zlags2.f - Man Page

subroutine zlags2 (upper, a1, a2, a3, b1, b2, b3, csu, snu, csv, snv, csq, snq)
ZLAGS2

ZLAGS2  

Purpose:

 ZLAGS2 computes 2-by-2 unitary matrices U, V and Q, such
 that if ( UPPER ) then

           U**H *A*Q = U**H *( A1 A2 )*Q = ( x  0  )
                             ( 0  A3 )     ( x  x  )
 and
           V**H*B*Q = V**H *( B1 B2 )*Q = ( x  0  )
                            ( 0  B3 )     ( x  x  )

 or if ( .NOT.UPPER ) then

           U**H *A*Q = U**H *( A1 0  )*Q = ( x  x  )
                             ( A2 A3 )     ( 0  x  )
 and
           V**H *B*Q = V**H *( B1 0  )*Q = ( x  x  )
                             ( B2 B3 )     ( 0  x  )
 where

   U = (   CSU    SNU ), V = (  CSV    SNV ),
       ( -SNU**H  CSU )      ( -SNV**H CSV )

   Q = (   CSQ    SNQ )
       ( -SNQ**H  CSQ )

 The rows of the transformed A and B are parallel. Moreover, if the
 input 2-by-2 matrix A is not zero, then the transformed (1,1) entry
 of A is not zero. If the input matrices A and B are both not zero,
 then the transformed (2,2) element of B is not zero, except when the
 first rows of input A and B are parallel and the second rows are
 zero.

Parameters

UPPER

          UPPER is LOGICAL
          = .TRUE.: the input matrices A and B are upper triangular.
          = .FALSE.: the input matrices A and B are lower triangular.

A1

          A1 is DOUBLE PRECISION

A2

          A2 is COMPLEX*16

A3

          A3 is DOUBLE PRECISION
          On entry, A1, A2 and A3 are elements of the input 2-by-2
          upper (lower) triangular matrix A.

B1

          B1 is DOUBLE PRECISION

B2

          B2 is COMPLEX*16

B3

          B3 is DOUBLE PRECISION
          On entry, B1, B2 and B3 are elements of the input 2-by-2
          upper (lower) triangular matrix B.

CSU

          CSU is DOUBLE PRECISION

SNU

          SNU is COMPLEX*16
          The desired unitary matrix U.

CSV

          CSV is DOUBLE PRECISION

SNV

          SNV is COMPLEX*16
          The desired unitary matrix V.

CSQ

          CSQ is DOUBLE PRECISION

SNQ

          SNQ is COMPLEX*16
          The desired unitary matrix Q.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 156 of file zlags2.f.