DLAGS2(l) ) DLAGS2(l)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 trans‐
pose 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 PRECI‐
SION 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) DOUBLE PRECISION B3 (input) DOUBLE PRECI‐
SION 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) DOUBLE PRECISION The desired orthogonal matrix
U.
CSV (output) DOUBLE PRECISION
SNV (output) DOUBLE PRECISION The desired orthogonal matrix
V.
CSQ (output) DOUBLE PRECISION
SNQ (output) DOUBLE PRECISION The desired orthogonal matrix
Q.
LAPACK version 3.0 15 June 2000 DLAGS2(l)
