def posLPSolver(A, eps, verbose = False, max_iterations = float("inf")):
assert eps > 0 and eps <= EPS_THRESHOLD, "Invalid epsilon value"
A = np.matrix(A)
m = utils.numNumRows(A)
n = utils.numNumColumns(A)
beta = float("inf") # the scaling factor so that min(max[A[:,j]]) = 1
max_of_cols = np.zeros(n)
for i in range(n):
max_of_cols[i] = np.max(utils.getColumn(A, i))
if max_of_cols[i] < beta:
beta = max_of_cols[i]
# Scale down A to ensure that min(max[A[:,j]]) = 1
A /= beta
max_of_cols /= beta
mu = eps / (4 * np.log(m*n/eps))
alpha = eps * mu / 4
T = int(np.ceil(6 * np.log(2*n) / (alpha * eps)))
T = min(max_iterations, T)
obj_vals = np.array([])
ref = np.zeros(n)
x = np.zeros(n)
k = (1 - eps/2) / n
for i in range(n):
x[i] = k / max_of_cols[i]
if verbose:
print "A"
print A
print "Matrix dimensions =", A.shape
print "Number of iterations =", T, "\n"
print "mu = ", mu
print "x0 =", x
time.sleep(1)
for k in range(T+1):
x_new = np.zeros(n)
Ax = utils.matrixVectorProduct(A, x)
y = np.exp((Ax - 1.0) / mu)
if k % RESOLUTION == 0:
print "k =", str(k), "...."
obj_vals = np.append(obj_vals, sum(x))
if verbose and k % RESOLUTION == 0:
print "1-Norm difference =", str(LA.norm(x - ref, 1))
ref = x
for i in range(n):
v_i = 0
for j in range(m):
v_i += utils.getItem(A, j, i) * y[j]
v_i -= 1.0
x_new[i] = x[i] * np.exp(-alpha * trunc(v_i, eps))
if verbose and k % RESOLUTION == 0:
print i, v_i, trunc(v_i, eps)
x = x_new
# Scale x back up
x = x * beta / (1 + eps)
return x.tolist(), obj_vals
def posLPSolver(A, eps, verbose = False, max_iterations = float("inf")):
assert eps > 0 and eps <= EPS_THRESHOLD, "Invalid epsilon value"
A = np.matrix(A)
m = utils.numNumRows(A)
n = utils.numNumColumns(A)
beta = float("inf") # the scaling factor so that min(max[A[:,j]]) = 1
max_of_cols = np.zeros(n)
for i in range(n):
max_of_cols[i] = np.max(utils.getColumn(A, i))
if max_of_cols[i] < beta:
beta = max_of_cols[i]
# Scale down A to ensure that min(max[A[:,j]]) = 1
A /= beta
max_of_cols /= beta
mu = eps / (4 * np.log(m*n/eps))
alpha = mu / 20
# NOTE: The base of the log has to be 2!!
W = np.log(1 / eps) / np.log(2) # log(1/eps) = number of groups
w = int(np.ceil(W))
T = int(np.ceil(10 * W * np.log(2*n) / (alpha * eps)))
T = min(max_iterations, T)
if verbose:
print "Matrix dimensions =", A.shape
print "Number of iterations =", T, "\n"
print "Nmber of groups =", w
time.sleep(1)
x = np.zeros(n)
k = (1 - eps/2) / n
for i in range(n):
x[i] = k / max_of_cols[i]
obj_vals = np.array([])
ref = np.zeros(n)
for k in range(T+1):
if k % RESOLUTION == 0:
print "k =", str(k), "...."
obj_vals = np.append(obj_vals, sum(x))
t = np.random.randint(0, w)
if verbose and k % RESOLUTION == 0:
print "1-Norm difference =", str(LA.norm(x - ref, 1))
print "t =", t
print "Bounds =", str(eps * pow(2,t)), "to", str(eps * pow(2,t+1))
ref = x
x_new = np.zeros(n)
Ax = utils.matrixVectorProduct(A, x)
y = np.exp((Ax - 1.0) / mu)
t = np.random.randint(0, w)
for i in range(n):
v_i = 0
for j in range(m):
v_i += utils.getItem(A, j, i) * y[j]
v_i -= 1.0
x_new[i] = x[i] * np.exp(-alpha * trunc(v_i, t, eps))
if verbose and k % RESOLUTION == 0:
print i, v_i, trunc(v_i, t, eps)
pass
x = x_new
# Scale x back up
x = x * beta / (1 + eps)
return x.tolist(), obj_vals