def calc_part_factor(self):
"""
Compute participation factor of states in eigenvalues
Returns
-------
"""
mu, N = numpy.linalg.eig(self.As)
# TODO: use scipy.sparse.linalg.eigs(self.As)
N = matrix(N)
n = len(mu)
idx = range(n)
W = matrix(spmatrix(1.0, idx, idx, (n, n), N.typecode))
gesv(N, W)
partfact = mul(abs(W.T), abs(N))
b = matrix(1.0, (1, n))
WN = b * partfact
partfact = partfact.T
for item in idx:
mu_real = mu[item].real
mu_imag = mu[item].imag
mu[item] = complex(round(mu_real, 4), round(mu_imag, 4))
partfact[item, :] /= WN[item]
# participation factor
self.mu = matrix(mu)
self.part_fact = matrix(partfact)
return self.mu, self.part_fact
def denseSolve(A,b):
''' solves an Ax = b matrix system with gesv'''
if isinstance(A,np.ndarray):
aLocal = cvxopt.matrix(A)
bLocal = cvxopt.matrix(b)
lapack.gesv(aLocal,bLocal)
return np.array(bLocal).flatten()
else:
return linsolve(A,b)
def L1Regression(A, b, alpha, trace=False):
"""
solves
minimize_{x} ||A*x-b||^2_2 + alpha*||x||_1
"""
(n, m) = A.size
Id = spmatrix(1.0, range(m), range(m)) ##unit matrix
G = matrix([A.T, -A.T])
h = matrix(alpha, (2 * m, 1))
solvers.options['show_progress'] = trace
sol = solvers.qp(Id, b, G, h)
z = sol['x']
x = A.trans() * (b - z)
A_tA = A.trans() * A
lapack.gesv(A_tA, x)
return x
def L1Regression(A,b,alpha,trace=False):
"""
solves
minimize_{x} ||A*x-b||^2_2 + alpha*||x||_1
"""
(n,m)=A.size
Id = spmatrix(1.0, range(m),range(m)) ##unit matrix
G = matrix([A.T,-A.T])
h = matrix(alpha, (2*m,1))
solvers.options['show_progress'] = trace
sol= solvers.qp(Id, b, G, h)
z= sol['x']
x= A.trans()*(b-z)
A_tA = A.trans()*A
lapack.gesv(A_tA, x)
return x
def compute_eigs(As):
(mu, N) = eig(matrix(As))
N = matrix(N)
n = len(mu)
idx = range(n)
W = matrix(spmatrix(1.0, idx, idx, (n, n), v.typecode))
gesv(N, W)
pf = mul(abs(W.T), abs(V))
b = matrix(1.0, (1, n))
WN = b * pf
pf = pf.T
for item in idx:
mur = mu[item].real
mui = mu[item].imag
mu[item] = complex(round(mur, 5), round(mui, 5))
pf[item, :] /= WN[item]
def PLS2D_getBeta(theta, ZtX, ZtY, XtX, ZtZ, XtY, YtX, YtZ, XtZ, YtY, n, P,
tinds, rinds, cinds):
# Obtain Lambda
Lambda = mapping2D(theta, tinds, rinds, cinds)
# Obtain Lambda'
Lambdat = spmatrix.trans(Lambda)
# Obtain Lambda'Z'Y and Lambda'Z'X
LambdatZtY = Lambdat * ZtY
LambdatZtX = Lambdat * ZtX
# Set the factorisation to use LL' instead of LDL'
cholmod.options['supernodal'] = 2
# Obtain the cholesky decomposition
LambdatZtZLambda = Lambdat * ZtZ * Lambda
I = spmatrix(1.0, range(Lambda.size[0]), range(Lambda.size[0]))
chol_dict = sparse_chol2D(LambdatZtZLambda + I,
perm=P,
retF=True,
retP=False,
retL=False)
F = chol_dict['F']
# Obtain C_u (annoyingly solve writes over the second argument,
# whereas spsolve outputs)
Cu = LambdatZtY[P, :]
cholmod.solve(F, Cu, sys=4)
# Obtain RZX
RZX = LambdatZtX[P, :]
cholmod.solve(F, RZX, sys=4)
# Obtain RXtRX
RXtRX = XtX - matrix.trans(RZX) * RZX
# Obtain beta estimates (note: gesv also replaces the second
# argument)
betahat = XtY - matrix.trans(RZX) * Cu
try:
lapack.posv(RXtRX, betahat)
except:
lapack.gesv(RXtRX, betahat)
return (betahat)
def part_factor(As):
"""Compute participation factor of states in eigenvalues"""
mu, N = numpy.linalg.eig(As)
N = matrix(N)
n = len(mu)
idx = range(n)
W = matrix(spmatrix(1.0, idx, idx, (n, n), N.typecode))
gesv(N, W)
partfact = mul(abs(W.T), abs(N))
b = matrix(1.0, (1, n))
WN = b * partfact
partfact = partfact.T
for item in idx:
mu_real = mu[item].real
mu_imag = mu[item].imag
mu[item] = complex(round(mu_real, 4), round(mu_imag, 4))
partfact[item, :] /= WN[item]
# participation factor:
return matrix(mu), matrix(partfact)
def compute_eig(As):
mu, N = eig(matrix(As))
N = matrix(N)
n = len(mu)
idx = range(n)
W = matrix(spmatrix(1.0, idx, idx, (n, n), N.typecode))
gesv(N, W)
# W = np.linalg.pinv(N)
# W = matrix(W)
pf = mul(abs(W.T), abs(N))
b = matrix(1.0, (1, n))
WN = b * pf
pf = pf.T
for item in idx:
mur = mu[item].real
mui = mu[item].imag
mu[item] = complex(round(mur, 5), round(mui, 5))
pf[item, :] /= WN[item]
# print(pf)
return pf
def calc_part_factor(self, As=None):
"""
Compute participation factor of states in eigenvalues
Returns
-------
"""
if As is None:
As = self.As
mu, N = np.linalg.eig(As)
N = matrix(N)
n = len(mu)
idx = range(n)
mu_complex = np.array([0] * n, dtype=complex)
W = matrix(spmatrix(1.0, idx, idx, As.shape, N.typecode))
gesv(N, W)
partfact = mul(abs(W.T), abs(N))
b = matrix(1.0, (1, n))
WN = b * partfact
partfact = partfact.T
for item in idx:
mu_real = float(mu[item].real)
mu_imag = float(mu[item].imag)
mu_complex[item] = complex(round(mu_real, 5), round(mu_imag, 5))
partfact[item, :] /= WN[item]
# participation factor
self.mu = matrix(mu_complex)
self.part_fact = matrix(partfact)
return self.mu, self.part_fact
Solution:
(x, y, z) = ( 3/10, 2/5, 0)
CVXOPT cvxopt.lapack.gesv(A, B[, ipiv = None]) Solves
A X = B,
where A and B are real or complex matrices, with A square and nonsingular.
On entry, B contains the right-hand side B; on exit it contains the solution X.
To run:
python pyalad/test_linear_solver.py
"""
tA = np.array([[2, 1, 3], [2, 6, 8], [6, 8, 18]], dtype=float)
tb = np.array([1, 3, 5], dtype=float)
print tA
print tb
A = matrix(tA)
b = matrix(tb)
print A
print b
x = matrix(b)
print x
lapack.gesv(A, x)
print A * x
print(3. / 10, 2. / 5, 0)
def find_ellipsoid(self):
# return None if not enough data is available
if(self.pa.size[1] < 3 or self.pb.size[1] < 3):
return None
# homogenize coordinates
pah = self.homogenize(self.pa)
pbh = self.homogenize(self.pb)
dim = pah.size[0]
num_pah = pah.size[1]
num_pbh = pbh.size[1]
# get the c vector
num_vars = 1+(dim-1)*(dim-1)+2*num_pah+dim*dim
c = matrix([0.0]*num_vars, (num_vars,1))
c[0,0] = -self.c1
for i in xrange(dim-1):
for j in xrange(dim-1):
if(i == j):
c[1+i*(dim-1)+j,0] = self.c2
for i in xrange(num_pah):
c[1+(dim-1)*(dim-1)+i,0] = self.c3
for i in xrange(num_pah):
c[1+(dim-1)*(dim-1)+num_pah+i,0] = 0.0
for i in xrange(dim*dim):
c[1+(dim-1)*(dim-1)+num_pah+num_pah+i,0] = 0.0
# get Gl and hl
# separation constraint
Gl_t = []
for i in xrange(num_pah):
row = [0.0]*(1+(dim-1)*(dim-1)+num_pah)+[0.0]*num_pah
row[(1+(dim-1)*(dim-1)+num_pah)+i] = -1.0
for j in xrange(dim):
for k in xrange(dim):
row.append(pah[j,i]*pah[k,i])
Gl_t.append(row)
for i in xrange(num_pbh):
row = [1.0]+[0.0]*((dim-1)*(dim-1)+2*num_pah)
for j in xrange(dim):
for k in xrange(dim):
row.append(-1.0*pbh[j,i]*pbh[k,i])
Gl_t.append(row)
# l1 norm constraint
for i in xrange(num_pah):
row = [0.0]*num_vars
row[1+(dim-1)*(dim-1)+i] = -1.0
row[1+(dim-1)*(dim-1)+num_pah+i] = -1.0
Gl_t.append(row)
for i in xrange(num_pah):
row = [0.0]*num_vars
row[1+(dim-1)*(dim-1)+i] = -1.0
row[1+(dim-1)*(dim-1)+num_pah+i] = 1.0
Gl_t.append(row)
# construct Gl and hl
Gl = matrix(Gl_t).trans()
col = [0.0]*(num_pah+num_pbh)+[-1.0]*num_pah+[1.0]*num_pah
hl = matrix(col,(3*num_pah+num_pbh,1))
# get Gs and hs
# positive semidefinite constraint
# E must be positive semidefinite
Gs = []
for i in xrange(1+(dim-1)*(dim-1)+2*num_pah):
Gs.append([0.0]*(dim*dim))
for i in xrange(dim*dim):
v = [0.0]*(dim*dim)
rpos = int(math.floor(float(i)/float(dim)))
cpos = i % dim
if(rpos == cpos):
v[i] = -1.0
else:
v[i] = -0.5
v[cpos*dim+rpos] = -0.5
Gs.append(v)
Gs = [matrix(Gs)]
hs = [matrix([0.0]*(dim*dim),(dim,dim))]
# block matrix must be positive semidefinite
Gs2 = []
Gs2.append([0.0]*(((dim-1)*2)*((dim-1)*2)))
for i in xrange((dim-1)*(dim-1)):
v = [0.0]*(((dim-1)*2)*((dim-1)*2))
rpos = int(math.floor(float(i)/float(dim-1)))
cpos = i % (dim-1)
if(rpos == cpos):
v[(rpos+dim-1)*(dim-1)*2+(dim-1)+cpos] = -1.0
else:
v[(rpos+dim-1)*(dim-1)*2+(dim-1)+cpos] = -0.5
v[(cpos+dim-1)*(dim-1)*2+(dim-1)+rpos] = -0.5
Gs2.append(v)
for i in xrange(2*num_pah):
Gs2.append([0.0]*(((dim-1)*2)*((dim-1)*2)))
for i in xrange(dim*dim):
v = [0.0]*(((dim-1)*2)*((dim-1)*2))
rpos = int(math.floor(float(i)/float(dim)))
cpos = i % dim
if(rpos == 0 or cpos == 0):
Gs2.append(v)
else:
rpos = rpos-1
cpos = cpos-1
if(rpos == cpos):
v[rpos*(dim-1)*2+cpos] = -1.0
else:
v[rpos*(dim-1)*2+cpos] = -0.5
v[cpos*(dim-1)*2+rpos] = -0.5
Gs2.append(v)
Gs.append(matrix(Gs2))
zero_block = matrix([0.0]*((dim-1)*(dim-1)),((dim-1), (dim-1)))
eye_block = spmatrix(1.0, range(dim-1), range(dim-1))
hs2 = matrix([[zero_block, eye_block], [eye_block, zero_block]])
hs.append(hs2)
# get A and b
# symmetry constraint
A_t = []
for i in xrange(dim):
for j in xrange(i, dim):
if(i != j):
v = [0.0]*(num_vars)
v[1+(dim-1)*(dim-1)+2*num_pah+i*dim+j] = 1.0
v[1+(dim-1)*(dim-1)+2*num_pah+j*dim+i] = -1.0
A_t.append(v)
for i in xrange(dim-1):
for j in xrange(i, dim-1):
if(i != j):
v = [0.0]*(num_vars)
v[1+i*(dim-1)+j] = 1.0
v[1+j*(dim-1)+i] = -1.0
A_t.append(v)
A = matrix(A_t).trans()
b = matrix([0.0]*A.size[0],(A.size[0],1))
# solve it
passed = False
ntime = 10
while(passed == False and ntime > 0):
try:
sol = solvers.sdp(c, Gl, hl, Gs, hs, A, b)
passed = True
except ZeroDivisionError:
time.sleep(0.001)
ntime = ntime-1
except Exception:
time.sleep(0.001)
ntime = ntime-1
if(passed == False):
tmp_nrow = self.pa.size[0]
tmp_c = mean_ps(self.pa).trans()
tmp_E = matrix(spmatrix(1.0, range(tmp_nrow), range(tmp_nrow)))
tmp_rho = 1.0
return {'c':tmp_c, 'E':tmp_E, 'rho':tmp_rho}
# parse out solution
x = sol['x']
k = x[0]
E_hat = matrix(x[1+(dim-1)*(dim-1)+2*num_pah:], (dim,dim))
F = E_hat[1:,1:]
v = E_hat[1:,0]
s = E_hat[0,0]
ipiv = matrix(0, (dim-1,1))
gesv(-F, v, ipiv)
c = v
btm = 1-(s-c.trans()*F*c)+0.00000001
for i in xrange(F.size[0]):
for j in xrange(F.size[1]):
F[i,j] = F[i,j]/btm
E = F
rho = k
# function return
return {'c':c, 'E':E, 'rho':rho}
__author__ = 'stefan'
from cvxopt import matrix, normal
from cvxopt.lapack import gesv, getrs
n = 10
A = normal(n,n)
b = normal(n)
ipiv = matrix(0, (n,1))
x = +b
gesv(A, x, ipiv) # x = A^{-1}*b
x2 = +b
getrs(A, ipiv, x2, trans='T') # x2 = A^{-T}*b
x += x2
print(x)
def find_ellipsoid(self):
# homogenize coordinates
pah = self.homogenize(self.pa)
pbh = self.homogenize(self.pb)
dim = pah.size[0]
num_pah = pah.size[1]
num_pbh = pbh.size[1]
# get the c vector
c = matrix([-1.0]+[0.0]*(dim*dim), (1+dim*dim,1))
# get Gl and hl
# separation constraint
Gl_t = []
for i in xrange(num_pah):
row = [0.0]
for j in xrange(dim):
for k in xrange(dim):
row.append(pah[j,i]*pah[k,i])
Gl_t.append(row)
for i in xrange(num_pbh):
row = [1.0]
for j in xrange(dim):
for k in xrange(dim):
row.append(-1.0*pbh[j,i]*pbh[k,i])
Gl_t.append(row)
Gl = matrix(Gl_t).trans()
hl = matrix([1.0]*num_pah+[0.0]*num_pbh,(num_pah+num_pbh,1))
# get Gs and hs
# positive semidefinite constraint
Gs = []
Gs.append([0.0]*(dim*dim))
for i in xrange(dim*dim):
v = [0.0]*(dim*dim)
rpos = int(math.floor(float(i)/float(dim)))
cpos = i % dim
if(rpos == cpos):
v[i] = -1.0
else:
v[i] = -0.5
v[cpos*dim+rpos] = -0.5
Gs.append(v)
Gs = [matrix(Gs)]
hs = [matrix([0.0]*(dim*dim),(dim,dim))]
# get A and b
# symmetry constraint
A_t = []
for i in xrange(dim):
for j in xrange(i, dim):
if(i != j):
v = [0.0]*(1+dim*dim)
v[1+i*dim+j] = 1.0
v[1+j*dim+i] = -1.0
A_t.append(v)
A = matrix(A_t).trans()
b = matrix([0.0]*A.size[0],(A.size[0],1))
# solve it
passed = False
ntime = 10
while(passed == False and ntime > 0):
try:
sol = solvers.sdp(c, Gl, hl, Gs, hs, A, b)
passed = True
except ZeroDivisionError:
time.sleep(0.001)
ntime = ntime-1
except Exception:
time.sleep(0.001)
ntime = ntime-1
if(passed == False):
return None
# parse out solution
x = sol['x']
k = x[0]
E_hat = matrix(x[1:], (dim,dim))
F = E_hat[1:,1:]
v = E_hat[1:,0]
s = E_hat[0,0]
ipiv = matrix(0, (dim-1,1))
gesv(-F, v, ipiv)
c = v
btm = 1-(s-c.trans()*F*c)+0.00000001
for i in xrange(F.size[0]):
for j in xrange(F.size[1]):
F[i,j] = F[i,j]/btm
E = F
rho = k
# function return
return {'c':c, 'E':E, 'rho':rho}
def PeLS2D(theta, ZtX, ZtY, XtX, ZtZ, XtY, YtX, YtZ, XtZ, YtY, n, P, I, tinds,
rinds, cinds):
# Obtain Lambda
Lambda = mapping2D(theta, tinds, rinds, cinds)
# Obtain Lambda'
Lambdat = spmatrix.trans(Lambda)
# Obtain Lambda'Z'Y and Lambda'Z'X
LambdatZtY = Lambdat * ZtY
LambdatZtX = Lambdat * ZtX
# Obtain the cholesky decomposition
LambdatZtZLambda = Lambdat * (ZtZ * Lambda)
chol_dict = sparse_chol2D(LambdatZtZLambda + I,
perm=P,
retF=True,
retP=False,
retL=False)
F = chol_dict['F']
# Obtain C_u (annoyingly solve writes over the second argument,
# whereas spsolve outputs)
Cu = LambdatZtY[P, :]
cholmod.solve(F, Cu, sys=4)
# Obtain RZX
RZX = LambdatZtX[P, :]
cholmod.solve(F, RZX, sys=4)
# Obtain RXtRX
RXtRX = XtX - matrix.trans(RZX) * RZX
# Obtain beta estimates (note: gesv also replaces the second
# argument)
betahat = XtY - matrix.trans(RZX) * Cu
try:
lapack.posv(RXtRX, betahat)
except:
lapack.gesv(RXtRX, betahat)
# Obtain u estimates
uhat = Cu - RZX * betahat
cholmod.solve(F, uhat, sys=5)
cholmod.solve(F, uhat, sys=8)
# Obtain b estimates
bhat = Lambda * uhat
# Obtain residuals sum of squares
resss = YtY - 2 * YtX * betahat - 2 * YtZ * bhat + 2 * matrix.trans(
betahat) * XtZ * bhat + matrix.trans(
betahat) * XtX * betahat + matrix.trans(bhat) * ZtZ * bhat
# Obtain penalised residual sum of squares
pss = resss + matrix.trans(uhat) * uhat
# Obtain Log(|L|^2)
logdet = 2 * sum(cvxopt.log(cholmod.diag(F)))
# Obtain log likelihood
logllh = -logdet / 2 - n / 2 * (1 + np.log(2 * np.pi * pss[0, 0]) -
np.log(n))
return (-logllh)
def PLS2D_getSigma2(theta, ZtX, ZtY, XtX, ZtZ, XtY, YtX, YtZ, XtZ, YtY, n, P,
I, tinds, rinds, cinds):
# Obtain Lambda
#t1 = time.time()
Lambda = mapping2D(theta, tinds, rinds, cinds)
#t2 = time.time()
#print(t2-t1)#3.170967102050781e-05 9
# Obtain Lambda'
#t1 = time.time()
Lambdat = spmatrix.trans(Lambda)
#t2 = time.time()
#print(t2-t1)# 3.5762786865234375e-06
# Obtain Lambda'Z'Y and Lambda'Z'X
#t1 = time.time()
LambdatZtY = Lambdat * ZtY
LambdatZtX = Lambdat * ZtX
#t2 = time.time()
#print(t2-t1)#1.049041748046875e-05 13
# Obtain the cholesky decomposition
#t1 = time.time()
LambdatZtZLambda = Lambdat * (ZtZ * Lambda)
#t2 = time.time()
#print(t2-t1)#3.790855407714844e-05 2
#t1 = time.time()
chol_dict = sparse_chol2D(LambdatZtZLambda + I,
perm=P,
retF=True,
retP=False,
retL=False)
F = chol_dict['F']
#t2 = time.time()
#print(t2-t1)#0.0001342296600341797 1
# Obtain C_u (annoyingly solve writes over the second argument,
# whereas spsolve outputs)
#t1 = time.time()
Cu = LambdatZtY[P, :]
cholmod.solve(F, Cu, sys=4)
#t2 = time.time()
#print(t2-t1)#1.5974044799804688e-05 5
# Obtain RZX
#t1 = time.time()
RZX = LambdatZtX[P, :]
cholmod.solve(F, RZX, sys=4)
#t2 = time.time()
#print(t2-t1)#1.2159347534179688e-05 7
# Obtain RXtRX
#t1 = time.time()
RXtRX = XtX - matrix.trans(RZX) * RZX
#t2 = time.time()
#print(t2-t1)#9.775161743164062e-06 11
# Obtain beta estimates (note: gesv also replaces the second
# argument)
#t1 = time.time()
betahat = XtY - matrix.trans(RZX) * Cu
try:
lapack.posv(RXtRX, betahat)
except:
lapack.gesv(RXtRX, betahat)
#t2 = time.time()
#print(t2-t1)#1.7404556274414062e-05 6
# Obtain u estimates
#t1 = time.time()
uhat = Cu - RZX * betahat
cholmod.solve(F, uhat, sys=5)
cholmod.solve(F, uhat, sys=8)
#t2 = time.time()
#print(t2-t1)#1.2874603271484375e-05 8
# Obtain b estimates
#t1 = time.time()
bhat = Lambda * uhat
#t2 = time.time()
#print(t2-t1)#2.86102294921875e-06 15
# Obtain residuals sum of squares
#t1 = time.time()
resss = YtY - 2 * YtX * betahat - 2 * YtZ * bhat + 2 * matrix.trans(
betahat) * XtZ * bhat + matrix.trans(
betahat) * XtX * betahat + matrix.trans(bhat) * ZtZ * bhat
#t2 = time.time()
#print(t2-t1)#3.409385681152344e-05 4
# Obtain penalised residual sum of squares
#t1 = time.time()
pss = resss + matrix.trans(uhat) * uhat
return (pss / n)
def solve_SAT2(self,cnf,number_of_variables,number_of_clauses):
#Solves CNFSAT by a Polynomial Time Approximation scheme:
# - Encode each clause as a linear equation in n variables: missing variables and negated variables are 0, others are 1
# - Solve previous system of equations by least squares algorithm to fit a line
# - Variable value above 0.5 is set to 1 and less than 0.5 is set to 0
# - Rounded of assignment array satisfies the CNFSAT with high probability
#Returns: a tuple with set of satisfying assignments
satass=[]
x=[]
self.solve_SAT(cnf,number_of_variables,number_of_clauses)
for clause in self.cnfparsed:
equation=[]
for n in xrange(number_of_variables):
equation.append(0)
#print "clause:",clause
for literal in clause:
if literal[0] != "!":
equation[int(literal[1:])-1]=1
else:
equation[int(literal[2:])-1]=0
self.equationsA.append(equation)
for n in xrange(number_of_clauses):
self.equationsB.append(1)
a = np.array(self.equationsA)
b = np.array(self.equationsB)
init_guess = []
for n in xrange(number_of_variables):
init_guess.append(0.00000000001)
initial_guess = np.array(init_guess)
self.A=a
self.B=b
#print "a:",a
#print "b:",b
#print "a.shape:",a.shape
#print "b.shape:",b.shape
matrixa=matrix(a,tc='d')
matrixb=matrix(b,tc='d')
x=None
if number_of_variables == number_of_clauses:
if self.Algorithm=="lsqr()":
#x = np.dot(np.linalg.inv(a),b)
#x = gmres(a,b)
#x = lgmres(a,b)
#x = minres(a,b)
#x = bicg(a,b)
#x = cg(a,b)
#x = cgs(a,b)
#x = bicgstab(a,b)
x = lsqr(a,b,atol=0,btol=0,conlim=0,show=True)
if self.Algorithm=="lapack()":
try:
x = gesv(matrixa,matrixb)
#x = gels(matrixa,matrixb)
#x = sysv(matrixa,matrixb)
#x = getrs(matrixa,matrixb)
x = [matrixb]
except:
print "Exception:",sys.exc_info()
return None
if self.Algorithm=="l1regls()":
l1x = l1regls(matrixa,matrixb)
ass=[]
x=[]
for n in l1x:
ass.append(n)
x.append(ass)
if self.Algorithm=="lsmr()":
x = lsmr(a,b,atol=0,btol=0,conlim=0,show=True,x0=initial_guess)
else:
if self.Algorithm=="solve()":
x = solve(a,b)
if self.Algorithm=="lstsq()":
x = lstsq(a,b,lapack_driver='gelsy')
if self.Algorithm=="lsqr()":
x = lsqr(a,b,atol=0,btol=0,conlim=0,show=True)
if self.Algorithm=="lsmr()":
#x = lsmr(a,b,atol=0.1,btol=0.1,maxiter=5,conlim=10,show=True)
x = lsmr(a,b,atol=0,btol=0,conlim=0,show=True,x0=initial_guess)
if self.Algorithm=="spsolve()":
x = dsolve.spsolve(csc_matrix(a),b)
if self.Algorithm=="pinv2()":
x=[]
#pseudoinverse_a=pinv(a)
pseudoinverse_a=pinv2(a,check_finite=False)
x.append(matmul(pseudoinverse_a,b))
if self.Algorithm=="lsq_linear()":
x = lsq_linear(a,b,lsq_solver='exact')
if self.Algorithm=="lapack()":
try:
#x = gesv(matrixa,matrixb)
x = gels(matrixa,matrixb)
#x = sysv(matrixa,matrixb)
#x = getrs(matrixa,matrixb)
x = [matrixb]
except:
print "Exception:",sys.exc_info()
return None
if self.Algorithm=="l1regls()":
l1x = l1regls(matrixa,matrixb)
ass=[]
x=[]
for n in l1x:
ass.append(n)
x.append(ass)
print "solve_SAT2(): ",self.Algorithm,": x:",x
if x is None:
return None
cnt=0
binary_parity=0
real_parity=0.0
if rounding_threshold == "Randomized":
randomized_rounding_threshold=float(random.randint(1,100000))/100000.0
else:
min_assignment=min(x[0])
max_assignment=max(x[0])
randomized_rounding_threshold=(min_assignment + max_assignment)/2
print "randomized_rounding_threshold = ", randomized_rounding_threshold
print "approximate assignment :",x[0]
for e in x[0]:
if e > randomized_rounding_threshold:
satass.append(1)
binary_parity += 1
else:
satass.append(0)
binary_parity += 0
real_parity += e
cnt+=1
print "solve_SAT2(): real_parity = ",real_parity
print "solve_SAT2(): binary_parity = ",binary_parity
return (satass,real_parity,binary_parity,x[0])
def solve_SAT2(self, cnf, number_of_variables, number_of_clauses):
#Solves CNFSAT by a Polynomial Time Approximation scheme:
# - Encode each clause as a linear equation in n variables: missing variables and negated variables are 0, others are 1
# - Solve previous system of equations by least squares algorithm to fit a line
# - Variable value above 0.5 is set to 1 and less than 0.5 is set to 0
# - Rounded of assignment array satisfies the CNFSAT with high probability
#Returns: a tuple with set of satisfying assignments
satass = []
x = []
self.solve_SAT(cnf, number_of_variables, number_of_clauses)
for clause in self.cnfparsed:
equation = []
for n in xrange(number_of_variables):
equation.append(0)
#print "clause:",clause
for literal in clause:
if literal[0] != "!":
equation[int(literal[1:]) - 1] = 1
else:
equation[int(literal[2:]) - 1] = 0
self.equationsA.append(equation)
for n in xrange(number_of_clauses):
self.equationsB.append(1)
a = np.array(self.equationsA)
b = np.array(self.equationsB)
init_guess = []
for n in xrange(number_of_variables):
init_guess.append(0.00000000001)
initial_guess = np.array(init_guess)
self.A = a
self.B = b
#print "a:",a
#print "b:",b
#print "a.shape:",a.shape
#print "b.shape:",b.shape
matrixa = matrix(a, tc='d')
matrixb = matrix(b, tc='d')
x = None
if number_of_variables == number_of_clauses:
if self.Algorithm == "lsqr()":
#x = np.dot(np.linalg.inv(a),b)
#x = gmres(a,b)
#x = lgmres(a,b)
#x = minres(a,b)
#x = bicg(a,b)
#x = cg(a,b)
#x = cgs(a,b)
#x = bicgstab(a,b)
x = lsqr(a, b, atol=0, btol=0, conlim=0, show=True)
if self.Algorithm == "lapack()":
try:
x = gesv(matrixa, matrixb)
#x = gels(matrixa,matrixb)
#x = sysv(matrixa,matrixb)
#x = getrs(matrixa,matrixb)
x = [matrixb]
except:
print "Exception:", sys.exc_info()
return None
if self.Algorithm == "l1regls()":
l1x = l1regls(matrixa, matrixb)
ass = []
x = []
for n in l1x:
ass.append(n)
x.append(ass)
if self.Algorithm == "lsmr()":
x = lsmr(a,
b,
atol=0,
btol=0,
conlim=0,
show=True,
x0=initial_guess)
else:
if self.Algorithm == "solve()":
x = solve(a, b)
if self.Algorithm == "lstsq()":
x = lstsq(a, b, lapack_driver='gelsy')
if self.Algorithm == "lsqr()":
x = lsqr(a, b, atol=0, btol=0, conlim=0, show=True)
if self.Algorithm == "lsmr()":
#x = lsmr(a,b,atol=0.1,btol=0.1,maxiter=5,conlim=10,show=True)
x = lsmr(a,
b,
atol=0,
btol=0,
conlim=0,
show=True,
x0=initial_guess)
if self.Algorithm == "spsolve()":
x = dsolve.spsolve(csc_matrix(a), b)
if self.Algorithm == "pinv2()":
x = []
#pseudoinverse_a=pinv(a)
pseudoinverse_a = pinv2(a, check_finite=False)
x.append(matmul(pseudoinverse_a, b))
if self.Algorithm == "lsq_linear()":
x = lsq_linear(a, b, lsq_solver='exact')
if self.Algorithm == "lapack()":
try:
#x = gesv(matrixa,matrixb)
x = gels(matrixa, matrixb)
#x = sysv(matrixa,matrixb)
#x = getrs(matrixa,matrixb)
x = [matrixb]
except:
print "Exception:", sys.exc_info()
return None
if self.Algorithm == "l1regls()":
l1x = l1regls(matrixa, matrixb)
ass = []
x = []
for n in l1x:
ass.append(n)
x.append(ass)
print "solve_SAT2(): ", self.Algorithm, ": x:", x
if x is None:
return None
cnt = 0
binary_parity = 0
real_parity = 0.0
if rounding_threshold == "Randomized":
randomized_rounding_threshold = float(random.randint(
1, 100000)) / 100000.0
else:
min_assignment = min(x[0])
max_assignment = max(x[0])
randomized_rounding_threshold = (min_assignment +
max_assignment) / 2
print "randomized_rounding_threshold = ", randomized_rounding_threshold
print "approximate assignment :", x[0]
for e in x[0]:
if e > randomized_rounding_threshold:
satass.append(1)
binary_parity += 1
else:
satass.append(0)
binary_parity += 0
real_parity += e
cnt += 1
print "solve_SAT2(): real_parity = ", real_parity
print "solve_SAT2(): binary_parity = ", binary_parity
return (satass, real_parity, binary_parity, x[0])