975 lines
53 KiB
Plaintext
975 lines
53 KiB
Plaintext
/**
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@defgroup lapack_top LAPACK
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@{
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@defgroup solve_top Linear solve, AX = B
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@{
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@defgroup gesv_driver_grp LU: General matrix, driver
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@{
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@defgroup gesv_driver --- full ---
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@defgroup gesv gesv: factor and solve
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@defgroup gesvx gesvx: factor and solve, expert
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@defgroup gesvxx gesvxx: factor and solve, extra precise
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@defgroup gesv_mixed gesv: factor and solve, mixed precision
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@defgroup gbsv_driver --- banded ---
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@defgroup gbsv gbsv: factor and solve
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@defgroup gbsvx gbsvx: factor and solve, expert
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@defgroup gbsvxx gbsvxx: factor and solve, extra precise
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@defgroup gtsv_driver --- tridiagonal ---
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@defgroup gtsv gtsv: factor and solve
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@defgroup gtsvx gtsvx: factor and solve, expert
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@}
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@defgroup gesv_comp_grp LU: computational routines (factor, cond, etc.)
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@{
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@defgroup gesv_comp --- full ---
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@defgroup gecon gecon: condition number estimate
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@defgroup getrf getrf: triangular factor
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@defgroup getrf2 getrf2: triangular factor panel, recursive?
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@defgroup getf2 getf2: triangular factor panel, level 2
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@defgroup getrs getrs: triangular solve using factor
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@defgroup getri getri: triangular inverse
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@defgroup gerfs gerfs: iterative refinement
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@defgroup gerfsx gerfsx: iterative refinement, expert
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@defgroup geequ geequ: equilibration
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@defgroup geequb geequb: equilibration, power of 2
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@defgroup laqge laqge: row/col scale matrix
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@defgroup laswp laswp: swap permutation
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@defgroup getc2 getc2: triangular factor, with complete pivoting
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@defgroup gesc2 gesc2: triangular solve using factor, with complete pivoting
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@defgroup latdf latdf: Dif-estimate with complete pivoting LU, step in tgsen
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@defgroup la_gercond la_gercond: Skeel condition number estimate
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@defgroup la_gerpvgrw la_gerpvgrw: reciprocal pivot growth
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@defgroup la_gerfsx_extended la_gerfsx_extended: step in gerfsx
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@defgroup gbsv_comp --- banded ---
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@defgroup gbcon gbcon: condition number estimate
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@defgroup gbtrf gbtrf: triangular factor
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@defgroup gbtf2 gbtf2: triangular factor, level 2
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@defgroup gbtrs gbtrs: triangular solve using factor
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@defgroup gbrfs gbrfs: iterative refinement
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@defgroup gbrfsx gbrfsx: iterative refinement, expert
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@defgroup gbequ gbequ: equilibration
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@defgroup gbequb gbequb: equilibration, power of 2
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@defgroup laqgb laqgb: row/col scale matrix
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@defgroup la_gbrcond la_gbrcond: Skeel condition number estimate
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@defgroup la_gbrpvgrw la_gbrpvgrw: reciprocal pivot growth
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@defgroup la_gbrfsx_extended la_gbrfsx_extended: step in gbrfsx
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@defgroup gtsv_comp --- tridiagonal ---
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@defgroup gtcon gtcon: condition number estimate
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@defgroup gttrf gttrf: triangular factor
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@defgroup gttrs gttrs: triangular solve using factor
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@defgroup gtts2 gtts2: triangular solve using factor
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@defgroup gtrfs gtrfs: iterative refinement
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@}
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@defgroup posv_driver_grp Cholesky: Hermitian/symmetric positive definite matrix, driver
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@{
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@defgroup posv_driver --- full ---
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@defgroup posv posv: factor and solve
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@defgroup posvx posvx: factor and solve, expert
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@defgroup posvxx posvxx: factor and solve, extra precise
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@defgroup posv_mixed posv: factor and solve, mixed precision
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@defgroup ppsv_driver --- packed ---
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@defgroup ppsv ppsv: factor and solve
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@defgroup ppsvx ppsvx: factor and solve, expert
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@defgroup pfsv_driver --- rectangular full packed (RFP) ---
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@defgroup pfsv pfsv: factor and solve [not available]
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@defgroup pbsv_driver --- banded ---
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@defgroup pbsv pbsv: factor and solve
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@defgroup pbsvx pbsvx: factor and solve, expert
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@defgroup ptsv_driver --- tridiagonal ---
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@defgroup ptsv ptsv: factor and solve
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@defgroup ptsvx ptsvx: factor and solve, expert
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@}
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@defgroup posv_comp_grp Cholesky: computational routines (factor, cond, etc.)
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@{
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@defgroup posv_comp --- full ---
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@defgroup pocon pocon: condition number estimate
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@defgroup potrf potrf: triangular factor
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@defgroup potrf2 potrf2: triangular factor panel, recursive?
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@defgroup potf2 potf2: triangular factor panel, level 2
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@defgroup pstrf pstrf: triangular factor, with pivoting
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@defgroup pstf2 pstf2: triangular factor, with pivoting panel, level 2
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@defgroup potrs potrs: triangular solve using factor
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@defgroup potri potri: triangular inverse
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@defgroup porfs porfs: iterative refinement
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@defgroup porfsx porfsx: iterative refinement, expert
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@defgroup poequ poequ: equilibration
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@defgroup poequb poequb: equilibration, power of 2
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@defgroup laqhe laqhe: row/col scale matrix
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@defgroup la_porcond la_porcond: Skeel condition number estimate
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@defgroup la_porpvgrw la_porpvgrw: reciprocal pivot growth
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@defgroup la_porfsx_extended la_porfsx_extended: step in porfsx
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@defgroup ppsv_comp --- packed ---
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@defgroup ppcon ppcon: condition number estimate
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@defgroup pptrf pptrf: triangular factor
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@defgroup pptrs pptrs: triangular solve using factor
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@defgroup pptri pptri: triangular inverse
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@defgroup pprfs pprfs: iterative refinement
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@defgroup ppequ ppequ: equilibration
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@defgroup laqhp laqhp: row/col scale matrix
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@defgroup pfsv_comp --- rectangular full packed (RFP) ---
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@defgroup pftrf pftrf: triangular factor
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@defgroup pftrs pftrs: triangular solve using factor
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@defgroup pftri pftri: triangular inverse
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@defgroup pbsv_comp --- banded ---
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@defgroup pbcon pbcon: condition number estimate
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@defgroup pbtrf pbtrf: triangular factor
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@defgroup pbtf2 pbtf2: triangular factor panel, level 2
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@defgroup pbtrs pbtrs: triangular solve using factor
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@defgroup pbrfs pbrfs: iterative refinement
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@defgroup pbequ pbequ: equilibration
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@defgroup laqhb laqhb: row/col scale matrix
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@defgroup ptsv_comp --- tridiagonal ---
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@defgroup ptcon ptcon: condition number estimate
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@defgroup pttrf pttrf: triangular factor
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@defgroup pttrs pttrs: triangular solve using factor
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@defgroup ptts2 ptts2: triangular solve using factor, unblocked
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@defgroup ptrfs ptrfs: iterative refinement
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@}
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@defgroup hesv_driver_grp LDL: Hermitian/symmetric indefinite matrix, driver
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@{
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@defgroup hesv_driver --- full, rook pivoting ---
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@defgroup hesv {he,sy}sv: rook (v1)
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@defgroup hesv_rook {he,sy}sv_rook: rook (v2)
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@defgroup hesv_rk {he,sy}sv_rk: rook (v3)
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@defgroup hesvx {he,sy}svx: rook (v1, expert)
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@defgroup hesvxx {he,sy}svxx: rook (v1, expert)
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@defgroup hpsv_driver --- packed, rook pivoting ---
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@defgroup hpsv {hp,sp}sv: factor and solve
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@defgroup hpsvx {hp,sp}svx: factor and solve, expert
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@defgroup hesv_aa_driver --- full, Aasen ---
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@defgroup hesv_aa {he,sy}sv_aa: Aasen
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@defgroup hesv_aa_2stage {he,sy}sv_aa_2stage: Aasen, blocked 2-stage
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@}
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@defgroup hesv_comp_grp LDL: computational routines (factor, cond, etc.)
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@{
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@defgroup hesv_comp_v1 --- full, rook v1 ---
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@defgroup hecon {he,sy}con: condition number estimate
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@defgroup hetrf {he,sy}trf: triangular factor
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@defgroup lahef la{he,sy}f: step in hetrf
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@defgroup hetf2 {he,sy}tf2: triangular factor, level 2
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@defgroup hetrs {he,sy}trs: triangular solve using factor
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@defgroup hetri {he,sy}tri: triangular inverse
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@defgroup herfs {he,sy}rfs: iterative refinement
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@defgroup herfsx {he,sy}rfsx: iterative refinement, expert
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@defgroup heequb {he,sy}equb: equilibration, power of 2
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@defgroup syconv syconv: convert to/from L and D from hetrf
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@defgroup hecon_3 {he,sy}con_3: condition number estimate
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@defgroup hetri2 {he,sy}tri2: inverse
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@defgroup hetri2x {he,sy}tri2x: inverse
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@defgroup hetri_3 {he,sy}tri_3: inverse
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@defgroup hetri_3x {he,sy}tri_3x: inverse
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@defgroup hetrs2 {he,sy}trs2: solve using factor
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@defgroup hetrs_3 {he,sy}trs_3: solve using factor
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@defgroup heswapr {he,sy}swapr: apply 2-sided permutation
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@defgroup la_hercond la_hercond: Skeel condition number estimate
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@defgroup la_herfsx_extended la_herfsx_extended: step in herfsx
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@defgroup la_herpvgrw la_herpvgrw: reciprocal pivot growth
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@defgroup hpsv_comp --- packed, rook v1 ---
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@defgroup hpcon {hp,sp}con: condition number estimate
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@defgroup hptrf {hp,sp}trf: triangular factor
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@defgroup hptrs {hp,sp}trs: triangular solve using factor
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@defgroup hptri {hp,sp}tri: triangular inverse
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@defgroup hprfs {hp,sp}rfs: iterative refinement
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@defgroup hesv_comp_v2 --- full, rook v2 ---
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@defgroup hecon_rook {he,sy}con_rook: condition number estimate
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@defgroup hetrf_rook {he,sy}trf_rook: triangular factor
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@defgroup lahef_rook la{he,sy}f_rook: triangular factor step
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@defgroup hetf2_rook {he,sy}tf2_rook: triangular factor, level 2
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@defgroup hetrs_rook {he,sy}trs_rook: triangular solve using factor
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@defgroup hetri_rook {he,sy}tri_rook: triangular inverse
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@defgroup hesv_comp_v3 --- full, rook v3 ---
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@defgroup hetrf_rk {he,sy}trf_rk: triangular factor
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@defgroup lahef_rk la{he,sy}f_rk: triangular factor step
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@defgroup hetf2_rk {he,sy}tf2_rk: triangular factor, level 2
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@defgroup syconvf syconvf: convert to/from hetrf to hetrf_rk format
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@defgroup syconvf_rook syconvf_rook: convert to/from hetrf_rook to hetrf_rk format
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@defgroup hesv_comp_aasen --- full, Aasen ---
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@defgroup hetrf_aa {he,sy}trf_aa: triangular factor
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@defgroup lahef_aa la{he,sy}f_aa: triangular factor partial factor
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@defgroup hetrs_aa {he,sy}trs_aa: triangular solve using factor
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@defgroup hesv_comp_aasen2 --- full, Aasen, blocked 2-stage ---
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@defgroup hetrf_aa_2stage {he,sy}trf_aa_2stage: triangular factor
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@defgroup hetrs_aa_2stage {he,sy}trs_aa_2stage: triangular solve using factor
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@}
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@defgroup trsv_comp_grp Triangular computational routines (solve, cond, etc.)
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@{
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@defgroup trsv_comp --- full ---
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@defgroup trcon trcon: condition number estimate
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@defgroup trtrs trtrs: triangular solve
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@defgroup latrs latrs: triangular solve with robust scaling
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@defgroup latrs3 latrs3: triangular solve with robust scaling, level 3
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@defgroup trtri trtri: triangular inverse
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@defgroup trti2 trti2: triangular inverse, level 2
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@defgroup trrfs trrfs: triangular iterative refinement
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@defgroup lauum lauum: triangular multiply: U^H U
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@defgroup lauu2 lauu2: triangular multiply: U^H U, level 2
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@defgroup tpsv_comp --- packed ---
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@defgroup tpcon tpcon: condition number estimate
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@defgroup tptrs tptrs: triangular solve
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@defgroup latps latps: triangular solve with robust scaling
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@defgroup tptri tptri: triangular inverse
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@defgroup tprfs tprfs: triangular iterative refinement
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@defgroup tfsv_comp --- rectangular full packed (RFP) ---
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@defgroup tftri tftri: triangular inverse, RFP
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@defgroup tbsv_comp --- banded ---
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@defgroup tbcon tbcon: condition number estimate
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@defgroup tbtrs tbtrs: triangular solve
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@defgroup latbs latbs: triangular solve with scaling
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@defgroup tbrfs tbrfs: triangular iterative refinement
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@}
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@defgroup solve_aux_grp Auxiliary routines
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@{
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@defgroup lacn2 lacn2: 1-norm estimate, e.g., || A^{-1} ||_1 in gecon
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@defgroup lacon lacon: 1-norm estimate, e.g., || A^{-1} ||_1 in gecon, old
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@defgroup la_lin_berr la_lin_berr: backward error
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@}
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@}
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@defgroup gels_top Least squares
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@{
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@defgroup gels_driver_grp Standard least squares, min || Ax - b ||_2
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@{
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@defgroup gels gels: least squares using QR/LQ
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@defgroup gelst gelst: least squares using QR/LQ with T matrix
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@defgroup gelss gelss: least squares using SVD, QR iteration
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@defgroup gelsd gelsd: least squares using SVD, divide and conquer
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@defgroup gelsy gelsy: least squares using complete orthogonal factor
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@defgroup getsls getsls: least squares using tall-skinny QR/LQ
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@}
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@defgroup ggls_driver_grp Constrained least squares
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@{
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@defgroup gglse gglse: equality-constrained least squares
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@defgroup ggglm ggglm: Gauss-Markov linear model
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@}
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@defgroup gels_aux_grp Auxiliary routines
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@{
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@defgroup laic1 laic1: condition estimate, step in gelsy
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@defgroup lals0 lals0: back multiplying factors, step in gelsd
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@defgroup lalsa lalsa: SVD of coefficient matrix, step in gelsd
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@defgroup lalsd lalsd: uses SVD for least squares, step in gelsd
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@}
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@}
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@defgroup unitary_top Orthogonal/unitary factors (QR, CS, etc.)
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@{
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@defgroup geqr_comp_grp QR
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@{
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@defgroup geqr_comp1 --- flexible ---
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@defgroup geqr geqr: QR factor, flexible
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@defgroup gemqr gemqr: multiply by Q from geqr
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@defgroup geqr_comp2 --- classic ---
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@defgroup geqrf geqrf: QR factor
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@defgroup geqr2 geqr2: QR factor, level 2
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@defgroup ungqr {un,or}gqr: generate explicit Q from geqrf
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@defgroup ung2r {un,or}g2r: generate explicit Q from geqrf, level 2
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@defgroup unmqr {un,or}mqr: multiply by Q from geqrf
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@defgroup unm2r {un,or}m2r: multiply by Q from geqrf, level 2
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@defgroup geqr_comp3 --- with T ---
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@defgroup geqrt geqrt: QR factor, with T
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@defgroup geqrt2 geqrt2: QR factor, with T, level 2
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@defgroup geqrt3 geqrt3: QR factor, with T, recursive panel
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@defgroup gemqrt gemqrt: multiply by Q from geqrt
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@defgroup geqr_comp4 --- positive ---
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@defgroup geqrfp geqrfp: QR factor, diag( R ) ≥ 0
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@defgroup geqr2p geqr2p: QR factor, diag( R ) ≥ 0, level 2
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@}
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@defgroup geqpf_comp_grp QR with pivoting
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@{
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@defgroup geqp3 geqp3: QR factor with pivoting, level 3
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@defgroup laqp2 laqp2: step of geqp3
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@defgroup laqps laqps: step of geqp3
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@}
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@defgroup getsqr_comp_grp QR, tall-skinny
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@{
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@defgroup latsqr latsqr: tall-skinny QR factor
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@defgroup ungtsqr {un,or}gtsqr: generate Q from latsqr
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@defgroup ungtsqr_row {un,or}gtsqr_row: generate Q from latsqr
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@defgroup larfb_gett larfb_gett: step in ungtsqr_row
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@defgroup lamtsqr lamtsqr: multiply by Q from latsqr
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@defgroup getsqrhrt getsqrhrt: tall-skinny QR factor, with Householder reconstruction
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@defgroup unhr_col {un,or}hr_col: Householder reconstruction
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@defgroup launhr_col_getrfnp la{un,or}hr_col_getrfnp: LU factor without pivoting
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@defgroup launhr_col_getrfnp2 la{un,or}hr_col_getrfnp2: LU factor without pivoting, level 2
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@}
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@defgroup tpqr_comp_grp QR, triangular-pentagonal
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@{
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@defgroup tpqrt tpqrt: QR factor
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@defgroup tpqrt2 tpqrt2: QR factor, level 2
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@defgroup tpmqrt tpmqrt: applies Q
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@defgroup tprfb tprfb: applies Q (like larfb)
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@}
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@defgroup ggqr_comp_grp Generalized QR
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@{
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@defgroup ggqrf ggqrf: Generalized QR factor
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@}
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@defgroup gelq_comp_grp LQ
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@{
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@defgroup gelq_comp1 --- flexible ---
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@defgroup gelq gelq: LQ factor, flexible
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@defgroup gemlq gemlq: multiply by Q from gelq
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@defgroup gelq_comp2 --- classic ---
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@defgroup gelqf gelqf: LQ factor
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@defgroup gelq2 gelq2: LQ factor, level 2
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@defgroup unglq {un,or}glq: generate explicit Q from gelqf
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@defgroup ungl2 {un,or}gl2: generate explicit Q, level 2, step in unglq
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@defgroup unmlq {un,or}mlq: multiply by Q from gelqf
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@defgroup unml2 {un,or}ml2: multiply by Q, level 2, step in unmlq
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@defgroup gelq_comp3 --- with T ---
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@defgroup gelqt gelqt: LQ factor, with T
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@defgroup gelqt3 gelqt3: LQ factor, with T, recursive
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@defgroup gemlqt gemlqt: multiply by Q from gelqt
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@}
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@defgroup geswlq_comp_grp LQ, short-wide
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@{
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@defgroup laswlq laswlq: short-wide LQ factor
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@defgroup lamswlq lamswlq: multiply by Q from laswlq
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@}
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@defgroup tplq_comp_grp LQ, triangular-pentagonal
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@{
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@defgroup tplqt tplqt: QR factor
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@defgroup tplqt2 tplqt2: QR factor, level 2
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@defgroup tpmlqt tpmlqt: applies Q
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@}
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@defgroup geql_comp_grp QL
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@{
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@defgroup geqlf geqlf: QL factor
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@defgroup geql2 geql2: QL factor, level 2
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@defgroup ungql {un,or}gql: generate explicit Q from geqlf
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@defgroup unmql {un,or}mql: multiply by Q from geqlf
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@defgroup ung2l {un,or}g2l: step in ungql
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@defgroup unm2l {un,or}m2l: step in unmql
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@}
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@defgroup gerq_comp_grp RQ
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@{
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@defgroup gerqf gerqf: RQ factor
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@defgroup gerq2 gerq2: RQ factor, level 2
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@defgroup ungrq {un,or}grq: generate explicit Q from gerqf
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@defgroup unmrq {un,or}mrq: multiply by Q from gerqf
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@defgroup unmr2 {un,or}mr2: step in unmrq
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@defgroup ungr2 {un,or}gr2: step in ungrq
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@}
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@defgroup ggrq_comp_grp Generalized RQ
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@{
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@defgroup ggrqf ggrqf: Generalized RQ factor
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@}
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@defgroup gerz_comp_grp RZ
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@{
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|
@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
|
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@defgroup lantp lantp: triangular matrix, packed
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@defgroup lantb lantb: triangular matrix, banded
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@}
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@defgroup blas0_like_grp Scalar operations
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@{
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@defgroup isnan isnan: test for NaN
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@defgroup laisnan laisnan: test for NaN, unoptimized
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@defgroup ladiv ladiv: complex divide
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@defgroup lapy2 lapy2: robust sqrt( x^2 + y^2 )
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@defgroup lapy3 lapy3: robust sqrt( x^2 + y^2 + z^2 )
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@defgroup larmm larmm: scale factor to avoid overflow, step in latrs
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@}
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@defgroup blas1_like_grp Level 1 BLAS-like vector ops
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@{
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@defgroup lacgv lacgv: conjugate vector
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@defgroup lasrt lasrt: sort vector
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@defgroup lassq lassq: sum-of-squares, avoiding over/underflow
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@defgroup rscl rscl: scale vector by reciprocal
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@}
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@defgroup blas2_like_grp Level 2 BLAS-like matrix-vector ops
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@{
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@defgroup ilalc ilalc: find non-zero col
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@defgroup ilalr ilalr: find non-zero row
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@defgroup lascl lascl: scale matrix
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@defgroup la_geamv la_geamv: matrix-vector multiply |A| * |x|, general
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@defgroup la_gbamv la_gbamv: matrix-vector multiply |A| * |x|, general banded
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@defgroup la_heamv la_heamv: matrix-vector multiply |A| * |x|, Hermitian/symmetric
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@defgroup lascl2 lascl2: diagonal scale matrix, A = D A
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@defgroup larscl2 larscl2: reciprocal diagonal scale matrix, A = D^{-1} A
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@defgroup la_wwaddw la_wwaddw: add to double-double or single-single vector
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@}
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@defgroup blas3_like_grp Level 3 BLAS-like matrix-matrix ops
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@{
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@defgroup lagtm lagtm: tridiagonal matrix-matrix multiply
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@defgroup lacrm lacrm: complex * real matrix-matrix multiply
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@defgroup larcm larcm: real * complex matrix-matrix multiply
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@defgroup hfrk hfrk: Hermitian rank-k update, RFP format
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@defgroup tfsm tfsm: triangular-matrix solve, RFP format
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@}
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@}
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@defgroup aux_top Auxiliary routines
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@{
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@defgroup aux_grp Other auxiliary routines
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@{
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@defgroup lsame lsame: string comparison
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@defgroup lsamen lsamen: string comparison
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@defgroup roundup_lwork roundup_lwork: fix rounding integer to float
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@defgroup second second: wall clock timer
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@}
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@defgroup params_grp Parameters
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@{
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@defgroup lamch lamch: machine parameters
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@defgroup lamc1 lamc1: ??
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@defgroup lamc2 lamc2: ??
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@defgroup lamc3 lamc3: ??
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@defgroup lamc4 lamc4: ??
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@defgroup lamc5 lamc5: ??
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@defgroup labad labad: over/underflow on obsolete pre-IEEE machines
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@defgroup ilaver ilaver: LAPACK version
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@defgroup ilaenv ilaenv: tuning parameters
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@defgroup ilaenv2stage ilaenv2stage: tuning parameters for 2-stage eig
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@defgroup iparam2stage iparam2stage: sets parameters for 2-stage eig
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@defgroup ieeeck ieeeck: verify inf and NaN are safe
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@defgroup la_constants la_constants: Fortran 95 module of constants
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@defgroup blast_aux --- BLAST constants ---
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@defgroup iladiag iladiag: diag string to BLAST const
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@defgroup ilaprec ilaprec: precision string to BLAST const
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@defgroup ilatrans ilatrans: trans string to BLAST const
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@defgroup ilauplo ilauplo: uplo string to BLAST const
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@defgroup la_transtype la_transtype: BLAST const to string
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@}
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@defgroup xerbla_grp Error reporting
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@{
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@defgroup xerbla xerbla: error reporting
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@defgroup xerbla_array xerbla_array: error reporting, callable from C
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@}
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@}
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@}
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@defgroup blas_top BLAS
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BLAS are defined by three papers:
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Basic linear algebra subprograms for {FORTRAN} usage, Lawson et al, 1979.
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An extended set of {FORTRAN} basic linear algebra subprograms, Dongarra et al, 1988.
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A set of level 3 basic linear algebra subprograms, Dongarra et al, 1990.
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Some BLAS-like routines (e.g., csymv, crot, csum1, icmax1) exist in
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LAPACK rather than the classic BLAS.
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These were extended by the Extra Precision BLAS (XBLAS, not documented here)
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https://www.netlib.org/xblas/
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@{
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@defgroup scalar_grp Scalar operations
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@{
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@defgroup abs1 abs1: | real( x ) | + | imag( x ) |
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@}
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@defgroup blas1_grp Level 1 BLAS: vector ops
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@{
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@defgroup asum asum: sum | real( x_i ) | + | imag( x_i ) |
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@defgroup sum1 sum1: sum | x_i | (in LAPACK)
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@defgroup axpy axpy: y = ax + y
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@defgroup copy copy: y = x
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@defgroup dot dot: x^H x and x^T x
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@defgroup iamax iamax: argmax_i | real( x_i ) | + | imag( x_i ) |
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@defgroup imax1 imax1: argmax_i | x_i | (in LAPACK)
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@defgroup nrm2 nrm2: || x ||_2
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@defgroup scal scal: x = alpha x
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@defgroup swap swap: x <=> y
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@defgroup rot_comp --- Givens/Jacobi plane rotations ---
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@defgroup rot rot: apply plane rotation ([cz]rot in LAPACK)
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@defgroup rotg rotg: generate plane rotation (cf. lartg)
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@defgroup rotm rotm: apply modified (fast) plane rotation
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@defgroup rotmg rotmg: generate modified (fast) plane rotation
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@}
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@defgroup blas2_grp Level 2 BLAS: matrix-vector ops
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@{
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@defgroup blas2_full --- full ---
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@defgroup gemv gemv: general matrix-vector multiply
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@defgroup ger ger: general matrix rank-1 update
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@defgroup hemv {he,sy}mv: Hermitian/symmetric matrix-vector multiply ([cz]symv in LAPACK)
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@defgroup her {he,sy}r: Hermitian/symmetric rank-1 update
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@defgroup her2 {he,sy}r2: Hermitian/symmetric rank-2 update
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@defgroup trmv trmv: triangular matrix-vector multiply
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@defgroup trsv trsv: triangular matrix-vector solve
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@defgroup blas2_packed --- packed ---
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@defgroup hpmv {hp,sp}mv: Hermitian/symmetric matrix-vector multiply
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@defgroup hpr {hp,sp}r: Hermitian/symmetric rank-1 update
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@defgroup hpr2 {hp,sp}r2: Hermitian/symmetric rank-2 update
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@defgroup tpmv tpmv: triangular matrix-vector multiply
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@defgroup tpsv tpsv: triangular matrix-vector solve
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@defgroup blas2_banded --- banded ---
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@defgroup gbmv gbmv: general matrix-vector multiply
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@defgroup hbmv {hb,sb}mv: Hermitian/symmetric matrix-vector multiply
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@defgroup tbmv tbmv: triangular matrix-vector multiply
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@defgroup tbsv tbsv: triangular matrix-vector solve
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@}
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@defgroup blas3_grp Level 3 BLAS: matrix-matrix ops
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|
@{
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@defgroup gemm gemm: general matrix-matrix multiply
|
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@defgroup hemm {he,sy}mm: Hermitian/symmetric matrix-matrix multiply
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@defgroup herk {he,sy}rk: Hermitian/symmetric rank-k update
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@defgroup her2k {he,sy}r2k: Hermitian/symmetric rank-2k update
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@defgroup trmm trmm: triangular matrix-matrix multiply
|
|
@defgroup trsm trsm: triangular matrix-matrix solve
|
|
@}
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@}
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**/
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