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zlags2.3lapack

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.