Package index • eigencore

User entry points

High-level functions for partial eigenvalue and SVD computation.

eig_partial(): Compute a partial eigendecomposition.
eig_full(): Compute a full dense eigendecomposition
svd_partial(): Compute a partial singular-value decomposition.
generalized_schur(): Compute a dense generalized Schur decomposition
generalized_svd(): Compute a dense generalized singular value decomposition

RSpectra-compatible shims

Drop-in replacements for RSpectra::eigs(), eigs_sym(), and svds().

eigs(): RSpectra-compatible eigen shim.
eigs_sym(): RSpectra-compatible symmetric eigen shim.
svds(): RSpectra-compatible SVD shim.

Problems and planning

Build problem descriptors and inspect the solver plan.

eigen_problem(): Define an eigenproblem.
svd_problem(): Define an SVD problem.
plan_solver(): Plan a solver for a problem.
solve(<eigencore_eigen_problem>): Solve a planned eigenproblem.
solve(<eigencore_svd_problem>): Solve a planned SVD problem.

Operators

Block-native linear operators and operator algebra.

linear_operator(): Create a block-native linear operator.
as_operator(): Convert an object to an eigencore operator.
adjoint(): Return the adjoint operator.
check_adjoint(): Check an operator adjoint identity.
compose(): Compose two operators.
crossprod_operator(): Create A^* A as an operator.
symmetric_operator(): Mark an operator as symmetric/Hermitian.
scale_cols(): Scale operator columns.
scale_rows(): Scale operator rows.
center(): Center an operator by rows or columns.

Targets

Selectors describing which part of the spectrum you want.

largest(): Target the largest algebraic values.
smallest(): Target the smallest algebraic values.
largest_magnitude(): Target the largest values by magnitude.
smallest_magnitude(): Target the smallest values by magnitude.
largest_real(): Target the largest real part.
smallest_real(): Target the smallest real part.
largest_imaginary(): Target the largest imaginary part.
smallest_imaginary(): Target the smallest imaginary part.
both_ends(): Target both algebraic ends.
nearest(): Target values nearest a shift.

Methods

Solver families and method descriptors.

auto(): Automatic solver choice.
lanczos(): Hermitian Lanczos method descriptor.
lobpcg(): LOBPCG method descriptor.
golub_kahan(): Golub-Kahan bidiagonalization method descriptor.
randomized(): Randomized SVD method descriptor.
shift_invert(): Shift-invert method descriptor.

Preconditioners

Preconditioner factories for iterative solvers.

shifted_cholesky_preconditioner(): Shifted Cholesky preconditioner.
shifted_diagonal_preconditioner(): Shifted diagonal preconditioner.
shifted_tridiagonal_preconditioner(): Shifted tridiagonal preconditioner.

Spaces and structure tags

euclidean(): Euclidean vector space descriptor.
hermitian(): Hermitian/symmetric operator structure descriptor.
general(): General operator structure descriptor.

Results, certificates, diagnostics

Inspecting solver output and the numerical evidence.

certificate(): Extract a result certificate.
residuals(<eigencore_eigen_result>) residuals(<eigencore_svd_result>) residuals(<eigencore_certificate>): Extract residual diagnostics.
backward_error(): Extract backward-error diagnostics.
values(): Extract computed values.
alpha_beta(): Extract homogeneous generalized coordinates.
vectors(): Extract eigenvectors.
left_vectors(): Extract left singular vectors or left eigenvectors.
right_vectors(): Extract right singular vectors.
diagnostics(): Extract diagnostics.