"""
/***********************************************************************************************************\
This Cython script associated with paper:
Ruben Tikidji-Hamburyan , Tarek El-Ghazawi , Jason Triplett
Novel Models of Visual Topographic Map Alignment into Superior Colliculus
Copyright: Ruben Tikidji-Hamburyan <rath@gwu.edu> Apr.2016 - Sep.2016
\************************************************************************************************************/
"""
from __future__ import division
import numpy as np
cimport numpy as np
import sys,os
from libc.math cimport sqrt,exp,floor
from libc.stdlib cimport rand,srand,RAND_MAX,malloc
from libc.stdio cimport *
import time
PTYPE = np.uint
DTYPE = np.float64
ctypedef np.uint_t PTYPE_T
ctypedef np.float64_t DTYPE_T
cdef extern from "stdio.h":
#FILE * fopen ( const char * filename, const char * mode )
FILE *fopen(const char *, const char *)
#int fclose ( FILE * stream )
int fclose(FILE *)
#int fprintf(FILE *stream, const char *format, ...)
int fprintf(FILE *, const char *, ...)
#void * malloc(
#Afinity
cdef double cAaf = 20., cBaf = 30.
#Competition
cdef double cApr = 5., cBpr = 1., cDpr = 1.
#Activity
cdef double cBca = 11., cGca = 200., cRca = 3, cVca=11, cSca=1., cA2Pca=1.5 #???
cdef unsigned int xsize, ysize, Nstep, ic_sizeX, ic_sizeY
cdef double xscl = 0, yscl = 0
cdef unsigned int cNorm, Don=1, Den3sigma=0
cdef double *pDf=NULL, *pLf=NULL
cdef inline double FdEpr(PTYPE_T na, unsigned long nd):
return cBpr*na**2-cApr*sqrt(na) + cDpr*nd**2
cdef inline double FdEaf(long xs, long ys, long xl, long yl, PTYPE_T p ):
return ( cAaf*exp(float(xs)*xscl-1.)*exp(-float(xl)*xscl ) \
- cBaf*exp(float(ys)*yscl-1.)*exp( float(yl)*yscl-1.) )*float(p)
cdef inline double Lfactor(long xs, long ys, long xl, long yl, double sigma):
return exp( - sqrt( float( (xs-xl)**2 + (ys-yl)**2 ) ) / sigma )
cdef inline double Dfactor(long xs, long ys, long xl, long yl, double sigma):
if Don: return exp( - float( (xs-xl)**2 + (ys-yl)**2 ) / (2. * sigma**2) )
else: return 1.0
cdef inline double FdEcaW(long xs, long ys, long xl, long yl, float add, np.ndarray[PTYPE_T, ndim=4] p):
cdef double norm = Dfactor(xs,ys,xl,yl,cVca) * add, res = norm, df
cdef unsigned int xls, yls
for xls in xrange(xsize):
for yls in xrange(ysize):
if p[xs,ys,xls,yls] == 0: continue
df = Dfactor(xs,ys,xls,yls,cVca) * float(p[xs,ys,xls,yls])
res += Lfactor(xl,yl,xls,yls,cBca) * df
norm += df
if norm > 0. and cNorm:
res /= norm
res += cRca*exp( - sqrt( (float(xs-xl)/cBca/cSca)**2 + (float(ys-yl)/cBca)**2 ) )
return - cGca * res
cdef inline double FdEcaM(long xs, long ys, long xl, long yl, float add, np.ndarray[PTYPE_T, ndim=4] p):
cdef double norm = Dfactor(xs,ys,xl,yl,cVca) * add, res = norm, df
cdef unsigned int xls, yls
for xls in xrange(xsize):
for yls in xrange(ysize):
if p[xs,ys,xls,yls] == 0: continue
df = Dfactor(xs,ys,xls,yls,cVca) * float(p[xs,ys,xls,yls])
res += Lfactor(xl,yl,xls,yls,cBca) * df
norm += df
if norm > 0. and cNorm:
res /= norm
res += cRca * (\
cA2Pca * exp( - sqrt( (float(xs-xl*0.5 )/cBca/cSca)**2 + (float(ys-yl)/cBca)**2 ) )\
+ exp( - sqrt( (float(xs-xl*0.5-xsize/2)/cBca/cSca)**2 + (float(ys-yl)/cBca)**2 ) )\
)
return - cGca * res
cdef inline double FdEcaW_JC(long xs, long ys, long xl, long yl, float add, np.ndarray[PTYPE_T, ndim=4] p):
return - cGca * exp( - sqrt(float((xs-xl)**2+(ys-yl)**2))/cBca /cSca )
cdef inline double FdEcaM_JC(long xs, long ys, long xl, long yl, float add, np.ndarray[PTYPE_T, ndim=4] p):
return - cGca * (\
cA2Pca * exp( - sqrt( (float(xs-xl*0.5 )/cBca/cSca)**2 + (float(ys-yl)/cBca)**2 ) )\
+ exp( - sqrt( (float(xs-xl*0.5-xsize/2)/cBca/cSca)**2 + (float(ys-yl)/cBca)**2 ) )\
)
cdef inline double FdEcaW_SC(long xs, long ys, long xl, long yl, float add, np.ndarray[PTYPE_T, ndim=4] p):
cdef double res = 0.
cdef unsigned int xls, yls
for xls in xrange(xsize):
for yls in xrange(ysize):
res += exp( - sqrt( (float(xs-xls)/cBca/cSca)**2 + (float(ys-yls)/cBca)**2 ) ) * Dfactor(xs,ys,xls,yls,cRca)
return - cGca * res
cdef inline double FdEcaM_SC(long xs, long ys, long xl, long yl, float add, np.ndarray[PTYPE_T, ndim=4] p):
cdef double res = 0.
cdef unsigned int xls, yls
for xls in xrange(xsize):
for yls in xrange(ysize):
res += cA2Pca * exp( - sqrt( (float(xs-xl*0.5 )/cBca/cSca)**2 + (float(ys-yl)/cBca)**2 ) ) * Dfactor(xs,ys,int(xl*0.5 ),yl,cRca)
res += exp( - sqrt( (float(xs-xl*0.5-xsize/2)/cBca/cSca)**2 + (float(ys-yl)/cBca)**2 ) ) * Dfactor(xs,ys,int(xl*0.5-xsize/2),yl,cRca)
return - cGca * res
cdef inline double random():
return float(rand())/float(RAND_MAX)
cdef inline unsigned int randint( unsigned int maxi):
cdef unsigned int x = int( floor( float(rand()) * float(maxi) / float(RAND_MAX) ) )
if x >= maxi: return maxi-1
if x < 0 : return 0
return x
def chaser(ixsize, iysize, iNstep,
E12 = 1e5,
Aaf = 20., Baf = 30.,
Bca = 11., Gca = 200., Rca=3., Vca=11., Sca=1., A2Pca=1.5,
Apr = 5., Bpr = 1., Dpr = 1.,
TotalEnergy = False, Init = 'RANDOM',
StartRec = False, StopRec = True,
Knocked = False, Indicator = False,
Log = True, Reporting = False,
Graphs = False, RunDB = True,
Model = 3 , Norm = True,
ParentDir = "" , timestemp = "" ):
global xscl, yscl
global cAaf,cBaf,cApr,cBpr,cDpr,cBca,cGca,cRca,cVca,cSca,cA2Pca
global xsize, ysize, Nstep, ic_sizeX, ic_sizeY
global cNorm, Don, Den3sigma
global pDf,pLf
cAaf,cBaf,cApr,cBpr,cDpr,cBca,cGca,cRca,cVca,cSca, cA2Pca = Aaf,Baf,Apr,Bpr,Dpr,Bca,Gca,Rca,Vca,Sca,A2Pca
xsize, ysize, Nstep = ixsize, iysize, iNstep
cNorm = Norm
cdef unsigned int fTotalEnergy = int(TotalEnergy),\
fIndicator = int(Indicator),\
fLog = int(Log),\
fReporting = int(Reporting),\
nGraphs = 0
cdef double cE12 = E12
timestemp_t = timestemp.encode("UTF-8")
cdef char *timestemp_c = timestemp_t
filenameprefix = ParentDir + timestemp
xscl = 1./float(xsize)
yscl = 1./float(ysize)
cdef FILE *log = NULL
logfilename_t = filenameprefix+"-log.csv"
logfilename_t = logfilename_t.encode("UTF-8")
cdef char *logfilename = logfilename_t
cdef FILE *recdb = NULL
redbfilename_t = filenameprefix+"-rec.db"
redbfilename_t = redbfilename_t.encode("UTF-8")
cdef char *redbfilename = redbfilename_t
cdef long xs, ys, xl, yl, Niter, itr_c = 0, npos=0
cdef np.ndarray[long, ndim=1] pXs, pYs, pXl, pYl
cdef double Epr=0., Eaf=0., Eca=0., E=0.
if Model == 5:
Den3sigma = int( np.ceil(cVca*3) )
pDf = <double *>malloc(Den3sigma**2*sizeof(double))
for xl in xrange(Den3sigma):
for yl in xrange(Den3sigma):
pDf[xl+yl*Den3sigma] = exp( - float( xl**2 + yl**2 ) / (2. * cVca**2) )
pLf = <double *>malloc(xsize*ysize*sizeof(double))
for xl in xrange(xsize):
for yl in xrange(ysize):
pLf[xl+yl*xsize ] = exp( - sqrt( float( xl**2 + yl**2 ) ) / cBca )
#Backword compability
if type(Init) is bool:
Init = "RANDOM" if Init else None
if Graphs:
if type(Graphs) is bool:
nGraphs = 20
elif type(Graphs) is float:
nGraphs = int(xsize*ysize*Graphs)
elif type(Graphs) is int:
nGraphs = int(Graphs)
if RunDB:
if not type(RunDB) is str:
RunDB = timestemp + "-rundb.csv"
print "#############################"
print "# :MODEL ID: #"
print " > Time Stamp :",timestemp
print "# :PARAMETERS: #"
print " > Aaf :",cAaf
print " > Baf :",cBaf
print " > Apr :",cApr
print " > Bpr :",cBpr
print " > Dpr :",cDpr
print " > Bca :",cBca
print " > Gca :",cGca
print " > Rca :",cRca
print " > Vca :",cVca
print " > Sca :",cSca
print " > A2Pca :",cA2Pca
print " > XxY :",xsize,"x",ysize
print " > Nstep :",Nstep
print " > E1/2 :",cE12
print "# :FLAGS: #"
print " > Model :",Model,
if Model == 1: print "(Just Correlation)"
elif Model == 2: print "(Sclaed Correlation)"
elif Model == 3: print "(V1 and Retinal Inputs Interation)"
elif Model == 4: print "(V1 and Retinal Inputs Interation withput convolution)"
print " > Normalization :",bool(cNorm)
print " > Knocked :",Knocked
print " > TotalEnergy :",bool(fTotalEnergy)
print " > Init :",Init
print " > StartRec :",StartRec
print " > StopRec :",StopRec
print " > Log :",bool(fLog)
print " > Reporting :",bool(fReporting)
if fReporting:
print " > every iter :",fReporting
print " > Graphs :",bool(nGraphs)
if nGraphs:
print " > rendom cells:",nGraphs
print " > Indicator :",bool(fIndicator)
print "# :PATHS: #"
print " > ParentDir :",ParentDir
print " > Prefix :",filenameprefix
print "# :FILES: #"
if fLog:
print " > Log :",logfilename
if StartRec or StopRec or bool(fReporting):
print " > Record :",redbfilename
print " > RunDB :",RunDB
print "#############################\n"
if type(RunDB) is str:
with open(RunDB,"a") as fd:
#TIMESTEMP,xsize,ysize,Aaf,Baf,Bca,Gca,Rca,Vca,Sca,A2Pca,Apr,Bpr,Dpr,E12,Nstep,Knocked,TotalEnergy,Init,Record,Log,StartRec,StopRec,Report,Indicator,Model,Normalization
fd.write("%s,%d,%d,%g,%g,%g,%g,%g,%g,%g,%g,%g,%g,%g,%g,%d,%s,%s,%s,%s,%s,%s,%s,%s,%s,%s,%s\n"%(\
timestemp,xsize,ysize,\
Aaf,Baf,Bca,Gca,Rca,Vca,Sca,A2Pca,Apr, Bpr, Dpr,\
E12,Nstep,\
"Y" if Knocked else "N",
"Y" if bool(fTotalEnergy) else "N",
Init,
filenameprefix+"-rec.db" if StartRec or StopRec or bool(fReporting) else "N",
filenameprefix+"-log.csv" if bool(fLog) else "N",
"Y" if StartRec else "N",
"Y" if StopRec else "N",
str(fReporting) if bool(fReporting) else "N",
"Y" if bool(fIndicator) else "N",
"JC" if Model == 1 else "SC" if Model == 2 else "INT" if Model == 3 else "INT-D" if Model == 4 else "DI",
"Y" if bool(cNorm) else 'N' ) )
### Squared distances
#cBca,cSca = cBca**2,cSca**2
print "#############################"
print "# Create synaptic densities #"
cdef np.ndarray[PTYPE_T, ndim=2] ax = np.zeros((xsize, ysize),dtype=PTYPE)
cdef np.ndarray[PTYPE_T, ndim=2] dn = np.zeros((xsize, ysize),dtype=PTYPE)
cdef np.ndarray[PTYPE_T, ndim=4] p = np.zeros([xsize,ysize,xsize,ysize], dtype=PTYPE)
print "# DONE #"
print "#############################\n"
if Knocked:
if Model == 1:
FdEca = FdEcaM_JC
elif Model == 2:
FdEca = FdEcaM_SC
elif Model == 3:
FdEca = FdEcaM
elif Model == 4:
FdEca = FdEcaM
Don = 0
else:
FdEca = FdEcaM
else:
if Model == 1:
FdEca = FdEcaW_JC
elif Model == 2:
FdEca = FdEcaW_SC
elif Model == 3:
FdEca = FdEcaW
elif Model == 4:
FdEca = FdEcaW
Don = 0
else:
FdEca = FdEcaW
srand( np.random.randint( RAND_MAX ) )
if Init == "RANDOM":
print "#############################"
print "# Random Initialization #"
Niter = int( xsize * ysize * 50) # half of population
for i in xrange(Niter):
xs = randint(xsize)
ys = randint(ysize)
xl = randint(xsize)
yl = randint(ysize)
ax[xs,ys] += 1
dn[xl,yl] += 1
p[xs,ys,xl,yl] += 1
print "# DONE #"
print "#############################\n"
elif Init == None:
pass
else:
if type(Init) is str:
Init = (Init,-1)
if len(Init) < 2: Init = (Init, -1)
print "#############################"
print "# Init conditions from File #"
print " > File :", Init[0]
print " > Fentch record :", Init[1],type(Init[1])
lastrec = None
with open(Init[0],"r") as fd:
for nl,l in enumerate(fd.readlines()):
if len(l) <= 5: continue
if type(Init[1]) is str:
if l.split(":")[0] == Init[1] : lastrec = l
elif type(Init[1]) is int:
if Init[1] >= 0 and nl == Init[1] : lastrec = l
elif Init[1] < 0: lastrec = l
if lastrec == None:
print " ERROR: Cannon find required record in ",Init, "... Skip"
exit(1)
else:
lastrec = lastrec.split(":")
if len(lastrec) < 5:
print " ERROR: Last line in ",Init, "Has not records ....Skip"
exit(1)
else:
for xs,ys,xl,yl,pn in [ ( int(xyxyp) for xyxyp in r.split(",") ) for r in lastrec[4:] ]:
if xs >= xsize or ys >= ysize or xl >= xsize or yl >= ysize:
print " ERROR: dementions {} doesn't match ....Skip".format(xs,ys,xl,yl,p)
continue
p[xs,ys,xl,yl] = pn
print "# DONE #"
print "#############################\n"
if Init != None and bool(fTotalEnergy):
print "#############################"
print "# Calculate initial Energy #"
for a,d in zip(ax,dn):
for na,nd in zip(a,d):
Epr += FdEpr(na, nd)
#NP
#Epr = np.sum(Bpr*ax**2-Apr*np.sqrt(ax)) + np.sum(Dpr*dn**2)
pXs, pYs, pXl, pYl = np.where( p > 0. )
for xs, ys, xl, yl in zip(pXs, pYs, pXl, pYl):
Eaf += FdEaf(xs, ys, xl, yl, p[xs, ys, xl, yl])
Eca += FdEca(xs, ys, xl, yl, 0., p) * p[xs, ys, xl, yl]
#DB>>
# import time
# tb= time.time()
# print "TB:",tb
# Eca += FdEca(xs, ys, xl, yl, 0., p) * p[xs, ys, xl, yl]
# te= time.time()
# print te-tb
# exit(0)
#<<DB
#NP
# Eaf = sum( ( cAaf*np.exp(1.-pXs.astype(float)*xscl)*np.exp(1.-pXl.astype(float)*xscl)\
# - cBaf*np.exp(1.-pYs.astype(float)*yscl)*np.exp(1.-pYl.astype(float)*yscl))*p[pXs,pYs,pXl,pYl] )
# Eca = sum( -cGca * np.exp( - np.sqrt((pXs-pXl)**2+(pYs-pYl)**2)/cBca )*p[pXs, pYs, pXl, pYl] )
print " > Chemoaffinity :", Eaf
print " > Competition :", Epr
print " > Activity :", Eca
E = Eaf + Eca + Epr
print " > Total :", E
print "#############################\n"
#DB>>
# exit(0)
#<<DB
if Graphs and Init != None:
from matplotlib import pyplot as plt
from matplotlib import cm
cmap = cm.get_cmap('jet')
Gax = plt.subplot(121)
Gcells=[ [randint(xsize),randint(ysize),cmap(float(i)/float(nGraphs))] for i in xrange(nGraphs)]
for xs,ys,c in Gcells:
pXl, pYl = np.where( p[xs,ys,:,:].astype(int) > 0 )
for xl,yl in zip(pXl, pYl):
plt.plot([xs,xl],[ys,yl],"-*",c=c,mfc=c,mec=c,lw=int(p[xs,ys,xl,yl]) )
if fLog:
log = fopen(logfilename,"w")
if log == NULL:
sys.stderr.write("Cannot open Log file: '%s' for writing" %(filenameprefix+"-log.csv"))
raise
fprintf(log,"iter,+/-,xs,ys,xl,yl,dEpr,dEaf,dEca,dE,E,P0\n")
if StartRec or StopRec or bool(fReporting):
recdb = fopen(redbfilename,"w")
if recdb == NULL:
sys.stderr.write("Cannot open Record file: '%s' for writing" %(filenameprefix+"-rec.db"))
raise
if StartRec:
fprintf(recdb,"%s:%010d",timestemp_c,itr_c)
fprintf(recdb,":%g",E)
pXs, pYs, pXl, pYl = np.where( p.astype(int) > 0 )
npos = int(pXs.shape[0])
fprintf(recdb,":%d",npos)
for xs,ys,xl,yl in zip(pXs, pYs, pXl, pYl):
fprintf(recdb,":%d,%d,%d,%d,%d",xs,ys,xl,yl,p[xs,ys,xl,yl])
fprintf(recdb,"\n")
cdef double P0, dEpr, dEaf, dEca, dE
Niter = xsize*ysize*Nstep
#DB>>
#Niter = Nstep
#<<DB
for itr in xrange(Niter):
itr_c = itr
# Add new synapse
xs, ys, xl, yl = randint(xsize),randint(ysize),randint(xsize),randint(ysize)
dEpr = FdEpr(ax[xs,ys]+1,dn[xl,yl]+1) - FdEpr(ax[xs,ys],dn[xl,yl])
dEaf = FdEaf(xs,ys,xl,yl,1)
dEca = FdEca(xs,ys,xl,yl,1.,p)
dE = dEpr + dEaf + dEca
if dE > 100:
P0 = 0.
elif dE < -100:
P0 = 1.
else:
P0 = 1./(1.+exp(4.*dE) )
if TotalEnergy:
P0 *= E/(cE12+E)
Pplus = False
if np.random.random() < P0:
Pplus = True
p[xs,ys,xl,yl] += 1
ax[xs,ys] += 1
dn[xl,yl] += 1
Epr += dEpr
Eaf += dEaf
Eca += dEca
E += dE
if fLog:
fprintf(log,"%d,+,%d,%d,%d,%d,%g,%g,%g,%g,%g,%g\n",itr_c,xs,ys,xl,yl,dEpr,dEaf,dEca,dEpr + dEaf + dEca,E,P0)
if E <= 0. and fTotalEnergy: break
if not (itr%1000) and fIndicator:
sys.stderr.write("%d (+) %g %g [%g,%g,%g] %g ||"%(itr,E,dEpr + dEaf + dEca,dEpr,dEaf,dEca,P0))
#Remove connection
cnt=0
xs, ys, xl, yl = randint(xsize),randint(ysize),randint(xsize),randint(ysize)
while p[xs,ys,xl,yl] == 0 and cnt < 1000 :
xs, ys, xl, yl = randint(xsize),randint(ysize),randint(xsize),randint(ysize)
cnt += 1
if cnt < 1000:
dEpr = FdEpr(ax[xs,ys]-1,dn[xl,yl]-1) - FdEpr(ax[xs,ys],dn[xl,yl])
dEaf = -FdEaf(xs,ys,xl,yl,1)
dEca = -FdEca(xs,ys,xl,yl,1.,p)
dE = dEpr + dEaf + dEca
if dE > 100:
P0 = 0.
elif dE < -100:
P0 = 1.
else:
P0 = 1./(1.+exp(4.*dE) )
if TotalEnergy:
P0 *= E/(cE12+E)
Pminus = False
if np.random.random() < P0:
Pminus = True
p[xs,ys,xl,yl] -= 1
ax[xs,ys] -= 1
dn[xl,yl] -= 1
Epr += dEpr
Eaf += dEaf
Eca += dEca
E += dE
if fLog:
fprintf(log,"%d,-,%d,%d,%d,%d,%g,%g,%g,%g,%g,%g\n",itr_c,xs,ys,xl,yl,dEpr,dEaf,dEca,dEpr + dEaf + dEca,E,P0)
if not (itr%1000) and fIndicator:
sys.stderr.write(" (-) %g %g [%g,%g,%g] %g \r[%s%s] "%(E,dEpr + dEaf + dEca,dEpr,dEaf,dEca,P0,"+" if Pplus else " ","-" if Pminus else " "))
else:
if not (itr%1000) and fIndicator:
sys.stderr.write(" (-) Not found \r[%s%s] "%("+" if Pplus else " "," " ))
if E <= 0. and fTotalEnergy: break
if fReporting and (not (itr%fReporting)):
fprintf(recdb,"%s:%010d",timestemp_c,itr_c)
fprintf(recdb,":%g",E)
pXs, pYs, pXl, pYl = np.where( p.astype(int) > 0 )
npos = int(pXs.shape[0])
fprintf(recdb,":%d",npos)
for xs,ys,xl,yl in zip(pXs, pYs, pXl, pYl):
fprintf(recdb,":%d,%d,%d,%d,%d",xs,ys,xl,yl,p[xs,ys,xl,yl])
fprintf(recdb,"\n")
print
print "#############################"
print "# STATISTIC #"
print " > Mean Number of Axons :",np.mean(ax)
print " > Mean Number of Dendrites :",np.mean(dn)
print "#############################\n"
if StopRec:
fprintf(recdb,"%s:%010d",timestemp_c,itr_c)
fprintf(recdb,":%g",E)
pXs, pYs, pXl, pYl = np.where( p.astype(int) > 0 )
npos = int(pXs.shape[0])
fprintf(recdb,":%d",npos)
for xs,ys,xl,yl in zip(pXs, pYs, pXl, pYl):
fprintf(recdb,":%d,%d,%d,%d,%d",xs,ys,xl,yl,p[xs,ys,xl,yl])
fprintf(recdb,"\n")
if StartRec or StopRec or bool(fReporting):
fclose(recdb)
if fLog:
fclose(log)
if Graphs:
if Init == None:
from matplotlib import pyplot as plt
from matplotlib import cm
cmap = cm.get_cmap('jet')
Gcells=[ [randint(xsize),randint(ysize),cmap(float(i)/float(nGraphs))] for i in xrange(nGraphs)]
else:
plt.subplot(122,sharex=Gax,sharey=Gax)
for xs,ys,c in Gcells:
pXl, pYl = np.where( p[xs,ys,:,:] > 0 )
for xl,yl in zip(pXl, pYl):
plt.plot([xs,xl],[ys,yl],"-*",c=c,mfc=c,mec=c,lw=int(p[xs,ys,xl,yl]) )
plt.title("Model: "+timestemp)
plt.xlim(0,xsize)
plt.ylim(0,ysize)
plt.show()
return p
