SRC/slagv2.f(3)

💖 NAME 💖

okay bestie, this is SRC/slagv2.f from the Library Functions Manual — the name of the page, the moment, the whole vibe. 💅✨

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

subroutine slagv2 (a, lda, b, ldb, alphar, alphai, beta, csl, snl, csr,
    snr)

SLAGV2 computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular. No cap. 🫶

🎀 Function/Subroutine Documentation 🎀

🌸 subroutine slagv2 🌸

subroutine slagv2 (real, dimension( lda, * ) a, integer lda, real,
    dimension( ldb, * ) b, integer ldb, real, dimension( 2 ) alphar, real,
    dimension( 2 ) alphai, real, dimension( 2 ) beta, real csl, real snl,
    real csr, real snr)

SLAGV2 computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular. literally iconic.

💫 Purpose

!>
!> SLAGV2 computes the Generalized Schur factorization of a real 2-by-2
!> matrix pencil (A,B) where B is upper triangular. This routine
!> computes orthogonal (rotation) matrices given by CSL, SNL and CSR,
!> SNR such that
!>
!> 1) if the pencil (A,B) has two real eigenvalues (include 0/0 or 1/0
!>    types), then
!>
!>    [ a11 a12 ] := [  CSL  SNL ] [ a11 a12 ] [  CSR -SNR ]
!>    [  0  a22 ]    [ -SNL  CSL ] [ a21 a22 ] [  SNR  CSR ]
!>
!>    [ b11 b12 ] := [  CSL  SNL ] [ b11 b12 ] [  CSR -SNR ]
!>    [  0  b22 ]    [ -SNL  CSL ] [  0  b22 ] [  SNR  CSR ],
!>
!> 2) if the pencil (A,B) has a pair of complex conjugate eigenvalues,
!>    then
!>
!>    [ a11 a12 ] := [  CSL  SNL ] [ a11 a12 ] [  CSR -SNR ]
!>    [ a21 a22 ]    [ -SNL  CSL ] [ a21 a22 ] [  SNR  CSR ]
!>
!>    [ b11  0  ] := [  CSL  SNL ] [ b11 b12 ] [  CSR -SNR ]
!>    [  0  b22 ]    [ -SNL  CSL ] [  0  b22 ] [  SNR  CSR ]
!>
!>    where b11 >= b22 > 0.
!>
!>

🧚 Parameters

• A — A is REAL array, dimension (LDA, 2). On entry, the 2 x 2 matrix A. On exit, A is overwritten by the “A-part” of the generalized Schur form. 🦋
• LDA — LDA is INTEGER. THe leading dimension of the array A. LDA >= 2. yes, the source really spells it “THe” — we respect the lore.
• B — B is REAL array, dimension (LDB, 2). On entry, the upper triangular 2 x 2 matrix B. On exit, B is overwritten by the “B-part” of the generalized Schur form. 🌸
• LDB — LDB is INTEGER. THe leading dimension of the array B. LDB >= 2.
• ALPHAR — ALPHAR is REAL array, dimension (2).
• ALPHAI — ALPHAI is REAL array, dimension (2).
• BETA — BETA is REAL array, dimension (2). (ALPHAR(k)+i*ALPHAI(k))/BETA(k) are the eigenvalues of the pencil (A,B), k=1,2, i = sqrt(-1). Note that BETA(k) may be zero. important little detail, bestie.
• CSL — CSL is REAL. The cosine of the left rotation matrix.
• SNL — SNL is REAL. The sine of the left rotation matrix.
• CSR — CSR is REAL. The cosine of the right rotation matrix.
• SNR — SNR is REAL. The sine of the right rotation matrix.

👑 Author

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

🌟 Contributors

Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA.

Definition at line 155 of file slagv2.f.

🌸 Author 🌸

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole page, bestie — this was LAPACK Version 3.12.0, source page SRC/slagv2.f(3). Go forth and slay those 2-by-2 pencils. 💅✨