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plot_feasibilities.py
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plot_feasibilities.py
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from builtins import map
from builtins import range
import numpy as np
from gpkit import Model, Variable, ConstraintSet, GPCOLORS, GPBLU
from gpkit.small_scripts import mag
from robust.robust_gp_tools import RobustGPTools
def plot_feasibilities(x, y, m, rm=None, design_feasibility=True, skipfailures=False, numberofsweeps=150):
interesting_vars = [x, y]
rmtype = None
if rm:
rmtype = rm.type_of_uncertainty_set
# posynomials = m.unsubbed
# old = []
# while set(old) != set(interesting_vars):
# old = interesting_vars
# for p in posynomials:
# if set([var.key.name for var in interesting_vars]) & set([var.key.name for var in p.varkeys.keys()]):
# interesting_vars = list(set(interesting_vars) | set([m[var.key.name] for var in p.varkeys.keys() if var.key.pr is not None]))
class FeasCircle(Model):
"""SKIP VERIFICATION"""
def setup(self, m, sol, rob=False):
r = 4
additional_constraints = []
slacks = []
thetas = []
for count in range((len(interesting_vars) - 1)):
th = Variable("\\theta_%s" % count, np.linspace(0, 2 * np.pi, numberofsweeps), "-")
thetas += [th]
for i_set in range(len(interesting_vars)):
if rob:
eta_x = RobustGPTools.generate_etas(interesting_vars[i_set])
else:
eta_x = 0
xo = mag(m.solution(interesting_vars[i_set]))
x_center = np.log(xo)
def f(c, index=i_set, x_val=x_center):
product = 1
for j in range(index):
product *= np.cos(c[thetas[j]])
if index != len(interesting_vars) - 1:
product *= np.sin(c[thetas[index]])
return np.exp(x_val) * np.exp(r * product)
if rmtype == 'box':
def g(c, index=i_set, x_val=x_center, x_nom=xo, eta=eta_x):
product = 1
for j in range(index):
product *= np.cos(c[thetas[j]])
if index != len(interesting_vars) - 1:
product *= np.sin(c[thetas[index]])
return np.exp(max(r*np.abs(product) - (np.log(x_nom) + eta - x_val), 0))
else:
def g(c, index=i_set, x_val=x_center, x_nom=xo, eta=eta_x):
product = 1
for j in range(index):
product *= np.cos(c[thetas[j]])
if index != len(interesting_vars) - 1:
product *= np.sin(c[thetas[index]])
return np.exp(np.abs((np.log(x_nom) + eta - x_val - r)*product))
x_i = Variable('x_%s' % i_set, f, interesting_vars[i_set].unitstr())
s_i = Variable("s_%s" % i_set)
slacks += [s_i]
uncertaintyset = Variable('uncertaintyset_%s' % i_set, g)
var = RobustGPTools.variables_bynameandmodels(m, **interesting_vars[i_set].key.descr)
if len(var) > 1:
raise Exception("vector uncertain variables are not supported yet")
else:
var = var[0]
additional_constraints += [s_i >= 1, s_i <= uncertaintyset*1.000001, var / s_i <= x_i, x_i <= var * s_i]
cost_ref = Variable('cost_ref', 1, m.cost.unitstr(), "reference cost")
self.cost = sum([sl ** 2 for sl in slacks]) * m.cost / cost_ref
feas_slack = ConstraintSet(additional_constraints)
if design_feasibility:
return [m, feas_slack], {k: v for k, v in list(sol["freevariables"].items())
if k in m.varkeys and k.key.fix is True}
else:
return [m, feas_slack], {k: v for k, v in list(sol["freevariables"].items())
if k in m.varkeys}
# plot original feasibility set
# plot boundary of uncertainty set
sol = None
if rm:
fc = FeasCircle(m, rm.get_robust_model().solution, rob=True)
for interesting_var in interesting_vars:
del fc.substitutions[interesting_var]
sol = fc.solve(skipsweepfailures=skipfailures)
ofc = FeasCircle(m, m.solution)
for interesting_var in interesting_vars:
del ofc.substitutions[interesting_var]
origfeas = ofc.solve(skipsweepfailures=skipfailures)
from matplotlib import pyplot as plt
fig, axes = plt.subplots(2)
def plot_uncertainty_set(ax):
xo, yo = list(map(mag, list(map(m.solution, [x, y]))))
ax.plot(xo, yo, "k.")
if rm:
eta_x = RobustGPTools.generate_etas(x)
eta_y = RobustGPTools.generate_etas(y)
x_center = np.log(xo)
y_center = np.log(yo)
ax.plot(np.exp(x_center), np.exp(y_center), "kx")
if rmtype == "elliptical":
th = np.linspace(0, 2 * np.pi, 50)
ax.plot(np.exp(x_center) * np.exp(np.cos(th)) ** (np.log(xo) + eta_x - x_center),
np.exp(y_center) * np.exp(np.sin(th)) ** (np.log(yo) + eta_y - y_center), "k",
linewidth=1)
elif rmtype:
p = Polygon(
np.array([[xo * np.exp(-1*eta_x)] + [xo * np.exp(eta_x)] * 2 + [xo * np.exp(-1*eta_x)],
[yo * np.exp(-1*eta_y)] * 2 + [yo * np.exp(eta_y)] * 2]).T,
True, edgecolor="black", facecolor="none", linestyle="dashed")
ax.add_patch(p)
orig_a, orig_b = list(map(mag, list(map(origfeas, [x, y]))))
a_i, b_i, a, b = [None] * 4
if rm:
x_index = interesting_vars.index(x)
y_index = interesting_vars.index(y)
a_i, b_i, a, b = list(map(mag, list(map(sol, ["x_%s" % x_index, "x_%s" % y_index, x, y]))))
for i in range(len(a)):
axes[0].loglog([a_i[i], a[i]], [b_i[i], b[i]], color=GPCOLORS[1], linewidth=0.2)
else:
axes[0].loglog([orig_a[0]], [orig_b[0]], "k-")
from matplotlib.patches import Polygon
# from matplotlib.collections import PatchCollection
perimeter = np.array([orig_a, orig_b]).T
p = Polygon(perimeter, True, color=GPBLU, linewidth=0)
axes[0].add_patch(p)
if rm:
perimeter = np.array([a, b]).T
p = Polygon(perimeter, True, color=GPCOLORS[1], alpha=0.5, linewidth=0)
axes[0].add_patch(p)
plot_uncertainty_set(axes[0])
axes[0].axis("equal")
# axes[0].set_ylim([0.1, 1])
axes[0].set_ylabel(y)
perimeter = np.array([orig_a, orig_b]).T
p = Polygon(perimeter, True, color=GPBLU, linewidth=0)
axes[1].add_patch(p)
if rm:
perimeter = np.array([a, b]).T
p = Polygon(perimeter, True, color=GPCOLORS[1], alpha=0.5, linewidth=0)
axes[1].add_patch(p)
plot_uncertainty_set(axes[1])
# axes[1].set_xlim([0, 6])
# axes[1].set_ylim([0, 1])
axes[1].set_xlabel(x)
axes[1].set_ylabel(y)
fig.suptitle("%s vs %s feasibility space" % (x, y))
plt.show(block=False)