1ZLAGS2(1)           LAPACK auxiliary routine (version 3.2)           ZLAGS2(1)
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NAME

6       ZLAGS2  -  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 ),
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SYNOPSIS

14       SUBROUTINE ZLAGS2( UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU,  CSV,  SNV,
15                          CSQ, SNQ )
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17           LOGICAL        UPPER
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19           DOUBLE         PRECISION A1, A3, B1, B3, CSQ, CSU, CSV
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21           COMPLEX*16     A2, B2, SNQ, SNU, SNV
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PURPOSE

24       ZLAGS2  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.
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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.
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41       A1      (input) DOUBLE PRECISION
42               A2      (input) COMPLEX*16 A3      (input) DOUBLE PRECISION  On
43               entry,  A1,  A2  and  A3 are elements of the input 2-by-2 upper
44               (lower) triangular matrix A.
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46       B1      (input) DOUBLE PRECISION
47               B2      (input) COMPLEX*16 B3      (input) DOUBLE PRECISION  On
48               entry,  B1,  B2  and  B3 are elements of the input 2-by-2 upper
49               (lower) triangular matrix B.
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51       CSU     (output) DOUBLE PRECISION
52               SNU     (output) COMPLEX*16 The desired unitary matrix U.
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54       CSV     (output) DOUBLE PRECISION
55               SNV     (output) COMPLEX*16 The desired unitary matrix V.
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57       CSQ     (output) DOUBLE PRECISION
58               SNQ     (output) COMPLEX*16 The desired unitary matrix Q.
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62 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                       ZLAGS2(1)
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