NAME

       slags2.f -

SYNOPSIS

   Functions/Subroutines
       subroutine slags2 (UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV, SNV, CSQ, SNQ)
           SLAGS2 computes 2-by-2 orthogonal matrices U, V, and Q, and applies them to matrices A
           and B such that the rows of the transformed A and B are parallel.

Function/Subroutine Documentation

   subroutine slags2 (logical UPPER, real A1, real A2, real A3, real B1, real B2, real B3, real
       CSU, real SNU, real CSV, real SNV, real CSQ, real SNQ)
       SLAGS2 computes 2-by-2 orthogonal matrices U, V, and Q, and applies them to matrices A and
       B such that the rows of the transformed A and B are parallel.

       Purpose:

            SLAGS2 computes 2-by-2 orthogonal matrices U, V and Q, such
            that if ( UPPER ) then

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

            or if ( .NOT.UPPER ) then

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

            The rows of the transformed A and B are parallel, where

              U = (  CSU  SNU ), V = (  CSV SNV ), Q = (  CSQ   SNQ )
                  ( -SNU  CSU )      ( -SNV CSV )      ( -SNQ   CSQ )

            Z**T denotes the transpose of Z.

       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 REAL

           A2

                     A2 is REAL

           A3

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

           B1

                     B1 is REAL

           B2

                     B2 is REAL

           B3

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

           CSU

                     CSU is REAL

           SNU

                     SNU is REAL
                     The desired orthogonal matrix U.

           CSV

                     CSV is REAL

           SNV

                     SNV is REAL
                     The desired orthogonal matrix V.

           CSQ

                     CSQ is REAL

           SNQ

                     SNQ is REAL
                     The desired orthogonal matrix Q.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           September 2012

Author

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