import numpy as np
import matplotlib.pyplot as plt
x = np.arange(0,12,0.01)
y = np.sin(x)
plt.plot(x,y)
k = np.diff(y)/np.diff(x)
plt.grid()
plt.plot(x[:-1],k)

x = np.arange(0,1,0.001)
y = np.exp(x)
plt.plot(x,y,'ro')
k = np.diff(y)/np.diff(x)
plt.plot(x[1:],k,'b')

import numpy as np
import matplotlib.pyplot as plt
x = np.arange(-5.2,-0.9,0.01)
y = x**5+15*x**4+85*x**3+225*x**2+274*x+120
j = np.heaviside(y,0)
k = np.abs(np.diff(j))
plt.plot(x,y,'black')
plt.plot(x[1:],k,'r')

vec = np.argwhere(k==1)
print(x[vec])

import numpy as np
import matplotlib.pyplot as plt
x = np.arange(-5.2,-0.9,0.01)
y = x**5+15*x**4+85*x**3+225*x**2+274*x+120
a = np.diff(y)/np.diff(x)
j = np.heaviside(a,0)
k = np.abs(np.diff(j))
plt.plot(x,y,'black')
plt.plot(x[2:],k,'r')

vec = np.argwhere(k==1)
print(x[vec])

import numpy as np
import matplotlib.pyplot as plt
step = 0.1
x = np.arange(-1,1,step)
y = np.arange(-1,1,step)
for i in x:
    for j in y:
        plt.plot(i,j,'o')

import numpy as np
import matplotlib.pyplot as plt
step=0.005
x=np.arange(-1,1,step)
y=np.arange(-1,1,step)

def dist(x,y):
    return np.sqrt(x**2+y**2)

z=np.zeros([len(x),len(y)])
x0,y0 = -0.7269,0.1889


for j in range(len(x)):
    for k in range(len(y)):
        counter=0
        px,py=x[j],y[k]
        while (dist(px,py)<2 and counter< 500):
            p1=px*px-py*py
            p2=2*px*py
            px,py=p1+x0,p2+y0
            counter+=1
        z[j,k]=counter

plt.figure(figsize=(10,10))
plt.imshow(z);
plt.colorbar();

import numpy as np
import matplotlib.pyplot as plt
r1 = np.random.rand(1000)*1
r12 = np.random.rand(1000)*1+0.8
r2 = np.random.rand(1000)*1+2
r3 = np.random.rand(1000)*1+3
r4 = np.random.rand(1000)*1+4
a1 = np.random.rand(1000)*6.28
a2 = np.random.rand(1000)*6.28
a3 = np.random.rand(1000)*6.28
a4 = np.random.rand(1000)*6.28
plt.plot(r1*np.cos(a1),r1*np.sin(a1),'ro')
plt.plot(r2*np.cos(a2),r2*np.sin(a2),'go')
plt.plot(r3*np.cos(a3),r3*np.sin(a3),'bo')
plt.plot(r4*np.cos(a4),r4*np.sin(a4),'mo')
plt.plot(r12*np.cos(a4),r12*np.sin(a4),'ro')

import numpy as np
import matplotlib.pyplot as plt
h = 0.001
x = np.arange(0,2,h)
y = x*0
y[0] = 5

for n in range(1,len(x)):
    y[n]=y[n-1]+h*y[n-1]*(1-y[n-1])
plt.plot(x,y)

import numpy as np
import matplotlib.pyplot as plt
x = np.arange(2,8,0.001)
y = x*(x**2-1)*(np.sin(x)-1/2)*(6*x-2)
plt.plot(x,y)
x1 = np.arange(7,8,0.001)
y1 = x1*(x1**2-1)*(np.sin(x1)-1/2)*(6*x1-2)
s = np.sum(y1[1:]+y1[:-1])/2*0.001
print(s)

l=[1,1]
for i in range(13):
    l.append(l[i]+l[i+1])
print(l)
print("the answer is =", l[14])

import numpy as np
import matplotlib.pyplot as plt
x = np.arange(0,2,0.001)
y = x*0
y[0]=1
h=0.001
for n in range(1,len(x)):
    y[n]=y[n-1]+h*(y[n-1]+np.cos(y[n-1]))
plt.plot(x,y)

a = np.arange(0,6.29,0.01)
plt.plot(np.cos(a)*3,np.sin(a)*3)
plt.plot(np.cos(a)*2+5,np.sin(a)*2)
plt.plot(np.cos(a)+8,np.sin(a))

x = np.array([-1,-1,1,1,-1])
y = np.array([1,-1,-1,1,1])
for j in range(1,5):
    plt.plot(j*x,j*y)

import numpy as np
import matplotlib.pyplot as plt
x = np.arange(1,2,h)
h = 0.001
y = x*0
y[1] = 1
for j in range(1,len(x)):
    y[j] = y[j-1] + h*(y[j-1] + x[j-1]**2)
plt.plot(x,y)

import numpy as np
import matplotlib.pyplot as plt
x = np.array([-1,-1,1,1,-1,0,1])
y = np.array([1,-1,-1,1,1,2,1])
plt.plot(x,y)

import numpy as np
import matplotlib.pyplot as plt
a = np.arange(0,2*np.pi+1,2*np.pi/9)
plt.plot(np.cos(a),np.sin(a))

import numpy as np
y = np.array([1,2,3,4,5])
y1 = y[:-1]
y2 = y[1:]
x = y2*y1
print(x)

import numpy as np
x = np.arange(1,1601+1,8)
print(sum(x))

import numpy as np
x1 = np.arange(1,1601+1,16)
x2 = np.arange(-9,-1601+1,-16)
b = sum(x1) + sum(x2)
print(b)

import numpy as np
import matplotlib.pyplot as plt
x = np.arange(0.5,2.2,0.001)
y = x**3 - 4.5*x**2 + 6.5*x - 3
plt.plot(x,y)
y1 = np.argwhere(np.diff(np.heaviside(y,0)))
plt.plot(x[y1],y[y1],'ro')
y2 = np.diff(y)/np.diff(x)
y3 = np.argwhere(np.diff(np.heaviside(y2,0)))
plt.plot(x[y3],y[y3],'go')

import numpy as np
y = np.array([1,2,3,4,5])
y1 = y[:-1]
y2 = y[1:]
x = y2*y1 - y1
print(x)

import numpy as np
def func(y):
    y1 = y[:-1]
    y2 = y[1:]
    return y2*y1 - y1
print(func(np.array([1,2,3,4,5])))

import numpy as np
import matplotlib.pyplot as plt
x = np.arange(2,3,0.001)
y = (x**3-1)*(np.sin(x)**2-1)*(4*x-4) - np.sin(x) + 1
plt.plot(x,y)

x1 = np.arange(2,4,0.001)
y1 = (x1**3-1)*(np.sin(x1)**2-1)*(4*x1-4) - np.sin(x1) + 1
s = np.sum(y1[1:]+y1[:-1])/2*0.001
print(s)

l=[1,1]
for i in range(250):
    l.append(l[i]+l[i+1])
for j in l:
    if j%5==0:
        print(j)

import numpy as np
import matplotlib.pyplot as plt
a = np.arange(0,2*np.pi,0.001)
plt.plot(np.cos(a),np.sin(a))
x = np.array([-1,-1,1,1,-1])
y = np.array([1,-1,-1,1,1])
plt.plot(x,y)

import numpy as np
import matplotlib.pyplot as plt
h=0.001
x = np.arange(2,5,h)
y = x*0
y[2]=2
for n in range(1,len(x)):
    y[n] = (2*y[n-1]*h) + y[n-1]
plt.plot(x,y)
y1 = np.diff(y)/np.diff(x)
plt.plot(x[:-1],y1)

import numpy as np
import matplotlib.pyplot as plt
a = np.arange(0,2*np.pi,0.001)
plt.plot(np.cos(a),np.sin(a))
x = np.array([0,2,2,0,0])
y = np.array([2,2,4,4,2])
plt.plot(x,y)
x1 = np.array([0,2,0,0])
y1 = np.array([0,0,2,0])
plt.plot(x1,y1)

import numpy as np
a = np.diff(np.diff([1,1,1,2,2,2]))
print("התשובה בשאלה 1 היא =", a)

b = np.heaviside(np.heaviside([-1, 0 ,-1, -1],-1),-1)
print("התשובה בשאלה 2 היא =",b)

c = 5*sum(np.diff(np.heaviside([1,1,1,2,2,2,1,1,1])))
print("התשובה בשאלה 3 היא =",c)

x=[-1,0,-1,-1]
for j in range(2000000):
      x=np.heaviside(np.heaviside(x,-1),-1)
print(x)

import numpy as np
import matplotlib.pyplot as plt
x = np.array([-0.2,0.2,0.2,0.5,0,-0.5,-0.2,-0.2])
y = np.array([0,0,4,4,8,4,4,0])
plt.plot (x,y)
beta = 180/40*3.28
x1 = y*np.cos(beta)-x*np.sin(beta)
plt.plot(x1,y)

import numpy as np
import matplotlib.pyplot as plt
x = np.arange(-3,3,0.001)
y = x*(x+1)*(x+2)*(x-1)*(x-2)
plt.plot(x,y)
y1 = np.diff(y)/np.diff(x)
plt.plot(x[:-1],y1)
y2 = np.argwhere(np.diff(np.heaviside(y,0)))
plt.plot(x[y2],y[y2],'ro')
y3 = np.argwhere(np.diff(np.heaviside(y1,0)))
plt.plot(x[y3],y[y3],'go')
y4 = np.diff(y1)/np.diff(x[:-1])
y5 = np.argwhere(np.diff(np.heaviside(y4,0)))
plt.plot(x[y5],y[y5],'bo')
print(x[y2])

import numpy as np
import matplotlib.pyplot as plt
def mse(x):
    l = x**2
    return sum(l)/len(x)
mse(np.array([2,4,6,8]))