linalg¶

class pyviennacl.linalg.bicgstab_tag(tolerance=1e-08, max_iterations=400, max_iterations_before_restart=200)¶

Instruct the solver to solve using the stabilised bi-conjugate gradient (BiCGStab) solver.

Assumes that the system matrix is non-symmetric.

Used for supplying solver parameters.

error¶: The estimated relative error at the end of the solver run

iters¶: The number of solver iterations

max_iterations¶: The maximum number of iterations before a restart

tolerance¶: The relative tolerance

class pyviennacl.linalg.cg_tag(tolerance=1e-08, max_iterations=300)¶

Instruct the solver to solve using the conjugate gradient solver.

Assumes that the system matrix is symmetric positive definite.

Used for supplying solver parameters.

error¶: The estimated relative error at the end of the solver run

iters¶: The number of solver iterations

max_iterations¶: The maximum number of iterations

tolerance¶: The relative tolerance

pyviennacl.linalg.eig(A, tag)¶

Solve an eigenvalue problem for matrix A, with results depending on tag.

A : Matrix tag : eigenvalue computation tag instance

Must be one of * power_iter_tag * lanczos_tag See the help for each tag class for more information.

x : {scalar, array-like}: Return type depends on tag * if power_iter_tag, then a scalar of type dtype(A).type * if lanczos_tag, then an ndarray vector with same dtype as A

TypeError: If A is not a Matrix instance, or if tag is not understood

class pyviennacl.linalg.gmres_tag(tolerance=1e-08, max_iterations=300, krylov_dim=20)¶

Instruct the solver to solve using the GMRES solver.

Used for supplying solver parameters.

error¶: The estimated relative error at the end of the solver run

iters¶: The number of solver iterations

krylov_dim¶: The maximum dimension of the Krylov space before restart

max_iterations¶: The maximum number of iterations

max_restarts¶: The maximum number of GMRES restarts

tolerance¶: The relative tolerance

class pyviennacl.linalg.lanczos_tag(factor=0.75, num_eig=10, method=0, krylov=100)¶

Instruct the eigenvalue computation to use the Lanczos algorithm.

Used for supplying eigenvalue computation parameters.

factor¶: The tolerance factor for reorthogonalisation batches, expressed as the exponent of epsilon.

krylov_size¶: The size of the Kylov space.

method¶: The reorthogonalisation method choice.

num_eigenvalues¶: The number of eigenvalues to return.

class pyviennacl.linalg.lower_tag¶: Instruct the solver to solve for a lower triangular system matrix

pyviennacl.linalg.norm(x, ord=None)¶

Returns the vector norm of x, if that is defined.

The norm returned depends on the ord parameter, as in SciPy.

ord : {1, 2, inf}: Order of the norm. inf means NumPy’s inf object.

pyviennacl.linalg.plane_rotation(vec1, vec2, alpha, beta)¶

Computes (vec1, vec2) <- (alpha*vec1+beta*vec2, -beta*vec1+alpha*vec2)

vec1 : Vector vec2 : Vector alpha : any Python, NumPy or PyViennaCL scalar (real or integer) beta : any Python, NumPy or PyViennaCL scalar (real or integer)

None

The dtypes of the parameters must match.

Operates in-place on vec1 and vec2.

class pyviennacl.linalg.power_iter_tag(factor=1e-08, max_iterations=50000)¶

Instruct the eigenvalue computation to use the power iteration algorithm.

Used for supplying eigenvalue computation parameters.

factor¶

The termination factor.

If the eigenvalue does not change more than this value, the algorithm stops.

max_iterations¶: The maximum number of iterations

pyviennacl.linalg.prod(A, B)¶: Returns Mul(A, B) where that is defined (see the help for Mul), otherwise returns (A * B).

pyviennacl.linalg.solve(A, B, tag, precond=None)¶

Solve the linear system expressed by A x = B for x.

A : (M, M) dense or sparse Matrix: A square matrix
B : {Vector, Matrix}: Right-hand side in A x = B
tag : solver tag instance: Describes the system matrix and solver algorithm. Must be one of: * upper_tag * unit_upper_tag * lower_tag * unit_lower_tag * cg_tag * bicgstab_tag * gmres_tag See the help for each tag class for more information.

x : {Vector, Matrix}: Shape and class of x matches shape and class of B.

TypeError: If A is not a Matrix or SparseMatrixBase instance, or B is neither a Matrix nor a Vector instance, or if tag is unsupported.

class pyviennacl.linalg.unit_lower_tag¶: Instruct the solver to solve for a unit lower triangular system matrix

class pyviennacl.linalg.unit_upper_tag¶: Instruct the solver to solve for a unit upper triangular system matrix

class pyviennacl.linalg.upper_tag¶: Instruct the solver to solve for an upper triangular system matrix