def show_frontier(X, Y, maxX=False, maxY=True, dots=False,
XMAX=None, YMIN=None, ax=None, label=None, **style):
"""Plot Pareto frontier.
Args:
X, Y: data.
maxX, maxY: (bool) whether to maximize or minimize along respective
coordinate.
dots: (bool) highlight points on the frontier (will use same color as
`style`).
ax: use an existing axis if non-null.
style: keyword arguments, which will be passed to lines connecting the
points on the Pareto frontier.
XMAX: max value along x-axis
YMIN: min value along y-axis
"""
if ax is None:
ax = pl.gca()
sty = {'c': 'b', 'alpha': 0.3, 'zorder': 0}
sty.update(style)
assert not maxX and maxY, 'need to update some hardcoded logic'
f = pareto_frontier(X, Y, maxX=maxX, maxY=maxY)
if not f:
print yellow % '[warn] Empty frontier'
return
if dots:
xs, ys = zip(*f)
ax.scatter(xs, ys, lw=0, alpha=0.5, c=sty['c'])
XMAX = XMAX if XMAX is not None else max(X)
YMIN = YMIN if YMIN is not None else min(Y)
assert XMAX >= max(X)
assert YMIN <= min(Y)
# Connect corners of frontier. The first and last points on frontier have
# lines which surround the point cloud.
f = [(min(X), YMIN)] + f + [(XMAX, max(Y))]
# Make line segments from adjacent points
pts = np.array([x for ((a,b), (c,d)) in window(f, 2) for x in [[a,b], [c,b], [c,b], [c,d]]])
# Plot
ax.plot(pts[:,0], pts[:,1], label=label, **sty)
def show_frontier(X, Y, maxX=False, maxY=True, dots=False, ax=None, label=None, **style):
"""Plot Pareto frontier.
Args:
X, Y: data.
maxX, maxY: (bool) whether to maximize or minimize along respective
coordinate.
dots: (bool) highlight points on the frontier (will use same color as
`style`).
ax: use an existing axis if non-null.
style: keyword arguments, which will be passed to lines connecting the
points on the Pareto frontier.
"""
if ax is None:
ax = pl.gca()
sty = {'c': 'b', 'alpha': 0.3, 'zorder': 0}
sty.update(style)
f = pareto_frontier(X, Y, maxX=maxX, maxY=maxY)
if not f:
print yellow % '[warn] Empty frontier'
return
if dots:
xs, ys = zip(*f)
ax.scatter(xs, ys, lw=0, alpha=0.5, c=sty['c'])
# Connect corners of frontier. The first and last points on frontier have
# lines which surround the point cloud.
p, q = f[0], f[-1]
(a,b) = min(X), max(X)
(c,d) = min(Y), max(Y)
# connect points with line segments
pts = []
pts.extend([p, (a,c)])
pts.extend(x for ((a,b), (c,d)) in window(f, 2) for x in [[a,b], [c,b], [c,b], [c,d]])
pts.extend([q, (b,d)])
# make plot
pts = np.array(pts)
ax.plot(pts[:,0], pts[:,1], label=label, **sty)
def graphviz(self, output):
from arsenal.iterextras import window
with open(output, 'w') as f:
print('digraph {', file=f)
terminals = set()
for x in list(self.incoming):
for e in self.incoming[x]:
print(' "%s" [label=\"\",shape=point];' % id(e), file=f)
print(' "%s" -> "%s";' % (id(e), e.head), file=f)
for b in e.body:
print(' "%s" -> "%s" [arrowhead=none];' % (b, id(e)),
file=f)
if not self.incoming[b]:
terminals.add(b)
if terminals:
print(terminals)
f.write('{ rank = same; %s; }\n' %
('; '.join('"%s"' % (x, ) for x in terminals)))
for a, b in window(sorted(terminals, key=lambda x: x[0]), 2):
f.write(
'"%s" -> "%s" [dir=none, style=invis, penwidth=1];\n' %
(a, b))
f.write('{ rank = same; "%s"; "%s"; }\n' % (a, b))
print('}', file=f)
def show_frontier(X, Y, maxX=False, maxY=True, dots=False,
XMIN=None, XMAX=None,
YMIN=None, YMAX=None,
ax=None, label=None,
interpolation='pessimistic', **style):
"""Plot Pareto frontier.
Args:
X, Y: data.
maxX, maxY: (bool) whether to maximize or minimize along respective
coordinate.
dots: (bool) highlight points on the frontier (will use same color as
`style`).
ax: use an existing axis if non-null.
style: keyword arguments, which will be passed to lines connecting the
points on the Pareto frontier.
XMAX: max value along x-axis
YMIN: min value along y-axis
"""
if ax is None:
ax = pl.gca()
sty = {'c': 'b', 'alpha': 0.3, 'zorder': 0}
sty.update(style)
if interpolation == 'linear-convex':
# Convex hull by itself doesn't work, but what we have is ok because its
# the intersection of the convex hull with the pareto frontier, which is
# handled below.
from scipy.spatial import ConvexHull
X = np.array(X)
Y = np.array(Y)
hull = ConvexHull(np.array([X,Y]).T)
X = X[hull.vertices]
Y = Y[hull.vertices]
# assert not maxX and maxY, 'need to update some hardcoded logic'
f = pareto_frontier(X, Y, maxX=maxX, maxY=maxY)
if not f:
print(yellow % '[warn] Empty frontier')
return
if dots:
xs, ys = list(zip(*f))
ax.scatter(xs, ys, lw=0, alpha=0.5, c=sty['c'])
XMIN = min(min(X), XMIN) if XMIN is not None else min(X)
XMAX = max(max(X), XMAX) if XMAX is not None else max(X)
YMIN = min(min(Y), YMIN) if YMIN is not None else min(Y)
YMAX = max(max(Y), YMAX) if YMAX is not None else max(Y)
# if 0:
# # This version lets you clip away points. I found it a little problematic to use.
# XMIN = XMIN if XMIN is not None else min(X)
# XMAX = XMAX if XMAX is not None else max(X)
# YMIN = YMIN if YMIN is not None else min(Y)
# YMAX = YMAX if YMAX is not None else max(Y)
# if (max(X) > XMAX or min(X) < XMIN or min(Y) > YMIN or max(Y) < YMAX):
# print '[PARETO] Warning: data out of bounds!'
# Connect corners of frontier. The first and last points on frontier have
# lines which surround the point cloud.
# TODO: make this look nicer...
if maxX and maxY:
f = [(XMAX, YMIN)] + f + [(XMIN, YMAX)]
elif not maxX and maxY:
f = [(XMIN, YMIN)] + f + [(XMAX, YMAX)]
elif maxX and not maxY:
f = [(XMAX, YMAX)] + f + [(XMIN, YMIN)]
else:
f = [(XMIN, YMAX)] + f + [(XMAX, YMIN)]
if interpolation == 'pessimistic':
# Make line segments from adjacent points
pts = np.array([x for ((a,b), (c,d)) in window(f, 2) for x in [[a,b], [c,b], [c,b], [c,d]]])
elif interpolation in {'linear','linear-convex'}:
# Make line segments from adjacent points
pts = np.array([x for ((a,b), (c,d)) in window(f, 2) for x in [[a,b], [c,d]]])
# Plot
ax.plot(pts[:,0], pts[:,1], label=label, **sty)
return pts
def show_frontier(X, Y, maxX=False, maxY=True, dots=False,
XMIN=None, XMAX=None,
YMIN=None, YMAX=None,
ax=None, label=None,
interpolation='pessimistic', **style):
"""Plot Pareto frontier.
Args:
X, Y: data.
maxX, maxY: (bool) whether to maximize or minimize along respective
coordinate.
dots: (bool) highlight points on the frontier (will use same color as
`style`).
ax: use an existing axis if non-null.
style: keyword arguments, which will be passed to lines connecting the
points on the Pareto frontier.
XMAX: max value along x-axis
YMIN: min value along y-axis
"""
if ax is None:
ax = pl.gca()
sty = {'c': 'b', 'alpha': 0.3, 'zorder': 0}
sty.update(style)
if interpolation == 'linear-convex':
# Convex hull by itself doesn't work, but what we have is ok because its
# the intersection of the convex hull with the pareto frontier, which is
# handled below.
from scipy.spatial import ConvexHull
X = np.array(X)
Y = np.array(Y)
hull = ConvexHull(np.array([X,Y]).T)
X = X[hull.vertices]
Y = Y[hull.vertices]
# assert not maxX and maxY, 'need to update some hardcoded logic'
f = pareto_frontier(X, Y, maxX=maxX, maxY=maxY)
if not f:
print yellow % '[warn] Empty frontier'
return
if dots:
xs, ys = zip(*f)
ax.scatter(xs, ys, lw=0, alpha=0.5, c=sty['c'])
XMIN = min(min(X), XMIN) if XMIN is not None else min(X)
XMAX = max(max(X), XMAX) if XMAX is not None else max(X)
YMIN = min(min(Y), YMIN) if YMIN is not None else min(Y)
YMAX = max(max(Y), YMAX) if YMAX is not None else max(Y)
# if 0:
# # This version lets you clip away points. I found it a little problematic to use.
# XMIN = XMIN if XMIN is not None else min(X)
# XMAX = XMAX if XMAX is not None else max(X)
# YMIN = YMIN if YMIN is not None else min(Y)
# YMAX = YMAX if YMAX is not None else max(Y)
# if (max(X) > XMAX or min(X) < XMIN or min(Y) > YMIN or max(Y) < YMAX):
# print '[PARETO] Warning: data out of bounds!'
# Connect corners of frontier. The first and last points on frontier have
# lines which surround the point cloud.
# TODO: make this look nicer...
if maxX and maxY:
f = [(XMAX, YMIN)] + f + [(XMIN, YMAX)]
elif not maxX and maxY:
f = [(XMIN, YMIN)] + f + [(XMAX, YMAX)]
elif maxX and not maxY:
f = [(XMAX, YMAX)] + f + [(XMIN, YMIN)]
else:
f = [(XMIN, YMAX)] + f + [(XMAX, YMIN)]
if interpolation == 'pessimistic':
# Make line segments from adjacent points
pts = np.array([x for ((a,b), (c,d)) in window(f, 2) for x in [[a,b], [c,b], [c,b], [c,d]]])
elif interpolation in {'linear','linear-convex'}:
# Make line segments from adjacent points
pts = np.array([x for ((a,b), (c,d)) in window(f, 2) for x in [[a,b], [c,d]]])
# Plot
ax.plot(pts[:,0], pts[:,1], label=label, **sty)
return pts
print '[fit] fitting...'
from ldp.viz.parametric_fit import fit
ff, gg = fit(runtime, accuracy)
print '[fit] done.'
pts = zip(penalty, runtime, accuracy)
# Add two fake points:
# TODO: some magic numbers...
pts = [(None, runtime.max() * 2.0, accuracy.max() * 1.01)
] + pts + [(None, runtime.min() * .98, accuracy.min() * .98)]
ddd = []
skip = []
for (((p1, x1, y1), (p, x2, y2), (p3, x3, y3))) in window(pts, 3):
# slopes give a range for lambda values to try.
m12 = (y2 - y1) / (x2 - x1)
m23 = (y3 - y2) / (x3 - x2)
#print 'penalty=%g point=%s, lambda=%s' % (p, [x2,y2], [m12, m23])
if m12 >= m23:
# This point is not on the convex Pareto frontier. So, we back off to
# the slope between the neighboring points
m31 = (y3 - y1) / (x3 - x1)
#print 'penalty=%g point=%s not on convex frontier.' % (p, [x2,y2]), 'try', m31
m12 = m23 = m31
skip.append([x2, y2])
