%matplotlib inline
import scipy.stats as stats
from IPython.core.pylabtools import figsize
import numpy as np
figsize(12.5, 4)

import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

jet = plt.cm.jet
fig = plt.figure()
x = y = np.linspace(0, 5, 100)
X, Y = np.meshgrid(x, y)

plt.subplot(121)
uni_x = stats.uniform.pdf(x, loc=0, scale=5)
uni_y = stats.uniform.pdf(y, loc=0, scale=5)
M = np.dot(uni_x[:, None], uni_y[None, :])
im = plt.imshow(M, interpolation='none', origin='lower',
                cmap=jet, vmax=1, vmin=-.15, extent=(0, 5, 0, 5))

plt.xlim(0, 5)
plt.ylim(0, 5)
plt.title("Landscape formed by Uniform priors.")

ax = fig.add_subplot(122, projection='3d')
ax.plot_surface(X, Y, M, cmap=plt.cm.jet, vmax=1, vmin=-.15)
ax.view_init(azim=390)
plt.title("Uniform prior landscape; alternate view");

figsize(12.5, 5)
fig = plt.figure()
plt.subplot(121)

exp_x = stats.expon.pdf(x, scale=3)
exp_y = stats.expon.pdf(x, scale=10)
M = np.dot(exp_x[:, None], exp_y[None, :])
CS = plt.contour(X, Y, M)
im = plt.imshow(M, interpolation='none', origin='lower',
                cmap=jet, extent=(0, 5, 0, 5))
#plt.xlabel("prior on $p_1$")
#plt.ylabel("prior on $p_2$")
plt.title("$Exp(3), Exp(10)$ prior landscape")

ax = fig.add_subplot(122, projection='3d')
ax.plot_surface(X, Y, M, cmap=jet)
ax.view_init(azim=390)
plt.title("$Exp(3), Exp(10)$ prior landscape; \nalternate view");

# create the observed data

# sample size of data we observe, trying varying this (keep it less than 100 ;)
N = 1

# the true parameters, but of course we do not see these values...
lambda_1_true = 1
lambda_2_true = 3

#...we see the data generated, dependent on the above two values.
data = np.concatenate([
    stats.poisson.rvs(lambda_1_true, size=(N, 1)),
    stats.poisson.rvs(lambda_2_true, size=(N, 1))
], axis=1)
print("observed (2-dimensional,sample size = %d):" % N, data)

# plotting details.
x = y = np.linspace(.01, 5, 100)
likelihood_x = np.array([stats.poisson.pmf(data[:, 0], _x)
                        for _x in x]).prod(axis=1)
likelihood_y = np.array([stats.poisson.pmf(data[:, 1], _y)
                        for _y in y]).prod(axis=1)
L = np.dot(likelihood_x[:, None], likelihood_y[None, :])
observed (2-dimensional,sample size = 1): [[0 2]]
In [4]:
figsize(12.5, 12)
# matplotlib heavy lifting below, beware!
plt.subplot(221)
uni_x = stats.uniform.pdf(x, loc=0, scale=5)
uni_y = stats.uniform.pdf(x, loc=0, scale=5)
M = np.dot(uni_x[:, None], uni_y[None, :])
im = plt.imshow(M, interpolation='none', origin='lower',
                cmap=jet, vmax=1, vmin=-.15, extent=(0, 5, 0, 5))
plt.scatter(lambda_2_true, lambda_1_true, c="k", s=50, edgecolor="none")
plt.xlim(0, 5)
plt.ylim(0, 5)
plt.title("Landscape formed by Uniform priors on $p_1, p_2$.")

plt.subplot(223)
plt.contour(x, y, M * L)
im = plt.imshow(M * L, interpolation='none', origin='lower',
                cmap=jet, extent=(0, 5, 0, 5))
plt.title("Landscape warped by %d data observation;\n Uniform priors on $p_1, p_2$." % N)
plt.scatter(lambda_2_true, lambda_1_true, c="k", s=50, edgecolor="none")
plt.xlim(0, 5)
plt.ylim(0, 5)

plt.subplot(222)
exp_x = stats.expon.pdf(x, loc=0, scale=3)
exp_y = stats.expon.pdf(x, loc=0, scale=10)
M = np.dot(exp_x[:, None], exp_y[None, :])

plt.contour(x, y, M)
im = plt.imshow(M, interpolation='none', origin='lower',
                cmap=jet, extent=(0, 5, 0, 5))
plt.scatter(lambda_2_true, lambda_1_true, c="k", s=50, edgecolor="none")
plt.xlim(0, 5)
plt.ylim(0, 5)
plt.title("Landscape formed by Exponential priors on $p_1, p_2$.")

plt.subplot(224)
# This is the likelihood times prior, that results in the posterior.
plt.contour(x, y, M * L)
im = plt.imshow(M * L, interpolation='none', origin='lower',
                cmap=jet, extent=(0, 5, 0, 5))

plt.scatter(lambda_2_true, lambda_1_true, c="k", s=50, edgecolor="none")
plt.title("Landscape warped by %d data observation;\n Exponential priors on \
$p_1, p_2$." % N)
plt.xlim(0, 5)
plt.ylim(0, 5);

from pandas import read_csv
from pandas import datetime
from matplotlib import pyplot as plt
def parser(x):
    return datetime.strptime('190'+x,"%Y-%m")
series = read_csv('sales-of-shampoo-over-a-three-ye.csv',
                 header=0,parse_dates=[0],index_col=0,
                  squeeze=True, date_parser=parser)
print(series.head())
series.plot()
plt.show()

# split data into train and test
X = series.values
train, test = X[0:-12], X[-12:]

from pandas import read_csv
from pandas import datetime
from sklearn.metrics import mean_squared_error
from math import sqrt
from matplotlib import pyplot
# load dataset
def parser(x):
  return datetime.strptime('190'+x, '%Y-%m')
series = read_csv('sales-of-shampoo-over-a-three-ye.csv',
                  header=0, parse_dates=[0], index_col=0,
                  squeeze=True, date_parser=parser)
# split data into train and test
X = series.values
train, test = X[0:-12], X[-12:]
# walk-forward validation
history = [x for x in train]
predictions = list()
for i in range(len(test)):
  # make prediction
  predictions.append(history[-1])
  # observation
  history.append(test[i])
# report performance
rmse = sqrt(mean_squared_error(test, predictions))
print('RMSE: %.3f' % rmse)
# line plot of observed vs predicted
pyplot.plot(test)
pyplot.plot(predictions)
pyplot.show()

from pandas import read_csv
from pandas import datetime
from pandas import DataFrame
from pandas import concat

# frame a sequence as a supervised learning problem
def timeseries_to_supervised(data, lag=1):
  df = DataFrame(data)
  columns = [df.shift(i) for i in range(1, lag+1)]
  columns.append(df)
  df = concat(columns, axis=1)
  df.fillna(0, inplace=True)
  return df

# load dataset
def parser(x):
  return datetime.strptime('190'+x, '%Y-%m')
series = read_csv('sales-of-shampoo-over-a-three-ye.csv', header=0, parse_dates=[0], index_col=0, squeeze=True, date_parser=parser)
# transform to supervised learning
X = series.values
supervised = timeseries_to_supervised(X, 1)
print(supervised)

from pandas import read_csv
from pandas import datetime
from pandas import Series

# create a differenced series
def difference(dataset, interval=1):
  diff = list()
  for i in range(interval, len(dataset)):
      value = dataset[i] - dataset[i - interval]
      diff.append(value)
  return Series(diff)

# invert differenced value
def inverse_difference(history, yhat, interval=1):
  return yhat + history[-interval]

# load dataset
def parser(x):
  return datetime.strptime('190'+x, '%Y-%m')
series = read_csv('sales-of-shampoo-over-a-three-ye.csv', header=0, parse_dates=[0], index_col=0, squeeze=True, date_parser=parser)
print(series.head())
# transform to be stationary
differenced = difference(series, 1)
print(differenced.head())
# invert transform
inverted = list()
for i in range(len(differenced)):
  value = inverse_difference(series, differenced[i], len(series)-i)
  inverted.append(value)
inverted = Series(inverted)
print(inverted.head())
differenced.plot()
plt.show()

from pandas import read_csv
from pandas import datetime
from pandas import Series
from sklearn.preprocessing import MinMaxScaler
# load dataset
def parser(x):
  return datetime.strptime('190'+x, '%Y-%m')
series = read_csv('sales-of-shampoo-over-a-three-ye.csv', header=0, parse_dates=[0], index_col=0, squeeze=True, date_parser=parser)
print(series.head())
# transform scale
X = series.values
X = X.reshape(len(X), 1)
scaler = MinMaxScaler(feature_range=(-1, 1))
scaler = scaler.fit(X)
scaled_X = scaler.transform(X)
scaled_series = Series(scaled_X[:, 0])
print(scaled_series.head())
# invert transform
inverted_X = scaler.inverse_transform(scaled_X)
inverted_series = Series(inverted_X[:, 0])
print(inverted_series.head())

from pandas import DataFrame
from pandas import Series
from pandas import concat
from pandas import read_csv
from pandas import datetime
from sklearn.metrics import mean_squared_error
from sklearn.preprocessing import MinMaxScaler
from keras.models import Sequential
from keras.layers import Dense
from keras.layers import LSTM
from math import sqrt
from matplotlib import pyplot
import numpy

# date-time parsing function for loading the dataset
def parser(x):
  return datetime.strptime('190'+x, '%Y-%m')

# frame a sequence as a supervised learning problem
def timeseries_to_supervised(data, lag=1):
  df = DataFrame(data)
  columns = [df.shift(i) for i in range(1, lag+1)]
  columns.append(df)
  df = concat(columns, axis=1)
  df.fillna(0, inplace=True)
  return df

# create a differenced series
def difference(dataset, interval=1):
  diff = list()
  for i in range(interval, len(dataset)):
      value = dataset[i] - dataset[i - interval]
      diff.append(value)
  return Series(diff)

# invert differenced value
def inverse_difference(history, yhat, interval=1):
  return yhat + history[-interval]

# scale train and test data to [-1, 1]
def scale(train, test):
  # fit scaler
  scaler = MinMaxScaler(feature_range=(-1, 1))
  scaler = scaler.fit(train)
  # transform train
  train = train.reshape(train.shape[0], train.shape[1])
  train_scaled = scaler.transform(train)
  # transform test
  test = test.reshape(test.shape[0], test.shape[1])
  test_scaled = scaler.transform(test)
  return scaler, train_scaled, test_scaled

# inverse scaling for a forecasted value
def invert_scale(scaler, X, value):
  new_row = [x for x in X] + [value]
  array = numpy.array(new_row)
  array = array.reshape(1, len(array))
  inverted = scaler.inverse_transform(array)
  return inverted[0, -1]

# fit an LSTM network to training data
def fit_lstm(train, batch_size, nb_epoch, neurons):
  X, y = train[:, 0:-1], train[:, -1]
  X = X.reshape(X.shape[0], 1, X.shape[1])
  model = Sequential()
  model.add(LSTM(neurons, batch_input_shape=(batch_size, X.shape[1], X.shape[2]), stateful=True))
  model.add(Dense(1))
  model.compile(loss='mean_squared_error', optimizer='adam')
  for i in range(nb_epoch):
      model.fit(X, y, epochs=1, batch_size=batch_size, verbose=0, shuffle=False)
      model.reset_states()
  return model

# make a one-step forecast
def forecast_lstm(model, batch_size, X):
  X = X.reshape(1, 1, len(X))
  yhat = model.predict(X, batch_size=batch_size)
  return yhat[0,0]

# load dataset
series = read_csv('sales-of-shampoo-over-a-three-ye.csv', header=0, parse_dates=[0], index_col=0, squeeze=True, date_parser=parser)

# transform data to be stationary
raw_values = series.values
diff_values = difference(raw_values, 1)

# transform data to be supervised learning
supervised = timeseries_to_supervised(diff_values, 1)
supervised_values = supervised.values

# split data into train and test-sets
train, test = supervised_values[0:-12], supervised_values[-12:]

# transform the scale of the data
scaler, train_scaled, test_scaled = scale(train, test)

# fit the model
lstm_model = fit_lstm(train_scaled, 1, 3000, 4)
# forecast the entire training dataset to build up state for forecasting
train_reshaped = train_scaled[:, 0].reshape(len(train_scaled), 1, 1)
lstm_model.predict(train_reshaped, batch_size=1)

# walk-forward validation on the test data
predictions = list()
for i in range(len(test_scaled)):
  # make one-step forecast
  X, y = test_scaled[i, 0:-1], test_scaled[i, -1]
  yhat = forecast_lstm(lstm_model, 1, X)
  # invert scaling
  yhat = invert_scale(scaler, X, yhat)
  # invert differencing
  yhat = inverse_difference(raw_values, yhat, len(test_scaled)+1-i)
  # store forecast
  predictions.append(yhat)
  expected = raw_values[len(train) + i + 1]
  print('Month=%d, Predicted=%f, Expected=%f' % (i+1, yhat, expected))

#report performance
rmse = sqrt(mean_squared_error(raw_values[-12:], predictions))
print('Test RMSE: %.3f' % rmse)
# line plot of observed vs predicted
pyplot.plot(raw_values[-12:])
pyplot.plot(predictions)
pyplot.show()

import numpy as np
import matplotlib.pyplot as plt


class GameOfLife(object):

  def __init__(self, cells_shape):
    """
    Parameters
    ----------
    cells_shape : 一个元组，表示画布的大小。

    Examples
    --------
    建立一个高20，宽30的画布
    game = GameOfLife((20, 30))
    
    """

    # 矩阵的四周不参与运算
    self.cells = np.zeros(cells_shape)

    real_width = cells_shape[0] - 2
    real_height = cells_shape[1] - 2

    self.cells[1:-1, 1:-1] = np.random.randint(2, size=(real_width, real_height))
    self.timer = 0
    self.mask = np.ones(9)
    self.mask[4] = 0

  def update_state(self):
    """更新一次状态"""
    buf = np.zeros(self.cells.shape)
    cells = self.cells
    for i in range(1, cells.shape[0] - 1):
      for j in range(1, cells.shape[0] - 1):
        # 计算该细胞周围的存活细胞数
        neighbor = cells[i-1:i+2, j-1:j+2].reshape((-1, ))
        neighbor_num = np.convolve(self.mask, neighbor, 'valid')[0]
        if neighbor_num == 3:
          buf[i, j] = 1
        elif neighbor_num == 2:
          buf[i, j] = cells[i, j]
        else:
          buf[i, j] = 0
    self.cells = buf
    self.timer += 1

  def plot_state(self):
    """画出当前的状态"""
    plt.title('Iter :{}'.format(self.timer))
    plt.imshow(self.cells)
    plt.show()

  def update_and_plot(self, n_iter):
    """更新状态并画图
    Parameters
    ----------
    n_iter : 更新的轮数
    """
    plt.ion()
    for _ in range(n_iter):
      plt.title('Iter :{}'.format(self.timer))
      plt.imshow(self.cells)
      self.update_state()
      plt.pause(0.2)
    plt.ioff()


if __name__ == '__main__':
  game = GameOfLife(cells_shape=(60, 60))
  game.update_and_plot(200)