for x in xrange(train.shape[1]):
colU = u[y, :]
rowV = svT[:, x]
assert np.allclose(train[y, x], single_dot(u, svT, x, y))
"""
##
plt.title('SVD reconstruction error on {}x{} matrix'.format(*train.shape))
plt.xlabel('Low rank approximation (k)')
plt.ylabel('Frobenius norm')
plt.ylim(0, max(svdY))
plt.legend(loc='best')
plt.savefig('reconstruct_fro_{}x{}.pdf'.format(*train.shape))
plt.show(block=True)
##
plt.plot(orthoX,
orthoY,
label="SVD",
color='black',
linewidth=2,
linestyle='--')
for label, X, Y in incr_ortho:
plt.plot(X, Y, label=label)
plt.title('SVD orthogonality error on {}x{} matrix'.format(*train.shape))
plt.xlabel('Low rank approximation (k)')
plt.ylabel('Deviation from orthogonality')
plt.semilogy()
#plt.ylim(0, max(orthoY))
plt.legend(loc='best')
plt.savefig('reconstruct_ortho_{}x{}.pdf'.format(*train.shape))
plt.show(block=True)
yd = np.arange(len(xd))[::-1] + 1
lxd = np.log(xd)
lyd = np.log(yd)
loglins = linear_model.BayesianRidge()
loglogs = linear_model.BayesianRidge()
loglind = linear_model.BayesianRidge()
loglogd = linear_model.BayesianRidge()
loglins.fit(xs, lys)
loglogs.fit(lxs, lys)
loglind.fit(xd, lyd)
loglogd.fit(lxd, lyd)
subplot(221)
plt.semilogy(xs, ys, "k.", ms=12)
plt.semilogy(xs, np.exp(loglins.predict(xs)), linewidth=3)
title("Size")
ylabel("Log-Linear")
subplot(222)
plt.semilogy(xd, yd, "k.", ms=12)
plt.semilogy(xd, np.exp(loglind.predict(xd)), linewidth=3)
title("Duration")
subplot(223)
plt.loglog(xs, ys, "k.", ms=12)
plt.loglog(np.exp(lxs), np.exp(loglogs.predict(lxs)), linewidth=3)
ylabel("Log-Log")
subplot(224)
plt.plot(X, Y, label='iSVD u={}'.format(num))
"""
print 'Testing raw SVD => exact reconstruction'
svT = scipy.linalg.diagsvd(s, u.shape[0], vT.shape[1]).dot(vT)
for y in xrange(train.shape[0]):
for x in xrange(train.shape[1]):
colU = u[y, :]
rowV = svT[:, x]
assert np.allclose(train[y, x], single_dot(u, svT, x, y))
"""
##
plt.title('SVD reconstruction error on {}x{} matrix'.format(*train.shape))
plt.xlabel('Low rank approximation (k)')
plt.ylabel('Frobenius norm')
plt.ylim(0, max(svdY))
plt.legend(loc='best')
plt.savefig('reconstruct_fro_{}x{}.pdf'.format(*train.shape))
plt.show(block=True)
##
plt.plot(orthoX, orthoY, label="SVD", color='black', linewidth=2, linestyle='--')
for label, X, Y in incr_ortho:
plt.plot(X, Y, label=label)
plt.title('SVD orthogonality error on {}x{} matrix'.format(*train.shape))
plt.xlabel('Low rank approximation (k)')
plt.ylabel('Deviation from orthogonality')
plt.semilogy()
#plt.ylim(0, max(orthoY))
plt.legend(loc='best')
plt.savefig('reconstruct_ortho_{}x{}.pdf'.format(*train.shape))
plt.show(block=True)
loglins = linear_model.BayesianRidge()
loglogs = linear_model.BayesianRidge()
loglind = linear_model.BayesianRidge()
loglogd = linear_model.BayesianRidge()
loglins.fit(xs, lys)
loglogs.fit(lxs, lys)
loglind.fit(xd, lyd)
loglogd.fit(lxd, lyd)
subplot(221)
plt.semilogy(xs, ys, "k.", ms=12)
plt.semilogy(xs, np.exp(loglins.predict(xs)), linewidth=3)
title("Size")
ylabel("Log-Linear")
subplot(222)
plt.semilogy(xd, yd, "k.", ms=12)
plt.semilogy(xd, np.exp(loglind.predict(xd)), linewidth=3)
title("Duration")
subplot(223)
plt.loglog(xs, ys, "k.", ms=12)
plt.loglog(np.exp(lxs), np.exp(loglogs.predict(lxs)), linewidth=3)
ylabel("Log-Log")
subplot(224)
