dlags2(3)

NAME

DLAGS2 - compute 2-by-2 orthogonal 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 ) The rows of the transformed A and B are parallel, where

U = ( CSU SNU ), V = ( CSV SNV ), Q = ( CSQ SNQ ) ( -SNU CSU ) (

-SNV CSV ) ( -SNQ CSQ ) Z' denotes the transpose of Z

SYNOPSIS

SUBROUTINE  DLAGS2(  UPPER,  A1,  A2, A3, B1, B2, B3, CSU,
SNU, CSV, SNV, CSQ, SNQ )
    LOGICAL        UPPER
    DOUBLE         PRECISION A1, A2, A3, B1, B2, B3,  CSQ,
CSU, CSV, SNQ, SNU, SNV

PURPOSE

DLAGS2 computes 2-by-2 orthogonal 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

) The rows of the transformed A and B are parallel, where U = (

CSU SNU ), V = ( CSV SNV ), Q = ( CSQ SNQ ) ( -SNU CSU ) ( -SNV

CSV ) ( -SNQ CSQ ) Z' denotes the transpose of Z.

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) DOUBLE PRECISION A3 (input)

DOUBLE PRECISION On entry, A1, A2 and A3 are elements of the in

put 2-by-2 upper (lower) triangular matrix A.

B1 (input) DOUBLE PRECISION

B2 (input) DOUBLE PRECISION B3 (input)

DOUBLE PRECISION On entry, B1, B2 and B3 are elements of the in

put 2-by-2 upper (lower) triangular matrix B.

CSU (output) DOUBLE PRECISION

SNU (output) DOUBLE PRECISION The desired or

thogonal matrix U.

CSV (output) DOUBLE PRECISION

SNV (output) DOUBLE PRECISION The desired or

thogonal matrix V.

CSQ (output) DOUBLE PRECISION

SNQ (output) DOUBLE PRECISION The desired or

thogonal matrix Q.

LAPACK version 3.0 15 June 2000

DLAGS2(3)