# -*- coding: utf-8 -*-
from scipy.integrate import odeint
from pylab import * # for plotting commands
import numpy as np

       
#~ def pole_wektorowe(zakres_A,zakres_B,k ):
    #~ A,B = meshgrid( zakres_A, zakres_B )
    #~ dA = -k*A*A*B
    #~ dB = -k*A*A*B
    #~ quiver(A,B,dA,dB)
    
def dokladne(y,t,K,lamb,eps):
    u = y[0]
    v = y[1]
    du = -u + (u+K-lamb)*v
    dv = 1/eps*(u-(u+K)*v)
    return array([du, dv])   
def dlugie(y,t,K,lamb,eps):
    u = y[0]
    v = y[1]
    du = -lamb*u/(u+K)
    dv = 0
    return array([du, dv])
def krotkie(y,t,K,lamb,eps):
    u = y[0]
    v = y[1]
    du = 0
    dv = 1-(1+K)*v
    return array([du, dv])
def pole_wektorowe(zakres_u,zakres_v,K,lamb,eps ):
    u,v = meshgrid( zakres_u, zakres_v )
    du = -u + (u+K-lamb)*v
    dv = 1/eps*(u-(u+K)*v)
    quiver(u,v,du,dv)

K = 1.1
lamb = 1.
eps = 0.001

figure(1)    
pole_wektorowe(np.arange(0.01,0.03,0.001), np.arange(0.01,0.03,0.001), K,lamb,eps)
show()
time = np.linspace(0,10,1000000)
y = odeint(dokladne,[1,0],time, args =(K,lamb,eps))
#plot(y[:,0],y[:,1]) # u(t), v(t)


y_krotkie = odeint(krotkie,[1,0],time, args =(K,lamb,eps))
y_dlugie = odeint(dlugie,[1,0],time, args =(K,lamb,eps))
##

figure(2)
semilogx(time,y[:,0]) # u(t)
semilogx(time,y[:,1]) # v(t)

semilogx(time*eps,y_krotkie[:,0]) # u(t)
semilogx(time*eps,y_krotkie[:,1]) # v(t)

#semilogx(time,y_dlugie[:,0]) # u(t)
#semilogx(time,y_dlugie[:,0]/(y_dlugie[:,0]+K)) # v(t)
legend(('u','v','u_k','v_k','u_d','v_d'))
show()

figure()
s = np.linspace(0, 10, 1000)
k2=1.
Km = 0.5
e0 = 1
dp_dt = k2*e0*s/(Km+s)
plot(s, dp_dt)
show()