Linear Algebra

O2scl

Linear algebra contents

• Linear algebra introduction

• Specializations for Armadillo and Eigen

• Linear algebra enums

Linear algebra introduction

O₂scl contains a small set of linear algebra routines but is also is designed to be used with Armadillo and/or Eigen, both of which are high performance C++ linear algebra libraries. In the case that O₂scl was compiled with support for either the Armadillo or Eigen libraries, some O₂scl template functions are overloaded with the respective Armadillo or Eigen versions.

The fallback O₂scl linear algebra routines offer a more generic and flexible interface: they work for almost all vector and matrix types. For matrix types using operator(,), the BLAS and linear algebra routines routines are inside the o2scl_cblas and o2scl_linalg namespaces. For matrix types using operator[][], the BLAS and linear algebra routines are inside the o2scl_cblas_bracket and o2scl_linalg_bracket namespaces.

The linear algebra classes and functions include:

• Householder transformations, src/linalg/householder.h

  • o2scl_linalg::householder_transform()

  • o2scl_linalg::householder_transform_subcol()

  • o2scl_linalg::householder_transform_subrow()

  • o2scl_linalg::householder_hm()

  • o2scl_linalg::householder_hm_subcol()

  • o2scl_linalg::householder_hm_subrow()

  • o2scl_linalg::householder_hv()

  • o2scl_linalg::householder_hv_subcol()

  • o2scl_linalg::householder_hm1()

  • o2scl_linalg::householder_hm1_sub()

  • o2scl_linalg::householder_mh()

  • o2scl_linalg::householder_mh_subrow()

• Householder solver, src/linalg/hh.h

  • o2scl_linalg::HH_svx()

  • o2scl_linalg::HH_solve()

• LU decomposition and solver, src/linalg/lu.h

  • o2scl_linalg::diagonal_has_zero()

  • o2scl_linalg::LU_decomp()

  • o2scl_linalg::LU_svx()

  • o2scl_linalg::LU_decomp_alt()

  • o2scl_linalg::LU_solve()

  • o2scl_linalg::LU_refine()

  • o2scl_linalg::LU_invert()

  • o2scl_linalg::LU_det()

  • o2scl_linalg::LU_lndet()

  • o2scl_linalg::LU_sgndet()

• Cholesky decomposition, src/linalg/cholesky.h

  • o2scl_linalg::cholesky_decomp()

  • o2scl_linalg::cholesky_det()

  • o2scl_linalg::cholesky_solve()

  • o2scl_linalg::cholesky_invert()

  • o2scl_linalg::cholesky_decomp_unit()

• QR decomposition, src/linalg/qr.h

  • o2scl_linalg::QR_decomp()

  • o2scl_linalg::QR_QTvec()

  • o2scl_linalg::QR_unpack()

  • o2scl_linalg::QR_svx()

  • o2scl_linalg::QR_solve()

  • o2scl_linalg::QR_update()

  • o2scl_linalg::QR_decomp_unpack()

• QR solver, src/linalg/qrpt.h

  • o2scl_linalg::QRPT_decomp()

• Solve tridiagonal systems, src/linalg/tridiag.h

  • ubvector_2_mem

  • ubvector_4_mem

  • ubvector_5_mem

  • o2scl_linalg::solve_tridiag_sym()

  • o2scl_linalg::solve_tridiag_nonsym()

  • o2scl_linalg::solve_cyc_tridiag_sym()

  • o2scl_linalg::solve_cyc_tridiag_nonsym()

• Givens rotations, src/linalg/givens.h

  • o2scl_linalg::apply_givens_qr()

  • o2scl_linalg::apply_givens_lq()

  • o2scl_linalg::apply_givens_vec()

• Bidiagonalizations, src/linalg/bidiag.h

  • o2scl_linalg::bidiag_decomp()

  • o2scl_linalg::bidiag_unpack()

  • o2scl_linalg::bidiag_unpack2()

  • o2scl_linalg::bidiag_unpack_B()

• Singular value decompositions, src/linalg/svd.h

• Singular value decompositions step, src/linalg/svdstep.h

• Lanczos diagonalization in lanczos which also can compute the eigenvalues of a tridiagonal matrix.

There is also a set of linear solvers for generic matrix and vector types which descend from linear_solver . These classes provide GSL-like solvers, but are generalized so that they are compatible with vector and matrix types which allow access through operator[].

Specializations for Armadillo and Eigen

Armadillo and Eigen linear solvers are wrapped to have a consistent interface with the fallback O₂scl linear solvers. See o2scl_linalg::linear_solver_arma, o2scl_linalg::linear_solver_eigen_houseQR, o2scl_linalg::linear_solver_eigen_colQR, o2scl_linalg::linear_solver_eigen_fullQR, o2scl_linalg::linear_solver_eigen_partLU, o2scl_linalg::linear_solver_eigen_fullLU, o2scl_linalg::linear_solver_eigen_LLT, and o2scl_linalg::linear_solver_eigen_LDLT.

Specializations for o2scl_linalg::QR_decomp_unpack() are

… (see qr.h)

Linear algebra enums

enum o2scl_cblas::o2cblas_order

Matrix order, either column-major or row-major.

Values:

enumerator o2cblas_RowMajor

enumerator o2cblas_ColMajor

enum o2scl_cblas::o2cblas_transpose

Transpose operations.

Values:

enumerator o2cblas_NoTrans

enumerator o2cblas_Trans

enumerator o2cblas_ConjTrans

enum o2scl_cblas::o2cblas_uplo

Upper- or lower-triangular.

Values:

enumerator o2cblas_Upper

enumerator o2cblas_Lower

enum o2scl_cblas::o2cblas_diag

Unit or generic diagonal.

Values:

enumerator o2cblas_NonUnit

enumerator o2cblas_Unit

enum o2scl_cblas::o2cblas_side

Left or right sided operation.

Values:

enumerator o2cblas_Left

enumerator o2cblas_Right