numeric-linalg

Educational material on the SciPy implementation of numerical linear algebra algorithms

Name	Size	Mode
..
lapack/DOCS/groups-usr.dox	54069B	-rw-r--r--

/**

@defgroup lapack_top                LAPACK
@{
    @defgroup solve_top             Linear solve, AX = B
    @{
        @defgroup gesv_driver_grp   LU: General matrix, driver
        @{
            @defgroup gesv_driver   --- full ---
            @defgroup gesv          gesv:           factor and solve
            @defgroup gesvx         gesvx:          factor and solve, expert
            @defgroup gesvxx        gesvxx:         factor and solve, extra precise
            @defgroup gesv_mixed    gesv:           factor and solve, mixed precision

            @defgroup gbsv_driver   --- banded ---
            @defgroup gbsv          gbsv:           factor and solve
            @defgroup gbsvx         gbsvx:          factor and solve, expert
            @defgroup gbsvxx        gbsvxx:         factor and solve, extra precise

            @defgroup gtsv_driver   --- tridiagonal ---
            @defgroup gtsv          gtsv:           factor and solve
            @defgroup gtsvx         gtsvx:          factor and solve, expert
        @}

        @defgroup gesv_comp_grp     LU: computational routines (factor, cond, etc.)
        @{
            @defgroup gesv_comp     --- full ---
            @defgroup gecon         gecon:          condition number estimate
            @defgroup getrf         getrf:          triangular factor
            @defgroup getrf2        getrf2:         triangular factor panel, recursive?
            @defgroup getf2         getf2:          triangular factor panel, level 2
            @defgroup getrs         getrs:          triangular solve using factor
            @defgroup getri         getri:          triangular inverse
            @defgroup gerfs         gerfs:          iterative refinement
            @defgroup gerfsx        gerfsx:         iterative refinement, expert
            @defgroup geequ         geequ:          equilibration
            @defgroup geequb        geequb:         equilibration, power of 2
            @defgroup laqge         laqge:          row/col scale matrix
            @defgroup laswp         laswp:          swap permutation

            @defgroup getc2         getc2:          triangular factor, with complete pivoting
            @defgroup gesc2         gesc2:          triangular solve using factor, with complete pivoting
            @defgroup latdf         latdf:          Dif-estimate with complete pivoting LU, step in tgsen

            @defgroup la_gercond    la_gercond: Skeel condition number estimate
            @defgroup la_gerpvgrw   la_gerpvgrw: reciprocal pivot growth
            @defgroup la_gerfsx_extended  la_gerfsx_extended:  step in gerfsx

            @defgroup gbsv_comp     --- banded ---
            @defgroup gbcon         gbcon:          condition number estimate
            @defgroup gbtrf         gbtrf:          triangular factor
            @defgroup gbtf2         gbtf2:          triangular factor, level 2
            @defgroup gbtrs         gbtrs:          triangular solve using factor
            @defgroup gbrfs         gbrfs:          iterative refinement
            @defgroup gbrfsx        gbrfsx:         iterative refinement, expert
            @defgroup gbequ         gbequ:          equilibration
            @defgroup gbequb        gbequb:         equilibration, power of 2
            @defgroup laqgb         laqgb:          row/col scale matrix
            @defgroup la_gbrcond    la_gbrcond:     Skeel condition number estimate
            @defgroup la_gbrpvgrw   la_gbrpvgrw:    reciprocal pivot growth
            @defgroup la_gbrfsx_extended  la_gbrfsx_extended:  step in gbrfsx

            @defgroup gtsv_comp     --- tridiagonal ---
            @defgroup gtcon         gtcon:          condition number estimate
            @defgroup gttrf         gttrf:          triangular factor
            @defgroup gttrs         gttrs:          triangular solve using factor
            @defgroup gtts2         gtts2:          triangular solve using factor
            @defgroup gtrfs         gtrfs:          iterative refinement
        @}

        @defgroup posv_driver_grp   Cholesky: Hermitian/symmetric positive definite matrix, driver
        @{
            @defgroup posv_driver   --- full ---
            @defgroup posv          posv:           factor and solve
            @defgroup posvx         posvx:          factor and solve, expert
            @defgroup posvxx        posvxx:         factor and solve, extra precise
            @defgroup posv_mixed    posv:           factor and solve, mixed precision

            @defgroup ppsv_driver   --- packed ---
            @defgroup ppsv          ppsv:           factor and solve
            @defgroup ppsvx         ppsvx:          factor and solve, expert

            @defgroup pfsv_driver   --- rectangular full packed (RFP) ---
            @defgroup pfsv          pfsv:           factor and solve [not available]

            @defgroup pbsv_driver   --- banded ---
            @defgroup pbsv          pbsv:           factor and solve
            @defgroup pbsvx         pbsvx:          factor and solve, expert

            @defgroup ptsv_driver   --- tridiagonal ---
            @defgroup ptsv          ptsv:           factor and solve
            @defgroup ptsvx         ptsvx:          factor and solve, expert
        @}

        @defgroup posv_comp_grp     Cholesky: computational routines (factor, cond, etc.)
        @{
            @defgroup posv_comp     --- full ---
            @defgroup pocon         pocon:          condition number estimate
            @defgroup potrf         potrf:          triangular factor
            @defgroup potrf2        potrf2:         triangular factor panel, recursive?
            @defgroup potf2         potf2:          triangular factor panel, level 2
            @defgroup pstrf         pstrf:          triangular factor, with pivoting
            @defgroup pstf2         pstf2:          triangular factor, with pivoting panel, level 2
            @defgroup potrs         potrs:          triangular solve using factor
            @defgroup potri         potri:          triangular inverse
            @defgroup porfs         porfs:          iterative refinement
            @defgroup porfsx        porfsx:         iterative refinement, expert
            @defgroup poequ         poequ:          equilibration
            @defgroup poequb        poequb:         equilibration, power of 2
            @defgroup laqhe         laqhe:          row/col scale matrix
            @defgroup la_porcond    la_porcond:     Skeel condition number estimate
            @defgroup la_porpvgrw   la_porpvgrw:    reciprocal pivot growth
            @defgroup la_porfsx_extended  la_porfsx_extended:  step in porfsx

            @defgroup ppsv_comp     --- packed ---
            @defgroup ppcon         ppcon:          condition number estimate
            @defgroup pptrf         pptrf:          triangular factor
            @defgroup pptrs         pptrs:          triangular solve using factor
            @defgroup pptri         pptri:          triangular inverse
            @defgroup pprfs         pprfs:          iterative refinement
            @defgroup ppequ         ppequ:          equilibration
            @defgroup laqhp         laqhp:          row/col scale matrix

            @defgroup pfsv_comp     --- rectangular full packed (RFP) ---
            @defgroup pftrf         pftrf:          triangular factor
            @defgroup pftrs         pftrs:          triangular solve using factor
            @defgroup pftri         pftri:          triangular inverse

            @defgroup pbsv_comp     --- banded ---
            @defgroup pbcon         pbcon:          condition number estimate
            @defgroup pbtrf         pbtrf:          triangular factor
            @defgroup pbtf2         pbtf2:          triangular factor panel, level 2
            @defgroup pbtrs         pbtrs:          triangular solve using factor
            @defgroup pbrfs         pbrfs:          iterative refinement
            @defgroup pbequ         pbequ:          equilibration
            @defgroup laqhb         laqhb:          row/col scale matrix

            @defgroup ptsv_comp     --- tridiagonal ---
            @defgroup ptcon         ptcon:          condition number estimate
            @defgroup pttrf         pttrf:          triangular factor
            @defgroup pttrs         pttrs:          triangular solve using factor
            @defgroup ptts2         ptts2:          triangular solve using factor, unblocked
            @defgroup ptrfs         ptrfs:          iterative refinement
        @}

        @defgroup hesv_driver_grp   LDL: Hermitian/symmetric indefinite matrix, driver
        @{
            @defgroup hesv_driver   --- full, rook pivoting ---
            @defgroup hesv          {he,sy}sv:      rook (v1)
            @defgroup hesv_rook     {he,sy}sv_rook: rook (v2)
            @defgroup hesv_rk       {he,sy}sv_rk:   rook (v3)
            @defgroup hesvx         {he,sy}svx:     rook (v1, expert)
            @defgroup hesvxx        {he,sy}svxx:    rook (v1, expert)

            @defgroup hpsv_driver   --- packed, rook pivoting ---
            @defgroup hpsv          {hp,sp}sv:      factor and solve
            @defgroup hpsvx         {hp,sp}svx:     factor and solve, expert

            @defgroup hesv_aa_driver  --- full, Aasen ---
            @defgroup hesv_aa       {he,sy}sv_aa:   Aasen
            @defgroup hesv_aa_2stage  {he,sy}sv_aa_2stage:  Aasen, blocked 2-stage
        @}

        @defgroup hesv_comp_grp     LDL: computational routines (factor, cond, etc.)
        @{
            @defgroup hesv_comp_v1  --- full, rook v1 ---
            @defgroup hecon         {he,sy}con:     condition number estimate
            @defgroup hetrf         {he,sy}trf:     triangular factor
            @defgroup lahef         la{he,sy}f:     step in hetrf
            @defgroup hetf2         {he,sy}tf2:     triangular factor, level 2
            @defgroup hetrs         {he,sy}trs:     triangular solve using factor
            @defgroup hetri         {he,sy}tri:     triangular inverse
            @defgroup herfs         {he,sy}rfs:     iterative refinement
            @defgroup herfsx        {he,sy}rfsx:    iterative refinement, expert
            @defgroup heequb        {he,sy}equb:    equilibration, power of 2
            @defgroup syconv        syconv:         convert to/from L and D from hetrf

            @defgroup hecon_3       {he,sy}con_3:   condition number estimate
            @defgroup hetri2        {he,sy}tri2:    inverse
            @defgroup hetri2x       {he,sy}tri2x:   inverse
            @defgroup hetri_3       {he,sy}tri_3:   inverse
            @defgroup hetri_3x      {he,sy}tri_3x:  inverse
            @defgroup hetrs2        {he,sy}trs2:    solve using factor
            @defgroup hetrs_3       {he,sy}trs_3:   solve using factor

            @defgroup heswapr             {he,sy}swapr:         apply 2-sided permutation
            @defgroup la_hercond          la_hercond:           Skeel condition number estimate
            @defgroup la_herfsx_extended  la_herfsx_extended:   step in herfsx
            @defgroup la_herpvgrw         la_herpvgrw:          reciprocal pivot growth

            @defgroup hpsv_comp     --- packed, rook v1 ---
            @defgroup hpcon         {hp,sp}con:     condition number estimate
            @defgroup hptrf         {hp,sp}trf:     triangular factor
            @defgroup hptrs         {hp,sp}trs:     triangular solve using factor
            @defgroup hptri         {hp,sp}tri:     triangular inverse
            @defgroup hprfs         {hp,sp}rfs:     iterative refinement

            @defgroup hesv_comp_v2  --- full, rook v2 ---
            @defgroup hecon_rook    {he,sy}con_rook:  condition number estimate
            @defgroup hetrf_rook    {he,sy}trf_rook:  triangular factor
            @defgroup lahef_rook    la{he,sy}f_rook:  triangular factor step
            @defgroup hetf2_rook    {he,sy}tf2_rook:  triangular factor, level 2
            @defgroup hetrs_rook    {he,sy}trs_rook:  triangular solve using factor
            @defgroup hetri_rook    {he,sy}tri_rook:  triangular inverse

            @defgroup hesv_comp_v3  --- full, rook v3 ---
            @defgroup hetrf_rk      {he,sy}trf_rk:  triangular factor
            @defgroup lahef_rk      la{he,sy}f_rk:  triangular factor step
            @defgroup hetf2_rk      {he,sy}tf2_rk:  triangular factor, level 2
            @defgroup syconvf       syconvf:        convert to/from hetrf      to hetrf_rk format
            @defgroup syconvf_rook  syconvf_rook:   convert to/from hetrf_rook to hetrf_rk format

            @defgroup hesv_comp_aasen  --- full, Aasen ---
            @defgroup hetrf_aa      {he,sy}trf_aa:  triangular factor
            @defgroup lahef_aa      la{he,sy}f_aa:  triangular factor partial factor
            @defgroup hetrs_aa      {he,sy}trs_aa:  triangular solve using factor

            @defgroup hesv_comp_aasen2 --- full, Aasen, blocked 2-stage ---
            @defgroup hetrf_aa_2stage  {he,sy}trf_aa_2stage:  triangular factor
            @defgroup hetrs_aa_2stage  {he,sy}trs_aa_2stage:  triangular solve using factor
        @}

        @defgroup trsv_comp_grp     Triangular computational routines (solve, cond, etc.)
        @{
            @defgroup trsv_comp     --- full ---
            @defgroup trcon         trcon:          condition number estimate
            @defgroup trtrs         trtrs:          triangular solve
            @defgroup latrs         latrs:          triangular solve with robust scaling
            @defgroup latrs3        latrs3:         triangular solve with robust scaling, level 3
            @defgroup trtri         trtri:          triangular inverse
            @defgroup trti2         trti2:          triangular inverse, level 2
            @defgroup trrfs         trrfs:          triangular iterative refinement
            @defgroup lauum         lauum:          triangular multiply: U^H U
            @defgroup lauu2         lauu2:          triangular multiply: U^H U, level 2

            @defgroup tpsv_comp     --- packed ---
            @defgroup tpcon         tpcon:          condition number estimate
            @defgroup tptrs         tptrs:          triangular solve
            @defgroup latps         latps:          triangular solve with robust scaling
            @defgroup tptri         tptri:          triangular inverse
            @defgroup tprfs         tprfs:          triangular iterative refinement

            @defgroup tfsv_comp     --- rectangular full packed (RFP) ---
            @defgroup tftri         tftri:          triangular inverse, RFP

            @defgroup tbsv_comp     --- banded ---
            @defgroup tbcon         tbcon:          condition number estimate
            @defgroup tbtrs         tbtrs:          triangular solve
            @defgroup latbs         latbs:          triangular solve with scaling
            @defgroup tbrfs         tbrfs:          triangular iterative refinement
        @}

        @defgroup solve_aux_grp     Auxiliary routines
        @{
            @defgroup lacn2         lacn2:          1-norm estimate, e.g., || A^{-1} ||_1 in gecon
            @defgroup lacon         lacon:          1-norm estimate, e.g., || A^{-1} ||_1 in gecon, old
            @defgroup la_lin_berr   la_lin_berr:    backward error
        @}
    @}

    @defgroup gels_top Least squares
    @{
        @defgroup gels_driver_grp   Standard least squares, min || Ax - b ||_2
        @{
            @defgroup gels          gels:           least squares using QR/LQ
            @defgroup gelst         gelst:          least squares using QR/LQ with T matrix
            @defgroup gelss         gelss:          least squares using SVD, QR iteration
            @defgroup gelsd         gelsd:          least squares using SVD, divide and conquer
            @defgroup gelsy         gelsy:          least squares using complete orthogonal factor
            @defgroup getsls        getsls:         least squares using tall-skinny QR/LQ
        @}

        @defgroup ggls_driver_grp   Constrained least squares
        @{
            @defgroup gglse         gglse:          equality-constrained least squares
            @defgroup ggglm         ggglm:          Gauss-Markov linear model
        @}

        @defgroup gels_aux_grp      Auxiliary routines
        @{
            @defgroup laic1         laic1:          condition estimate, step in gelsy
            @defgroup lals0         lals0:          back multiplying factors, step in gelsd
            @defgroup lalsa         lalsa:          SVD of coefficient matrix, step in gelsd
            @defgroup lalsd         lalsd:          uses SVD for least squares, step in gelsd
        @}
    @}

    @defgroup unitary_top Orthogonal/unitary factors (QR, CS, etc.)
    @{
        @defgroup geqr_comp_grp     QR
        @{
            @defgroup geqr_comp1    --- flexible ---
            @defgroup geqr          geqr:           QR factor, flexible
            @defgroup gemqr         gemqr:          multiply by Q from geqr

            @defgroup geqr_comp2    --- classic ---
            @defgroup geqrf         geqrf:          QR factor
            @defgroup geqr2         geqr2:          QR factor, level 2
            @defgroup ungqr         {un,or}gqr:     generate explicit Q from geqrf
            @defgroup ung2r         {un,or}g2r:     generate explicit Q from geqrf, level 2
            @defgroup unmqr         {un,or}mqr:     multiply by Q from geqrf
            @defgroup unm2r         {un,or}m2r:     multiply by Q from geqrf, level 2

            @defgroup geqr_comp3    --- with T ---
            @defgroup geqrt         geqrt:          QR factor, with T
            @defgroup geqrt2        geqrt2:         QR factor, with T, level 2
            @defgroup geqrt3        geqrt3:         QR factor, with T, recursive panel
            @defgroup gemqrt        gemqrt:         multiply by Q from geqrt

            @defgroup geqr_comp4    --- positive ---
            @defgroup geqrfp        geqrfp:         QR factor, diag( R ) ≥ 0
            @defgroup geqr2p        geqr2p:         QR factor, diag( R ) ≥ 0, level 2
        @}

        @defgroup geqpf_comp_grp    QR with pivoting
        @{
            @defgroup geqp3         geqp3:          QR factor with pivoting, level 3
            @defgroup laqp2         laqp2:          step of geqp3
            @defgroup laqps         laqps:          step of geqp3
        @}

        @defgroup getsqr_comp_grp   QR, tall-skinny
        @{
            @defgroup latsqr        latsqr:         tall-skinny QR factor
            @defgroup ungtsqr       {un,or}gtsqr:   generate Q from latsqr
            @defgroup ungtsqr_row   {un,or}gtsqr_row:   generate Q from latsqr
            @defgroup larfb_gett    larfb_gett:     step in ungtsqr_row
            @defgroup lamtsqr       lamtsqr:        multiply by Q from latsqr
            @defgroup getsqrhrt     getsqrhrt:      tall-skinny QR factor, with Householder reconstruction
            @defgroup unhr_col      {un,or}hr_col:  Householder reconstruction
            @defgroup launhr_col_getrfnp   la{un,or}hr_col_getrfnp:   LU factor without pivoting
            @defgroup launhr_col_getrfnp2  la{un,or}hr_col_getrfnp2:  LU factor without pivoting, level 2
        @}

        @defgroup tpqr_comp_grp     QR, triangular-pentagonal
        @{
            @defgroup tpqrt         tpqrt:          QR factor
            @defgroup tpqrt2        tpqrt2:         QR factor, level 2
            @defgroup tpmqrt        tpmqrt:         applies Q
            @defgroup tprfb         tprfb:          applies Q (like larfb)
        @}

        @defgroup ggqr_comp_grp     Generalized QR
        @{
            @defgroup ggqrf         ggqrf:          Generalized QR factor
        @}

        @defgroup gelq_comp_grp     LQ
        @{
            @defgroup gelq_comp1    --- flexible ---
            @defgroup gelq          gelq:           LQ factor, flexible
            @defgroup gemlq         gemlq:          multiply by Q from gelq

            @defgroup gelq_comp2    --- classic ---
            @defgroup gelqf         gelqf:          LQ factor
            @defgroup gelq2         gelq2:          LQ factor, level 2
            @defgroup unglq         {un,or}glq:     generate explicit Q from gelqf
            @defgroup ungl2         {un,or}gl2:     generate explicit Q, level 2, step in unglq
            @defgroup unmlq         {un,or}mlq:     multiply by Q from gelqf
            @defgroup unml2         {un,or}ml2:     multiply by Q, level 2, step in unmlq

            @defgroup gelq_comp3    --- with T ---
            @defgroup gelqt         gelqt:          LQ factor, with T
            @defgroup gelqt3        gelqt3:         LQ factor, with T, recursive
            @defgroup gemlqt        gemlqt:         multiply by Q from gelqt
        @}

        @defgroup geswlq_comp_grp   LQ, short-wide
        @{
            @defgroup laswlq        laswlq:         short-wide LQ factor
            @defgroup lamswlq       lamswlq:        multiply by Q from laswlq
        @}

        @defgroup tplq_comp_grp     LQ, triangular-pentagonal
        @{
            @defgroup tplqt         tplqt:          QR factor
            @defgroup tplqt2        tplqt2:         QR factor, level 2
            @defgroup tpmlqt        tpmlqt:         applies Q
        @}

        @defgroup geql_comp_grp     QL
        @{
            @defgroup geqlf         geqlf:          QL factor
            @defgroup geql2         geql2:          QL factor, level 2
            @defgroup ungql         {un,or}gql:     generate explicit Q from geqlf
            @defgroup unmql         {un,or}mql:     multiply by Q from geqlf
            @defgroup ung2l         {un,or}g2l:     step in ungql
            @defgroup unm2l         {un,or}m2l:     step in unmql
        @}

        @defgroup gerq_comp_grp     RQ
        @{
            @defgroup gerqf         gerqf:          RQ factor
            @defgroup gerq2         gerq2:          RQ factor, level 2
            @defgroup ungrq         {un,or}grq:     generate explicit Q from gerqf
            @defgroup unmrq         {un,or}mrq:     multiply by Q from gerqf
            @defgroup unmr2         {un,or}mr2:     step in unmrq
            @defgroup ungr2         {un,or}gr2:     step in ungrq
        @}

        @defgroup ggrq_comp_grp     Generalized RQ
        @{
            @defgroup ggrqf         ggrqf:          Generalized RQ factor
        @}

        @defgroup gerz_comp_grp     RZ
        @{
            @defgroup tzrzf         tzrzf:          RZ factor
            @defgroup latrz         latrz:          RZ factor step
            @defgroup unmrz         {un,or}mrz:     multiply by Z from tzrzf
            @defgroup unmr3         {un,or}mr3:     step in unmrz
            @defgroup larz          larz:           apply reflector
            @defgroup larzb         larzb:          apply block reflector
            @defgroup larzt         larzt:          generate T matrix
        @}

        @defgroup gecs_comp_grp     Cosine-Sine (CS) decomposition
        @{
            @defgroup bbcsd         bbcsd:          ??
            @defgroup uncsd         {un,or}csd:     ??
            @defgroup uncsd2by1     {un,or}csd2by1: ??
            @defgroup unbdb         {un,or}bdb:     bidiagonalize partitioned unitary matrix, step in uncsd
            @defgroup unbdb1        {un,or}bdb1:    step in uncsd2by1
            @defgroup unbdb2        {un,or}bdb2:    step in uncsd2by1
            @defgroup unbdb3        {un,or}bdb3:    step in uncsd2by1
            @defgroup unbdb4        {un,or}bdb4:    step in uncsd2by1
            @defgroup unbdb5        {un,or}bdb5:    step in uncsd2by1
            @defgroup unbdb6        {un,or}bdb6:    step in uncsd2by1

            @defgroup lapmr         lapmr:          permute rows
            @defgroup lapmt         lapmt:          permute cols
        @}

        @defgroup reflector_aux_grp Householder reflectors
        @{
            @defgroup larf          larf:           apply Householder reflector
            @defgroup larfx         larfx:          apply Householder reflector, unrolled
            @defgroup larfy         larfy:          apply Householder reflector symmetrically (2-sided)
            @defgroup larfb         larfb:          apply block Householder reflector
            @defgroup larfg         larfg:          generate Householder reflector
            @defgroup larfgp        larfgp:         generate Householder reflector, beta ≥ 0
            @defgroup larft         larft:          generate T matrix
        @}

        @defgroup rot_aux_grp       Givens/Jacobi plane rotations
        @{
            @defgroup lartg         lartg:          generate plane rotation, more accurate than BLAS rot
            @defgroup lartgp        lartgp:         generate plane rotation, more accurate than BLAS rot
            @defgroup lasr          lasr:           apply series of plane rotations
            @defgroup largv         largv:          generate vector of plane rotations
            @defgroup lartv         lartv:          apply vector of plane rotations to vectors
            @defgroup lar2v         lar2v:          apply vector of plane rotations to 2x2 matrices
            @defgroup lacrt         lacrt:          apply plane rotation (unused?)
        @}
    @}

    @defgroup geev_top              Non-symmetric eigenvalues
    @{
        @defgroup geev_driver_grp   Standard eig driver, AV = VΛ
        @{
            @defgroup geev          geev:           eig
            @defgroup geevx         geevx:          eig, expert

            @defgroup gees          gees:           Schur form
            @defgroup geesx         geesx:          Schur form, expert
        @}

        @defgroup ggev_driver_grp   Generalized eig driver
        @{
            @defgroup ggev3         ggev3:          eig
            @defgroup ggev          ggev:           eig, unblocked
            @defgroup ggevx         ggevx:          eig, expert

            @defgroup gges3         gges3:          Schur form
            @defgroup gges          gges:           Schur form, unblocked
            @defgroup ggesx         ggesx:          Schur form, expert
        @}

        @defgroup gedmd             DMD driver, Dynamic Mode Decomposition

        @defgroup geev_comp_grp     Eig computational routines
        @{
            @defgroup gebal         gebal:          balance matrix
            @defgroup gehrd         gehrd:          reduction to Hessenberg
            @defgroup gehd2         gehd2:          reduction to Hessenberg, level 2
            @defgroup lahr2         lahr2:          step in gehrd
            @defgroup unghr         {un,or}ghr:     generate Q from gehrd
            @defgroup unmhr         {un,or}mhr:     multiply by Q from gehrd
            @defgroup gebak         gebak:          back-transform eigvec
            @defgroup hseqr         hseqr:          Hessenberg eig, QR iteration
            @defgroup hsein         hsein:          Hessenberg inverse iteration for eigvec
            @defgroup trevc         trevc:          eigenvectors of triangular Schur form, old
            @defgroup trevc3        trevc3:         eigenvectors of triangular Schur form, blocked
            @defgroup laln2         laln2:          1x1 or 2x2 solve, step in trevc

            @defgroup trsyl         trsyl:          Sylvester equation
            @defgroup trsyl3        trsyl3:         Sylvester equation, level 3
            @defgroup lasy2         lasy2:          Sylvester equation

            @defgroup trsna         trsna:          eig condition numbers
            @defgroup laqtr         laqtr:          quasi-triangular solve

            @defgroup trexc         trexc:          reorder Schur form
            @defgroup trsen         trsen:          reorder Schur form
            @defgroup laexc         laexc:          reorder Schur form

            @defgroup lanv2         lanv2:          2x2 Schur factor

            @defgroup laqr_group    --- hseqr auxiliary ---
            @defgroup laein         laein:          eigvec by Hessenberg inverse iteration
            @defgroup lahqr         lahqr:          eig of Hessenberg, step in hseqr
            @defgroup laqr0         laqr0:          eig of Hessenberg, step in hseqr
            @defgroup laqr1         laqr1:          step in hseqr
            @defgroup laqr2         laqr2:          step in hseqr
            @defgroup laqr3         laqr3:          step in hseqr
            @defgroup laqr4         laqr4:          eig of Hessenberg, step in hseqr
            @defgroup laqr5         laqr5:          step in hseqr

            @defgroup iparmq        iparmq:         set parameters for hseqr

            @defgroup laqz_group    --- ggev3, gges3 auxiliary ---
            @defgroup laqz0         laqz0:          step in ggev3, gges3
            @defgroup laqz1         laqz1:          step in ggev3, gges3
            @defgroup laqz2         laqz2:          step in ggev3, gges3
            @defgroup laqz3         laqz3:          step in ggev3, gges3
            @defgroup laqz4         laqz4:          step in ggev3, gges3
        @}

        @defgroup ggev_comp_grp     Generalized eig computational routines
        @{
            @defgroup ggbal         ggbal:          balance matrix
            @defgroup gghrd         gghrd:          reduction to Hessenberg
            @defgroup gghd3         gghd3:          reduction to Hessenberg, level 3
            @defgroup hgeqz         hgeqz:          generalized Hessenberg eig
            @defgroup ggbak         ggbak:          back-transform eigvec
            @defgroup tgsen         tgsen:          reorder generalized Schur form
            @defgroup tgsna         tgsna:          reciprocal cond est
            @defgroup tgsyl         tgsyl:          Sylvester equation
            @defgroup tgsy2         tgsy2:          Sylvester equation panel (?)
            @defgroup unm22         {un,or}m22:     multiply by banded Q, step in gghd3
            @defgroup lagv2         lagv2:          2x2 generalized Schur factor
            @defgroup tgevc         tgevc:          eigvec of pair of matrices
            @defgroup tgexc         tgexc:          reorder generalized Schur form
            @defgroup tgex2         tgex2:          reorder generalized Schur form
        @}
    @}

    @defgroup heev_top              Hermitian/symmetric eigenvalues
    @{
        @defgroup heev_driver_grp   Standard eig driver, AV = VΛ
        @{
            @defgroup heev_driver   --- full ---
            @defgroup heev          {he,sy}ev:      eig, QR iteration
            @defgroup heevd         {he,sy}evd:     eig, divide and conquer
            @defgroup heevr         {he,sy}evr:     eig, MRRR
            @defgroup heevx         {he,sy}evx:     eig, bisection

            @defgroup heev_driver2  --- full, 2-stage ---
            @defgroup heev_2stage   {he,sy}ev_2stage:   eig, QR iteration
            @defgroup heevd_2stage  {he,sy}evd_2stage:  eig, divide and conquer
            @defgroup heevr_2stage  {he,sy}evr_2stage:  eig, MRRR
            @defgroup heevx_2stage  {he,sy}evx_2stage:  eig, bisection

            @defgroup hpev_driver   --- packed ---
            @defgroup hpev          {hp,sp}ev:      eig, QR iteration
            @defgroup hpevd         {hp,sp}evd:     eig, divide and conquer
            @defgroup hpevx         {hp,sp}evx:     eig, bisection

            @defgroup hbev_driver   --- banded ---
            @defgroup hbev          {hb,sb}ev:      eig, QR iteration
            @defgroup hbevd         {hb,sb}evd:     eig, divide and conquer
            @defgroup hbevx         {hb,sb}evx:     eig, bisection

            @defgroup hbev_driver2  --- banded, 2nd-stage ---
            @defgroup hbev_2stage   {hb,sb}ev_2stage:   eig, QR iteration
            @defgroup hbevd_2stage  {hb,sb}evd_2stage:  eig, divide and conquer
            @defgroup hbevx_2stage  {hb,sb}evx_2stage:  eig, bisection

            @defgroup stev_driver   --- tridiagonal ---
            @defgroup stev          stev:           eig, QR iteration
            @defgroup stevd         stevd:          eig, divide and conquer
            @defgroup stevr         stevr:          eig, MRRR
            @defgroup stevx         stevx:          eig, bisection
            @defgroup pteqr         pteqr:          eig, positive definite tridiagonal

            @defgroup stebz         stebz:          eig, Kahan
            @defgroup sterf         sterf:          eig, QR iteration
            @defgroup stedc         stedc:          eig, divide and conquer
            @defgroup stegr         stegr:          eig, bisection, see stemr
            @defgroup stein         stein:          eig, inverse iteration
            @defgroup stemr         stemr:          eig, relatively robust representation (RRR)
            @defgroup steqr         steqr:          eig, QR iteration
        @}

        @defgroup hegv_driver_grp   Generalized eig driver, AV = BVΛ, etc.
        @{
            @defgroup hegv_driver   --- full ---
            @defgroup hegv          {he,sy}gv:      eig, QR iteration
            @defgroup hegv_2stage   {he,sy}gv_2stage: eig, QR iteration, 2-stage
            @defgroup hegvd         {he,sy}gvd:     eig, divide and conquer
            @defgroup hegvx         {he,sy}gvx:     eig, bisection

            @defgroup hpgv_driver   --- packed ---
            @defgroup hpgv          {hp,sp}gv:      eig, QR iteration
            @defgroup hpgvd         {hp,sp}gvd:     eig, divide and conquer
            @defgroup hpgvx         {hp,sp}gvx:     eig, bisection

            @defgroup hbgv_driver   --- banded ---
            @defgroup hbgv          {hb,sb}gv:      eig, QR iteration
            @defgroup hbgvd         {hb,sb}gvd:     eig, divide and conquer
            @defgroup hbgvx         {hb,sb}gvx:     eig, bisection
        @}

        @defgroup heev_comp_grp     Eig computational routines
        @{
            @defgroup heev_comp     --- full ---
            @defgroup disna         disna:          eig condition numbers
            @defgroup hetrd         {he,sy}trd:     reduction to tridiagonal
            @defgroup hetd2         {he,sy}td2:     reduction to tridiagonal, level 2
            @defgroup latrd         latrd:          step in hetrd
            @defgroup ungtr         {un,or}gtr:     generate Q from hetrd
            @defgroup unmtr         {un,or}mtr:     multiply by Q from hetrd

            @defgroup hetrd_2stage  {he,sy}trd_2stage: reduction to tridiagonal, 2-stage
            @defgroup hetrd_he2hb   {he,sy}trd_he2hb:   full to band (1st stage)
            @defgroup hetrd_hb2st   {he,sy}trd_hb2st:   band to tridiagonal (2nd stage)
            @defgroup hb2st_kernels {hb,sb}2st_kernels: band to tridiagonal (2nd stage)

            @defgroup lae2          lae2:           2x2 eig, step in steqr, stemr
            @defgroup laesy         laesy:          2x2 eig
            @defgroup laev2         laev2:          2x2 eig
            @defgroup lagtf         lagtf:          LU factor of (T - λI)
            @defgroup lagts         lagts:          LU solve  of (T - λI) x = y

            @defgroup hpev_comp     --- packed ---
            @defgroup hptrd         {hp,sp}trd:     reduction to tridiagonal
            @defgroup upgtr         {up,op}gtr:     generate Q from hetrd
            @defgroup upmtr         {up,op}mtr:     multiply by Q from hptrd

            @defgroup hbev_comp     --- banded ---
            @defgroup hbtrd         {hb,sb}trd:     reduction to tridiagonal
        @}

        @defgroup hegv_comp_grp     Generalized eig computational routines
        @{
            @defgroup hegst         {he,sy}gst:     reduction to standard form
            @defgroup hegs2         {he,sy}gs2:     reduction to standard form, level 2
            @defgroup hpgst         {hp,sp}gst:     reduction to standard form, packed
            @defgroup hbgst         {hb,sb}gst:     reduction to standard form, banded
            @defgroup pbstf         pbstf:          split Cholesky factor, use with hbgst
            @defgroup lag2          lag2:           2x2 eig
        @}

        @defgroup stev_comp_grp     tridiag bisection routines
        @{
            @defgroup laebz         laebz:          counts eigvals <= value
            @defgroup laneg         laneg:          Sturm count
        @}

        @defgroup laed_comp_grp     tridiag divide and conquer (D&C) routines
        @{
            @defgroup laed0         laed0:          D&C step: top level solver
            @defgroup laed1         laed1:          D&C step: merge subproblems
            @defgroup laed2         laed2:          D&C step: deflation
            @defgroup laed3         laed3:          D&C step: secular equation
            @defgroup laed4         laed4:          D&C step: secular equation nonlinear solver
            @defgroup laed5         laed5:          D&C step: secular equation, 2x2
            @defgroup laed6         laed6:          D&C step: secular equation Newton step
            @defgroup lamrg         lamrg:          permutation to merge 2 sorted lists

            @defgroup laed_comp2    --- eig value only or update Q ---
            @defgroup laed7         laed7:          D&C step: merge subproblems
            @defgroup laed8         laed8:          D&C step: deflation
            @defgroup laed9         laed9:          D&C step: secular equation
            @defgroup laeda         laeda:          D&C step: z vector
        @}

        @defgroup larr_comp_grp     tridiag RRR routines
        @{
            @defgroup larra         larra:          step in stemr
            @defgroup larrb         larrb:          step in stemr
            @defgroup larrc         larrc:          step in stemr
            @defgroup larrd         larrd:          step in stemr, tridiag eig
            @defgroup larre         larre:          step in stemr
            @defgroup larrf         larrf:          step in stemr, find relative robust representation (RRR)
            @defgroup larrj         larrj:          step in stemr, refine eigval estimates
            @defgroup larrk         larrk:          step in stemr, compute one eigval
            @defgroup larrr         larrr:          step in stemr, test to do expensive tridiag eig algorithm
            @defgroup larrv         larrv:          eig tridiagonal, step in stemr & stegr
            @defgroup lar1v         lar1v:          step in larrv, hence stemr & stegr
        @}
    @}

    @defgroup svd_top               Singular Value Decomposition (SVD)
    @{
        @defgroup svd_driver_grp    Standard SVD driver, A = UΣV^H
        @{
            @defgroup gesvd_driver  --- full ---
            @defgroup gesvd         gesvd:          SVD, QR iteration
            @defgroup gesvdq        gesvdq:         SVD, QR with pivoting
            @defgroup gesdd         gesdd:          SVD, divide and conquer
            @defgroup gesvdx        gesvdx:         SVD, bisection
            @defgroup gejsv         gejsv:          SVD, Jacobi, high-level
            @defgroup gesvj         gesvj:          SVD, Jacobi, low-level

            @defgroup bdsvd_driver  --- bidiagonal ---
            @defgroup bdsqr         bdsqr:          bidiagonal SVD, QR iteration (dqds)
            @defgroup bdsdc         bdsdc:          bidiagonal SVD, divide and conquer
            @defgroup bdsvdx        bdsvdx:         bidiagonal SVD, bisection
        @}

        @defgroup ggsvd_driver_grp  Generalized SVD driver
        @{
            @defgroup ggsvd3        ggsvd3:         SVD, QR iteration
        @}

        @defgroup gesvd_comp_grp    SVD computational routines
        @{
            @defgroup gebrd         gebrd:          reduction to bidiagonal
            @defgroup gebd2         gebd2:          reduction to bidiagonal, level 2
            @defgroup labrd         labrd:          step in gebrd
            @defgroup gbbrd         gbbrd:          band to bidiagonal
            @defgroup ungbr         {un,or}gbr:     generate Q, P from gebrd
            @defgroup unmbr         {un,or}mbr:     multiply by Q, P from gebrd

            @defgroup gesvd_aux     --- auxiliary routines ---
            @defgroup gsvj0         gsvj0:          step in gesvj
            @defgroup gsvj1         gsvj1:          step in gesvj
            @defgroup las2          las2:           2x2 triangular SVD
            @defgroup lasv2         lasv2:          2x2 triangular SVD
            @defgroup lartgs        lartgs:         generate plane rotation for bidiag SVD
        @}

        @defgroup ggsvd_comp_grp    Generalized SVD computational routines
        @{
            @defgroup ggsvp3        ggsvp3:         step in ggsvd
            @defgroup tgsja         tgsja:          generalized SVD of trapezoidal matrices, step in ggsvd3
            @defgroup lags2         lags2:          2x2 orthogonal factor, step in tgsja
            @defgroup lapll         lapll:          linear dependence of 2 vectors
        @}

        @defgroup lasq_comp_grp     bidiag QR iteration routines
        @{
            @defgroup lasq1         lasq1:          dqds step
            @defgroup lasq2         lasq2:          dqds step
            @defgroup lasq3         lasq3:          dqds step
            @defgroup lasq4         lasq4:          dqds step
            @defgroup lasq5         lasq5:          dqds step
            @defgroup lasq6         lasq6:          dqds step
        @}

        @defgroup lasd_comp_grp     bidiag D&C routines
        @{
            @defgroup lasd0         lasd0:          D&C step: top level solver
            @defgroup lasdt         lasdt:          D&C step: tree
            @defgroup lasd1         lasd1:          D&C step: merge subproblems
            @defgroup lasd2         lasd2:          D&C step: deflation
            @defgroup lasd3         lasd3:          D&C step: secular equation
            @defgroup lasd4         lasd4:          D&C step: secular equation nonlinear solver
            @defgroup lasd5         lasd5:          D&C step: secular equation, 2x2
            @defgroup lasdq         lasdq:          D&C step: leaf using bdsqr

            @defgroup lasd_comp2    --- singular values only or factored form ---
            @defgroup lasda         lasda:          D&C step: top level solver
            @defgroup lasd6         lasd6:          D&C step: merge subproblems
            @defgroup lasd7         lasd7:          D&C step: deflation
            @defgroup lasd8         lasd8:          D&C step: secular equation
        @}
    @}

    @defgroup blas_like_top         BLAS-like
    @{
        @defgroup set_grp           Initialize, copy, convert
        @{
            @defgroup laset         laset:          set matrix
            @defgroup larnv         larnv:          random vector
            @defgroup laruv         laruv:          random uniform vector

            @defgroup lacpy         lacpy:          copy matrix

            @defgroup lacp2         lacp2:          general matrix, convert real to complex
            @defgroup _lag2_        _lag2_:         general matrix, convert double <=> single
            @defgroup _lat2_        _lat2_:         triangular matrix, convert double <=> single

            @defgroup tfttp         tfttp:          triangular matrix, RFP    (tf) to packed (tp)
            @defgroup tfttr         tfttr:          triangular matrix, RFP    (tf) to full   (tr)
            @defgroup tpttf         tpttf:          triangular matrix, packed (tp) to RFP    (tf)
            @defgroup tpttr         tpttr:          triangular matrix, packed (tp) to full   (tr)
            @defgroup trttf         trttf:          triangular matrix, full   (tr) to RFP    (tf)
            @defgroup trttp         trttp:          triangular matrix, full   (tr) to packed (tp)
        @}

        @defgroup norm_grp          Matrix norm
        @{
            @defgroup lange         lange:          general matrix
            @defgroup langb         langb:          general matrix, banded
            @defgroup langt         langt:          general matrix, tridiagonal

            @defgroup lanhs         lanhs:          Hessenberg

            @defgroup lanhe         lan{he,sy}:     Hermitian/symmetric matrix
            @defgroup lanhf         lan{hf,sf}:     Hermitian/symmetric matrix, RFP
            @defgroup lanhp         lan{hp,sp}:     Hermitian/symmetric matrix, packed
            @defgroup lanhb         lan{hb,sb}:     Hermitian/symmetric matrix, banded
            @defgroup lanht         lan{ht,st}:     Hermitian/symmetric matrix, tridiagonal

            @defgroup lantr         lantr:          triangular matrix
            @defgroup lantp         lantp:          triangular matrix, packed
            @defgroup lantb         lantb:          triangular matrix, banded
        @}

        @defgroup blas0_like_grp    Scalar operations
        @{
            @defgroup isnan         isnan:          test for NaN
            @defgroup laisnan       laisnan:        test for NaN, unoptimized
            @defgroup ladiv         ladiv:          complex divide
            @defgroup lapy2         lapy2:          robust sqrt( x^2 + y^2 )
            @defgroup lapy3         lapy3:          robust sqrt( x^2 + y^2 + z^2 )
            @defgroup larmm         larmm:          scale factor to avoid overflow, step in latrs
        @}

        @defgroup blas1_like_grp    Level 1 BLAS-like vector ops
        @{
            @defgroup lacgv         lacgv:          conjugate vector
            @defgroup lasrt         lasrt:          sort vector
            @defgroup lassq         lassq:          sum-of-squares, avoiding over/underflow
            @defgroup rscl          rscl:           scale vector by reciprocal
        @}

        @defgroup blas2_like_grp    Level 2 BLAS-like matrix-vector ops
        @{
            @defgroup ilalc         ilalc:          find non-zero col
            @defgroup ilalr         ilalr:          find non-zero row
            @defgroup lascl         lascl:          scale matrix
            @defgroup la_geamv      la_geamv:       matrix-vector multiply |A| * |x|, general
            @defgroup la_gbamv      la_gbamv:       matrix-vector multiply |A| * |x|, general banded
            @defgroup la_heamv      la_heamv:       matrix-vector multiply |A| * |x|, Hermitian/symmetric
            @defgroup lascl2        lascl2:         diagonal scale matrix, A = D A
            @defgroup larscl2       larscl2:        reciprocal diagonal scale matrix, A = D^{-1} A
            @defgroup la_wwaddw     la_wwaddw:      add to double-double or single-single vector
        @}

        @defgroup blas3_like_grp    Level 3 BLAS-like matrix-matrix ops
        @{
            @defgroup lagtm         lagtm:          tridiagonal matrix-matrix multiply
            @defgroup lacrm         lacrm:          complex * real matrix-matrix multiply
            @defgroup larcm         larcm:          real * complex matrix-matrix multiply
            @defgroup hfrk          hfrk:           Hermitian rank-k update, RFP format
            @defgroup tfsm          tfsm:           triangular-matrix solve, RFP format
        @}
    @}

    @defgroup aux_top               Auxiliary routines
    @{
        @defgroup aux_grp           Other auxiliary routines
        @{
            @defgroup lsame         lsame:          string comparison
            @defgroup lsamen        lsamen:         string comparison
            @defgroup roundup_lwork roundup_lwork:  fix rounding integer to float
            @defgroup second        second:         wall clock timer
        @}

        @defgroup params_grp        Parameters
        @{
            @defgroup lamch         lamch:          machine parameters
            @defgroup lamc1         lamc1:          ??
            @defgroup lamc2         lamc2:          ??
            @defgroup lamc3         lamc3:          ??
            @defgroup lamc4         lamc4:          ??
            @defgroup lamc5         lamc5:          ??
            @defgroup labad         labad:          over/underflow on obsolete pre-IEEE machines
            @defgroup ilaver        ilaver:         LAPACK version
            @defgroup ilaenv        ilaenv:         tuning parameters
            @defgroup ilaenv2stage  ilaenv2stage:   tuning parameters for 2-stage eig
            @defgroup iparam2stage  iparam2stage:   sets parameters for 2-stage eig
            @defgroup ieeeck        ieeeck:         verify inf and NaN are safe
            @defgroup la_constants  la_constants:   Fortran 95 module of constants

            @defgroup blast_aux     --- BLAST constants ---
            @defgroup iladiag       iladiag:        diag      string to BLAST const
            @defgroup ilaprec       ilaprec:        precision string to BLAST const
            @defgroup ilatrans      ilatrans:       trans     string to BLAST const
            @defgroup ilauplo       ilauplo:        uplo      string to BLAST const
            @defgroup la_transtype  la_transtype:   BLAST const to string
        @}

        @defgroup xerbla_grp        Error reporting
        @{
            @defgroup xerbla        xerbla:         error reporting
            @defgroup xerbla_array  xerbla_array:   error reporting, callable from C
        @}
    @}
@}

@defgroup blas_top BLAS
BLAS are defined by three papers:
Basic linear algebra subprograms for {FORTRAN} usage, Lawson et al, 1979.
An extended set of {FORTRAN} basic linear algebra subprograms, Dongarra et al, 1988.
A set of level 3 basic linear algebra subprograms, Dongarra et al, 1990.
Some BLAS-like routines (e.g., csymv, crot, csum1, icmax1) exist in
LAPACK rather than the classic BLAS.
These were extended by the Extra Precision BLAS (XBLAS, not documented here)
https://www.netlib.org/xblas/

@{
        @defgroup scalar_grp        Scalar operations
        @{
            @defgroup abs1          abs1:           | real( x ) | + | imag( x ) |
        @}

        @defgroup blas1_grp         Level 1 BLAS: vector ops
        @{
            @defgroup asum          asum:           sum | real( x_i ) | + | imag( x_i ) |
            @defgroup sum1          sum1:           sum | x_i | (in LAPACK)
            @defgroup axpy          axpy:           y = ax + y
            @defgroup copy          copy:           y = x
            @defgroup dot           dot:            x^H x and x^T x
            @defgroup iamax         iamax:          argmax_i | real( x_i ) | + | imag( x_i ) |
            @defgroup imax1         imax1:          argmax_i | x_i | (in LAPACK)
            @defgroup nrm2          nrm2:           || x ||_2
            @defgroup scal          scal:           x = alpha x
            @defgroup swap          swap:           x <=> y

            @defgroup rot_comp      --- Givens/Jacobi plane rotations ---
            @defgroup rot           rot:            apply plane rotation ([cz]rot in LAPACK)
            @defgroup rotg          rotg:           generate plane rotation (cf. lartg)
            @defgroup rotm          rotm:           apply modified (fast) plane rotation
            @defgroup rotmg         rotmg:          generate modified (fast) plane rotation
        @}

        @defgroup blas2_grp         Level 2 BLAS: matrix-vector ops
        @{
            @defgroup blas2_full    --- full ---
            @defgroup gemv          gemv:           general matrix-vector multiply
            @defgroup ger           ger:            general matrix rank-1 update

            @defgroup hemv          {he,sy}mv:      Hermitian/symmetric matrix-vector multiply ([cz]symv in LAPACK)
            @defgroup her           {he,sy}r:       Hermitian/symmetric rank-1 update
            @defgroup her2          {he,sy}r2:      Hermitian/symmetric rank-2 update

            @defgroup trmv          trmv:           triangular matrix-vector multiply
            @defgroup trsv          trsv:           triangular matrix-vector solve

            @defgroup blas2_packed  --- packed ---
            @defgroup hpmv          {hp,sp}mv:      Hermitian/symmetric matrix-vector multiply
            @defgroup hpr           {hp,sp}r:       Hermitian/symmetric rank-1 update
            @defgroup hpr2          {hp,sp}r2:      Hermitian/symmetric rank-2 update

            @defgroup tpmv          tpmv:           triangular matrix-vector multiply
            @defgroup tpsv          tpsv:           triangular matrix-vector solve

            @defgroup blas2_banded  --- banded ---
            @defgroup gbmv          gbmv:           general matrix-vector multiply

            @defgroup hbmv          {hb,sb}mv:      Hermitian/symmetric matrix-vector multiply

            @defgroup tbmv          tbmv:           triangular matrix-vector multiply
            @defgroup tbsv          tbsv:           triangular matrix-vector solve
        @}

        @defgroup blas3_grp         Level 3 BLAS: matrix-matrix ops
        @{
            @defgroup gemm          gemm:           general matrix-matrix multiply
            @defgroup gemmtr        gemmtr:         general matrix-matrix multiply with triangular output


            @defgroup hemm          {he,sy}mm:      Hermitian/symmetric matrix-matrix multiply
            @defgroup herk          {he,sy}rk:      Hermitian/symmetric rank-k update
            @defgroup her2k         {he,sy}r2k:     Hermitian/symmetric rank-2k update

            @defgroup trmm          trmm:           triangular matrix-matrix multiply
            @defgroup trsm          trsm:           triangular matrix-matrix solve
        @}
@}

**/