def modelling_cycle():
#--------------- initialization -------------------#
# initial_data = test_data
initial_data = test_data_one
# fig_init = plt.figure()
# fig_init.canvas.manager.set_window_title('Initial data')
# plt.plot(initial_data, color='g')
wavelet_families = pywt.families()
print 'Wavelet families:', ', '.join(wavelet_families)
wavelet_family = wavelet_families[4]
selected_wavelet = pywt.wavelist(wavelet_family)[0]
wavelet = pywt.Wavelet(selected_wavelet)
print 'Selected wavelet:', selected_wavelet
max_level = pywt.swt_max_level(len(initial_data))
# decomposition_level = max_level / 2
decomposition_level = 3
print 'Max level:', max_level, '\t Decomposition level:', decomposition_level
#--------------- decomposition -------------------#
w_initial_coefficients = pywt.swt(initial_data, wavelet, level=decomposition_level)
w_selected_coefficiets = select_levels_from_swt(w_initial_coefficients)
w_node_coefficients = select_node_levels_from_swt(w_initial_coefficients) #something terribly wrong here, yet the rest works!
#------------------ threshold --------------------#
threshold = measure_threshold(w_initial_coefficients)
w_threshold_coeff = w_initial_coefficients[:]
apply_threshold(w_threshold_coeff)
plot_initial_updated(w_initial_coefficients, w_threshold_coeff)
# plt.figure()
# for coeff in w_selected_coefficiets:
# plt.plot(coeff)
# plt.figure()
# for coeff in w_node_coefficients:
# plt.plot(coeff)
# plt.show()
#--------------- modification -------------------#
r = R()
w_new_coefficients = [0] * len(w_selected_coefficiets)
for index in range(0, len(w_selected_coefficiets)):
r.i_data = w_selected_coefficiets[index]
r('hw <- HoltWinters( ts(i_data, frequency = 12), gamma = TRUE )')
r('pred <- predict(hw, 50, prediction.interval = TRUE)')
w_new_coefficients[index] = append(w_selected_coefficiets[index], r.pred[:,0])
index += 1
w_new_node_coefficients = [0] * len(w_node_coefficients)
for index in range(0, len(w_node_coefficients)):
r.i_data = w_node_coefficients[index]
r('hw <- HoltWinters( ts(i_data, frequency = 12), gamma = TRUE )')
r('pred <- predict(hw, 50, prediction.interval = TRUE)')
w_new_node_coefficients[index] = append(w_node_coefficients[index], r.pred[:,0])
index += 1
#----
# plt.figure()
# for coeff in w_new_coefficients:
# plt.plot(coeff)
# plt.figure()
# for coeff in w_new_node_coefficients:
# plt.plot(coeff)
# plt.show()
#--------------- reconstruction -------------------#
# wInitialwithUpdated_Nodes = update_node_levels_swt(w_initial_coefficients, w_new_node_coefficients)
# plot_initial_updated(w_initial_coefficients, w_new_node_coefficients, True)
# plot_initial_updated(w_initial_coefficients, wInitialwithUpdated_Nodes) (!)
# plt.figure()
# for dyad in wInitialwithUpdated_Nodes:
# plt.plot(dyad[0])
# plt.plot(dyad[1])
#
# plt.figure()
# for dyad in w_initial_coefficients:
# plt.plot(dyad[0])
# plt.plot(dyad[1])
#
# plt.show()
# w_updated_coefficients = update_selected_levels_swt(w_initial_coefficients, w_selected_coefficiets)
# w_updated_coefficients = update_selected_levels_swt(w_initial_coefficients, w_new_coefficients)
#----
# w_updated_coefficients = update_swt(w_initial_coefficients, w_selected_coefficiets, w_node_coefficients)
w_updated_coefficients_nodes = update_swt(w_initial_coefficients, w_new_coefficients, w_new_node_coefficients)
w_updated_coefficients = update_selected_levels_swt(w_initial_coefficients, w_new_coefficients)
plot_initial_updated(w_initial_coefficients, w_updated_coefficients_nodes)
plot_initial_updated(w_initial_coefficients, w_updated_coefficients)
reconstructed_Stationary_nodes = iswt(w_updated_coefficients_nodes, selected_wavelet)
reconstructed_Stationary = iswt(w_updated_coefficients, selected_wavelet)
fig_sta_r = plt.figure()
fig_sta_r.canvas.manager.set_window_title('SWT reconstruction')
plt.plot(reconstructed_Stationary)
fig_sta_r_n = plt.figure()
fig_sta_r_n.canvas.manager.set_window_title('SWT reconstruction (nodes)')
plt.plot(reconstructed_Stationary_nodes)
plt.show()
def __modelling_cycle():
initial_data = test_data
fig_init = plt.figure()
fig_init.canvas.manager.set_window_title('Initial data')
plt.plot(initial_data, color='g')
#--------------- wavelet decomposition -------------------#
decomposition_level = 2
wavelet_families = pywt.families()
wavelet_family = wavelet_families[0]
selected_wavelet = pywt.wavelist(wavelet_family)[0]
wavelet = pywt.Wavelet(selected_wavelet) #NB: taking first variant of wavelet (e.g. haar1)
# discrete (non stationary) multilevel decomposition
wCoefficients_Discrete = pywt.wavedec(initial_data, wavelet, level=decomposition_level) #NB: output length also depends on wavelet type
# stationary (Algorithme à trous ~ does not decimate coefficients at every transformation level) multilevel decomposition
wCoefficients_Stationary = pywt.swt(initial_data, wavelet, level=decomposition_level)
fig_discrete = plt.figure(); n_coeff = 1
fig_discrete.canvas.manager.set_window_title('Discrete decomposition [ ' + str(decomposition_level) + ' level(s) ]')
for coeff in wCoefficients_Discrete:
# print coeff
fig_discrete.add_subplot(len(wCoefficients_Discrete), 1, n_coeff); n_coeff += 1
plt.plot(coeff)
fig_stationary = plt.figure(); n_coeff = 1; rows = 0
fig_stationary.canvas.manager.set_window_title('Stationary decomposition [ ' + str(decomposition_level) + ' level(s) ]')
for item in wCoefficients_Stationary: rows += len(item)
i = 0; j = 0 # tree coeffs
for coeff in wCoefficients_Stationary:
for subcoeff in coeff:
print i, j
# print subcoeff
fig_stationary.add_subplot(rows, 1, n_coeff); n_coeff += 1
plt.plot(subcoeff)
j += 1
i += 1
plt.show()
fig_stat_sum = plt.figure(); n_coeff = 1
fig_stat_sum.canvas.manager.set_window_title('SWT sum by levels [ ' + str(decomposition_level) + ' level(s) ]')
for coeff in wCoefficients_Stationary:
sum = coeff[0] + coeff[1]
fig_stat_sum.add_subplot(len(wCoefficients_Discrete), 1, n_coeff); n_coeff += 1
plt.plot(sum)
# plt.show()
#------------------ modelling by level -------------------#
r = R()
r.i_data = initial_data # or r['i_data'] = initial_data
### Holt-Winters ###
# non-seasonal Holt-Winters
print r('hw <- HoltWinters( i_data, gamma = FALSE )')
# seasonal Holt-Winters
r.freq = 4 #series sampling (month, days, years, etc)
# print r( 'hw <- HoltWinters( ts ( %s, frequency = %s ) )' % ( Str4R(r.i_data), Str4R(r.freq) ) )
# print r( 'hw <- HoltWinters( ts ( %s, frequency = %s, start = c(1,1) ) )' % ( Str4R(r.i_data), Str4R(r.freq) ) )
# resulting Square Estimation Sum
print r.hw['SSE']
# bruteforce frequency search
# print 'test ahead:'
# sse_dict = {}
# for i in xrange(2, 50):
# r.freq = i
## r( 'hw <- HoltWinters( ts ( %s, frequency = %s, start = c(1,1) ) )' % ( Str4R(r.i_data), Str4R(r.freq) ) )
# r( 'hw <- HoltWinters( ts ( %s, frequency = %s ) )' % ( Str4R(r.i_data), Str4R(r.freq) ) )
# print r.hw['SSE']
# sse_dict[r.hw['SSE']] = i; i += 1
# print 'Resulting:'
# m = min(sse_dict.keys())
# print sse_dict[m], m
fig = plt.figure()
fig.canvas.manager.set_window_title('Holt-winters model')
ax = fig.add_subplot(111)
# ax.plot(r.hw['fitted'][:,0]) # the colums are: xhat, level, trend
# plt.show()
# forecast length
r.steps_ahead = 50
# print r('pred <- predict(%s, %s, prediction.interval = TRUE)' % ( Str4R(r.hw), Str4R(r.steps_ahead)) )
# print r( 'pred <- predict(hw, %s, prediction.interval = TRUE)', Str4R(r.steps_ahead) )
print r( 'pred <- predict(hw, 50, prediction.interval = TRUE)')
# plt.plot(r.pred)
ax.plot(initial_data)
ax.plot(append(r.hw['fitted'][:,0], r.pred[:,0])) # concatenating reconstructed model and resulting forecast
# plt.show()
#------------------ reconstruction -------------------#
# multilevel idwt
reconstructed_Discrete = pywt.waverec(wCoefficients_Discrete, selected_wavelet)
fig_dis_r = plt.figure()
fig_dis_r.canvas.manager.set_window_title('DWT reconstruction')
plt.plot(reconstructed_Discrete)
# plt.show()
# multilevel stationary
reconstructed_Stationary = iswt(wCoefficients_Stationary, selected_wavelet)
fig_sta_r = plt.figure()
fig_sta_r.canvas.manager.set_window_title('SWT reconstruction')
plt.plot(reconstructed_Stationary)
plt.show()
print 'end'
