DLAQTR(3)

📦 version 3.12.0, in opensuse-leap 16.0

💅 DLAQTR(3) — Library Functions Manual 💅

Okay so bestie, welcome to DLAQTR(3) from the Library Functions Manual. The header is also lowkey flexing /home/abui...RC/dlaqtr.f(3) twice, which is giving main character energy. Anyway, let's get into it. 🫶

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dlaqtr.f

Yeah, the NAME section is literally just the file path. No cap. 💀

✨ SYNOPSIS ✨

Functions/Subroutines

  • subroutine DLAQTR (ltran, lreal, n, t, ldt, b, w, scale, x, work, info) — DLAQTR solves a real quasi-triangular system of equations, or a complex quasi-triangular system of special form, in real arithmetic.

🫶 Function/Subroutine Documentation 🫶

subroutine DLAQTR (logical ltran, logical lreal, integer n, double
    precision, dimension( ldt, * ) t, integer ldt, double precision,
    dimension( * ) b, double precision w, double precision scale, double
    precision, dimension( * ) x, double precision, dimension( * ) work,
    integer info)

DLAQTR solves a real quasi-triangular system of equations, or a complex quasi-triangular system of special form, in real arithmetic.

🎀 Purpose 🎀

Okay so here's the main character moment: DLAQTR solves the real quasi-triangular system

op(T)*p = scale*c,               if LREAL = .TRUE.

or the complex quasi-triangular systems

op(T + iB)*(p+iq) = scale*(c+id),  if LREAL = .FALSE.

in real arithmetic, where T is upper quasi-triangular. If LREAL = .FALSE., then the first diagonal block of T must be 1 by 1, and B is the specially structured matrix

                B = [ b(1) b(2) ... b(n) ]
                    [       w            ]
                    [           w        ]
                    [              .     ]
                    [                 w  ]

Also: op(A) = A or A**T, and A**T denotes the transpose of matrix A.

On input, X = [ c ].  On output, X = [ p ].
              [ d ]                  [ q ]

This subroutine is designed for the condition number estimation in routine DTRSNA. Obsessed. 💖

💅 Parameters 💅

LTRAN

LTRAN is LOGICAL. On entry, LTRAN specifies the option of conjugate transpose:

= .FALSE.,    op(T+i*B) = T+i*B,
= .TRUE.,     op(T+i*B) = (T+i*B)**T.

LREAL

LREAL is LOGICAL. On entry, LREAL specifies the input matrix structure:

= .FALSE.,    the input is complex
= .TRUE.,     the input is real

N

N is INTEGER. On entry, N specifies the order of T+i*B. N >= 0.

T

T is DOUBLE PRECISION array, dimension (LDT,N). On entry, T contains a matrix in Schur canonical form. If LREAL = .FALSE., then the first diagonal block of T must be 1 by 1. The source says "mu"; it means must. Typo era. 😭

LDT

LDT is INTEGER. The leading dimension of the matrix T. LDT >= max(1,N).

B

B is DOUBLE PRECISION array, dimension (N). On entry, B contains the elements to form the matrix B as described above. If LREAL = .TRUE., B is not referenced.

W

W is DOUBLE PRECISION. On entry, W is the diagonal element of the matrix B. If LREAL = .TRUE., W is not referenced.

SCALE

SCALE is DOUBLE PRECISION. On exit, SCALE is the scale factor.

X

X is DOUBLE PRECISION array, dimension (2*N). On entry, X contains the right hand side of the system. On exit, X is overwritten by the solution.

WORK

WORK is DOUBLE PRECISION array, dimension (N).

INFO

INFO is INTEGER. On exit, INFO is set to:

  • 0: successful exit.
  • 1: some diagonal 1 by 1 block has been perturbed by a small number SMIN to keep nonsingularity.
  • 2: some diagonal 2 by 2 block has been perturbed by a small number in DLALN2 to keep nonsingularity.
NOTE: In the interests of speed, this routine does not check the inputs for errors. 💀 Like, it trusts you. Be trustworthy.

👑 Author 👑

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

Definition at line 163 of file dlaqtr.f.

🌈 Author (generated) 🌈

Generated automatically by Doxygen for LAPACK from the source code.

💖 Cute sign-off: this page is LAPACK Version 3.12.0, and the footer path is /home/abui...RC/dlaqtr.f(3). There's no separate date in the footer, bestie — it's just that path holding it down. Slay. 🎀

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