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KK.py
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896 lines (815 loc) · 35.4 KB
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# -*- coding: utf-8 -*-
# @Time : 2018/7/20 10:00
# @Author : SilverMaple
# @Site : https:#github.com/SilverMaple
# @File : KK.py
import math
import random
import traceback
import numpy
import win_unicode_console
from numpy.random.mtrand import rand, randint
from FR import Community
from visualization import COLOR_CONFIG
VERTEXES_COUNT = 0
NETWORK_FILE = 'f1.txt'
COMMUNITY_FILE = 'f2.txt'
paper1 = "Tomihisa Kamada and Satoru Kawai: An algorithm for drawing general " \
"indirect graphs. Information Processing Letters 31(1):7-15, 1989"
paper2 = "Tomihisa Kamada: On visualization of abstract objects and relations. " \
"Ph.D. dissertation, Dept. of Information Science, Univ. of Tokyo, Dec. 1988."
# Kamada-Kawai algorithm
class KKLayout:
# Creates an instance for the specified graph and distance metric.
def __init__(self):
self.graph = None
self.vertexes = []
self.edges = []
self.setAttribute(iterations=500, epsilon=0.1, k=1, l=0.9)
self.get_vertexes_count()
def setAttribute(self, iterations, epsilon, k, l):
self.EPSILON = epsilon # 0.1
self.currentIteration = None
self.maxIterations = iterations # 2000
self.status = "KKLayout"
self.L = None # 弹簧长度系数，即边的理想长度
self.K = k # 1 # 弹簧强度系数，对算法结果影响不大
self.dm = [] # 最短距离矩阵，使用Dijkstra最短路径算法
self.isAdjustForGravity = True
self.isExchangeVertices = True
self.vertices = []
self.positions = []
self.PLOT_WIDTH = 500
self.PLOT_HEIGHT = 500
self.size = {'width': self.PLOT_WIDTH, 'height': self.PLOT_HEIGHT}
# Retrieves graph distances between vertices of the visible graph
self.distance = []
# The diameter of the visible graph.In other words, the maximum over all pairs
# of vertices of the length of the shortest path between a and b of the visible graph.
# 图直径
self.diameter = 5.0 # 5.0
# A multiplicative factor which partly specifies the "preferred" length of an edge (L).
self.length_factor = l # 0.9
# A multiplicative factor which specifies the fraction of the graph's diameter to be
# used as the inter-vertex distance between disconnected vertices.
self.disconnected_multiplier = 0.7 # 0.5
self.locations = []
self.minEnergy = None
self.minIndex = -1
self.finalPos = None
def get_vertexes_count(self):
global VERTEXES_COUNT
VERTEXES_COUNT *= 0
lines = open(COMMUNITY_FILE, 'r', encoding='utf-8').readlines()
for i in range(len(lines)):
# global VERTEXES_COUNT
line = lines[i]
name, members_list = line.split(':')
VERTEXES_COUNT += len(members_list.split())
def setSize(self, width, height):
self.size = {'width': width, 'height': height}
# Returns True once the current iteration has passed the maximum count.
def done(self):
if self.currentIteration > self.maxIterations:
return True
return False
def initialize(self):
# 1
# for i in range(11):
# connections = []
# RandCx1 = randint(0, 2)
# for j in range(RandCx1+1):
# RandCx2 = rand(0, 10)
# if RandCx2 != j:
# connections.append(RandCx2)
# nodes.append({'idx': i, "conn": connections})
self.graph = []
for i in range(len(self.vertexes)):
connections = []
for j in range(len(self.edges)):
if i+1 in self.edges[j]:
if i+1 == self.edges[j][0]:
connections.append(self.edges[j][1]-1)
else:
connections.append(self.edges[j][0]-1)
self.graph.append({'idx': i, "conn": connections})
# 2
self.currentIteration = 0
if self.graph != None and self.size != None:
height = self.size['height']
width = self.size['width']
n = len(self.graph)
# self.dm = [] # new Array[n][n]
self.dm = numpy.zeros((n, n))
self.vertices = self.graph
self.positions = []
# assign IDs to all visible vertices
loopTimes = 1
# while True:
for i in range(loopTimes):
try:
index = 0
for v in self.graph:
xyd = self.transform()
self.vertices[index] = v
self.positions.append(xyd)
index += 1
break
except Exception as e:
print(e)
# self.diameter = 5.0 # DistanceStatistics. < V, E > diameter(graph, distance, True)
L0 = min(height, width)
self.L = (L0 / self.diameter) * self.length_factor # length_factor used to be hardcoded to 0.9
# L = 0.75 * sqrt(height * width / n)
for i in range(n-1):
for j in range(i+1, n):
d_ij = self.getDistance(self.vertices[i], self.vertices[j])
d_ji = self.getDistance(self.vertices[j], self.vertices[i])
dist = self.diameter * self.disconnected_multiplier
if d_ij != None:
dist = min(d_ij, dist)
if d_ji != None:
dist = min(d_ji, dist)
self.dm[i][j] = dist
self.dm[j][i] = dist
# init node 's position
# @return ArrayObject
def transform(self):
# x = randint(10, self.size['width'] - 1)
# y = randint(10, self.size['height'] - 1)
x = random.uniform(10, self.PLOT_WIDTH)
y = random.uniform(10, self.PLOT_HEIGHT)
return {'x': x, 'y': y}
# For now, it is just a very simple strategy to get weight of distance
# TODO: fix it!
# @ param from
# @ param to
# @return distance weight
def getDistance(self, v1, v2):
fromid = v1['idx']
toid = v2['idx']
if toid in v1['conn']:
weight = 1
else:
weight = None
return weight
def step(self):
try:
self.currentIteration += 1
energy = self.calcEnergy()
if self.minEnergy:
if energy < self.minEnergy:
self.minEnergy = energy
self.minIndex = self.currentIteration
self.finalPos = self.positions
else:
self.minEnergy = energy
self.finalPos = self.positions
self.status = "Kamada-Kawai V=" + str(len(self.graph)) + "(" + str(len(self.graph)) \
+ ")" + " IT: " + str(self.currentIteration) + " E=" + str(energy)
print(self.status)
n = len(self.graph)
if n == 0:
return
maxDeltaM = 0
pm = -1 # the node having max deltaM
for i in range(n):
deltam = self.calcDeltaM(i)
if maxDeltaM < deltam:
maxDeltaM = deltam
pm = i
if pm == -1:
return
# 找到偏移量最大的点下标，进行迭代偏移直至偏移量小于阈值
for i in range(100):
dxy = self.calcDeltaXY(pm)
self.positions[pm]['x'] = self.positions[pm]['x'] + dxy[0]
self.positions[pm]['y'] = self.positions[pm]['y'] + dxy[1]
deltam = self.calcDeltaM(pm)
if deltam < self.EPSILON:
6880
break
# 调整网络坐标
if self.isAdjustForGravity:
self.adjustForGravity()
if self.isExchangeVertices and maxDeltaM < self.EPSILON:
energy = self.calcEnergy()
for i in range(n-1):
for j in range(i+1, n):
xenergy = self.calcEnergyIfExchanged(i, j)
if energy > xenergy:
sx = self.positions[i]['x']
sy = self.positions[i]['y']
self.positions[i]['x'] = self.positions[j]['x'] #.setLocation(xydata[j])
self.positions[i]['y'] = self.positions[j]['y']
self.positions[j]['x'] = sx
self.positions[j]['y'] = sy
return
except Exception as e:
traceback.print_exc()
print(e)
# Shift all vertices so that the center of gravity is located at
# the center of the screen.
def adjustForGravity(self):
d = self.size
height = d['height']
width = d['width']
gx = 0
gy = 0
cnt = len(self.positions)
for i in range(cnt):
gx += self.positions[i]['x']
gy += self.positions[i]['y']
gx /= cnt
gy /= cnt
diffx = width / 2 - gx
diffy = height / 2 - gy
for i in range(cnt):
self.positions[i]['x'] = self.positions[i]['x'] + diffx
self.positions[i]['y'] = self.positions[i]['y'] + diffy
# Determines a step to new position of the vertex m.
def calcDeltaXY(self, m):
dE_dxm = 0 # E对x偏微分
dE_dym = 0 # E对y偏微分
d2E_d2xm = 0
d2E_dxmdym = 0
d2E_dymdxm = 0
d2E_d2ym = 0
for i in range(len(self.vertices)):
if i != m:
dist = self.dm[m][i]
l_mi = self.L * dist
k_mi = self.K / (dist * dist)
dx = self.positions[m]['x'] - self.positions[i]['x']
dy = self.positions[m]['y'] - self.positions[i]['y']
d = math.sqrt(dx * dx + dy * dy)
ddd = d * d * d
dE_dxm += k_mi * (1 - l_mi / d) * dx
dE_dym += k_mi * (1 - l_mi / d) * dy
d2E_d2xm += k_mi * (1 - l_mi * dy * dy / ddd)
d2E_dxmdym += k_mi * l_mi * dx * dy / ddd
d2E_d2ym += k_mi * (1 - l_mi * dx * dx / ddd)
# d2E_dymdxm equals to d2E_dxmdym.
d2E_dymdxm = d2E_dxmdym
denomi = d2E_d2xm * d2E_d2ym - d2E_dxmdym * d2E_dymdxm
deltaX = (d2E_dxmdym * dE_dym - d2E_d2ym * dE_dxm) / denomi
deltaY = (d2E_dymdxm * dE_dxm - d2E_d2xm * dE_dym) / denomi
return [deltaX, deltaY]
# Calculates the gradient of energy function at the vertex m.
def calcDeltaM(self, m):
dEdxm = 0
dEdym = 0
for i in range(len(self.vertices)):
if i != m:
dist = self.dm[m][i]
l_mi = self.L * dist
k_mi = self.K / (dist * dist)
dx = self.positions[m]['x'] - self.positions[i]['x']
dy = self.positions[m]['y'] - self.positions[i]['y']
d = math.sqrt(dx * dx + dy * dy)
common = k_mi * (1 - l_mi / d)
dEdxm += common * dx
dEdym += common * dy
return math.sqrt(dEdxm * dEdxm + dEdym * dEdym)
# Calculates the energy function E.
def calcEnergy(self):
energy = 0
for i in range(len(self.vertices)- 1):
for j in range(i+1, len(self.vertices)):
dist = self.dm[i][j] # i，j两个节点的图距离
l_ij = self.L * dist # i，j两个节点的理想距离等于图距离与常数乘积
k_ij = self.K / (dist * dist) # i，j两点之间的力强度
dx = self.positions[i]['x'] - self.positions[j]['x']
57A6
dy = self.positions[i]['y'] - self.positions[j]['y']
d = math.sqrt(dx * dx + dy * dy) # 坐标距离
energy += k_ij / 2 * (dx * dx + dy * dy + l_ij * l_ij - 2 * l_ij * d)
return energy
# Calculates the energy function E as if positions of the
# specified vertices are exchanged.
def calcEnergyIfExchanged(self, p, q):
if p >= q:
raise Exception("p should be < q")
energy = 0 # < 0
for i in range(len(self.vertices) - 1):
for j in range(i+1, len(self.vertices)):
ii = i
jj = j
if i == p:
ii = q
if j == q:
jj = p
dist = self.dm[i][j]
l_ij = self.L * dist
k_ij = self.K / (dist * dist)
dx = self.positions[ii]['x'] - self.positions[jj]['x']
dy = self.positions[ii]['y'] - self.positions[jj]['y']
d = math.sqrt(dx * dx + dy * dy)
energy += k_ij / 2 * (dx * dx + dy * dy + l_ij * l_ij - 2 * l_ij * d)
return energy
def reset(self):
self.currentIteration = 0
# 从文件中导入关系图，每一行表示两个节点之间的一条连接，格式如下所示：
# 2 1
# 3 1
# 3 2
# 4 1
# ...
def import_network_information(self):
lines = open(NETWORK_FILE, 'r').readlines()
self.vertexes = [i+1 for i in range(VERTEXES_COUNT)]
for line in lines:
a, b = line.replace('\n', '').split(' ')
a = int(a)
b = int(b)
self.edges.append((a, b))
# 从文件中导入社区信息，每一行表示一个社区信息，社区名字与具体成员以英文冒号分隔，成员之间以空格分隔，格式如下所示：
# 社区1:1 2 4 5 6 7 8 11 12 13 14 17 18 20 22
# 社区2:3 9 10 15 16 19 21 23 24 25 26 27 28 29 30
# ...
def set_community_member(self):
lines = open(COMMUNITY_FILE, 'r', encoding='utf-8').readlines()
self.communities = [Community() for i in range(len(lines))]
for i in range(len(lines)):
line = lines[i]
name, members_list = line.split(':')
self.communities[i].name = name
members = members_list.strip().split(' ')
for m in members:
if not m.isdigit():
continue
m = int(m)
# 设置顶点颜色形状
self.communities[i].vertexes.append(m)
def normalizeScope(self):
margin = 30
minx = min(self.positions[i][0] for i in self.positions)
miny = min(self.positions[i][1] for i in self.positions)
maxx = max(self.positions[i][0] for i in self.positions)
maxy = max(self.positions[i][1] for i in self.positions)
factorx = self.PLOT_WIDTH / (maxx - minx)
factory = self.PLOT_HEIGHT / (maxy- miny)
for i in self.positions:
self.positions[i][0] = (self.positions[i][0] - minx) * factorx
self.positions[i][1] = (self.positions[i][1] - miny) * factory
minx = min(self.positions[i][0] for i in self.positions)
miny = min(self.positions[i][1] for i in self.positions)
maxx = max(self.positions[i][0] for i in self.positions)
maxy = max(self.positions[i][1] for i in self.positions)
fitnessX = (self.PLOT_WIDTH - 2*margin) / (maxx + (self.PLOT_WIDTH - (maxx-minx))/2)
fitnessY = (self.PLOT_HEIGHT - 2*margin) / (maxy + (self.PLOT_HEIGHT - (maxy-miny))/2)
# print(fitnessX, fitnessY)
for i in self.positions:
self.positions[i][0] = (self.positions[i][0] + (self.PLOT_WIDTH - (maxx-minx))/2) * fitnessX + margin
self.positions[i][1] = (self.positions[i][1] + (self.PLOT_HEIGHT - (maxy-miny))/2) * fitnessY + margin
def outputPoints(self):
# "228.918895098647" "319.544170947533" "#FF0000FF"
f = open('points.txt', 'w')
cs = COLOR_CONFIG
# cs = ['#FF0099FF', '#CC00FFFF', '#3300FFFF']
# 转化格式
self.positionsIndex = {i: (self.finalPos[i-1]['x'], self.finalPos[i-1]['y'])
for i in range(1, len(self.finalPos)+1)}
# self.positionsIndex = {i: (self.positions[i-1]['x'], self.positions[i-1]['y'])
# for i in range(1, len(self.positions)+1)}
for i in range(len(self.positionsIndex)):
color = None
for ci in range(len(self.communities)):
if i+1 in self.communities[ci].vertexes:
try:
color = cs[ci]
except Exception as e:
print(i)
print(e)
break
f.write('"' + str(self.positionsIndex[i+1][0]*0.95) + '" "' + str(self.positionsIndex[i+1][1]*0.95) + '" "' + color +'"\n')
f.flush()
f.close()
def outputLayout(self):
win_unicode_console.enable()
print('Reading file....')
self.setAttribute(iterations=500, epsilon=0.1, k=1, l=0.9)
self.import_network_information()
self.set_community_member()
self.runKK()
# self.normalizeScope()
self.outputPoints()
print(self.minEnergy, self.minIndex)
# print(self.finalPos)
def runKK(self):
self.initialize()
while not self.done():
self.step()
print(self.minEnergy, self.minIndex)
class KK3DLayout:
# Creates an instance for the specified graph and distance metric.
def __init__(self):
self.graph = None
self.vertexes = []
self.edges = []
self.setAttribute(iterations=500, epsilon=0.1, k=1, l=0.9)
self.get_vertexes_count()
def setAttribute(self, iterations, epsilon, k, l):
self.EPSILON = epsilon # 0.1
self.currentIteration = None
self.maxIterations = iterations # 2000
self.status = "KKLayout"
self.L = None # 弹簧长度系数，即边的理想长度
self.K = k # 1 # 弹簧强度系数，对算法结果影响不大
self.dm = [] # 最短距离矩阵，使用Dijkstra最短路径算法
self.isAdjustForGravity = True
self.isExchangeVertices = True
self.vertices = []
self.positions = []
self.PLOT_WIDTH = 500
self.PLOT_HEIGHT = 500
self.size = {'width': self.PLOT_WIDTH, 'height': self.PLOT_HEIGHT}
# Retrieves graph distances between vertices of the visible graph
self.distance = []
# The diameter of the visible graph.In other words, the maximum over all pairs
# of vertices of the length of the shortest path between a and b of the visible graph.
# 图直径
self.diameter = 5.0 # 5.0
# A multiplicative factor which partly specifies the "preferred" length of an edge (L).
self.length_factor = l # 0.9
# A multiplicative factor which specifies the fraction of the graph's diameter to be
# used as the inter-vertex distance between disconnected vertices.
self.disconnected_multiplier = 0.7 # 0.5
self.locations = []
self.minEnergy = None
self.minIndex = -1
self.finalPos = None
def get_vertexes_count(self):
global VERTEXES_COUNT
VERTEXES_COUNT *= 0
lines = open(COMMUNITY_FILE, 'r', encoding='utf-8').readlines()
for i in range(len(lines)):
# global VERTEXES_COUNT
line = lines[i]
name, members_list = line.split(':')
VERTEXES_COUNT += len(members_list.split())
def setSize(self, width, height):
self.size = {'width': width, 'height': height}
# Returns True once the current iteration has passed the maximum count.
def done(self):
if self.currentIteration > self.maxIterations:
return True
return False
def initialize(self):
# 1
# for i in range(11):
# connections = []
# RandCx1 = randint(0, 2)
# for j in range(RandCx1+1):
# RandCx2 = rand(0, 10)
# if RandCx2 != j:
# connections.append(RandCx2)
# nodes.append({'idx': i, "conn": connections})
self.graph = []
for i in range(len(self.vertexes)):
connections = []
for j in range(len(self.edges)):
if i+1 in self.edges[j]:
if i+1 == self.edges[j][0]:
connections.append(self.edges[j][1]-1)
else:
connections.append(self.edges[j][0]-1)
self.graph.append({'idx': i, "conn": connections})
# 2
self.currentIteration = 0
if self.graph != None and self.size != None:
height = self.size['height']
width = self.size['width']
n = len(self.graph)
# self.dm = [] # new Array[n][n]
self.dm = numpy.zeros((n, n))
self.vertices = self.graph
self.positions = []
# assign IDs to all visible vertices
loopTimes = 1
# while True:
for i in range(loopTimes):
try:
index = 0
for v in self.graph:
xyd = self.transform()
self.vertices[index] = v
self.positions.append(xyd)
index += 1
break
except Exception as e:
print(e)
# self.diameter = 5.0 # DistanceStatistics. < V, E > diameter(graph, distance, True)
L0 = min(height, width)
self.L = (L0 / self.diameter) * self.length_factor # length_factor used to be hardcoded to 0.9
# L = 0.75 * sqrt(height * width / n)
for i in range(n-1):
for j in range(i+1, n):
d_ij = self.getDistance(self.vertices[i], self.vertices[j])
d_ji = self.getDistance(self.vertices[j], self.vertices[i])
dist = self.diameter * self.disconnected_multiplier
if d_ij != None:
dist = min(d_ij, dist)
if d_ji != None:
dist = min(d_ji, dist)
self.dm[i][j] = dist
self.dm[j][i] = dist
# init node 's position
# @return ArrayObject
def transform(self):
# x = randint(10, self.size['width'] - 1)
# y = randint(10, self.size['height'] - 1)
x = random.uniform(10, self.PLOT_WIDTH)
y = random.uniform(10, self.PLOT_HEIGHT)
z = random.uniform(10, (self.PLOT_WIDTH+self.PLOT_HEIGHT)/2)
return {'x': x, 'y': y, 'z': z}
# For now, it is just a very simple strategy to get weight of distance
# TODO: fix it!
# @ param from
# @ param to
# @return distance weight
def getDistance(self, v1, v2):
fromid = v1['idx']
toid = v2['idx']
if toid in v1['conn']:
weight = 1
else:
weight = None
return weight
def step(self):
try:
self.currentIteration += 1
energy = self.calcEnergy()
if self.minEnergy:
if energy < self.minEnergy:
self.minEnergy = energy
self.minIndex = self.currentIteration
self.finalPos = self.positions
else:
self.minEnergy = energy
self.finalPos = self.positions
self.status = "Kamada-Kawai V=" + str(len(self.graph)) + "(" + str(len(self.graph)) \
+ ")" + " IT: " + str(self.currentIteration) + " E=" + str(energy)
print(self.status)
n = len(self.graph)
if n == 0:
return
maxDeltaM = 0
pm = -1 # the node having max deltaM
for i in range(n):
deltam = self.calcDeltaM(i)
if maxDeltaM < deltam:
maxDeltaM = deltam
pm = i
if pm == -1:
return
# 找到偏移量最大的点下标，进行迭代偏移直至偏移量小于阈值
for i in range(100):
dxy = self.calcDeltaXY(pm)
self.positions[pm]['x'] = self.positions[pm]['x'] + dxy[0]
self.positions[pm]['y'] = self.positions[pm]['y'] + dxy[1]
self.positions[pm]['z'] = self.positions[pm]['z'] + dxy[2]
deltam = self.calcDeltaM(pm)
if deltam < self.EPSILON:
break
# 调整网络坐标
if self.isAdjustForGravity:
self.adjustForGravity()
if self.isExchangeVertices and maxDeltaM < self.EPSILON:
energy = self.calcEnergy()
for i in range(n-1):
for j in range(i+1, n):
xenergy = self.calcEnergyIfExchanged(i, j)
if energy > xenergy:
sx = self.positions[i]['x']
sy = self.positions[i]['y']
sz = self.positions[i]['z']
self.positions[i]['x'] = self.positions[j]['x'] #.setLocation(xydata[j])
self.positions[i]['y'] = self.positions[j]['y']
self.positions[i]['z'] = self.positions[j]['z']
self.positions[j]['x'] = sx
self.positions[j]['y'] = sy
self.positions[j]['z'] = sz
return
except Exception as e:
traceback.print_exc()
print(e)
# Shift all vertices so that the center of gravity is located at
# the center of the screen.
def adjustForGravity(self):
d = self.size
height = d['height']
width = d['width']
gx = 0
gy = 0
gz = 0
cnt = len(self.positions)
for i in range(cnt):
gx += self.positions[i]['x']
gy += self.positions[i]['y']
gz += self.positions[i]['z']
gx /= cnt
gy /= cnt
gz /= cnt
diffx = width / 2 - gx
diffy = height / 2 - gy
diffz = (width+height) / 2 - gy
for i in range(cnt):
self.positions[i]['x'] = self.positions[i]['x'] + diffx
self.positions[i]['y'] = self.positions[i]['y'] + diffy
self.positions[i]['z'] = self.positions[i]['z'] + diffz
# 三维空间的偏微分方程结果未知，无法计算
# TODO: fix it!
# Determines a step to new position of the vertex m.
def calcDeltaXY(self, m):
dE_dxm = 0 # E对x偏微分
dE_dym = 0 # E对y偏微分
d2E_d2xm = 0
d2E_dxmdym = 0
d2E_dymdxm = 0
d2E_d2ym = 0
for i in range(len(self.vertices)):
if i != m:
dist = self.dm[m][i]
l_mi = self.L * dist
k_mi = self.K / (dist * dist)
dx = self.positions[m]['x'] - self.positions[i]['x']
dy = self.positions[m]['y'] - self.positions[i]['y']
d = math.sqrt(dx * dx + dy * dy)
ddd = d * d * d
dE_dxm += k_mi * (1 - l_mi / d) * dx
dE_dym += k_mi * (1 - l_mi / d) * dy
d2E_d2xm += k_mi * (1 - l_mi * dy * dy / ddd)
d2E_dxmdym += k_mi * l_mi * dx * dy / ddd
d2E_d2ym += k_mi * (1 - l_mi * dx * dx / ddd)
# d2E_dymdxm equals to d2E_dxmdym.
d2E_dymdxm = d2E_dxmdym
denomi = d2E_d2xm * d2E_d2ym - d2E_dxmdym * d2E_dymdxm
deltaX = (d2E_dxmdym * dE_dym - d2E_d2ym * dE_dxm) / denomi
deltaY = (d2E_dymdxm * dE_dxm - d2E_d2xm * dE_dym) / denomi
return [deltaX, deltaY]
# Calculates the gradient of energy function at the vertex m.
def calcDeltaM(self, m):
dEdxm = 0
dEdym = 0
dEdzm = 0
for i in range(len(self.vertices)):
if i != m:
dist = self.dm[m][i]
l_mi = self.L * dist
k_mi = self.K / (dist * dist)
dx = self.positions[m]['x'] - self.positions[i]['x']
dy = self.positions[m]['y'] - self.positions[i]['y']
dz = self.positions[m]['z'] - self.positions[i]['z']
d = math.sqrt(dx * dx + dy * dy + dz * dz)
common = k_mi * (1 - l_mi / d)
dEdxm += common * dx
dEdym += common * dy
dEdzm += common * dz
return math.sqrt(dEdxm * dEdxm + dEdym * dEdym + dEdzm * dEdzm)
# Calculates the energy function E.
def calcEnergy(self):
energy = 0
for i in range(len(self.vertices)- 1):
for j in range(i+1, len(self.vertices)):
dist = self.dm[i][j] # i，j两个节点的图距离
l_ij = self.L * dist # i，j两个节点的理想距离等于图距离与常数乘积
k_ij = self.K / (dist * dist) # i，j两点之间的力强度
dx = self.positions[i]['x'] - self.positions[j]['x']
dy = self.positions[i]['y'] - self.positions[j]['y']
dz = self.positions[i]['z'] - self.positions[j]['z']
d = math.sqrt(dx * dx + dy * dy + dz * dz) # 坐标距离
energy += k_ij / 2 * (dx * dx + dy * dy + dz * dz + l_ij * l_ij - 2 * l_ij * d)
return energy
# Calculates the energy function E as if positions of the
# specified vertices are exchanged.
def calcEnergyIfExchanged(self, p, q):
if p >= q:
raise Exception("p should be < q")
energy = 0 # < 0
for i in range(len(self.vertices) - 1):
for j in range(i+1, len(self.vertices)):
ii = i
jj = j
if i == p:
ii = q
if j == q:
jj = p
dist = self.dm[i][j]
l_ij = self.L * dist
k_ij = self.K / (dist * dist)
dx = self.positions[ii]['x'] - self.positions[jj]['x']
dy = self.positions[ii]['y'] - self.positions[jj]['y']
dz = self.positions[ii]['z'] - self.positions[jj]['z']
d = math.sqrt(dx * dx + dy * dy + dz * dz)
energy += k_ij / 2 * (dx * dx + dy * dy + dz * dz + l_ij * l_ij - 2 * l_ij * d)
return energy
def reset(self):
self.currentIteration = 0
# 从文件中导入关系图，每一行表示两个节点之间的一条连接，格式如下所示：
# 2 1
# 3 1
# 3 2
# 4 1
# ...
def import_network_information(self):
lines = open(NETWORK_FILE, 'r').readlines()
self.vertexes = [i+1 for i in range(VERTEXES_COUNT)]
for line in lines:
a, b = line.replace('\n', '').split(' ')
a = int(a)
b = int(b)
self.edges.append((a, b))
# 从文件中导入社区信息，每一行表示一个社区信息，社区名字与具体成员以英文冒号分隔，成员之间以空格分隔，格式如下所示：
# 社区1:1 2 4 5 6 7 8 11 12 13 14 17 18 20 22
# 社区2:3 9 10 15 16 19 21 23 24 25 26 27 28 29 30
# ...
def set_community_member(self):
lines = open(COMMUNITY_FILE, 'r', encoding='utf-8').readlines()
self.communities = [Community() for i in range(len(lines))]
for i in range(len(lines)):
line = lines[i]
name, members_list = line.split(':')
self.communities[i].name = name
members = members_list.strip().split(' ')
for m in members:
if not m.isdigit():
continue
m = int(m)
# 设置顶点颜色形状
self.communities[i].vertexes.append(m)
def normalizeScope(self):
margin = 30
minx = min(self.positions[i][0] for i in self.positions)
miny = min(self.positions[i][1] for i in self.positions)
minz = min(self.positions[i][2] for i in self.positions)
maxx = max(self.positions[i][0] for i in self.positions)
maxy = max(self.positions[i][1] for i in self.positions)
maxz = max(self.positions[i][2] for i in self.positions)
factorx = self.PLOT_WIDTH / (maxx - minx)
factory = self.PLOT_HEIGHT / (maxy- miny)
factorz = (self.PLOT_WIDTH+self.PLOT_HEIGHT) / (2 * (maxz- minz))
for i in self.positions:
self.positions[i][0] = (self.positions[i][0] - minx) * factorx
self.positions[i][1] = (self.positions[i][1] - miny) * factory
self.positions[i][2] = (self.positions[i][2] - minz) * factorz
minx = min(self.positions[i][0] for i in self.positions)
miny = min(self.positions[i][1] for i in self.positions)
minz = min(self.positions[i][2] for i in self.positions)
maxx = max(self.positions[i][0] for i in self.positions)
maxy = max(self.positions[i][1] for i in self.positions)
maxz = max(self.positions[i][2] for i in self.positions)
fitnessX = (self.PLOT_WIDTH - 2*margin) / (maxx + (self.PLOT_WIDTH - (maxx-minx))/2)
fitnessY = (self.PLOT_HEIGHT - 2*margin) / (maxy + (self.PLOT_HEIGHT - (maxy-miny))/2)
fitnessZ = ((self.PLOT_WIDTH+self.PLOT_HEIGHT)/2 - 2*margin) / \
(maxz + ((self.PLOT_WIDTH+self.PLOT_HEIGHT)/2 - (maxz-minz))/2)
# print(fitnessX, fitnessY)
for i in self.positions:
self.positions[i][0] = (self.positions[i][0] + (self.PLOT_WIDTH - (maxx-minx))/2) * fitnessX + margin
self.positions[i][1] = (self.positions[i][1] + (self.PLOT_HEIGHT - (maxy-miny))/2) * fitnessY + margin
self.positions[i][2] = (self.positions[i][2] + ((self.PLOT_WIDTH+self.PLOT_HEIGHT)/2 - (maxz-minz))/2) * fitnessZ + margin
def outputPoints(self, dynamic=None):
if dynamic is None:
# 转化格式
self.positionsIndex = {i: (self.finalPos[i-1]['x'], self.finalPos[i-1]['y'], self.finalPos[i-1]['z'])
for i in range(1, len(self.finalPos)+1)}
return self.positionsIndex
else:
return self.dynamicPositions
def outputLayout(self, dynamic=None):
win_unicode_console.enable()
print('Reading file....')
self.setAttribute(iterations=500, epsilon=0.1, k=1, l=0.9)
self.import_network_information()
self.set_community_member()
self.runKK(dynamic=dynamic)
# self.normalizeScope()
print(self.minEnergy, self.minIndex)
print(self.finalPos)
return self.outputPoints(dynamic=dynamic)
def runKK(self, dynamic=None):
self.dynamicPositions = []
self.initialize()
temp = {i: (self.positions[i-1]['x'], self.positions[i-1]['y'], self.positions[i-1]['z'])
for i in range(1, len(self.positions)+1)}
self.dynamicPositions.append(temp)
while not self.done():
self.step()
if dynamic:
temp = {i: (self.positions[i - 1]['x'], self.positions[i - 1]['y'], self.positions[i - 1]['z'])
for i in range(1, len(self.positions) + 1)}
self.dynamicPositions.append(temp)
print(self.minEnergy, self.minIndex)
if __name__ == '__main__':
nodes = []
# Create 11 random nodes
# for i in range(11):
# connections = []
# RandCx1 = randint(0, 2)
# for j in range(RandCx1+1):
# RandCx2 = rand(0, 10)
# if RandCx2 != j:
# connections.append(RandCx2)
# nodes.append({'idx': i, "conn": connections})
# kklayout = KKLayout(nodes)
# kklayout.runKK()
kklayout = KKLayout()
kklayout.outputLayout()