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,NTopLEs=3)
# 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():
#__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 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 plotFigure5(saveFig=False):
print('Demand Curve')
# Define Network and Domain
Network = CreateNetworkExample(ex=2)
Domain = CloudServices(Network=Network)
Domain2 = CloudServices(Network=Network,poly_splice=False)
# Define parameters for demand function
i = 0
j = 3
pi = np.arange(0,.8,.001)
pJ = .01
qi = qJ = 1
# Compute demand for curve both with and without polynomial splice
Q = np.zeros_like(pi)
Q2 = Q.copy()
t = np.zeros_like(pi)
for p in range(len(pi)):
_Q, _t = Domain.Demand_ij(i,j,pi[p],qi,pJ,qJ)
_Q2, _ = Domain2.Demand_ij(i,j,pi[p],qi,pJ,qJ)
Q[p] = _Q
Q2[p] = _Q2
t[p] = _t
# Compute critical points: (in)elasticity, splice, zero-utility
e = pi[np.argmax(t >= 1/np.sqrt(2))]
Qe = Q[np.argmax(t >= 1/np.sqrt(2))]/12.
p0 = pi[np.argmax(t >= Domain.t0)]
Qp0 = Q[np.argmax(t >= Domain.t0)]/12.
pf = pi[np.argmax(t >= Domain.tf)]
Qpf = Q[np.argmax(t >= Domain.tf)]/12.
fig = plt.figure()
ax = fig.add_subplot(111)
# Plot demand curve
Qij, = ax.plot(pi,Q/12.,'k-', linewidth=5)
exp, = ax.plot(pi,Q2/12.,'k--', linewidth=5)
ax.plot(p0,Qp0,'ow',markersize=10)
ax.plot(pf,Qpf,'ow',markersize=10)
eps = .05
ax.plot([-eps,.8+eps],[0,0],'k-.')
ax.plot([0,0],[-eps,1+eps],'k-.')
# Annotate critical points
ax.annotate('inelastic', xy=(.04, .97), xycoords='data',
xytext=(.1, .7), textcoords='data',
arrowprops=dict(arrowstyle='simple',facecolor='black'),
ha='center', va='center', size=18,
)
ax.annotate('elastic', xy=(e, Qe), xycoords='data',
xytext=(e+.2, Qe+.2), textcoords='data',
arrowprops=dict(frac=0.1,headwidth=10,width=4,
facecolor='black',shrink=.1),
ha='center', va='center', size=18,
)
ax.annotate('splice', xy=(p0, Qp0), xycoords='data',
xytext=(p0+.2, Qp0+.2), textcoords='data',
arrowprops=dict(frac=0.1,headwidth=10,width=4,
facecolor='black',shrink=.1),
ha='center', va='center', size=18,
)
ax.annotate('zero-cutoff', xy=(pf, Qpf+.02), xycoords='data',
xytext=(pf, Qpf+.2*np.sqrt(2)), textcoords='data',
arrowprops=dict(frac=0.1,headwidth=10,width=4,
facecolor='black',shrink=.1),
ha='center', va='center', size=18,
)
ax.set_xlim(-eps,.8+eps)
ax.set_ylim(-eps,1+eps)
leg = plt.legend([Qij,exp], [r'$Q_{ij}^{}$', r'$H_{i}e^{-t_{ij}^2}$'],
fontsize=20,fancybox=True)
plt.setp(leg.get_texts()[0], fontsize='20', va='center')
plt.setp(leg.get_texts()[1], fontsize='20', va='bottom')
plt.axis('off')
if saveFig:
plt.savefig("Demand.png",bbox_inches='tight')
return fig, ax
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)