def Demo():
#__BLOOD_BANK__##################################################
# Define Network and Domain
Network = CreateRandomNetwork(nC=2, nB=2, nD=2, nR=2, seed=0)
Domain = BloodBank(Network=Network, alpha=2)
# Set Method
Method = CashKarp(Domain=Domain, P=BoxProjection(lo=0), Delta0=1e-6)
# Initialize Starting Point
Start = np.zeros(Domain.Dim)
# Calculate Initial Gap
gap_0 = Domain.gap_rplus(Start)
# Set Options
Init = Initialization(Step=-1e-10)
Term = Termination(MaxIter=25000, Tols=[(Domain.gap_rplus, 1e-6 * gap_0)])
Repo = Reporting(
Requests=[Domain.gap_rplus, 'Step', 'F Evaluations', 'Projections'])
Misc = Miscellaneous()
Options = DescentOptions(Init, Term, Repo, Misc)
# Print Stats
PrintSimStats(Domain, Method, Options)
# Start Solver
tic = time.time()
BloodBank_Results = Solve(Start, Method, Domain, Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options, BloodBank_Results, Method, toc)
def Demo():
# __MACHINE_LEARNING_NETWORK____#################################################
# Define Domain
Network = CreateRandomNetwork()
Domain = MLN(Network)
# Set Method
Method = Euler(Domain=Domain,FixStep=True,P=BoxProjection(lo=Domain.los,hi=Domain.his))
# Set Options
Term = Termination(MaxIter=500)
Repo = Reporting(Requests=['Step', 'F Evaluations',
'Projections','Data'])
Misc = Miscellaneous()
Init = Initialization(Step=-1e-3)
Options = DescentOptions(Init,Term,Repo,Misc)
# Initialize Starting Point
Start = np.random.rand(Domain.dim)*(Domain.his-Domain.los) + Domain.los
Start[20:22] = [-.5,.5]
Start[22:24] = [.5,.5]
Start[24:26] = [.5,.5]
Start[26:28] = [1.,0.]
Start[28:32] = [-.5,-.25,-.75,-.5]
# Print Stats
PrintSimStats(Domain,Method,Options)
# Start Solver
tic = time.time()
MLN_Results = Solve(Start,Method,Domain,Options) # Use same Start
toc = time.time() - tic
# Print Results
PrintSimResults(Options,MLN_Results,Method,toc)
########################################################
# Animate Network
########################################################
# Construct MP4 Writer
fps = 5
FFMpegWriter = animation.writers['ffmpeg']
metadata = dict(title='MLN', artist='Matplotlib')
writer = FFMpegWriter(fps=fps, metadata=metadata)
# Collect Frames
Frames = MLN_Results.PermStorage['Data'][::fps]
# Save Animation to File
fig, ax = plt.subplots()
MLN_ani = animation.FuncAnimation(fig, Domain.UpdateVisual,
init_func=Domain.InitVisual,
frames=len(Frames),
fargs=(ax, Frames))
MLN_ani.save('MLN.mp4', writer=writer)
def Demo():
# __APPROXIMATE_LINEAR_FIELD__##############################################
# Load Dummy Data
X = np.random.rand(1000, 2) * 2 - 1
scale = np.array([0.8, 1.2])
y = 0.5 * np.sum(scale * X**2, axis=1)
# Construct Field
ALF = ApproxLF(X=X, dy=y, eps=1e-8)
# Set Method
# Method = Euler(Domain=ALF,FixStep=True)
Method = HeunEuler(Domain=ALF, Delta0=1e-2)
# Initialize Starting Field
A = np.array([[0, 1], [-1, 0]])
# A = np.eye(LF.XDim)
# A = np.random.rand(LF.XDim,LF.XDim)
# A = np.array([[5,0.],[0.,5]])
b = np.zeros(ALF.XDim)
Start = np.hstack([A.flatten(), b])
print(Start)
# Set Options
Init = Initialization(Step=-1.0)
Term = Termination(MaxIter=1000) #,Tols=[(LF.error,1e-10)])
Repo = Reporting(Requests=[ALF.error, 'Step', 'F Evaluations', 'Data'])
Misc = Miscellaneous()
Options = DescentOptions(Init, Term, Repo, Misc)
# Print Stats
PrintSimStats(ALF, Method, Options)
# Start Solver
tic = time.time()
Results = Solve(Start, Method, ALF, Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options, Results, Method, toc)
error = np.asarray(Results.PermStorage[ALF.error])
params = Results.PermStorage['Data'][-1]
A, b = ALF.UnpackFieldParams(params)
print(A)
print(b)
print(error[-1])
def Demo():
# __CONSTRAINED_OPTIMIZATION__##############################################
# Define Domain: f(x) = x_1 + 2*x_2 - 1
Domain = NewDomain(F=lambda x: np.array([1, 2]), Dim=2)
Domain.Min = 0.
Domain.f_Error = lambda x: x[0] + 2 * x[1] - 1 - Domain.Min
# Define Polytope Constraints: Gx<=h & Ax=b
G = -np.eye(Domain.Dim)
h = np.zeros(Domain.Dim)
A = np.ones((1, Domain.Dim))
b = 1.
# Set Method
P = PolytopeProjection(G=G, h=h, A=A, b=b)
Method = Euler(Domain=Domain, FixStep=True, P=P)
# Initialize Starting Point
Start = np.array([0, 1])
# Set Options
Init = Initialization(Step=-0.1)
Term = Termination(MaxIter=1000, Tols=[(Domain.f_Error, 1e-6)])
Repo = Reporting(Requests=[
Domain.f_Error, 'Step', 'F Evaluations', 'Projections', 'Data'
])
Misc = Miscellaneous()
Options = DescentOptions(Init, Term, Repo, Misc)
# Print Stats
PrintSimStats(Domain, Method, Options)
# Start Solver
tic = time.time()
Results = Solve(Start, Method, Domain, Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options, Results, Method, toc)
error = np.asarray(Results.PermStorage[Domain.f_Error])
plt.plot(error, '-o', lw=2)
plt.title('Projected Subgradient')
plt.xlabel('Iterations')
plt.ylabel('Objective error')
plt.ylim([-.1, 1.1])
plt.show()
def Demo():
#__Gaussian_Mixture_GAN__#############################################
# Define Network and Domain
Domain = GMGAN(dyn='FCC')
# Set Method
# Method = Euler_LEGS(Domain=Domain,FixStep=True,NTopLEs=2)
# Method = HeunEuler_LEGS(Domain=Domain,Delta0=1e-5,NTopLEs=2)
# Method = CashKarp_LEGS(Domain=Domain,Delta0=1e-5,NTopLEs=2)
# Method = HeunEuler(Domain=Domain,Delta0=1e-5)
Method = HeunEuler_PhaseSpace(Domain=Domain, Delta0=1e-3, MaxStep=-.5)
# Method = Euler(Domain=Domain,FixStep=True)
# Initialize Starting Point
Start = Domain.get_weights()
# Set Options
Init = Initialization(Step=-1.)
Term = Termination(MaxIter=3e2)
# Repo = Reporting(Requests=['Step','Data','Lyapunov',Domain.gap])
Repo = Reporting(Requests=['Step'])
Misc = Miscellaneous()
Options = DescentOptions(Init, Term, Repo, Misc)
# Print Stats
PrintSimStats(Domain, Method, Options)
# Start Solver
tic = time.time()
GMGAN_Results = Solve(Start, Method, Domain, Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options, GMGAN_Results, Method, toc)
Domain.set_weights(GMGAN_Results.TempStorage['Data'][-1])
fig, ax = Domain.visualize_dist()
plt.savefig('gmgan_test.png')
Steps = np.array(GMGAN_Results.PermStorage['Step'])
plt.clf()
plt.semilogy(-Steps)
plt.savefig('steps.png')
embed()
def Demo():
#__CLOUD_SERVICES__##################################################
# Define Network and Domain
Network = CreateNetworkExample(ex=5)
Domain = CloudServices(Network=Network, gap_alpha=2)
# Set Method
eps = 1e-2
Method = HeunEuler_LEGS(Domain=Domain, P=BoxProjection(lo=eps), Delta0=1e0)
# Initialize Starting Point
Start = np.ones(Domain.Dim)
# Calculate Initial Gap
gap_0 = Domain.gap_rplus(Start)
# Set Options
Init = Initialization(Step=-1e-3)
Term = Termination(MaxIter=1e5, Tols=[(Domain.gap_rplus, 1e-12 * gap_0)])
Repo = Reporting(Requests=[
Domain.gap_rplus, 'Step', 'F Evaluations', 'Projections', 'Data',
Domain.eig_stats, 'Lyapunov'
])
Misc = Miscellaneous()
Options = DescentOptions(Init, Term, Repo, Misc)
# Print Stats
PrintSimStats(Domain, Method, Options)
# Start Solver
tic = time.time()
CloudServices_Results = Solve(Start, Method, Domain, Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options, CloudServices_Results, Method, toc)
x = CloudServices_Results.PermStorage['Data'][-1]
print('p,q,Q,pi,Nash?')
print(x[:Domain.Dim // 2])
print(x[Domain.Dim // 2:])
print(Domain.Demand(x)[0])
print(Domain.CloudProfits(x))
print(all(Domain.Nash(x)[0]))
def Demo():
#__LIENARD_SYSTEM__##################################################
# Define Network and Domain
Domain = Lienard()
# Set Method
Method = Euler_LEGS(Domain=Domain, FixStep=True, NTopLEs=2)
# Method = HeunEuler_LEGS(Domain=Domain,Delta0=1e-5,NTopLEs=2)
# Method = CashKarp_LEGS(Domain=Domain,Delta0=1e-5,NTopLEs=2)
# Initialize Starting Point
Start = np.array([1.5, 0])
# Set Options
Init = Initialization(Step=1e-3)
Term = Termination(MaxIter=1e5, Tols=[(Domain.gap, 1e-3)])
Repo = Reporting(Requests=['Step', 'Data', 'Lyapunov', Domain.gap])
Misc = Miscellaneous()
Options = DescentOptions(Init, Term, Repo, Misc)
# Print Stats
PrintSimStats(Domain, Method, Options)
# Start Solver
tic = time.time()
Lienard_Results = Solve(Start, Method, Domain, Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options, Lienard_Results, Method, toc)
# Plot Lyapunov Exponents
plt.plot(Lienard_Results.PermStorage['Lyapunov'])
plt.show()
# Plot System Trajectory
data = ListONP2NP(Lienard_Results.PermStorage['Data'])
plt.plot(data[:, 0], data[:, 1])
ax = plt.gca()
ax.set_xlim([-2.5, 2.5])
ax.set_ylim([-2.5, 2.5])
ax.set_aspect('equal')
plt.show()
def score_matrixfac(train, test, mask, step=1e-5, iters=100, k=500):
# Define Domain
n, d = train.shape
sh_P = (n, k)
sh_Q = (d, k)
Domain = MatrixFactorization(Data=train, sh_P=sh_P, sh_Q=sh_Q)
# Set Method
# Method = Euler(Domain=Domain,FixStep=True)
Method = HeunEuler(Domain=Domain, Delta0=1e-1, MinStep=1e-7, MaxStep=1e-2)
# Initialize Starting Point
globalmean = train.sum() / train.nnz
scale = np.sqrt(globalmean / k)
# P = np.random.rand(n,k)
# Q = np.random.rand(d,k)
P = scale * np.ones(sh_P)
Q = scale * np.ones(sh_Q)
Start = np.hstack((P.flatten(), Q.flatten()))
# Set Options
Init = Initialization(Step=step)
Term = Termination(MaxIter=iters)
Repo = Reporting(Requests=['Step', 'F Evaluations'])
Misc = Miscellaneous()
Options = DescentOptions(Init, Term, Repo, Misc)
# Print Stats
PrintSimStats(Domain, Method, Options)
# Start Solver
tic = time.time()
Results = Solve(Start, Method, Domain, Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options, Results, Method, toc)
# Retrieve result
parameters = np.asarray(Results.TempStorage['Data'][-1])
pred = Domain.predict(parameters)
return rmse(pred, test, mask)
def score_svdmethod(train,
test,
mask,
tau=6e3,
step=1.9,
fixstep=True,
iters=250):
# Define Domain
Domain = SVDMethod(Data=train, tau=tau)
# Set Method
# Method = Euler(Domain=Domain,FixStep=fixstep)
Method = HeunEuler(Domain=Domain, Delta0=1e2, MinStep=1e0, MaxStep=1e3)
# Initialize Starting Point
# globalmean = train.sum()/train.nnz
# Start = globalmean*np.ones(train.shape)
Start = np.zeros(train.shape).flatten()
# Set Options
Init = Initialization(Step=step)
Term = Termination(MaxIter=iters, Tols=[(Domain.rel_error, 0.2)])
Repo = Reporting(Requests=[Domain.rel_error, 'Step', 'F Evaluations'])
Misc = Miscellaneous()
Options = DescentOptions(Init, Term, Repo, Misc)
# Print Stats
PrintSimStats(Domain, Method, Options)
# Start Solver
tic = time.time()
Results = Solve(Start, Method, Domain, Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options, Results, Method, toc)
# Retrieve result
Y = np.asarray(Results.TempStorage['Data'][-1]).reshape(train.shape)
pred = Domain.shrink(Y, Domain.tau)
return rmse(pred, test, mask), Results.PermStorage[Domain.rel_error]
def Demo():
#__SUPPLY_CHAIN__##################################################
# Define Network and Domain
Network = CreateRandomNetwork(I=2, Nm=2, Nd=2, Nr=1, seed=0)
Domain = SupplyChain(Network=Network, alpha=2)
# Set Method
Method = CashKarp(Domain=Domain, P=BoxProjection(lo=0), Delta0=1e-5)
# Initialize Starting Point
x = 10 * np.ones(np.product(Domain.x_shape))
gam = np.ones(np.sum([np.product(g) for g in Domain.gam_shapes]))
lam = np.zeros(np.sum([np.product(l) for l in Domain.lam_shapes]))
Start = np.concatenate((x, gam, lam))
# Calculate Initial Gap
gap_0 = Domain.gap_rplus(Start)
# Set Options
Init = Initialization(Step=-1e-10)
Term = Termination(MaxIter=25000, Tols=[(Domain.gap_rplus, 1e-3 * gap_0)])
Repo = Reporting(Requests=[
Domain.gap_rplus, 'Step', 'F Evaluations', 'Projections', 'Data'
])
Misc = Miscellaneous()
Options = DescentOptions(Init, Term, Repo, Misc)
# Print Stats
PrintSimStats(Domain, Method, Options)
# Start Solver
tic = time.time()
SupplyChain_Results = Solve(Start, Method, Domain, Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options, SupplyChain_Results, Method, toc)
def score_mixturemean(train, test, mask, step=-1e-3, iters=100):
# Define Domain
Domain = MixtureMean(Data=train)
# Set Method
Method = Euler(Domain=Domain, P=BoxProjection(lo=0., hi=1.))
# Method = Euler(Domain=Domain,P=EntropicProjection())
# Method = HeunEuler(Domain=Domain,P=EntropicProjection(),Delta0=1e-5,
# MinStep=-1e-1,MaxStep=-1e-4)
# Initialize Starting Point
# Start = np.array([.452,.548])
Start = np.array([.452])
# Set Options
Init = Initialization(Step=step)
Term = Termination(MaxIter=iters)
Repo = Reporting(Requests=['Step', 'F Evaluations'])
Misc = Miscellaneous()
Options = DescentOptions(Init, Term, Repo, Misc)
# Print Stats
PrintSimStats(Domain, Method, Options)
# Start Solver
tic = time.time()
Results = Solve(Start, Method, Domain, Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options, Results, Method, toc)
# Retrieve result
parameters = np.asarray(Results.TempStorage['Data'][-1])
pred = Domain.predict(parameters)
return rmse(pred, test, mask)
def Demo():
#__MHPH__##################################################
trials = range(1000,8000+1,2000)
MHPH_Results = [[] for i in trials]
for n in trials:
#Define Dimension and Domain
Domain = MHPH(Dim=n)
# Set Method
Method = HeunEuler(Domain=Domain,P=EntropicProjection(),Delta0=1e-1)
# Method = RipCurl(Domain=Domain,P=EntropicProjection(),factor=0.1,FixStep=True)
# Set Options
Init = Initialization(Step=-1)
Term = Termination(MaxIter=100,Tols=[[Domain.gap_simplex,1e-3]])
Repo = Reporting(Requests=[Domain.gap_simplex])
Misc = Miscellaneous()
Options = DescentOptions(Init,Term,Repo,Misc)
#Initialize Starting Point
Start = np.ones(Domain.Dim)/np.double(Domain.Dim)
# Print Stats
PrintSimStats(Domain,Method,Options)
tic = time.time()
ind = int(n/2000)-4
MHPH_Results[ind] = Solve(Start,Method,Domain,Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options,MHPH_Results[ind],Method,toc)
def Demo():
#__SERVICE_ORIENTED_INTERNET__##############################################
N = 10 # number of possible maps
T = 1000 # number of time steps
eta = 1e-3 # learning rate
print('Creating Domains')
# Define Domains and Compute Equilbria
Domains = []
X_Stars = []
CurlBounds = []
n = 0
while len(Domains) < N:
# Create Domain
Network = CreateRandomNetwork(m=3, n=2, o=2, seed=None)
Domain = SOI(Network=Network, alpha=2)
# Initialize Starting Point
Start = np.zeros(Domain.Dim)
# Assert PD
J = approx_jacobian(Domain.F, Start)
eigs = np.linalg.eigvals(J + J.T)
if not np.all(eigs > 0):
continue
_J = approx_jacobian(Domain.F, Start + 0.5)
assert np.allclose(J, _J,
atol=1e-5) # assert J is constant (unique for SOI)
# Record Domain
Domains += [Domain]
# Calculate Initial Gap
gap_0 = Domain.gap_rplus(Start)
# Calculate Curl Bound
CurlBounds += [
np.sqrt(8) *
svds(J, k=1, which='LM', return_singular_vectors=False).item()
]
# Set Method
Method = HeunEuler(Domain=Domain, P=BoxProjection(lo=0), Delta0=1e-3)
# Set Options
Init = Initialization(Step=-1e-10)
Term = Termination(MaxIter=25000,
Tols=[(Domain.gap_rplus, 1e-6 * gap_0)])
Repo = Reporting(Requests=[Domain.gap_rplus])
Misc = Miscellaneous()
Options = DescentOptions(Init, Term, Repo, Misc)
# Print Stats
PrintSimStats(Domain, Method, Options)
# Start Solver
tic = time.time()
SOI_Results = Solve(Start, Method, Domain, Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options, SOI_Results, Method, toc)
# Record X_Star
X_Star = SOI_Results.TempStorage['Data'][-1]
X_Stars += [X_Star]
n += 1
X_Stars = np.asarray(X_Stars)
print('Starting Online Learning')
# Set First Prediction
X = np.zeros(X_Stars.shape[1])
# Select First Domain
idx = np.random.choice(len(Domains))
# Domain Sequence
idx_seq = []
X_seq = []
F_seq = []
ts = range(T)
for t in ts:
print('t = ' + str(t), end='\r')
# record prediction
X_seq += [X]
# record domain
idx_seq += [idx]
# retrieve domain
Domain = Domains[idx]
# record F
FX = Domain.F(X)
F_seq += [FX]
# update prediction
X = BoxProjection(lo=0).P(X, -eta, FX)
# update domain
idx = np.random.choice(len(Domains))
print('Computing Optimal Strategy')
weights = np.bincount(idx_seq, minlength=len(Domains)) / len(idx_seq)
print('Weights: ', weights)
# Compute Equilibrium of Average Domain
Domain = AverageDomains(Domains, weights=weights)
# Set Method
Method = HeunEuler_PhaseSpace(Domain=Domain,
P=BoxProjection(lo=0),
Delta0=1e-5)
# Initialize Starting Point
Start = np.zeros(Domain.Dim)
# Assert PSD - sum of PSD is PSD doesn't hurt to check
J = approx_jacobian(Domain.F, Start)
eigs = np.linalg.eigvals(J + J.T)
assert np.all(eigs > 0)
sigma = min(eigs)
# Calculate Initial Gap
gap_0 = Domain.gap_rplus(Start)
# Set Options
Init = Initialization(Step=-1e-10)
Term = Termination(MaxIter=25000, Tols=[(Domain.gap_rplus, 1e-10 * gap_0)])
Repo = Reporting(Requests=[Domain.gap_rplus])
Misc = Miscellaneous()
Options = DescentOptions(Init, Term, Repo, Misc)
# Print Stats
PrintSimStats(Domain, Method, Options)
# Start Solver
tic = time.time()
SOI_Results = Solve(Start, Method, Domain, Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options, SOI_Results, Method, toc)
print('Computing Regrets')
# Record X_Opt
X_Opt = SOI_Results.TempStorage['Data'][-1]
# Record constants for bounds
L = np.sqrt(np.mean(np.linalg.norm(F_seq, axis=1)**2.))
# B = np.linalg.norm(X_Opt)
B = 2. * np.max(np.linalg.norm(X_Stars, axis=1))
eta_opt = B / (L * np.sqrt(2 * T))
bound_opt = B * L * np.sqrt(2 * T)
reg_bound = (B**2) / (2 * eta) + eta * T * L**2
opt_distances = []
equi_distances = []
regret_standards = []
regret_news = []
Fnorms = []
stokes_exact = []
stokes = []
areas_exact = []
areas = []
ts = range(T)
for t in ts:
print('t = ' + str(t), end='\r')
idx = idx_seq[t]
X = X_seq[t]
# retrieve domain
Domain = Domains[idx]
# retrieve equilibrium / reference vector
if t > 0:
equi = X_seq[t - 1]
else:
# equi = np.zeros_like(X)
equi = X
# calculate distance
opt_distances += [np.linalg.norm(X_Opt - X)]
equi_distances += [np.linalg.norm(equi - X)]
# calculate standard regret
ci_predict = ContourIntegral(Domain, LineContour(equi, X))
predict_loss = integral(ci_predict)
ci_opt = ContourIntegral(Domain, LineContour(equi, X_Opt))
predict_opt = integral(ci_opt)
regret_standards += [predict_loss - predict_opt]
# calculate new regret
ci_new = ContourIntegral(Domain, LineContour(X_Opt, X))
regret_news += [integral(ci_new)]
# calculate bound
area_exact = herons(X_Opt, X, equi) # exact area
area = eta_opt * L * (np.linalg.norm(X) + B)
areas_exact += [area_exact]
areas += [area]
stokes_exact += [CurlBounds[idx] * area_exact]
stokes += [CurlBounds[idx] * area]
# stokes += [np.max(CurlBounds[idx]*regret_news[-1]/sigma,0)]
# calculate Fnorm
Fnorms += [np.linalg.norm(F_seq[t])]
ts_p1 = range(1, T + 1)
opt_distances_avg = np.divide(np.cumsum(opt_distances), ts_p1)
equi_distances_avg = np.divide(np.cumsum(equi_distances), ts_p1)
regret_standards_avg = np.divide(np.cumsum(regret_standards), ts_p1)
regret_news_avg = np.divide(np.cumsum(regret_news), ts_p1)
areas_exact_avg = np.divide(np.cumsum(areas_exact), ts_p1)
areas_avg = np.divide(np.cumsum(areas), ts_p1)
stokes_exact_avg = np.divide(np.cumsum(stokes_exact), ts_p1)
stokes_avg = np.divide(np.cumsum(stokes), ts_p1)
Fnorms_avg = np.divide(np.cumsum(Fnorms), ts_p1)
np.savez_compressed('NoRegret_MLN_new.npz',
opt_d_avg=opt_distances_avg,
equi_d_avg=equi_distances_avg,
rs_avg=regret_standards_avg,
rn_avg=regret_news_avg,
stokes_exact=stokes_exact_avg,
stokes=stokes_avg)
plt.subplot(2, 1, 2)
plt.semilogy(ts,
opt_distances_avg,
'k',
label='Average Distance to Optimal')
plt.semilogy(ts,
equi_distances_avg,
'r',
label='Average Distance to Reference')
plt.semilogy(ts, areas_exact_avg, 'g-', label='Area (exact)')
plt.semilogy(ts, areas_avg, 'm-', label='Area')
plt.semilogy(ts, Fnorms_avg, 'b-', label='Fnorms')
# plt.title('Demonstration of No-Regret on MLN')
plt.xlabel('Time Step')
plt.ylabel('Euclidean Distance')
# plt.legend()
lgd1 = plt.legend(bbox_to_anchor=(1.05, 1), loc=2)
plt.subplot(2, 1, 1)
plt.plot(ts,
regret_standards_avg,
'r--o',
markevery=T // 20,
label=r'regret$_{s}$')
plt.plot(ts, regret_news_avg, 'b-', label=r'regret$_{n}$')
plt.fill_between(ts,
regret_news_avg - stokes,
regret_news_avg + stokes,
facecolor='c',
alpha=0.2,
zorder=5,
label='Stokes Bound')
plt.fill_between(ts,
regret_news_avg - stokes_exact,
regret_news_avg + stokes_exact,
facecolor='c',
alpha=0.2,
zorder=5,
label='Stokes Bound (exact)')
# plt.plot(ts, np.zeros_like(ts), 'w-', lw=1)
# plt.xlabel('Time Step')
plt.ylabel('Aggregate System-Wide Loss')
plt.xlim([0, T])
plt.ylim([-5000, 5000])
# plt.legend(loc='lower right')
lgd2 = plt.legend(bbox_to_anchor=(1.05, 1), loc=2)
plt.title('Demonstration of No-Regret on MLN')
plt.savefig('NoRegret_MLN_new.pdf',
format='pdf',
additional_artists=[lgd1, lgd2],
bbox_inches='tight')
fontsize = 18
plt.figure()
plt.subplot(1, 1, 1)
plt.plot(ts,
regret_standards_avg,
'r--o',
markevery=T // 20,
label=r'regret$_{s}$')
plt.plot(ts, regret_news_avg, 'b-', label=r'regret$_{n}$')
# plt.fill_between(ts, regret_news_avg-stokes, regret_news_avg+stokes,
# facecolor='c', alpha=0.2, zorder=5, label='Stokes Bound')
plt.fill_between(ts,
regret_news_avg - stokes_exact,
regret_news_avg + stokes_exact,
facecolor='c',
alpha=0.2,
zorder=5,
label='Stokes Bound')
plt.plot(ts, np.zeros_like(ts), 'w-', lw=1)
plt.xlabel('Time Step', fontsize=fontsize)
plt.ylabel('Negative Auto-Welfare', fontsize=fontsize)
plt.xlim([0, T])
plt.ylim([0, 5000])
# plt.legend(loc='lower right')
lgd = plt.legend(bbox_to_anchor=(1.05, 1), loc=2, fontsize=fontsize)
plt.title('Demonstration of No-Regret on MLN', fontsize=fontsize)
plt.savefig('NoRegret_MLN_new2.pdf',
format='pdf',
additional_artists=[lgd],
bbox_inches='tight')
plt.figure()
plt.subplot(1, 1, 1)
plt.plot(ts,
-regret_standards_avg,
'r--o',
markevery=T // 20,
label=r'regret$_{2}$')
plt.plot(ts, -regret_news_avg, 'b-', label=r'regret$_{1}$')
# plt.fill_between(ts, regret_news_avg-stokes, regret_news_avg+stokes,
# facecolor='c', alpha=0.2, zorder=5, label='Stokes Bound')
plt.fill_between(ts,
-regret_news_avg - stokes_exact,
-regret_news_avg + stokes_exact,
facecolor='c',
alpha=0.2,
zorder=5,
label='Stokes Bound')
plt.plot(ts, np.zeros_like(ts), 'w-', lw=1)
plt.xlabel('Time Step', fontsize=fontsize)
plt.ylabel('Auto-Welfare Regret', fontsize=fontsize)
plt.xlim([0, T])
plt.ylim([-5000, 0])
# plt.legend(loc='lower right')
lgd = plt.legend(bbox_to_anchor=(1.05, 1), loc=2, fontsize=fontsize)
plt.title('Demonstration of No-Regret on MLN', fontsize=fontsize)
plt.savefig('NoRegret_MLN_new3.pdf',
format='pdf',
additional_artists=[lgd],
bbox_inches='tight')
plt.figure()
plt.subplot(1, 1, 1)
plt.plot(ts, regret_news_avg, 'b-')
# plt.fill_between(ts, regret_news_avg-stokes, regret_news_avg+stokes,
# facecolor='c', alpha=0.2, zorder=5, label='Stokes Bound')
# plt.fill_between(ts, -regret_news_avg-stokes_exact, -regret_news_avg+stokes_exact,
# facecolor='c', alpha=0.2, zorder=5, label='Stokes Bound')
plt.plot(ts, np.zeros_like(ts), 'w-', lw=1)
plt.xlabel('Time Step', fontsize=fontsize)
plt.ylabel('OMO Path Integral Regret', fontsize=fontsize)
plt.xlim([0, T])
plt.ylim([0, 5000])
# plt.legend(loc='lower right')
# lgd = plt.legend(bbox_to_anchor=(1.05, 1), loc=2, fontsize=fontsize)
plt.title('Demonstration of No-Regret on MLN', fontsize=fontsize)
plt.savefig('NoRegret_MLN_new4.pdf', format='pdf', bbox_inches='tight')
sat_exact = np.logical_or(
regret_standards_avg >= regret_news_avg - stokes_exact,
regret_standards_avg <= regret_news_avg + stokes_exact)
sat = np.logical_or(regret_standards_avg >= regret_news_avg - stokes,
regret_standards_avg <= regret_news_avg + stokes)
embed()
def Demo():
#__SERVICE_ORIENTED_INTERNET__##############################################
N = 2 # number of possible maps
T = 100 # number of time steps
eta = .01 # learning rate
# Define Domains and Compute Equilbria
Domains = []
X_Stars = []
CurlBounds = []
# for n in range(N):
n = 0
while len(X_Stars) < N:
# Create Domain
Network = CreateRandomNetwork(m=3,n=2,o=2,seed=n)
Domain = SOI(Network=Network,alpha=2)
# Record Domain
Domains += [Domain]
# Set Method
Method = HeunEuler(Domain=Domain,P=BoxProjection(lo=0),Delta0=1e-3)
# Initialize Starting Point
Start = np.zeros(Domain.Dim)
# Calculate Initial Gap
gap_0 = Domain.gap_rplus(Start)
# Calculate Curl Bound
J = approx_jacobian(Domain.F,Start)
if not np.all(np.linalg.eigvals(J+J.T) >= 0):
pass
_J = approx_jacobian(Domain.F,Start+0.5)
assert np.allclose(J,_J,atol=1e-5)
CurlBounds += [np.sqrt(18)*svds(J,k=1,which='LM',return_singular_vectors=False).item()]
# Set Options
Init = Initialization(Step=-1e-10)
Term = Termination(MaxIter=25000,Tols=[(Domain.gap_rplus,1e-6*gap_0)])
Repo = Reporting(Requests=[Domain.gap_rplus])
Misc = Miscellaneous()
Options = DescentOptions(Init,Term,Repo,Misc)
# Print Stats
PrintSimStats(Domain,Method,Options)
# Start Solver
tic = time.time()
SOI_Results = Solve(Start,Method,Domain,Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options,SOI_Results,Method,toc)
# Record X_Star
X_Star = SOI_Results.TempStorage['Data'][-1]
X_Stars += [X_Star]
n += 1
X_Stars = np.asarray(X_Stars)
# Compute Equilibrium of Average Domain
Domain = AverageDomains(Domains)
# Set Method
Method = HeunEuler_PhaseSpace(Domain=Domain,P=BoxProjection(lo=0),Delta0=1e-3)
# Initialize Starting Point
Start = np.zeros(Domain.Dim)
J = approx_jacobian(Domain.F,Start)
assert np.all(np.linalg.eigvals(J+J.T) >= 0)
# Calculate Initial Gap
gap_0 = Domain.gap_rplus(Start)
# Set Options
Init = Initialization(Step=-1e-10)
Term = Termination(MaxIter=25000,Tols=[(Domain.gap_rplus,1e-10*gap_0)])
Repo = Reporting(Requests=[Domain.gap_rplus])
Misc = Miscellaneous()
Options = DescentOptions(Init,Term,Repo,Misc)
# Print Stats
PrintSimStats(Domain,Method,Options)
# Start Solver
tic = time.time()
SOI_Results = Solve(Start,Method,Domain,Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options,SOI_Results,Method,toc)
# Record X_Opt
X_Opt = SOI_Results.TempStorage['Data'][-1]
# X_Opt = X_Stars[0]
print('Starting Online Learning')
# Set First Prediction
X = np.zeros(X_Stars.shape[1])
# Select First Domain
idx = np.argmax(np.linalg.norm(X_Stars - X,axis=1))
distances = []
loss_infs = []
regret_standards = []
regret_news = []
stokes = []
ts = range(T)
for t in ts:
print('t = '+str(t))
# retrieve domain
Domain = Domains[idx]
# retrieve equilibrium / reference vector
# equi = X_Stars[idx]
equi = np.zeros_like(X_Stars[idx])
# calculate distance
distances += [np.linalg.norm(X_Opt-X)]
# calculate infinity loss
# loss_infs += [infinity_loss(Domain,X)]
# calculate standard regret
ci_predict = ContourIntegral(Domain,LineContour(equi,X))
predict_loss = integral(ci_predict)
ci_opt = ContourIntegral(Domain,LineContour(equi,X_Opt))
predict_opt = integral(ci_opt)
regret_standards += [predict_loss - predict_opt]
# calculate new regret
ci_new = ContourIntegral(Domain,LineContour(X_Opt,X))
regret_news += [integral(ci_new)]
# calculate bound
# area = 0.5*np.prod(np.sort([np.linalg.norm(X_Opt-equi),np.linalg.norm(X-X_Opt),np.linalg.norm(equi-X)])[:2]) # area upper bound
area = herons(X_Opt,X,equi) # exact area
stokes += [CurlBounds[idx]*area]
# update prediction
X = BoxProjection(lo=0).P(X,-eta,Domain.F(X))
# update domain
idx = np.argmax(np.linalg.norm(X_Stars - X,axis=1))
# embed()
ts_p1 = range(1,T+1)
distances_avg = np.divide(np.cumsum(distances),ts_p1)
# loss_infs_avg = np.divide(np.cumsum(loss_infs),ts_p1)
regret_standards_avg = np.divide(np.cumsum(regret_standards),ts_p1)
regret_news_avg = np.divide(np.cumsum(regret_news),ts_p1)
stokes = np.divide(np.cumsum(stokes),ts_p1)
# np.savez_compressed('NoRegret_MLN.npz',d_avg=distances_avg,
# linf_avg=loss_infs_avg,rs_avg=regret_standards_avg,
# rn_avg=regret_news_avg,stokes=stokes)
plt.subplot(2, 1, 2)
plt.plot(ts, distances_avg, 'k',label='Average Distance')
plt.title('Demonstration of No-Regret on MLN')
plt.ylabel('Euclidean Distance')
plt.legend()
plt.subplot(2, 1, 1)
# plt.plot(ts, loss_infs_avg, 'k--', label=r'loss$_{\infty}$')
plt.plot(ts, regret_standards_avg, 'r--o', markevery=T//20,
label=r'regret$_{s}$')
plt.plot(ts, regret_news_avg, 'b-', label=r'regret$_{n}$')
# plt.fill_between(ts, regret_news_avg-stokes, regret_news_avg+stokes,
# facecolor='c', alpha=0.2, zorder=0, label='Stokes Bound')
plt.plot(ts, np.zeros_like(ts), 'w-', lw=1)
plt.xlabel('Time Step')
plt.ylabel('Aggregate System-Wide Loss')
plt.xlim([0,T])
# plt.ylim([-250,1000])
plt.legend()
plt.title('Demonstration of No-Regret on MLN')
plt.savefig('NoRegret_MLN2')
# data = np.load('NoRegret2.npz')
# distances_avg = data['d_avg']
# loss_infs_avg = data['linf_avg']
# regret_standards_avg = data['rs_avg']
# regret_news_avg = data['rn_avg']
# stokes = data['stokes']
# ts = range(len(distances_avg))
embed()
def Demo():
#__BLOOD_BANK__##################################################
#############################################################
# Phase 1 - Left hospital has relatively low demand for blood
#############################################################
# Define Network and Domain
Network = CreateNetworkExample(ex=1)
Domain = BloodBank(Network=Network, alpha=2)
# Set Method
Method = ABEuler(Domain=Domain, P=BoxProjection(lo=0), Delta0=1e-5)
# Initialize Starting Point
Start = np.zeros(Domain.Dim)
# Calculate Initial Gap
gap_0 = Domain.gap_rplus(Start)
# Set Options
Init = Initialization(Step=-1e-10)
Term = Termination(MaxIter=10000, Tols=[(Domain.gap_rplus, 1e-3 * gap_0)])
Repo = Reporting(Requests=[
Domain.gap_rplus, 'Step', 'F Evaluations', 'Projections', 'Data'
])
Misc = Miscellaneous()
Options = DescentOptions(Init, Term, Repo, Misc)
# Print Stats
PrintSimStats(Domain, Method, Options)
# Start Solver
tic = time.time()
BloodBank_Results_Phase1 = Solve(Start, Method, Domain, Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options, BloodBank_Results_Phase1, Method, toc)
#########################################################
# Phase 2 - Left hospital has comparable demand for blood
#########################################################
# Define Network and Domain
Network = CreateNetworkExample(ex=2)
Domain = BloodBank(Network=Network, alpha=2)
# Set Method
Method = ABEuler(Domain=Domain, P=BoxProjection(lo=0), Delta0=1e-5)
# Initialize Starting Point
Start = BloodBank_Results_Phase1.PermStorage['Data'][-1]
# Calculate Initial Gap
gap_0 = Domain.gap_rplus(Start)
# Set Options
Init = Initialization(Step=-1e-10)
Term = Termination(MaxIter=10000, Tols=[(Domain.gap_rplus, 1e-3 * gap_0)])
Repo = Reporting(Requests=[
Domain.gap_rplus, 'Step', 'F Evaluations', 'Projections', 'Data'
])
Misc = Miscellaneous()
Options = DescentOptions(Init, Term, Repo, Misc)
# Print Stats
PrintSimStats(Domain, Method, Options)
# Start Solver
tic = time.time()
BloodBank_Results_Phase2 = Solve(Start, Method, Domain, Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options, BloodBank_Results_Phase2, Method, toc)
########################################################
# Phase 3 - Left hospital has excessive demand for blood
########################################################
# Define Network and Domain
Network = CreateNetworkExample(ex=3)
Domain = BloodBank(Network=Network, alpha=2)
# Set Method
Method = ABEuler(Domain=Domain, P=BoxProjection(lo=0), Delta0=1e-5)
# Initialize Starting Point
Start = BloodBank_Results_Phase2.PermStorage['Data'][-1]
# Calculate Initial Gap
gap_0 = Domain.gap_rplus(Start)
# Set Options
Init = Initialization(Step=-1e-10)
Term = Termination(MaxIter=10000, Tols=[(Domain.gap_rplus, 1e-3 * gap_0)])
Repo = Reporting(Requests=[
Domain.gap_rplus, 'Step', 'F Evaluations', 'Projections', 'Data'
])
Misc = Miscellaneous()
Options = DescentOptions(Init, Term, Repo, Misc)
# Print Stats
PrintSimStats(Domain, Method, Options)
# Start Solver
tic = time.time()
BloodBank_Results_Phase3 = Solve(Start, Method, Domain, Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options, BloodBank_Results_Phase3, Method, toc)
########################################################
# Animate Network
########################################################
# Construct MP4 Writer
fps = 15
FFMpegWriter = animation.writers['ffmpeg']
metadata = dict(title='BloodBank', artist='Matplotlib')
writer = FFMpegWriter(fps=fps, metadata=metadata)
# Collect Frames
frame_skip = 5
freeze = 5
Dyn_1 = BloodBank_Results_Phase1.PermStorage['Data']
Frz_1 = [Dyn_1[-1]] * fps * frame_skip * freeze
Dyn_2 = BloodBank_Results_Phase2.PermStorage['Data']
Frz_2 = [Dyn_2[-1]] * fps * frame_skip * freeze
Dyn_3 = BloodBank_Results_Phase3.PermStorage['Data']
Frz_3 = [Dyn_3[-1]] * fps * frame_skip * freeze
Frames = np.concatenate((Dyn_1, Frz_1, Dyn_2, Frz_2, Dyn_3, Frz_3),
axis=0)[::frame_skip]
# Normalize Colormap by Flow at each Network Level
Domain.FlowNormalizeColormap(Frames, cm.Reds)
# Mark Annotations
t1 = 0
t2 = t1 + len(BloodBank_Results_Phase1.PermStorage['Data']) // frame_skip
t3 = t2 + fps * freeze
t4 = t3 + len(BloodBank_Results_Phase2.PermStorage['Data']) // frame_skip
t5 = t4 + fps * freeze
t6 = t5 + len(BloodBank_Results_Phase3.PermStorage['Data']) // frame_skip
Dyn_1_ann = '$Demand_{1}$ $<$ $Demand_{2}$ & $Demand_{3}$\n(Equilibrating)'
Frz_1_ann = '$Demand_{1}$ $<$ $Demand_{2}$ & $Demand_{3}$\n(Converged)'
Dyn_2_ann = '$Demand_{1}$ ~= $Demand_{2}$ & $Demand_{3}$\n(Equilibrating)'
Frz_2_ann = '$Demand_{1}$ ~= $Demand_{2}$ & $Demand_{3}$\n(Converged)'
Dyn_3_ann = '$Demand_{1}$ $>$ $Demand_{2}$ & $Demand_{3}$\n(Equilibrating)'
Frz_3_ann = '$Demand_{1}$ $>$ $Demand_{2}$ & $Demand_{3}$\n(Converged)'
anns = sorted([(t1, plt.title, Dyn_1_ann), (t2, plt.title, Frz_1_ann),
(t3, plt.title, Dyn_2_ann), (t4, plt.title, Frz_2_ann),
(t5, plt.title, Dyn_3_ann), (t6, plt.title, Frz_3_ann)],
key=lambda x: x[0],
reverse=True)
# Save Animation to File
fig, ax = plt.subplots()
BloodBank_ani = animation.FuncAnimation(fig,
Domain.UpdateVisual,
init_func=Domain.InitVisual,
frames=len(Frames),
fargs=(ax, Frames, anns),
blit=True)
BloodBank_ani.save('BloodBank.mp4', writer=writer)
def Demo():
#__SERVICE_ORIENTED_INTERNET__##############################################
N = 10 # number of possible maps
T = 1000 # number of time steps
eta = 1e-3 # learning rate
print('Creating Domains')
# Define Domains and Compute Equilbria
Domains = []
X_Stars = []
CurlBounds = []
n = 0
while len(Domains) < N:
# Create Domain
Network = CreateRandomNetwork(m=3, n=2, o=2, seed=None)
Domain = SOI(Network=Network, alpha=2)
# Initialize Starting Point
Start = np.zeros(Domain.Dim)
# Assert PD
J = approx_jacobian(Domain.F, Start)
eigs = np.linalg.eigvals(J + J.T)
eigs_i = np.abs(np.linalg.eigvals(J - J.T))
if not np.all(eigs > 0):
continue
print(eigs.min(), eigs.max())
print(eigs_i.min(), eigs_i.max())
_J = approx_jacobian(Domain.F, Start + 0.5)
assert np.allclose(J, _J,
atol=1e-5) # assert J is constant (unique for SOI)
# Record Domain
Domains += [Domain]
# Calculate Initial Gap
gap_0 = Domain.gap_rplus(Start)
# Calculate Curl Bound
CurlBounds += [
np.sqrt(18) *
svds(J, k=1, which='LM', return_singular_vectors=False).item()
]
# Set Method
Method = HeunEuler(Domain=Domain, P=BoxProjection(lo=0), Delta0=1e-3)
# Set Options
Init = Initialization(Step=-1e-10)
Term = Termination(MaxIter=25000,
Tols=[(Domain.gap_rplus, 1e-6 * gap_0)])
Repo = Reporting(Requests=[Domain.gap_rplus])
Misc = Miscellaneous()
Options = DescentOptions(Init, Term, Repo, Misc)
# Print Stats
PrintSimStats(Domain, Method, Options)
# Start Solver
tic = time.time()
SOI_Results = Solve(Start, Method, Domain, Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options, SOI_Results, Method, toc)
# Record X_Star
X_Star = SOI_Results.TempStorage['Data'][-1]
X_Stars += [X_Star]
n += 1
X_Stars = np.asarray(X_Stars)
print('Starting Online Learning')
# Set First Prediction
X = np.zeros(X_Stars.shape[1])
# X = np.mean(X_Stars,axis=0)
# X += np.random.rand(*X.shape)*np.linalg.norm(X)
# Select First Domain
# idx = np.argmax(np.linalg.norm(X_Stars - X,axis=1))
idx = np.random.choice(len(Domains))
# Domain Sequence
idx_seq = []
X_seq = []
F_seq = []
ts = range(T)
for t in ts:
print('t = ' + str(t), end='\r')
# record prediction
X_seq += [X]
# record domain
idx_seq += [idx]
# retrieve domain
Domain = Domains[idx]
# record F
FX = Domain.F(X)
F_seq += [FX]
# update prediction
X = BoxProjection(lo=0).P(X, -eta, FX)
# update domain
# idx = np.argmax(np.linalg.norm(X_Stars - X,axis=1))
idx = np.random.choice(len(Domains))
L = np.sqrt(np.mean(np.linalg.norm(F_seq, axis=1)**2.))
print('Computing Optimal Strategy')
weights = np.bincount(idx_seq, minlength=len(Domains)) / len(idx_seq)
print(weights)
# Compute Equilibrium of Average Domain
Domain = AverageDomains(Domains, weights=weights)
# Set Method
Method = HeunEuler_PhaseSpace(Domain=Domain,
P=BoxProjection(lo=0),
Delta0=1e-5)
# Initialize Starting Point
Start = np.zeros(Domain.Dim)
# Assert PSD - sum of PSD is PSD doesn't hurt to check
J = approx_jacobian(Domain.F, Start)
eigs = np.linalg.eigvals(J + J.T)
eigs_i = np.abs(np.linalg.eigvals(J - J.T))
assert np.all(eigs > 0)
print(eigs.min(), eigs.max())
print(eigs_i.min(), eigs_i.max())
# Calculate Initial Gap
gap_0 = Domain.gap_rplus(Start)
# Set Options
Init = Initialization(Step=-1e-10)
Term = Termination(MaxIter=25000, Tols=[(Domain.gap_rplus, 1e-10 * gap_0)])
Repo = Reporting(Requests=[Domain.gap_rplus])
Misc = Miscellaneous()
Options = DescentOptions(Init, Term, Repo, Misc)
# Print Stats
PrintSimStats(Domain, Method, Options)
# Start Solver
tic = time.time()
SOI_Results = Solve(Start, Method, Domain, Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options, SOI_Results, Method, toc)
print('Computing Regrets')
# Record X_Opt
X_Opt = SOI_Results.TempStorage['Data'][-1]
# X_Opt = X_Stars[0]
B = np.linalg.norm(X_Opt)
eta_opt = B / (L * np.sqrt(2 * T))
bound_opt = B * L * np.sqrt(2 * T)
reg_bound = (B**2) / (2 * eta) + eta * T * L**2
distances = []
loss_infs = []
regret_standards = []
regret_news = []
stokes = []
ts = range(T)
for t in ts:
print('t = ' + str(t), end='\r')
idx = idx_seq[t]
X = X_seq[t]
# retrieve domain
Domain = Domains[idx]
# retrieve equilibrium / reference vector
equi = X_Stars[idx]
# equi = np.zeros_like(X_Stars[idx])
# calculate distance
distances += [np.linalg.norm(X_Opt - X)]
# calculate infinity loss
# loss_infs += [infinity_loss(Domain,X)]
# calculate standard regret
ci_predict = ContourIntegral(Domain, LineContour(equi, X))
predict_loss = integral(ci_predict)
ci_opt = ContourIntegral(Domain, LineContour(equi, X_Opt))
predict_opt = integral(ci_opt)
regret_standards += [predict_loss - predict_opt]
# calculate new regret
ci_new = ContourIntegral(Domain, LineContour(X_Opt, X))
regret_news += [integral(ci_new)]
# calculate bound
# area = 0.5*np.prod(np.sort([np.linalg.norm(X_Opt-equi),np.linalg.norm(X-X_Opt),np.linalg.norm(equi-X)])[:2]) # area upper bound
area = herons(X_Opt, X, equi) # exact area
stokes += [CurlBounds[idx] * area]
# # update prediction
# X = BoxProjection(lo=0).P(X,-eta,Domain.F(X))
# # update domain
# idx = np.argmax(np.linalg.norm(X_Stars - X,axis=1))
# embed()
ts_p1 = range(1, T + 1)
distances_avg = np.divide(np.cumsum(distances), ts_p1)
# loss_infs_avg = np.divide(np.cumsum(loss_infs),ts_p1)
regret_standards_avg = np.divide(np.cumsum(regret_standards), ts_p1)
regret_news_avg = np.divide(np.cumsum(regret_news), ts_p1)
stokes = np.divide(np.cumsum(stokes), ts_p1)
# np.savez_compressed('NoRegret_MLN2c.npz',d_avg=distances_avg,
# linf_avg=loss_infs_avg,rs_avg=regret_standards_avg,
# rn_avg=regret_news_avg,stokes=stokes)
plt.subplot(2, 1, 2)
plt.plot(ts, distances_avg, 'k', label='Average Distance')
# plt.title('Demonstration of No-Regret on MLN')
plt.xlabel('Time Step')
plt.ylabel('Euclidean Distance')
plt.legend()
plt.subplot(2, 1, 1)
# plt.plot(ts, loss_infs_avg, 'k--', label=r'loss$_{\infty}$')
plt.plot(ts,
regret_standards_avg,
'r--o',
markevery=T // 20,
label=r'regret$_{s}$')
plt.plot(ts, regret_news_avg, 'b-', label=r'regret$_{n}$')
# plt.fill_between(ts, regret_news_avg-stokes, regret_news_avg+stokes,
# facecolor='c', alpha=0.2, zorder=0, label='Stokes Bound')
plt.plot(ts, np.zeros_like(ts), 'w-', lw=1)
# plt.xlabel('Time Step')
plt.ylabel('Aggregate System-Wide Loss')
plt.xlim([0, T])
# plt.ylim([-200,200])
plt.legend(loc='lower right')
plt.title('Demonstration of No-Regret on MLN')
plt.savefig('NoRegret_MLN2c')
# data = np.load('NoRegret2.npz')
# distances_avg = data['d_avg']
# loss_infs_avg = data['linf_avg']
# regret_standards_avg = data['rs_avg']
# regret_news_avg = data['rn_avg']
# stokes = data['stokes']
# ts = range(len(distances_avg))
embed()
def Demo():
#__LQ_GAN__##############################################
# Interpolation between F and RipCurl should probably be nonlinear
# in terms of L2 norms of matrices if the norms essentially represent the largest eigenvalues
# what's an example of a pseudomonotone field? stretch vertically linearly a bit? quasimonotone?
# the extragradient method uses the same step size for the first and second step, as the step size goes
# to zero, extragradient asymptotes to the projection method
# modified extragradient methods use different step sizes. if we keep the first step size fixed to some
# positive value and shrink the second, the dynamics of extragradient remain as desired
# this is essentially what HE_PhaseSpace is showing
# HE and HE_PhaseSpace are designed to "simulate" a trajectory - they do not actually change the effective
# dynamics of the vector field
# Define Network and Domain
Domain = LQ(sig=1)
# Set Method
lo = [-np.inf, 1e-2]
# Method = Euler(Domain=Domain,FixStep=True,P=BoxProjection(lo=lo))
# Method = EG(Domain=Domain,FixStep=True,P=BoxProjection(lo=lo))
# Method = HeunEuler(Domain=Domain,Delta0=1e-4,P=BoxProjection(lo=lo))
Method = HeunEuler_PhaseSpace(Domain=Domain,
Delta0=1e-2,
P=BoxProjection(lo=lo))
# Initialize Starting Point
# Start = np.random.rand(Domain.Dim)
scale = 30
Start = np.array([50., 50.])
xoff = 0
yoff = 0
# no difference between eigenvalues of J at [1.,3.5] and eigenvalues of an outward spiral: a = np.array([[-1,6.92],[-6.92,-1]])
j = Domain.J(Start)
print('original evs')
print(np.linalg.eigvals(j))
print(np.linalg.eigvals(j + j.T))
f = Domain.F(Start)
jsym = j + j.T
# print(f.dot(jsym.dot(f)))
tf = Domain.TF(Start)
print('tf')
print(tf)
print(np.linalg.eigvals(tf))
jrc = Domain.JRipCurl(Start)
print('jrc')
print(jrc)
print(0.5 * (jrc + jrc.T))
print(np.linalg.eigvals(jrc + jrc.T))
jreg = Domain.JReg(Start)
print('jreg')
print(jreg)
print(0.5 * (jreg + jreg.T))
print(np.linalg.eigvals(jreg + jreg.T))
jasy = j - j.T
print('exact')
print(0.5 * np.dot(jasy.T, jasy))
for gam in np.linspace(0, 1, 20):
# print(Domain.JRegEV(Start,gam))
print(Domain.JRCEV(Start, gam))
jap = approx_jacobian(Domain.F, Start)
print(jap)
print(np.linalg.eigvals(0.5 * (jap + jap.T)))
y = np.array([0, 1])
x = np.array([1, 1e-1])
pre = np.dot(Domain.F(y), x - y)
post = np.dot(Domain.F(x), x - y)
print(pre)
print(post)
d = 2
W2 = Domain.sym(np.random.rand(d, d))
w1 = np.random.rand(d)
A = np.tril(np.random.rand(d, d))
A[range(d), range(d)] = np.clip(A[range(d), range(d)], 1e-6, np.inf)
b = np.random.rand(d)
dmult = np.hstack([W2.flatten(), w1, A.flatten(), b])
jmult = Domain.Jmult(dmult)
jskew = (jmult - jmult.T)
print(np.linalg.matrix_rank(jskew, tol=1e-16))
W2 = Domain.sym(np.ones((d, d)))
w1 = np.ones(d)
A = np.tril(np.ones((d, d)))
A[range(d), range(d)] = np.clip(A[range(d), range(d)], 0, np.inf)
b = np.ones(d)
dmult = np.hstack([W2.flatten(), w1, A.flatten(), b])
jmult = Domain.Jmult(dmult)
jskew = (jmult - jmult.T)
print(np.linalg.matrix_rank(jskew))
W2 = Domain.sym(np.zeros((d, d)))
w1 = np.zeros(d)
A = np.tril(np.ones((d, d)))
A[range(d), range(d)] = np.clip(A[range(d), range(d)], 0, np.inf)
b = np.zeros(d)
dmult = np.hstack([W2.flatten(), w1, A.flatten(), b])
jmult = Domain.Jmult(dmult)
jskew = (jmult - jmult.T)
print(np.linalg.matrix_rank(jskew))
np.set_printoptions(linewidth=200)
s = (d**2 + d) // 2
jskewblock = jskew[:s, s + d:s + d + s]
embed()
# Set Options
Init = Initialization(Step=-1e-5)
Term = Termination(MaxIter=1000, Tols=[(Domain.dist, 1e-4)])
Repo = Reporting(
Requests=['Step', 'F Evaluations', 'Projections', 'Data', Domain.dist])
Misc = Miscellaneous()
Options = DescentOptions(Init, Term, Repo, Misc)
# Print Stats
PrintSimStats(Domain, Method, Options)
# Start Solver
tic = time.time()
LQ_Results = Solve(Start, Method, Domain, Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options, LQ_Results, Method, toc)
data = np.array(LQ_Results.PermStorage['Data'])
X, Y = np.meshgrid(
np.arange(-2 * scale + xoff, 2 * scale + xoff, .2 * scale),
np.arange(1e-2 + yoff, 4 * scale + yoff, .2 * scale))
U = np.zeros_like(X)
V = np.zeros_like(Y)
for i in range(X.shape[0]):
for j in range(X.shape[1]):
vec = -Domain.F([X[i, j], Y[i, j]])
U[i, j] = vec[0]
V[i, j] = vec[1]
fig = plt.figure()
ax = fig.add_subplot(111)
Q = plt.quiver(X[::3, ::3],
Y[::3, ::3],
U[::3, ::3],
V[::3, ::3],
pivot='mid',
units='inches')
ax.plot(data[:, 0], data[:, 1], '-r')
ax.plot([data[0, 0]], [data[0, 1]], 'k*')
ax.plot([data[-1, 0]], [data[-1, 1]], 'b*')
ax.set_xlim([-2 * scale + xoff, 2 * scale + xoff])
ax.set_ylim([-.1 * scale + yoff, 4 * scale + yoff])
ax.set_xlabel('x')
ax.set_ylabel('y')
# plt.show()
# plt.savefig('original.png')
# plt.savefig('EGoriginal.png')
# plt.savefig('RipCurl.png')
# plt.savefig('RipCurl2.png')
# plt.savefig('EG.png')
# plt.savefig('GReg.png')
plt.savefig('Testing.png')
def Demo():
#__SPHERE__##################################################
# Define Dimension and Domain
Domain = Sphere(Dim=100)
# Set Method
Method = HeunEuler(Domain=Domain, P=IdentityProjection(), Delta0=1e-2)
# Set Options
Init = Initialization(Step=-1e-1)
Term = Termination(MaxIter=1000, Tols=[[Domain.f_Error, 1e-3]])
Repo = Reporting(Requests=[Domain.f_Error])
Misc = Miscellaneous()
Options = DescentOptions(Init, Term, Repo, Misc)
# Initialize Starting Point
Start = 100 * np.ones(Domain.Dim)
# Print Stats
PrintSimStats(Domain, Method, Options)
# Start Solver
tic = time.time()
SPHERE_Results = Solve(Start, Method, Domain, Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options, SPHERE_Results, Method, toc)
#__KOJIMA-SHINDO__##################################################
# Define Dimension and Domain
Domain = KojimaShindo()
# Set Method
Method = HeunEuler(Domain=Domain, P=EntropicProjection(), Delta0=1e-1)
# Set Options
Init = Initialization(Step=-1e-1)
Term = Termination(MaxIter=1000, Tols=[[Domain.gap_simplex, 1e-3]])
Repo = Reporting(Requests=[Domain.gap_simplex])
Misc = Miscellaneous()
Options = DescentOptions(Init, Term, Repo, Misc)
# Initialize Starting Point
Start = np.ones(Domain.Dim) / np.double(Domain.Dim)
# Print Stats
PrintSimStats(Domain, Method, Options)
# Start Solver
tic = time.time()
KS_Results = Solve(Start, Method, Domain, Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options, KS_Results, Method, toc)
#__WATSON__##################################################
trials = xrange(10)
WAT_Results = [[] for i in trials]
for p in trials:
#Define Dimension and Domain
Domain = Watson(Pos=p)
# Set Method
Method = HeunEuler(Domain=Domain, P=EntropicProjection(), Delta0=1e-1)
# Set Options
Init = Initialization(Step=-1e-1)
Term = Termination(MaxIter=1000, Tols=[[Domain.gap_simplex, 1e-3]])
Repo = Reporting(Requests=[Domain.gap_simplex])
Misc = Miscellaneous()
Options = DescentOptions(Init, Term, Repo, Misc)
#Initialize Starting Point
Start = np.ones(Domain.Dim) / np.double(Domain.Dim)
# Print Stats
PrintSimStats(Domain, Method, Options)
tic = time.time()
WAT_Results[p] = Solve(Start, Method, Domain, Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options, WAT_Results[p], Method, toc)
#__SUN__##################################################
trials = xrange(8000, 10000 + 1, 2000)
Sun_Results = [[] for i in trials]
for n in trials:
#Define Dimension and Domain
Domain = Sun(Dim=n)
# Set Method
Method = HeunEuler(Domain=Domain, P=EntropicProjection(), Delta0=1e-1)
# Set Options
Init = Initialization(Step=-1e-1)
Term = Termination(MaxIter=1000, Tols=[[Domain.gap_simplex, 1e-3]])
Repo = Reporting(Requests=[Domain.gap_simplex])
Misc = Miscellaneous()
Options = DescentOptions(Init, Term, Repo, Misc)
#Initialize Starting Point
Start = np.ones(Domain.Dim) / np.double(Domain.Dim)
# Print Stats
PrintSimStats(Domain, Method, Options)
tic = time.time()
ind = n / 2000 - 4
Sun_Results[ind] = Solve(Start, Method, Domain, Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options, Sun_Results[ind], Method, toc)
def Demo():
# __PENN_TREE_BANK____#################################################
# Load Data
# seq = np.arange(1000)
train, valid, test, id_to_word, vocab = ptb_raw_data(
'/Users/imgemp/Desktop/Data/simple-examples/data/')
words, given_embeddings = pickle.load(open(
'/Users/imgemp/Desktop/Data/polyglot-en.pkl', 'rb'),
encoding='latin1')
words_low = [word.lower() for word in words]
word_to_id = dict(zip(words_low, range(len(words))))
word_to_id['<eos>'] = word_to_id['</s>']
y0 = get_y0(train, vocab)
EDim = 5
fix_embedding = False
learn_embedding = True
if fix_embedding:
EDim = given_embeddings.shape[1]
learn_embedding = False
# Define Domain
Domain = PennTreeBank(seq=train,
y0=None,
EDim=EDim,
batch_size=100,
learn_embedding=learn_embedding,
ord=1)
# Set Method
P = PTBProj(Domain.EDim)
# Method = Euler(Domain=Domain,FixStep=True,P=P)
Method = HeunEuler(Domain=Domain,
P=P,
Delta0=1e-4,
MinStep=-3.,
MaxStep=0.)
# Method = CashKarp(Domain=Domain,P=P,Delta0=1e-1,MinStep=-5.,MaxStep=0.)
# Set Options
Term = Termination(MaxIter=10000)
Repo = Reporting(
Interval=10,
Requests=[Domain.Error, Domain.PercCorrect, Domain.Perplexity,
'Step']) #,
# 'Step', 'F Evaluations',
# 'Projections','Data'])
Misc = Miscellaneous()
Init = Initialization(Step=-1e-3)
Options = DescentOptions(Init, Term, Repo, Misc)
# Initialize Starting Point
if fix_embedding:
missed = 0
params = np.random.rand(Domain.param_len)
avg_norm = np.linalg.norm(given_embeddings, axis=1).mean()
embeddings = []
for i in range(vocab):
word = id_to_word[i]
if word in word_to_id:
embedding = given_embeddings[word_to_id[word]]
else:
missed += 1
embedding = np.random.rand(Domain.EDim)
embedding *= avg_norm / np.linalg.norm(embedding)
embeddings += [embedding]
polyglot_embeddings = np.hstack(embeddings)
Start = np.hstack((params, polyglot_embeddings))
print(np.linalg.norm(polyglot_embeddings))
print(
'Missing %d matches in polyglot dictionary -> given random embeddings.'
% missed)
else:
# params = np.random.rand(Domain.param_len)*10
# embeddings = np.random.rand(EDim*vocab)*.1
# Start = np.hstack((params,embeddings))
# assert Start.shape[0] == Domain.Dim
Start = np.random.rand(Domain.Dim)
Start = P.P(Start)
# Compute Initial Error
print('Initial training error: %g' % Domain.Error(Start))
print('Initial perplexity: %g' % Domain.Perplexity(Start))
print('Initial percent correct: %g' % Domain.PercCorrect(Start))
# Print Stats
PrintSimStats(Domain, Method, Options)
# Start Solver
tic = time.time()
PTB_Results = Solve(Start, Method, Domain, Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options, PTB_Results, Method, toc)
# Plot Results
err = np.asarray(PTB_Results.PermStorage[Domain.Error])
pc = np.asarray(PTB_Results.PermStorage[Domain.PercCorrect])
perp = np.asarray(PTB_Results.PermStorage[Domain.Perplexity])
steps = np.asarray(PTB_Results.PermStorage['Step'])
t = np.arange(0, len(steps) * Repo.Interval, Repo.Interval)
fig = plt.figure()
ax = fig.add_subplot(411)
ax.semilogy(t, err)
ax.set_ylabel('Training Error')
ax.set_title('Penn Tree Bank Training Evaluation')
ax = fig.add_subplot(412)
ax.semilogy(t, perp)
ax.set_ylabel('Perplexity')
ax = fig.add_subplot(413)
ax.plot(t, pc)
ax.set_ylabel('Percent Correct')
ax = fig.add_subplot(414)
ax.plot(t, steps)
ax.set_ylabel('Step Size')
ax.set_xlabel('Iterations (k)')
plt.savefig('PTB')
params_embeddings = np.asarray(PTB_Results.TempStorage['Data']).squeeze()
params, embeddings = np.split(params_embeddings, [Domain.param_len])
embeddings_split = np.split(embeddings, vocab)
dists_comp = pdist(np.asarray(embeddings_split))
dists_min = np.min(dists_comp)
dists_max = np.max(dists_comp)
dists = squareform(dists_comp)
dists2 = np.asarray([np.linalg.norm(e) for e in embeddings_split])
print('pairwise dists', np.mean(dists), dists_min, dists_max)
print('embedding norms', np.mean(dists2), np.min(dists2), np.max(dists2))
print('params', np.mean(params), np.min(np.abs(params)),
np.max(np.abs(params)))
def Demo():
# __KACZMARZ__###############################################################
# Define Domain
Domain = NewDomain(F=lambda x: 0, Dim=5)
# Define Hyperplanes
dim = max(Domain.Dim - 1, 1)
N = 3
hyps = [np.random.rand(Domain.Dim, dim) for n in xrange(N)]
# Set Method
P_random = HyperplaneProjection(hyperplanes=hyps, sequence='random')
Method = Euler(Domain=Domain, FixStep=True, P=P_random)
# Initialize Starting Point
Start = np.ones(Domain.Dim)
# Set Options
Init = Initialization(Step=0.)
Term = Termination(MaxIter=50)
Repo = Reporting(Requests=['Step', 'Data'])
Misc = Miscellaneous()
Options = DescentOptions(Init, Term, Repo, Misc)
# Print Stats
PrintSimStats(Domain, Method, Options)
# Start Solver
tic = time.time()
Results = Solve(Start, Method, Domain, Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options, Results, Method, toc)
data_random = Results.PermStorage['Data']
# Set Method
P_cyclic = HyperplaneProjection(hyperplanes=hyps, sequence='cyclic')
Method = Euler(Domain=Domain, FixStep=True, P=P_cyclic)
# Print Stats
PrintSimStats(Domain, Method, Options)
# Start Solver
tic = time.time()
Results = Solve(Start, Method, Domain, Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options, Results, Method, toc)
data_cyclic = Results.PermStorage['Data']
# Set Method
P_distal = HyperplaneProjection(hyperplanes=hyps, sequence='distal')
Method = Euler(Domain=Domain, FixStep=True, P=P_distal)
# Print Stats
PrintSimStats(Domain, Method, Options)
# Start Solver
tic = time.time()
Results = Solve(Start, Method, Domain, Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options, Results, Method, toc)
data_distal = Results.PermStorage['Data']
# diff_norm_random = np.linalg.norm(np.diff(data_random),axis=1)
# diff_norm_cyclic = np.linalg.norm(np.diff(data_cyclic),axis=1)
# diff_norm_distal = np.linalg.norm(np.diff(data_distal),axis=1)\
# plt.plot(diff_norm_random,label='random')
# plt.plot(diff_norm_cyclic,label='cyclic')
# plt.plot(diff_norm_distal,label='distal')
er = [
np.linalg.norm(P_random.errors(d), axis=1).max() for d in data_random
]
ec = [
np.linalg.norm(P_cyclic.errors(d), axis=1).max() for d in data_cyclic
]
ed = [
np.linalg.norm(P_distal.errors(d), axis=1).max() for d in data_distal
]
plt.plot(er, label='random')
plt.plot(ec, label='cyclic')
plt.plot(ed, label='distal')
plt.legend()
plt.title('Kaczmarz Algorithm')
plt.xlabel('Iterations')
plt.ylabel('Maximum distance from any hyperplane')
plt.show()
def Demo():
#__SUPPLY_CHAIN__##################################################
#############################################################
# Example 1 from Nagurney's Paper
#############################################################
# Define Network and Domain
Network = CreateNetworkExample(ex=1)
Domain = SupplyChain(Network=Network, alpha=2)
# Set Method
Method = ABEuler(Domain=Domain, P=BoxProjection(lo=0), Delta0=1e-2)
# Initialize Starting Point
x = 10 * np.ones(np.product(Domain.x_shape))
gam = np.ones(np.sum([np.product(g) for g in Domain.gam_shapes]))
lam = np.zeros(np.sum([np.product(l) for l in Domain.lam_shapes]))
Start = np.concatenate((x, gam, lam))
# Calculate Initial Gap
gap_0 = Domain.gap_rplus(Start)
# Set Options
Init = Initialization(Step=-1e-10)
Term = Termination(MaxIter=25000, Tols=[(Domain.gap_rplus, 1e-3 * gap_0)])
Repo = Reporting(Requests=[
Domain.gap_rplus, 'Step', 'F Evaluations', 'Projections', 'Data'
])
Misc = Miscellaneous()
Options = DescentOptions(Init, Term, Repo, Misc)
# Print Stats
PrintSimStats(Domain, Method, Options)
# Start Solver
tic = time.time()
SupplyChain_Results_Phase1 = Solve(Start, Method, Domain, Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options, SupplyChain_Results_Phase1, Method, toc)
#############################################################
# Increased Demand of Firm 2's Product
#############################################################
# Define Network and Domain
Network = CreateNetworkExample(ex=2)
Domain = SupplyChain(Network=Network, alpha=2)
# Set Method
Method = ABEuler(Domain=Domain, P=BoxProjection(lo=0), Delta0=1e-2)
# Initialize Starting Point
Start = SupplyChain_Results_Phase1.PermStorage['Data'][-1]
# Calculate Initial Gap
gap_0 = Domain.gap_rplus(Start)
# Set Options
Init = Initialization(Step=-1e-10)
Term = Termination(MaxIter=25000, Tols=[(Domain.gap_rplus, 1e-3 * gap_0)])
Repo = Reporting(Requests=[
Domain.gap_rplus, 'Step', 'F Evaluations', 'Projections', 'Data'
])
Misc = Miscellaneous()
Options = DescentOptions(Init, Term, Repo, Misc)
# Print Stats
PrintSimStats(Domain, Method, Options)
# Start Solver
tic = time.time()
SupplyChain_Results_Phase2 = Solve(Start, Method, Domain, Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options, SupplyChain_Results_Phase2, Method, toc)
########################################################
# Animate Network
########################################################
# Construct MP4 Writer
fps = 15
FFMpegWriter = animation.writers['ffmpeg']
metadata = dict(title='SupplyChain', artist='Matplotlib')
writer = FFMpegWriter(fps=fps, metadata=metadata)
# Collect Frames
frame_skip = 5
freeze = 5
Dyn_1 = SupplyChain_Results_Phase1.PermStorage['Data']
Frz_1 = [Dyn_1[-1]] * fps * frame_skip * freeze
Dyn_2 = SupplyChain_Results_Phase2.PermStorage['Data']
Frz_2 = [Dyn_2[-1]] * fps * frame_skip * freeze
Frames = np.concatenate((Dyn_1, Frz_1, Dyn_2, Frz_2), axis=0)[::frame_skip]
# Normalize Colormap by Flow at each Network Level
Domain.FlowNormalizeColormap(Frames, cm.rainbow)
# Mark Annotations
t1 = 0
t2 = t1 + len(SupplyChain_Results_Phase1.PermStorage['Data']) // frame_skip
t3 = t2 + fps * freeze
t4 = t3 + len(SupplyChain_Results_Phase2.PermStorage['Data']) // frame_skip
Dyn_1_ann = 'Control Network\n(Equilibrating)'
Frz_1_ann = 'Control Network\n(Converged)'
Dyn_2_ann = 'Market Increases Demand for Firm 2' 's Product\n(Equilibrating)'
Frz_2_ann = 'Market Increases Demand for Firm 2' 's Product\n(Converged)'
anns = sorted([(t1, plt.title, Dyn_1_ann), (t2, plt.title, Frz_1_ann),
(t3, plt.title, Dyn_2_ann), (t4, plt.title, Frz_2_ann)],
key=lambda x: x[0],
reverse=True)
# Save Animation to File
fig, ax = plt.subplots()
SupplyChain_ani = animation.FuncAnimation(fig,
Domain.UpdateVisual,
init_func=Domain.InitVisual,
frames=len(Frames),
fargs=(ax, Frames, anns),
blit=True)
SupplyChain_ani.save('Videos/SupplyChain.mp4', writer=writer)
def Demo_1dLQGAN(root='figures/'):
##############################################################################
# Compre Trajectories Plot ###################################################
##############################################################################
# Define Network and Domain
dim = 1
s = (dim**2+dim)//2
mu = np.array([0])
sig = np.array([[1]])
np.set_printoptions(linewidth=200)
# Set Constraints
loA = -np.inf*np.ones((dim,dim))
loA[range(dim),range(dim)] = 1e-2
lo = np.hstack(([-np.inf]*(dim+s), loA[np.tril_indices(dim)], [-np.inf]*dim))
P = BoxProjection(lo=lo)
xoff = 0
yoff = 0
scale = 30
datas = []
dists = []
methods = ['Fcc','Fsim','Feg','Fcon','Freg','EG','Falt','Funr']
for method in methods:
if method == 'EG':
Step = -1e-2
Iters = 10000
Domain = LQGAN(mu=mu,sig=sig,preconditioner='Fsim')
Method = EG(Domain=Domain,FixStep=True,P=P)
elif method == 'Fsim':
Step = -1e-3
Iters = 100000
Domain = LQGAN(mu=mu,sig=sig,preconditioner='Fsim')
Method = Euler(Domain=Domain,FixStep=True,P=P)
# Method = HeunEuler_PhaseSpace(Domain=Domain,Delta0=1e-5,MinStep=-1.,P=P)
elif method == 'Fcon':
Step = -1e-6
# Iters = 2750
Iters = 3000
Domain = LQGAN(mu=mu,sig=sig,preconditioner=method)
Method = HeunEuler_PhaseSpace(Domain=Domain,Delta0=1e-5,P=P)
elif method == 'Falt' or method == 'Funr':
Step = -5e-3
# Iters = 2750
Iters = 10000
Domain = LQGAN(mu=mu,sig=sig,preconditioner=method)
# Method = HeunEuler_PhaseSpace(Domain=Domain,Delta0=1e-5,P=P)
Method = Euler(Domain=Domain,FixStep=True,P=P)
else:
Step = -1e-5
Iters = 10000
Domain = LQGAN(mu=mu,sig=sig,preconditioner=method)
Method = HeunEuler_PhaseSpace(Domain=Domain,Delta0=1e-5,P=P)
# Initialize Starting Point
Start = np.array([50.,0.,30.,0.])
# Set Options
Init = Initialization(Step=Step)
Term = Termination(MaxIter=Iters,Tols=[(Domain.dist_Euclidean,1e-4)])
Repo = Reporting(Requests=['Step', 'F Evaluations',
'Projections','Data',Domain.dist_Euclidean])
Misc = Miscellaneous()
Options = DescentOptions(Init,Term,Repo,Misc)
# Print Stats
PrintSimStats(Domain,Method,Options)
# Start Solver
tic = time.time()
LQ_Results = Solve(Start,Method,Domain,Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options,LQ_Results,Method,toc)
datas += [np.array(LQ_Results.PermStorage['Data'])]
dists += [np.array(LQ_Results.PermStorage[Domain.dist_Euclidean])]
X, Y = np.meshgrid(np.linspace(-2*scale + xoff, 2*scale + xoff, 21), np.arange(1e-2 + yoff, 4*scale + yoff, .2*scale))
U = np.zeros_like(X)
V = np.zeros_like(Y)
for i in range(X.shape[0]):
for j in range(X.shape[1]):
vec = -Domain._F(np.array([X[i,j],0.,Y[i,j],0.]))
U[i,j] = vec[0]
V[i,j] = vec[2]
fs = 18
fig = plt.figure()
ax = fig.add_subplot(111)
Q = plt.quiver(X[::3, ::3], Y[::3, ::3], U[::3, ::3], V[::3, ::3],
pivot='mid', units='inches')
colors = ['r','c','b','k','g','m','gray','orange']
methods = [r'$F_{cc}$',r'$F$',r'$F_{eg}$',r'$F_{con}$',r'$F_{reg}$',r'$EG$',r'$F_{alt}$',r'$F_{unr}$']
for data, color, method in zip(datas,colors,methods):
if method == 'EG' or method == 'Funr':
ax.plot(data[:,0],data[:,2],'-.',color=color,label=method,zorder=0)
else:
ax.plot(data[:,0],data[:,2],color=color,label=method,zorder=0)
ax.plot([data[0,0]],[data[0,2]],'k*')
ax.plot(mu,sig[0],'*',color='gold')
# ax.set_xlim([-2*scale + xoff,2*scale + xoff])
# ax.set_ylim([-.1*scale + yoff,4*scale + yoff])
ax.set_xlim([-60., 60.])
ax.set_ylim([-.1*scale + yoff, 100.])
ax.set_xlabel(r'$w_2$', fontsize=fs)
ax.set_ylabel(r'$a$', fontsize=fs)
for tick in ax.xaxis.get_major_ticks():
tick.label.set_fontsize(14)
for tick in ax.yaxis.get_major_ticks():
tick.label.set_fontsize(14)
plt.title('Trajectories for Various Equilibrium Algorithms', fontsize=16)
# plt.legend(fontsize=fs, loc="upper left")
fs = 24
# locs = [(15,25),(-35,80),(0,40),(42.5,3.0),(20,2.5),(-30,35),(-40,20),(-20,20)]
# locs = [(15,25),(-35,80),(2.5,40),(42.5,3.0),(20,2.5),(-45,45),(-42.5,5),(-22.5,5)]
locs = [(15,25),(-35,75),(2.5,40),(42.5,3.0),(20,2.5),(-45,45),(-42.5,5),(-22.5,5)]
for method,color,loc in zip(methods,colors,locs):
ax.annotate(method, xy=loc, color=color, zorder=1, fontsize=fs,
bbox=dict(facecolor='white', edgecolor='white', pad=0.0))
plt.savefig(root+'trajcomp.png',bbox_inches='tight')
##############################################################################
# Euclidean Distance to Equilibrium vs Iterations ############################
##############################################################################
# Old Version of Plot
# # fig = plt.figure()
# # ax = fig.add_subplot(111)
# # colors = ['r','gray','b','k','g']
# # for dist, color, method in zip(dists,colors,methods):
# # ax.plot(dist,color=color,label=method)
# # ax.set_xlabel('Iterations')
# # ax.set_ylabel('Distance to Equilibrium')
# # plt.legend()
# # plt.title('Iteration vs Distance to Equilibrium for Various Equilibrium Algorithms')
# # plt.savefig('runtimecomp.png')
# More Recent Version of Plot
fig,(ax,ax2) = plt.subplots(1,2,sharey=True, facecolor='w')
for dist, color, method in zip(dists,colors,methods):
# if method == 'simGD':
iters = np.arange(dist.shape[0])/1000
# print(dist[:5])
ax.plot(iters,dist,color=color,label=method)
ax2.plot(iters,dist,color=color,label=method)
# else:
# ax.plot(dist,color=color,label=method)
ax.set_xlim(-.1,10)
ax.set_xticks([0,2,4,6,8,10])
ax2.set_xlim(50,100)
ax.set_ylim(-5,95)
ax2.set_ylim(-5,95)
# hide the spines between ax and ax2
ax.spines['right'].set_visible(False)
ax2.spines['left'].set_visible(False)
ax.yaxis.tick_left()
ax.tick_params(labelright='off')
ax2.yaxis.tick_right()
ax2.set_xticks([75,100])
d = .015 # how big to make the diagonal lines in axes coordinates
# arguments to pass plot, just so we don't keep repeating them
kwargs = dict(transform=ax.transAxes, color='k', clip_on=False)
ax.plot((1-d,1+d), (-d,+d), **kwargs)
ax.plot((1-d,1+d),(1-d,1+d), **kwargs)
kwargs.update(transform=ax2.transAxes) # switch to the bottom axes
ax2.plot((-d,+d), (1-d,1+d), **kwargs)
ax2.plot((-d,+d), (-d,+d), **kwargs)
# ax.set_xlabel('Iterations')
fig.text(0.5, 0.02, 'Thousand Iterations', ha='center', fontsize=12)
ax.set_ylabel('Distance to Equilibrium',fontsize=12)
# ax.legend()
ax2.legend(fontsize=18)
plt.suptitle('Iteration vs Distance to Equilibrium for Various Equilibrium Algorithms')
plt.savefig(root+'runtimecomp.png')
##############################################################################
# Individual Trajectory Plots ################################################
##############################################################################
# Set Constraints
loA = -np.inf*np.ones((dim,dim))
loA[range(dim),range(dim)] = 1e-4
lo = np.hstack(([-np.inf]*(dim+s), loA[np.tril_indices(dim)], [-np.inf]*dim))
P = BoxProjection(lo=lo)
xlo, xhi = -5, 5
ylo, yhi = 0, 2
methods = ['Fcc','Feg','Fcon','Freg','Falt','Funr']
colors = ['r','b','k','g','gray','orange']
for method, color in zip(methods,colors):
Step = -1e-5
Iters = 10000
Domain = LQGAN(mu=mu,sig=sig,preconditioner=method)
Method = HeunEuler_PhaseSpace(Domain=Domain,Delta0=1e-5,P=P)
# Iters = 10000
# Method = Euler(Domain=Domain,FixStep=True)
# Initialize Starting Point
Start = np.array([3.,0.,0.2,0.])
# Set Options
Init = Initialization(Step=Step)
Term = Termination(MaxIter=Iters,Tols=[(Domain.dist_Euclidean,1e-4)])
Repo = Reporting(Requests=['Step', 'F Evaluations',
'Projections','Data',Domain.dist_Euclidean])
Misc = Miscellaneous()
Options = DescentOptions(Init,Term,Repo,Misc)
# Print Stats
PrintSimStats(Domain,Method,Options)
# Start Solver
tic = time.time()
LQ_Results = Solve(Start,Method,Domain,Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options,LQ_Results,Method,toc)
data = np.array(LQ_Results.PermStorage['Data'])
X, Y = np.meshgrid(np.linspace(xlo, xhi, 50), np.linspace(ylo, yhi, 50))
U = np.zeros_like(X)
V = np.zeros_like(Y)
for i in range(X.shape[0]):
for j in range(X.shape[1]):
vec = -Domain.F(np.array([X[i,j],0.,Y[i,j],0.]))
U[i,j] = vec[0]
V[i,j] = vec[2]
fig = plt.figure()
ax = fig.add_subplot(111)
Q = plt.quiver(X[::3, ::3], Y[::3, ::3], U[::3, ::3], V[::3, ::3],
pivot='mid', units='inches')
ax.plot(data[:,0],data[:,2],color=color,label=method)
ax.plot([data[0,0]],[data[0,2]],'k*')
ax.plot(mu,sig[0],'c*')
ax.set_xlim([xlo, xhi])
ax.set_ylim([0, yhi])
ax.set_xlabel(r'$w_2$')
ax.set_ylabel(r'$a$')
plt.title('Dynamics for '+method)
plt.savefig(root+method+'_dyn')
def Demo():
#__SERVICE_ORIENTED_INTERNET__##############################################
N = 10 # number of possible maps
T = 1000 # number of time steps
eta = .01 # learning rate
Ot = 0 # reference vector will be origin for all maps
# Define Domains and Compute Equilbria
Domains = []
X_Stars = []
for n in range(N):
# Create Domain
Network = CreateRandomNetwork(m=3, n=2, o=2, seed=n)
Domain = SOI(Network=Network, alpha=2)
# Record Domain
Domains += [Domain]
# Set Method
Method = HeunEuler(Domain=Domain, P=BoxProjection(lo=0), Delta0=1e-3)
# Initialize Starting Point
Start = np.zeros(Domain.Dim)
# Calculate Initial Gap
gap_0 = Domain.gap_rplus(Start)
# Set Options
Init = Initialization(Step=-1e-10)
Term = Termination(MaxIter=25000,
Tols=[(Domain.gap_rplus, 1e-6 * gap_0)])
Repo = Reporting(Requests=[Domain.gap_rplus])
Misc = Miscellaneous()
Options = DescentOptions(Init, Term, Repo, Misc)
# Print Stats
PrintSimStats(Domain, Method, Options)
# Start Solver
tic = time.time()
SOI_Results = Solve(Start, Method, Domain, Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options, SOI_Results, Method, toc)
# Record X_Star
X_Star = SOI_Results.TempStorage['Data'][-1]
X_Stars += [X_Star]
X_Stars = np.asarray(X_Stars)
X_Opt = np.mean(X_Stars, axis=0)
Ot = Ot * np.ones(X_Stars.shape[1])
print('Starting Online Learning')
# Set First Prediction
X = np.zeros(X_Stars.shape[1])
# Select First Domain
idx = np.argmax(np.linalg.norm(X_Stars - X, axis=1))
distances = []
loss_infs = []
regret_standards = []
regret_news = []
ts = range(T)
for t in ts:
print('t = ' + str(t))
# retrieve domain
Domain = Domains[idx]
# retrieve equilibrium
equi = X_Stars[idx]
# calculate distance
distances += [np.linalg.norm(equi - X)]
# calculate infinity loss
loss_infs += [infinity_loss(Domain, X)]
# calculate standard regret
ci_predict = ContourIntegral(Domain, LineContour(Ot, X))
predict_loss = integral(ci_predict)
ci_opt = ContourIntegral(Domain, LineContour(Ot, X_Opt))
predict_opt = integral(ci_opt)
regret_standards += [predict_loss - predict_opt]
# calculate new regret
ci_new = ContourIntegral(Domain, LineContour(X_Opt, X))
regret_news += [integral(ci_new)]
# update prediction
X = BoxProjection(lo=0).P(X, -eta, Domain.F(X))
# update domain
idx = np.argmax(np.linalg.norm(X_Stars - X, axis=1))
ts_p1 = range(1, T + 1)
distances_avg = np.divide(distances, ts_p1)
loss_infs_avg = np.divide(loss_infs, ts_p1)
regret_standards_avg = np.divide(regret_standards, ts_p1)
regret_news_avg = np.divide(regret_news, ts_p1)
np.savez_compressed('NoRegret.npz',
d_avg=distances_avg,
linf_avg=loss_infs_avg,
rs_avg=regret_standards_avg,
rn_avg=regret_news_avg)
plt.subplot(2, 1, 1)
plt.plot(ts, distances_avg, 'k', label='Average Distance')
plt.title('Demonstration of No-Regret on MLN')
plt.ylabel('Euclidean Distance')
plt.legend()
plt.subplot(2, 1, 2)
plt.plot(ts, loss_infs_avg, 'k--', label=r'loss$_{\infty}$')
plt.plot(ts,
regret_standards_avg,
'r--o',
markevery=T // 20,
label=r'regret$_{s}$')
plt.plot(ts, regret_news_avg, 'b-', label=r'regret$_{n}$')
plt.xlabel('Time Step')
plt.ylabel('Aggregate System-Wide Loss')
plt.xlim([0, T])
plt.ylim([-500, 5000])
plt.legend()
plt.savefig('NoRegret')
def Demo():
#__ONLINE_MONOTONE_EQUILIBRATION_DEMO_OF_A_SERVICE_ORIENTED_INTERNET__######
# Define Number of Different VIs
N = 10
np.random.seed(0)
# Define Initial Network and Domain
World = np.random.randint(N)
Worlds = [World]
Network = CreateRandomNetwork(m=3, n=2, o=2, seed=World)
Domain = SOI(Network=Network, alpha=2)
# Define Initial Strategy
Strategies = [np.zeros(Domain.Dim)]
eta = 0.1
for t in range(1000):
#__PERFORM_SINGLE_UPDATE
print('Time ' + str(t))
# Set Method
Method = Euler(Domain=Domain, P=BoxProjection(lo=0))
# Set Options
Init = Initialization(Step=-eta)
Term = Termination(MaxIter=1)
Repo = Reporting(Requests=['Data'])
Misc = Miscellaneous()
Options = DescentOptions(Init, Term, Repo, Misc)
# Run Update
Result = Solve(Strategies[-1], Method, Domain, Options)
# Get New Strategy
Strategy = Result.PermStorage['Data'][-1]
Strategies += [Strategy]
#__DEFINE_NEXT_VI
# Define Initial Network and Domain
World = np.random.randint(N)
Worlds += [World]
Network = CreateRandomNetwork(m=3, n=2, o=2, seed=World)
Domain = SOI(Network=Network, alpha=2)
# Scrap Last Strategy / World
Strategies = np.asarray(Strategies[:-1])
Worlds = Worlds[:-1]
# Store Equilibrium Strategies
Equilibria = dict()
for w in np.unique(Worlds):
print('World ' + str(w))
#__FIND_EQUILIBRIUM_SOLUTION_OF_VI
# Define Initial Network and Domain
Network = CreateRandomNetwork(m=3, n=2, o=2, seed=w)
Domain = SOI(Network=Network, alpha=2)
# Set Method
Method = HeunEuler(Domain=Domain, P=BoxProjection(lo=0), Delta0=1e-5)
# Initialize Starting Point
Start = np.zeros(Domain.Dim)
# Calculate Initial Gap
gap_0 = Domain.gap_rplus(Start)
# Set Options
Init = Initialization(Step=-1e-10)
Term = Termination(MaxIter=25000,
Tols=[(Domain.gap_rplus, 1e-6 * gap_0)])
Repo = Reporting(Requests=[Domain.gap_rplus, 'Step', 'Data'])
Misc = Miscellaneous()
Options = DescentOptions(Init, Term, Repo, Misc)
# Print Stats
PrintSimStats(Domain, Method, Options)
# Start Solver
tic = time.time()
Results = Solve(Start, Method, Domain, Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options, Results, Method, toc)
# Get Equilibrium Strategy
Equilibrium = Results.PermStorage['Data'][-1]
Equilibria[w] = Equilibrium
# Matched Equilibria & Costs
Equilibria_Matched = np.asarray([Equilibria[w] for w in Worlds])
# Compute Mean of Equilibria
Mean_Equilibrium = np.mean(Equilibria_Matched, axis=0)
# Compute Strategies Distance From Mean Equilibrium
Distance_From_Mean = np.linalg.norm(Strategies - Mean_Equilibrium, axis=1)
# Plot Results
fig = plt.figure()
ax1 = fig.add_subplot(1, 1, 1)
ax1.plot(Distance_From_Mean, label='Distance from Mean')
ax1.set_title('Online Monotone Equilibration of Dynamic SOI Network')
ax1.legend()
ax1.set_xlabel('Time')
plt.savefig('OMEfast.png')
embed()
def Demo():
#__AFFINE_GAN__##############################################
# what happens if we force the diagonal of G to lie in R+?
# G and -G are both equilibrium solutions -- need to rule one out
# Define Network and Domain
mean = np.array([1, 2])
cov = np.array([[1, 0.5], [0.5, 2]])
lam, phi = np.linalg.eig(cov)
mat = np.diag(np.sqrt(lam)).dot(phi)
# Domain = AffineGAN(u=mean,S=cov,batch_size=1000,alpha=0.,expansion=False)
# Set Method
# Method = Euler(Domain=Domain,FixStep=True)
# Method = EG(Domain=Domain,FixStep=True)
# Initialize Starting Point
# Start = np.random.rand(Domain.Dim)
Start = np.zeros(2 * mean.size + cov.size)
# d0, G0 = Domain.get_args(Start)
# u0 = G0[:,-1]
# S0 = G0[:,:Domain.dim]
# print(u0)
# print(S0)
lo = -np.inf * np.ones_like(Start)
for d in range(mean.size):
lo[mean.size + d * (mean.size + 1) + d] = 0.
iter_schedule = [2000, 4000, 4000]
step_schedule = [1e-1, 1e-2, 1e-2]
batch_schedule = [100, 100, 10]
Vs = []
for it, step, batch_size in zip(iter_schedule, step_schedule,
batch_schedule):
Domain = AffineGAN(u=mean,
S=cov,
batch_size=batch_size,
alpha=0.,
expansion=False)
# Set Method
# Method = Euler(Domain=Domain,FixStep=True,P=BoxProjection(lo=lo))
Method = EG(Domain=Domain, FixStep=True, P=BoxProjection(lo=lo))
# Set Options
Init = Initialization(Step=-step)
Term = Termination(MaxIter=it)
Repo = Reporting(Requests=[
Domain.V, 'Step', 'F Evaluations', 'Projections', 'Data'
])
Misc = Miscellaneous()
Options = DescentOptions(Init, Term, Repo, Misc)
# Print Stats
PrintSimStats(Domain, Method, Options)
# Start Solver
tic = time.time()
AG_Results = Solve(Start, Method, Domain, Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options, AG_Results, Method, toc)
Vs += AG_Results.PermStorage[Domain.V]
Start = AG_Results.TempStorage['Data'][-1]
# d, G = Domain.get_args(data)
# u = G[:,-1]
# S = G[:,:Domain.dim]
# print(u)
# print(S)
print(mat)
# embed()
for data in AG_Results.PermStorage['Data'][::400]:
num_samples = 1000
real, fake = Domain.generate(data, num_samples)
# u_est = np.mean(fake,axis=0)
# S_est = np.dot(fake.T,fake)/num_samples
# print(u_est)
# print(S_est)
fig, axs = plt.subplots(2)
axs[0].scatter(fake[:, 0],
fake[:, 1],
s=40,
facecolors='none',
edgecolors='r',
label='fake',
zorder=1)
axs[0].scatter(real[:, 0],
real[:, 1],
s=40,
marker='*',
facecolors='none',
edgecolors='k',
label='real',
zorder=0)
axs[0].set_title('Comparing Distributions')
axs[0].set_xlim([-5, 10])
axs[0].set_ylim([-5, 10])
axs[0].legend()
axs[1].plot(Vs)
axs[1].set_xlabel('Iteration')
axs[1].set_ylabel('Minimax Objective (V)')
plt.show()
def Demo():
# __POWER_ITERATION__##################################################
# Define Domain
A = np.asarray([[-4, 10], [7, 5]])
A = A.dot(A) # symmetrize
# mars = np.load('big_means.npy')
# A = mars.T.dot(mars)
eigs = np.linalg.eigvals(A)
rho = max(eigs) - min(eigs)
rank = np.count_nonzero(eigs)
# Domain = PowerIteration(A=A)
Domain = Rayleigh(A=A)
# Set Method
Method_Standard = Euler(Domain=Domain,
FixStep=True,
P=NormBallProjection())
# Initialize Starting Point
Start = np.ones(Domain.Dim)
# Set Options
Init = Initialization(Step=-1e-3)
Term = Termination(MaxIter=100, Tols=[(Domain.res_norm, 1e-6)])
Repo = Reporting(Requests=[
Domain.res_norm, 'Step', 'F Evaluations', 'Projections', 'Data'
])
Misc = Miscellaneous()
Options = DescentOptions(Init, Term, Repo, Misc)
# Print Stats
PrintSimStats(Domain, Method_Standard, Options)
# Start Solver
tic = time.time()
Results_Standard = Solve(Start, Method_Standard, Domain, Options)
toc_standard = time.time() - tic
# Print Results
PrintSimResults(Options, Results_Standard, Method_Standard, toc_standard)
# data_standard = Results_Standard.PermStorage['Data']
# eigval_standard = (A.dot(data_standard[-1])/data_standard[-1]).mean()
# eigvec_standard = data_standard[-1]
res_standard = Results_Standard.PermStorage[Domain.res_norm]
# Set Method
# Method_CK = CashKarp(Domain=Domain,Delta0=1e-4,P=NormBallProjection())
Method_CK = HeunEuler(Domain=Domain, Delta0=1e-4, P=NormBallProjection())
# Print Stats
PrintSimStats(Domain, Method_CK, Options)
# Start Solver
tic = time.time()
Results_CK = Solve(Start, Method_CK, Domain, Options)
toc_CK = time.time() - tic
# Print Results
PrintSimResults(Options, Results_CK, Method_CK, toc_CK)
# data_CK = Results_CK.PermStorage['Data']
# eigval_CK = (A.dot(data_CK[-1])/data_CK[-1]).mean()
# eigvec_CK = data_CK[-1]
res_CK = Results_CK.PermStorage[Domain.res_norm]
# Set Method
# Method_CKPS = CashKarp_PhaseSpace(Domain=Domain,Delta0=1e-4,
# P=NormBallProjection())
Method_CKPS = HeunEuler_PhaseSpace(Domain=Domain,
Delta0=1e-1,
P=NormBallProjection())
# Print Stats
PrintSimStats(Domain, Method_CKPS, Options)
# Start Solver
tic = time.time()
Results_CKPS = Solve(Start, Method_CKPS, Domain, Options)
toc_CKPS = time.time() - tic
# Print Results
PrintSimResults(Options, Results_CK, Method_CK, toc_CKPS)
# data_CKPS = Results_CKPS.PermStorage['Data']
# eigval_CKPS = (A.dot(data_CKPS[-1])/data_CKPS[-1]).mean()
# eigvec_CKPS = data_CKPS[-1]
res_CKPS = Results_CKPS.PermStorage[Domain.res_norm]
# tic = time.time()
# eigval_NP, eigvec_NP = eigh(A,eigvals=(Domain.Dim-1,Domain.Dim-1))
# toc_NP = time.time() - start
# Plot Results
fig = plt.figure()
ax = fig.add_subplot(2, 1, 1)
# label = 'Standard Power Iteration with scaling' +\
# r' $A \cdot v / ||A \cdot v||$'
label = 'Standard'
ax.plot(res_standard, label=label)
fevals_CK = Results_CK.PermStorage['F Evaluations'][-1]
# label = Method_CK.__class__.__name__+r' Power Iteration'
# label += r' $\Delta_0=$'+'{:.0e}'.format(Method_CK.Delta0)
label = 'CK'
x = np.linspace(0, fevals_CK, len(res_CK))
ax.plot(x, res_CK, label=label)
fevals_CKPS = Results_CKPS.PermStorage['F Evaluations'][-1]
# label = Method_CKPS.__class__.__name__+' Power Iteration'
# label += r' $\Delta_0=$'+'{:.0e}'.format(Method_CKPS.Delta0)
label = 'CKPS'
x = np.linspace(0, fevals_CKPS, len(res_CKPS))
ax.plot(x, res_CKPS, '-.', label=label)
xlabel = r'# of $A \cdot v$ Evaluations'
ax.set_xlabel(xlabel)
ylabel = r'Norm of residual ($||\frac{A \cdot v}{||A \cdot v||}$'
ylabel += r'$ - \frac{v}{||v||}||$)'
ax.set_ylabel(ylabel)
sizestr = str(A.shape[0]) + r' $\times$ ' + str(A.shape[1])
if rho > 100:
rhostr = r'$\rho(A)=$' + '{:.0e}'.format(rho)
else:
rhostr = r'$\rho(A)=$' + str(rho)
rnkstr = r'$rank(A)=$' + str(rank)
plt.title(sizestr + ' Matrix with ' + rhostr + ', ' + rnkstr)
ax.legend()
xlim = min(max(len(res_standard), fevals_CK, fevals_CKPS), Term.Tols[0])
xlim = int(np.ceil(xlim / 10.) * 10)
ax.set_xlim([0, xlim])
ax.set_yscale('log', nonposy='clip')
ax2 = fig.add_subplot(2, 1, 2)
# label = 'Standard Power Iteration with scaling' +\
# r' $A \cdot v / ||A \cdot v||$'
label = 'Standard'
ax2.plot(res_standard, label=label)
# label = Method_CK.__class__.__name__+r' Power Iteration'
# label += r' $\Delta_0=$'+'{:.0e}'.format(Method_CK.Delta0)
label = 'CK'
ax2.plot(res_CK, label=label)
# label = Method_CKPS.__class__.__name__+' Power Iteration'
# label += r' $\Delta_0=$'+'{:.0e}'.format(Method_CKPS.Delta0)
label = 'CKPS'
ax2.plot(res_CKPS, '-.', label=label)
xlabel = r'# of Iterations'
ax2.set_xlabel(xlabel)
ylabel = r'Norm of residual ($||\frac{A \cdot v}{||A \cdot v||}$'
ylabel += r'$ - \frac{v}{||v||}||$)'
ax2.set_ylabel(ylabel)
ax2.legend()
xlim = min(max(len(res_standard), len(res_CK), len(res_CKPS)),
Term.Tols[0])
xlim = int(np.ceil(xlim / 10.) * 10)
ax2.set_xlim([0, xlim])
ax2.set_yscale('log', nonposy='clip')
plt.show()
embed()
def Demo():
#__SPHERE__##################################################
# Define Dimension and Domain
Domain = MonotoneCycle()
# Set Method
MethodEuler = Euler(Domain=Domain,P=IdentityProjection(),FixStep=True)
MethodEG = EG(Domain=Domain,P=IdentityProjection(),FixStep=True)
# Set Options
Init = Initialization(Step=-1e-1)
Term = Termination(MaxIter=100)
Repo = Reporting(Requests=['Data'])
Misc = Miscellaneous()
Options = DescentOptions(Init,Term,Repo,Misc)
# Initialize Starting Point
Start = np.ones(Domain.Dim)
# Print Stats
PrintSimStats(Domain,MethodEuler,Options)
# Start Solver
tic = time.time()
Euler_Results = Solve(Start,MethodEuler,Domain,Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options,Euler_Results,MethodEuler,toc)
# Print Stats
PrintSimStats(Domain,MethodEG,Options)
# Start Solver
tic = time.time()
EG_Results = Solve(Start,MethodEG,Domain,Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options,EG_Results,MethodEG,toc)
data_Euler = ListONP2NP(Euler_Results.PermStorage['Data'])
data_EG = ListONP2NP(EG_Results.PermStorage['Data'])
X, Y = np.meshgrid(np.arange(-2.5, 2.5, .2), np.arange(-2.5, 2.5, .2))
U = np.zeros_like(X)
V = np.zeros_like(Y)
for i in range(X.shape[0]):
for j in range(X.shape[1]):
vec = -Domain.F([X[i,j],Y[i,j]])
U[i,j] = vec[0]
V[i,j] = vec[1]
# plt.figure()
# plt.title('Arrows scale with plot width, not view')
# Q = plt.quiver(X, Y, U, V, units='width')
# qk = plt.quiverkey(Q, 0.9, 0.9, 2, r'$2 \frac{m}{s}$', labelpos='E',
# coordinates='figure')
fig = plt.figure()
ax = fig.add_axes([0.1, 0.1, 0.6, 0.75])
plt.title("Extragradient vs Simultaneous Gradient Descent")
Q = plt.quiver(X[::3, ::3], Y[::3, ::3], U[::3, ::3], V[::3, ::3],
pivot='mid', units='inches')
vec_Euler = -Domain.F(data_Euler[-1,:])
vec_EG = -Domain.F(data_EG[-1,:])
print(data_Euler[-1])
print(vec_Euler)
plt.quiver(data_Euler[-1][0], data_Euler[-1][1], vec_Euler[0], vec_Euler[1], pivot='mid', units='inches', color='b',
headwidth=5)
plt.quiver(data_EG[-1][0], data_EG[-1][1], vec_EG[0], vec_EG[1], pivot='mid', units='inches', color='r',
headwidth=5)
plt.scatter(X[::3, ::3], Y[::3, ::3], color='gray', s=5)
plt.plot(data_Euler[:,0],data_Euler[:,1],'b',linewidth=5,label='Simultaneous\nGradient Descent')
plt.plot(data_EG[:,0],data_EG[:,1],'r',linewidth=5,label='Extragradient')
plt.plot([0],[0],linestyle="None",marker=(5,1,0),markersize=20,color='gold',label='Equilibrium')
plt.axis([-2.5,2.5,-2.5,2.5])
plt.legend(loc='center left', bbox_to_anchor=(1, 0.5), borderaxespad=0.5)
# plt.ion()
# plt.show()
plt.savefig('EGvsEuler.png')
def Demo():
#__LQ_GAN__##############################################
# NEED TO WRITE CODE TO GENERATE N LQ-GANS PER DIMENSION FOR M DIMENSIONS
# THEN RUN EACH ALGORITHM FROM L STARTING POINTS AND MEASURE RUNTIME AND STEPS
# UNTIL DESIRED DEGREE OF ACCURACY IS MET, MEASURE ACCURACY WITH EUCLIDEAN DISTANCE TO X^*
# AND KL DIVERGENCE https://stats.stackexchange.com/questions/60680/kl-divergence-between-two-multivariate-gaussians/60699
# COMPUTE MIN/MAX/AVG/STD RUNTIME OVER N X L RUNS PER DIMENSION
# Interpolation between F and RipCurl should probably be nonlinear
# in terms of L2 norms of matrices if the norms essentially represent the largest eigenvalues
# what's an example of a pseudomonotone field? stretch vertically linearly a bit? quasimonotone?
# the extragradient method uses the same step size for the first and second step, as the step size goes
# to zero, extragradient asymptotes to the projection method
# modified extragradient methods use different step sizes. if we keep the first step size fixed to some
# positive value and shrink the second, the dynamics of extragradient remain as desired
# this is essentially what HE_PhaseSpace is showing
# HE and HE_PhaseSpace are designed to "simulate" a trajectory - they do not actually change the effective
# dynamics of the vector field
# Define Network and Domain
dim = 1
s = (dim**2 + dim) // 2
mu = 10 * np.random.rand(dim)
mu = np.array([0])
L = 10 * np.random.rand(dim, dim)
L[range(dim), range(dim)] = np.clip(L[range(dim), range(dim)], 1e-1,
np.inf)
L = np.tril(L)
sig = np.dot(L, L.T)
sig = np.array([[1]])
np.set_printoptions(linewidth=200)
print('mu, sig, sig eigs')
print(mu)
print(sig)
print(np.linalg.eigvals(sig))
# Set Constraints
loA = -np.inf * np.ones((dim, dim))
loA[range(dim), range(dim)] = 1e-2
lo = np.hstack(
([-np.inf] * (dim + s), loA[np.tril_indices(dim)], [-np.inf] * dim))
P = BoxProjection(lo=lo)
xoff = 0
yoff = 0
scale = 30
datas = []
dists = []
methods = ['ccGD', 'simGD', 'preEG', 'conGD', 'regGD', 'EG']
# methods = ['simGD']
# methods = ['ccGD']
for method in methods:
if method == 'EG':
Step = -1e-2
Iters = 10000
Domain = LQ(mu=mu, sig=sig, method='simGD')
Method = EG(Domain=Domain, FixStep=True, P=P)
elif method == 'simGD':
Step = -1e-3
Iters = 100000
Domain = LQ(mu=mu, sig=sig, method='simGD')
Method = Euler(Domain=Domain, FixStep=True, P=P)
# Method = HeunEuler_PhaseSpace(Domain=Domain,Delta0=1e-5,MinStep=-1.,P=P)
elif method == 'conGD':
Step = -1e-6
# Iters = 2750
Iters = 3000
Domain = LQ(mu=mu, sig=sig, method=method)
Method = HeunEuler_PhaseSpace(Domain=Domain, Delta0=1e-5, P=P)
else:
Step = -1e-5
Iters = 10000
Domain = LQ(mu=mu, sig=sig, method=method)
Method = HeunEuler_PhaseSpace(Domain=Domain, Delta0=1e-5, P=P)
# Initialize Starting Point
Start = np.array([50., 0., 30., 0.])
# Set Options
Init = Initialization(Step=Step)
Term = Termination(MaxIter=Iters, Tols=[(Domain.dist, 1e-4)])
Repo = Reporting(Requests=[
'Step', 'F Evaluations', 'Projections', 'Data', Domain.dist
])
Misc = Miscellaneous()
Options = DescentOptions(Init, Term, Repo, Misc)
# Print Stats
PrintSimStats(Domain, Method, Options)
# Start Solver
tic = time.time()
LQ_Results = Solve(Start, Method, Domain, Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options, LQ_Results, Method, toc)
datas += [np.array(LQ_Results.PermStorage['Data'])]
dists += [np.array(LQ_Results.PermStorage[Domain.dist])]
X, Y = np.meshgrid(
np.arange(-2 * scale + xoff, 2 * scale + xoff, .2 * scale),
np.arange(1e-2 + yoff, 4 * scale + yoff, .2 * scale))
U = np.zeros_like(X)
V = np.zeros_like(Y)
for i in range(X.shape[0]):
for j in range(X.shape[1]):
vec = -Domain.F(np.array([X[i, j], 0., Y[i, j], 0.]))
U[i, j] = vec[0]
V[i, j] = vec[2]
fig = plt.figure()
ax = fig.add_subplot(111)
Q = plt.quiver(X[::3, ::3],
Y[::3, ::3],
U[::3, ::3],
V[::3, ::3],
pivot='mid',
units='inches')
colors = ['r', 'gray', 'b', 'k', 'g', 'm']
# colors = ['gray']
# colors = ['r']
for data, color, method in zip(datas, colors, methods):
if method == 'EG':
ax.plot(data[:, 0], data[:, 2], '--', color=color, label=method)
else:
ax.plot(data[:, 0], data[:, 2], color=color, label=method)
ax.plot([data[0, 0]], [data[0, 2]], 'k*')
ax.plot(mu, sig[0], 'c*')
ax.set_xlim([-2 * scale + xoff, 2 * scale + xoff])
ax.set_ylim([-.1 * scale + yoff, 4 * scale + yoff])
ax.set_xlabel(r'$w_2$')
ax.set_ylabel(r'$a$')
plt.title('Trajectories for Various Equilibrium Algorithms')
plt.legend()
# plt.show()
# plt.savefig('original.png')
# plt.savefig('EGoriginal.png')
# plt.savefig('RipCurl.png')
# plt.savefig('RipCurl2.png')
# plt.savefig('EG.png')
# plt.savefig('GReg.png')
# plt.savefig('Testing.png')
# plt.savefig('trajcomp_ccGD.png')
# plt.savefig('trajcomp.png')
plt.savefig('trajcomp_test.png')
def Demo():
# __ROSENBROCK__############################################################
# __STEEPEST_DESCENT__######################################################
# Define Domain
Domain = Rosenbrock(Dim=2)
# Set Method
Method = Euler(Domain=Domain, FixStep=True)
# Method = HeunEuler_PhaseSpace(Domain=Domain,Delta0=1e-1)
# Method = HeunEuler_AdaGrad_PhaseSpace(Domain=Domain,Delta0=1e-1)
# Set Options
Term = Termination(MaxIter=20000, Tols=[(Domain.f_Error, 1e-6)])
Repo = Reporting(Requests=[
Domain.f_Error, 'Step', 'F Evaluations', 'Projections', 'Data'
])
Misc = Miscellaneous()
# Set starting point and step size ranges
r = 2
rads = np.linspace(0, 2 * np.pi, num=4, endpoint=False)
steps = -np.logspace(-5, -3, num=3, endpoint=True)
# steps = -np.logspace(-8,-6,num=3,endpoint=True)
# Construct figure
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.view_init(azim=-160.)
X = np.arange(-1.5, 3.5, 0.25)
Y = np.arange(-1.5, 3.5, 0.25)
X, Y = np.meshgrid(X, Y)
Z = np.zeros_like(X)
for i in xrange(Z.shape[0]):
for j in xrange(Z.shape[1]):
Z[i, j] = Domain.f(np.array([X[i, j], Y[i, j]]))
ax.plot_surface(X,
Y,
Z,
rstride=1,
cstride=1,
cmap=cm.coolwarm,
linewidth=0,
antialiased=False)
ax.set_xlim3d(np.min(X), np.max(X))
ax.set_ylim3d(np.min(Y), np.max(Y))
ax.set_zlim3d(np.min(Z), np.max(Z))
ax.set_xlabel('X axis')
ax.set_ylabel('Y axis')
ax.zaxis.set_rotate_label(False) # disable automatic rotation
ax.set_zlabel('f(X,Y)', rotation=90)
ax.text2D(0.05,
0.95,
'Steepest Descent on the\nRosenbrock Function',
transform=ax.transAxes)
lw = cycle(range(2 * len(steps), 0, -2))
plt.ion()
plt.show()
# Compute trajectories
for rad, step in itertools.product(rads, steps):
# Initialize Starting Point
assert Domain.Dim == 2
Start = Domain.ArgMin + r * np.asarray([np.cos(rad), np.sin(rad)])
# Set Options
Init = Initialization(Step=step)
Options = DescentOptions(Init, Term, Repo, Misc)
# Print Stats
PrintSimStats(Domain, Method, Options)
# Start Solver
tic = time.time()
Rosenbrock_Results = Solve(Start, Method, Domain, Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options, Rosenbrock_Results, Method, toc)
# Plot Results
data_SD = Rosenbrock_Results.PermStorage['Data']
res_SD = np.asarray(Rosenbrock_Results.PermStorage[Domain.f_Error])
res_SD[np.isnan(res_SD)] = np.inf
trajX = []
trajY = []
trajZ = []
for i in xrange(len(data_SD)):
trajX.append(data_SD[i][0])
trajY.append(data_SD[i][1])
trajZ.append(res_SD[i])
ax.plot(trajX, trajY, trajZ, lw=next(lw))
plt.draw()
plt.ioff()
plt.show()
# __NEWTONS_METHOD____######################################################
# Define Domain
Domain = Rosenbrock(Dim=2, Newton=True)
# Set Method
Method = Euler(Domain=Domain, FixStep=True)
# Set Options
Term = Termination(MaxIter=20000, Tols=[(Domain.f_Error, 1e-6)])
Repo = Reporting(Requests=[
Domain.f_Error, 'Step', 'F Evaluations', 'Projections', 'Data'
])
Misc = Miscellaneous()
Init = Initialization(Step=-1e-3)
Options = DescentOptions(Init, Term, Repo, Misc)
# Print Stats
PrintSimStats(Domain, Method, Options)
# Start Solver
tic = time.time()
Rosenbrock_Results = Solve(Start, Method, Domain,
Options) # Use same Start
toc = time.time() - tic
# Print Results
PrintSimResults(Options, Rosenbrock_Results, Method, toc)
# Plot Results
data_N = Rosenbrock_Results.PermStorage['Data']
res_N = np.asarray(Rosenbrock_Results.PermStorage[Domain.f_Error])
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(res_N, label='Newton' 's Method')
ax.plot(res_SD, label='Steepest Descent')
ax.set_yscale('log')
ax.set_xlabel('Iterations (k)')
ax.set_ylabel('f(X,Y) [log-scale]')
ax.set_title('Rosenbrock Test: Newton' 's Method vs Steepest Descent')
ax.legend()
plt.show()
fig = plt.figure()
ax = fig.add_subplot(111)
diff_N = [np.linalg.norm(d - Domain.ArgMin) for d in data_N]
diff_SD = [np.linalg.norm(d - Domain.ArgMin) for d in data_SD]
ax.plot(diff_N, label='Newton' 's Method')
ax.plot(diff_SD, label='Steepest Descent')
ax.set_yscale('log')
ax.set_xlabel('Iterations (k)')
ax.set_ylabel(r'$||x-x^*||$ [log-scale]')
ax.set_title('Rosenbrock Test: Newton' 's Method vs Steepest Descent')
ax.legend()
plt.show()