DLAGV2(3)

💖 DLAGV2(3) — LAPACK Library Functions Manual 💖

okay bestie, this page is DLAGV2(3) from the LAPACK Library Functions Manual. The source file is /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dlagv2.f — yes, the whole path, no cap. 🫶

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dlagv2.f

✨ SYNOPSIS ✨

Functions/Subroutines:

subroutine DLAGV2 (a, lda, b, ldb, alphar, alphai, beta, csl, snl, csr,
    snr)
    DLAGV2 computes the Generalized Schur factorization of a real 2-by-2
    matrix pencil (A,B) where B is upper triangular.

🛠️ Function/Subroutine Documentation 🛠️

subroutine DLAGV2 (double precision, dimension( lda, * ) a, integer lda,
    double precision, dimension( ldb, * ) b, integer ldb, double precision,
    dimension( 2 ) alphar, double precision, dimension( 2 ) alphai, double
    precision, dimension( 2 ) beta, double precision csl, double precision
    snl, double precision csr, double precision snr)

DLAGV2 computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular. 💅

🎯 Purpose 🎯

So the actual glow-up here: DLAGV2 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 DOUBLE PRECISION 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.
• B — B is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (2).
• ALPHAI — ALPHAI is DOUBLE PRECISION array, dimension (2).
• BETA — BETA is DOUBLE PRECISION 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.
• CSL — CSL is DOUBLE PRECISION. The cosine of the left rotation matrix.
• SNL — SNL is DOUBLE PRECISION. The sine of the left rotation matrix.
• CSR — CSR is DOUBLE PRECISION. The cosine of the right rotation matrix.
• SNR — SNR is DOUBLE PRECISION. 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 dlagv2.f.

📝 Author 📝

Generated automatically by Doxygen for LAPACK from the source code.

---

💖 that’s the whole page, bestie. Source/version sign-off: LAPACK Version 3.12.0, /home/abui...RC/dlagv2.f(3). slay. 💖