CLAGS2(3)

🎀 CLAGS2(3) — Library Functions Manual 🎀

okay bestie, welcome to the CLAGS2(3) page from the Library Functions Manual 💖 this one lives at /home/abui...RC/clags2.f(3) and it’s all about a Fortran subroutine doing very cute 2-by-2 unitary matrix transformations. no cap, it’s giving linear algebra main character energy. ✨

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/clags2.f — that’s the whole path, bestie, not me being dramatic. 🫶

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

subroutine CLAGS2 (upper, a1, a2, a3, b1, b2, b3, csu, snu, csv, snv,
    csq, snq)

CLAGS2 — yes, that’s the icon herself. 💅

🌈 Function/Subroutine Documentation 🌈

subroutine CLAGS2 (logical upper, real a1, complex a2, real a3, real b1,
    complex b2, real b3, real csu, complex snu, real csv, complex snv, real
    csq, complex snq)

CLAGS2 — again, but with all the types spelled out. slay. 👑

💖 Purpose 💖

okay so CLAGS2 computes 2-by-2 unitary matrices U, V and Q, such that if UPPER is true, then:

U**H *A*Q = U**H *( A1 A2 )*Q = ( x  0  )
                  ( 0  A3 )     ( x  x  )
and
V**H*B*Q = V**H *( B1 B2 )*Q = ( x  0  )
                 ( 0  B3 )     ( x  x  )

or if .NOT.UPPER then:

U**H *A*Q = U**H *( A1 0  )*Q = ( x  x  )
                  ( A2 A3 )     ( 0  x  )
and
V**H *B*Q = V**H *( B1 0  )*Q = ( x  x  )
                  ( B2 B3 )     ( 0  x  )

where:

U = (   CSU    SNU ), V = (  CSV    SNV ),
    ( -SNU**H  CSU )      ( -SNV**H CSV )

Q = (   CSQ    SNQ )
    ( -SNQ**H  CSQ )

the rows of the transformed A and B are parallel. moreover, if the input 2-by-2 matrix A is not zero, then the transformed (1,1) entry of A is not zero. if the input matrices A and B are both not zero, then the transformed (2,2) element of B is not zero, except when the first rows of input A and B are parallel and the second rows are zero. that’s the whole vibe check, and yes, that exception is important. 😭

🧚 Parameters 🧚

• UPPER — UPPER is LOGICAL; = .TRUE. means the input matrices A and B are upper triangular; = .FALSE. means the input matrices A and B are lower triangular. 💅
• A1 — A1 is REAL.
• A2 — A2 is COMPLEX.
• 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 COMPLEX.
• 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 COMPLEX; the desired unitary matrix U. 👑
• CSV — CSV is REAL.
• SNV — SNV is COMPLEX; the desired unitary matrix V. 💜
• CSQ — CSQ is REAL.
• SNQ — SNQ is COMPLEX; the desired unitary matrix Q. 🎀

👑 AUTHOR 👑

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

definition at line 156 of file clags2.f. 📌

🧚 AUTHOR (auto-generated) 🧚

generated automatically by Doxygen for LAPACK from the source code. no thoughts, just Doxygen doing its thing. 💀

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okay that’s the whole CLAGS2(3) saga, bestie. this page is from LAPACK, Version 3.12.0, and the footer path is /home/abui...RC/clags2.f(3). now go forth and slay those unitary matrices. 💖✨🎀