def plot_projection(X, L, center, ax, pgfname, stretch, **kwargs):
U = orth(np.atleast_2d(L).T)
P = np.outer(U, U.T)
center = center - P.dot(center)
# Line we project onto
line = np.vstack([
center - stretch * L,
center + stretch * L,
])
ax.plot(line[:, 0], line[:, 1], **kwargs)
pgf = PGF()
pgf.add('x', line[:, 0])
pgf.add('y', line[:, 1])
pgf.write(pgfname + '_line.dat')
# projection lines
lines = [] # lines from points to the projection axis
dots = [] # dots on the projection axis
for x in X:
lines.append(x)
lines.append(center + P.dot(x))
dots.append(lines[-1])
lines.append(np.nan * np.ones(2))
lines = np.vstack(lines)
ax.plot(lines[:, 0], lines[:, 1], ':', **kwargs)
dots = np.vstack(dots)
ax.plot(dots[:, 0], dots[:, 1], '.', **kwargs)
pgf = PGF()
pgf.add('x', lines[:, 0])
pgf.add('y', lines[:, 1])
pgf.write(pgfname + '_lines.dat')
pgf = PGF()
pgf.add('x', dots[:, 0])
pgf.add('y', dots[:, 1])
pgf.write(pgfname + '_dots.dat')
fX = fun(X)
grads = fun.grad(X)
#for i, M in tqdm(enumerate(Mvec), desc = 'sample %3d' % rep, total = len(Mvec)):
for i, M in enumerate(Mvec):
print("\n\n#### samples M = %d, rep %d" % (M,rep))
start_time = time.clock()
lipschitz.fit(X[:M], fX[:M])
stop_time = time.clock()
time_samp[rep, i] = stop_time - start_time
Hsamp = np.copy(lipschitz.H)
mismatch_samp[rep, i] = metric(Hsamp)
print("mismatch: ", mismatch_samp[rep,i], "time :", time_samp[rep,i])
# Now export the data to PGF
pgf = PGF()
pgf.add('M', Mvec)
p0, p25, p50, p75, p100 = np.percentile(mismatch_samp[:rep+1], [0, 25, 50, 75, 100], axis =0,
interpolation = 'nearest')
pgf.add('p0', p0)
pgf.add('p25', p25)
pgf.add('p50', p50)
pgf.add('p75', p75)
pgf.add('p100', p100)
pgf.write('data/fig_convergence_samp.dat')
# Now the time part
pgf = PGF()
pgf.add('M', Mvec)
p0, p25, p50, p75, p100 = np.percentile(time_samp[:rep+1], [0, 25, 50, 75, 100], axis =0)
pgf.add('p0', p0)
p100 = np.zeros(len(Npoints))
for k, N in enumerate(Npoints):
def compute_dist(trial):
X = alg(N, trial)
return design_dispersion(X)
print(f"starting N={N:3d}, alg {name}")
dists = Parallel(n_jobs=20, verbose=100)(delayed(compute_dist)(i)
for i in range(Ntrials))
# dists = []
# for trial in range(Ntrials):
# X = alg(fun.domain, N, L, trial)
# dist = design_dispersion(X, fun.domain, L)
# dists.append(dist)
# print(f'M : {N:3d} | dispersion {dist:10.4e}')
p0[k], p25[k], p50[k], p75[k], p100[k] = np.percentile(
dists, [0, 25, 50, 75, 100])
# Write incremental data
pgf = PGF()
pgf.add('N', Npoints)
pgf.add('p0', p0)
pgf.add('p25', p25)
pgf.add('p50', p50)
pgf.add('p75', p75)
pgf.add('p100', p100)
pgf.write(f'data/fig_design_rate_{name}.dat')
if __name__ == '__main__':
np.random.seed(0)
dom = psdr.BoxDomain(-np.ones(2), np.ones(2))
fig, axes = plt.subplots(1, 2, figsize=(10, 5))
# Number of samples
M = 20
# Latin Hypercube sampling
X = psdr.latin_hypercube_maximin(dom, M, maxiter=1000)
pgf = PGF()
pgf.add('x', X[:, 0])
pgf.add('y', X[:, 1])
pgf.write('data/fig_latin_lhs_sample.dat')
ax = axes[0]
ax.plot(X[:, 0], X[:, 1], 'k.')
ax.set_title('Latin Hypercube')
L = np.array([[1, 0]])
center = np.array([0, -1.3])
plot_projection(X,
L,
center,
ax,
'data/fig_latin_lhs_hor',
lip_con = psdr.LipschitzConstant()
lip_con.fit(grads=gradX)
# scale by function variation
fXg = fun(Xg)
#uncertain = (ub - lb)/(np.max(fXg) - np.min(fXg))
rnge = np.max(fXg) - np.min(fXg)
X_iso = psdr.minimax_lloyd(fun.domain, M)
X_lip = psdr.minimax_lloyd(fun.domain, M, L=lip_mat.L)
# Isotropic sampling/ scalar Lipschitz
lb, ub = lip_con.uncertainty(X_iso, fun(X_iso), Xg)
p = np.percentile(ub - lb, [0, 25, 50, 75, 100])
print(p)
pgf = PGF()
for i, t in enumerate([0, 25, 50, 75, 100]):
pgf.add('p%d' % t, [p[i]])
pgf.add('range', [rnge])
pgf.write('data/tab_sample_%s_scalar_isotropic_uncertainty.dat' % (name))
# Isotropic sampling/ matrix Lipschitz
lb, ub = lip_mat.uncertainty(X_iso, fun(X_iso), Xg)
p = np.percentile(ub - lb, [0, 25, 50, 75, 100])
print(p)
pgf = PGF()
for i, t in enumerate([0, 25, 50, 75, 100]):
pgf.add('p%d' % t, [p[i]])
pgf.add('range', [rnge])
pgf.write('data/tab_sample_%s_matrix_isotropic_uncertainty.dat' % (name))
'random \n→ maximin \n→ minimax',
'coffeehouse \n→ minimax',
'coffeehouse \n→ maximin \n→ minimax',
'coffeehouse \n→ maximin \n→ scale \n→ minimax',
])
names = [
'random_minimax',
'random_maximin_minimax',
'coffeehouse_minimax',
'coffeehouse_maximin_minimax',
'coffeehouse_maximin_scale_minimax',
]
for coll, name in zip(ax.collections, names):
x, y = np.array(coll.get_offsets()).T
print(x)
print(y)
pgf = PGF()
pgf.add('x', x)
pgf.add('y', y)
pgf.write('data/fig_initialization_%s.dat' % name)
best = np.min(np.hstack(data))
print(best)
ax.axhline(best, color='k')
ax.set_xlabel('method')
ax.set_ylabel('minimax distance')
plt.show()
c1 = fun.domain.corner(u)
c2 = fun.domain.corner(-u)
X4 = np.array([t * c1 + (1 - t) * c2 for t in np.linspace(0, 1, len(X1))])
fX4 = fun(X4)
name4 = 'line'
for X, fX, name in zip([X1, X2, X3, X4], [fX1, fX2, fX3, fX4],
[name1, name2, name3, name4]):
print(" === %10s === " % name)
lb, ub = Lmat.uncertainty(X, fX, Xt)
print("average uncertainty", np.mean(ub - lb))
print("max uncertainty", np.max(ub - lb))
p = np.percentile(ub - lb, [0, 25, 50, 75, 100])
pgf = PGF()
for i, t in enumerate([0, 25, 50, 75, 100]):
pgf.add('p%d' % t, [p[i]])
pgf.write('data/fig_sample_Lmat_uncertainty_%s.dat' % name)
# Lipschitz constant
lb, ub = Lcon.uncertainty(X, fX, Xt)
print("average uncertainty", np.mean(ub - lb))
print("max uncertainty", np.max(ub - lb))
p = np.percentile(ub - lb, [0, 25, 50, 75, 100])
pgf = PGF()
for i, t in enumerate([0, 25, 50, 75, 100]):
pgf.add('p%d' % t, [p[i]])
pgf.write('data/fig_sample_Lcon_uncertainty_%s.dat' % name)
funs.append(psdr.demos.OTLCircuit())
names.append('otl')
# Borehole
funs.append(psdr.demos.Borehole())
names.append('borehole')
# Wing Weight
funs.append(psdr.demos.WingWeight())
names.append('wing')
act = psdr.ActiveSubspace()
lip = psdr.LipschitzMatrix()
m = max([len(fun.domain) for fun in funs])
pgf = PGF()
pgf.add('i', np.arange(1, m + 1))
for fun, name in zip(funs, names):
X = fun.domain.sample(1e3)
grads = fun.grad(X)
act.fit(grads)
lip.fit(grads=grads)
ew = np.nan * np.zeros(m)
ew[0:len(fun.domain)] = scipy.linalg.eigvalsh(act.C)[::-1]
pgf.add('%s_C' % name, ew)
ew[0:len(fun.domain)] = scipy.linalg.eigvalsh(lip.H)[::-1]
pgf.add('%s_H' % name, ew)
pgf.write('data/tab_eigs.dat')
for qoi in qois:
Iall = np.isfinite(Yall[:, qoi])
#norm = np.linalg.norm(Yall[Iall,qoi])
norm = (np.nanmax(Yall[Iall, qoi]) - np.nanmin(Yall[Iall, qoi])) * np.sqrt(
np.sum(Iall))
err_rand_vec = []
err_doe_vec = []
for k in ks:
I = np.isfinite(Yrand[:, qoi]) & (np.arange(Yrand.shape[0]) < k)
pra = PolynomialRidgeApproximation(degree=3,
subspace_dimension=1,
n_init=1)
pra.fit(Xrand_norm[I], Yrand[I, qoi])
#err_rand = np.mean(np.abs(pra.predict(Xall_norm[Iall]) - Yall[Iall,qoi]))/norm
err_rand = np.linalg.norm(
pra.predict(Xall_norm[Iall]) - Yall[Iall, qoi]) / norm
err_rand_vec.append(err_rand)
I = np.isfinite(Ydoe[:, qoi]) & (np.arange(Ydoe.shape[0]) < k)
pra.fit(Xdoe_norm[I], Ydoe[I, qoi])
err_doe = np.linalg.norm(
pra.predict(Xall_norm[Iall]) - Yall[Iall, qoi]) / norm
#err_doe = np.mean(np.abs(pra.predict(Xall_norm[Iall]) - Yall[Iall,qoi]))/norm
err_doe_vec.append(err_doe)
print "%4d: err rand %5.2e; doe %5.2e" % (k, err_rand, err_doe)
pgf = PGF()
pgf.add('k', ks)
pgf.add('doe', err_doe_vec)
pgf.add('rand', err_rand_vec)
pgf.write('fig_err_qoi%d.dat' % (qoi, ))
try:
res = prob.solve(warm_start = True)
if prob.status == cp.OPTIMAL:
Nsucceed += 1
dist = np.linalg.norm(z.value - yi)
if dist < eps:
Ninside += 1
except cp.SolverError:
pass
if randomize:
mean = float(Ninside/Nsucceed)
Ns[i] = int( mean*ngrid)
Nstd[i] = np.sqrt(mean - mean**2)*float(ngrid)
else:
Ns[i] = Ninside
Nstd[i] = 0
print('eps=%5.2g \t N=%12.7e' % (eps, Ns[i]))
# Now save the data
pgf = PGF()
pgf.add('eps', epsilons[:i+1])
pgf.add('N', Ns[:i+1])
pgf.add('Nstd', Nstd[:i+1])
pgf.write('data/fig_covering_%s.dat' % name)
# Now compute rates
for resp_name in responses:
resp = responses[resp_name]
# Now fit and test response surface
try:
resp.fit(X, fX)
# Record the sup norm error
data[resp_name][i, it] = np.max(
np.abs(resp(Xt).flatten() - ft.flatten())) / scale
except (KeyboardInterrupt, SystemExit):
raise
except:
pass
print("\t err %10s: %8.2e" %
(resp_name, data[resp_name][i, it]))
# Now save the data
for resp_name in data:
fname = 'fig_sample_%s_%s_%s.dat' % (fun_name, samp_name,
resp_name)
pgf = PGF()
pgf.add('N', Nvec[:i + 1])
p0, p25, p50, p75, p100 = np.nanpercentile(
data[resp_name][:i + 1, :], [0, 25, 50, 75, 100], axis=1)
pgf.add('p0', p0)
pgf.add('p25', p25)
pgf.add('p50', p50)
pgf.add('p75', p75)
pgf.add('p100', p100)
pgf.write('data/' + fname)
plt.clf()
# Samples to use when estimating dispersion
#X0 = psdr.maximin_coffeehouse(fun.domain, 5000, L = L, N0 = 50)
X0 = np.vstack(
[psdr.random_sample(fun.domain, 5000),
fun.domain.sample_grid(2)])
plt.clf()
# Now perform designs
for alg, alg_name, M in zip(algs, alg_names, Ms):
dispersion = []
# We can get a very sloppy fit with more points
for i in range(M):
np.random.seed(i)
X = alg(fun.domain, Nsamp, L)
dist = psdr.fill_distance_estimate(fun.domain,
X,
L=L,
X0=np.copy(X0))
dispersion.append(dist)
print(f'{alg_name:20s} : {i:4d} dispersion {dist:10.5e}')
ax = sns.swarmplot(dispersion)
x, y = np.array(ax.collections[-1].get_offsets()).T
pgf = PGF()
pgf.add('x', x)
pgf.add('y', y)
pgf.write(f'data/fig_design_{name}_{alg_name}.dat')
import numpy as np
from psdr.pgf import PGF
pgf = PGF()
pgf.read('data/fig_covering_mat.dat')
eps = np.array(pgf['eps'])
Ns = np.array(pgf['N'])
slope = np.zeros(eps.shape)
for i in range(len(slope)):
I = slice(max(0, i - 1), min(len(slope), i + 1))
xx = np.log10(eps[I])
yy = np.log10(Ns[I])
# Fit a line
p = np.polyfit(xx, yy, 1)
slope[i] = p[0]
# Median filter
slope_median = np.zeros(slope.shape)
for i in range(len(slope)):
slope_median[i] = np.median(slope[max(0, i - 3):min(len(slope), i + 3)])
pgf = PGF()
pgf.add('eps', eps)
pgf.add('slope', slope)
pgf.add('median', slope_median)
pgf.write('data/fig_covering_mat_slope.dat')
import psdr
from psdr.pgf import PGF
np.random.seed(0)
m = 2
domain = psdr.BoxDomain(-np.ones(m), np.ones(m))
L = np.array([[1, 0],[-1,4]])/4
print("without Lipschitz")
X = psdr.minimax_lloyd(domain, 9, maxiter = 500)
print(X)
d = psdr.geometry.fill_distance(domain, X)
print(d)
pgf = PGF()
pgf.add('x', X[:,0])
pgf.add('y', X[:,1])
pgf.write('data/fig_cover_scalar.dat')
print("with Lipschitz")
X = psdr.minimax_lloyd(domain, 3, L = L)
print(X)
d = psdr.geometry.fill_distance(domain, X, L = L)
print(d)
pgf = PGF()
pgf.add('x', X[:,0])
pgf.add('y', X[:,1])
pgf.write('data/fig_cover_matrix.dat')
import numpy as np
from psdr.pgf import PGF
pgf = PGF()
pgf.read('data/fig_covering_mat.dat')
delta = np.array(pgf['eps'])
Ndelta = np.array(pgf['N'])
delta2 = 10.**((np.log10(delta[1:]) + np.log10(delta[0:-1])) / 2.)
slope2 = (np.log10(Ndelta[1:]) - np.log10(Ndelta[0:-1])) / (
np.log10(delta[1:]) - np.log10(delta[0:-1]))
delta2 = delta2[np.isfinite(slope2)]
slope2 = slope2[np.isfinite(slope2)]
# Median filter
slope_median = np.zeros(slope2.shape)
for i in range(len(slope2)):
slope_median[i] = np.median(slope2[max(0, i - 3):min(len(slope2), i + 3)])
pgf = PGF()
pgf.add('eps', delta2)
pgf.add('slope', slope2)
pgf.add('median', slope_median)
pgf.write('data/fig_covering_mat_rate.dat')
if False:
Iplus = slice(5, len(delta))
Iminus = slice(0, len(delta) - 5)
delta5 = 10.**((np.log10(delta[Iplus]) + np.log10(delta[Iminus])) / 2.)
slope5 = (np.log10(Ndelta[Iplus]) - np.log10(Ndelta[Iminus])) / (
M = 20
# Ridge subspace
u = np.ones((m, 1)) / np.sqrt(m)
proj_domain = psdr.BoxDomain([-np.sqrt(m)], [np.sqrt(m)])
import matplotlib.pyplot as plt
# Get data for drawing plot
XX = np.linspace(-np.sqrt(m), np.sqrt(m), 1000).reshape(-1, 1) @ u.T
fXX = fun(XX)
fig, ax = plt.subplots(1, 2)
ax[0].plot((u.T @ XX.T).flatten(), fXX)
pgf = PGF()
pgf.add('x', (u.T @ XX.T).flatten())
pgf.add('y', fXX)
pgf.write('data/fig_sine_fun.dat')
# plot minimax design
X = psdr.minimax_design_1d(fun.domain, M, L=L[0, :].reshape(1, -1))
minimax_dist = psdr.fill_distance(proj_domain, (u.T @ X.T).T)
ax[0].plot((u.T @ X.T).flatten(), fun(X), 'r.')
pgf = PGF()
pgf.add('x', (u.T @ X.T).flatten())
pgf.add('y', fun(X))
pgf.write('data/fig_sine_minimax.dat')
# Plot a random design
ax = axes[1]
ax.set_title('Lipschitz Bounds')
ax.plot(X.flatten(), fX, 'k.')
ax.plot(xx, f(xx), 'b-')
ax.plot(xx, yy_lip, 'r-')
ax.fill_between(xx.flatten(), lb, ub, color='g', alpha=0.5)
axes[0].set_ylim(axes[1].get_ylim())
fig.tight_layout()
plt.show()
# Save PGF data
pgf = PGF()
pgf.add('x', X.flatten())
pgf.add('fx', fX)
pgf.write('data/fig_gp_data.dat')
pgf = PGF()
pgf.add('x', xx.flatten())
pgf.add('fx', f(xx))
pgf.add('gpr', yy_gpr)
pgf.add('gpr_lb', yy_gpr - yy_std)
pgf.add('gpr_ub', yy_gpr + yy_std)
pgf.add('lip_lb', lb)
pgf.add('lip_ub', ub)
pgf.write('data/fig_gp.dat')
fig, axes = plt.subplots(1, 2, figsize=(10, 5))
M = 20
# First 9 lock
Ls = [np.array([[2, 1]]), np.array([[1, 2]])]
for ax, slack in zip(axes, [1, 0.5]):
X = []
for i in range(M):
x = psdr.seq_maximin_sample(dom,
X,
Ls=Ls,
slack=slack,
Nsamp=int(1e3))
X.append(x)
X = np.vstack(X)
pgf = PGF()
pgf.add('x', X[:, 0])
pgf.add('y', X[:, 1])
pgf.write('data/fig_lock_s%g_sample.dat' % slack)
ax.plot(X[:, 0], X[:, 1], 'k.')
ax.set_title('slack=%g' % slack)
centers = [np.array([1.1, -1.1]), np.array([2, 0])]
colors = ['b', 'r']
for i, (L, center, color) in enumerate(zip(Ls, centers, colors)):
plot_projection(X,
L,
center,
ax,
'data/fig_lock_s%g_L%d' % (slack, i),
stretch=1.2,
lam3 = np.zeros(epsilon.shape)
lam4 = np.zeros(epsilon.shape)
lam5 = np.zeros(epsilon.shape)
lam6 = np.zeros(epsilon.shape)
for k, eps in enumerate(epsilon):
L = lipschitz(X, fX, eps)
rank[k] = np.linalg.matrix_rank(L)
obj[k] = np.linalg.norm(L, 'fro')
ew, ev = np.linalg.eigh(L)
ew = ew[::-1]
lam1[k] = ew[0]
lam2[k] = ew[1]
lam3[k] = ew[2]
lam4[k] = ew[3]
lam5[k] = ew[4]
lam6[k] = ew[5]
print(f"=====> epsilon {eps:8.2e}, rank {rank[k]:2d}, obj {obj[k]:10.5e}")
pgf = PGF()
pgf.add('epsilon', epsilon)
pgf.add('rank', rank)
pgf.add('obj', obj)
pgf.add('lam1', lam1)
pgf.add('lam2', lam2)
pgf.add('lam3', lam3)
pgf.add('lam4', lam4)
pgf.add('lam5', lam5)
pgf.add('lam6', lam6)
pgf.write('data/fig_epsilon_rank.dat')
