def visualize(collection,
maximize=False,
showbest=True,
showmean=True,
latexify=False,
fontfamily="serif",
scale='linear',
analysis=True,
print_pareto=False):
"""
Visualize the progress of an optimization.
Args:
collection (pymongo Collection): The pymongo colllection containing your
rocketsled optimization. For example, if you set you opt_label to
'opt123', and used the same db as your LaunchPad, you could use
lpad.db.opt123
maximize (bool): Whether to plot optimizing for minimum or maximum.
showbest (bool): Point out the best point on legend and on plot. If more
than one best point (i.e., multiple equal maxima), show them all. If
multiobjective, shows best for each objective, and prints the best
value and x for each objective.
showmean (bool): Show the mean and standard deviation for the guesses
as the computations are carried out.
latexify (bool): Use LaTeX for formatting.
fontfamily (str): The font family to use for rendering. Choose from
'serif', 'sans-serif', 'fantasy', 'monospace', or 'cursive'.
scale (str): Whether to scale the plot's y axis according to log ('log')
or 'linear' scale.
analysis (bool): If True, stdouts info from analyze().
print_pareto (bool): If True, display all Pareto-optimal objective
values.
Returns:
Either None, a matplotlib plot, or a pymongo iterator. See 'mode' for
details.
"""
dtypes = Dtypes()
fxstr = "$f(x)$" if latexify else "f(x)"
opt = max if maximize else min
objs = collection.find_one({'index': {'$exists': 1}})['y']
n_objs = len(objs) if isinstance(objs, (list, tuple)) else 1
dt = datetime.datetime.now()
dtdata = [dt.year, dt.month, dt.day, dt.hour, dt.minute, dt.second]
timestr = "{}-{}-{} {}:{}.{}".format(*dtdata)
t0 = time.time()
if latexify:
plt.rc('text', usetex=True)
else:
plt.rc('text', usetex=False)
plt.rc('font', family=fontfamily, size=9)
N_COLS = 3
# print(int(math.ceil(float(n_objs)/float(N_COLS))))
if n_objs < N_COLS:
f, axarr = plt.subplots(n_objs, squeeze=False)
else:
f, axarr = plt.subplots(N_COLS,
int(math.ceil(n_objs / N_COLS)),
squeeze=False)
docset = collection.find({'index': {'$exists': 1}})
docs = [None] * docset.count()
for i, doc in enumerate(docset):
docs[i] = {'y': doc['y'], 'index': doc['index'], 'x': doc['x']}
if n_objs > 1:
Y = np.asarray([doc['y'] for doc in docs])
pareto_set = Y[pareto(Y, maximize=maximize)].tolist()
pareto_graph = [(i + 1, doc['y']) for i, doc in enumerate(docs)
if doc['y'] in pareto_set]
pareto_i = [i[0] for i in pareto_graph]
for obj in range(n_objs):
ax = axarr[obj % N_COLS, int(math.floor(obj / N_COLS))]
i = []
fx = []
best = []
mean = []
std = []
n = collection.find().count() - 2
for doc in docs:
fx.append(doc['y'] if n_objs == 1 else doc['y'][obj])
i.append(doc['index'])
best.append(opt(fx))
mean.append(np.mean(fx))
std.append(np.std(fx))
if time.time() - t0 > 60:
warnings.warn(
"Gathering data from the db is taking a while. Ensure"
"the latency to your db is low and the bandwidth"
"is as high as possible!")
mean = np.asarray(mean)
std = np.asarray(std)
ax.scatter(i, fx, color='blue', label=fxstr, s=10)
ax.plot(i,
best,
color='orange',
label="best {} value found so far"
"".format(fxstr))
if showmean:
ax.plot(i,
mean,
color='grey',
label="mean {} value (with std "
"dev.)".format(fxstr))
ax.fill_between(i, mean + std, mean - std, color='grey', alpha=0.3)
ax.set_xlabel("{} evaluation".format(fxstr))
ax.set_ylabel("{} value".format(fxstr))
best_val = opt(best)
if showbest:
if latexify:
best_label = "Best value: $f(x) = {}$" \
"".format(latex_float(best_val))
else:
best_label = "Best value: f(x) = {:.2E}".format(best_val)
best = collection.find({'y': best_val})
for b in best:
bl = None if n_objs > 1 else best_label
ax.scatter([b['index']], [best_val],
color='darkgreen',
s=50,
linewidth=3,
label=bl,
facecolors='none',
edgecolors='darkgreen')
artext = "$x = $ [" if latexify else "x = ["
for i, xi in enumerate(b['x']):
if i > 0:
artext += ". \mbox{~~~~~}" if latexify else " "
if type(xi) in dtypes.floats:
if latexify:
artext += "${}$,\n".format(latex_float(xi))
else:
artext += "{:.2E},\n".format(xi)
else:
artext += str(xi) + ",\n"
artext = artext[:-2] + "]"
objstr = "objective {}".format(obj) if n_objs > 1 else ""
if maximize:
print("max(f(x)) {} is {} at x = {}".format(
objstr, best_val, b['x']))
else:
print("min(f(x)) {} is {} at x = {}".format(
objstr, best_val, b['x']))
ax.annotate(artext,
xy=(b['index'] + 0.5, best_val),
xytext=(b['index'] + float(n) / 12.0, best_val),
arrowprops=dict(color='green'),
color='darkgreen',
bbox=dict(facecolor='white', alpha=1.0))
else:
best_label = ""
if n_objs > 1:
pareto_fx = [i[1][obj] for i in pareto_graph]
ax.scatter(pareto_i,
pareto_fx,
color='red',
label="Pareto optimal",
s=20)
if n_objs > 1:
ax.set_title("Objective {}: {}".format(obj + 1, best_label))
ax.set_yscale(scale)
plt.gcf().set_size_inches(10, 10)
if analysis:
print(analyze(collection))
if print_pareto and n_objs > 1:
print("Pareto Frontier: {} points".format(len(pareto_set)))
pareto_y = [doc['y'] for doc in docs if doc['y'] in pareto_set]
pareto_x = [doc['x'] for doc in docs if doc['y'] in pareto_set]
for i, _ in enumerate(pareto_set):
print("f(x) = {} @ x = {}".format(pareto_y[i], pareto_x[i]))
if n_objs % N_COLS != 0 and n_objs > N_COLS:
for i in range(n_objs % N_COLS, N_COLS):
plt.delaxes(axarr[i, -1])
plt.legend()
# plt.tight_layout(pad=0.01, w_pad=0.01, h_pad=0.01)
plt.subplots_adjust(wspace=0.3, hspace=0.5)
plt.suptitle("Rocketsled optimization results for {} - "
"{}".format(collection.name, timestr),
y=0.99)
plt.show()
def plot(self,
show_best=True,
show_mean=True,
latexify=False,
font_family="serif",
scale='linear',
summarize=True,
print_pareto=False):
"""
Visualize the progress of an optimization.
Args:
maximize (bool): Whether to plot optimizing for minimum or maximum.
show_best (bool): Point out the best point on legend and on plot. If
more than one best point (i.e., multiple equal maxima), show
them all. If multiobjective, shows best for each objective, and
prints the best value and x for each objective.
show_mean (bool): Show the mean and standard deviation for the
guesses as the computations are carried out.
latexify (bool): Use LaTeX for formatting.
font_family (str): The font family to use for rendering. Choose from
'serif', 'sans-serif', 'fantasy', 'monospace', or 'cursive'.
scale (str): Whether to scale the plot's y axis according to log
('log') or 'linear' scale.
summarize (bool): If True, stdouts summary from .summarize.
print_pareto (bool): If True, display all Pareto-optimal objective
values.
Returns:
A matplotlib plot object handle
"""
if not self.is_configured:
raise NotConfiguredError(
"Use MissionControl.configure to configure"
"your optimization collection before "
"plotting!")
maximize = self.config["maximize"]
fxstr = "$f(x)$" if latexify else "f(x)"
opt = max if maximize else min
objs = self.c.find_one({'index': {'$exists': 1}})['y']
n_objs = len(objs) if isinstance(objs, (list, tuple)) else 1
dt = datetime.datetime.now()
dtdata = [dt.year, dt.month, dt.day, dt.hour, dt.minute, dt.second]
timestr = "{}-{}-{} {}:{}.{}".format(*dtdata)
t0 = time.time()
if latexify:
plt.rc('text', usetex=True)
else:
plt.rc('text', usetex=False)
plt.rc('font', family=font_family, size=9)
n_cols = 3
if n_objs < n_cols:
f, axarr = plt.subplots(n_objs, squeeze=False)
else:
f, axarr = plt.subplots(n_cols,
int(math.ceil(n_objs / n_cols)),
squeeze=False)
docset = self.c.find({'index': {'$exists': 1}})
docs = [None] * docset.count()
for i, doc in enumerate(docset):
docs[i] = {'y': doc['y'], 'index': doc['index'], 'x': doc['x']}
if n_objs > 1:
all_y = np.asarray([doc['y'] for doc in docs])
pareto_set = all_y[pareto(all_y, maximize=maximize)].tolist()
pareto_graph = [(i + 1, doc['y']) for i, doc in enumerate(docs)
if doc['y'] in pareto_set]
pareto_i = [i[0] for i in pareto_graph]
print("Optimization Analysis:")
print("Number of objectives: {}".format(n_objs))
for obj in range(n_objs):
ax = axarr[obj % n_cols, int(math.floor(obj / n_cols))]
i = []
fx = []
best = []
mean = []
std = []
n = self.c.find().count() - 2
for doc in docs:
fx.append(doc['y'] if n_objs == 1 else doc['y'][obj])
i.append(doc['index'])
best.append(opt(fx))
mean.append(np.mean(fx))
std.append(np.std(fx))
if time.time() - t0 > 60:
self.logger.warn(
"Gathering data from the db is taking a while. Ensure"
"the latency to your db is low and the bandwidth"
"is as high as possible!")
mean = np.asarray(mean)
std = np.asarray(std)
ax.scatter(i, fx, color='blue', label=fxstr, s=10)
ax.plot(i,
best,
color='orange',
label="best {} value found so far"
"".format(fxstr))
if show_mean:
ax.plot(i,
mean,
color='grey',
label="mean {} value (with std "
"dev.)".format(fxstr))
ax.fill_between(i,
mean + std,
mean - std,
color='grey',
alpha=0.3)
ax.set_xlabel("{} evaluation".format(fxstr))
ax.set_ylabel("{} value".format(fxstr))
best_val = opt(best)
if show_best:
if latexify:
best_label = "Best value: $f(x) = {}$" \
"".format(latex_float(best_val))
else:
best_label = "Best value: f(x) = {:.2E}".format(best_val)
best = self.c.find({'y': best_val})
if n_objs == 1:
print("\tNumber of optima: {}".format(best.count()))
else:
print("\tNumber of optima for objective {}: {}"
"".format(obj + 1, best.count()))
for b in best:
bl = None if n_objs > 1 else best_label
ax.scatter([b['index']], [best_val],
color='darkgreen',
s=50,
linewidth=3,
label=bl,
facecolors='none',
edgecolors='darkgreen')
artext = "$x = $ [" if latexify else "x = ["
for i, xi in enumerate(b['x']):
if i > 0:
artext += ". \mbox{~~~~~}" if latexify else " "
if type(xi) in dtypes.floats:
if latexify:
artext += "${}$,\n".format(latex_float(xi))
else:
artext += "{:.2E},\n".format(xi)
else:
artext += str(xi) + ",\n"
artext = artext[:-2] + "]"
objstr = "objective {}".format(obj +
1) if n_objs > 1 else ""
if maximize:
print("\t\tmax(f(x)) {} is {} at x = {}"
"".format(objstr, best_val, b['x']))
else:
print("\t\tmin(f(x)) {} is {} at x = {}"
"".format(objstr, best_val, b['x']))
ax.annotate(artext,
xy=(b['index'] + 0.5, best_val),
xytext=(b['index'] + float(n) / 12.0,
best_val),
arrowprops=dict(color='green'),
color='darkgreen',
bbox=dict(facecolor='white', alpha=1.0))
else:
best_label = ""
if n_objs > 1:
pareto_fx = [i[1][obj] for i in pareto_graph]
ax.scatter(pareto_i,
pareto_fx,
color='red',
label="Pareto optimal",
s=20)
if n_objs > 1:
ax.set_title("Objective {}: {}".format(obj + 1, best_label))
ax.set_yscale(scale)
plt.gcf().set_size_inches(10, 10)
if summarize:
print(self.summarize())
if print_pareto and n_objs > 1:
print("Pareto Frontier: {} points, ranked by hypervolume".format(
len(pareto_set)))
pareto_y = [doc['y'] for doc in docs if doc['y'] in pareto_set]
pareto_x = [doc['x'] for doc in docs if doc['y'] in pareto_set]
# Order y by hypervolume
hypervolumes = [np.prod(y) for y in pareto_y]
pareto_y_ordered = [
y for _, y in sorted(zip(hypervolumes, pareto_y), reverse=True)
]
pareto_x_ordered = [
x for _, x in sorted(zip(hypervolumes, pareto_x), reverse=True)
]
hypervolumes_ordered = sorted(hypervolumes, reverse=True)
for i, _ in enumerate(pareto_set):
print("f(x) = {} @ x = {} with hypervolume {}".format(
pareto_y_ordered[i], pareto_x_ordered[i],
hypervolumes_ordered[i]))
if n_objs % n_cols != 0 and n_objs > n_cols:
for i in range(n_objs % n_cols, n_cols):
plt.delaxes(axarr[i, -1])
plt.legend()
# plt.tight_layout(pad=0.01, w_pad=0.01, h_pad=0.01)
plt.subplots_adjust(wspace=0.3, hspace=0.5)
plt.suptitle("Rocketsled optimization results for {} - "
"{}".format(self.c.name, timestr),
y=0.99)
return plt
def plot(self, show_best=True, show_mean=True, latexify=False,
font_family="serif", scale='linear', summarize=True,
print_pareto=False):
"""
Visualize the progress of an optimization.
Args:
show_best (bool): Point out the best point on legend and on plot. If
more than one best point (i.e., multiple equal maxima), show
them all. If multiobjective, shows best for each objective, and
prints the best value and x for each objective.
show_mean (bool): Show the mean and standard deviation for the
guesses as the computations are carried out.
latexify (bool): Use LaTeX for formatting.
font_family (str): The font family to use for rendering. Choose from
'serif', 'sans-serif', 'fantasy', 'monospace', or 'cursive'.
scale (str): Whether to scale the plot's y axis according to log
('log') or 'linear' scale.
summarize (bool): If True, stdouts summary from .summarize.
print_pareto (bool): If True, display all Pareto-optimal objective
values.
Returns:
A matplotlib plot object handle
"""
if not self.is_configured:
raise NotConfiguredError("Use MissionControl.configure to configure"
"your optimization collection before "
"plotting!")
maximize = self.config["maximize"]
fxstr = "$f(x)$" if latexify else "f(x)"
opt = max if maximize else min
objs = self.c.find_one({'index': {'$exists': 1}})['y']
n_objs = len(objs) if isinstance(objs, (list, tuple)) else 1
dt = datetime.datetime.now()
dtdata = [dt.year, dt.month, dt.day, dt.hour, dt.minute, dt.second]
timestr = "{}-{}-{} {}:{}.{}".format(*dtdata)
t0 = time.time()
if latexify:
plt.rc('text', usetex=True)
else:
plt.rc('text', usetex=False)
plt.rc('font', family=font_family, size=9)
n_cols = 3
if n_objs < n_cols:
_, ax_arr = plt.subplots(n_objs, squeeze=False)
else:
_, ax_arr = plt.subplots(n_cols, int(math.ceil(n_objs / n_cols)),
squeeze=False)
docset = self.c.find({'index': {'$exists': 1}})
docs = [None] * docset.count()
for i, doc in enumerate(docset):
docs[i] = {'y': doc['y'], 'index': doc['index'], 'x': doc['x']}
if n_objs > 1:
all_y = np.asarray([doc['y'] for doc in docs])
pareto_set = all_y[pareto(all_y, maximize=maximize)].tolist()
pareto_graph = [(i + 1, doc['y']) for i, doc in enumerate(docs)
if doc['y'] in pareto_set]
pareto_i = [i[0] for i in pareto_graph]
print("Optimization Analysis:")
print("Number of objectives: {}".format(n_objs))
for obj in range(n_objs):
ax = ax_arr[obj % n_cols, int(math.floor(obj / n_cols))]
i = []
fx = []
best = []
mean = []
std = []
n = self.c.find().count() - 2
for doc in docs:
fx.append(doc['y'] if n_objs == 1 else doc['y'][obj])
i.append(doc['index'])
best.append(opt(fx))
mean.append(np.mean(fx))
std.append(np.std(fx))
if time.time() - t0 > 60:
self.logger.warn(
"Gathering data from the db is taking a while. Ensure"
"the latency to your db is low and the bandwidth"
"is as high as possible!")
mean = np.asarray(mean)
std = np.asarray(std)
ax.scatter(i, fx, color='blue', label=fxstr, s=10)
ax.plot(i, best, color='orange', label="best {} value found so far"
"".format(fxstr))
if show_mean:
ax.plot(i, mean, color='grey', label="mean {} value (with std "
"dev.)".format(fxstr))
ax.fill_between(i, mean + std, mean - std, color='grey',
alpha=0.3)
ax.set_xlabel("{} evaluation".format(fxstr))
ax.set_ylabel("{} value".format(fxstr))
best_val = opt(best)
if show_best:
if latexify:
best_label = "Best value: $f(x) = {}$" \
"".format(latex_float(best_val))
else:
best_label = "Best value: f(x) = {:.2E}".format(best_val)
best = self.c.find({'y': best_val})
if n_objs == 1:
print("\tNumber of optima: {}".format(best.count()))
else:
print("\tNumber of optima for objective {}: {}"
"".format(obj + 1, best.count()))
for b in best:
bl = None if n_objs > 1 else best_label
ax.scatter([b['index']], [best_val], color='darkgreen',
s=50,
linewidth=3, label=bl, facecolors='none',
edgecolors='darkgreen')
artext = "$x = $ [" if latexify else "x = ["
for i, xi in enumerate(b['x']):
if i > 0:
artext += ". \mbox{~~~~~}" if latexify else " "
if type(xi) in dtypes.floats:
if latexify:
artext += "${}$,\n".format(latex_float(xi))
else:
artext += "{:.2E},\n".format(xi)
else:
artext += str(xi) + ",\n"
artext = artext[:-2] + "]"
objstr = "objective {}".format(
obj + 1) if n_objs > 1 else ""
if maximize:
print("\t\tmax(f(x)) {} is {} at x = {}"
"".format(objstr, best_val, b['x']))
else:
print("\t\tmin(f(x)) {} is {} at x = {}"
"".format(objstr, best_val, b['x']))
ax.annotate(artext,
xy=(b['index'] + 0.5, best_val),
xytext=(b['index'] + float(n) / 12.0, best_val),
arrowprops=dict(color='green'),
color='darkgreen',
bbox=dict(facecolor='white', alpha=1.0))
else:
best_label = ""
if n_objs > 1:
pareto_fx = [i[1][obj] for i in pareto_graph]
ax.scatter(pareto_i, pareto_fx, color='red',
label="Pareto optimal", s=20)
if n_objs > 1:
ax.set_title("Objective {}: {}".format(obj + 1, best_label))
ax.set_yscale(scale)
plt.gcf().set_size_inches(10, 10)
if summarize:
print(self.summarize())
if print_pareto and n_objs > 1:
print("Pareto Frontier: {} points, ranked by hypervolume".format(
len(pareto_set)))
pareto_y = [doc['y'] for doc in docs if doc['y'] in pareto_set]
pareto_x = [doc['x'] for doc in docs if doc['y'] in pareto_set]
# Order y by hypervolume
hypervolumes = [np.prod(y) for y in pareto_y]
pareto_y_ordered = [y for _, y in
sorted(zip(hypervolumes, pareto_y),
reverse=True)]
pareto_x_ordered = [x for _, x in
sorted(zip(hypervolumes, pareto_x),
reverse=True)]
hypervolumes_ordered = sorted(hypervolumes, reverse=True)
for i, _ in enumerate(pareto_set):
print("f(x) = {} @ x = {} with hypervolume {}".format(
pareto_y_ordered[i], pareto_x_ordered[i],
hypervolumes_ordered[i]))
if n_objs % n_cols != 0 and n_objs > n_cols:
for i in range(n_objs % n_cols, n_cols):
plt.delaxes(ax_arr[i, -1])
plt.legend()
# plt.tight_layout(pad=0.01, w_pad=0.01, h_pad=0.01)
plt.subplots_adjust(wspace=0.3, hspace=0.5)
plt.suptitle("Rocketsled optimization results for {} - "
"{}".format(self.c.name, timestr), y=0.99)
return plt
def test_latex_float(self):
f1 = 3.494388373744
f2 = 3.223421e-16
self.assertTrue(latex_float(f1), "3.49")
self.assertTrue(latex_float(f2), "3.22 \times 10^{-16}")
def test_latex_float(self):
f1 = 3.494388373744
f2 = 3.223421e-16
self.assertTrue(latex_float(f1), "3.49")
self.assertTrue(latex_float(f2), "3.22 \times 10^{-16}")