SRC/slags2.f(3)

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version 3.12.1 · 4 versions
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💅 SRC/slags2.f(3) 💅

okay bestie, welcome to the manual page for SRC/slags2.f from the Library Functions Manual. It's giving LAPACK, it's giving orthogonal matrices, and it's honestly iconic. 💖

🌸 NAME 🌸

SRC/slags2.f

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

subroutine slags2 (upper, a1, a2, a3, b1, b2, b3, csu, snu, csv, snv,
    csq, snq)

SLAGS2 computes 2-by-2 orthogonal matrices U, V, and Q, and applies them to matrices A and B so the rows of the transformed A and B are parallel. 🦋

🛠️ Function/Subroutine Documentation 🛠️

💫 subroutine slags2 💫

subroutine slags2 (logical upper, real a1, real a2, real a3, real b1, real
    b2, real b3, real csu, real snu, real csv, real snv, real csq, real snq)

SLAGS2 computes 2-by-2 orthogonal matrices U, V, and Q, and applies them to matrices A and B such that the rows of the transformed A and B are parallel. (Yes bestie, that's the whole point, and it ate. 💅)

🎯 Purpose 🎯

okay so here's the exact vibe math — copy it, don't touch it:

!>
!> SLAGS2 computes 2-by-2 orthogonal matrices U, V and Q, such
!> that if ( UPPER ) then
!>
!>           U**T *A*Q = U**T *( A1 A2 )*Q = ( x  0  )
!>                             ( 0  A3 )     ( x  x  )
!> and
!>           V**T*B*Q = V**T *( B1 B2 )*Q = ( x  0  )
!>                            ( 0  B3 )     ( x  x  )
!>
!> or if ( .NOT.UPPER ) then
!>
!>           U**T *A*Q = U**T *( A1 0  )*Q = ( x  x  )
!>                             ( A2 A3 )     ( 0  x  )
!> and
!>           V**T*B*Q = V**T*( B1 0  )*Q = ( x  x  )
!>                           ( B2 B3 )     ( 0  x  )
!>
!> The rows of the transformed A and B are parallel, where
!>
!>   U = (  CSU  SNU ), V = (  CSV SNV ), Q = (  CSQ   SNQ )
!>       ( -SNU  CSU )      ( -SNV CSV )      ( -SNQ   CSQ )
!>
!> Z**T denotes the transpose of Z.
!>
!>

So yeah: the rows of the transformed A and B end up parallel, and Z**T denotes the transpose of Z. No cap. 🌈

🌸 Parameters 🌸

  • UPPER — UPPER is LOGICAL. = .TRUE. means the input matrices A and B are upper triangular; = .FALSE. means they're lower triangular. 🦋
  • A1 — A1 is REAL
  • A2 — A2 is REAL
  • A3 — A3 is REAL. On entry, A1, A2 and A3 are elements of the input 2-by-2 upper (lower) triangular matrix A.
  • B1 — B1 is REAL
  • B2 — B2 is REAL
  • B3 — B3 is REAL. On entry, B1, B2 and B3 are elements of the input 2-by-2 upper (lower) triangular matrix B.
  • CSU — CSU is REAL
  • SNU — SNU is REAL. The desired orthogonal matrix U. 💜
  • CSV — CSV is REAL
  • SNV — SNV is REAL. The desired orthogonal matrix V. 💜
  • CSQ — CSQ is REAL
  • SNQ — SNQ is REAL. The desired orthogonal matrix Q. 💜

💖 Author 💖

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

Definition at line 150 of file slags2.f.

👑 Author 👑

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That's the whole page, bestie 💖. Footer sign-off: LAPACK, Version 3.12.0, source SRC/slags2.f(3). There's no date in the footer, so I'm not inventing one — periodt. 🎀

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