SRC/slaqtr.f(3)

💖 SLAQTR — real quasi-triangular systems, but make it group-chat 💖

okay bestie, this is the manual page for SRC/slaqtr.f(3) from the Library Functions Manual — and yes, it's giving linear algebra with main character energy 💅

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🌸 NAME 🌸

SRC/slaqtr.f — literally the file, no cap 💖

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🎀 SYNOPSIS 🎀

🧚 Functions/Subroutines 🧚

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

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💅 Function/Subroutine Documentation 💅

🌟 subroutine slaqtr 🌟

subroutine slaqtr (logical ltran, logical lreal, integer n, real, dimension(
ldt, * ) t, integer ldt, real, dimension( * ) b, real w, real scale,
real, dimension( * ) x, real, dimension( * ) work, integer info)

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

🦋 Purpose 🦋

SLAQTR 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, B is the specially structured matrix

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

op(A) = A or A**T, 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 STRSNA.

💖 Parameters 💖

• LTRAN — 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 — LOGICAL. On entry, LREAL specifies the input matrix structure:
  • = .FALSE., the input is complex
  • = .TRUE., the input is real
• N — INTEGER. On entry, N specifies the order of T+i*B. N >= 0.
• T — REAL 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.
• LDT — INTEGER. The leading dimension of the matrix T. LDT >= max(1,N).
• B — REAL 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 — REAL. On entry, W is the diagonal element of the matrix B. If LREAL = .TRUE., W is not referenced.
• SCALE — REAL. On exit, SCALE is the scale factor.
• X — REAL array, dimension (2*N). On entry, X contains the right hand side of the system. On exit, X is overwritten by the solution.
• WORK — REAL array, dimension (N).
• INFO — INTEGER. On exit, INFO is set to:
  • 0: successful exit.
  • 1: the some diagonal 1 by 1 block has been perturbed by a small number SMIN to keep nonsingularity.
  • 2: the some diagonal 2 by 2 block has been perturbed by a small number in SLALN2 to keep nonsingularity.

NOTE: In the interests of speed, this routine does not check the inputs for errors. bestie, that's a real note — don't come for me 😭

🌟 Author 🌟

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

Definition at line 163 of file slaqtr.f.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole page, bestie — LAPACK Version 3.12.0, manual name SRC/slaqtr.f(3), and yes this is the cute sign-off 💖🫶