1CLAGS2(1)           LAPACK auxiliary routine (version 3.2)           CLAGS2(1)
2
3
4

NAME

6       CLAGS2  -  computes  2-by-2 unitary matrices U, V and Q, such that if (
7       UPPER ) then   U'*A*Q = U'*( A1 A2 )*Q = ( x 0 )  ( 0 A3 ) ( x x )  and
8       V'*B*Q = V'*( B1 B2 )*Q = ( x 0 )  ( 0 B3 ) ( x x )  or if ( .NOT.UPPER
9       ) then   U'*A*Q = U'*( A1 0 )*Q = ( x x )  ( A2  A3  )  (  0  x  )  and
10       V'*B*Q  =  V'*( B1 0 )*Q = ( x x )  ( B2 B3 ) ( 0 x ) where   U = ( CSU
11       SNU ), V = ( 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         Q = (     CSQ      SNQ )
28             ( -CONJG(SNQ)  CSQ )
29       Z' denotes the conjugate transpose of Z.
30       The rows of the transformed A and B  are  parallel.  Moreover,  if  the
31       input  2-by-2 matrix A is not zero, then the transformed (1,1) entry of
32       A is not zero. If the input matrices A and B are both  not  zero,  then
33       the  transformed  (2,2) element of B is not zero, except when the first
34       rows of input A and B are parallel and the second rows are zero.
35

ARGUMENTS

37       UPPER   (input) LOGICAL
38               = .TRUE.: the input matrices A and B are upper triangular.
39               = .FALSE.: the input matrices A and B are lower triangular.
40
41       A1      (input) REAL
42               A2      (input) COMPLEX A3      (input) REAL On entry,  A1,  A2
43               and  A3 are elements of the input 2-by-2 upper (lower) triangu‐
44               lar matrix A.
45
46       B1      (input) REAL
47               B2      (input) COMPLEX B3      (input) REAL On entry,  B1,  B2
48               and  B3 are elements of the input 2-by-2 upper (lower) triangu‐
49               lar matrix B.
50
51       CSU     (output) REAL
52               SNU     (output) COMPLEX The desired unitary matrix U.
53
54       CSV     (output) REAL
55               SNV     (output) COMPLEX The desired unitary matrix V.
56
57       CSQ     (output) REAL
58               SNQ     (output) COMPLEX The desired unitary matrix Q.
59
60
61
62 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                       CLAGS2(1)
Impressum