מבחן.ipynb

Kernel: Python 3 (system-wide)

import numpy as np
import matplotlib.pyplot as plt

h = 0.01
x = np.arange(2,5,h)
y = x*0

y[0] = 2

for j in range(len(x)-1):
    y[j+1] = 2*h*y[j]+y[j]

plt.subplot(1,2,1)
plt.plot(x,y,'b')

y = np.diff(y)/np.diff(x)

plt.subplot(1,2,2)
plt.plot(x[1:],y,'r')

[<matplotlib.lines.Line2D at 0x7f26cf1db2e8>]

counter = 0
num = 0
num1 = 1
num2 = 1

arr = np.zeros(50)

while counter != 50:
    num2 = num1+num
    num = num1
    num1 = num2
    if num2%5 == 0:
        arr[counter] = num2
        counter+=1

print(arr)

[5.00000000e+00 5.50000000e+01 6.10000000e+02 6.76500000e+03
 7.50250000e+04 8.32040000e+05 9.22746500e+06 1.02334155e+08
 1.13490317e+09 1.25862690e+10 1.39583862e+11 1.54800876e+12
 1.71676802e+13 1.90392491e+14 2.11148508e+15 2.34167283e+16
 2.59695497e+17 2.88006719e+18 3.19404346e+19 3.54224848e+20
 3.92841376e+21 4.35667763e+22 4.83162953e+23 5.35835925e+24
 5.94251148e+25 6.59034622e+26 7.30880595e+27 8.10559001e+28
 8.98923707e+29 9.96921668e+30 1.10560307e+32 1.22613260e+33
 1.35980189e+34 1.50804340e+35 1.67244576e+36 1.85477077e+37
 2.05697230e+38 2.28121724e+39 2.52990869e+40 2.80571173e+41
 3.11158199e+42 3.45079731e+43 3.82699286e+44 4.24420012e+45
 4.70689006e+46 5.22002106e+47 5.78909207e+48 6.42020149e+49
 7.12011256e+50 7.89632583e+51]

import numpy as np
import matplotlib.pyplot as plt

x = np.arange(0,6.29,0.01)
plt.plot(np.sin(x),np.cos(x))

x = np.array([-1,1,1,-1,-1])
y = np.array([1,1,-1,-1,1])
plt.plot(x,y)

[<matplotlib.lines.Line2D at 0x7f26cefe84a8>]

import numpy as np
import matplotlib.pyplot as plt


x = np.array([0,1.25,0.5,0.5,-0.5,-0.5,-1.25,0])
y = np.array([2,0.75,0.75,-0.75,-0.75,0.75,0.75,2])

plt.plot(x,y,'b')

a = 90 # in dgrees
a = a*3.14 / 180 #to radian

x1 = x*np.cos(a)-y*np.sin(a)
y1 = x*np.sin(a)+y*np.cos(a)

plt.plot(x1,y1,'g')

[<matplotlib.lines.Line2D at 0x7f2529aac7f0>]

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)

z1 = np.heaviside(y,0)
z2 = np.diff(z1)
vec = np.argwhere(z2!=0)
plt.plot(x[vec],y[vec],'go')

print(x[vec])

z1 = np.heaviside(y1,0)
z2 = np.diff(z1)
vec = np.argwhere(z2==-1)
plt.plot(x[vec],y[vec],'ro')

y2 = np.diff(y1)/np.diff(x[1:])
z1 = np.heaviside(y2,0)
z2 = np.diff(z1)
vec = np.argwhere(z2!=0)
plt.plot(x[vec],y[vec],'ko')

plt.grid()



#ה
'''
[[-2.00000000e+00]
 [-1.00000000e+00]
 [-3.30402372e-13]
 [ 1.00000000e+00]
 [ 2.00000000e+00]]
'''

[[-2.00000000e+00]
 [-1.00000000e+00]
 [-3.30402372e-13]
 [ 1.00000000e+00]
 [ 2.00000000e+00]]
[(array([-2.]), array([-2.64321898e-12])), (array([-1.]), array([1.32160949e-12])), (array([-3.30402372e-13]), array([-1.32160949e-12])), (array([1.]), array([2.64321898e-12])), (array([2.]), array([-1.32160949e-11]))]

import numpy as np
import matplotlib.pyplot as plt


x = np.array([0,1,0,0,1,1,0,0])
y = np.array([0,0,1,1.5,1.5,1,1,0])

plt.plot(x,y,'k')

x = np.arange(0,6.29,0.01)
plt.plot(0.5*np.sin(x),0.5*np.cos(x),'k')

[<matplotlib.lines.Line2D at 0x7f26cca12550>]

import numpy as np
import matplotlib.pyplot as plt

y1 = np.array([1,2,3])
y2 = np.array([3,4,5])

def mse(y):
    return np.sum(y**2)/len(y)

print(mse(y1-y2))

4.0

import numpy as np

y = np.array([1,2,3,4])
y1 = y[0]

yn_1 = y[1:]
y = y[:-1]

b = y*yn_1 - y1

print(r)

[2 3 4]
[1 2 3]
[ 1  5 11]

import numpy as np
import matplotlib.pyplot as plt


x = np.arange(2,3,0.01)
y = (x**3-1)*(np.sin(x)**2-1)*(4*x-4)-np.sin(x)+1

plt.plot(x,y)

x = np.arange(2,4,0.01)
y = (x**3-1)*(np.sin(x)**2-1)*(4*x-4)-np.sin(x)+1
area = np.abs(np.sum(((y[1:]+y[:-1])/2)*np.diff(x)))

print(area)

399.69892927735634

from numpy import diff,heaviside

x=[-1,0,-1,-1]

heaviside(heaviside([-1,0,-1,-1],-1),-1)

print (x)

[-1, 0, -1, -1]