def PerformanceProfile(A,
th_max,
file_name,
alg_legend,
n_intervals=100,
markevery=1):
"""
Modified from https://github.com/StevenElsworth/PerformanceProfiles
"""
m, n = A.shape
minA = np.min(A, 1)
fig, ax = myfigure(nrows=1, ncols=1, fig_ratio=0.71, fig_scale=1.6)
# Use definition at some points theta
n_intervals = 100
p_step = 1
# increase to make plot look smoother.
theta = np.linspace(1, th_max, num=n_intervals)
T = np.zeros([n_intervals, 1])
linestyle = ['-', '--', '-.', ':']
marker = ['o', '^', '*', 'x', 'v', '<', 'h', 'p']
for j in np.arange(0, n):
for k in np.arange(0, n_intervals):
T[k] = np.sum(A[:, j] <= theta[k] * minA) / m
plt.plot(theta,
T,
linestyle=linestyle[j % 4],
marker=marker[j % 8],
markevery=markevery)
plt.xlim([1, th_max])
plt.ylim([0, 1.01])
plt.xlabel(r'$\theta$')
plt.ylabel(r'$p$')
plt.grid()
if not alg_legend == None:
plt.legend(alg_legend, loc=4)
plt.tight_layout()
plt.savefig(file_name, facecolor='w', edgecolor='w')
ABBA_patches = abba.get_patches(ts, pieces, string, centers)
# Construct mean of each patch
d = {}
for key in ABBA_patches:
d[key] = list(np.mean(ABBA_patches[key], axis=0))
# Stitch patches together
patched_ts = np.array([ts[0]])
for letter in string:
patch = d[letter]
patch -= patch[0] - patched_ts[-1] # shift vertically
patched_ts = np.hstack((patched_ts, patch[1:]))
# Plot SAX representation
fig, (ax1, ax2) = myfigure(nrows=2, ncols=1, fig_ratio=0.71, fig_scale=1)
ax1.plot(ts, color='k', label='original time series')
ax1.plot(APLA, '--', label='reconstruction after compression')
ax1.plot(reconstructed_ts, ':', label='reconstruction after digitization')
ax1.legend()
print('Symbolic representation:', string)
ax2.plot(ts[0:250], color='k', label='original time series')
next(ax2._get_lines.prop_cycler)
ax2.plot(reconstructed_ts[0:250], ':', label='standard reconstruction')
ax2.plot(patched_ts[0:250], '-.', label='patched reconstruction')
ax2.legend()
plt.savefig('patches.pdf', dpi=300, transparent=True)
np.zeros([32, 1]),
np.ones([6, 1]),
np.zeros([27, 1])
])
# Normalise
t11 = t11 - np.mean(t11)
t11 /= np.std(t11, ddof=1)
t12 = t12 - np.mean(t12)
t12 /= np.std(t12, ddof=1)
t21 = t21 - np.mean(t21)
t21 /= np.std(t21, ddof=1)
t22 = t22 - np.mean(t22)
t22 /= np.std(t22, ddof=1)
fig, ax = myfigure(nrows=1, ncols=1, fig_ratio=0.5, fig_scale=1.7)
ax.axis([0, 100, -1, 3.5])
ax.plot(t21)
ax.plot(t22)
ax.plot([])
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)
plt.tight_layout()
plt.savefig('shift_in_time.pdf')
fig, ax = myfigure(nrows=1, ncols=1, fig_ratio=0.5, fig_scale=1.7)
ax.axis([0, 100, -1, 3.5])
ax.plot(t11)
ax.plot(t12)
ax.plot([])
ax.spines['top'].set_visible(False)
abba = ABBA(tol=tolerance, min_k=10, max_k=30)
string, centres = abba.transform(ts)
ts_new = np.array(abba.inverse_transform(string, centres, ts[0]))
pieces = abba.compress(ts)
ts_con = abba.inverse_compress(ts[0], pieces)
print('np.linalg.norm(ts_con-ts) =', np.linalg.norm(ts_con-ts))
print('should be bounded by = ', np.sqrt(len(ts))*tolerance)
print('dtw(ts_con - ts_new) = ', dtw(ts_con, ts_new))
print('dtw(ts - ts_new) = ', dtw(ts, ts_new))
# Plot ABBA representation
fig, ax = myfigure(nrows=1, ncols=1, fig_ratio=0.71, fig_scale=1.6)
plt.plot(ts, color='k')
plt.plot(ts_con, color='#D95319', linestyle='--')
plt.plot(ts_new, color='#0072BD', linestyle=':')
plt.xlim([1, 7200])
plt.ylim([-2.3, 2.3])
plt.legend(['original time series', 'reconstruction after compression', 'reconstruction after digitization'], loc=9)
plt.savefig('decoke_'+str(abba.tol)+'_scl'+str(abba.scl)+'.pdf')
# Construct list of vertical errors
v_error = np.zeros((len(string), 1))
for ind, letter in enumerate(string):
pc = centres[ord(letter)-97,:]
v_error[ind] = pieces[ind][1]-pc[1]
import SAX
from ABBA import ABBA
import matplotlib.pyplot as plt
np.random.seed(0)
from util import myfigure
# Construct noisy sine wave with linear trend
linspace = np.linspace(0, 16 * 2 * np.pi, 500)
ts = np.sin(linspace)
ts += 0.2 * np.random.randn(500)
ts += np.linspace(0, 4, 500)
# Plot SAX representation
fig, (ax1, ax2, ax3, ax4) = myfigure(nrows=4,
ncols=1,
fig_ratio=0.71,
fig_scale=1)
plt.subplots_adjust(left=0.125,
bottom=None,
right=0.95,
top=None,
wspace=None,
hspace=None)
ts1 = ts
ts1 -= np.mean(ts1)
ts1 /= np.std(ts1)
reduced_ts = SAX.compress(ts1, width=4)
symbolic_ts = SAX.digitize(reduced_ts, number_of_symbols=9)
print('SAX representation length:', len(symbolic_ts))
reduced_ts = SAX.reverse_digitize(symbolic_ts, number_of_symbols=9)
ts_SAX = SAX.reconstruct(reduced_ts, width=4)