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This commit is contained in:
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d580ea4c89
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56c0948ba7
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@ -1,192 +0,0 @@
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import matplotlib.pyplot as plt
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import collections
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from enum import Enum, auto
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from random import randint
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Point = collections.namedtuple("Point", ("x", "y"))
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class Side(Enum):
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ON = auto()
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ABOVE = auto()
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BELOW = auto()
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def sidedness(slope, intersection, p3, eps=0.0000001):
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print(slope * p3[0] + intersection )
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# finds where a point is in regards to a line
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if p3[1] - eps <= slope * p3[0] + intersection <= p3[1] + eps or p3[0] - eps <= (p3[1] - intersection)/slope <= p3[0] + eps:
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return Side.ON
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elif p3[1] > slope * p3[0] + intersection:
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return Side.ABOVE
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return Side.BELOW
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def diplay_prune_points(points, p1, p2):
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xs = [p[0] for p in points]
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ys = [p[1] for p in points]
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plt.plot(xs, ys, 'ro')
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plt.plot([p1[0], p2[0]], [p1[1], p2[1]])
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plt.show()
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def solve1D(points, xm, iteration_num):
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#print("iter:", iteration_num)
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point = points[iteration_num]
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if iteration_num == 0:
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return -float('Inf'), -float('Inf')
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# lad point[1] = point[0] * a + b <=> y = x * a + b
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# isolere b og sæt ind i constraints
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a = None
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b = point[1] - point[0] # * a
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# minimere xm*a + b, hvor b har ny værdi
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# Vi regner kun med koefficienterne
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# obj_fun = (xm - point[0]) + points[1] = (xm*a - xi*a) + y
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# max eller min
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#print("XM og point[0]:", xm, point[0])
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a = xm - point[0]
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#print("a lige her:", a)
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a_constraint_list = []
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# looping over the i constraints
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for p in points[:iteration_num]:
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# we can't make a straigt vertical line
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if p[0] == point[0]:
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if p[1] > point[1]:
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p[0] = p[0] + 0.0001
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else:
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point[0] = point[0] + 0.0001
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print(p, point)
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# Spring over den i'te constraint
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if p != point:
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# y_j - yi
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c = p[1] - point[1]
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# x_j * a - xi * a
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a_diff = p[0] - point[0]
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print(c, a_diff, c/a_diff)
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# det her er forkert og skal fikses
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if a >= 0 and a_diff < 0:
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a_constraint_list.append(-float('Inf'))
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else:
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a_constraint_list.append(c/a_diff)
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# hvis a > 0 så min
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# hvis a < 0 så max.
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if a >= 0:
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v1 = max(a_constraint_list)
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v2 = point[1] - point[0] * v1
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v = (v1, v2)
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elif a < 0:
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v1 = min(a_constraint_list)
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v2 = point[1] - point[0] * v1
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v = (v1, v2)
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return v
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def findBridge(points, xm):
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if xm > 0:
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v = (-float('Inf'), -float('Inf'))
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elif xm < 0:
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4 # noget
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else:
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# TODO: xm == 0
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4
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# looping over constraints
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for point in points:
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# checking for violation
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if not point[1] <= point[0] * v[0] + v[1]:
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v = solve1D(points, xm, points.index(point))
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#print("HER OVER: ", v)
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slope = v[0]
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intercept = v[1]
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line_points = [p for p in points if sidedness(slope, intercept, p) == Side.ON]
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if len(line_points) > 3:
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print("Halli HAllo")
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print(line_points)
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return line_points[0], line_points[1]
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def find_median(points):
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if len(points) % 2 == 0:
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first_med_idx = int(len(points) / 2 - 1)
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second_med_idx = int(len(points) / 2)
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return (points[first_med_idx][0] + points[second_med_idx][0]) / 2
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else:
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idx = int((len(points)-1) / 2)
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return points[idx][0]
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def upperHull(points, all_points):
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print("Punkter:", points)
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if len(points) < 2:
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return []
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xm = find_median(points)
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# end-points of bridge
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(xi, yi), (xj, yj) = findBridge(points, xm)
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#print(xm)
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print((xi, yi), (xj, yj))
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prune_points = [p for p in points if p[0] < xi or xj < p[0]] + [(xi, yi), (xj, yj)]
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# Neden for er mest for visualisering
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prune_all_points = [p for p in all_points if p[0] < xi or xj < p[0]] + [(xi, yi), (xj, yj)]
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diplay_prune_points(prune_all_points, (xi, yi), (xj, yj))
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Pl = [p for p in prune_points if p[0] < xm]
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Pr = [p for p in prune_points if p[0] >= xm]
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#print("Pl:", Pl, "Pr", Pr)
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print("\n")
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# recurse results and return
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ret = [(xi, yi), (xj, yj)]
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ret = ret + [p for p in upperHull(Pl, prune_all_points) if p not in ret]
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ret = ret + [p for p in upperHull(Pr, prune_all_points) if p not in ret]
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return ret
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p1 = (2, 1)
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p2 = (3, 4)
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p3 = (5, 2)
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p4 = (6, 5)
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list_of_points = []
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list_of_points.append(p1)
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list_of_points.append(p2)
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list_of_points.append(p3)
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list_of_points.append(p4)
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xs = [p[0] for p in list_of_points]
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ys = [p[1] for p in list_of_points]
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plt.plot(xs, ys, 'ro')
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plt.show()
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result = list(sorted(upperHull(list_of_points, list_of_points)))
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result
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res_xs = [p[0] for p in result]
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res_ys = [p[1] for p in result]
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#print("result", result)
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plt.plot(res_xs, res_ys)
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plt.plot(xs, ys, 'ro')
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plt.show()
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172
h2/mbc.py
172
h2/mbc.py
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@ -1,12 +1,8 @@
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import statistics
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from math import inf, isnan, sqrt
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from typing import Set, List, Tuple
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import util
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from scipy.optimize import linprog
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import scipy
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import random
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from math import sqrt
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from typing import Set
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from util import Side, Point, gen_point, display, display_line_only, gen_circular_point, gen_weird_point, gen_triangular_point
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from util import Side, Point, gen_point, display, gen_circular_point, gen_triangular_point
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def sidedness(slope: float, intersection: float, p3: Point, flipper: callable, eps=0.0000001) -> Side:
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@ -18,54 +14,20 @@ def sidedness(slope: float, intersection: float, p3: Point, flipper: callable, e
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return Side.BELOW
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def solve_1dlp(c: float, constraints: List[Tuple[float, float]]):
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"""
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:param c: c1
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:param constraints: [(ai, bi), ...]
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:return: x1
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"""
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min_ = -10000
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max_ = 10000
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for constraint in constraints:
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(a, b) = constraint
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if a == 0:
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assert(b >= 0)
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if a > 0:
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max_ = min(b/a, max_)
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elif a < 0:
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min_ = max(b/a, min_)
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if c > 0:
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return min_
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else:
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return max_
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assert solve_1dlp(1, [(-1, -2)]) == 2
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assert solve_1dlp(1, [(-1, -2), (-1, -3)]) == 3
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assert solve_1dlp(1, [(-1, -3), (-1, -2)]) == 3
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assert solve_1dlp(-1, [(1, 3), (1, 2)]) == 2
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assert solve_1dlp(1, [(-1, 3), (-1, 2)]) == -2
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def new_solve_1dlp(c, constraints, idx):
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def solve_1dlp(c, constraints):
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c1, c2 = c
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((a1, a2), b) = constraints[-1]
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q, p = b / a2, a1 /a2
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q, p = b / a2, a1 / a2
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interval = [-9999999, 9999999]
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interval = [-10_000, 10_000]
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for new_idx, ((lel_a1, lel_a2), lel_b) in enumerate(constraints):
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for (lel_a1, lel_a2), lel_b in constraints:
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bj, aj = (lel_b - lel_a2 * q), (lel_a1 - lel_a2 * p)
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if aj < 0 and bj / aj > interval[0]:
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interval[0] = bj / aj
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elif aj > 0 and bj / aj < interval[1]:
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interval[1] = bj/aj
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interval[1] = bj / aj
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c = -(c1 - c2 * p)
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if c < 0:
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return interval[1], q - (p * interval[1])
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def new_solve_2dlp(c, constraints):
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def solve_2dlp(c, constraints):
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c1, c2 = c
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x1 = -10000 if c1 > 0 else 10000
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x2 = -10000 if c2 > 0 else 10000
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x1 = -10_000 if c1 > 0 else 10_000
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x2 = -10_000 if c2 > 0 else 10_000
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for idx, ((a1, a2), b) in enumerate(constraints):
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for i, ((a1, a2), b) in enumerate(constraints, start=1):
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if not (a1*x1 + a2*x2 <= b):
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x1,x2 = new_solve_1dlp(c, constraints[:idx+1], idx)
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return x1,x2
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def solve_2dlp(c: Tuple[float, float], constraints: List[Tuple[Tuple[float, float], float]]):
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"""
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:param c: (c1, c2)
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:param constraints: [(ai1, ai2, bi), ...]
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:return: x1, x2
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"""
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c1, c2 = c
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x1 = -10000 if c1 > 0 else 10000
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x2 = -10000 if c2 > 0 else 10000
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#random.shuffle(constraints)
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for idx, ((a1, a2), b) in enumerate(constraints[1:]):
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#print("x1 and x2", x1, x2)
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#print("{} + {} <= {}".format(a1*x1, a2*x2, b))
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#print("pls",a1*x1 + a2*x2)
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#print("yes"*10) if isnan(a1*x1+a2*x2) else print("no"*10)
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if not (a1*x1 + a2*x2 <= b):
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constraint_for_1d = []
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new_obj = c[0] - ((c[1]*a1)/a2)
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for constraint in constraints[:idx]:
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(a_i1, a_i2), b_i = constraint
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a_prime = a_i1 - ((a_i2*a1)/a2)
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b_prime = b_i - ((a_i2*b)/a2)
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constraint_for_1d.append((a_prime, b_prime))
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#print("obj", new_obj)
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#print("const", constraint_for_1d)
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#print("lol",[cons[0] for cons in constraint_for_1d])
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#res = linprog([new_obj], [[cons[0]] for cons in constraint_for_1d], [[cons[1]] for cons in constraint_for_1d], bounds=[(None, None)])
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x1 = solve_1dlp(new_obj, constraint_for_1d)
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#x1 = res.x
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#print(res)
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x2 = ((b/a2) - (a1/a2)*x1)
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x1, x2 = solve_1dlp(c, constraints[:i])
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return x1, x2
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@ -147,72 +58,27 @@ def find_median(points):
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return median[0]
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def mbc_ch(points: Set[Point], flipper: callable) -> Set[Point]:
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def mbc_ch(points: Set[Point], flipper: callable) -> Set[Point]:
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if len(points) < 2:
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return points
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# Find the point with median x-coordinate, and partition the points on this point
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med_x = find_median(points)
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#med_x = statistics.median(p.x for p in points)
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#print(med_x)
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# Find left and right points in regards to median
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pl = {p for p in points if p.x < med_x}
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pr = {p for p in points if p.x >= med_x}
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#print("pl\n",pl)
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#print("pr\n",pr)
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c = [flipper(med_x), flipper(1)]
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A = [[flipper(-p.x), flipper(-1)] for p in points]
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b = [flipper(-p.y) for p in points]
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# Find the bridge over the vertical line in pm
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#slope, intercept = solve_2dlp((flipper(med_x), flipper(1)),
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# [((flipper(-p.x), flipper(-1)), flipper(-p.y)) for p in points]) # confirmed correct
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slope, intercept = new_solve_2dlp((flipper(med_x), flipper(1)),
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slope, intercept = solve_2dlp((flipper(med_x), flipper(1)),
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[((flipper(-p.x), flipper(-1)), flipper(-p.y)) for p in points])
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#print("slope, intercept:",slope, intercept)
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res = linprog(c, A, b, bounds=[[None, None], [None, None]], options={"tol": 0.01})
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#print("res0, res1:",res.x[0], res.x[1])
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#slope, intercept = res.x[0], res.x[1]
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#display_line_only(points, slope, intercept, [])
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# Find the two points which are on the line, should work
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#on = {p for p in points if sidedness(slope, intercept, p, flipper) == Side.ON}
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#print("On Points:",on)
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#left_point = min(on)
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#right_point = max(on)
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# Find the two points which are on the line
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dist_to_line = lambda p: abs(intercept + slope * p.x - p.y)/sqrt(1 + slope**2)
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left_point = min(pl, key = dist_to_line)
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left_point = min(pl, key=dist_to_line)
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right_point = min(pr, key=dist_to_line)
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#display_line_only(points, slope, intercept, [left_point, right_point])
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#left_point = next(p for p in pl if sidedness(slope, intercept, p, flipper) == Side.ON)
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#right_point = next(p for p in pr if sidedness(slope, intercept, p, flipper) == Side.ON)
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def find_med_point(points, med_x):
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for p in points:
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if med_x+0.001 >= p.x >= med_x-0.001:
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return {p}
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return {}
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#print("med point:",find_med_point(points, med_x))
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#display_line_only(points, slope, intercept, {left_point, right_point})
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# Prune the points between the two line points
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pl = {p for p in pl if p.x <= left_point.x}
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pr = {p for p in pr if p.x >= right_point.x}
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@ -227,11 +93,9 @@ def mbc(points: Set[Point]) -> Set[Point]:
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if __name__ == '__main__':
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random.seed(1337_420)
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points = {gen_point(0, 20) for _ in range(20)}
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#points = {gen_circular_point(1, 100, 50) for _ in range(200)}
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points = {gen_circular_point(1, 100, 50) for _ in range(200)}
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#points = {gen_triangular_point(Point(1,1), Point(51,1), Point(26, 30)) for _ in range(200)}
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#points = {Point(x=-33.11091053638924, y=38.88967778961347), Point(x=61.20269947424177, y=-78.96305419217254), Point(x=99.44053842147957, y=-89.11579172297581), Point(x=-92.40380889537532, y=84.33904351991652), Point(x=-90.63139185545595, y=-91.13793846505985)}
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#points = {Point(x=5.2, y=9.7), Point(x=5.3, y=4.9), Point(x=3.3, y=3.6), Point(x=9.2, y=4.8), Point(x=9.7, y=5.7), Point(x=5.6, y=8.7)}
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upper_hull_points = mbc_ch(points, lambda x: x)
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