In [2]:
import sqlite3
import numpy as np
import scipy.linalg as lg
import scipy.integrate as it
import matplotlib.pyplot as plt
import scipy.constants as ct
import copy
from matplotlib.mlab import griddata
from matplotlib.colors import LogNorm
from matplotlib import ticker
%matplotlib inline
plt.rcParams['figure.figsize'] = (10.0, 8.0)
hbar=ct.physical_constants["Planck constant over 2 pi in eV s"][0]
T=300
kbT=T*ct.physical_constants["Boltzmann constant in eV/K"][0]

In [3]:
sqlname="system_individualmps.sql"
sqlstatement="SELECT pairs.seg1, pairs.seg2, pairs.Jeff2s, seg1.eSinglet, seg1.UnXnNs, seg1.UxNxXs, seg2.eSinglet, seg2.UnXnNs, seg2.UxNxXs FROM pairs JOIN segments seg1 ON seg1._id =pairs.seg1 JOIN segments seg2 ON seg2._id =pairs.seg2"
con = sqlite3.connect(sqlname)
with con:
    cur = con.cursor()
    cur.execute(sqlstatement)
    rows = cur.fetchall()
sql=np.array(rows)
lowerlimit=0
reorg12=sql[:,4]+sql[:,8]
dG12=-sql[:,3]+sql[:,6]
reorg21=sql[:,5]+sql[:,7]
dG21=-dG12
rates12=2*np.pi/hbar*sql[:,2]/np.sqrt(4*np.pi*kbT*reorg12)*np.exp(-(dG12+reorg12)**2/(4*reorg12*kbT))
rates21=2*np.pi/hbar*sql[:,2]/np.sqrt(4*np.pi*kbT*reorg21)*np.exp(-(dG21+reorg21)**2/(4*reorg21*kbT))
maxi=np.max([np.max(rates12),np.max(rates21)])
print maxi

sqlstatement="SELECT box11,box12,box13,box21,box22,box23,box31,box32,box33 from frames"
con = sqlite3.connect(sqlname)
with con:
    cur = con.cursor()
    cur.execute(sqlstatement)
    vecs = cur.fetchall()
    box=np.array(vecs).reshape((3,3))
    print box
sqlstatement="SELECT posX,posY,posZ from segments"
con = sqlite3.connect(sqlname)
with con:
    cur = con.cursor()
    cur.execute(sqlstatement)
    rows2 = cur.fetchall()
    positions=np.array(rows2)

#dimension=int(max(np.max(sql[:,0]),np.max(sql[:,1])))
dimension=1568
print dimension

matrix=np.zeros((dimension,dimension))
print len(rows)
for k in range(len(rows)):
    rate12=rates12[k]
    rate21=rates21[k]
    row=rows[k]
    i=row[0]-1
    j=row[1]-1 
    matrix[i,j]=rate12
    matrix[i,i]-=rate12
    matrix[j,i]=rate21
    matrix[j,j]-=rate21
    
initial=np.zeros(dimension)
initial[0]=1.0


5.76568162428e+14
[[ 10.73884   0.        0.     ]
 [  0.       10.78449   0.     ]
 [  0.        0.       10.39411]]
1568
56151

In [4]:
if False:
    with open("matrix.txt",'w') as f:
            for i in range(1,dimension+1):
                for j in range(1,dimension+1):
                    if matrix[i-1,j-1]!=0.0:
                        f.write("{:6d} {:6d} {:+1.17e}\n".format(i,j,matrix[i-1,j-1]))

In [5]:
if False:
    sqlname="system_individualmps.sql"
    sqlstatement = "SELECT pairs.id,pairs.seg1, pairs.seg2, pairs.rate12s, pairs.rate21s FROM pairs"
    
    con = sqlite3.connect(sqlname)
    with con:
        cur = con.cursor()
        cur.execute(sqlstatement)
        rows = cur.fetchall()
    sql=np.array(rows)
    #print rows[0]
    print max(np.max(sql[:,3]),np.max(sql[:,4]))
    minimum=min(np.min(sql[:,3]),np.min(sql[:,4]))
    print minimum
    maximum=max(np.max(sql[:,3]),np.max(sql[:,4]))
    dimension=int(max(np.max(sql[:,1]),np.max(sql[:,2])))
    print dimension
    lowerlimit=0
    #print rows[0]
    matrix=np.zeros((dimension,dimension))
    
    for row in rows:
        i=row[1]-1
        j=row[2]-1
        if row[3]>lowerlimit:
            matrix[i,j]=row[3]
            matrix[i,i]-=(row[3])
        
        if row[4]>lowerlimit:
            matrix[j,i]=row[4]
            matrix[j,j]-=(row[4])
        
    
        
    
   
    print np.sum(matrix==0)
    print (np.sum(matrix!=0)-dimension)/2

In [6]:
def f(t,y):
    return np.dot(matrix,y)
def jac(t,y):
    return matrix
print np.sum(initial)


1.0

In [26]:
r = it.ode(f, jac).set_integrator('Isoda',  with_jacobian=True)
r.set_initial_value(initial)

t1 = 10e-13
print t1
dt = 10e-17
solution=[]
time=[]
while r.successful() and r.t < t1:
    r.integrate(r.t+dt)
    solution.append(r.y)
    time.append(r.t)


1e-12

In [8]:
seg1=[]
seg2=[]
for sol in solution:
    seg1.append(sol[0])
    seg2.append(sol[700])
#print seg1
plt.plot(time,seg1,c='r')
plt.plot(time,seg2,c='b')
#plt.xscale('log')
plt.show()



In [9]:
timearray=np.array(time)
solutionarray=np.array(solution).T
print np.shape(timearray),np.shape(solutionarray)


(10001,) (1568, 10001)

In [10]:
print np.shape(positions)


(1568, 3)

In [11]:
results=np.vstack((time,solutionarray))

In [12]:
np.savetxt("poft.txt",results,header="Occupationprobability over time", fmt='%.4e')

In [13]:
class segment(object):
    def __init__(self,id,pos):
        self.id=id
        self.pos=pos
        self.ghost=False
        
    def addpoft(self,poft,time):
        self.poft=poft
        self.time=time
        
    def shift(self,pos,Ghost=True):
        self.pos+=pos
        self.ghost=Ghost

In [14]:
def plotcontour(x,y,z,box,seg,time):
    x=np.array(x)
    y=np.array(y)
    z=np.array(z)
    numcols, numrows = 100, 100
    xi = np.linspace(x.min(), x.max(), numcols)
    yi = np.linspace(y.min(), y.max(), numrows)
    xi, yi = np.meshgrid(xi, yi)
    zi = griddata(x, y, z, xi, yi)
    fig, ax = plt.subplots()
    im = ax.contourf(xi, yi, zi,locator=ticker.LogLocator(),vmin=1e-8, vmax=1e-2)
    ax.scatter(x, y, c=z, s=10,vmin=zi.min(), vmax=zi.max())
    fig.colorbar(im)
    plt.title("{:1.3e} s".format(time))
    # drawing simbox
    #print seg.pos
    x1=seg.pos[0]-0.5*box[0,0]
    y1=seg.pos[1]-0.5*box[1,1]
    x2=x1+box[0,0]
    y2=y1+box[1,1]
    ax.plot([x1, x2], [y1, y1], color='k', linestyle='-', linewidth=2)
    ax.plot([x1, x1], [y1, y2], color='k', linestyle='-', linewidth=2)
    ax.plot([x2, x2], [y1, y2], color='k', linestyle='-', linewidth=2)
    ax.plot([x1, x2], [y2, y2], color='k', linestyle='-', linewidth=2)
    return fig

In [15]:
segments =[]
i=0
for row in rows2:
    segments.append(segment(i,np.array(row)))
    i+=1

for j,i in zip(segments,range(np.shape(solutionarray)[0])):
    j.addpoft(solutionarray[i],timearray)

In [16]:
for segment in segments[1:10]:
    plt.plot(segment.time,segment.poft)



In [17]:
print box
seg_pbc=[]
a=range(-1,2)
for segment in segments:
    for i in a:
        for j in a:
            for k in a:
                if i==0 and j==0 and k==0:
                    seg_pbc.append(segment)
                else:
                    temp=copy.deepcopy(segment)
                    
                    vector=i*box[:,0]+j*box[:,1]+k*box[:,2]
                    
                    temp.shift(vector)
               
                    seg_pbc.append(temp)


[[ 10.73884   0.        0.     ]
 [  0.       10.78449   0.     ]
 [  0.        0.       10.39411]]

In [18]:
for i in range(len(seg_pbc)):
    if seg_pbc[i].poft[0]>0.5 and seg_pbc[i].ghost==False:
        print i,seg_pbc[i].pos


13 [ 0.34141351  2.99195552  0.70540362]

In [19]:
xyplane=[]
for segment in seg_pbc:
    if np.abs(segment.pos[2]-seg_pbc[300].pos[2])<0.3:
        xyplane.append(segment)

In [25]:
print len(xyplane)
x=[]
y=[]
for seg in xyplane:
    x.append(seg.pos[0])
    y.append(seg.pos[1])
times=seg_pbc[13].time
j=0
for i in range(0,len(times)/15,1):
    #print times[i]
    
    p0=[]
    for seg in xyplane:
        p0.append(seg.poft[i])
    
    fig=plotcontour(x,y,p0,box,seg_pbc[13],times[i])
    plt.savefig("contour_{:04d}_s.png".format(j))
    plt.close()
    j+=1


756

In [ ]: