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LAPACK Auxiliary Functions

These are functions that support more advanced LAPACK routines <lapackfunc>. The auxiliary functions are divided into the following categories:

  • vecmat. Some basic operations with vectors and matrices that are not part of the BLAS standard.
  • householder. Generation and application of Householder matrices.
  • bidiag. Computations specialized in bidiagonal matrices.
  • tridiag. Computations specialized in tridiagonal matrices.
  • symmetric. Computations specialized in symmetric matrices.
  • orthonormal. Generation and application of orthonormal matrices.
  • unitary. Generation and application of unitary matrices.

Note

Throughout the APIs' descriptions, we use the following notations:

  • x[i] stands for the i-th element of vector x, while A[i,j] represents the element in the i-th row and j-th column of matrix A. Indices are 1-based, i.e. x[1] is the first element of x.
  • If X is a real vector or matrix, XT indicates its transpose; if X is complex, then XH represents its conjugate transpose. When X could be real or complex, we use X' to indicate X transposed or X conjugate transposed, accordingly.
  • x_i  = xi; we sometimes use both notations, xi when displaying mathematical equations, and x_i in the text describing the function parameters.

Vector and Matrix manipulations

List of vector and matrix manipulations

rocsolver<type>lacgv()

rocsolver_zlacgv

rocsolver_clacgv

rocsolver<type>laswp()

rocsolver_zlaswp

rocsolver_claswp

rocsolver_dlaswp

rocsolver_slaswp

Householder reflections

List of Householder functions

rocsolver<type>larfg()

rocsolver_zlarfg

rocsolver_clarfg

rocsolver_dlarfg

rocsolver_slarfg

rocsolver<type>larft()

rocsolver_zlarft

rocsolver_clarft

rocsolver_dlarft

rocsolver_slarft

rocsolver<type>larf()

rocsolver_zlarf

rocsolver_clarf

rocsolver_dlarf

rocsolver_slarf

rocsolver<type>larfb()

rocsolver_zlarfb

rocsolver_clarfb

rocsolver_dlarfb

rocsolver_slarfb

Bidiagonal forms

List of functions for bidiagonal forms

rocsolver<type>labrd()

rocsolver_zlabrd

rocsolver_clabrd

rocsolver_dlabrd

rocsolver_slabrd

rocsolver<type>bdsqr()

rocsolver_zbdsqr

rocsolver_cbdsqr

rocsolver_dbdsqr

rocsolver_sbdsqr

Tridiagonal forms

List of functions for tridiagonal forms

rocsolver<type>latrd()

rocsolver_zlatrd

rocsolver_clatrd

rocsolver_dlatrd

rocsolver_slatrd

rocsolver<type>sterf()

rocsolver_dsterf

rocsolver_ssterf

rocsolver<type>steqr()

rocsolver_zsteqr

rocsolver_csteqr

rocsolver_dsteqr

rocsolver_ssteqr

rocsolver<type>stedc()

rocsolver_zstedc

rocsolver_cstedc

rocsolver_dstedc

rocsolver_sstedc

Symmetric matrices

List of functions for symmetric matrices

rocsolver<type>lasyf()

rocsolver_zlasyf

rocsolver_clasyf

rocsolver_dlasyf

rocsolver_slasyf

Orthonormal matrices

List of functions for orthonormal matrices

rocsolver<type>org2r()

rocsolver_dorg2r

rocsolver_sorg2r

rocsolver<type>orgqr()

rocsolver_dorgqr

rocsolver_sorgqr

rocsolver<type>orgl2()

rocsolver_dorgl2

rocsolver_sorgl2

rocsolver<type>orglq()

rocsolver_dorglq

rocsolver_sorglq

rocsolver<type>org2l()

rocsolver_dorg2l

rocsolver_sorg2l

rocsolver<type>orgql()

rocsolver_dorgql

rocsolver_sorgql

rocsolver<type>orgbr()

rocsolver_dorgbr

rocsolver_sorgbr

rocsolver<type>orgtr()

rocsolver_dorgtr

rocsolver_sorgtr

rocsolver<type>orm2r()

rocsolver_dorm2r

rocsolver_sorm2r

rocsolver<type>ormqr()

rocsolver_dormqr

rocsolver_sormqr

rocsolver<type>orml2()

rocsolver_dorml2

rocsolver_sorml2

rocsolver<type>ormlq()

rocsolver_dormlq

rocsolver_sormlq

rocsolver<type>orm2l()

rocsolver_dorm2l

rocsolver_sorm2l

rocsolver<type>ormql()

rocsolver_dormql

rocsolver_sormql

rocsolver<type>ormbr()

rocsolver_dormbr

rocsolver_sormbr

rocsolver<type>ormtr()

rocsolver_dormtr

rocsolver_sormtr

Unitary matrices

List of functions for unitary matrices

rocsolver<type>ung2r()

rocsolver_zung2r

rocsolver_cung2r

rocsolver<type>ungqr()

rocsolver_zungqr

rocsolver_cungqr

rocsolver<type>ungl2()

rocsolver_zungl2

rocsolver_cungl2

rocsolver<type>unglq()

rocsolver_zunglq

rocsolver_cunglq

rocsolver<type>ung2l()

rocsolver_zung2l

rocsolver_cung2l

rocsolver<type>ungql()

rocsolver_zungql

rocsolver_cungql

rocsolver<type>ungbr()

rocsolver_zungbr

rocsolver_cungbr

rocsolver<type>ungtr()

rocsolver_zungtr

rocsolver_cungtr

rocsolver<type>unm2r()

rocsolver_zunm2r

rocsolver_cunm2r

rocsolver<type>unmqr()

rocsolver_zunmqr

rocsolver_cunmqr

rocsolver<type>unml2()

rocsolver_zunml2

rocsolver_cunml2

rocsolver<type>unmlq()

rocsolver_zunmlq

rocsolver_cunmlq

rocsolver<type>unm2l()

rocsolver_zunm2l

rocsolver_cunm2l

rocsolver<type>unmql()

rocsolver_zunmql

rocsolver_cunmql

rocsolver<type>unmbr()

rocsolver_zunmbr

rocsolver_cunmbr

rocsolver<type>unmtr()

rocsolver_zunmtr

rocsolver_cunmtr