---
name: "zlags2"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/zlags2/3lapack"
---

# zlags2(3lapack)

computes 2-by-2 unitary matrices U, V and Q, such that if ( UPPER ) then U'\*A\*Q = U'\*( A1 A2 )\*Q = ( x 0 ) ( 0 A3 ) ( x x ) and V'\*B\*Q = V'\*( B1 B2 )\*Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then U'\*A\*Q = U'\*( A1 0 )\*Q = ( x x ) ( A2 A3 ) ( 0 x ) and V'\*B\*Q = V'\*( B1 0 )\*Q = ( x x ) ( B2 B3 ) ( 0 x ) where U = ( CSU SNU ), V = ( CSV SNV ),

## NAME

ZLAGS2 - computes 2-by-2 unitary matrices U, V and Q, such that if ( UPPER ) then   U'\*A\*Q = U'\*( A1 A2 )\*Q = ( x 0 )  ( 0 A3 ) ( x x ) and  V'\*B\*Q = V'\*( B1 B2 )\*Q = ( x 0 )  ( 0 B3 ) ( x x )  or if ( .NOT.UPPER ) then   U'\*A\*Q = U'\*( A1 0 )\*Q = ( x x )  ( A2 A3 ) ( 0 x ) and  V'\*B\*Q = V'\*( B1 0 )\*Q = ( x x )  ( B2 B3 ) ( 0 x ) where   U = ( CSU SNU ), V = ( CSV SNV ),

## SYNOPSIS

- SUBROUTINE ZLAGS2(

  UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV, SNV, CSQ, SNQ )

- LOGICAL

  UPPER

- DOUBLE

  PRECISION A1, A3, B1, B3, CSQ, CSU, CSV

- COMPLEX\*16

  A2, B2, SNQ, SNU, SNV

## PURPOSE

ZLAGS2 computes 2-by-2 unitary matrices U, V and Q, such that if ( UPPER ) then\
       ( -CONJG(SNU)  CSU )      ( -CONJG(SNV) CSV )\
\
   Q = (     CSQ      SNQ )\
\
       ( -CONJG(SNQ)  CSQ )\
 Z' denotes the conjugate transpose of Z.\
 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.\

## ARGUMENTS

- UPPER (input) LOGICAL

  \= .TRUE.: the input matrices A and B are upper triangular.\
   \= .FALSE.: the input matrices A and B are lower triangular.

- A1 (input) DOUBLE PRECISION

  A2      (input) COMPLEX\*16 A3      (input) DOUBLE PRECISION On entry, A1, A2 and A3 are elements of the input 2-by-2 upper (lower) triangular matrix A.

- B1 (input) DOUBLE PRECISION

  B2      (input) COMPLEX\*16 B3      (input) DOUBLE PRECISION On entry, B1, B2 and B3 are elements of the input 2-by-2 upper (lower) triangular matrix B.

- CSU (output) DOUBLE PRECISION

  SNU     (output) COMPLEX\*16 The desired unitary matrix U.

- CSV (output) DOUBLE PRECISION

  SNV     (output) COMPLEX\*16 The desired unitary matrix V.

- CSQ (output) DOUBLE PRECISION

  SNQ     (output) COMPLEX\*16 The desired unitary matrix Q.