[RFC]: add LAPACK routines

[Pranavchiku]

Description

This RFC proposes adding complete LAPACK routines to stdlib.

BLAS Routines

• [ ] DTRSM ( Level: 3 )
  • [ ] JavaScript https://github.com/stdlib-js/stdlib/pull/2518
  • [ ] C
  • [ ] Fortran
• [ ] DGER ( Level: 2 )
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] dsyrk ( Level: 3 )
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DSPR ( Level: 2 )
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DTPSV ( Level: 2 )
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DTPMV ( Level: 2 )
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DSYR ( Level: 2 )
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DTBSV ( Level: 2 )
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DSYMV ( Level: 2 )
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DGEMM ( Level: 3 )
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DTRMV ( Level: 2 )
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran

Easy

The routines listed below are independent and do not depend on others.

• [ ] DLASWP
  • [x] JavaScript https://github.com/stdlib-js/stdlib/pull/2483
  • [ ] C
  • [ ] Fortran
• [ ] DGTTRF
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DGTTS2
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DPOTF2
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DPOEQU
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DLA_PORPVGRW
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DPPEQU
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DPBEQU
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DPTCON
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DPPTRF
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DPPTS2
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DLASYF
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DSYCONV
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DSYSWAPR
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DLA_SYRPVGRW
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DSYCONVF
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DSYCONVF_ROOK
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DLAUU2
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran

Medium

Routines that depends on other LAPACK routines

• [ ] DPPTRI depends on dtpri
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DPPTRS depends on dptts2
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DPTRFS depends on dpttrs
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran

Depends on auxiliary or BLAS routines

• [ ] DGEEQU depends on dlamch
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DGEEQUB depends on dlamch
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DLAQGE depends on dlamch
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DGETC2 depends on dger
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DGBTF2 depends on dger
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DGBEQU depends on dlamch
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DGBEQUB depends on dlamch
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] LAQGB depends on dlamch
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DPSTF2 depends on dlamch
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DPOTRS depends on dtrms.
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DPOEQUB depends on dlamch
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DLAQSY depends on dlamch
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DPPTRF depends on dspr and dtpsv
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DPPTRS depends on dtpsv
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DTPTRI depends on dtpmv
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DLAQSP depends on dlamch
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DPBTF2 depends on dsyr
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DPBTRS depends on dtbsv
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DLAQSB depends on dlamch
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DSYTRS depends on dger
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DSYTRI depends on dsymv
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DSYTRS_3 depends on dtrsm
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DSPTRS depends on dger
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DSPTRI depends on dspmv
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DSYTRI_ROOK depends on dsymv
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DLASYF_RK depends on dgemm
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DSYTF2_RK depends on dsyr
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DTRTRS depends on dtrsm
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DTRTI2 depends on dtrmv
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DTPTRS depends on dtpsv
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DTPMV depends on dtptri
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] DTBTRS depends on dtbsv
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran

Auxiliary routines

• [ ] DLAMCH depends on LSAME which is a BLAS auxiliary routine.
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran
• [ ] LACN2
  • [ ] JavaScript
  • [ ] C
  • [ ] Fortran

Related Issues

None.

Questions

No.

Other

Status of iteration across packages

checked all packages from LU: computational routines, Cholesky: computational routines, LDL: computational routines, Triangular computational routines and listed ones which can be knocked off easily.

Checklist

• [X] I have read and understood the Code of Conduct.
• [X] Searched for existing issues and pull requests.
• [X] The issue name begins with RFC:.

[Pranavchiku]

Dependency for dgesv:

• [ ] dgesv
  • [ ] dgetrf
    • [ ] ilaenv
    • [ ] dgetrf2
      • [ ] dlamch
      • [x] dscal
      • [ ] dgemm
      • [x] dlaswp
      • [ ] dtrsm
  • [ ] dgetrs
    • [ ] dtrsm
    • [x] dlaswp

[Pranavchiku]

dptsv is another low hanging fruit:

• [ ] dptsv
  • [x] dpptrf https://github.com/stdlib-js/stdlib/pull/2578
  • [ ] dpttrs
    • [ ] dptts2 https://github.com/stdlib-js/stdlib/pull/2625

[Pranavchiku]

• [ ] dtrts
  • [ ] dtrsm https://github.com/stdlib-js/stdlib/pull/2518

[Pranavchiku]

• [ ] dtrti2 #2754
  • [x] dtrmv #2540

[Pranavchiku]

• [ ] dlauu2
  • [ ] dgemv

[Pranavchiku]

• [ ] dtptrs
  • [ ] dtpsv