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-3)
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 = range(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 = range(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 = int(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():
#__CLOUD_SERVICES__##################################################
# Define Network and Domain
Network = CreateNetworkExample(ex=2)
Domain = CloudServices(Network=Network, gap_alpha=2)
# Set Method
eps = 1e-2
Method = HeunEuler_LEGS(Domain=Domain, P=BoxProjection(lo=eps), Delta0=1e0)
# Set Options
Init = Initialization(Step=-1e-3)
Term = Termination(MaxIter=1e5)
Repo = Reporting(Requests=['Data', 'Step'])
Misc = Miscellaneous()
Options = DescentOptions(Init, Term, Repo, Misc)
args = (Method, Domain, Options)
sim = Solve
# Print Stats
PrintSimStats(Domain, Method, Options)
# Construct grid
grid = [np.array([.5, 3.5, 6])] * Domain.Dim
grid = ListONP2NP(grid)
grid = aug_grid(grid)
Dinv = np.diag(1. / grid[:, 3])
# Compute results
results = MCT(sim,
args,
grid,
nodes=16,
limit=40,
AVG=0.00,
eta_1=1.2,
eta_2=.95,
eps=1.,
L=16,
q=8,
r=1.1,
Dinv=Dinv)
ref, data, p, iters, avg, bndry_ids, starts = results
# Save results
sim_data = [results, Domain, grid]
np.save('cloud_' + time.strftime("%Y%m%d_%H%M%S"), sim_data)
# Plot BoAs
obs = (4, 9) # Look at new green-tech company
consts = np.array(
[3.45, 2.42, 3.21, 2.27, np.inf, .76, .97, .75, 1.03, np.inf])
txt_locs = [(1.6008064516129032, 1.6015625), (3.2, 3.2), (3.33, 2.53)]
xlabel = '$p_' + repr(obs[0]) + '$'
ylabel = '$q_' + repr(obs[1]) + '$'
title = 'Boundaries of Attraction for Cloud Services Market'
figBoA, axBoA = plotBoA(ref,
data,
grid,
obs=obs,
consts=consts,
txt_locs=txt_locs,
xlabel=xlabel,
ylabel=ylabel,
title=title)
# Plot Probablity Distribution
figP, axP = plotDistribution(p, grid, obs=obs, consts=consts)
def plotFigure6(saveFig=False):
print('CloudServices BoA')
msg = 'This method will run for about a week.\n' +\
'Email [email protected] for the results .npy file directly.\n' +\
'Continue? (y/n) '
cont = input(msg)
if cont != 'y':
return
# Define Network and Domain
Network = CreateNetworkExample(ex=2)
Domain = CloudServices(Network=Network, gap_alpha=2)
# Set Method
eps = 1e-2
Method = HeunEuler_LEGS(Domain=Domain, P=BoxProjection(lo=eps), Delta0=1e0)
# Set Options
Init = Initialization(Step=-1e-3)
Term = Termination(MaxIter=1e5)
Repo = Reporting(Requests=['Data', 'Step'])
Misc = Miscellaneous()
Options = DescentOptions(Init, Term, Repo, Misc)
args = (Method, Domain, Options)
sim = Solve
# Print Stats
PrintSimStats(Domain, Method, Options)
# Construct grid
grid = [np.array([.5, 3.5, 6])] * Domain.Dim
grid = ListONP2NP(grid)
grid = aug_grid(grid)
Dinv = np.diag(1. / grid[:, 3])
# Compute results
results = MCT(sim,
args,
grid,
nodes=16,
limit=40,
AVG=0.00,
eta_1=1.2,
eta_2=.95,
eps=1.,
L=16,
q=8,
r=1.1,
Dinv=Dinv)
ref, data, p, iters, avg, bndry_ids, starts = results
# Save results
sim_data = [results, Domain, grid]
np.save('cloud_' + time.strftime("%Y%m%d_%H%M%S"), sim_data)
# Plot BoAs
obs = (4, 9) # Look at new green-tech company
consts = np.array(
[3.45, 2.42, 3.21, 2.27, np.inf, .76, .97, .75, 1.03, np.inf])
txt_locs = [(1.6008064516129032, 1.6015625), (3.2, 3.2), (3.33, 2.53)]
xlabel = '$p_' + repr(obs[0]) + '$'
ylabel = '$q_' + repr(obs[1]) + '$'
title = 'Boundaries of Attraction for Cloud Services Market'
fig, ax = plotBoA(ref,
data,
grid,
obs=obs,
consts=consts,
txt_locs=txt_locs,
xlabel=xlabel,
ylabel=ylabel,
title=title)
if saveFig:
plt.savefig('BoA.png', bbox_inches='tight')
return fig, ax
def Demo():
#__SUPPLY_CHAIN_NETWORK__###################################################
N = 10 # number of possible maps
T = 1000 # number of time steps
eta = .01 # learning rate
# Define Domains and Compute Equilbria
Domains = []
X_Stars = []
CurlBounds = []
for n in range(N):
# Create Domain
Network = CreateRandomNetwork(I=3, Nm=2, Nd=2, Nr=1, seed=n)
Domain = SupplyChain(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)
_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-3 * 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()
SupplyChain_Results = Solve(Start, Method, Domain, Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options, SupplyChain_Results, Method, toc)
# Record X_Star
X_Star = SupplyChain_Results.TempStorage['Data'][-1]
X_Stars += [X_Star]
X_Stars = np.asarray(X_Stars)
# Compute Equilibrium of Average Domain
Domain = AverageDomains(Domains)
# 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-3 * 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()
SupplyChain_Results = Solve(Start, Method, Domain, Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options, SupplyChain_Results, Method, toc)
# Record X_Opt
# X_Opt = SupplyChain_Results.TempStorage['Data'][-1]
X_Opt = np.mean(X_Stars, axis=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))
idx = 0
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]
# 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(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))
idx = (idx + 1) % X_Stars.shape[0]
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)
stokes = np.asarray(stokes)
np.savez_compressed('NoRegret_SCN.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, 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(1, 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$_{n}$')
ax.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 Supply Chain Network')
plt.savefig('NoRegret_SCN')
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")
s = 2
Q = plt.quiver(X[::s, ::s],
Y[::s, ::s],
U[::s, ::s],
V[::s, ::s],
pivot='mid',
units='inches',
color='r')
# 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[::s, ::s], Y[::s, ::s], color='r', 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.axis('off')
plt.axis('square')
plt.savefig('StrawberryFields.png')
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 xrange(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():
#__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():
#__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)
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(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])
# 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)
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 = []
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)
# 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 = herons(X_Opt, X, equi) # exact area
areas += [area]
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_avg = np.divide(np.cumsum(areas), ts_p1)
stokes_avg = np.divide(np.cumsum(stokes), ts_p1)
Fnorms_avg = np.divide(np.cumsum(Fnorms), ts_p1)
np.savez_compressed('NoRegret_MLN2d.npz',
opt_d_avg=opt_distances_avg,
equi_d_avg=equi_distances_avg,
rs_avg=regret_standards_avg,
rn_avg=regret_news_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_avg, 'g-', 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.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.pdf',
format='pdf',
additional_artists=[lgd1, lgd2],
bbox_inches='tight')
sat = np.logical_or(regret_standards_avg >= regret_news_avg - stokes,
regret_standards_avg <= regret_news_avg + stokes)
embed()
def Demo():
#__BLOOD_BANK__##################################################
#############################################################
# Example 1 from Nagurney's Paper
#############################################################
# Define Network and Domain
Network = CreateNetworkExample(ex=1)
Domain = SOI(Network=Network,alpha=2)
# Set Method
Method = ABEuler(Domain=Domain,P=BoxProjection(lo=0),Delta0=1e-2)
# 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-6*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()
SOI_Results_Phase1 = Solve(Start,Method,Domain,Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options,SOI_Results_Phase1,Method,toc)
#########################################################
# Example 2 from Nagurney's Paper
#########################################################
# Define Network and Domain
Network = CreateNetworkExample(ex=2)
Domain = SOI(Network=Network,alpha=2)
# Set Method
Method = ABEuler(Domain=Domain,P=BoxProjection(lo=0),Delta0=1e-5)
# Initialize Starting Point
Start = SOI_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()
SOI_Results_Phase2 = Solve(Start,Method,Domain,Options)
toc = time.time() - tic
# Print Results
PrintSimResults(Options,SOI_Results_Phase2,Method,toc)
########################################################
# Animate Network
########################################################
# Construct MP4 Writer
fps = 15
FFMpegWriter = animation.writers['ffmpeg']
metadata = dict(title='SOI', artist='Matplotlib')
writer = FFMpegWriter(fps=fps, metadata=metadata)
# Collect Frames
frame_skip = 5
freeze = 5
Dyn_1 = SOI_Results_Phase1.PermStorage['Data']
Frz_1 = [Dyn_1[-1]]*fps*frame_skip*freeze
Dyn_2 = SOI_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(SOI_Results_Phase1.PermStorage['Data']) // frame_skip
t3 = t2 + fps*freeze
t4 = t3 + len(SOI_Results_Phase2.PermStorage['Data']) // frame_skip
Dyn_1_ann = 'Control Network\n(Equilibrating)'
Frz_1_ann = 'Control Network\n(Converged)'
Dyn_2_ann = 'Market 1 Increases Demand for Service 1 by Provider 1' + \
'\n(Equilibrating)'
Frz_2_ann = 'Market 1 Increases Demand for Service 1 by Provider 1' + \
'\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()
SOI_ani = animation.FuncAnimation(fig, Domain.UpdateVisual,
init_func=Domain.InitVisual,
frames=len(Frames),
fargs=(ax, Frames, anns), blit=True)
SOI_ani.save('Videos/SOI.mp4', writer=writer)
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()