def SDPTDoALocate(self, RN1, RN2, TDoA, TDoAStd):
"""
Apply SDP approximation and localization
"""
RN1 = cvxm.matrix(RN1)
RN2 = cvxm.matrix(RN2)
TDoA = cvxm.matrix(TDoA)
c = 3e08
RDoA = c*TDoA
RDoAStd=cvxm.matrix(c*TDoAStd)
mtdoa,ntdoa=cvxm.size(RN1)
Im = cvxm.eye(mtdoa)
Y=cvxm.optvar('Y',mtdoa+1,mtdoa+1)
t=cvxm.optvar('t',ntdoa,1)
prob=cvxm.problem(cvxm.minimize(cvxm.norm2(t)))
prob.constr.append(Y>=0)
prob.constr.append(Y[mtdoa,mtdoa]==1)
for i in range(ntdoa):
X0=cvxm.matrix([[Im, -cvxm.transpose(RN1[:,i])],[-RN1[:,i], cvxm.transpose(RN1[:,i])*RN1[:,i]]])
X1=cvxm.matrix([[Im, -cvxm.transpose(RN2[:,i])],[-RN2[:,i], cvxm.transpose(RN2[:,i])*RN2[:,i]]])
prob.constr.append(-RDoAStd[i,0]*t[i]<cvxm.trace(X0*Y)+cvxm.trace(X1*Y)-RDoA[i,0]**2)
prob.constr.append(RDoAStd[i,0]*t[i]>cvxm.trace(X0*Y)+cvxm.trace(X1*Y)-RDoA[i,0]**2)
prob.solve()
Pval=Y.value
X_cvx=Pval[:2,-1]
return X_cvx
def SDPRSSLocate(self, RN, PL0, d0, RSS, RSSnp, RSSStd, Rest):
RoA=self.getRange(RN, PL0, d0, RSS, RSSnp, RSSStd, Rest)
RN=cvxm.matrix(RN)
RSS=cvxm.matrix(RSS)
RSSnp=cvxm.matrix(RSSnp)
RSSStd=cvxm.matrix(RSSStd)
PL0=cvxm.matrix(PL0)
RoA=cvxm.matrix(RoA)
mrss,nrss=cvxm.size(RN)
Si = array([(1/d0**2)*10**((RSS[0,0]-PL0[0,0])/(5.0*RSSnp[0,0])),(1/d0**2)*10**((RSS[1,0]-PL0[1,0])/(5.0*RSSnp[1,0])),(1/d0**2)*10**((RSS[2,0]-PL0[2,0])/(5.0*RSSnp[2,0])),(1/d0**2)*10**((RSS[3,0]-PL0[3,0])/(5.0*RSSnp[3,0]))])
#Si = array([(1/d0**2)*10**(-(RSS[0,0]-PL0[0,0])/(5.0*RSSnp[0,0])),(1/d0**2)*10**(-(RSS[0,1]-PL0[1,0])/(5.0*RSSnp[0,1])),(1/d0**2)*10**(-(RSS[0,2]-PL0[2,0])/(5.0*RSSnp[0,2])),(1/d0**2)*10**(-(RSS[0,3]-PL0[3,0])/(5.0*RSSnp[0,3]))])
Im = cvxm.eye(mrss)
Y=cvxm.optvar('Y',mrss+1,mrss+1)
t=cvxm.optvar('t',nrss,1)
prob=cvxm.problem(cvxm.minimize(cvxm.norm2(t)))
prob.constr.append(Y>=0)
prob.constr.append(Y[mrss,mrss]==1)
for i in range(nrss):
X0=cvxm.matrix([[Im, -cvxm.transpose(RN[:,i])],[-RN[:,i], cvxm.transpose(RN[:,i])*RN[:,i]]])
prob.constr.append(-RSSStd[i,0]*t[i]<Si[i]*cvxm.trace(X0*Y)-1)
prob.constr.append(RSSStd[i,0]*t[i]>Si[i]*cvxm.trace(X0*Y)-1)
prob.solve()
Pval=Y.value
X_cvx=Pval[:2,-1]
return X_cvx
def SDPToALocate(self, RN, ToA, ToAStd):
"""
Apply SDP approximation and localization
"""
RN = cvxm.matrix(RN)
ToA = cvxm.matrix(ToA)
c = 3e08 # Speed of light
RoA = c*ToA
RoAStd = c*ToAStd
RoAStd = cvxm.matrix(RoAStd)
mtoa,ntoa=cvxm.size(RN)
Im = cvxm.eye(mtoa)
Y=cvxm.optvar('Y',mtoa+1,mtoa+1)
t=cvxm.optvar('t',ntoa,1)
prob=cvxm.problem(cvxm.minimize(cvxm.norm2(t)))
prob.constr.append(Y>=0)
prob.constr.append(Y[mtoa,mtoa]==1)
for i in range(ntoa):
X0=cvxm.matrix([[Im, -cvxm.transpose(RN[:,i])],[-RN[:,i], cvxm.transpose(RN[:,i])*RN[:,i]]])
prob.constr.append(-t[i]<(cvxm.trace(X0*Y)-RoA[i]**2)*(1/RoAStd[i]))
prob.constr.append(t[i]>(cvxm.trace(X0*Y)-RoA[i]**2)*(1/RoAStd[i]))
prob.solve()
Pval=Y.value
X_cvx=Pval[:2,-1]
return X_cvx
def solve_nu_svm(out, labels, nu, solver, reg):
'''
solve boosting formulation used by gelher and nowozin
@param out: matrix (N,F) of predictions (for each f_i) for all examples
@param labels: vector (N,1) label for each example
@param nu: regularization constant
@param solver: which solver to use. options: 'mosek', 'glpk'
'''
# get dimension
N = out.size[0]
F = out.size[1]
assert N == len(labels), str(N) + " " + str(len(labels))
norm_fact = 1.0 / (nu * float(N))
print "normalization factor %f" % (norm_fact)
# avoid point-wise product
label_matrix = cvxmod.zeros((N, N))
for i in xrange(N):
label_matrix[i, i] = labels[i]
#### parameters
f = cvxmod.param("f", N, F)
y = cvxmod.param("y", N, N, symm=True)
norm = cvxmod.param("norm", 1)
#### varibales
# rho
rho = cvxmod.optvar("rho", 1)
# dim = (N x 1)
chi = cvxmod.optvar("chi", N)
# dim = (F x 1)
beta = cvxmod.optvar("beta", F)
# Q
Q = cvxmod.eye(F)
# regularize vs ones
if reg:
objective = 0.5 * cvxmod.atoms.quadform(beta, Q) - (1.0 / float(
F)) * cvxmod.sum(beta) - rho * nu + norm_fact * cvxmod.sum(chi)
#objective = 0.5*cvxmod.atoms.quadform(beta, Q) - (1.0/float(F))*cvxmod.sum(beta) -rho*nu + norm_fact*cvxmod.sum(chi)
else:
objective = 0.5 * cvxmod.atoms.quadform(
beta, Q) - rho * nu + norm_fact * cvxmod.sum(chi)
print objective
# create problem
p = cvxmod.problem(cvxmod.minimize(objective))
# create contraints for probability simplex
#p.constr.append(beta |cvxmod.In| probsimp(F))
#p.constr.append(cvxmod.sum(beta)==1.0)
p.constr.append(beta >= 0.0)
p.constr.append(chi >= 0.0)
# attempt to perform non-sparse boosting
#p.constr.append(square(norm2(beta)) <= 1.0)
# y f beta y f*beta y*f*beta
# (N x N) (N x F) (F x 1) --> (N x N) (N x 1) --> (N x 1)
p.constr.append(y * (f * beta) + chi >= rho)
# set values for parameters
f.value = out
y.value = label_matrix
norm.value = norm_fact
print "solving problem"
print "============================================="
print p
print "============================================="
# start solver
p.solve(lpsolver=solver)
# print variables
cvxmod.printval(chi)
cvxmod.printval(beta)
cvxmod.printval(rho)
return numpy.array(cvxmod.value(beta))