import numpy as np
import matplotlib.pyplot as plt 
from matplotlib import rcParams

# Definition der Funktionen g_A und g_B
def gA(x,y,a,b,c,d):
    g = ((a+d-c-b)*y + (b-d))*(x-x*x)
    return g

def gB(x,y,a,b,c,d):
    g = ((a+d-c-b)*x + (c-d))*(y-y*y)
    return g

# Loesen der DGL
def solve_dgl(numpoints,tend,x0,y0,Aa,Ab,Ac,Ad,Ba,Bb,Bc,Bd):
    sol = np.empty([numpoints,3])
    t = np.linspace(0,tend,numpoints)
    dt = t[1] - t[0]
    sol[0][0] = t[0]
    sol[0][1] = x0
    sol[0][2] = y0
    for i in range(1,numpoints):
        sol[i][0] = t[i]
        dx = gA(sol[i-1,1],sol[i-1,2],Aa,Ab,Ac,Ad)*dt
        dy = gB(sol[i-1,1],sol[i-1,2],Ba,Bb,Bc,Bd)*dt
        sol[i][1] = sol[i-1,1] + dx
        sol[i][2] = sol[i-1,2] + dy
    return sol

# Groessenfestlegung der Labels usw. im Bild
rcParams.update({
    'text.usetex'       : True,
    'axes.titlesize' : 22,
    'axes.labelsize' : 20,  
    'xtick.labelsize' : 20 ,
    'ytick.labelsize' : 20 
})

#Festlegung der Auszahlungsmatrix des unsymmetrischen (2x2)-Spiels, Anfangspopulation, Endzeit
# Klasse der Eckenspiele (Corner Class Games)
#Aa=10
#Ab=4
#Ac=12
#Ad=5
#Ba=10
#Bb=12
#Bc=7
#Bd=5
#tend=7
#x0=0.9
#y0=0.2
# Klasse der Sattelspiele (Saddle Class Games)
Aa=10
Ab=4
Ac=9
Ad=5
Ba=10
Bb=7
Bc=4
Bd=5
tend=12
x0=0.6
y0=0.1
# Klasse der Zentrumsspiele (Center Class Games)
#Aa=10
#Ab=4
#Ac=7
#Ad=5
#Ba=10
#Bb=12
#Bc=9
#Bd=5
#tend=8.5
#x0=0.6
#y0=0.01

# Weitere Festlegungen
numpoints = 1000

# Loesung der DGL fuer eine Anfangspopulation (x0,y0)
Loes = solve_dgl(numpoints,tend,x0,y0,Aa,Ab,Ac,Ad,Ba,Bb,Bc,Bd)

# Fuer die Darstellung des Feldliniendiagramms streamplot
SY,SX = np.mgrid[0:1:100j,0:1:100j]
SgA = gA(SX,SY,Aa,Ab,Ac,Ad)
SgB = gB(SX,SY,Ba,Bb,Bc,Bd)
# Die Farbe wird die Geschwindigkeit der Aenderung des Populationsvektors anzeigen
speed = np.sqrt(SgA*SgA + SgB*SgB)
colorspeed = speed/speed.max()

# Plotten des Bildes
fig, ax = plt.subplots()
strm = ax.streamplot(SX,SY,SgA,SgB,density=[2, 2], linewidth=1,color=colorspeed, cmap=plt.cm.cool)
ax.plot(Loes[:,1],Loes[:,2],c="black", linewidth=1.5, linestyle='-')
ax.plot(Loes[0,1],Loes[0,2], marker='o', color='grey', markersize=8)
for i in np.linspace(numpoints/30,numpoints-2,10):
    ax.arrow(Loes[int(i),1],Loes[int(i),2], Loes[int(i)+1,1] -Loes[int(i),1], Loes[int(i)+1,2] -Loes[int(i),2], head_width=0.02, head_length=0.03, fc='black', ec='black')
# Erzeugung der nebenstehenden Farblegende colorbar   
cbar = fig.colorbar(strm.lines,ax=ax,pad=0.02)
cbar.set_label(r'$\sqrt{{g_A}^2 + {g_B}^2}$',size=20)

# Achsenbeschriftungen usw.
plt.xlim(0,1)
plt.ylim(0,1)
plt.xticks([0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1],["$0$","","$0.2$","","$0.4$","","$0.6$","","$0.8$","","$1$"])
plt.yticks([0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1],["$0$","","$0.2$","","$0.4$","","$0.6$","","$0.8$","","$1$"])
plt.ylabel(r"$\rm y$")
plt.xlabel(r"$\rm x$")

#Speichern der Bilder als (.png , benötigt dvipng unter Linux)- und .pdf-Datei
saveFig="./bimatrix.png"
plt.savefig(saveFig, dpi=100,bbox_inches="tight",pad_inches=0.05,format="png")
saveFig="./bimatrix.pdf"
plt.savefig(saveFig,bbox_inches="tight",pad_inches=0.05,format="pdf")
plt.show()