zlags2(3)

NAME

ZLAGS2 - compute 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 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 ), ( -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. More

over, if the input 2-by-2 matrix A is not zero, then the trans

formed (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 paral

lel 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.

LAPACK version 3.0 15 June 2000

ZLAGS2(3)