def calc_r(u, L): # calculate r
"""
Calculates r as:
r = u[L] / (1 - norm2^2( u[L-1] ) ) * u[1:L-1]
"""
if (L==2): # 0, 1 -> L-1=1
r = u[L-1] / (1-fun.norm2(u[0])) * u[0]
else: #
r = u[L-1] / (1-fun.norm2(u[0:L-1])) * u[0:L-1]
return r
def qp_relax(h, P, Ku, L):
"""
Implementation of the proposed algorithm by [ZM15].
Returns a tuple with the calculated computation rate and the integer valued coefficient vector aQ.
Parameters
----------
h: array-like
channel coefficient vector
P: float
Power
Ku: int
upper bound for K (maximal possible value in aQ)
L: int
length of channel vector/ aQ (=number of senders in the system)
"""
K = 0 # K
Kl = 0 # running K
d = 0.0
h_abs = np.absolute(h)# calculates the absolute of h
t = np.ones(L) # signs of original channel vector
a = np.ones(L) # coefficient vector
t = np.copysign(t, h)# copies signs of h elementwise to t (+/-1)
p = np.argsort(h_abs, kind='quicksort') # indexes of sorted channel vector
h_abs_sorted = np.copy(h_abs[p]) # ascending ordered vector
b = 1 + P * fun.norm2(h) # part of denominator in Computation Rate formula in [1]
u = normalize_vector(P, b, h_abs_sorted) # normalized channel vector
r = calc_r(u, L) #
aC1 = init_aC(L, r) # normalized initial a
aC = np.zeros(L) # used to test k*aC1
""" DETERMINE K """
if fun.nf(Ku, aC1) < b:
K = Ku
else:
Kl = 1
while (Ku != (Kl+1)):
K = fun.fl(0.5*(Ku+Kl))
if fun.nf(K, aC1) < b:
Kl = K
else:
Ku = K
K = Kl
""" Quantization """
aQ = np.zeros(L, dtype=np.int)
aQ[L-1] = 1
""" norm2(aQ) = 1 , (aQ)^T * u = u[L-1] """
# initially the maximum comp rate achievable is at fmin
# fmin is reached if only one element in coeff vector is 1
fmin = 1 - np.power(u[L-1], 2)
if K == 1: # prevent from having empty range at K=1
k_range = [1]
else:
k_range = range(1, K+1)
for k in k_range:
aC = k * aC1
d = np.dot(aC, u)
""" QUESTION:
paper: for l <-1 to L-1
in python: range(0, L) ? or range(0, L-1)
alg python
1 0
2 1
3 2
… …
L-1 L-2
L L-1 range(0, L) = 0, 1, 2 … L-1 L=4: 0,1,2,3
range(0, L-1) = 0, 1, 2 … L-1-1 L=4: 0,1,2
"""
for l in range(0, L-1): # 1 -> L-1
v = aC[l]
aC[l] = np.floor( aC[l] )
d += (aC[l] - v) * u[l]
# calculate condition term
x = (2*aC[l]) - 2*d*u[l] + 1 - u[l]**2
if x<0:
aC[l] += 1
d += u[l]
# print "l={}, aC={}, x<0={}".format(l, aC, x<0)
f = fun.norm2(aC) - np.power(d, 2)
# print "\tR={0}, Rmax={1}, Rref={2}".format(comp_rate(f), comp_rate(fmin), fun.comp_rate(h_abs_sorted, aC, P))
# print "\tk={}, fmin={}, f={}, aQ={}".format(k, fmin, f, aQ)
if f<fmin: # the less fmin, the bigger compRate
aQ = np.copy(aC)
fmin = f
# recover coefficient vector
for l in range(0,L):
sign = t[p[l]]
a[p[l]] = sign * aQ[l]
compRate = comp_rate(fmin) # computation rate
# print "R={1:.4}, a={0}".format(a, compRate)
return (compRate, a)
def calc_fmin(aQ, u):
aQ_norm2 = fun.norm2(aQ)
dotprod = np.dot(aQ, u)
return aQ_norm2 - np.power(dotprod, 2)