1CLAGS2(1)           LAPACK auxiliary routine (version 3.1)           CLAGS2(1)
2
3
4

NAME

6       CLAGS2  -  2-by-2  unitary  matrices U, V and Q, such that if ( UPPER )
7       then   U'*A*Q = U'*( A1 A2 )*Q = ( x 0 )  ( 0 A3 ) ( x x ) and   V'*B*Q
8       = V'*( B1 B2 )*Q = ( x 0 )  ( 0 B3 ) ( x x )  or if ( .NOT.UPPER ) then
9       U'*A*Q = U'*( A1 0 )*Q = ( x x )  ( A2 A3 ) ( 0 x ) and  V'*B*Q =  V'*(
10       B1  0  )*Q  = ( x x )  ( B2 B3 ) ( 0 x ) where   U = ( CSU SNU ), V = (
11       CSV SNV ),
12

SYNOPSIS

14       SUBROUTINE CLAGS2( UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU,  CSV,  SNV,
15                          CSQ, SNQ )
16
17           LOGICAL        UPPER
18
19           REAL           A1, A3, B1, B3, CSQ, CSU, CSV
20
21           COMPLEX        A2, B2, SNQ, SNU, SNV
22

PURPOSE

24       CLAGS2  computes  2-by-2  unitary  matrices  U, V and Q, such that if (
25       UPPER ) then
26             ( -CONJG(SNU)  CSU )      ( -CONJG(SNV) CSV )
27
28         Q = (     CSQ      SNQ )
29             ( -CONJG(SNQ)  CSQ )
30
31       Z' denotes the conjugate transpose of Z.
32
33       The rows of the transformed A and B  are  parallel.  Moreover,  if  the
34       input  2-by-2 matrix A is not zero, then the transformed (1,1) entry of
35       A is not zero. If the input matrices A and B are both  not  zero,  then
36       the  transformed  (2,2) element of B is not zero, except when the first
37       rows of input A and B are parallel and the second rows are zero.
38
39

ARGUMENTS

41       UPPER   (input) LOGICAL
42               = .TRUE.: the input matrices A and B are upper triangular.
43               = .FALSE.: the input matrices A and B are lower triangular.
44
45       A1      (input) REAL
46               A2      (input) COMPLEX A3      (input) REAL On entry,  A1,  A2
47               and  A3 are elements of the input 2-by-2 upper (lower) triangu‐
48               lar matrix A.
49
50       B1      (input) REAL
51               B2      (input) COMPLEX B3      (input) REAL On entry,  B1,  B2
52               and  B3 are elements of the input 2-by-2 upper (lower) triangu‐
53               lar matrix B.
54
55       CSU     (output) REAL
56               SNU     (output) COMPLEX The desired unitary matrix U.
57
58       CSV     (output) REAL
59               SNV     (output) COMPLEX The desired unitary matrix V.
60
61       CSQ     (output) REAL
62               SNQ     (output) COMPLEX The desired unitary matrix Q.
63
64
65
66 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       CLAGS2(1)
Impressum