larrc(3)

📦
version 3.12.1 · 9 versions
, in arch rolling

💅 larrc — larrc: step in stemr

Okay bestie, so this one is a page from the LAPACK library manual — a library functions situation — and the whole thing is literally just two Fortran subroutines sitting here being iconic. The name is larrc, and the vibe is "a step in stemr." That's it. That's the whole NAME section. Slay. 💖

✨ SYNOPSIS ✨

🧚 Functions

  • subroutine dlarrc (jobt, n, vl, vu, d, e, pivmin, eigcnt, lcnt, rcnt, info) — DLARRC computes the number of eigenvalues of the symmetric tridiagonal matrix. 🫶
  • subroutine slarrc (jobt, n, vl, vu, d, e, pivmin, eigcnt, lcnt, rcnt, info) — SLARRC computes the number of eigenvalues of the symmetric tridiagonal matrix. Same energy, single-precision edition. ✨

🌸 Detailed Description

There's a Detailed Description heading here with nothing under it — she's mysterious, she's minimal, she's giving main character energy with zero dialogue. 🙈

👑 Function Documentation

💜 subroutine dlarrc (character jobt, integer n, double precision vl, double precision vu, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision pivmin, integer eigcnt, integer lcnt, integer rcnt, integer info)

DLARRC computes the number of eigenvalues of the symmetric tridiagonal matrix. No cap. 💅

🎀 Purpose:

!>
!> Find the number of eigenvalues of the symmetric tridiagonal matrix T
!> that are in the interval (VL,VU] if JOBT = 'T', and of L D L^T
!> if JOBT = 'L'.
!>

So basically: if JOBT = 'T' she counts the eigenvalues of the symmetric tridiagonal matrix T that live in the interval (VL,VU], and if JOBT = 'L' she does the same thing but for L D L^T. Notice the interval is open on the left and closed on the right — that's (VL,VU] bestie, not [VL,VU], and the difference is literally the whole point. 🔥

🦋 Parameters

  • JOBT
!>          JOBT is CHARACTER*1
!>          = 'T':  Compute Sturm count for matrix T.
!>          = 'L':  Compute Sturm count for matrix L D L^T.
!>

It's a CHARACTER*1, okay? Pass 'T' and you get the Sturm count for matrix T. Pass 'L' and you get the Sturm count for matrix L D L^T. Two options, both valid, pick your fighter. ⭐

  • N
!>          N is INTEGER
!>          The order of the matrix. N > 0.
!>

An INTEGER, the order of the matrix, and she must be N > 0. Zero and below? Not invited to the function call. 💀

  • VL
!>          VL is DOUBLE PRECISION
!>          The lower bound for the eigenvalues.
!>

DOUBLE PRECISION and it's the lower bound for the eigenvalues. The bottom of the range, the floor of the group chat. 🍓

  • VU
!>          VU is DOUBLE PRECISION
!>          The upper bound for the eigenvalues.
!>

Also DOUBLE PRECISION, and it's the upper bound for the eigenvalues. Together with VL she forms the iconic interval (VL,VU]. 🌈

  • D
!>          D is DOUBLE PRECISION array, dimension (N)
!>          JOBT = 'T': The N diagonal elements of the tridiagonal matrix T.
!>          JOBT = 'L': The N diagonal elements of the diagonal matrix D.
!>

A DOUBLE PRECISION array, dimension (N). When JOBT = 'T' it's the N diagonal elements of the tridiagonal matrix T; when JOBT = 'L' it's the N diagonal elements of the diagonal matrix D. Same array, different lore depending on JOBT. 👑

  • E
!>          E is DOUBLE PRECISION array, dimension (N)
!>          JOBT = 'T': The N-1 offdiagonal elements of the matrix T.
!>          JOBT = 'L': The N-1 offdiagonal elements of the matrix L.
!>

Also a DOUBLE PRECISION array, dimension (N) — but she only uses the N-1 offdiagonal elements. For JOBT = 'T' that's the N-1 offdiagonal elements of matrix T; for JOBT = 'L' it's the N-1 offdiagonal elements of matrix L. Yes, the dimension is (N) and the count is N-1, that's not a typo, that's just how she lives. ✨

  • PIVMIN
!>          PIVMIN is DOUBLE PRECISION
!>          The minimum pivot in the Sturm sequence for T.
!>

DOUBLE PRECISION, and it's the minimum pivot in the Sturm sequence for T. Small but mighty. 🧚

  • EIGCNT
!>          EIGCNT is INTEGER
!>          The number of eigenvalues of the symmetric tridiagonal matrix T
!>          that are in the interval (VL,VU]
!>

An INTEGER holding the number of eigenvalues of the symmetric tridiagonal matrix T that are in the interval (VL,VU]. This is the whole reason we showed up, honestly. 💖

  • LCNT
!>          LCNT is INTEGER
!>

An INTEGER. That's the energy. She exists. 🎀

  • RCNT
!>          RCNT is INTEGER
!>          The left and right negcounts of the interval.
!>

An INTEGER — together with LCNT these are the left and right negcounts of the interval. 🦋

  • INFO
!>          INFO is INTEGER
!>

An INTEGER. No further comment, she speaks for herself. 💀

🌟 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

🫶 Contributors:

Beresford Parlett, University of California, Berkeley, USA Jim Demmel, University of California, Berkeley, USA Inderjit Dhillon, University of Texas, Austin, USA Osni Marques, LBNL/NERSC, USA Christof Voemel, University of California, Berkeley, USA

Definition at line 135 of file dlarrc.f. 💅

💜 subroutine slarrc (character jobt, integer n, real vl, real vu, real, dimension( * ) d, real, dimension( * ) e, real pivmin, integer eigcnt, integer lcnt, integer rcnt, integer info)

SLARRC computes the number of eigenvalues of the symmetric tridiagonal matrix. Literally the same job as dlarrc but she's working in REAL instead of DOUBLE PRECISION. ✨

🎀 Purpose:

!>
!> Find the number of eigenvalues of the symmetric tridiagonal matrix T
!> that are in the interval (VL,VU] if JOBT = 'T', and of L D L^T
!> if JOBT = 'L'.
!>

Same mission, same interval (VL,VU], same JOBT = 'T' vs JOBT = 'L' situation. Count those eigenvalues, bestie. 🔥

🦋 Parameters

  • JOBT
!>          JOBT is CHARACTER*1
!>          = 'T':  Compute Sturm count for matrix T.
!>          = 'L':  Compute Sturm count for matrix L D L^T.
!>

CHARACTER*1. 'T' for the Sturm count of matrix T, 'L' for the Sturm count of matrix L D L^T. 🌸

  • N
!>          N is INTEGER
!>          The order of the matrix. N > 0.
!>

INTEGER, the order of the matrix, and again: N > 0. Respect the constraint. ⭐

  • VL
!>          VL is REAL
!>          The lower bound for the eigenvalues.
!>

REAL this time (not DOUBLE PRECISION, don't get it twisted), and it's the lower bound for the eigenvalues. 🍓

  • VU
!>          VU is REAL
!>          The upper bound for the eigenvalues.
!>

REAL, the upper bound for the eigenvalues. 🌈

  • D
!>          D is REAL array, dimension (N)
!>          JOBT = 'T': The N diagonal elements of the tridiagonal matrix T.
!>          JOBT = 'L': The N diagonal elements of the diagonal matrix D.
!>

REAL array, dimension (N). JOBT = 'T' → the N diagonal elements of the tridiagonal matrix T. JOBT = 'L' → the N diagonal elements of the diagonal matrix D. 👑

  • E
!>          E is REAL array, dimension (N)
!>          JOBT = 'T': The N-1 offdiagonal elements of the matrix T.
!>          JOBT = 'L': The N-1 offdiagonal elements of the matrix L.
!>

REAL array, dimension (N), holding the N-1 offdiagonal elements — of matrix T when JOBT = 'T', of matrix L when JOBT = 'L'. ✨

  • PIVMIN
!>          PIVMIN is REAL
!>          The minimum pivot in the Sturm sequence for T.
!>

REAL, the minimum pivot in the Sturm sequence for T. 🧚

  • EIGCNT
!>          EIGCNT is INTEGER
!>          The number of eigenvalues of the symmetric tridiagonal matrix T
!>          that are in the interval (VL,VU]
!>

INTEGER, the number of eigenvalues of the symmetric tridiagonal matrix T that are in the interval (VL,VU]. The moment. 💖

  • LCNT
!>          LCNT is INTEGER
!>

INTEGER. Short and sweet. 🎀

  • RCNT
!>          RCNT is INTEGER
!>          The left and right negcounts of the interval.
!>

INTEGER — she and LCNT are the left and right negcounts of the interval. 🦋

  • INFO
!>          INFO is INTEGER
!>

INTEGER. That's the whole description, and honestly? Respect. 💀

🌟 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

🫶 Contributors:

Beresford Parlett, University of California, Berkeley, USA Jim Demmel, University of California, Berkeley, USA Inderjit Dhillon, University of Texas, Austin, USA Osni Marques, LBNL/NERSC, USA Christof Voemel, University of California, Berkeley, USA

Definition at line 135 of file slarrc.f. 💅

🌟 Author

Generated automatically by Doxygen for LAPACK from the source code. Not a human, just Doxygen doing her little autogenerated thing. 🤖✨

Okay that's the whole page, bestie — every parameter, every !> comment, both subroutines, all the authors, all the contributors, both "Definition at line 135" notes, and the Doxygen credit. Nothing dropped, nothing invented. Periodt. 💅

LAPACK, Version 3.12.0 — that's the source and version, and the date on the original footer is the LAPACK release date, so go off, calendar. 🎀 Byeee, ily, go count some eigenvalues in (VL,VU] 🫶💖

📦 where this page comes from