import numpy as np
import matplotlib.pyplot as plt

xDets={
    "max":10,
    "min":-10,
    "step":1
    }
yDets={
    "max":10,
    "min":-10,
    "step":1
    }
plotlims={
    "maxSteps":30000,
    "solStepSize":0.05,
    }
initialPoints =[[0,1]]
initialPointsT =[]
colors=['g','m','y','r']
def diff(x,y):
    return 1-x+4*y

def diffsT(x,y):
    return [x+y,x-y]

def diffsHigher(ys,x):
    return x*ys[0]+ys[1]+ys[2]/x

def isInBounds(x,y):
    return xDets["min"]<=x and xDets["max"]>=x and yDets["min"]<=y and yDets["max"]>=y
def plotSoln(x0,y0):
    points=[]
    x,y=x0,y0
    steps=0
    while steps<plotlims["maxSteps"] and isInBounds(x,y) and [x,y] not in points:
        diffs=[1,diff(x,y)]
        points.append([x,y])
        steps+=1
        norm=np.sqrt(diffs[0]**2+diffs[1]**2)
        x+= plotlims["solStepSize"]*diffs[0]/norm
        y+= plotlims["solStepSize"]*diffs[1]/norm
    steps=0
    x,y=x0,y0
    diffs =[1,diff(x,y)]
    steps+=1
    norm=np.sqrt(diffs[0]**2+diffs[1]**2)
    x-= plotlims["solStepSize"]*diffs[0]/norm
    y-= plotlims["solStepSize"]*diffs[1]/norm
    while steps<plotlims["maxSteps"] and isInBounds(x,y)and [x,y] not in points:
        points.insert(0,[x,y])
        diffs =[1,diff(x,y)]
        steps+=1
        norm=np.sqrt(diffs[0]**2+diffs[1]**2)
        x-= plotlims["solStepSize"]*diffs[0]/norm
        y-= plotlims["solStepSize"]*diffs[1]/norm
    return points
def bplot(x0,y0):
    points = []
    x,y=x0,y0
    steps=0
    ss=plotlims["solStepSize"]
    while steps<plotlims["maxSteps"] and isInBounds(x,y) and [x,y] not in points:
        points.append([x,y])
        x+=ss
        y=((1-x)*ss+y)/(1-4*ss)
        steps +=1
    steps=0
    x,y=x0,y0
    y=(1-4*ss)*y+(1-x)*ss
    x-=ss
    while steps<plotlims["maxSteps"] and isInBounds(x,y) and [x,y] not in points:
        points.insert(0,[x,y])
        y=(1-4*ss)*y+(1-x)*ss
        x-=ss
        steps +=1
    return points
def getSize(xDets,yDets):
    xSteps=int(np.ceil((xDets["max"]-xDets["min"])/xDets["step"])+1)
    ySteps=int(np.ceil((yDets["max"]-yDets["min"])/yDets["step"])+1)
    return xSteps,ySteps
def plotSolnT(x0,y0):
    points=[]
    x,y=x0,y0
    steps=0
    while steps<plotlims["maxSteps"] and isInBounds(x,y) and [x,y] not in points:
        diffs=diffsT(x,y)
        points.append([x,y])
        steps+=1
        norm=np.sqrt(diffs[0]**2+diffs[1]**2)
        x+= plotlims["solStepSize"]*diffs[0]/norm
        y+= plotlims["solStepSize"]*diffs[1]/norm
    steps=0
    x,y=x0,y0
    diffs =[1,diffsT(x,y)]
    steps+=1
    norm=np.sqrt(diffs[0]**2+diffs[1]**2)
    x-= plotlims["solStepSize"]*diffs[0]/norm
    y-= plotlims["solStepSize"]*diffs[1]/norm
    while steps<plotlims["maxSteps"] and isInBounds(x,y)and [x,y] not in points:
        diffs=diffsT(x,y)
        points.insert(0,[x,y])
        steps+=1
        norm=np.sqrt(diffs[0]**2+diffs[1]**2)
        x-= plotlims["solStepSize"]*diffs[0]/norm
        y-= plotlims["solStepSize"]*diffs[1]/norm
    return points
fig, ax=plt.subplots()
for idx,pt in enumerate(initialPoints):
    soln=np.array(plotSoln(pt[0],pt[1]))
    plt.plot(soln[:,0],soln[:,1],color=colors[idx])

for idx,pt in enumerate(initialPoints):
    soln=np.array(bplot(pt[0],pt[1]))
    plt.plot(soln[:,0],soln[:,1],color=colors[idx+len(initialPoints)])
for idx,pt in enumerate(initialPointsT):
    soln=np.arry(plotSoln(pt[0],pt[1]))
    plt.plot(soln[:,0],soln[:,1],color=colors[idx+len(initialPoints)])
ax.set(xlim=(xDets["min"],xDets["max"]),ylim=(yDets["min"],yDets["max"]))
ax.axhline(y=0, color='k')
ax.axvline(x=0, color='k')

plt.show()