SRC/zlags2.f(3)

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version 3.12.1 · 7 versions
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🎀 NAME 🎀

Bestie, this page is from the Library Functions Manual and it's all about SRC/zlags2.f — yes, that's the name, and we're keeping it exactly like that 💅.

✨ SYNOPSIS ✨

🧚 Functions/Subroutines

  • subroutine zlags2 (upper, a1, a2, a3, b1, b2, b3, csu, snu, csv, snv, csq, snq)
    • ZLAGS2

🦋 Function/Subroutine Documentation 🦋

subroutine zlags2 (logical upper, double precision a1, complex*16 a2, double
    precision a3, double precision b1, complex*16 b2, double precision b3,
    double precision csu, complex*16 snu, double precision csv, complex*16
    snv, double precision csq, complex*16 snq)

ZLAGS2 — okay so this is the subroutine, and it is highkey iconic 👑.

Purpose:

ZLAGS2 computes 2-by-2 unitary matrices U, V and Q, such that if ( UPPER ) 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. No cap, that's literally the deal 🔥.

🌸 Parameters 🌸

  • UPPER — UPPER is LOGICAL.
    • = .TRUE.: the input matrices A and B are upper triangular.
    • = .FALSE.: the input matrices A and B are lower triangular.
  • A1 — A1 is DOUBLE PRECISION.
  • A2 — A2 is COMPLEX*16.
  • A3 — A3 is DOUBLE PRECISION.
    • On entry, A1, A2 and A3 are elements of the input 2-by-2 upper (lower) triangular matrix A.
  • B1 — B1 is DOUBLE PRECISION.
  • B2 — B2 is COMPLEX*16.
  • B3 — B3 is DOUBLE PRECISION.
    • On entry, B1, B2 and B3 are elements of the input 2-by-2 upper (lower) triangular matrix B.
  • CSU — CSU is DOUBLE PRECISION.
  • SNU — SNU is COMPLEX*16.
    • The desired unitary matrix U.
  • CSV — CSV is DOUBLE PRECISION.
  • SNV — SNV is COMPLEX*16.
    • The desired unitary matrix V.
  • CSQ — CSQ is DOUBLE PRECISION.
  • SNQ — SNQ is COMPLEX*16.
    • 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 zlags2.f.

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code.

Cute sign-off bestie: this page is LAPACK Version 3.12.0, SRC/zlags2.f(3) — go slay those 2-by-2 unitaries, periodt 💅✨🦋

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