4.6. Examples: Lecture 4#
4.6.1. Use of `random ()` and `randint ()`#
random_01.py
#!/usr/bin/python
'''
generazione di numeri pseudo-casuali distribuiti uniformemente fra 0 ed 1
python3 random_01.py 10
'''
import sys
import random
def main () :
'''
Funzione che implementa il programma principale
- documentazione di random https://docs.python.org/3/library/random.html
'''
if len(sys.argv) < 2 :
print ('usage: ', sys.argv[0], 'numero')
exit ()
randlist = []
for i in range (int (sys.argv[1])):
# Return the next random floating point number in the range 0.0 <= X < 1.0
randlist.append (random.random ())
print (i, randlist[-1])
randlistint = []
for i in range (int (sys.argv[1])):
# Return the next random floating point number in the range 0.0 <= X < 1.0
randlistint.append (random.randint (0, 100))
print (i, randlistint[-1])
# ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ----
if __name__ == "__main__":
main ()
4.6.2. Use of `random.seed ()`#
random_02.py
#!/usr/bin/python
'''
generazione di numeri pseudo-casuali distribuiti uniformemente fra 0 ed 1
a partire da un determinato seed
python3 random_02.py 10 2.5
'''
import sys
import random
def main () :
'''
Funzione che implementa il programma principale
'''
if len(sys.argv) < 3 :
print ('usage: ', sys.argv[0], 'numero seed')
exit ()
random.seed (float (sys.argv[2]))
randlist = []
for i in range (int (sys.argv[1])):
# Return the next random floating point number in the range 0.0 <= X < 1.0
randlist.append (random.random ())
print (i, randlist[-1])
# ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ----
if __name__ == "__main__":
main ()
4.6.3. Drawing of the obtained sequence of numbers#
random_03.py
#!/usr/bin/python
'''
generazione di numeri pseudo-casuali distribuiti uniformemente fra 0 ed 1
a partire da un determinato seed e disegno della distribuzione
python3 random_03.py 200 2.4
'''
import sys
import random
import matplotlib.pyplot as plt
import numpy as np
from math import floor
def main () :
'''
Funzione che implementa il programma principale
'''
if len(sys.argv) < 3 :
print ('usage: ', sys.argv[0], 'numero seed')
exit ()
random.seed (float (sys.argv[2]))
randlist = []
for i in range (int (sys.argv[1])):
# Return the next random floating point number in the range 0.0 <= X < 1.0
randlist.append (random.random ())
print (i, randlist[-1])
# plotting of the generated list of numbers in a histogram
xMin = 0. # minimum of the histogram drawing range
xMax = 1. # maximum of the histogram drawing range
nBins = floor (len (randlist) / 20.) + 1 # number of bins of the hitogram
bin_edges = np.linspace (xMin, xMax, nBins) # edges o the histogram bins
# check the bin edges
print (bin_edges)
print (len (bin_edges))
# disegno della funzione
fig, ax = plt.subplots ()
ax.set_title ('Histogram of random numbers', size=14)
ax.set_xlabel('random value')
ax.set_ylabel('events in bin')
ax.hist (randlist, # list of numbers
bins = bin_edges,
color = 'orange',
# normed = True,
)
plt.show ()
# ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ----
if __name__ == "__main__":
main ()
4.6.4. Porting of the generation code to a library#
random_04.py
#!/usr/bin/python
'''
generazione di numeri pseudo-casuali distribuiti uniformemente fra 0 ed 1
a partire da un determinato seed e disegno della distribuzione,
separando la generazione dal programma principale
python3 random_04.py 2000 2.4
'''
import sys
import random
import matplotlib.pyplot as plt
import numpy as np
from math import floor
from myrand import generate_uniform
def main () :
'''
Funzione che implementa il programma principale
'''
if len(sys.argv) < 3 :
print ('usage: ', sys.argv[0], 'numero seed')
exit ()
randlist = generate_uniform (int (sys.argv[1]), float (sys.argv[2]))
# plotting of the generated list of numbers in a histogram
xMin = 0. # minimum of the histogram drawing range
xMax = 1. # maximum of the histogram drawing range
nBins = floor (len (randlist) / 20.) + 1 # number of bins of the hitogram
bin_edges = np.linspace (xMin, xMax, nBins) # edges o the histogram bins
# disegno della funzione
fig, ax = plt.subplots ()
ax.set_title ('Histogram of random numbers', size=14)
ax.set_xlabel('random value')
ax.set_ylabel('events in bin')
ax.hist (randlist, # list of numbers
bins = bin_edges,
color = 'orange',
# normed = True,
)
plt.show ()
# ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ----
if __name__ == "__main__":
main ()
myrand.py
#!/usr/bin/python
import random
from math import sqrt
def generate_uniform (N, seed = 0.) :
'''
generazione di N numeri pseudo-casuali distribuiti fra 0 ed 1
a partire da un determinato seed
'''
if seed != 0. : random.seed (float (seed))
randlist = []
for i in range (N):
# Return the next random floating point number in the range 0.0 <= X < 1.0
randlist.append (random.random ())
return randlist
# ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ----
def rand_range (xMin, xMax) :
'''
generazione di un numero pseudo-casuale distribuito fra xMin ed xMax
'''
return xMin + random.random () * (xMax - xMin)
# ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ----
def generate_range (xMin, xMax, N, seed = 0.) :
'''
generazione di N numeri pseudo-casuali distribuiti fra xMin ed xMax
a partire da un determinato seed
'''
if seed != 0. : random.seed (float (seed))
randlist = []
for i in range (N):
# Return the next random floating point number in the range 0.0 <= X < 1.0
randlist.append (rand_range (xMin, xMax))
return randlist
# ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ----
def rand_TAC (f, xMin, xMax, yMax) :
'''
generazione di un numero pseudo-casuale
con il metodo try and catch
'''
x = rand_range (xMin, xMax)
y = rand_range (0, yMax)
while (y > f (x)) :
x = rand_range (xMin, xMax)
y = rand_range (0, yMax)
return x
# ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ----
def generate_TAC (f, xMin, xMax, yMax, N, seed = 0.) :
'''
generazione di N numeri pseudo-casuali
con il metodo try and catch, in un certo intervallo,
a partire da un determinato seed
'''
if seed != 0. : random.seed (float (seed))
randlist = []
for i in range (N):
# Return the next random floating point number in the range 0.0 <= X < 1.0
randlist.append (rand_TAC (f, xMin, xMax, yMax))
return randlist
# ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ----
def rand_TCL (xMin, xMax, N_sum = 10) :
'''
generazione di un numero pseudo-casuale
con il metodo del teorema centrale del limite
su un intervallo fissato
'''
y = 0.
for i in range (N_sum) :
y = y + rand_range (xMin, xMax)
y /= N_sum ;
return y ;
# ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ----
def generate_TCL (xMin, xMax, N, N_sum = 10, seed = 0.) :
'''
generazione di N numeri pseudo-casuali
con il metodo del teorema centrale del limite, in un certo intervallo,
a partire da un determinato seed
'''
if seed != 0. : random.seed (float (seed))
randlist = []
for i in range (N):
# Return the next random floating point number in the range 0.0 <= X < 1.0
randlist.append (rand_TCL (xMin, xMax, N_sum))
return randlist
# ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ----
def rand_TCL_ms (mean, sigma, N_sum = 10) :
'''
generazione di un numero pseudo-casuale
con il metodo del teorema centrale del limite
note media e sigma della gaussiana
'''
y = 0.
delta = sqrt (3 * N_sum) * sigma
xMin = mean - delta
xMax = mean + delta
for i in range (N_sum) :
y = y + rand_range (xMin, xMax)
y /= N_sum ;
return y ;
# ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ----
def generate_TCL_ms (mean, sigma, N, N_sum = 10, seed = 0.) :
'''
generazione di N numeri pseudo-casuali
con il metodo del teorema centrale del limite, note media e sigma della gaussiana,
a partire da un determinato seed
'''
if seed != 0. : random.seed (float (seed))
randlist = []
delta = sqrt (3 * N_sum) * sigma
xMin = mean - delta
xMax = mean + delta
for i in range (N):
# Return the next random floating point number in the range 0.0 <= X < 1.0
randlist.append (rand_TCL (xMin, xMax, N_sum))
return randlist
4.6.5. Generation of pseudo-random numbers uniformly within (xMin, xMax)#
random_05.py
#!/usr/bin/python
'''
generazione di numeri pseudo-casuali distribuiti uniformemente fra xMin ed xMax
a partire da un determinato seed e disegno della distribuzione,
separando la generazione dal programma principale
python3 random_05.py 2.2 4.3 2000 2.4
'''
import sys
import random
import matplotlib.pyplot as plt
import numpy as np
from math import floor
from myrand import generate_range
def main () :
'''
Funzione che implementa il programma principale
'''
if len(sys.argv) < 5 :
print ('usage: ', sys.argv[0], 'xMin xMax numero seed')
exit ()
xMin = float (sys.argv[1]) # minimum of the histogram drawing range
xMax = float (sys.argv[2]) # maximum of the histogram drawing range
seed = float (sys.argv[4])
N = int (sys.argv[3])
print (' -------- ')
print (' minimum : ', xMin)
print (' maximum : ', xMax)
print (' seed : ', seed)
print (' N : ', N)
print (' -------- ')
randlist = generate_range (xMin, xMax, N, seed)
# plotting of the generated list of numbers in a histogram
nBins = floor (len (randlist) / 20.) + 1 # number of bins of the hitogram
bin_edges = np.linspace (xMin, xMax, nBins) # edges o the histogram bins
# disegno della funzione
fig, ax = plt.subplots ()
ax.set_title ('Histogram of random numbers', size=14)
ax.set_xlabel ('random value')
ax.set_ylabel ('events in bin')
ax.hist (randlist, # list of numbers
bins = bin_edges,
color = 'orange',
# normed = True,
)
plt.show ()
# ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ----
if __name__ == "__main__":
main ()
4.6.6. Visualisation of a pseudo-random sequence#
random_06.py
#!/usr/bin/python
'''
generazione di numeri pseudo-casuali distribuiti uniformemente fra xMin ed xMax
a partire da un determinato seed e disegno della sequenza di numeri,
separando la generazione dal programma principale
python3 random_06.py 2.2 4.3 20 2.4
'''
import sys
import random
import matplotlib.pyplot as plt
import numpy as np
from math import floor
from myrand import generate_range
def main () :
'''
Funzione che implementa il programma principale
'''
if len(sys.argv) < 5 :
print ('usage: ', sys.argv[0], 'xMin xMax numero seed')
exit ()
xMin = float (sys.argv[1]) # minimum of the histogram drawing range
xMax = float (sys.argv[2]) # maximum of the histogram drawing range
seed = float (sys.argv[4])
N = int (sys.argv[3])
print (' -------- ')
print (' minimum : ', xMin)
print (' maximum : ', xMax)
print (' seed : ', seed)
print (' N : ', N)
print (' -------- ')
# list of uniformly generated numbers
randlist = generate_range (xMin, xMax, N, seed)
# list of the position indices of the pseudo-random numbers in randlist
index = range (len (randlist))
# disegno della funzione
fig, ax = plt.subplots ()
ax.set_title ('Sequence of random numbers', size=14)
ax.set_xlabel ('index in the sequence')
ax.set_ylabel ('random value')
# ax.scatter (index, randlist)
ax.plot (index, randlist, marker = 'o')
plt.show ()
# ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ----
if __name__ == "__main__":
main ()
4.6.7. Visualisation of a pseudo-random sequence and its distribution#
random_07.py
#!/usr/bin/python
'''
generazione di numeri pseudo-casuali distribuiti uniformemente fra xMin ed xMax
a partire da un determinato seed e disegno congiunto della loro distribuzione e sequenza,
separando la generazione dal programma principale
reference documentation:
https://matplotlib.org/stable/gallery/axes_grid1/scatter_hist_locatable_axes.html#sphx-glr-gallery-axes-grid1-scatter-hist-locatable-axes-py
python3 random_07.py 2.2 4.3 100 2.4
'''
import sys
import random
import matplotlib.pyplot as plt
from mpl_toolkits.axes_grid1 import make_axes_locatable
import numpy as np
from math import floor
from myrand import generate_range
def main () :
'''
Funzione che implementa il programma principale
'''
if len(sys.argv) < 5 :
print ('usage: ', sys.argv[0], 'xMin xMax numero seed')
exit ()
xMin = float (sys.argv[1]) # minimum of the histogram drawing range
xMax = float (sys.argv[2]) # maximum of the histogram drawing range
seed = float (sys.argv[4])
N = int (sys.argv[3])
print (' -------- ')
print (' minimum : ', xMin)
print (' maximum : ', xMax)
print (' seed : ', seed)
print (' N : ', N)
print (' -------- ')
# list of uniformly generated numbers
randlist = generate_range (xMin, xMax, N, seed)
# list of the position indices of the pseudo-random numbers in randlist
index = range (len (randlist))
# disegno della funzione
fig, ax = plt.subplots ()
ax.set_title ('Sequence of random numbers', size=14)
ax.set_xlabel ('index in the sequence')
ax.set_ylabel ('random value')
# ax.scatter (index, randlist)
ax.plot (index, randlist, marker = 'o')
# create a new axis on the left of the current axes
divider = make_axes_locatable (ax)
# below height and pad are in inches
ax_histy = divider.append_axes ("right", 1.2, pad=0.1, sharey=ax)
ax_histy.set_xlabel ('counts')
# make some labels invisible
ax_histy.yaxis.set_tick_params (labelleft=False)
nBins = floor (len (randlist) / 10.) + 1 # number of bins of the hitogram
bin_edges = np.linspace (xMin, xMax, nBins) # edges o the histogram bins
ax_histy.hist (randlist, # list of numbers
bins = bin_edges,
color = 'orange',
orientation='horizontal',
# normed = True,
)
plt.show ()
# ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ----
if __name__ == "__main__":
main ()
4.6.8. Generation of pseudo-random numbers with the try-and-catch method#
random_08.py
#!/usr/bin/python
'''
generazione di numeri pseudo-casuali distribuiti secondo una distribuzione arbitraria
con il metodo try-and-catch fra xMin ed xMax
a partire da un determinato seed e disegno della distribuzione,
separando la generazione dal programma principale
python3 random_08.py 0. 10 2. 20000 2.4
'''
import sys
import random
import matplotlib.pyplot as plt
import numpy as np
from math import floor
from myrand import generate_TAC
def func (x, scale = 1) :
'''
funzione definita positiva sotto la quale generare numeri casuali
'''
return scale * (np.cos (x) + 1.)
# ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ----
def main () :
'''
Funzione che implementa il programma principale
'''
if len(sys.argv) < 6 :
print ('usage: ', sys.argv[0], 'xMin xMax numero seed')
exit ()
xMin = float (sys.argv[1]) # minimum of the histogram drawing range
xMax = float (sys.argv[2]) # maximum of the histogram drawing range
yMax = float (sys.argv[3]) # maximum of the histogram drawing range
seed = float (sys.argv[5])
N = int (sys.argv[4])
print (' -------- ')
print (' minimum : ', xMin)
print (' maximum : ', xMax)
print (' seed : ', seed)
print (' N : ', N)
print (' -------- ')
randlist = generate_TAC (func, xMin, xMax, yMax, N, seed)
# plotting of the generated list of numbers in a histogram
nBins = floor (len (randlist) / 400.) # number of bins of the hitogram
bin_edges = np.linspace (xMin, xMax, nBins + 1) # edges o the histogram bins
# disegno della funzione
fig, ax = plt.subplots ()
ax.set_title ('Histogram of random numbers', size=14)
ax.set_xlabel ('random value')
ax.set_ylabel ('events in bin')
ax.hist (randlist, # list of numbers
bins = bin_edges,
color = 'orange',
# normed = True,
)
plt.show ()
# ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ----
if __name__ == "__main__":
main ()
4.6.9. Generation of pseudo-random numbers with the central limit theorem method#
random_09.py
#!/usr/bin/python
'''
generazione di numeri pseudo-casuali distribuiti secondo una distribuzione Gaussiana
con il metodo del teorema centrale del limite fra xMin ed xMax
a partire da un determinato seed e disegno della distribuzione,
separando la generazione dal programma principale
python3 random_09.py 0. 10 20000 2.4 10
'''
import sys
import random
import matplotlib.pyplot as plt
import numpy as np
from math import floor
from myrand import generate_TCL
def main () :
'''
Funzione che implementa il programma principale
'''
if len(sys.argv) < 6:
print ('usage: ', sys.argv[0], 'xMin xMax numero seed')
exit ()
xMin = float (sys.argv[1]) # minimum of the histogram drawing range
xMax = float (sys.argv[2]) # maximum of the histogram drawing range
seed = float (sys.argv[4])
N = int (sys.argv[3])
N_sum = int (sys.argv[5])
print (' -------- ')
print (' minimum : ', xMin)
print (' maximum : ', xMax)
print (' seed : ', seed)
print (' N : ', N)
print (' N_sum : ', N_sum)
print (' -------- ')
randlist = generate_TCL (xMin, xMax, N, N_sum, seed)
# plotting of the generated list of numbers in a histogram
nBins = floor (len (randlist) / 400.) # number of bins of the hitogram
bin_edges = np.linspace (xMin, xMax, nBins + 1) # edges o the histogram bins
# disegno della funzione
fig, ax = plt.subplots ()
ax.set_title ('Histogram of random numbers', size=14)
ax.set_xlabel ('random value')
ax.set_ylabel ('events in bin')
ax.hist (randlist, # list of numbers
bins = bin_edges,
color = 'orange',
# normed = True,
)
plt.show ()
# ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ----
if __name__ == "__main__":
main ()