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abner-math/Mesquita.py

Last active August 29, 2015 14:07
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Statistical software to calculate over some models
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Mesquita.py
#!/usr/bin/python
# -*-coding=utf-8 -*-
#-----------------------------------------------------------------
# Mesquita v1.0
# Created by: Abner Matheus
# E-mail: [email protected]
# Github: http://github.com/picoledelimao
#-----------------------------------------------------------------
import math
class MatematicaException(Exception): pass
class ProbabilidadeException(Exception): pass
class BinomialException(ProbabilidadeException): pass
class HipergeometricoException(ProbabilidadeException): pass
class GeometricoException(ProbabilidadeException): pass
class PoissonException(ProbabilidadeException): pass
class UniformeException(ProbabilidadeException): pass
class ExponencialException(ProbabilidadeException): pass
class NormalException(ProbabilidadeException): pass
class Matematica:
#combina dois numeros inteiros, n > p
@staticmethod
def combinacao(n, p):
if n < p or p < 0 or not(isinstance(n, int) and isinstance(p, int)):
raise MatematicaException("Parâmetros inválidos na combinação")
n_fatorado = reduce(lambda x, y: x * y, [x for x in range(n, n-p, -1)] + [1])
try:
return float(n_fatorado)/math.factorial(p)
except: return n_fatorado/math.factorial(p)
#----------------------------------------------------------------
# Modelos discretos
#----------------------------------------------------------------
class ModeloDiscreto:
#variacao do 'x' na reta real
def variacao(self, x):
raise NotImplementedError()
#funcao de probabilidade
def f(self):
raise NotImplementedError()
#funcao de probabilidade acumulada
def F(self):
raise NotImplementedError()
#esperanca da v.a.
def e(self):
raise NotImplementedError()
#variancia da v.a.
def var(self):
raise NotImplementedError()
#=================================================================
class Bernoulli(ModeloDiscreto):
#p: chance de sucesso
def __init__(self, p):
try:
self.p = float(p)
if not 0 <= self.p <= 1:
raise ProbabilidadeException("Parametro p não é uma probabilidade")
except:
raise ProbabilidadeException("Parametro p não é uma probabilidade")
def fp(self):
return self.p
def e(self):
return self.p
def var(self):
return self.p*(1-self.p)
class Binomial(Bernoulli):
#n: numero de repeticoes, p: chance de sucesso
def __init__(self, n, p):
try:
self.n = int(n)
except:
raise BinomialException("Parâmetro n deve ser um numero inteiro")
Bernoulli.__init__(self, p)
def variacao(self):
return [x for x in range(0, self.n + 1)]
def fp(self, x):
if not x in self.variacao():
raise BinomialException("x está fora da variação da v.a.")
combinacao = Matematica.combinacao(self.n, x)
chance_sucesso = math.pow(self.p, x)
chance_fracasso = math.pow(1 - self.p, self.n - x)
return combinacao*chance_sucesso*chance_fracasso
def F(self, x):
if x < 0:
return 0
elif x >= self.n:
return 1
count = 0
for p in range(0, int(x)+1):
count += self.fp(p)
return count
def e(self):
return self.n*self.p
def var(self):
return self.n*self.p*(1-self.p)
class Hipergeometrico(ModeloDiscreto):
#N: tamanho da populacao
#n: tamanho da amostra
#r: numero de elementos favoraveis
def __init__(self, N, r, n):
try:
self.N = int(N)
self.r = int(r)
self.n = int(n)
if self.N < self.n or self.N < self.r:
raise HipergeometricoException("Parâmetros inválidos")
except:
raise HipergeometricoException("Parâmetros inválidos")
def variacao(self):
return [x for x in range(max(0, self.n-(self.N-self.r)), min(self.r, self.n) + 1)]
def fp(self, x):
if not x in self.variacao():
raise HipergeometricoException("x está fora da variação da v.a.")
a = Matematica.combinacao(self.r, x)
b = Matematica.combinacao(self.N - self.r, self.n - x)
c = Matematica.combinacao(self.N, self.n)
return a*b/c
def F(self, x):
if x < max(0, self.n-(self.N-self.r)):
return 0
elif x >= min(self.r, self.n):
return 1
count = 0
for p in range(max(0, self.n-(self.N-self.r)), int(x)+1):
count += self.fp(p)
return count
def e(self):
return self.n*(self.r/float(self.N))
def var(self):
return self.n*(self.r/float(self.N))*(1-self.r/float(self.N))*(self.N-self.n)/float(self.N-1)
class Geometrico(Bernoulli):
#p: chance de sucesso
def __init__(self, p):
Bernoulli.__init__(self, p)
def variacao(self, x):
return isinstance(x, int) and x >= 1
def fp(self, x):
if not self.variacao(x):
raise GeometricoException("x está fora da variação da v.a.")
return math.pow(1-self.p, x-1)*self.p
def F(self, x):
if x <= 1:
return 0
count = 0
for p in range(1, int(x)+1):
count += self.fp(p)
return count
def e(self):
return 1/float(self.p)
def var(self):
return (1-self.p)/float(math.pow(self.p, 2))
class Poisson(ModeloDiscreto):
#alfa: media
def __init__(self, alfa):
try:
self.alfa = float(alfa)
except:
raise PoissonException("Parâmetro inválido")
def variacao(self, x):
return isinstance(x, int) and x >= 0
def fp(self, x):
if not self.variacao(x):
raise PoissonException("x está fora da variação da v.a.")
return math.pow(math.e, -self.alfa)*math.pow(self.alfa, x)/float(math.factorial(x))
def F(self, x):
if x <= 0:
return 0
count = 0
for p in range(0, int(x)+1):
count += self.fp(p)
return count
def e(self):
return self.alfa
def var(self):
return self.alfa
#----------------------------------------------------------------
# Modelos continuos
#----------------------------------------------------------------
class ModeloContinuo:
#funcao distribuicao de probabilidade entre dois pontos
def fdp(self, x, y):
raise NotImplementedError()
#funcao de probabilidade acumulada de -infinito ate o ponto
def F(self, x):
raise NotImplementedError()
#esperanca da v.a.
def e(self):
raise NotImplementedError()
#variancia da v.a.
def var(self):
raise NotImplementedError()
#=================================================================
class Uniforme(ModeloContinuo):
def __init__(self, a, b):
try:
self.a = float(a)
self.b = float(b)
if self.a >= self.b:
raise UniformeException("Parametro a é maior ou igual que o b")
except: raise UniformeException("Parâmetros inválidos")
def F(self, x):
if x <= self.a:
return 0
elif x >= self.b:
return 1
return (x-self.a)/float(self.b-self.a)
def fdp(self, x, y):
if y < x:
raise UniformeException("Ponto final é menor que ponto inicial")
return self.F(y) - self.F(x)
def e(self):
return (self.a + self.b)/2.0
def var(self):
return math.pow(self.b - self.a, 2)/12.0
class Exponencial(ModeloContinuo):
#alfa: o inverso da media
def __init__(self, alfa):
try:
self.alfa = float(alfa)
except: raise ExponencialException("Parâmetro inválido")
if self.alfa < 0:
raise ExponencialException("Parâmetro deve ser maior que 0")
def F(self, x):
if x <= 0:
return 0
return 1 - math.pow(math.e, -self.alfa*x)
def fdp(self, x, y):
if y < x:
raise ExponencialException("Ponto final é menor que o ponto inicial")
return self.F(y) - self.F(x)
def e(self):
return 1/float(self.alfa)
def var(self):
return 1/float(math.pow(self.alfa, 2))
class Normal(ModeloContinuo):
#u: media
#o2: variancia
def __init__(self, u, o2):
try:
self.u = float(u)
self.o2 = float(o2)
except:
raise NormalException("Parâmetros inválidos")
#tabela abaixo
self.tabela = {0.0: 0.5, 0.25: 0.5987, 2.0: 0.9772, 3.0: 0.9987, 0.5: 0.6915, 1.0: 0.8413, 3.37: 0.9996, 0.75: 0.7734, 2.83: 0.9977, 1.17: 0.879, 0.67: 0.7486, 2.28: 0.9887, 3.29: 0.9995, 3.21: 0.9993, 0.83: 0.7967, 0.6: 0.7257, 2.91: 0.9982, 3.5: 0.9998, 1.34: 0.9099, 2.25: 0.9878, 0.85: 0.8023, 3.51: 0.9998, 0.96: 0.8315, 0.66: 0.7454, 3.27: 0.9995, 0.78: 0.7823, 3.45: 0.9997, 1.67: 0.9525, 1.43: 0.9236, 2.65: 0.996, 2.03: 0.9788, 3.54: 0.9998, 2.36: 0.9909, 3.46: 0.9997, 0.14: 0.5557, 0.37: 0.6443, 1.2: 0.8849, 0.4: 0.6554, 2.62: 0.9956, 3.55: 0.9998, 2.04: 0.9793, 1.29: 0.9015, 0.46: 0.6772, 3.49: 0.9998, 0.56: 0.7123, 1.73: 0.9582, 1.51: 0.9345, 0.36: 0.6406, 3.41: 0.9997, 0.22: 0.5871, 1.09: 0.8621, 0.95: 0.8289, 0.26: 0.6026, 1.61: 0.9463, 3.24: 0.9994, 1.84: 0.9671, 2.06: 0.9803, 0.63: 0.7357, 1.81: 0.9649, 3.3: 0.9995, 1.54: 0.9382, 2.02: 0.9783, 1.95: 0.9744, 2.57: 0.9949, 2.4: 0.9918, 2.73: 0.9968, 1.9: 0.9713, 2.31: 0.9896, 0.42: 0.6628, 3.58: 0.9998, 2.52: 0.9941, 2.76: 0.9971, 2.84: 0.9977, 2.64: 0.9959, 2.17: 0.985, 2.97: 0.9985, 3.23: 0.9994, 1.94: 0.9738, 1.88: 0.9699, 3.33: 0.9996, 2.75: 0.997, 1.68: 0.9535, 2.43: 0.9925, 1.33: 0.9082, 1.85: 0.9678, 2.35: 0.9906, 2.27: 0.9884, 2.19: 0.9857, 1.77: 0.9616, 0.31: 0.6217, 1.96: 0.975, 3.14: 0.9992, 2.51: 0.994, 2.22: 0.9868, 0.73: 0.7673, 1.04: 0.8508, 1.49: 0.9319, 1.18: 0.881, 1.58: 0.9429, 1.01: 0.8438, 1.62: 0.9474, 0.1: 0.5398, 2.6: 0.9953, 1.72: 0.9573, 2.15: 0.9842, 1.76: 0.9608, 0.47: 0.6808, 1.05: 0.8531, 2.92: 0.9982, 1.1: 0.8643, 1.47: 0.9292, 3.13: 0.9991, 3.28: 0.9995, 0.09: 0.5359, 3.31: 0.9995, 0.76: 0.7764, 2.47: 0.9932, 1.63: 0.9484, 0.15: 0.5596, 3.07: 0.9989, 1.37: 0.9147, 0.7: 0.758, 2.85: 0.9978, 2.54: 0.9945, 1.23: 0.8907, 2.32: 0.9898, 0.97: 0.834, 0.74: 0.7704, 0.51: 0.695, 0.64: 0.7389, 2.55: 0.9946, 0.45: 0.6736, 2.78: 0.9973, 0.54: 0.7054, 1.44: 0.9251, 0.55: 0.7088, 0.01: 0.504, 3.39: 0.9997, 2.89: 0.9981, 2.81: 0.9975, 1.14: 0.8729, 1.8: 0.9641, 3.18: 0.9993, 1.22: 0.8888, 1.86: 0.9686, 3.16: 0.9992, 1.99: 0.9767, 3.02: 0.9987, 1.98: 0.9761, 3.26: 0.9994, 0.04: 0.516, 3.08: 0.999, 2.07: 0.9808, 0.34: 0.6331, 0.61: 0.7291, 3.11: 0.9991, 2.14: 0.9838, 3.03: 0.9988, 2.41: 0.992, 0.16: 0.5636, 0.41: 0.6591, 0.48: 0.6844, 1.36: 0.9131, 0.98: 0.8365, 3.19: 0.9993, 3.06: 0.9989, 3.43: 0.9997, 2.98: 0.9986, 3.35: 0.9996, 2.9: 0.9981, 1.5: 0.9332, 0.89: 0.8133, 1.64: 0.9495, 0.24: 0.5948, 0.52: 0.6985, 2.05: 0.9798, 1.59: 0.9441, 1.25: 0.8944, 0.3: 0.6179, 2.56: 0.9948, 2.63: 0.9957, 0.21: 0.5832, 2.71: 0.9966, 0.23: 0.591, 2.79: 0.9974, 2.12: 0.983, 0.71: 0.7611, 0.19: 0.5753, 1.87: 0.9693, 2.45: 0.9929, 1.45: 0.9265, 3.52: 0.9998, 1.89: 0.9706, 3.44: 0.9997, 3.36: 0.9996, 3.22: 0.9994, 0.07: 0.5279, 1.06: 0.8554, 3.53: 0.9998, 2.59: 0.9952, 1.53: 0.937, 3.47: 0.9997, 0.58: 0.719, 2.7: 0.9965, 3.56: 0.9998, 2.94: 0.9984, 0.28: 0.6103, 0.99: 0.8389, 1.41: 0.9207, 3.48: 0.9997, 1.7: 0.9554, 0.38: 0.648, 1.74: 0.9591, 1.78: 0.9625, 0.11: 0.5438, 1.38: 0.9162, 2.38: 0.9913, 1.92: 0.9726, 0.92: 0.8212, 1.82: 0.9656, 1.71: 0.9564, 0.35: 0.6368, 1.11: 0.8665, 0.13: 0.5517, 0.94: 0.8264, 1.12: 0.8686, 2.46: 0.9931, 1.55: 0.9394, 1.75: 0.9599, 0.68: 0.7517, 1.97: 0.9756, 0.44: 0.67, 2.68: 0.9963, 1.15: 0.8749, 2.09: 0.9817, 0.77: 0.7794, 1.28: 0.8997, 2.01: 0.9778, 0.53: 0.7019, 3.4: 0.9997, 3.57: 0.9998, 1.26: 0.8962, 2.3: 0.9893, 2.33: 0.9901, 1.31: 0.9049, 2.39: 0.9916, 0.82: 0.7939, 2.99: 0.9986, 0.84: 0.7995, 0.79: 0.7852, 0.81: 0.791, 0.59: 0.7224, 0.33: 0.6293, 2.26: 0.9881, 2.42: 0.9922, 0.86: 0.8051, 1.79: 0.9633, 1.03: 0.8485, 0.88: 0.8106, 2.34: 0.9904, 1.66: 0.9515, 0.05: 0.5199, 2.74: 0.9969, 2.21: 0.9864, 1.93: 0.9732, 2.61: 0.9955, 1.57: 0.9418, 2.2: 0.9861, 0.06: 0.5239, 3.17: 0.9992, 0.49: 0.6879, 0.2: 0.5793, 2.29: 0.989, 0.62: 0.7324, 1.13: 0.8708, 2.37: 0.9911, 2.13: 0.9834, 2.5: 0.9938, 3.2: 0.9993, 0.8: 0.7881, 1.3: 0.9032, 0.29: 0.6141, 2.48: 0.9934, 2.24: 0.9875, 2.44: 0.9927, 1.19: 0.883, 0.69: 0.7549, 0.87: 0.8078, 2.08: 0.9812, 2.82: 0.9976, 1.21: 0.8869, 2.95: 0.9984, 1.39: 0.9177, 1.91: 0.9719, 3.04: 0.9988, 3.15: 0.9992, 0.18: 0.5714, 1.52: 0.9357, 0.39: 0.6517, 0.93: 0.8238, 2.53: 0.9943, 1.24: 0.8925, 2.11: 0.9826, 2.16: 0.9846, 2.96: 0.9985, 2.49: 0.9936, 0.91: 0.8186, 2.67: 0.9962, 0.27: 0.6064, 0.72: 0.7642, 2.69: 0.9964, 2.18: 0.9854, 2.77: 0.9972, 2.87: 0.9979, 1.65: 0.9505, 2.1: 0.9821, 2.93: 0.9983, 0.65: 0.7422, 0.9: 0.8159, 1.07: 0.8577, 1.08: 0.8599, 1.32: 0.9066, 3.38: 0.9996, 3.09: 0.999, 2.8: 0.9974, 0.02: 0.508, 3.01: 0.9987, 2.23: 0.9871, 0.17: 0.5675, 0.43: 0.6664, 3.1: 0.999, 1.27: 0.898, 1.4: 0.9192, 2.66: 0.9961, 1.16: 0.877, 3.12: 0.9991, 2.58: 0.9951, 1.46: 0.9279, 0.08: 0.5319, 0.12: 0.5478, 1.69: 0.9545, 1.48: 0.9306, 1.42: 0.9222, 1.02: 0.8461, 1.56: 0.9406, 1.83: 0.9664, 3.42: 0.9997, 2.88: 0.998, 0.03: 0.512, 3.32: 0.9995, 3.25: 0.9994, 3.34: 0.9996, 3.05: 0.9989, 1.6: 0.9452, 2.86: 0.9979, 0.32: 0.6255, 1.35: 0.9115, 0.57: 0.7157, 2.72: 0.9967}
def F(self, x):
xNormalizada = (x - self.u)/float(math.sqrt(self.o2))
if xNormalizada < -3.5:
return 0
elif xNormalizada > 3.5:
return 1
chave = float("%.2f" % math.fabs(xNormalizada))
if xNormalizada < 0:
return 1 - self.tabela[chave]
else:
return self.tabela[chave]
def fdp(self, x, y):
if y < x:
raise NormalException("Ponto final é menor que o ponto inicial")
return self.F(y) - self.F(x)
def e(self):
return self.u
def var(self):
return self.o2
#----------------------------------------------------------------
# Interface gráfica
#----------------------------------------------------------------
if __name__ == '__main__':
from Tkinter import *
import tkMessageBox
class JanelaPrincipal:
def __init__(self, top_level):
self.frame1 = Frame(top_level)
self.frame1.pack(side=LEFT)
self.frame2 = Frame(top_level)
self.frame2.pack(side=RIGHT)
width = 50
height = 5
Label(self.frame1, text="Modelos discretos:").pack()
self.binomial = Button(self.frame1, text="Modelo binomial")
self.binomial['width'] = width
self.binomial['height'] = height
self.hipergeometrico = Button(self.frame1, text="Modelo hipergeométrico")
self.hipergeometrico['width'] = width
self.hipergeometrico['height'] = height
self.geometrico = Button(self.frame1, text="Modelo geométrico")
self.geometrico['width'] = width
self.geometrico['height'] = height
self.poisson = Button(self.frame1, text="Modelo de Poisson")
self.poisson['width'] = width
self.poisson['height'] = height
Label(self.frame2, text="Modelos contínuos:").pack()
self.uniforme = Button(self.frame2, text="Modelo uniforme")
self.uniforme['width'] = width
self.uniforme['height'] = height
self.exponencial = Button(self.frame2, text="Modelo exponencial")
self.exponencial['width'] = width
self.exponencial['height'] = height
self.normal = Button(self.frame2, text="Modelo normal")
self.normal['width'] = width
self.normal['height'] = height
self.binomial.pack()
self.hipergeometrico.pack()
self.geometrico.pack()
self.poisson.pack()
self.uniforme.pack()
self.exponencial.pack()
self.normal.pack()
self.binomial.bind("<Button-1>", self.clica_botao)
self.hipergeometrico.bind("<Button-1>", self.clica_botao)
self.geometrico.bind("<Button-1>", self.clica_botao)
self.poisson.bind("<Button-1>", self.clica_botao)
self.uniforme.bind("<Button-1>", self.clica_botao)
self.exponencial.bind("<Button-1>", self.clica_botao)
self.normal.bind("<Button-1>", self.clica_botao)
def clica_botao(self, event):
janela = Tk()
if event.widget == self.binomial:
janela.title("Modelo binomial")
JanelaBinomial(janela)
elif event.widget == self.hipergeometrico:
janela.title("Modelo hipergeométrico")
JanelaHipergeometrico(janela)
elif event.widget == self.geometrico:
janela.title("Modelo geométrico")
JanelaGeometrico(janela)
elif event.widget == self.poisson:
janela.title("Modelo de Poisson")
JanelaPoisson(janela)
elif event.widget == self.uniforme:
janela.title("Modelo uniforme")
JanelaUniforme(janela)
elif event.widget == self.exponencial:
janela.title("Modelo exponencial")
JanelaExponencial(janela)
elif event.widget == self.normal:
janela.title("Modelo normal")
JanelaNormal(janela)
janela.mainloop()
class Grafico:
def __init__(self, raiz):
self.width = 400
self.height = 400
self.canvas = Canvas(raiz, width=self.width, height=self.height)
self.canvas.pack()
def set_modelo(self, modelo_discreto, funcao, limiteX1, limiteX2, acumulada):
self.modelo = modelo_discreto
self.funcao = funcao
self.desenha(limiteX1, limiteX2, acumulada)
class GraficoDiscreto(Grafico):
def desenha(self, limiteX1, limiteX2, acumulada):
self.canvas.delete("all")
try:
variacao = self.modelo.variacao()
except:
if isinstance(self.modelo, Geometrico):
i = 1
while(self.modelo.F(i) < 0.95):
i += 1
if i > 100:
break
variacao = [x for x in range(1, i + 1)]
elif isinstance(self.modelo, Poisson):
i = 0
while(self.modelo.F(i) < 0.95):
i += 1
if i > 100:
break
variacao = [x for x in range(0, i + 1)]
variacao.insert(0, variacao[0] - 1)
variacao.insert(0, variacao[0] - 2)
variacao.append(variacao[-1] + 1)
variacao.append(variacao[-1] + 2)
#retas x e y, respectivamente
reta_y_posicao_x = self.width/float(len(variacao)) * (math.fabs(0 - variacao[0])) + 20
self.canvas.create_line(0, self.height - 20, self.width, self.height - 20)
if 0 in variacao:
self.canvas.create_line(reta_y_posicao_x, 0, reta_y_posicao_x, self.height)
else:
reta_y_posicao_x = 20
#desenha os pontos
for ponto in variacao:
try:
probabilidade = self.funcao(ponto)
x = self.width/float(len(variacao)) * (math.fabs(ponto - variacao[0])) + 20
y = (self.height - 40) * probabilidade
if limiteX1 != None and limiteX2 != None:
if limiteX1 <= ponto <= limiteX2:
self.canvas.create_oval(x - 2, self.height - y - 22, x + 2, self.height - y - 18, fill='red')
self.canvas.create_line(x, self.height - y - 20, x, self.height - 20, fill='red')
else:
self.canvas.create_oval(x - 2, self.height - y - 22, x + 2, self.height - y - 18, fill='black')
self.canvas.create_line(x, self.height - y - 20, x, self.height - 20, fill='black')
else:
self.canvas.create_oval(x - 2, self.height - y - 22, x + 2, self.height - y - 18, fill='black')
self.canvas.create_line(x, self.height - y - 20, x, self.height - 20, fill='black')
except: pass
limite = 11
if limite > len(variacao):
limite = len(variacao)
#desenha metricas na reta x
for i in range(1, limite):
index = i * (len(variacao) / float(limite))
if index != int(index):
index += 1
index = int(index)
x = self.width/float(len(variacao)) * (math.fabs(variacao[index] - variacao[0])) + 20
self.canvas.create_text(x, self.height - 10, text=str(variacao[index]))
#desenha metricas probabilidade
for i in range(1, 11):
y = self.height * i/11.0
self.canvas.create_text(reta_y_posicao_x - 10, self.height - y - 20, text=str(0.1 * i))
class JanelaDiscreta:
def __init__(self, top_level, *parametros):
self.top_level = top_level
self.frame_left = Frame(top_level)
self.frame_left.pack(side=LEFT)
self.frame_right = Frame(top_level)
self.frame_right.pack(side=RIGHT)
self.frame_params = {}
self.entries = {}
for i in range(len(parametros)):
parametro = parametros[i]
self.frame_params[parametro] = Frame(self.frame_left)
self.frame_params[parametro].pack()
Label(self.frame_params[parametro], text=parametro).pack(side=LEFT)
self.entries[parametro] = Entry(self.frame_params[parametro])
self.entries[parametro].pack()
self.frame_botao_ok = Frame(self.frame_left)
self.frame_botao_ok.pack()
self.botao_ok = Button(self.frame_botao_ok, text="Gerar")
self.botao_ok['width'] = 30
self.botao_ok.pack()
self.botao_ok.bind("<Button-1>", self.clica_botao_ok)
self.frame_fp = Frame(self.frame_right)
self.frame_fp.pack(side=LEFT)
self.frame_fda = Frame(self.frame_right)
self.frame_fda.pack(side=LEFT)
Label(self.frame_fp, text="Função de probabilidade:").pack()
self.graficoFd = GraficoDiscreto(self.frame_fp)
Label(self.frame_fda, text="Função de distribuição acumulada:").pack()
self.graficoF = GraficoDiscreto(self.frame_fda)
self.frame_1 = Frame(self.frame_left)
self.frame_2 = Frame(self.frame_1)
self.frame_2.pack()
Label(self.frame_2, text=" P(X = x):").pack(side=LEFT)
self.x = Entry(self.frame_2)
self.x.pack()
self.frame_3 = Frame(self.frame_1)
self.frame_3.pack()
Label(self.frame_3, text=" F(x):").pack(side=LEFT)
self.F = Entry(self.frame_3)
self.F.pack()
self.frame_4 = Frame(self.frame_1)
self.frame_4.pack()
self.botao_calcula = Button(self.frame_4, text="Calcular")
self.botao_calcula['width'] = 30
self.botao_calcula.pack()
self.botao_calcula.bind("<Button-1>", self.clica_botao_calcula)
self.frame_5 = Frame(self.frame_1)
self.frame_5.pack()
self.labelE = Label(self.frame_5, text="E(X): ")
self.labelE.pack()
self.labelVar = Label(self.frame_5, text="Var(X): ")
self.labelVar.pack()
self.labelP = Label(self.frame_5)
self.labelP.pack()
self.labelF = Label(self.frame_5)
self.labelF.pack()
def clica_botao_ok(self, event):
self.graficoFd.set_modelo(self.modelo, self.modelo.fp, None, None, False)
self.graficoF.set_modelo(self.modelo, self.modelo.F, None, None, True)
self.frame_1.pack()
try:
self.labelE.setParent(None)
self.labelVar.setParent(None)
except: pass
self.labelE['text'] = "E(X): %.5f" % self.modelo.e()
self.labelVar['text'] = "Var(X): %.5f" % self.modelo.var()
def clica_botao_calcula(self, event):
try:
x = int(self.x.get())
try:
self.labelP['text'] = "P(X = %d) = %.5f" % (x, self.modelo.fp(x))
self.graficoFd.set_modelo(self.modelo, self.modelo.fp, x, x, False)
except Exception, e:
tkMessageBox.showwarning("Ops...", e[0], parent=self.top_level)
except:
if self.x.get().replace(" ","") != "":
tkMessageBox.showwarning("Ops...", "x deve ser um número inteiro", parent=self.top_level)
self.graficoFd.set_modelo(self.modelo, self.modelo.fp, None, None, False)
self.labelP['text'] = ""
try:
x = float(self.F.get())
self.labelF['text'] = "F(%.2f) = %.5f" % (x, self.modelo.F(x))
self.graficoF.set_modelo(self.modelo, self.modelo.F, 0, x, True)
except:
self.graficoF.set_modelo(self.modelo, self.modelo.F, None, None, True)
self.labelF['text'] = ""
class JanelaBinomial(JanelaDiscreta):
def __init__(self, top_level):
JanelaDiscreta.__init__(self, top_level, "Parâmetro n", "Parâmetro p")
def clica_botao_ok(self, event):
n = self.entries["Parâmetro n"].get()
p = self.entries["Parâmetro p"].get()
try:
self.modelo = Binomial(n, p)
JanelaDiscreta.clica_botao_ok(self, event)
except Exception, e:
tkMessageBox.showwarning("Ops...", e[0], parent=self.top_level)
class JanelaHipergeometrico(JanelaDiscreta):
def __init__(self, top_level):
JanelaDiscreta.__init__(self, top_level, "Parâmetro N", "Parâmetro r", "Parâmetro n")
def clica_botao_ok(self, event):
N = self.entries["Parâmetro N"].get()
r = self.entries["Parâmetro r"].get()
n = self.entries["Parâmetro n"].get()
try:
self.modelo = Hipergeometrico(N, r, n)
JanelaDiscreta.clica_botao_ok(self, event)
except Exception, e:
tkMessageBox.showwarning("Ops...", e[0], parent=self.top_level)
class JanelaGeometrico(JanelaDiscreta):
def __init__(self, top_level):
JanelaDiscreta.__init__(self, top_level, "Parâmetro p")
def clica_botao_ok(self, event):
p = self.entries["Parâmetro p"].get()
try:
self.modelo = Geometrico(p)
JanelaDiscreta.clica_botao_ok(self, event)
except Exception, e:
tkMessageBox.showwarning("Ops...", e[0], parent=self.top_level)
class JanelaPoisson(JanelaDiscreta):
def __init__(self, top_level):
JanelaDiscreta.__init__(self, top_level, "Parâmetro gama")
def clica_botao_ok(self, event):
alfa = self.entries["Parâmetro gama"].get()
try:
self.modelo = Poisson(alfa)
JanelaDiscreta.clica_botao_ok(self, event)
except Exception, e:
tkMessageBox.showwarning("Ops...", e[0], parent=self.top_level)
class GraficoContinuo(Grafico):
def desenha(self, limiteX1, limiteX2, acumulada):
self.canvas.delete("all")
if isinstance(self.modelo, Uniforme):
a = self.modelo.a
b = self.modelo.b + 1
elif isinstance(self.modelo, Exponencial):
a = -1
b = 0
while self.modelo.F(b) < 0.995:
b += 1
if b > 100:
break
elif isinstance(self.modelo, Normal):
a = 0
while self.modelo.F(a) > 0:
a -= 1
b = 0
while self.modelo.F(b) < 1:
b += 1
l = math.fabs(b-a)/1000.0
tamanho = math.fabs(b-a)
variacao = [x*l+a for x in range(0, 1000)]
#retas x e y, respectivamente
reta_y_posicao_x = self.width/float(tamanho) * (math.fabs(0 - variacao[0])) + 20
self.canvas.create_line(0, self.height - 20, self.width, self.height - 20)
if variacao[0] <= 0 <= variacao[-1]:
self.canvas.create_line(reta_y_posicao_x, 0, reta_y_posicao_x, self.height)
else:
reta_y_posicao_x = 20
#desenha os pontos
for indice, ponto in enumerate(variacao):
try:
if acumulada:
probabilidade = self.funcao(ponto)
else:
probabilidade = self.funcao(variacao[indice], variacao[indice+1]) * 100
x = self.width/float(tamanho) * (math.fabs(ponto - variacao[0])) + 20
y = (self.height - 40) * probabilidade
if limiteX1 != None and limiteX2 != None:
if limiteX1 <= ponto <= limiteX2:
self.canvas.create_line(x, self.height - y - 20, x + 1, self.height - y - 20, fill='red')
self.canvas.create_line(x, self.height - y - 20, x, self.height - 20, fill='red')
else:
self.canvas.create_line(x, self.height - y - 20, x + 1, self.height - y - 20, fill='black')
self.canvas.create_line(x, self.height - y - 20, x, self.height - 20, fill='black')
else:
self.canvas.create_line(x, self.height - y - 20, x + 1, self.height - y - 20, fill='black')
self.canvas.create_line(x, self.height - y - 20, x, self.height - 20, fill='black')
except: pass
limite = 11
#desenha metricas na reta x
for i in range(1, limite):
index = i * len(variacao) / float(limite)
index = int(index)
tamanhoInicial = math.fabs(variacao[index] - variacao[0])
tamanhoTotal = math.fabs(variacao[-1] - variacao[0])
factor = tamanhoInicial / float(tamanhoTotal)
x = self.width * factor + 20
self.canvas.create_text(x, self.height - 10, text=str(variacao[index]))
#desenha metricas probabilidade
for i in range(1, 11):
y = self.height * i/11.0
self.canvas.create_text(reta_y_posicao_x - 10, self.height - y - 20, text=str(0.1 * i))
def desenha22(self, limiteX1, limiteX2, acumulada):
self.canvas.delete("all")
if isinstance(self.modelo, Uniforme):
variacao = [x for x in range(int(self.modelo.a * 100), int((self.modelo.b + 1) * 100 ))]
elif isinstance(self.modelo, Exponencial):
variacao = [x for x in range(0, 10 * 100)]
elif isinstance(self.modelo, Normal):
inflexao = 3.5 * self.modelo.o2 + self.modelo.u
inicial = (self.modelo.u - inflexao) * 100
final = (self.modelo.u + inflexao) * 100
variacao = [x for x in range(int(inicial), int(final))]
#retas x e y, respectivamente
reta_y_posicao_x = (self.width - 20)/float(len(variacao)) * (math.fabs(0 - variacao[0])) + 40
self.canvas.create_line(0, self.height - 20, self.width, self.height - 20)
self.canvas.create_line(reta_y_posicao_x, 0, reta_y_posicao_x, self.height)
#desenha os pontos
for ponto in variacao:
if acumulada:
probabilidade = self.funcao(ponto/100.0)
else:
probabilidade = self.funcao(ponto/100.0, ponto/100.0 + 1)
x = (self.width+40)/float(len(variacao)) * (math.fabs(ponto - variacao[0])) + 40
y = (self.height - 30) * probabilidade
if limiteX1 != None and limiteX2 != None:
if limiteX1 <= ponto/100.0 + 0.5 <= limiteX2:
self.canvas.create_line(x, self.height - y - 20, x + 1, self.height - 20, fill='red')
else:
self.canvas.create_line(x, self.height - y - 20, x + 1, self.height - 20, fill='black')
else:
self.canvas.create_line(x, self.height - y - 20, x + 1, self.height - 20, fill='black')
limite = 11
if limite > len(variacao):
limite = len(variacao)
#desenha metricas na reta x
for i in range(1, limite):
index = i * (len(variacao) / float(limite))
if index != int(index):
index += 1
index = int(index)
x = (self.width - 20)/float(len(variacao)) * (math.fabs(variacao[index] - variacao[0])) + 40
self.canvas.create_text(x, self.height - 10, text="%.2f" % (variacao[index]/100.0))
#desenha metricas probabilidade
for i in range(1, 11):
y = self.height / 11.0 * i
self.canvas.create_text(reta_y_posicao_x - 20, self.height - y - 10, text=str(0.1 * i))
class JanelaContinua:
def __init__(self, top_level, *parametros):
self.top_level = top_level
self.frame_left = Frame(top_level)
self.frame_left.pack(side=LEFT)
self.frame_right = Frame(top_level)
self.frame_right.pack(side=RIGHT)
self.frame_params = {}
self.entries = {}
for i in range(len(parametros)):
parametro = parametros[i]
self.frame_params[parametro] = Frame(self.frame_left)
self.frame_params[parametro].pack()
Label(self.frame_params[parametro], text=" " +parametro).pack(side=LEFT)
self.entries[parametro] = Entry(self.frame_params[parametro])
self.entries[parametro].pack()
self.frame_botao_ok = Frame(self.frame_left)
self.frame_botao_ok.pack()
self.botao_ok = Button(self.frame_botao_ok, text="Gerar")
self.botao_ok['width'] = 35
self.botao_ok.pack()
self.botao_ok.bind("<Button-1>", self.clica_botao_ok)
self.frame_fp = Frame(self.frame_right)
self.frame_fp.pack(side=LEFT)
self.frame_fda = Frame(self.frame_right)
self.frame_fda.pack(side=LEFT)
Label(self.frame_fp, text="Função distribuição de probabilidade:").pack()
self.graficoFd = GraficoContinuo(self.frame_fp)
Label(self.frame_fda, text="Função de distribuição acumulada:").pack()
self.graficoF = GraficoContinuo(self.frame_fda)
self.frame_1 = Frame(self.frame_left)
self.frame_2 = Frame(self.frame_1)
self.frame_2.pack()
Label(self.frame_2, text="P(a <= x <= b):").pack(side=LEFT)
self.x1 = Entry(self.frame_2)
self.x1.pack()
self.x2 = Entry(self.frame_2)
self.x2.pack(side=RIGHT)
self.frame_3 = Frame(self.frame_1)
self.frame_3.pack()
Label(self.frame_3, text=" F(x):").pack(side=LEFT)
self.F = Entry(self.frame_3)
self.F.pack()
self.frame_4 = Frame(self.frame_1)
self.frame_4.pack()
self.botao_calcula = Button(self.frame_4, text="Calcular")
self.botao_calcula['width'] = 35
self.botao_calcula.pack()
self.botao_calcula.bind("<Button-1>", self.clica_botao_calcula)
self.frame_5 = Frame(self.frame_1)
self.frame_5.pack()
self.labelE = Label(self.frame_5, text="E(X): ")
self.labelE.pack()
self.labelVar = Label(self.frame_5, text="Var(X): ")
self.labelVar.pack()
self.labelP = Label(self.frame_5)
self.labelP.pack()
self.labelF = Label(self.frame_5)
self.labelF.pack()
def clica_botao_ok(self, event):
self.graficoFd.set_modelo(self.modelo, self.modelo.fdp, None, None, False)
self.graficoF.set_modelo(self.modelo, self.modelo.F, None, None, True)
self.frame_1.pack()
try:
self.labelE.setParent(None)
self.labelVar.setParent(None)
except: pass
self.labelE['text'] = "E(X): %.5f" % self.modelo.e()
self.labelVar['text'] = "Var(X): %.5f" % self.modelo.var()
def clica_botao_calcula(self, event):
try:
x = float(self.x1.get())
y = float(self.x2.get())
try:
self.labelP['text'] = "P(%.2f <= X <= %.2f) = %.5f" % (x, y, self.modelo.fdp(x, y))
self.graficoFd.set_modelo(self.modelo, self.modelo.fdp, x, y, False)
except Exception, e:
tkMessageBox.showwarning("Ops...", e[0], parent=self.top_level)
except:
if self.x1.get().replace(" ","") != "" or self.x2.get().replace(" ","") != "":
tkMessageBox.showwarning("Ops...", "x deve ser um número inteiro", parent=self.top_level)
self.graficoFd.set_modelo(self.modelo, self.modelo.fdp, None, None, False)
self.labelP['text'] = ""
try:
x = float(self.F.get())
self.labelF['text'] = "F(%.2f) = %.5f" % (x, self.modelo.F(x))
self.graficoF.set_modelo(self.modelo, self.modelo.F, -9999999999999, x, True)
except:
self.graficoF.set_modelo(self.modelo, self.modelo.F, None, None, True)
self.labelF['text'] = ""
class JanelaUniforme(JanelaContinua):
def __init__(self, top_level):
JanelaContinua.__init__(self, top_level, "Parâmetro a", "Parâmetro b")
def clica_botao_ok(self, event):
a = self.entries["Parâmetro a"].get()
b = self.entries["Parâmetro b"].get()
try:
self.modelo = Uniforme(a, b)
JanelaContinua.clica_botao_ok(self, event)
except Exception, e:
tkMessageBox.showwarning("Ops...", e[0], parent=self.top_level)
class JanelaExponencial(JanelaContinua):
def __init__(self, top_level):
JanelaContinua.__init__(self, top_level, "Parâmetro alfa")
def clica_botao_ok(self, event):
a = self.entries["Parâmetro alfa"].get()
try:
self.modelo = Exponencial(a)
JanelaContinua.clica_botao_ok(self, event)
except Exception, e:
tkMessageBox.showwarning("Ops...", e[0], parent=self.top_level)
class JanelaNormal(JanelaContinua):
def __init__(self, top_level):
JanelaContinua.__init__(self, top_level, "Média", "Variância")
def clica_botao_ok(self, event):
u = self.entries["Média"].get()
o2 = self.entries["Variância"].get()
try:
self.modelo = Normal(u, o2)
JanelaContinua.clica_botao_ok(self, event)
except Exception, e:
tkMessageBox.showwarning("Ops...", e[0], parent=self.top_level)
raiz = Tk()
raiz.title("Mesquita 1.0")
JanelaPrincipal(raiz)
raiz.mainloop()
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