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Casper 2018-10-09 19:26:55 +02:00
parent 8a507c08fa
commit 26dfb6d305
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5 changed files with 146 additions and 311 deletions

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@ -1,21 +1,7 @@
# Use atan2 instead of acos to calc angle; atan2(x,y) of the point we potentially want to add
import random
from collections import namedtuple
import matplotlib.pyplot as plt
from math import acos, sqrt
Point = namedtuple('Point', 'x y')
Vector = namedtuple('Vector', 'x y')
def gen_point():
a = random.uniform(1, 5)
b = random.uniform(1, 5)
x_i = random.uniform(1, 5)
p_i = Point(x_i, a * x_i + b)
return p_i
from util import Vector, Point, gen_point, display
def calc_angle(v1: Vector, v2: Vector) -> float:
@ -31,25 +17,10 @@ def calc_angle(v1: Vector, v2: Vector) -> float:
return acos(hmmmmmmm)
def calc_vector(p1: Point, p2: Point) -> Vector:
return Vector((p2.x - p1.x), (p2.y - p1.y))
def display(points, hull):
x = [point.x for point in points]
y = [point.y for point in points]
h_x = [point.x for point in hull]
h_y = [point.y for point in hull]
plt.plot(h_x, h_y, 'ro-')
plt.scatter(x, y)
plt.show()
def rapper(points: set):
min_pt = min(points)
hull = [min_pt]

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@ -1,15 +1,4 @@
import random
from collections import namedtuple
from enum import Enum, auto
import matplotlib.pyplot as plt
Point = namedtuple('Point', ['x', 'y'])
class Side(Enum):
ON = auto()
ABOVE = auto()
BELOW = auto()
from util import gen_point, Side, Point, display
def sidedness(p1, p2, p3, eps=0.0000001):
@ -40,16 +29,6 @@ p3 = Point(5, 2)
# print(sidedness(p1, p2, p3))
def genPoint():
a = random.uniform(1, 5)
b = random.uniform(1, 5)
x_i = random.uniform(1, 5)
p_i = Point(x_i, a * x_i + b)
return p_i
def graham_scan(points):
# A funky issue where both a and b become negative in the sidedness test causes us to have to use
@ -78,20 +57,7 @@ def graham_scan(points):
return UH, LH
p = [genPoint() for _ in range(30)]
p = [gen_point() for _ in range(30)]
UH, LH = graham_scan(p)
x = [point.x for point in p]
y = [point.y for point in p]
UH_x = [point.x for point in UH]
UH_y = [point.y for point in UH]
LH_x = [point.x for point in LH]
LH_y = [point.y for point in LH]
plt.plot(UH_x, UH_y, 'ro-')
plt.plot(LH_x, LH_y, 'ro-')
plt.scatter(x,y)
plt.show()
display(p, {*UH, *LH})

168
h2/mbc.py
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@ -1,66 +1,11 @@
import random
import statistics
from collections import namedtuple
from enum import Enum, auto
from math import inf
from typing import Set, List, Tuple
import matplotlib.pyplot as plt
import numpy as np
from scipy.optimize import linprog
Point = namedtuple('Point', 'x y')
from util import Side, Point, gen_point, display
def gen_point(lower: int, upper: int) -> Point:
a = random.uniform(lower, upper)
b = random.uniform(lower, upper)
x_i = random.uniform(lower, upper)
p_i = Point(x_i, a * x_i + b)
p_i = Point(a, b)
return p_i
def display(points: Set[Point], hull: Set[Point]):
x = [point.x for point in points]
y = [point.y for point in points]
h_x = [point.x for point in hull]
h_y = [point.y for point in hull]
plt.plot(h_x, h_y, 'ro')
plt.scatter(x, y)
plt.show()
def display_line_only(points: Set[Point], slope: int, intercept: int, line_points: Set[Point]):
x = [point.x for point in points]
y = [point.y for point in points]
plt.scatter(x, y)
# Plot a line from slope and intercept
axes = plt.gca()
x_vals = np.array(axes.get_xlim())
y_vals = intercept + slope * x_vals
for point in line_points:
plt.plot(point.x, point.y, 'go')
plt.plot(x_vals, y_vals, '--')
plt.show()
class Side(Enum):
ON = auto()
ABOVE = auto()
BELOW = auto()
def sidedness(slope: int, intersection: int, p3: Point, linprog_flipper: callable, eps=0.0000001) -> Side:
def sidedness(slope: float, intersection: float, p3: Point, linprog_flipper: callable, eps=0.0000001) -> Side:
# finds where a point is in regards to a line
if linprog_flipper(p3.y) - eps <= linprog_flipper(slope * p3.x + intersection) <= linprog_flipper(p3.y) + eps:
return Side.ON
@ -75,38 +20,19 @@ def solve_1dlp(c: float, constraints: List[Tuple[float, float]]):
:param constraints: [(ai, bi), ...]
:return: x1
"""
min_ = -10000
max_ = 10000
for constraint in constraints:
(a, b) = constraint
if a == 0:
assert(b >= 0)
if a > 0:
max_ = min(b/a, max_)
else:
min_ = max(b/a, min_)
try:
if c > 0:
return min_
else:
return max_
return max(b/a for a, b in constraints if a < 0)
return min(b/a for a, b in constraints if a > 0)
except ValueError: # unbounded
return -inf if c > 0 else inf
# if c > 0:
# return max(b/a for a, b in constraints if a < 0)
# return min(b/a for a, b in constraints if a > 0)
#assert solve_1dlp(1, [(-1, -2)]) == 2
#assert solve_1dlp(1, [(-1, -2), (-1, -3)]) == 3
#assert solve_1dlp(1, [(-1, -3), (-1, -2)]) == 3
#assert solve_1dlp(-1, [(1, 3), (1, 2)]) == 2
#assert solve_1dlp(1, [(-1, 3), (-1, 2)]) == -2
assert solve_1dlp(1, [(-1, -2)]) == 2
assert solve_1dlp(1, [(-1, -2), (-1, -3)]) == 3
assert solve_1dlp(1, [(-1, -3), (-1, -2)]) == 3
assert solve_1dlp(-1, [(1, 3), (1, 2)]) == 2
assert solve_1dlp(1, [(-1, 3), (-1, 2)]) == -2
def solve_2dlp(c: Tuple[float, float], constraints: List[Tuple[Tuple[float, float], float]]):
@ -115,69 +41,20 @@ def solve_2dlp(c: Tuple[float, float], constraints: List[Tuple[Tuple[float, floa
:param constraints: [(ai1, ai2, bi), ...]
:return: x1, x2
"""
c1, c2 = c
x1, x2 = (-inf, -inf) if c1 > 0 else (inf, inf)
#random.shuffle(constraints)
if c[0] > 0:
x1 = -10000
else:
x1 = 10000
if c[1] > 0:
x2 = -10000
else:
x2 = 10000
our_constraints = []
for (a1, a2), b in constraints: # TODO: random.shuffle()
print("x1 and x2", x1, x2)
if len(our_constraints) == 0:
our_constraints.append(((a1, a2), b))
for i, ((a1, a2), b) in enumerate(constraints[1:], start=1):
if a1*x1 + a2*x2 <= b:
continue
print("{} + {} <= {}".format(a1*x1, a2*x2, b))
if not (a1*x1 + a2*x2 <= b):
constraint_for_1d = []
new_obj = c[0] - ((c[1]*a1)/a2)
for constraint in our_constraints:
(a_i1, a_i2), b_i = constraint
a_prime = a_i1 - ((a_i2*a1)/a2)
b_prime = b_i - ((a_i2*b)/a2)
constraint_for_1d.append((a_prime, b_prime))
print("obj", new_obj)
print("const", constraint_for_1d)
print("lol",[cons[0] for cons in constraint_for_1d])
# res = linprog([new_obj], [[cons[0]] for cons in constraint_for_1d], [[cons[1]] for cons in constraint_for_1d], bounds=[(None, None)])
x1 = solve_1dlp(new_obj, constraint_for_1d)
# x1 = res.x[0]
x2 = ((b/a2) - (a1/a2)*x1)
our_constraints.append(((a1, a2), b))
x1 = solve_1dlp(c1 - c2*a1/a2, [(ai1 - ai2*a1 / a2, bi - ai2*b / a2) for (ai1, ai2), bi in constraints[:i]])
x2 = (b - a1*x1) / a2
return x1, x2
# assert solve_2dlp((-3, -2), [((-1, 3), 12), ((1, 1), 8), ((2, -1), 10)]) == (6, 2)
c = (-3, -2)
constraints = [
((-1, 3), 12),
((1, 1), 8),
((2, -1), 10),
]
# = (6.0, 2.0)
result = solve_2dlp(c, constraints)
print(result)
#exit()
def mbc_ch(points: Set[Point], linprog_flipper: callable) -> Set[Point]:
if len(points) <= 2:
return points
@ -190,8 +67,8 @@ def mbc_ch(points: Set[Point], linprog_flipper: callable) -> Set[Point]:
pr = {p for p in points if p.x >= med_x}
# Find the bridge over the vertical line in pm
c = [linprog_flipper(med_x), linprog_flipper(1)]
A = [[linprog_flipper(-p.x), linprog_flipper(-1)] for p in points]
c = (linprog_flipper(med_x), linprog_flipper(1))
A = [(linprog_flipper(-p.x), linprog_flipper(-1)) for p in points]
b = [linprog_flipper(-p.y) for p in points]
#result = linprog(c, A, b, bounds=[(None, None), (None, None)], options={"tol": 0.00001})
@ -205,9 +82,6 @@ def mbc_ch(points: Set[Point], linprog_flipper: callable) -> Set[Point]:
left_point = next(p for p in pl if sidedness(slope, intercept, p, linprog_flipper) == Side.ON)
right_point = next(p for p in pr if sidedness(slope, intercept, p, linprog_flipper) == Side.ON)
# Prune the points between the two line points
pl = {p for p in pl if p.x <= left_point.x}
pr = {p for p in pr if p.x >= right_point.x}

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@ -1,41 +1,7 @@
import random
from collections import namedtuple
from enum import Enum, auto
from math import sqrt
from typing import Set
import matplotlib.pyplot as plt
Point = namedtuple('Point', 'x y')
class Side(Enum):
ON = auto()
ABOVE = auto()
BELOW = auto()
def display(points, hull):
x = [point.x for point in points]
y = [point.y for point in points]
h_x = [point.x for point in hull]
h_y = [point.y for point in hull]
plt.plot(h_x, h_y, 'ro')
plt.scatter(x, y)
plt.show()
def gen_point():
a = random.uniform(1, 5)
b = random.uniform(1, 5)
x_i = random.uniform(1, 5)
p_i = Point(x_i, a * x_i + b)
return p_i
from util import Point, gen_point, display
def distance(a, b, c):

58
h2/util.py Normal file
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@ -0,0 +1,58 @@
import random
from collections import namedtuple
from enum import Enum, auto
from typing import Set
import matplotlib.pyplot as plt
import numpy as np
Point = namedtuple('Point', 'x y')
Vector = namedtuple('Vector', 'x y')
def gen_point(lower: int = 0, upper: int = 10) -> Point:
a = random.uniform(lower, upper)
b = random.uniform(lower, upper)
x_i = random.uniform(lower, upper)
p_i = Point(x_i, a * x_i + b)
p_i = Point(a, b)
return p_i
def display(points: Set[Point], hull: Set[Point]):
x = [point.x for point in points]
y = [point.y for point in points]
h_x = [point.x for point in hull]
h_y = [point.y for point in hull]
plt.plot(h_x, h_y, 'ro')
plt.scatter(x, y)
plt.show()
def display_line_only(points: Set[Point], slope: int, intercept: int, line_points: Set[Point]):
x = [point.x for point in points]
y = [point.y for point in points]
plt.scatter(x, y)
# Plot a line from slope and intercept
axes = plt.gca()
x_vals = np.array(axes.get_xlim())
y_vals = intercept + slope * x_vals
for point in line_points:
plt.plot(point.x, point.y, 'go')
plt.plot(x_vals, y_vals, '--')
plt.show()
class Side(Enum):
ON = auto()
ABOVE = auto()
BELOW = auto()