# -*- coding: utf-8 -*-
"""
GEPARD - Gepard-Enabled PARticle Detection
Copyright (C) 2018 Lars Bittrich and Josef Brandt, Leibniz-Institut für
Polymerforschung Dresden e. V.
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program, see COPYING.
If not, see .
"""
import numpy as np
from numpy.linalg import norm
from libc.math cimport exp, sqrt
from libc.stdlib cimport rand, RAND_MAX
cimport numpy as np
cimport cython
DTYPE = np.float
ctypedef np.float_t DTYPE_t
ctypedef np.int32_t INT32_t
ctypedef np.int64_t INT64_t
@cython.cdivision(True)
cdef double pyrand():
return rand()/float(RAND_MAX)
@cython.cdivision(True)
cdef int randint(int N):
return rand()%N
@cython.boundscheck(False) # assume: no index larger than N-1
@cython.wraparound(False) # assume: no neg. index
cdef double getdist(int n1, int n2, np.ndarray[DTYPE_t, ndim=2] points):
cdef double dx, dy
cdef int N=points.shape[0]
if n1==N or n2==N:
return 0.0
dx = points[n1,0]-points[n2,0]
dy = points[n1,1]-points[n2,1]
return sqrt(dx*dx + dy*dy)
cpdef TotalDistance(city, R):
dist = np.sum(np.sqrt(np.sum(np.diff(R[city[:-1],:],axis=0)**2,axis=1)))
return dist
# use this only after debugging!
@cython.boundscheck(False) # assume: no index larger than N-1
@cython.wraparound(False) # assume: no neg. index
cdef reverse(np.ndarray[INT32_t, ndim=1] city, int n0, int n1):
cdef int nct, nn, j, k, l
nct = city.shape[0]
nn = cython.cdiv((1+ ((n1-n0) % nct)),2) # half the lenght of the segment to be reversed
# the segment is reversed in the following way n[0]<->n[1], n[0]+1<->n[1]-1, n[0]+2<->n[1]-2,...
# Start at the ends of the segment and swap pairs of cities, moving towards the center.
for j in range(nn):
k = (n0+j) % nct
l = (n1-j) % nct
city[k], city[l] = city[l], city[k] # swap
# use this only after debugging!
@cython.boundscheck(False) # assume: no index larger than N-1
@cython.wraparound(False) # assume: no neg. index
cdef np.ndarray[INT32_t, ndim=1] transpt(np.ndarray[INT32_t, ndim=1] city, int n0, int n1, int n2, int n3, int n4, int n5):
cdef int nct, j, i
cdef np.ndarray[INT32_t, ndim=1] newcity = np.empty_like(city)
nct = city.shape[0]
i = 0
# Segment in the range n[0]...n[1]
for j in range( (n1-n0)%nct + 1):
newcity[i] = city[ (j+n0)%nct ]
i += 1
# is followed by segment n[5]...n[2]
for j in range( (n2-n5)%nct + 1):
newcity[i] = city[ (j+n5)%nct ]
i += 1
# is followed by segment n[3]...n[4]
for j in range( (n4-n3)%nct + 1):
newcity[i] = city[ (j+n3)%nct ]
i += 1
return newcity
# use this only after debugging!
@cython.boundscheck(False) # assume: no index larger than N-1
@cython.wraparound(False) # assume: no neg. index
def tspcomp(np.ndarray[DTYPE_t, ndim=2] points, np.ndarray[INT32_t, ndim=1] city=None, int maxTsteps=100, double Tstart=0.2, double fCool=0.9, int usemat=1):
"""
maxTsteps = 50 # Temperature is lowered not more than maxTsteps
Tstart = 0.2 # Starting temperature - has to be high enough
fCool = 0.9 # Factor to multiply temperature at each cooling step
"""
cdef int ncity, maxSteps, maxAccepted, nct, t, i, accepted, n0, n1, n2, n3, n4, n5, nn, nc
cdef double Preverse, T, de, dist
cdef np.ndarray[INT32_t, ndim=1] ind
cdef np.ndarray[DTYPE_t, ndim=1] d
cdef np.ndarray[DTYPE_t, ndim=2] distmat
ncity = points.shape[0]
maxSteps = 100*ncity # Number of steps at constant temperature
maxAccepted = 10*ncity # Number of accepted steps at constant temperature
Preverse = 0.5 # How often to choose reverse/transpose trial move
# Choosing city coordinates
if usemat:
distmat = np.zeros((ncity+1,ncity+1))
for i in range(ncity):
ind = np.arange(i+1,ncity, dtype=np.int32)
d = norm(points[ind,:]-points[i,:][np.newaxis,:],axis=1)
distmat[i,i+1:-1] = d
distmat[i+1:-1,i] = d
# The index table -- the order the cities are visited.
if city is None:
city = np.arange(ncity+1, dtype=np.int32)
else:
assert city.shape[0]==ncity
city = np.concatenate((city,np.int32([ncity])))
# Distance of the travel at the beginning
dist = TotalDistance(city, points)
# Stores points of a move
nct = ncity+1 # number of cities
T = Tstart # temperature
for t in range(maxTsteps): # Over temperature
accepted = 0
for i in range(maxSteps): # At each temperature, many Monte Carlo steps
while True: # Will find two random cities sufficiently close by
# Two cities n[0] and n[1] are choosen at random
n0 = randint((nct)) # select one city
n1 = randint((nct-1)) # select another city, but not the same
if (n1 >= n0): n1 += 1 #
elif (n1 < n0): n0, n1 = n1, n0 # swap, because it must be: n[0]=3: break
# We want to have one index before and one after the two cities
# The order hence is [n2,n0,n1,n3]
n2 = (n0-1) % nct # index before n0 -- see figure in the lecture notes
n3 = (n1+1) % nct # index after n2 -- see figure in the lecture notes
if Preverse > pyrand():
# Here we reverse a segment
# What would be the cost to reverse the path between city[n[0]]-city[n[1]]?
if usemat:
de = distmat[city[n2],city[n1]] + distmat[city[n3], city[n0]] - \
distmat[city[n2],city[n0]] - distmat[city[n3], city[n1]]
else:
de = getdist(city[n2],city[n1], points) + getdist(city[n3],city[n0], points) - \
getdist(city[n2],city[n0], points) - getdist(city[n3],city[n1], points)
if de<0 or exp(-cython.cdiv(de,T))>pyrand(): # Metropolis
accepted += 1
dist += de
reverse(city, n0, n1)
else:
# Here we transpose a segment
nc = (n1+1+ randint((nn-1)))%nct # Another point outside n[0],n[1] segment. See picture in lecture nodes!
n4 = nc
n5 = (nc+1) % nct
# Cost to transpose a segment
if usemat:
de = -distmat[city[n1],city[n3]] - \
distmat[city[n0],city[n2]] - \
distmat[city[n4],city[n5]]
de += distmat[city[n0],city[n4]] + \
distmat[city[n1],city[n5]] + \
distmat[city[n2],city[n3]]
else:
de = -getdist(city[n1],city[n3], points) - \
getdist(city[n0],city[n2], points) - \
getdist(city[n4],city[n5], points) + \
getdist(city[n0],city[n4], points) + \
getdist(city[n1],city[n5], points) + \
getdist(city[n2],city[n3], points)
if de<0 or exp(-cython.cdiv(de,T))>pyrand(): # Metropolis
accepted += 1
dist += de
city = transpt(city, n0, n1, n2, n3, n4, n5)
if accepted > maxAccepted: break
print("T=%10.5f , distance= %10.5f , accepted steps= %d" %(T, dist, accepted))
T *= fCool # The system is cooled down
if accepted == 0: break # If the path does not want to change any more, we can stop
for i in range(nct):
if city[i]==ncity:
break
c = np.concatenate((city[i+1:], city[:i]))
return c, T