Python linalg.eigsh方法代碼示例

# 需要導入模塊: from scipy.sparse import linalg [as 別名]
# 或者: from scipy.sparse.linalg import eigsh [as 別名]
def solve_modal(model,k:int):
    """
    Solve eigen mode of the MDOF system
    
    params:
        model: FEModel.
        k: number of modes to extract.
    """
    K_,M_=model.K_,model.M_
    if k>model.DOF:
        logger.info('Warning: the modal number to extract is larger than the system DOFs, only %d modes are available'%model.DOF)
        k=model.DOF
    omega2s,modes = sl.eigsh(K_,k,M_,sigma=0,which='LM')
    delta = modes/np.sum(modes,axis=0)
    model.is_solved=True
    model.mode_=delta
    model.omega_=np.sqrt(omega2s).reshape((k,1)) 

# 需要導入模塊: from scipy.sparse import linalg [as 別名]
# 或者: from scipy.sparse.linalg import eigsh [as 別名]
def _calculate_sf(self, graph):
        """
        Calculating the features of a graph.

        Arg types:
            * **graph** *(NetworkX graph)* - A graph to be embedded.

        Return types:
            * **embedding** *(Numpy array)* - The embedding of a single graph.
        """
        number_of_nodes = graph.number_of_nodes()
        L_tilde = nx.normalized_laplacian_matrix(graph, nodelist=range(number_of_nodes))
        if number_of_nodes <= self.dimensions:
            embedding = eigsh(L_tilde, k=number_of_nodes-1, which='LM',
                              ncv=10*self.dimensions, return_eigenvectors=False)

            shape_diff = self.dimensions - embedding.shape[0] - 1
            embedding = np.pad(embedding, (1, shape_diff), 'constant', constant_values=0)
        else:
            embedding = eigsh(L_tilde, k=self.dimensions, which='LM',
                              ncv=10*self.dimensions, return_eigenvectors=False)
        return embedding 

# 需要導入模塊: from scipy.sparse import linalg [as 別名]
# 或者: from scipy.sparse.linalg import eigsh [as 別名]
def test_cXY_E0(nr_sites, gamma, rgen, ldim=2):
    if sys.version_info[:2] == (3, 3) and gamma == -0.5:
        # Skip this test on Python 3.3 because it fails on Travis (but
        # only for Python 3.3). eigsh() fails with:
        # scipy.sparse.linalg.eigen.arpack.arpack.ArpackNoConvergence:
        # ARPACK error -1: No convergence (xxx iterations, 0/1
        # eigenvectors converged) [ARPACK error -14: ZNAUPD did not
        # find any eigenvalues to sufficient accuracy.]
        pt.skip("Test fails on Travis for unknown reason")
        return

    # Verify that the analytical solution of the ground state energy
    # matches the numerical value from eigsh()
    E0 = physics.cXY_E0(nr_sites, gamma)
    H = physics.sparse_cH(physics.cXY_local_terms(nr_sites, gamma))
    # Fix start vector for eigsh()
    v0 = rgen.randn(ldim**nr_sites) + 1j * rgen.randn(ldim**nr_sites)
    ev = eigsh(H, k=1, which='SR', v0=v0, return_eigenvectors=False).min()
    assert abs(E0 - ev) <= 1e-13 

# 需要導入模塊: from scipy.sparse import linalg [as 別名]
# 或者: from scipy.sparse.linalg import eigsh [as 別名]
def _cov_eigen(self, X):
        """
        Perform direct computation of covariance matrix eigen{values,vectors},
        given a scipy.sparse matrix.

        Parameters
        ----------
        X : WRITEME

        Returns
        -------
        WRITEME
        """

        v, W = eigen_symmetric(X.T.dot(X) / X.shape[0], k=self.num_components)

        # The resulting components are in *ascending* order of eigenvalue, and
        # W contains eigenvectors in its *columns*, so we simply reverse both.
        return v[::-1], W[:, ::-1] 

# 需要導入模塊: from scipy.sparse import linalg [as 別名]
# 或者: from scipy.sparse.linalg import eigsh [as 別名]
def manifold_harmonics(verts, tris, K, scaled=True, return_D=False, return_eigenvalues=False):
    Q, vertex_area = compute_mesh_laplacian(
        verts, tris, 'cotangent', 
        return_vertex_area=True, area_type='lumped_mass'
    )
    if scaled:
        D = sparse.spdiags(vertex_area, 0, len(verts), len(verts))
    else:
        D = sparse.spdiags(np.ones_like(vertex_area), 0, len(verts), len(verts))

    try:
        lambda_dense, Phi_dense = eigsh(-Q, M=D, k=K, sigma=0)
    except RuntimeError, e:
        if e.message == 'Factor is exactly singular':
            logging.warn("factor is singular, trying some regularization and cholmod")
            chol_solve = factorized(-Q + sparse.eye(Q.shape[0]) * 1.e-9)
            OPinv = sparse.linalg.LinearOperator(Q.shape, matvec=chol_solve)
            lambda_dense, Phi_dense = eigsh(-Q, M=D, k=K, sigma=0, OPinv=OPinv)
        else:
            raise e 

# 需要導入模塊: from scipy.sparse import linalg [as 別名]
# 或者: from scipy.sparse.linalg import eigsh [as 別名]
def test_eigs_truss():
    """Eigenvalues of a bar"""
    nnodes = 513
    
    x = np.linspace(0, np.pi, nnodes)
    nodes = np.zeros((nnodes, 3))
    nodes[:, 0] = range(nnodes)
    nodes[:, 1] = x
    cons = np.zeros((nnodes, 2))
    cons[:, 1] = -1
    cons[0, 0] = -1 
    cons[-1, 0] = -1
    mats = np.array([[1.0, 1.0, 1.0]])
    elements = np.zeros((nnodes - 1, 5 ), dtype=int)
    elements[:, 0] = range(nnodes - 1)
    elements[:, 1] = 6
    elements[:, 3] = range(nnodes - 1)
    elements[:, 4] = range(1, nnodes)
    
    assem_op, bc_array, neq = ass.DME(cons, elements)
    stiff, mass = ass.assembler(elements, mats, nodes, neq, assem_op)
    
    vals, _ = eigsh(stiff, M=mass, which="SM")
    assert np.allclose(vals, np.linspace(1, 6, 6)**2, rtol=1e-2) 

# 需要導入模塊: from scipy.sparse import linalg [as 別名]
# 或者: from scipy.sparse.linalg import eigsh [as 別名]
def _method_1(data, num_pcs=None):
    """Compute OPCA when num_observations > num_dimensions."""
    data = np.nan_to_num(data - nanmean(data, axis=0))
    T = data.shape[0]
    corr_offset = np.dot(data[1:].T, data[:-1])
    corr_offset += corr_offset.T
    if num_pcs is None:
        eivals, eivects = eigh(corr_offset)
    else:
        eivals, eivects = eigsh(corr_offset, num_pcs, which='LA')
    eivals = np.real(eivals)
    eivects = np.real(eivects)
    idx = np.argsort(-eivals)  # sort the eigenvectors and eigenvalues
    eivals = old_div(eivals[idx], (2. * (T - 1)))
    eivects = eivects[:, idx]
    return eivals, eivects, np.dot(data, eivects) 

# 需要導入模塊: from scipy.sparse import linalg [as 別名]
# 或者: from scipy.sparse.linalg import eigsh [as 別名]
def ldos0d_wf(h,e=0.0,delta=0.01,num_wf = 10,robust=False,tol=0):
  """Calculates the local density of states of a hamiltonian and
     writes it in file, using arpack"""
  if h.dimensionality==0:  # only for 0d
    intra = csc_matrix(h.intra) # matrix
  else: raise # not implemented...
  if robust: # go to the imaginary axis for stability
    eig,eigvec = slg.eigs(intra,k=int(num_wf),which="LM",
                        sigma=e+1j*delta,tol=tol) 
    eig = eig.real # real part only
  else: # Hermitic Hamiltonian
    eig,eigvec = slg.eigsh(intra,k=int(num_wf),which="LM",sigma=e,tol=tol) 
  d = np.array([0.0 for i in range(intra.shape[0])]) # initialize
  for (v,ie) in zip(eigvec.transpose(),eig): # loop over wavefunctions
    v2 = (np.conjugate(v)*v).real # square of wavefunction
    fac = delta/((e-ie)**2 + delta**2) # factor to create a delta
    d += fac*v2 # add contribution
#  d /= num_wf # normalize
  d /= np.pi # normalize
  d = spatial_dos(h,d) # resum if necessary
  g = h.geometry  # store geometry
  write_ldos(g.x,g.y,d,z=g.z) # write in file 

# 需要導入模塊: from scipy.sparse import linalg [as 別名]
# 或者: from scipy.sparse.linalg import eigsh [as 別名]
def ldos_arpack(intra,num_wf=10,robust=False,tol=0,e=0.0,delta=0.01):
  """Use arpack to calculate hte local density of states at a certain energy"""
  if robust: # go to the imaginary axis for stability
    eig,eigvec = slg.eigs(intra,k=int(num_wf),which="LM",
                        sigma=e+1j*delta,tol=tol) 
    eig = eig.real # real part only
  else: # Hermitic Hamiltonian
    eig,eigvec = slg.eigsh(intra,k=int(num_wf),which="LM",sigma=e,tol=tol) 
  d = np.array([0.0 for i in range(intra.shape[0])]) # initialize
  for (v,ie) in zip(eigvec.transpose(),eig): # loop over wavefunctions
    v2 = (np.conjugate(v)*v).real # square of wavefunction
    fac = delta/((e-ie)**2 + delta**2) # factor to create a delta
    d += fac*v2 # add contribution
#  d /= num_wf # normalize
  d /= np.pi # normalize
  return d 

# 需要導入模塊: from scipy.sparse import linalg [as 別名]
# 或者: from scipy.sparse.linalg import eigsh [as 別名]
def occupied_states(hkgen,k,window=None,max_waves=None):
  """ Returns the WF of the occupied states in a 2d hamiltonian"""
  hk = hkgen(k) # get hamiltonian
  if max_waves is None: es,wfs = algebra.eigh(hk) # diagonalize all waves
  else:  es,wfs = slg.eigsh(csc_matrix(hk),k=max_waves,which="SA",
                      sigma=0.0,tol=arpack_tol,maxiter=arpack_maxiter)
  wfs = np.conjugate(wfs.transpose()) # wavefunctions
  occwf = []
  for (ie,iw) in zip(es,wfs):  # loop over states
    if window is None: # no energy window
      if ie < 0:  # if below fermi
        occwf.append(iw)  # add to the list
    else: # energy window provided
      if -abs(window)< ie < 0:  # between energy window and fermi
        occwf.append(iw)  # add to the list
  return np.array(occwf) 

# 需要導入模塊: from scipy.sparse import linalg [as 別名]
# 或者: from scipy.sparse.linalg import eigsh [as 別名]
def fsr_rankR(qsims, Wn, alpha = 0.99, R = 2000):
    vals, vecs = s_linalg.eigsh(Wn, k = R)
    p2 = diags((1.0 - alpha) / (1.0 - alpha*vals))
    vc = csr_matrix(vecs)
    p3 =  vc.dot(p2)
    vc_norm =  (vc.multiply(vc)).sum(axis = 0)
    out_sims = []
    for i in range(qsims.shape[0]):
        qsims_sparse = csr_matrix(qsims[i:i+1,:])
        p1 =(vc.T).dot(qsims_sparse.T)
        diff_sim = csr_matrix(p3)*csr_matrix(p1)
        out_sims.append(diff_sim.todense().reshape(-1,1))
    out_sims = np.concatenate(out_sims, axis = 1)
    ranks = np.argsort(-out_sims, axis = 0)
    return ranks 

# 需要導入模塊: from scipy.sparse import linalg [as 別名]
# 或者: from scipy.sparse.linalg import eigsh [as 別名]
def eigensolve( self, A , B , count=5 ):

    C = self.getConstraintsMatrix()

    A_constrained = dot( dot( C.transpose(), A ), C )
    B_constrained = dot( dot( C.transpose(), B ), C )

    eigvals , eigvecs = eigsh( A_constrained, count , B_constrained , sigma = 0. , which = 'LM' )

    x = zeros(shape=(len(self),count))

    for i,psi in enumerate(eigvecs.transpose()):
      x[:,i] = C * psi
      
    return eigvals,x 

# 需要導入模塊: from scipy.sparse import linalg [as 別名]
# 或者: from scipy.sparse.linalg import eigsh [as 別名]
def _svd(self, array, n_components, n_discard):
        """Returns first `n_components` left and right singular
        vectors u and v, discarding the first `n_discard`.

        """
        if self.svd_method == 'randomized':
            kwargs = {}
            if self.n_svd_vecs is not None:
                kwargs['n_oversamples'] = self.n_svd_vecs
            u, _, vt = randomized_svd(array, n_components,
                                      random_state=self.random_state,
                                      **kwargs)

        elif self.svd_method == 'arpack':
            u, _, vt = svds(array, k=n_components, ncv=self.n_svd_vecs)
            if np.any(np.isnan(vt)):
                # some eigenvalues of A * A.T are negative, causing
                # sqrt() to be np.nan. This causes some vectors in vt
                # to be np.nan.
                A = safe_sparse_dot(array.T, array)
                random_state = check_random_state(self.random_state)
                # initialize with [-1,1] as in ARPACK
                v0 = random_state.uniform(-1, 1, A.shape[0])
                _, v = eigsh(A, ncv=self.n_svd_vecs, v0=v0)
                vt = v.T
            if np.any(np.isnan(u)):
                A = safe_sparse_dot(array, array.T)
                random_state = check_random_state(self.random_state)
                # initialize with [-1,1] as in ARPACK
                v0 = random_state.uniform(-1, 1, A.shape[0])
                _, u = eigsh(A, ncv=self.n_svd_vecs, v0=v0)

        assert_all_finite(u)
        assert_all_finite(vt)
        u = u[:, n_discard:]
        vt = vt[n_discard:]
        return u, vt.T 

# 需要導入模塊: from scipy.sparse import linalg [as 別名]
# 或者: from scipy.sparse.linalg import eigsh [as 別名]
def test_eig(nr_sites, local_dim, rank, which, var_sites, rgen, request):
    if nr_sites <= var_sites:
        pt.skip("Nothing to test")
        return  # No local optimization can be defined
    if not (_pytest_want_long(request) or
            (nr_sites, local_dim, rank, var_sites, which) in {
                (3, 2, 4, 1, 'SA'), (4, 3, 5, 1, 'LM'), (5, 2, 1, 2, 'LA'),
                (6, 2, 4, 2, 'SA'),
            }):
        pt.skip("Should only be run in long tests")
    # With startvec_rank = 2 * rank and this seed, eig() gets
    # stuck in a local minimum. With startvec_rank = 3 * rank,
    # it does not.
    mpo = factory.random_mpo(nr_sites, local_dim, rank, randstate=rgen,
                             hermitian=True, normalized=True)
    mpo.canonicalize()
    op = mpo.to_array_global().reshape((local_dim**nr_sites,) * 2)
    v0 = factory._zrandn([local_dim**nr_sites], rgen)
    eigval, eigvec = eigsh(op, k=1, which=which, v0=v0)
    eigval, eigvec = eigval[0], eigvec[:, 0]

    eig_rank = (4 - var_sites) * rank
    eigval_mp, eigvec_mp = mp.eig(
        mpo, num_sweeps=5, var_sites=1, startvec_rank=eig_rank, randstate=rgen,
        eigs=ft.partial(eigsh, k=1, which=which, tol=1e-6, maxiter=250))
    eigvec_mp = eigvec_mp.to_array().flatten()

    overlap = np.inner(eigvec.conj(), eigvec_mp)
    assert_almost_equal(eigval, eigval_mp, decimal=14)
    assert_almost_equal(1, abs(overlap), decimal=14) 

# 需要導入模塊: from scipy.sparse import linalg [as 別名]
# 或者: from scipy.sparse.linalg import eigsh [as 別名]
def test_eig_sum(nr_sites, local_dim, rank, rgen):
    # Need at least three sites for var_sites = 2
    if nr_sites < 3:
        pt.skip("Nothing to test")
        return
    rank = max(1, rank // 2)
    mpo = factory.random_mpo(nr_sites, local_dim, rank, randstate=rgen,
                             hermitian=True, normalized=True)
    mpo.canonicalize()
    mps = factory.random_mpa(nr_sites, local_dim, rank, randstate=rgen,
                             dtype=np.complex_, normalized=True)
    mpas = [mpo, mps]

    vec = mps.to_array().ravel()
    op = mpo.to_array_global().reshape((local_dim**nr_sites,) * 2)
    op += np.outer(vec, vec.conj())
    eigvals, eigvec = np.linalg.eigh(op)

    # Eigenvals should be real for a hermitian matrix
    assert (np.abs(eigvals.imag) < 1e-10).all(), str(eigvals.imag)
    mineig_pos = eigvals.argmin()
    mineig, mineig_eigvec = eigvals[mineig_pos], eigvec[:, mineig_pos]
    mineig_mp, mineig_eigvec_mp = mp.eig_sum(
        mpas, num_sweeps=5, startvec_rank=5 * rank, randstate=rgen,
        eigs=ft.partial(eigsh, k=1, which='SA', tol=1e-6),
        var_sites=2)
    mineig_eigvec_mp = mineig_eigvec_mp.to_array().flatten()

    overlap = np.inner(mineig_eigvec.conj(), mineig_eigvec_mp)
    assert_almost_equal(mineig_mp, mineig)
    assert_almost_equal(abs(overlap), 1)