def cone_with_slice(angles, which, fill_args={}, ax=None, label=None,
Y=None):
ax, poly, constraint, rays = cone_rays(angles, which, ax=ax, fill_args=fill_args)
eta = rays[0]
representation = constraints((constraint, np.zeros(2)), None)
if Y is None:
Y = simulate_from_constraints(representation)
pyplot.scatter(Y[0], Y[1], s=100, label=label)
ax.fill(poly[:,0], poly[:,1], label=r'$C(y)$', **fill_args)
ax.arrow(0,0,eta[0]/200.,eta[1]/200., label=r'$\eta$', linewidth=5, head_width=0.05, fc='k')
Vp, _, Vm = representation.pivots(eta, Y)[:3]
Yperp = Y - (np.dot(eta, Y) /
np.linalg.norm(eta)**2 * eta)
if Vm == np.inf:
Vm = 10000
width_points = np.array([(Yperp + Vp*eta /
np.linalg.norm(eta)**2),
(Yperp + Vm*eta /
np.linalg.norm(eta)**2)])
ax.plot(width_points[:,0], width_points[:,1], 'r--', linewidth=2)
ax.scatter(width_points[:,0], width_points[:,1], label=r'${\cal V}$', s=150, marker='x', linewidth=2, c='k')
return ax, poly, constraint, rays
def cone_with_point(angles, which, fill_args={}, ax=None, label=None,
Y=None):
ax, poly, constraint, rays = cone_rays(angles, which, ax=ax, fill_args=fill_args)
eta = rays[0]
representation = constraints((constraint, np.zeros(2)), None)
if Y is None:
Y = simulate_from_constraints(representation)
pyplot.scatter(Y[0], Y[1], s=100, label=label)
return ax, poly, constraint, rays
def cone_with_point(angles, which, fill_args={}, ax=None, label=None, Y=None):
ax, poly, constraint, rays = cone_rays(angles,
which,
ax=ax,
fill_args=fill_args)
eta = rays[0]
representation = constraints((constraint, np.zeros(2)), None)
if Y is None:
Y = simulate_from_constraints(representation)
pyplot.scatter(Y[0], Y[1], s=100, label=label)
return ax, poly, constraint, rays
def cone_with_arrow(angles, which, fill_args={}, ax=None, label=None,
Y=None):
ax, poly, constraint, rays = cone_rays(angles, which, ax=ax, fill_args=fill_args)
eta = rays[0]
representation = constraints((constraint, np.zeros(2)), None)
if Y is None:
Y = simulate_from_constraints(representation)
pyplot.scatter(Y[0], Y[1], s=100, label=label)
ax.fill(poly[:,0], poly[:,1], label=r'$C(y)$', **fill_args)
ax.arrow(0,0,eta[0]/200.,eta[1]/200., label=r'$\eta$', linewidth=5, head_width=0.05, fc='k')
return ax, poly, constraint, rays
def hull_with_point(W, fill=True, fill_args={}, label=None, ax=None, Y=None):
f, A, b, pairs, angles, perimeter = just_hull(W,
fill=fill,
label=label,
ax=ax,
fill_args=fill_args)
representation = constraints((A, b), None)
if Y is None:
Y = simulate_from_constraints(representation)
a = f.gca()
a.scatter(Y[0], Y[1], label=r'$y$', s=100)
return f, A, b, pairs, angles, perimeter
def hull_with_point(W, fill=True, fill_args={}, label=None, ax=None,
Y=None):
f, A, b, pairs, angles, perimeter = just_hull(W,
fill=fill,
label=label,
ax=ax,
fill_args=fill_args)
representation = constraints((A,b), None)
if Y is None:
Y = simulate_from_constraints(representation)
a = f.gca()
a.scatter(Y[0], Y[1], label=r'$y$', s=100)
return f, A, b, pairs, angles, perimeter
def hull_with_slice(W,
fill=True,
fill_args={},
label=None,
ax=None,
Y=None,
eta=None):
f, A, b, pairs, angles, perimeter = just_hull(W,
fill=fill,
label=label,
ax=ax,
fill_args=fill_args)
representation = constraints((A, b), None)
if Y is None:
Y = simulate_from_constraints(representation)
ax.scatter(Y[0], Y[1], label=r'$y$', s=100)
if eta is None:
eta = np.random.standard_normal(2)
ax.arrow(0, 0, eta[0], eta[1], linewidth=5, head_width=0.05, fc='k')
Vp, _, Vm = representation.pivots(eta, Y)[:3]
Yperp = Y - (np.dot(eta, Y) / np.linalg.norm(eta)**2 * eta)
if Vm == np.inf:
Vm = 10000
width_points = np.array([(Yperp + Vp * eta / np.linalg.norm(eta)**2),
(Yperp + Vm * eta / np.linalg.norm(eta)**2)])
ax.plot(width_points[:, 0], width_points[:, 1], 'r--', linewidth=2)
ax.scatter(width_points[:, 0],
width_points[:, 1],
label=r'${\cal V}$',
s=150,
marker='x',
linewidth=2,
c='k')
return f, A, b, pairs, angles, perimeter
def cone_with_slice(angles, which, fill_args={}, ax=None, label=None, Y=None):
ax, poly, constraint, rays = cone_rays(angles,
which,
ax=ax,
fill_args=fill_args)
eta = rays[0]
representation = constraints((constraint, np.zeros(2)), None)
if Y is None:
Y = simulate_from_constraints(representation)
pyplot.scatter(Y[0], Y[1], s=100, label=label)
ax.fill(poly[:, 0], poly[:, 1], label=r'$C(y)$', **fill_args)
ax.arrow(0,
0,
eta[0] / 200.,
eta[1] / 200.,
label=r'$\eta$',
linewidth=5,
head_width=0.05,
fc='k')
Vp, _, Vm = representation.pivots(eta, Y)[:3]
Yperp = Y - (np.dot(eta, Y) / np.linalg.norm(eta)**2 * eta)
if Vm == np.inf:
Vm = 10000
width_points = np.array([(Yperp + Vp * eta / np.linalg.norm(eta)**2),
(Yperp + Vm * eta / np.linalg.norm(eta)**2)])
ax.plot(width_points[:, 0], width_points[:, 1], 'r--', linewidth=2)
ax.scatter(width_points[:, 0],
width_points[:, 1],
label=r'${\cal V}$',
s=150,
marker='x',
linewidth=2,
c='k')
return ax, poly, constraint, rays
def cone_with_arrow(angles, which, fill_args={}, ax=None, label=None, Y=None):
ax, poly, constraint, rays = cone_rays(angles,
which,
ax=ax,
fill_args=fill_args)
eta = rays[0]
representation = constraints((constraint, np.zeros(2)), None)
if Y is None:
Y = simulate_from_constraints(representation)
pyplot.scatter(Y[0], Y[1], s=100, label=label)
ax.fill(poly[:, 0], poly[:, 1], label=r'$C(y)$', **fill_args)
ax.arrow(0,
0,
eta[0] / 200.,
eta[1] / 200.,
label=r'$\eta$',
linewidth=5,
head_width=0.05,
fc='k')
return ax, poly, constraint, rays
def hull_with_slice(W, fill=True, fill_args={}, label=None, ax=None,
Y=None,
eta=None):
f, A, b, pairs, angles, perimeter = just_hull(W,
fill=fill,
label=label,
ax=ax,
fill_args=fill_args)
representation = constraints((A,b), None)
if Y is None:
Y = simulate_from_constraints(representation)
ax.scatter(Y[0], Y[1], label=r'$y$', s=100)
if eta is None:
eta = np.random.standard_normal(2)
ax.arrow(0,0,eta[0],eta[1], linewidth=5, head_width=0.05, fc='k')
Vp, _, Vm = representation.pivots(eta, Y)[:3]
Yperp = Y - (np.dot(eta, Y) /
np.linalg.norm(eta)**2 * eta)
if Vm == np.inf:
Vm = 10000
width_points = np.array([(Yperp + Vp*eta /
np.linalg.norm(eta)**2),
(Yperp + Vm*eta /
np.linalg.norm(eta)**2)])
ax.plot(width_points[:,0], width_points[:,1], 'r--', linewidth=2)
ax.scatter(width_points[:,0], width_points[:,1], label=r'${\cal V}$', s=150, marker='x', linewidth=2, c='k')
return f, A, b, pairs, angles, perimeter