Python solvers.qp方法代碼示例

# 需要導入模塊: from cvxopt import solvers [as 別名]
# 或者: from cvxopt.solvers import qp [as 別名]
def fit(self, Xs, Xt):
        '''
        Fit source and target using KMM (compute the coefficients)
        :param Xs: ns * dim
        :param Xt: nt * dim
        :return: Coefficients (Pt / Ps) value vector (Beta in the paper)
        '''
        ns = Xs.shape[0]
        nt = Xt.shape[0]
        if self.eps == None:
            self.eps = self.B / np.sqrt(ns)
        K = kernel(self.kernel_type, Xs, None, self.gamma)
        kappa = np.sum(kernel(self.kernel_type, Xs, Xt, self.gamma) * float(ns) / float(nt), axis=1)

        K = matrix(K)
        kappa = matrix(kappa)
        G = matrix(np.r_[np.ones((1, ns)), -np.ones((1, ns)), np.eye(ns), -np.eye(ns)])
        h = matrix(np.r_[ns * (1 + self.eps), ns * (self.eps - 1), self.B * np.ones((ns,)), np.zeros((ns,))])

        sol = solvers.qp(K, -kappa, G, h)
        beta = np.array(sol['x'])
        return beta 

# 需要導入模塊: from cvxopt import solvers [as 別名]
# 或者: from cvxopt.solvers import qp [as 別名]
def radius(K):
    """evaluate the radius of the MEB (Minimum Enclosing Ball) of examples in
    feature space.

    Parameters
    ----------
    K : (n,n) ndarray,
        the kernel that represents the data.

    Returns
    -------
    r : np.float64,
        the radius of the minimum enclosing ball of examples in feature space.
    """
    K = validation.check_K(K).numpy()
    n = K.shape[0]
    P = 2 * matrix(K)
    p = -matrix(K.diagonal())
    G = -spdiag([1.0] * n)
    h = matrix([0.0] * n)
    A = matrix([1.0] * n).T
    b = matrix([1.0])
    solvers.options['show_progress']=False
    sol = solvers.qp(P,p,G,h,A,b)
    return abs(sol['primal objective'])**.5 

# 需要導入模塊: from cvxopt import solvers [as 別名]
# 或者: from cvxopt.solvers import qp [as 別名]
def projection_in_norm(self, x, M):
        """
        Projection of x to simplex induced by matrix M. Uses quadratic programming.
        """
        m = M.shape[0]

        # Constrains matrices
        P = opt.matrix(2 * M)
        q = opt.matrix(-2 * M * x)
        G = opt.matrix(-np.eye(m))
        h = opt.matrix(np.zeros((m, 1)))
        A = opt.matrix(np.ones((1, m)))
        b = opt.matrix(1.)

        # Solve using quadratic programming
        sol = opt.solvers.qp(P, q, G, h, A, b)
        return np.squeeze(sol['x']) 

# 需要導入模塊: from cvxopt import solvers [as 別名]
# 或者: from cvxopt.solvers import qp [as 別名]
def _QP(self, x, y):
        # In QP formulation (dual): m variables, 2m+1 constraints (1 equation, 2m inequations)
        m = len(y)
        print x.shape, y.shape
        P = self._kernel(x) * np.outer(y, y)
        P, q = matrix(P, tc='d'), matrix(-np.ones((m, 1)), tc='d')
        G = matrix(np.r_[-np.eye(m), np.eye(m)], tc='d')
        h = matrix(np.r_[np.zeros((m,1)), np.zeros((m,1)) + self.C], tc='d')
        A, b = matrix(y.reshape((1,-1)), tc='d'), matrix([0.0])
        # print "P, q:"
        # print P, q
        # print "G, h"
        # print G, h
        # print "A, b"
        # print A, b
        solution = solvers.qp(P, q, G, h, A, b)
        if solution['status'] == 'unknown':
            print 'Not PSD!'
            exit(2)
        else:
            self.alphas = np.array(solution['x']).squeeze() 

# 需要導入模塊: from cvxopt import solvers [as 別名]
# 或者: from cvxopt.solvers import qp [as 別名]
def update_h(self):
        """ alternating least squares step, update H under the convexity
        constraint """
        def update_single_h(i):
            """ compute single H[:,i] """
            # optimize alpha using qp solver from cvxopt
            FA = base.matrix(np.float64(np.dot(-self.W.T, self.data[:,i])))
            al = solvers.qp(HA, FA, INQa, INQb, EQa, EQb)
            self.H[:,i] = np.array(al['x']).reshape((1, self._num_bases))

        EQb = base.matrix(1.0, (1,1))
        # float64 required for cvxopt
        HA = base.matrix(np.float64(np.dot(self.W.T, self.W)))
        INQa = base.matrix(-np.eye(self._num_bases))
        INQb = base.matrix(0.0, (self._num_bases,1))
        EQa = base.matrix(1.0, (1, self._num_bases))

        for i in range(self._num_samples):
            update_single_h(i) 

# 需要導入模塊: from cvxopt import solvers [as 別名]
# 或者: from cvxopt.solvers import qp [as 別名]
def update_w(self):
        """ alternating least squares step, update W under the convexity
        constraint """
        def update_single_w(i):
            """ compute single W[:,i] """
            # optimize beta     using qp solver from cvxopt
            FB = base.matrix(np.float64(np.dot(-self.data.T, W_hat[:,i])))
            be = solvers.qp(HB, FB, INQa, INQb, EQa, EQb)
            self.beta[i,:] = np.array(be['x']).reshape((1, self._num_samples))

        # float64 required for cvxopt
        HB = base.matrix(np.float64(np.dot(self.data[:,:].T, self.data[:,:])))
        EQb = base.matrix(1.0, (1, 1))
        W_hat = np.dot(self.data, pinv(self.H))
        INQa = base.matrix(-np.eye(self._num_samples))
        INQb = base.matrix(0.0, (self._num_samples, 1))
        EQa = base.matrix(1.0, (1, self._num_samples))

        for i in range(self._num_bases):
            update_single_w(i)

        self.W = np.dot(self.beta, self.data.T).T 

# 需要導入模塊: from cvxopt import solvers [as 別名]
# 或者: from cvxopt.solvers import qp [as 別名]
def optimize_portfolio(n, avg_ret, covs, r_min):
	P = covs
	# x = variable(n)
	q = matrix(numpy.zeros((n, 1)), tc='d')
	# inequality constraints Gx <= h
	# captures the constraints (avg_ret'x >= r_min) and (x >= 0)
	G = matrix(numpy.concatenate((
		-numpy.transpose(numpy.array(avg_ret)),
		-numpy.identity(n)), 0))
	h = matrix(numpy.concatenate((
		-numpy.ones((1,1))*r_min,
		numpy.zeros((n,1))), 0))
	# equality constraint Ax = b; captures the constraint sum(x) == 1
	A = matrix(1.0, (1,n))
	b = matrix(1.0)
	sol = solvers.qp(P, q, G, h, A, b)
	return sol

### setup the parameters 

# 需要導入模塊: from cvxopt import solvers [as 別名]
# 或者: from cvxopt.solvers import qp [as 別名]
def solve_qp(P, q, G, h,
             A=None, b=None, sym_proj=False,
             solver='cvxopt'):
    if sym_proj:
        P = .5 * (P + P.T)
    cvxmat(P)
    cvxmat(q)
    cvxmat(G)
    cvxmat(h)
    args = [cvxmat(P), cvxmat(q), cvxmat(G), cvxmat(h)]
    if A is not None:
        args.extend([cvxmat(A), cvxmat(b)])
    sol = qp(*args, solver=solver)
    if not ('optimal' in sol['status']):
        raise ValueError('QP optimum not found: %s' % sol['status'])
    return np.array(sol['x']).reshape((P.shape[1],)) 

# 需要導入模塊: from cvxopt import solvers [as 別名]
# 或者: from cvxopt.solvers import qp [as 別名]
def margin(K,Y):
    """evaluate the margin in a classification problem of examples in feature space.
    If the classes are not linearly separable in feature space, then the
    margin obtained is 0.

    Note that it works only for binary tasks.

    Parameters
    ----------
    K : (n,n) ndarray,
        the kernel that represents the data.
    Y : (n) array_like,
        the labels vector.
    """
    K, Y = validation.check_K_Y(K, Y, binary=True)
    n = Y.size()[0]
    Y = [1 if y==Y[0] else -1 for y in Y]
    YY = spdiag(Y)
    P = 2*(YY*matrix(K.numpy())*YY)
    p = matrix([0.0]*n)
    G = -spdiag([1.0]*n)
    h = matrix([0.0]*n)
    A = matrix([[1.0 if Y[i]==+1 else 0 for i in range(n)],
                [1.0 if Y[j]==-1 else 0 for j in range(n)]]).T
    b = matrix([[1.0],[1.0]],(2,1))
    solvers.options['show_progress']=False
    sol = solvers.qp(P,p,G,h,A,b)
    return sol['primal objective']**.5 

# 需要導入模塊: from cvxopt import solvers [as 別名]
# 或者: from cvxopt.solvers import qp [as 別名]
def opt_radius(K, init_sol=None): 
    n = K.shape[0]
    K = matrix(K.numpy())
    P = 2 * K
    p = -matrix([K[i,i] for i in range(n)])
    G = -spdiag([1.0] * n)
    h = matrix([0.0] * n)
    A = matrix([1.0] * n).T
    b = matrix([1.0])
    solvers.options['show_progress']=False
    sol = solvers.qp(P,p,G,h,A,b,initvals=init_sol)
    radius2 = (-p.T * sol['x'])[0] - (sol['x'].T * K * sol['x'])[0]
    return sol, radius2 

# 需要導入模塊: from cvxopt import solvers [as 別名]
# 或者: from cvxopt.solvers import qp [as 別名]
def opt_margin(K, YY, init_sol=None):
    '''optimized margin evaluation'''
    n = K.shape[0]
    P = 2 * (YY * matrix(K.numpy()) * YY)
    p = matrix([0.0]*n)
    G = -spdiag([1.0]*n)
    h = matrix([0.0]*n)
    A = matrix([[1.0 if YY[i,i]==+1 else 0 for i in range(n)],
                [1.0 if YY[j,j]==-1 else 0 for j in range(n)]]).T
    b = matrix([[1.0],[1.0]],(2,1))
    solvers.options['show_progress']=False
    sol = solvers.qp(P,p,G,h,A,b,initvals=init_sol) 
    margin2 = sol['primal objective']
    return sol, margin2 

# 需要導入模塊: from cvxopt import solvers [as 別名]
# 或者: from cvxopt.solvers import qp [as 別名]
def opt_margin(K,YY,init_sol=None):
	'''optimized margin evaluation'''
	n = K.shape[0]
	P = 2 * (YY * matrix(K) * YY)
	p = matrix([0.0]*n)
	G = -spdiag([1.0]*n)
	h = matrix([0.0]*n)
	A = matrix([[1.0 if YY[i,i]==+1 else 0 for i in range(n)],
				[1.0 if YY[j,j]==-1 else 0 for j in range(n)]]).T
	b = matrix([[1.0],[1.0]],(2,1))
	solvers.options['show_progress']=False
	sol = solvers.qp(P,p,G,h,A,b,initvals=init_sol)	
	margin2 = sol['primal objective']
	return margin2, sol['x'], sol 

# 需要導入模塊: from cvxopt import solvers [as 別名]
# 或者: from cvxopt.solvers import qp [as 別名]
def _fit(self,X,Y):    
        self.X = X
        values = np.unique(Y)
        Y = [1 if l==values[1] else -1 for l in Y]
        self.Y = Y
        npos = len([1.0 for l in Y if l == 1])
        nneg = len([1.0 for l in Y if l == -1])
        gamma_unif = matrix([1.0/npos if l == 1 else 1.0/nneg for l in Y])
        YY = matrix(np.diag(list(matrix(Y))))

        Kf = self.__kernel_definition__()
        ker_matrix = matrix(Kf(X,X).astype(np.double))
        #KLL = (1.0 / (gamma_unif.T * YY * ker_matrix * YY * gamma_unif)[0])*(1.0-self.lam)*YY*ker_matrix*YY
        KLL = (1.0-self.lam)*YY*ker_matrix*YY
        LID = matrix(np.diag([self.lam * (npos * nneg / (npos+nneg))]*len(Y)))
        Q = 2*(KLL+LID)
        p = matrix([0.0]*len(Y))
        G = -matrix(np.diag([1.0]*len(Y)))
        h = matrix([0.0]*len(Y),(len(Y),1))
        A = matrix([[1.0 if lab==+1 else 0 for lab in Y],[1.0 if lab2==-1 else 0 for lab2 in Y]]).T
        b = matrix([[1.0],[1.0]],(2,1))
        
        solvers.options['show_progress'] = False#True
        solvers.options['maxiters'] = self.max_iter
        sol = solvers.qp(Q,p,G,h,A,b)
        self.gamma = sol['x']
        if self.verbose:
            print ('[KOMD]')
            print ('optimization finished, #iter = %d' % sol['iterations'])
            print ('status of the solution: %s' % sol['status'])
            print ('objval: %.5f' % sol['primal objective'])
            
        bias = 0.5 * self.gamma.T * ker_matrix * YY * self.gamma
        self.bias = bias
        self.is_fitted = True
        self.ker_matrix = ker_matrix
        return self 

# 需要導入模塊: from cvxopt import solvers [as 別名]
# 或者: from cvxopt.solvers import qp [as 別名]
def fit_nnl2reg(self):
        try:
            from cvxopt import matrix, solvers
        except ImportError:
            raise ImportError("To infer titer models, you need a working installation of cvxopt")
        n_params = self.design_matrix.shape[1]
        P = matrix(np.dot(self.design_matrix.T, self.design_matrix) + self.lam_drop*np.eye(n_params))
        q = matrix( -np.dot( self.titer_dist, self.design_matrix))
        h = matrix(np.zeros(n_params)) # Gw <=h
        G = matrix(-np.eye(n_params))
        W = solvers.qp(P,q,G,h)
        return np.array([x for x in W['x']]) 

# 需要導入模塊: from cvxopt import solvers [as 別名]
# 或者: from cvxopt.solvers import qp [as 別名]
def projection_in_norm(self, x, M):
        """ Projection of x to simplex indiced by matrix M. Uses quadratic programming.
        """
        m = M.shape[0]

        P = matrix(2*M)
        q = matrix(-2 * M * x)
        G = matrix(-np.eye(m))
        h = matrix(np.zeros((m,1)))
        A = matrix(np.ones((1,m)))
        b = matrix(1.)

        sol = solvers.qp(P, q, G, h, A, b)
        return np.squeeze(sol['x'])