def plot_abscissa_eps_by_perf(pdata, perf_attr='logit_perf', eps=0.5, indicies=None, mean=False, abs=False, right_half_only=False):
if indicies is None:
indicies = range(len(pdata))
perfs = []
abscissas = []
for k in indicies:
p = pdata[k]
(X, Y, Z, smin) = compute_pseudospectra(p.W, bounds=[-3, 3, -3, 3], npts=50, invert=False)
zvals = Z[smin < eps]
if zvals.shape[0] > 0:
zreal = np.array([a.real for a in zvals])
if right_half_only:
zreal = zreal[zreal > 0]
if abs:
zreal = np.abs(zreal)
if len(zreal) > 0:
if mean:
abscissas.append(zreal.mean())
else:
abscissas.append(zreal.max())
perfs.append(p.logit_perf)
plt.plot(abscissas, perfs, 'bo')
plt.show()
def plot_smin_hist_by_perf(pdata, tau=1):
num_plots = 9
indx_off = [0, len(pdata)-num_plots]
weights = [[], []]
for k,offset in enumerate(indx_off):
pend = offset + num_plots
for m,p in enumerate(pdata[offset:pend]):
weights[k].append(p.W)
perrow = int(np.sqrt(num_plots))
percol = perrow
for j,offset in enumerate(indx_off):
fig = plt.figure()
fig.subplots_adjust(wspace=0.1, hspace=0.1)
for k in range(num_plots):
W = weights[j][k]
N = W.shape[0]
ax = fig.add_subplot(perrow, percol, k)
(X, Y, Z, smin) = compute_pseudospectra(W, bounds=[-3, 3, -3, 3], npts=50, invert=False)
a = np.real(Z)
K = smin / a
eatau = np.exp(a*tau)
maxg = eatau / (1.0 + ((eatau - 1.0) / K))
ax.hist(maxg[(a > 0) * (K > 1)].ravel(), bins=20)
#ax.hist(smin.ravel(), bins=20)
plt.show()
def plot_pseudospectra_hull_perf(pdata, perf_attr='logit_perf', eps=0.5, bounds=[-3, 3, -3, 3], npts=50):
num_plots = 25
indx_off = [0, len(pdata)-num_plots]
weights = [[], []]
for k,offset in enumerate(indx_off):
pend = offset + num_plots
for m,p in enumerate(pdata[offset:pend]):
weights[k].append(p.W)
perrow = int(np.sqrt(num_plots))
percol = perrow
for j,offset in enumerate(indx_off):
fig = plt.figure()
fig.subplots_adjust(wspace=0.1, hspace=0.1)
for k in range(num_plots):
W = weights[j][k]
N = W.shape[0]
(X, Y, Z, smin) = compute_pseudospectra(W, bounds=bounds, npts=npts, invert=False)
if np.sum(smin < eps) > 0:
xvals = X[smin < eps].ravel()
yvals = Y[smin < eps].ravel()
pnts = zip(xvals, yvals)
ch = np.array(convex_hull(pnts))
arclen = 0.0
for m in range(ch.shape[0]):
if m == 0:
p1 = ch[-1, :]
else:
p1 = ch[m-1, :]
p2 = ch[m, :]
arclen += np.linalg.norm(p2 - p1)
ax = fig.add_subplot(perrow, percol, k)
ax.fill(ch[:, 0], ch[:, 1], 'b')
ax.set_xlim((bounds[0], bounds[1]))
ax.set_ylim((bounds[2], bounds[3]))
ax.set_title('%0.1f' % arclen)
plt.show()
def plot_lower_bound_perf(pdata, tau=1, indicies=None):
if indicies is None:
indicies = range(len(pdata))
lb = []
perfs = []
for k in indicies:
p = pdata[k]
W = p.W
(X, Y, Z, smin) = compute_pseudospectra(W, bounds=[-3, 3, -3, 3], npts=50, invert=True)
a = np.real(Z)
K = smin / a
eatau = np.exp(a*tau)
maxg = eatau / (1.0 + ((eatau - 1.0) / K))
lb.append(maxg[(a > 0) * (K > 1)].ravel().mean())
perfs.append(p.logit_perf)
plt.plot(lb, perfs, 'go')
plt.show()
def compute_net_metrics(pdata, output_file):
npts = 40
data = []
for p in pdata:
J = fisher_memory_matrix(p.net.W, p.net.Win, use_dlyap=False, npts=npts)
feature_names = []
features = []
#compute weighted jtot
fmc = np.diag(J)
fmc[fmc < 0.0] = 0.0
indx = np.arange(len(fmc)) + 1.0
w = np.log2(indx)
wjtot = (w * fmc).sum()
feature_names.append('wjtot')
features.append(wjtot)
#compute upper-triangular abs sum
jt_vals = np.abs(J[np.triu_indices(len(J))])
fmm_sum = jt_vals.sum()
feature_names.append('fmm_sum')
features.append(fmm_sum)
#compute arc length of convex hull around pseudospectra
bounds=[-3, 3, -3, 3]
for eps in [0.5, 0.1]:
(X, Y, Z, smin) = compute_pseudospectra(p.net.W, bounds=bounds, npts=75, invert=False)
arclen = np.NAN
if np.sum(smin < eps) > 0:
arclen = 0.0
xvals = X[smin < eps].ravel()
yvals = Y[smin < eps].ravel()
pnts = zip(xvals, yvals)
ch = np.array(convex_hull(pnts))
for m in range(ch.shape[0]):
if m == 0:
p1 = ch[-1, :]
else:
p1 = ch[m-1, :]
p2 = ch[m, :]
arclen += np.linalg.norm(p2 - p1)
feature_names.append('arclen_%0.2f' % eps)
features.append(arclen)
#compute eigenvalues/schur decomposition
(T, U, sdim) = scipy.linalg.schur(p.net.W, 'complex', sort='rhp')
evals = np.diag(T)
for k,ev in enumerate(evals):
feature_names.append('ev%d_real' % k)
features.append(ev.real)
feature_names.append('ev%d_imag' % k)
features.append(ev.imag)
for i in range(p.net.W.shape[0]):
for j in range(i):
if i != j:
od = T[j, i]
feature_names.append('od%d%d_real' % (j, i))
features.append(od.real)
feature_names.append('od%d%d_imag' % (j, i))
features.append(od.imag)
feature_names.append('perf')
features.append(p.logit_perf)
data.append(features)
f = open(output_file, 'w')
f.write('%s\n' % ','.join(feature_names))
for row in data:
fstr = ['%0.12f' % x for x in row]
f.write('%s\n' % ','.join(fstr))
f.close()