clags2(3)

NAME

CLAGS2 - 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  CLAGS2(  UPPER,  A1,  A2, A3, B1, B2, B3, CSU,
SNU, CSV, SNV, CSQ, SNQ )
    LOGICAL        UPPER
    REAL           A1, A3, B1, B3, CSQ, CSU, CSV
    COMPLEX        A2, B2, SNQ, SNU, SNV

PURPOSE

CLAGS2 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) REAL

A2 (input) COMPLEX A3 (input) REAL On

entry, A1, A2 and A3 are elements of the input 2-by-2 upper (low

er) triangular matrix A.

B1 (input) REAL

B2 (input) COMPLEX B3 (input) REAL On

entry, B1, B2 and B3 are elements of the input 2-by-2 upper (low

er) triangular matrix B.

CSU (output) REAL

SNU (output) COMPLEX The desired unitary ma

trix U.

CSV (output) REAL

SNV (output) COMPLEX The desired unitary ma

trix V.

CSQ (output) REAL

SNQ (output) COMPLEX The desired unitary ma

trix Q.

LAPACK version 3.0 15 June 2000

CLAGS2(3)