רובוטרוניקס : קורס פייתון – 510 / שיעור 4 – גרף של פונקציה ושימוש ב NUMPY

קוד לשיעור נימצא בהמשך הדף

# learn python lesson 4 , www.robotronix.co.il

import matplotlib.pyplot as plt
import numpy as np

x = np.linspace(-2,2,100)

# the function
y = x**2-2

# setting the axes at the centre
fig = plt.figure()

# Add an Axes to the figure as part of a subplot arrangement. // default: (1, 1, 1)
ax = fig.add_subplot(1, 1, 1)

ax.spines['left'].set_position('center')
ax.spines['left'].set_color('blue')

ax.spines['bottom'].set_position('center')
ax.spines['bottom'].set_color('green')

ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')

# plot the function r='red'
plt.plot(x,y, 'red')

# show the plot
plt.show()

import matplotlib.pyplot as plt
import numpy as np

# 20 linearly spaced numbers
x = np.linspace( -np.pi , np.pi ,20)
print(x)

# function
y = np.sin(x)
print("print y array \r\n",y)

# setting the axes at the centre
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
ax.spines['left'].set_position('center')
ax.spines['bottom'].set_position('center')
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')

# plot the function
plt.plot(x,y, 'b') # b = blue

# show the plot
plt.show()

import matplotlib.pyplot as plt
import numpy as np

# 20 linearly spaced numbers
x = np.linspace(-np.pi ,np.pi ,60)

# function
y1 = 1*np.sin(x)

y2 = 2*np.sin(2*x)

y3 = 3*np.sin(4*x)

# axes
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
ax.spines['left'].set_position('center')
ax.spines['bottom'].set_position('center')
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')

# plot the functions
#x = np.linspace(-np.pi ,np.pi ,20)
plt.plot(x ,y1, 'b', label='y1=sin(x)')
plt.plot(x ,y2, 'r', label='y2=2sin(2x)')
plt.plot(x ,y3, 'y', label='y3=3sin(4x)')

plt.legend(loc='upper left')

# show the plot
plt.show()

import matplotlib.pyplot as plt
import numpy as np

# 20 linearly spaced numbers
x = np.linspace(-np.pi,np.pi,20)

# function
y1 = 1*np.sin(x)

y2 = 1*np.cos(x)

# axes
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
ax.spines['left'].set_position('center')
ax.spines['bottom'].set_position('center')
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')

# plot the functions
plt.plot(x,y1, 'b', label='y1=sin(x)')
plt.plot(x,y2, 'r', label='y2=cos(x)')

plt.legend(loc='upper right')

# show the plot
plt.show()

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# learn python lesson 4 , www.robotronix.co.il

import matplotlib.pyplot as plt

import numpy as np

x = np.linspace(-2,2,100)

# the function

y = x**2-2

# setting the axes at the centre

fig = plt.figure()

# Add an Axes to the figure as part of a subplot arrangement. // default: (1, 1, 1)

ax = fig.add_subplot(1, 1, 1)

ax.spines['left'].set_position('center')

ax.spines['left'].set_color('blue')

ax.spines['bottom'].set_position('center')

ax.spines['bottom'].set_color('green')

ax.spines['right'].set_color('none')

ax.spines['top'].set_color('none')

ax.xaxis.set_ticks_position('bottom')

ax.yaxis.set_ticks_position('left')

# plot the function r='red'

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

# show the plot

plt.show()

import matplotlib.pyplot as plt

import numpy as np

# 20 linearly spaced numbers

x = np.linspace( -np.pi , np.pi ,20)

print(x)

# function

y = np.sin(x)

print("print y array \r\n",y)

# setting the axes at the centre

fig = plt.figure()

ax = fig.add_subplot(1, 1, 1)

ax.spines['left'].set_position('center')

ax.spines['bottom'].set_position('center')

ax.spines['right'].set_color('none')

ax.spines['top'].set_color('none')

ax.xaxis.set_ticks_position('bottom')

ax.yaxis.set_ticks_position('left')

# plot the function

plt.plot(x,y, 'b') # b = blue

# show the plot

plt.show()

import matplotlib.pyplot as plt

import numpy as np

# 20 linearly spaced numbers

x = np.linspace(-np.pi ,np.pi ,60)

# function

y1 = 1*np.sin(x)

y2 = 2*np.sin(2*x)

y3 = 3*np.sin(4*x)

# axes

fig = plt.figure()

ax = fig.add_subplot(1, 1, 1)

ax.spines['left'].set_position('center')

ax.spines['bottom'].set_position('center')

ax.spines['right'].set_color('none')

ax.spines['top'].set_color('none')

ax.xaxis.set_ticks_position('bottom')

ax.yaxis.set_ticks_position('left')

# plot the functions

#x = np.linspace(-np.pi ,np.pi ,20)

plt.plot(x ,y1, 'b', label='y1=sin(x)')

plt.plot(x ,y2, 'r', label='y2=2sin(2x)')

plt.plot(x ,y3, 'y', label='y3=3sin(4x)')

plt.legend(loc='upper left')

# show the plot

plt.show()

import matplotlib.pyplot as plt

import numpy as np

# 20 linearly spaced numbers

x = np.linspace(-np.pi,np.pi,20)

# function

y1 = 1*np.sin(x)

y2 = 1*np.cos(x)

# axes

fig = plt.figure()

ax = fig.add_subplot(1, 1, 1)

ax.spines['left'].set_position('center')

ax.spines['bottom'].set_position('center')

ax.spines['right'].set_color('none')

ax.spines['top'].set_color('none')

ax.xaxis.set_ticks_position('bottom')

ax.yaxis.set_ticks_position('left')

# plot the functions

plt.plot(x,y1, 'b', label='y1=sin(x)')

plt.plot(x,y2, 'r', label='y2=cos(x)')

plt.legend(loc='upper right')

# show the plot

plt.show()

import matplotlib.pyplot as plt
import numpy as np

# 20 linearly spaced numbers
x = np.linspace(-10,10,200)

# function
y1 = 1*np.exp(x)
y2 = -1*np.exp(x)

# axes
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
ax.spines['left'].set_position('center')
ax.spines['bottom'].set_position('center')
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')

# plot the functions
plt.plot(x,y1, 'b', label='y1=exp(x)')
plt.plot(x,y2, 'r', label='y2=-exp(x)')

plt.legend(loc='upper left')

# show the plot
plt.show()

print("x",type(x))
print("y1",type(y1))

import matplotlib.pyplot as plt

import numpy as np

# 20 linearly spaced numbers

x = np.linspace(-10,10,200)

# function

y1 = 1*np.exp(x)

y2 = -1*np.exp(x)

# axes

fig = plt.figure()

ax = fig.add_subplot(1, 1, 1)

ax.spines['left'].set_position('center')

ax.spines['bottom'].set_position('center')

ax.spines['right'].set_color('none')

ax.spines['top'].set_color('none')

ax.xaxis.set_ticks_position('bottom')

ax.yaxis.set_ticks_position('left')

# plot the functions

plt.plot(x,y1, 'b', label='y1=exp(x)')

plt.plot(x,y2, 'r', label='y2=-exp(x)')

plt.legend(loc='upper left')

# show the plot

plt.show()

print("x",type(x))

print("y1",type(y1))

# learn python lesson 4 , www.robotronix.co.il

import matplotlib.pyplot as plt
import numpy as np

#Credit
#https://www.math.ubc.ca/~pwalls/math-python/integration/riemann-sums/

def derivative(f,a,method='central',h=0.01):
'''Compute the difference formula for f'(a) with step size h.

Parameters
----------
f : function
Vectorized function of one variable
a : number
Compute derivative at x = a
method : string
Difference formula: 'forward', 'backward' or 'central'
h : number
Step size in difference formula

Returns
-------
float
Difference formula:
central: f(a+h) - f(a-h))/2h
forward: f(a+h) - f(a))/h
backward: f(a) - f(a-h))/h
'''
if method == 'central':
return (f(a + h) - f(a - h))/(2*h)
elif method == 'forward':
return (f(a + h) - f(a))/h
elif method == 'backward':
return (f(a) - f(a - h))/h
else:
raise ValueError("Method must be 'central', 'forward' or 'backward'.")

x = np.linspace(-2,2,100)
f = lambda x: (2*x**2 + 2*x + 1)
y = f(x)

dydx = derivative(f,x)
print("dydx",type(dydx) , "\r\n",dydx)

# axes
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
ax.spines['left'].set_position('center')
ax.spines['bottom'].set_position('center')
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')

# plot the functions
plt.plot(x,y, 'b', label='y')

plt.plot(x,dydx, 'r', label='dydx')

plt.legend(loc='upper left')

# show the plot
plt.show()

# learn python lesson 4 , www.robotronix.co.il

import matplotlib.pyplot as plt

import numpy as np

#Credit

#https://www.math.ubc.ca/~pwalls/math-python/integration/riemann-sums/

def derivative(f,a,method='central',h=0.01):

'''Compute the difference formula for f'(a) with step size h.

Parameters

----------

f : function

Vectorized function of one variable

a : number

Compute derivative at x = a

method : string

Difference formula: 'forward', 'backward' or 'central'

h : number

Step size in difference formula

Returns

-------

float

Difference formula:

central: f(a+h) - f(a-h))/2h

forward: f(a+h) - f(a))/h

backward: f(a) - f(a-h))/h

'''

if method == 'central':

return (f(a + h) - f(a - h))/(2*h)

elif method == 'forward':

return (f(a + h) - f(a))/h

elif method == 'backward':

return (f(a) - f(a - h))/h

else:

raise ValueError("Method must be 'central', 'forward' or 'backward'.")

x = np.linspace(-2,2,100)

f = lambda x: (2*x**2 + 2*x + 1)

y = f(x)

dydx = derivative(f,x)

print("dydx",type(dydx) , "\r\n",dydx)

# axes

fig = plt.figure()

ax = fig.add_subplot(1, 1, 1)

ax.spines['left'].set_position('center')

ax.spines['bottom'].set_position('center')

ax.spines['right'].set_color('none')

ax.spines['top'].set_color('none')

ax.xaxis.set_ticks_position('bottom')

ax.yaxis.set_ticks_position('left')

# plot the functions

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

plt.plot(x,dydx, 'r', label='dydx')

plt.legend(loc='upper left')

# show the plot

plt.show()

# learn python lesson 4 , www.robotronix.co.il
import matplotlib.pyplot as plt
import numpy as np

#Credit
#https://www.math.ubc.ca/~pwalls/math-python/integration/riemann-sums/

f = lambda x : 2*x**2+5
a = 0; b = 5; N = 50
n = 10 # Use n*N+1 points to plot the function smoothly

x = np.linspace(a,b,N+1)
y = f(x)

X = np.linspace(a,b,n*N+1)
Y = f(X)

plt.figure(figsize=(15,5))

plt.subplot(1,3,2)
plt.plot(X,Y,'b')
x_mid = (x[:-1] + x[1:])/2 # Midpoints
y_mid = f(x_mid)
plt.plot(x_mid,y_mid,'b.',markersize=10)
plt.bar(x_mid,y_mid,width=(b-a)/N,alpha=0.2,edgecolor='b')
plt.title('Midpoint Riemann Sum, N = {}'.format(N))

plt.show()

# learn python lesson 4 , www.robotronix.co.il

import matplotlib.pyplot as plt

import numpy as np

#Credit

#https://www.math.ubc.ca/~pwalls/math-python/integration/riemann-sums/

f = lambda x : 2*x**2+5

a = 0; b = 5; N = 50

n = 10 # Use n*N+1 points to plot the function smoothly

x = np.linspace(a,b,N+1)

y = f(x)

X = np.linspace(a,b,n*N+1)

Y = f(X)

plt.figure(figsize=(15,5))

plt.subplot(1,3,2)

plt.plot(X,Y,'b')

x_mid = (x[:-1] + x[1:])/2 # Midpoints

y_mid = f(x_mid)

plt.plot(x_mid,y_mid,'b.',markersize=10)

plt.bar(x_mid,y_mid,width=(b-a)/N,alpha=0.2,edgecolor='b')

plt.title('Midpoint Riemann Sum, N = {}'.format(N))

plt.show()

matplotlib.org קישור לאתר של ה

https://matplotlib.org/stable/gallery/mplot3d/mixed_subplots.html?highlight=plt%20figure

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רובוטרוניקס : קורס פייתון – 510 / שיעור 6 – חיבור , חיסור , הכפלה של פונקציות והצגה גרפית

רובוטרוניקס : קורס פייתון – 510 / שיעור 14 לולאות While , for

רובוטרוניקס : קורס פייתון – 510 / שיעור 26 – כתיבה לקובץ טקסט

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