Index

_

__init__() (low_rank_toolbox.krylov.spaces.extended_krylov_space.ExtendedKrylovSpace method) (low_rank_toolbox.krylov.spaces.ExtendedKrylovSpace method) (low_rank_toolbox.krylov.spaces.inverted_krylov_space.InvertedKrylovSpace method) (low_rank_toolbox.krylov.spaces.InvertedKrylovSpace method) (low_rank_toolbox.krylov.spaces.krylov_space.KrylovSpace method) (low_rank_toolbox.krylov.spaces.KrylovSpace method) (low_rank_toolbox.krylov.spaces.rational_krylov_space.RationalKrylovSpace method) (low_rank_toolbox.krylov.spaces.RationalKrylovSpace method) (low_rank_toolbox.krylov.spaces.space_structure.SpaceStructure method) (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix method) (low_rank_toolbox.matrices.LowRankMatrix method), [1], [2], [3] (low_rank_toolbox.matrices.QR method), [1], [2], [3] (low_rank_toolbox.matrices.qr.QR method) (low_rank_toolbox.matrices.quasi_svd.QuasiSVD method) (low_rank_toolbox.matrices.QuasiSVD method), [1], [2], [3] (low_rank_toolbox.matrices.SVD method), [1], [2], [3] (low_rank_toolbox.matrices.svd.SVD method)

_alpha (low_rank_toolbox.krylov.spaces.krylov_space.KrylovSpace attribute) (low_rank_toolbox.krylov.spaces.KrylovSpace attribute) _beta (low_rank_toolbox.krylov.spaces.krylov_space.KrylovSpace attribute) (low_rank_toolbox.krylov.spaces.KrylovSpace attribute) _transposed (low_rank_toolbox.matrices.QR attribute), [1], [2] (low_rank_toolbox.matrices.qr.QR attribute)

A

A (low_rank_toolbox.krylov.spaces.extended_krylov_space.ExtendedKrylovSpace attribute) (low_rank_toolbox.krylov.spaces.ExtendedKrylovSpace attribute) (low_rank_toolbox.krylov.spaces.inverted_krylov_space.InvertedKrylovSpace attribute) (low_rank_toolbox.krylov.spaces.InvertedKrylovSpace attribute) (low_rank_toolbox.krylov.spaces.krylov_space.KrylovSpace attribute) (low_rank_toolbox.krylov.spaces.KrylovSpace attribute) (low_rank_toolbox.krylov.spaces.rational_krylov_space.RationalKrylovSpace attribute) (low_rank_toolbox.krylov.spaces.RationalKrylovSpace attribute) adaptive_randomized_svd() (in module low_rank_toolbox.randomized) adaptive_rangefinder() (in module low_rank_toolbox.randomized) Ak (low_rank_toolbox.krylov.spaces.space_structure.SpaceStructure property) allclose() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix method) (low_rank_toolbox.matrices.LowRankMatrix method), [1], [2]

Am (low_rank_toolbox.krylov.spaces.space_structure.SpaceStructure property) approximation_error() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix method) (low_rank_toolbox.matrices.LowRankMatrix method), [1], [2] Arnoldi() (in module low_rank_toolbox.krylov.utils) (in module low_rank_toolbox.krylov.utils.arnoldi) ARP() (in module low_rank_toolbox.cssp) (in module low_rank_toolbox.cssp.arp) augment_basis() (low_rank_toolbox.krylov.spaces.extended_krylov_space.ExtendedKrylovSpace method) (low_rank_toolbox.krylov.spaces.ExtendedKrylovSpace method) (low_rank_toolbox.krylov.spaces.krylov_space.KrylovSpace method) (low_rank_toolbox.krylov.spaces.KrylovSpace method) (low_rank_toolbox.krylov.spaces.rational_krylov_space.RationalKrylovSpace method) (low_rank_toolbox.krylov.spaces.RationalKrylovSpace method) (low_rank_toolbox.krylov.spaces.space_structure.SpaceStructure method)

B

basis (low_rank_toolbox.krylov.spaces.extended_krylov_space.ExtendedKrylovSpace attribute) (low_rank_toolbox.krylov.spaces.extended_krylov_space.ExtendedKrylovSpace property) (low_rank_toolbox.krylov.spaces.ExtendedKrylovSpace attribute) (low_rank_toolbox.krylov.spaces.ExtendedKrylovSpace property) (low_rank_toolbox.krylov.spaces.inverted_krylov_space.InvertedKrylovSpace attribute) (low_rank_toolbox.krylov.spaces.InvertedKrylovSpace attribute) (low_rank_toolbox.krylov.spaces.krylov_space.KrylovSpace attribute) (low_rank_toolbox.krylov.spaces.krylov_space.KrylovSpace property) (low_rank_toolbox.krylov.spaces.KrylovSpace attribute) (low_rank_toolbox.krylov.spaces.KrylovSpace property) (low_rank_toolbox.krylov.spaces.rational_krylov_space.RationalKrylovSpace attribute) (low_rank_toolbox.krylov.spaces.rational_krylov_space.RationalKrylovSpace property) (low_rank_toolbox.krylov.spaces.RationalKrylovSpace attribute) (low_rank_toolbox.krylov.spaces.RationalKrylovSpace property) (low_rank_toolbox.krylov.spaces.space_structure.SpaceStructure property)

block_Arnoldi() (in module low_rank_toolbox.krylov.utils) (in module low_rank_toolbox.krylov.utils.arnoldi) block_Lanczos() (in module low_rank_toolbox.krylov.utils) (in module low_rank_toolbox.krylov.utils.lanczos) block_rational_Arnoldi() (in module low_rank_toolbox.krylov.utils) (in module low_rank_toolbox.krylov.utils.arnoldi) block_shift_and_invert_Arnoldi() (in module low_rank_toolbox.krylov.utils) (in module low_rank_toolbox.krylov.utils.arnoldi)

C

check_inputs() (low_rank_toolbox.krylov.spaces.space_structure.SpaceStructure class method) compress() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix method) (low_rank_toolbox.matrices.LowRankMatrix method), [1], [2] compress_() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix method) (low_rank_toolbox.matrices.LowRankMatrix method), [1], [2] compression_ratio() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix method) (low_rank_toolbox.matrices.LowRankMatrix method), [1], [2] compute_all() (low_rank_toolbox.krylov.spaces.space_structure.SpaceStructure method) cond() (low_rank_toolbox.matrices.QR method), [1], [2] (low_rank_toolbox.matrices.qr.QR method) cond_estimate() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix method) (low_rank_toolbox.matrices.LowRankMatrix method), [1], [2] (low_rank_toolbox.matrices.quasi_svd.QuasiSVD method) (low_rank_toolbox.matrices.QuasiSVD method), [1], [2] Configuration (low_rank_toolbox.matrices.quasi_svd.QuasiSVD attribute) (low_rank_toolbox.matrices.QuasiSVD attribute), [1], [2] (low_rank_toolbox.matrices.SVD attribute), [1], [2] (low_rank_toolbox.matrices.svd.SVD attribute)

conj (low_rank_toolbox.matrices.QR attribute), [1], [2] (low_rank_toolbox.matrices.QR property), [1], [2] (low_rank_toolbox.matrices.qr.QR attribute) (low_rank_toolbox.matrices.qr.QR property) conj() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix method) (low_rank_toolbox.matrices.LowRankMatrix method), [1], [2] (low_rank_toolbox.matrices.quasi_svd.QuasiSVD method) (low_rank_toolbox.matrices.QuasiSVD method), [1], [2] Conversions (low_rank_toolbox.matrices.QR attribute), [1], [2] (low_rank_toolbox.matrices.qr.QR attribute) copy() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix method) (low_rank_toolbox.matrices.LowRankMatrix method), [1], [2] create_data_alias() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix static method) (low_rank_toolbox.matrices.LowRankMatrix static method), [1], [2] create_matrix_alias() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix static method) (low_rank_toolbox.matrices.LowRankMatrix static method), [1], [2]

D

deepshape (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix property) (low_rank_toolbox.matrices.LowRankMatrix property), [1], [2] DEIM() (in module low_rank_toolbox.cssp) (in module low_rank_toolbox.cssp.deim) diag() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix method) (low_rank_toolbox.matrices.LowRankMatrix method), [1], [2] (low_rank_toolbox.matrices.quasi_svd.QuasiSVD method) (low_rank_toolbox.matrices.QuasiSVD method), [1], [2] dot() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix method) (low_rank_toolbox.matrices.LowRankMatrix method), [1], [2] (low_rank_toolbox.matrices.QR method), [1], [2] (low_rank_toolbox.matrices.qr.QR method) (low_rank_toolbox.matrices.quasi_svd.QuasiSVD method) (low_rank_toolbox.matrices.QuasiSVD method), [1], [2] (low_rank_toolbox.matrices.SVD method), [1], [2] (low_rank_toolbox.matrices.svd.SVD method)

dot_sparse() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix method) (low_rank_toolbox.matrices.LowRankMatrix method), [1], [2]

E

expm() (low_rank_toolbox.matrices.quasi_svd.QuasiSVD method) (low_rank_toolbox.matrices.QuasiSVD method), [1], [2] (low_rank_toolbox.matrices.SVD method), [1], [2] (low_rank_toolbox.matrices.svd.SVD method) expm_multiply() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix method) (low_rank_toolbox.matrices.LowRankMatrix method), [1], [2]

ExtendedKrylovSpace (class in low_rank_toolbox.krylov.spaces) (class in low_rank_toolbox.krylov.spaces.extended_krylov_space) extract_optimal_poles() (in module low_rank_toolbox.krylov.data) (in module low_rank_toolbox.krylov.data.optimal_poles)

F

flatten() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix method) (low_rank_toolbox.matrices.LowRankMatrix method), [1], [2] from_dense() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix class method) (low_rank_toolbox.matrices.LowRankMatrix class method), [1], [2] from_full() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix class method) (low_rank_toolbox.matrices.LowRankMatrix class method), [1], [2] from_low_rank() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix class method) (low_rank_toolbox.matrices.LowRankMatrix class method), [1], [2] (low_rank_toolbox.matrices.QR class method), [1], [2] (low_rank_toolbox.matrices.qr.QR class method) (low_rank_toolbox.matrices.SVD class method), [1], [2] (low_rank_toolbox.matrices.svd.SVD class method) from_matrix() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix class method) (low_rank_toolbox.matrices.LowRankMatrix class method), [1], [2] (low_rank_toolbox.matrices.QR class method), [1], [2] (low_rank_toolbox.matrices.qr.QR class method) (low_rank_toolbox.matrices.SVD class method), [1], [2] (low_rank_toolbox.matrices.svd.SVD class method)

from_qr() (low_rank_toolbox.matrices.quasi_svd.QuasiSVD class method) (low_rank_toolbox.matrices.QuasiSVD class method), [1], [2] from_quasiSVD() (low_rank_toolbox.matrices.SVD class method), [1], [2] (low_rank_toolbox.matrices.svd.SVD class method) from_svd() (low_rank_toolbox.matrices.QR class method), [1], [2] (low_rank_toolbox.matrices.qr.QR class method) full() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix method) (low_rank_toolbox.matrices.LowRankMatrix method), [1], [2] (low_rank_toolbox.matrices.SVD method), [1], [2] (low_rank_toolbox.matrices.svd.SVD method) full_svd() (low_rank_toolbox.matrices.SVD class method), [1], [2] (low_rank_toolbox.matrices.svd.SVD class method)

G

gather() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix method) (low_rank_toolbox.matrices.LowRankMatrix method), [1], [2] generalized_nystrom() (in module low_rank_toolbox.randomized), [1] generate_random() (low_rank_toolbox.matrices.QR class method), [1], [2] (low_rank_toolbox.matrices.qr.QR class method) (low_rank_toolbox.matrices.quasi_svd.QuasiSVD class method) (low_rank_toolbox.matrices.QuasiSVD class method), [1], [2] (low_rank_toolbox.matrices.SVD class method), [1], [2] (low_rank_toolbox.matrices.svd.SVD class method)

get_block() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix method) (low_rank_toolbox.matrices.LowRankMatrix method), [1], [2] givens() (in module low_rank_toolbox.cssp.utils), [1] gpode() (in module low_rank_toolbox.cssp), [1] gpodr() (in module low_rank_toolbox.cssp), [1]

H

H (low_rank_toolbox.krylov.spaces.krylov_space.KrylovSpace attribute) (low_rank_toolbox.krylov.spaces.KrylovSpace attribute) (low_rank_toolbox.krylov.spaces.rational_krylov_space.RationalKrylovSpace attribute) (low_rank_toolbox.krylov.spaces.RationalKrylovSpace attribute) (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix property) (low_rank_toolbox.matrices.LowRankMatrix property), [1], [2] (low_rank_toolbox.matrices.QR attribute), [1], [2] (low_rank_toolbox.matrices.QR property), [1], [2] (low_rank_toolbox.matrices.qr.QR attribute) (low_rank_toolbox.matrices.qr.QR property) (low_rank_toolbox.matrices.quasi_svd.QuasiSVD property) (low_rank_toolbox.matrices.QuasiSVD property), [1], [2] (low_rank_toolbox.matrices.SVD property), [1], [2] (low_rank_toolbox.matrices.svd.SVD property)

H1 (low_rank_toolbox.krylov.spaces.extended_krylov_space.ExtendedKrylovSpace property) (low_rank_toolbox.krylov.spaces.ExtendedKrylovSpace property) H2 (low_rank_toolbox.krylov.spaces.extended_krylov_space.ExtendedKrylovSpace property) (low_rank_toolbox.krylov.spaces.ExtendedKrylovSpace property) hadamard() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix method) (low_rank_toolbox.matrices.LowRankMatrix method), [1], [2] (low_rank_toolbox.matrices.QR method), [1], [2] (low_rank_toolbox.matrices.qr.QR method) (low_rank_toolbox.matrices.quasi_svd.QuasiSVD method) (low_rank_toolbox.matrices.QuasiSVD method), [1], [2] (low_rank_toolbox.matrices.SVD method), [1], [2] (low_rank_toolbox.matrices.svd.SVD method)

I

invA (low_rank_toolbox.krylov.spaces.extended_krylov_space.ExtendedKrylovSpace attribute) (low_rank_toolbox.krylov.spaces.ExtendedKrylovSpace attribute) (low_rank_toolbox.krylov.spaces.inverted_krylov_space.InvertedKrylovSpace attribute) (low_rank_toolbox.krylov.spaces.InvertedKrylovSpace attribute) inverted_krylov_space (low_rank_toolbox.krylov.spaces.extended_krylov_space.ExtendedKrylovSpace attribute) (low_rank_toolbox.krylov.spaces.ExtendedKrylovSpace attribute) InvertedKrylovSpace (class in low_rank_toolbox.krylov.spaces) (class in low_rank_toolbox.krylov.spaces.inverted_krylov_space) is_memory_efficient (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix property) (low_rank_toolbox.matrices.LowRankMatrix property), [1], [2] is_orthogonal() (low_rank_toolbox.matrices.QR method), [1], [2] (low_rank_toolbox.matrices.qr.QR method) (low_rank_toolbox.matrices.quasi_svd.QuasiSVD method) (low_rank_toolbox.matrices.QuasiSVD method), [1], [2]

is_singular() (low_rank_toolbox.matrices.quasi_svd.QuasiSVD method) (low_rank_toolbox.matrices.QuasiSVD method), [1], [2] is_symmetric (low_rank_toolbox.krylov.spaces.krylov_space.KrylovSpace attribute) (low_rank_toolbox.krylov.spaces.KrylovSpace attribute) is_symmetric() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix method) (low_rank_toolbox.matrices.LowRankMatrix method), [1], [2] (low_rank_toolbox.matrices.quasi_svd.QuasiSVD method) (low_rank_toolbox.matrices.QuasiSVD method), [1], [2] is_upper_triangular() (low_rank_toolbox.matrices.QR method), [1], [2] (low_rank_toolbox.matrices.qr.QR method) is_well_conditioned() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix method) (low_rank_toolbox.matrices.LowRankMatrix method), [1], [2]

K

K (low_rank_toolbox.matrices.quasi_svd.QuasiSVD attribute) (low_rank_toolbox.matrices.quasi_svd.QuasiSVD property) (low_rank_toolbox.matrices.QuasiSVD attribute), [1], [2] (low_rank_toolbox.matrices.QuasiSVD property), [1], [2]

krylov_space (low_rank_toolbox.krylov.spaces.extended_krylov_space.ExtendedKrylovSpace attribute) (low_rank_toolbox.krylov.spaces.ExtendedKrylovSpace attribute) KrylovSpace (class in low_rank_toolbox.krylov.spaces) (class in low_rank_toolbox.krylov.spaces.krylov_space)

L

L (low_rank_toolbox.matrices.quasi_svd.QuasiSVD attribute) (low_rank_toolbox.matrices.quasi_svd.QuasiSVD property) (low_rank_toolbox.matrices.QuasiSVD attribute), [1], [2] (low_rank_toolbox.matrices.QuasiSVD property), [1], [2] Lanczos() (in module low_rank_toolbox.krylov.utils) (in module low_rank_toolbox.krylov.utils.lanczos) length (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix property) (low_rank_toolbox.matrices.LowRankMatrix property), [1], [2] load() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix class method) (low_rank_toolbox.matrices.LowRankMatrix class method), [1], [2] low_rank_toolbox.cssp module low_rank_toolbox.cssp.arp module low_rank_toolbox.cssp.deim module low_rank_toolbox.cssp.osinsky module low_rank_toolbox.cssp.oversampling_sqdeim module low_rank_toolbox.cssp.qdeim module low_rank_toolbox.cssp.sqdeim module low_rank_toolbox.cssp.utils module low_rank_toolbox.krylov module low_rank_toolbox.krylov.data module low_rank_toolbox.krylov.data.optimal_poles module low_rank_toolbox.krylov.solvers module low_rank_toolbox.krylov.solvers.lyapunov_solvers module low_rank_toolbox.krylov.solvers.sylvester_solvers module

low_rank_toolbox.krylov.spaces module low_rank_toolbox.krylov.spaces.extended_krylov_space module low_rank_toolbox.krylov.spaces.inverted_krylov_space module low_rank_toolbox.krylov.spaces.krylov_space module low_rank_toolbox.krylov.spaces.rational_krylov_space module low_rank_toolbox.krylov.spaces.space_structure module low_rank_toolbox.krylov.utils module low_rank_toolbox.krylov.utils.arnoldi module low_rank_toolbox.krylov.utils.lanczos module low_rank_toolbox.matrices module low_rank_toolbox.matrices.low_rank_matrix module low_rank_toolbox.matrices.qr module low_rank_toolbox.matrices.quasi_svd module low_rank_toolbox.matrices.svd module low_rank_toolbox.randomized module LowRankEfficiencyWarning LowRankMatrix (class in low_rank_toolbox.matrices), [1], [2] (class in low_rank_toolbox.matrices.low_rank_matrix) lstsq() (low_rank_toolbox.matrices.QR method), [1], [2] (low_rank_toolbox.matrices.qr.QR method) (low_rank_toolbox.matrices.quasi_svd.QuasiSVD method) (low_rank_toolbox.matrices.QuasiSVD method), [1], [2] (low_rank_toolbox.matrices.SVD method), [1], [2] (low_rank_toolbox.matrices.svd.SVD method)

M

m (low_rank_toolbox.krylov.spaces.krylov_space.KrylovSpace attribute) (low_rank_toolbox.krylov.spaces.KrylovSpace attribute) (low_rank_toolbox.krylov.spaces.rational_krylov_space.RationalKrylovSpace attribute) (low_rank_toolbox.krylov.spaces.RationalKrylovSpace attribute) matvec() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix method) (low_rank_toolbox.matrices.LowRankMatrix method), [1], [2] max_iter (low_rank_toolbox.krylov.spaces.rational_krylov_space.RationalKrylovSpace attribute) (low_rank_toolbox.krylov.spaces.RationalKrylovSpace attribute) memory_usage() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix method) (low_rank_toolbox.matrices.LowRankMatrix method), [1], [2] MemoryEfficiencyWarning module low_rank_toolbox.cssp low_rank_toolbox.cssp.arp low_rank_toolbox.cssp.deim low_rank_toolbox.cssp.osinsky low_rank_toolbox.cssp.oversampling_sqdeim low_rank_toolbox.cssp.qdeim low_rank_toolbox.cssp.sqdeim low_rank_toolbox.cssp.utils low_rank_toolbox.krylov low_rank_toolbox.krylov.data low_rank_toolbox.krylov.data.optimal_poles low_rank_toolbox.krylov.solvers low_rank_toolbox.krylov.solvers.lyapunov_solvers low_rank_toolbox.krylov.solvers.sylvester_solvers low_rank_toolbox.krylov.spaces low_rank_toolbox.krylov.spaces.extended_krylov_space low_rank_toolbox.krylov.spaces.inverted_krylov_space low_rank_toolbox.krylov.spaces.krylov_space low_rank_toolbox.krylov.spaces.rational_krylov_space low_rank_toolbox.krylov.spaces.space_structure low_rank_toolbox.krylov.utils low_rank_toolbox.krylov.utils.arnoldi low_rank_toolbox.krylov.utils.lanczos low_rank_toolbox.matrices low_rank_toolbox.matrices.low_rank_matrix low_rank_toolbox.matrices.qr low_rank_toolbox.matrices.quasi_svd low_rank_toolbox.matrices.svd low_rank_toolbox.randomized

multi_add() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix method) (low_rank_toolbox.matrices.LowRankMatrix method), [1], [2] (low_rank_toolbox.matrices.quasi_svd.QuasiSVD class method) (low_rank_toolbox.matrices.QuasiSVD class method), [1], [2] multi_dot() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix method) (low_rank_toolbox.matrices.LowRankMatrix method), [1], [2] (low_rank_toolbox.matrices.quasi_svd.QuasiSVD class method) (low_rank_toolbox.matrices.QuasiSVD class method), [1], [2]

N

ndim (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix property) (low_rank_toolbox.matrices.LowRankMatrix property), [1], [2] norm() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix method) (low_rank_toolbox.matrices.LowRankMatrix method), [1], [2] (low_rank_toolbox.matrices.QR method), [1], [2] (low_rank_toolbox.matrices.qr.QR method) (low_rank_toolbox.matrices.quasi_svd.QuasiSVD method) (low_rank_toolbox.matrices.QuasiSVD method), [1], [2] (low_rank_toolbox.matrices.SVD method), [1], [2] (low_rank_toolbox.matrices.svd.SVD method)

norm_squared() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix method) (low_rank_toolbox.matrices.LowRankMatrix method), [1], [2] (low_rank_toolbox.matrices.quasi_svd.QuasiSVD method) (low_rank_toolbox.matrices.QuasiSVD method), [1], [2] Norms (low_rank_toolbox.matrices.QR attribute), [1], [2] (low_rank_toolbox.matrices.qr.QR attribute) numerical_health_check() (low_rank_toolbox.matrices.quasi_svd.QuasiSVD method) (low_rank_toolbox.matrices.QuasiSVD method), [1], [2] numerical_rank (low_rank_toolbox.matrices.quasi_svd.QuasiSVD property) (low_rank_toolbox.matrices.QuasiSVD property), [1], [2]

O

Osinsky() (in module low_rank_toolbox.cssp) (in module low_rank_toolbox.cssp.osinsky)

oversampling_sQDEIM() (in module low_rank_toolbox.cssp) (in module low_rank_toolbox.cssp.oversampling_sqdeim)

P

plot_singular_value_decay() (low_rank_toolbox.matrices.quasi_svd.QuasiSVD method) (low_rank_toolbox.matrices.QuasiSVD method), [1], [2] poles (low_rank_toolbox.krylov.spaces.rational_krylov_space.RationalKrylovSpace attribute) (low_rank_toolbox.krylov.spaces.RationalKrylovSpace attribute) power() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix method) (low_rank_toolbox.matrices.LowRankMatrix method), [1], [2] project_onto_column_space() (low_rank_toolbox.matrices.quasi_svd.QuasiSVD method) (low_rank_toolbox.matrices.QuasiSVD method), [1], [2] project_onto_interpolated_tangent_space() (low_rank_toolbox.matrices.quasi_svd.QuasiSVD method) (low_rank_toolbox.matrices.QuasiSVD method), [1], [2] project_onto_row_space() (low_rank_toolbox.matrices.quasi_svd.QuasiSVD method) (low_rank_toolbox.matrices.QuasiSVD method), [1], [2] project_onto_tangent_space() (low_rank_toolbox.matrices.quasi_svd.QuasiSVD method) (low_rank_toolbox.matrices.QuasiSVD method), [1], [2]

Properties (low_rank_toolbox.matrices.QR attribute), [1], [2] (low_rank_toolbox.matrices.qr.QR attribute) (low_rank_toolbox.matrices.quasi_svd.QuasiSVD attribute) (low_rank_toolbox.matrices.QuasiSVD attribute), [1], [2] (low_rank_toolbox.matrices.SVD attribute), [1], [2] (low_rank_toolbox.matrices.svd.SVD attribute) pseudoinverse() (low_rank_toolbox.matrices.QR method), [1], [2] (low_rank_toolbox.matrices.qr.QR method) (low_rank_toolbox.matrices.quasi_svd.QuasiSVD method) (low_rank_toolbox.matrices.QuasiSVD method), [1], [2] (low_rank_toolbox.matrices.SVD method), [1], [2] (low_rank_toolbox.matrices.svd.SVD method)

Q

Q (low_rank_toolbox.krylov.spaces.extended_krylov_space.ExtendedKrylovSpace attribute) (low_rank_toolbox.krylov.spaces.extended_krylov_space.ExtendedKrylovSpace property) (low_rank_toolbox.krylov.spaces.ExtendedKrylovSpace attribute) (low_rank_toolbox.krylov.spaces.ExtendedKrylovSpace property) (low_rank_toolbox.krylov.spaces.inverted_krylov_space.InvertedKrylovSpace attribute) (low_rank_toolbox.krylov.spaces.InvertedKrylovSpace attribute) (low_rank_toolbox.krylov.spaces.krylov_space.KrylovSpace attribute) (low_rank_toolbox.krylov.spaces.KrylovSpace attribute) (low_rank_toolbox.krylov.spaces.rational_krylov_space.RationalKrylovSpace attribute) (low_rank_toolbox.krylov.spaces.RationalKrylovSpace attribute) (low_rank_toolbox.matrices.QR attribute), [1], [2] (low_rank_toolbox.matrices.QR property), [1], [2] (low_rank_toolbox.matrices.qr.QR attribute) (low_rank_toolbox.matrices.qr.QR property) Q1 (low_rank_toolbox.krylov.spaces.extended_krylov_space.ExtendedKrylovSpace attribute) (low_rank_toolbox.krylov.spaces.extended_krylov_space.ExtendedKrylovSpace property) (low_rank_toolbox.krylov.spaces.ExtendedKrylovSpace attribute) (low_rank_toolbox.krylov.spaces.ExtendedKrylovSpace property)

Q2 (low_rank_toolbox.krylov.spaces.extended_krylov_space.ExtendedKrylovSpace attribute) (low_rank_toolbox.krylov.spaces.extended_krylov_space.ExtendedKrylovSpace property) (low_rank_toolbox.krylov.spaces.ExtendedKrylovSpace attribute) (low_rank_toolbox.krylov.spaces.ExtendedKrylovSpace property) QDEIM() (in module low_rank_toolbox.cssp) (in module low_rank_toolbox.cssp.qdeim) QR (class in low_rank_toolbox.matrices), [1], [2] (class in low_rank_toolbox.matrices.qr) qr() (low_rank_toolbox.matrices.QR class method), [1], [2] (low_rank_toolbox.matrices.qr.QR class method) QuasiSVD (class in low_rank_toolbox.matrices), [1], [2] (class in low_rank_toolbox.matrices.quasi_svd)

R

R (low_rank_toolbox.matrices.QR attribute), [1], [2] (low_rank_toolbox.matrices.QR property), [1], [2] (low_rank_toolbox.matrices.qr.QR attribute) (low_rank_toolbox.matrices.qr.QR property) randomized_svd() (in module low_rank_toolbox.randomized), [1] rangefinder() (in module low_rank_toolbox.randomized), [1] rank (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix property) (low_rank_toolbox.matrices.LowRankMatrix property), [1], [2] (low_rank_toolbox.matrices.QR attribute), [1], [2] (low_rank_toolbox.matrices.qr.QR attribute) (low_rank_toolbox.matrices.quasi_svd.QuasiSVD attribute) (low_rank_toolbox.matrices.QuasiSVD attribute), [1], [2] (low_rank_toolbox.matrices.SVD attribute), [1], [2] (low_rank_toolbox.matrices.svd.SVD attribute)

rank_one_update() (low_rank_toolbox.matrices.quasi_svd.QuasiSVD method) (low_rank_toolbox.matrices.QuasiSVD method), [1], [2] rational_Arnoldi() (in module low_rank_toolbox.krylov.utils) (in module low_rank_toolbox.krylov.utils.arnoldi) RationalKrylovSpace (class in low_rank_toolbox.krylov.spaces) (class in low_rank_toolbox.krylov.spaces.rational_krylov_space) reduced_A (low_rank_toolbox.krylov.spaces.space_structure.SpaceStructure property) reduced_svd() (low_rank_toolbox.matrices.SVD class method), [1], [2] (low_rank_toolbox.matrices.svd.SVD class method) reorthogonalize() (low_rank_toolbox.matrices.quasi_svd.QuasiSVD method) (low_rank_toolbox.matrices.QuasiSVD method), [1], [2] rmatvec() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix method) (low_rank_toolbox.matrices.LowRankMatrix method), [1], [2]

S

S (low_rank_toolbox.matrices.quasi_svd.QuasiSVD attribute) (low_rank_toolbox.matrices.quasi_svd.QuasiSVD property) (low_rank_toolbox.matrices.QuasiSVD attribute), [1], [2] (low_rank_toolbox.matrices.QuasiSVD property), [1], [2] (low_rank_toolbox.matrices.SVD attribute), [1], [2] s (low_rank_toolbox.matrices.SVD attribute), [1], [2] (low_rank_toolbox.matrices.SVD property), [1], [2] S (low_rank_toolbox.matrices.svd.SVD attribute) s (low_rank_toolbox.matrices.svd.SVD attribute) (low_rank_toolbox.matrices.svd.SVD property) save() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix method) (low_rank_toolbox.matrices.LowRankMatrix method), [1], [2] scale_() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix method) (low_rank_toolbox.matrices.LowRankMatrix method), [1], [2] shape (low_rank_toolbox.matrices.QR attribute), [1], [2] (low_rank_toolbox.matrices.qr.QR attribute) (low_rank_toolbox.matrices.quasi_svd.QuasiSVD attribute) (low_rank_toolbox.matrices.QuasiSVD attribute), [1], [2] (low_rank_toolbox.matrices.SVD attribute), [1], [2] (low_rank_toolbox.matrices.svd.SVD attribute) shift_and_invert_Arnoldi() (in module low_rank_toolbox.krylov.utils) (in module low_rank_toolbox.krylov.utils.arnoldi) sing_vals (low_rank_toolbox.matrices.quasi_svd.QuasiSVD attribute) (low_rank_toolbox.matrices.QuasiSVD attribute), [1], [2] (low_rank_toolbox.matrices.SVD attribute), [1], [2] (low_rank_toolbox.matrices.svd.SVD attribute) sing_vals() (low_rank_toolbox.matrices.quasi_svd.QuasiSVD method) (low_rank_toolbox.matrices.QuasiSVD method), [1], [2] (low_rank_toolbox.matrices.SVD method), [1], [2] (low_rank_toolbox.matrices.svd.SVD method) singular_values() (low_rank_toolbox.matrices.SVD class method), [1], [2] (low_rank_toolbox.matrices.svd.SVD class method) size (low_rank_toolbox.krylov.spaces.extended_krylov_space.ExtendedKrylovSpace property) (low_rank_toolbox.krylov.spaces.ExtendedKrylovSpace property) (low_rank_toolbox.krylov.spaces.krylov_space.KrylovSpace property) (low_rank_toolbox.krylov.spaces.KrylovSpace property) (low_rank_toolbox.krylov.spaces.rational_krylov_space.RationalKrylovSpace property) (low_rank_toolbox.krylov.spaces.RationalKrylovSpace property) (low_rank_toolbox.krylov.spaces.space_structure.SpaceStructure property) (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix property) (low_rank_toolbox.matrices.LowRankMatrix property), [1], [2]

solve() (low_rank_toolbox.matrices.QR method), [1], [2] (low_rank_toolbox.matrices.qr.QR method) (low_rank_toolbox.matrices.quasi_svd.QuasiSVD method) (low_rank_toolbox.matrices.QuasiSVD method), [1], [2] (low_rank_toolbox.matrices.SVD method), [1], [2] (low_rank_toolbox.matrices.svd.SVD method) solve_lyapunov() (in module low_rank_toolbox.krylov.solvers) (in module low_rank_toolbox.krylov.solvers.lyapunov_solvers) solve_small_lyapunov() (in module low_rank_toolbox.krylov.solvers.lyapunov_solvers) solve_small_sylvester() (in module low_rank_toolbox.krylov.solvers.sylvester_solvers) solve_sparse_low_rank_non_symmetric_lyapunov() (in module low_rank_toolbox.krylov.solvers.lyapunov_solvers) solve_sparse_low_rank_sylvester() (in module low_rank_toolbox.krylov.solvers.sylvester_solvers) solve_sparse_low_rank_symmetric_lyapunov() (in module low_rank_toolbox.krylov.solvers.lyapunov_solvers) solve_sylvester() (in module low_rank_toolbox.krylov.solvers) (in module low_rank_toolbox.krylov.solvers.sylvester_solvers) solve_sylvester_large_A_small_B() (in module low_rank_toolbox.krylov.solvers.sylvester_solvers) SpaceStructure (class in low_rank_toolbox.krylov.spaces.space_structure) sQDEIM() (in module low_rank_toolbox.cssp) (in module low_rank_toolbox.cssp.sqdeim) sqrtm() (low_rank_toolbox.matrices.quasi_svd.QuasiSVD method) (low_rank_toolbox.matrices.QuasiSVD method), [1], [2] (low_rank_toolbox.matrices.SVD method), [1], [2] (low_rank_toolbox.matrices.svd.SVD method) sRRQR() (in module low_rank_toolbox.cssp.utils), [1] sRRQR_rank() (in module low_rank_toolbox.cssp.utils) sRRQR_tol() (in module low_rank_toolbox.cssp.utils) SVD (class in low_rank_toolbox.matrices), [1], [2] (class in low_rank_toolbox.matrices.svd) svd_type (low_rank_toolbox.matrices.quasi_svd.QuasiSVD property) (low_rank_toolbox.matrices.QuasiSVD property), [1], [2]

T

T (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix property) (low_rank_toolbox.matrices.LowRankMatrix property), [1], [2] (low_rank_toolbox.matrices.QR attribute), [1], [2] (low_rank_toolbox.matrices.QR property), [1], [2] (low_rank_toolbox.matrices.qr.QR attribute) (low_rank_toolbox.matrices.qr.QR property) (low_rank_toolbox.matrices.quasi_svd.QuasiSVD property) (low_rank_toolbox.matrices.QuasiSVD property), [1], [2] (low_rank_toolbox.matrices.SVD attribute), [1], [2] (low_rank_toolbox.matrices.SVD property), [1], [2] (low_rank_toolbox.matrices.svd.SVD attribute) (low_rank_toolbox.matrices.svd.SVD property) to_dense() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix method) (low_rank_toolbox.matrices.LowRankMatrix method), [1], [2] to_full() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix method) (low_rank_toolbox.matrices.LowRankMatrix method), [1], [2] to_qr() (low_rank_toolbox.matrices.quasi_svd.QuasiSVD method) (low_rank_toolbox.matrices.QuasiSVD method), [1], [2] to_sparse() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix method) (low_rank_toolbox.matrices.LowRankMatrix method), [1], [2] to_svd() (low_rank_toolbox.matrices.QR method), [1], [2] (low_rank_toolbox.matrices.qr.QR method) (low_rank_toolbox.matrices.quasi_svd.QuasiSVD method) (low_rank_toolbox.matrices.QuasiSVD method), [1], [2]

todense() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix method) (low_rank_toolbox.matrices.LowRankMatrix method), [1], [2] trace() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix method) (low_rank_toolbox.matrices.LowRankMatrix method), [1], [2] (low_rank_toolbox.matrices.quasi_svd.QuasiSVD method) (low_rank_toolbox.matrices.QuasiSVD method), [1], [2] transpose() (low_rank_toolbox.matrices.low_rank_matrix.LowRankMatrix method) (low_rank_toolbox.matrices.LowRankMatrix method), [1], [2] (low_rank_toolbox.matrices.quasi_svd.QuasiSVD method) (low_rank_toolbox.matrices.QuasiSVD method), [1], [2] truncate() (low_rank_toolbox.matrices.QR method), [1], [2] (low_rank_toolbox.matrices.qr.QR method) (low_rank_toolbox.matrices.quasi_svd.QuasiSVD method) (low_rank_toolbox.matrices.QuasiSVD method), [1], [2] (low_rank_toolbox.matrices.SVD method), [1], [2] (low_rank_toolbox.matrices.svd.SVD method) truncate_perpendicular() (low_rank_toolbox.matrices.SVD method), [1], [2] (low_rank_toolbox.matrices.svd.SVD method) truncated_svd() (low_rank_toolbox.matrices.SVD class method), [1], [2] (low_rank_toolbox.matrices.svd.SVD class method) Truncation (low_rank_toolbox.matrices.QR attribute), [1], [2] (low_rank_toolbox.matrices.qr.QR attribute) (low_rank_toolbox.matrices.SVD attribute), [1], [2] (low_rank_toolbox.matrices.svd.SVD attribute)

U

U (low_rank_toolbox.matrices.quasi_svd.QuasiSVD attribute) (low_rank_toolbox.matrices.quasi_svd.QuasiSVD property) (low_rank_toolbox.matrices.QuasiSVD attribute), [1], [2] (low_rank_toolbox.matrices.QuasiSVD property), [1], [2] (low_rank_toolbox.matrices.SVD attribute), [1], [2] (low_rank_toolbox.matrices.svd.SVD attribute) Uh (low_rank_toolbox.matrices.quasi_svd.QuasiSVD attribute) (low_rank_toolbox.matrices.quasi_svd.QuasiSVD property) (low_rank_toolbox.matrices.QuasiSVD attribute), [1], [2] (low_rank_toolbox.matrices.QuasiSVD property), [1], [2] (low_rank_toolbox.matrices.SVD attribute), [1], [2] (low_rank_toolbox.matrices.svd.SVD attribute)

Ut (low_rank_toolbox.matrices.quasi_svd.QuasiSVD attribute) (low_rank_toolbox.matrices.quasi_svd.QuasiSVD property) (low_rank_toolbox.matrices.QuasiSVD attribute), [1], [2] (low_rank_toolbox.matrices.QuasiSVD property), [1], [2] (low_rank_toolbox.matrices.SVD attribute), [1], [2] (low_rank_toolbox.matrices.svd.SVD attribute)

V

V (low_rank_toolbox.matrices.quasi_svd.QuasiSVD attribute) (low_rank_toolbox.matrices.quasi_svd.QuasiSVD property) (low_rank_toolbox.matrices.QuasiSVD attribute), [1], [2] (low_rank_toolbox.matrices.QuasiSVD property), [1], [2] (low_rank_toolbox.matrices.SVD attribute), [1], [2] (low_rank_toolbox.matrices.svd.SVD attribute) Validation (low_rank_toolbox.matrices.QR attribute), [1], [2] (low_rank_toolbox.matrices.qr.QR attribute) Vh (low_rank_toolbox.matrices.quasi_svd.QuasiSVD attribute) (low_rank_toolbox.matrices.quasi_svd.QuasiSVD property) (low_rank_toolbox.matrices.QuasiSVD attribute), [1], [2] (low_rank_toolbox.matrices.QuasiSVD property), [1], [2] (low_rank_toolbox.matrices.SVD attribute), [1], [2] (low_rank_toolbox.matrices.svd.SVD attribute)

Vt (low_rank_toolbox.matrices.quasi_svd.QuasiSVD attribute) (low_rank_toolbox.matrices.quasi_svd.QuasiSVD property) (low_rank_toolbox.matrices.QuasiSVD attribute), [1], [2] (low_rank_toolbox.matrices.QuasiSVD property), [1], [2] (low_rank_toolbox.matrices.SVD attribute), [1], [2] (low_rank_toolbox.matrices.svd.SVD attribute)

X

X (low_rank_toolbox.krylov.spaces.extended_krylov_space.ExtendedKrylovSpace attribute) (low_rank_toolbox.krylov.spaces.ExtendedKrylovSpace attribute) (low_rank_toolbox.krylov.spaces.inverted_krylov_space.InvertedKrylovSpace attribute) (low_rank_toolbox.krylov.spaces.InvertedKrylovSpace attribute) (low_rank_toolbox.krylov.spaces.krylov_space.KrylovSpace attribute) (low_rank_toolbox.krylov.spaces.KrylovSpace attribute) (low_rank_toolbox.krylov.spaces.rational_krylov_space.RationalKrylovSpace attribute) (low_rank_toolbox.krylov.spaces.RationalKrylovSpace attribute)