In [1]:
import numpy as np
import seaborn as sns
import matplotlib.pyplot as plt
from ipywidgets import widgets, interact
Int
In [2]:
def dice(num_of_sides = 6, loaded_num = 1, loaded_weight = 1):
'''
Virtual dice with output of a side. Default is an equally weighted dice.
Input:
num_of_sides: Number of sides for the dice. (Default = 6)
loaded_num : The number that is biased or "loaded". (Default = 1)
loaded_wght : Number used to get loaded weight. (Default = 1)
For equal weight distribution, the loaded number has
the same probability as any other dice number. (1/6, 1/3,..., 1/n)
Output: Int value corresponding to a side of the dice.
Example:
[dice(10, 7, 9) for output in range(20)] -> [7, 7, 7, 3, 7, 7, 7, 7, 7, 7, 7, 8, 7, 7, 7, 7, 1, 7, 7, 7]
[dice(6, 5, 3) for output in range(20)] -> [5, 5, 6, 5, 6, 5, 2, 6, 5, 2, 4, 6, 6, 5, 2, 3, 5, 5, 6, 5]
'''
if loaded_num > num_of_sides:
raise ValueError('The loaded number chosen is greater than the total number of sides on the dice!')
elif loaded_weight > num_of_sides:
raise ValueError('The loaded weight chosen is greater than the total number of sides on the dice!')
elif num_of_sides < 1:
raise ValueError('Total number of sides is less than one!')
sides = [num for num in range(1, num_of_sides+1)]
return np.random.choice(sides, p=wght(num_of_sides, loaded_num, loaded_weight))
def wght(num_of_sides = 6, loaded_num = 1, loaded_weight = 1):
'''
Weight function for the probabilities of a side on a roll.
Input:
num_of_sides: Number of sides for the dice. (Default = 6)
loaded_num : The number that is biased or "loaded". (Default = 1)
loaded_wght : Number used to get loaded weight. (Default = 1)
For equal weight distribution, the loaded number has
the same probability as any other dice number. (1/6, 1/3,..., 1/n)
Output: List of corresponding weights for each side.
Example:
Dice with 10 sides, loaded number to be 4, and the loaded weight to be
the chance of 3/10(rather than 1/10):
wght(10, 4, 3) -> [0.07777777777777778, 0.07777777777777778, 0.07777777777777778,
0.3,0.07777777777777778, 0.07777777777777778, 0.07777777777777778, 0.07777777777777778,
0.07777777777777778, 0.07777777777777778]
'''
if loaded_weight == 1:
return [1/num_of_sides]*len(range(num_of_sides))
ld_wght = loaded_weight/num_of_sides
wght_list = [(1-ld_wght)/(num_of_sides-1)]*len(range(num_of_sides))
wght_list[loaded_num-1] = ld_wght
return wght_list
def trials(num_of_trials=100, num_of_sides=6, loaded_num=1, loaded_weight=1):
'''
Trials consisting of a specified number of time the dice will be rolled. Output gives
a list of all the rolled values and a list of cumulative proportion per roll.
Input:
num_of_trials: Number of rolls. (Default = 100)
num_of_sides : Number of sides for the dice. (Default = 6)
loaded_num : The number that is biased or "loaded". (Default = 1)
loaded_wght : Number used to get loaded weight. (Default = 1)
For equal weight distribution, the loaded number has
the same probability as any other dice number. (1/6, 1/3,..., 1/n)
Output: (In this order.)
rollsList: List of rolled values. Length equal to the num_of_trials input.
cumltList: List of cumulative proportion per roll.
'''
sides = list(range(1, num_of_sides+1))
rollsList = []
cumltList = [[] for side in range(num_of_sides)]
cumlt = [0 for side in range(num_of_sides)]
for trial in range(num_of_trials):
roll = dice(num_of_sides, loaded_num, loaded_weight)
rollsList.append(roll)
for side in sides:
if roll == side:
cumlt[side-1] += 1
cumltList[side-1].append(cumlt[side-1]/(trial+1))
return rollsList, cumltList
In [3]:
def simu_dice(num_of_trials = 100, num_of_sides = 6, loaded_num = 1, loaded_wght = 1, \
plt_style = 'seaborn-ticks', cuml_tot = True, ret = False):
rolls, cuml = trials(num_of_trials, num_of_sides, loaded_num, loaded_wght)
plt.style.use(style=plt_style)
if cuml_tot is True:
for side in cuml:
ax = plt.plot(np.array([num+1 for num in range(len(rolls))]), np.array(side), \
label = 'Side {}'.format(cuml.index(side) + 1))
else:
ax = plt.plot(np.array([num+1 for num in range(len(rolls))]), np.array(cuml[loaded_num-1]), \
label = 'Side {}'.format(cuml.index(cuml[loaded_num-1]) + 1))
ax = plt.plot([num+1 for num in range(len(rolls))], np.array([1/num_of_sides]*len(rolls)), \
color = 'k', linewidth = 2, label = 'Theoretical \n Probability')
ax = plt.title(plt_style)
ax = plt.legend()
ax = plt.ylim(0.0, 1.0)
ax = plt.xlabel('# of Trials')
ax = plt.ylabel('Cumulative Proportions')
plt.show()
if ret is True:
return rolls, cuml
In [5]:
num_of_sides = widgets.IntSlider(6, 1, 25, 1)
interact(simu_dice, \
num_of_sides = widgets.IntSlider(6, 1, 25, 1) ,\
num_of_trials = widgets.IntSlider(100, 0, 100000, 100) ,\
loaded_num = widgets.IntSlider(1, 1, num_of_sides.max, 1) ,\
loaded_wght = widgets.IntSlider(1, 1, num_of_sides.max, 1) ,\
plt_style = tuple(style for style in plt.style.available) ,\
cuml_tot = True ,\
ret = widgets.fixed(False)
);
In [ ]:
from ipywidgets import widgets
from ipywidgets import interact
from IPython.display import display
In [ ]:
text = widgets.Text()
display(text)
def handle_submit(sender):
print('Butters')
text.on_submit(handle_submit)
In [ ]:
button = widgets.Button(description = 'Click me!')
display(button)
def on_button_click(b):
print('Button clicked!')
button.on_click(on_button_click)
In [ ]:
def f(x, y):
print(x)
print(y)
sld = interact(f, x=100, y=50)
chk = interact(f, x=True, y=False)
txt = interact(f, x='Suren', y='Butters')
In [ ]:
outputText = widgets.Text()
outputText
In [ ]:
inputText = widgets.Text()
def makeUpperCase(sender):
outputText.value = inputText.value.upper()
inputText.on_submit(makeUpperCase)
inputText
In [ ]:
t = np.arange(0.0, 1.1, .01)
def pltSin(A, f):
plt.plot(t, A*np.sin(2*np.pi*t*f))
plt.axis([0, 1, -10, 10])
plt.autoscale(False)
plt.show()
interact(pltSin, A = widgets.IntSlider(1, 0, 10, 1), f = widgets.FloatSlider(1, min=0, max=10, step=1))