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 trans
formed 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 trans
formed 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 ele
ments of the input 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 ele
ments of the input 2-by-2 upper (lower) triangular
matrix B.
CSU (output) DOUBLE PRECISION
SNU (output) DOUBLE PRECISION The desired
orthogonal matrix U.
SNV (output) DOUBLE PRECISION The desired
orthogonal matrix V.
CSQ (output) DOUBLE PRECISION
SNQ (output) DOUBLE PRECISION The desired
orthogonal matrix Q.
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