SLAGS2 - 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 SLAGS2( UPPER, A1, A2, A3, B1, B2, B3, CSU,
SNU, CSV, SNV, CSQ, SNQ )
LOGICAL UPPER
REAL A1, A2, A3, B1, B2, B3, CSQ, CSU, CSV,
SNQ, SNU, SNV
PURPOSE
SLAGS2 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) REAL
A2 (input) REAL A3 (input) REAL On
entry, A1, A2 and A3 are elements of the input
2-by-2 upper (lower) triangular matrix A.
B1 (input) REAL
B2 (input) REAL B3 (input) REAL On
entry, B1, B2 and B3 are elements of the input
2-by-2 upper (lower) triangular matrix B.
CSU (output) REAL
SNU (output) REAL The desired orthogonal
matrix U.
SNV (output) REAL The desired orthogonal
matrix V.
CSQ (output) REAL
SNQ (output) REAL The desired orthogonal
matrix Q.
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