, oznacz[it] + "--")
ps.ticks_changes(ax)
def analytic_model_fig(ax, var_md, time=1):
x_range = var_md["x_range"]
y_range = 0 * var_md["x_range"]
ind_cs = int(var_md["h"].shape[1]/2)
lamb = eq.d2_lambda_evol(time)
h_a = eq.d2_height(lamb, x_range, y_range)
v_a = eq.d2_velocity(lamb, x_range, y_range)
ax.plot(x_range, eq.d2_initial(x_range, y_range), 'k', x_range, h_a, 'b',
x_range, var_md["h"][:,ind_cs], "r")
ax.plot(x_range, 0*x_range, "k-", x_range, v_a, 'b--',
x_range, var_md["vx"][:,ind_cs], "r--")
ps.ticks_changes(ax)
def analytic_model_fig(ax, x_range, y_range, h_m, v_m, time=1):
lamb = eq.d2_lambda_evol(time)
h_a = eq.d2_height(lamb, x_range, y_range)
v_a = eq.d2_velocity(lamb, x_range, y_range)
ax.plot(x_range, eq.d2_initial(x_range, y_range), 'k', x_range, h_a, 'b',
x_range, h_m, "r")
ax.plot(x_range, 0*x_range, "k-", x_range, v_a, 'b--',
x_range, v_m, "r--")
#ax.set_ylim(-2,2)
ps.ticks_changes(ax)
def analytic_model_fig(ax, var_md, time=1):
x_range = var_md["x_range"]
y_range = 0 * var_md["x_range"]
ind_cs = int(var_md["h"].shape[1] / 2)
lamb = eq.d2_lambda_evol(time)
h_a = eq.d2_height(lamb, x_range, y_range)
v_a = eq.d2_velocity(lamb, x_range, y_range)
ax.plot(x_range, eq.d2_initial(x_range, y_range), 'k', x_range, h_a, 'b',
x_range, var_md["h"][:, ind_cs], "r")
ax.plot(x_range, 0 * x_range, "k-", x_range, v_a, 'b--', x_range,
var_md["vx"][:, ind_cs], "r--")
ps.ticks_changes(ax)
def analytic_model_fig(ax, x_range, y_range, h_m, v_m, time=1):
lamb = eq.d2_lambda_evol(time)
h_a = eq.d2_height(lamb, x_range, y_range)
v_a = eq.d2_velocity(lamb, x_range, y_range)
ax.plot(x_range, eq.d2_initial(x_range, y_range), 'k', x_range, h_a, 'b',
x_range, h_m, "r")
ax.plot(x_range, 0 * x_range, "k-", x_range, v_a, 'b--', x_range, v_m,
"r--")
#ax.set_ylim(-2,2)
ps.ticks_changes(ax)
def analytic_fig(ax, time_l = [0,1,2,3], x_range = np.linspace(-8,8,320),
y_range = np.zeros(320)):
oznacz = ['k', 'b', 'c', 'y', 'g', 'm', 'r']
y0 = eq.d2_initial(x_range, y_range)
for it, time in enumerate(time_l):
lamb = eq.d2_lambda_evol(time)
h = eq.d2_height(lamb, x_range, y_range)
v = eq.d2_velocity(lamb, x_range, y_range)
ax.plot(x_range, h, oznacz[it])
ax.plot(x_range, v, oznacz[it]+ "--")
ps.ticks_changes(ax)
def analytic_fig(ax,
time_l=[0, 1, 2, 3],
x_range=np.linspace(-8, 8, 320),
y_range=np.zeros(320)):
oznacz = ['k', 'b', 'c', 'y', 'g', 'm', 'r']
y0 = eq.d2_initial(x_range, y_range)
for it, time in enumerate(time_l):
lamb = eq.d2_lambda_evol(time)
h = eq.d2_height(lamb, x_range, y_range)
v = eq.d2_velocity(lamb, x_range, y_range)
ax.plot(x_range, h, oznacz[it])
ax.plot(x_range, v, oznacz[it] + "--")
ps.ticks_changes(ax)
