laqtr(3)

📦
version 3.12.1 · 9 versions
, in arch rolling

💅 laqtr — from the Library Functions Manual ✨

ok so bestie, pull up a chair, because this one is a LAPACK classic and it's honestly kind of iconic 🎀. it lives in the Library Functions Manual, and it's the kind of page you read at 2am while your matrix is being weird. no cap.

🌸 NAME 🌸

laqtr — laqtr: quasi-triangular solve 🦋

like, it solves a quasi-triangular system. that's the whole vibe. periodt.

✨ SYNOPSIS ✨

🎀 Functions 🎀

  • 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. 💖
  • 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. 💖

(they're literally the same girl in two outfits, one is double precision, one is real. iykyk.)

🔥 Detailed Description 🔥

so there's a Function Documentation section down here, and honestly it's giving main character energy. two whole routines, fully documented, no crumbs left. let's get into it 🌈

💜 Function Documentation 💜

🫶 subroutine dlaqtr 🫶

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. slay ✨

⭐ Purpose ⭐

DLAQTR solves the real quasi-triangular system op(T)p = scalec, 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 AT, AT 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.

like, look at that little staircase matrix B. she's structured. she's special. we love her 💅

🎀 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. (zero is valid, bestie, don't come for her)
  • 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 mu be 1 by 1. (yes the original says "mu", we don't edit, we respect the canon 🙈)
  • 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. (she's literally not even invited to that party 💀)
  • 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. she changes outfits mid-scene, iconic 🦋
  • WORK — WORK is DOUBLE PRECISION array, dimension (N).
  • INFO — INFO is 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 DLALN2 to keep nonsingularity.
⚠️ NOTE: In the interests of speed, this routine does not check the inputs for errors. fr fr, she trusts you completely. do NOT make her regret that 😭

👑 Author 👑

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 163 of file dlaqtr.f.

🫶 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. ate and left no crumbs ✨

⭐ Purpose ⭐

SLAQTR solves the real quasi-triangular system op(T)p = scalec, 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 AT, AT 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.

same energy, single precision edition. she's the little sister and she is ALSO that girl 🌸

🎀 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 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. (she spells it right, ok, we're not comparing them)
  • LDT — LDT is INTEGER. The leading dimension of the matrix T. LDT >= max(1,N).
  • B — B is 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 — W is REAL. On entry, W is the diagonal element of the matrix B. If LREAL = .TRUE., W is not referenced.
  • SCALE — SCALE is REAL. On exit, SCALE is the scale factor.
  • X — X is 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 — WORK is REAL array, dimension (N).
  • INFO — INFO is 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. same disclaimer, same trust issues, same speed demon energy 🔥

👑 Author 👑

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 163 of file slaqtr.f.

💖 Author 💖

Generated automatically by Doxygen for LAPACK from the source code.

🧚 and that's the whole page bestie. you now know more about quasi-triangular solves than like 99% of the group chat. go forth and estimate condition numbers responsibly 💜

LAPACK · Version 3.12.0 · laqtr(3) 🎀 mwah, that's the sign-off, love u, bye 🫶

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