dlags2(l) [redhat man page]

DLAGS2(l)								 )								 DLAGS2(l)

NAME

       DLAGS2 - compute 2-by-2 orthogonal matrices U, V and Q, such that if ( UPPER ) then  U'*A*Q = U'*( A1 A2 )*Q = ( x 0 ) ( 0 A3 ) ( x x ) and
       V'*B*Q = V'*( B1 B2 )*Q = ( x 0 ) ( 0 B3 ) ( x x )  or if ( .NOT.UPPER ) then  U'*A*Q = U'*( A1 0 )*Q = ( x x ) ( A2 A3	)  (  0  x  )  and
       V'*B*Q = V'*( 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' denotes the transpose of Z

SYNOPSIS

       SUBROUTINE DLAGS2( UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV, SNV, CSQ, SNQ )

	   LOGICAL	  UPPER

	   DOUBLE	  PRECISION A1, A2, A3, B1, B2, B3, CSQ, CSU, CSV, SNQ, SNU, SNV

PURPOSE

       DLAGS2 computes 2-by-2 orthogonal matrices U, V and Q, such that if ( UPPER ) then U'*A*Q = U'*( A1 A2 )*Q = ( x 0 ) ( 0 A3 ) ( x x  )  and
       V'*B*Q  = V'*( B1 B2 )*Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then U'*A*Q = U'*( A1 0 )*Q = ( x x ) ( A2 A3 ) ( 0 x ) and V'*B*Q
       = V'*( 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' denotes the transpose of Z.

ARGUMENTS

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

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

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

       CSU     (output) DOUBLE PRECISION
	       SNU     (output) DOUBLE PRECISION The desired orthogonal matrix U.

       CSV     (output) DOUBLE PRECISION
	       SNV     (output) DOUBLE PRECISION The desired orthogonal matrix V.

       CSQ     (output) DOUBLE PRECISION
	       SNQ     (output) DOUBLE PRECISION The desired orthogonal matrix Q.

LAPACK version 3.0						   15 June 2000 							 DLAGS2(l)

ZLAGS2(l)								 )								 ZLAGS2(l)

NAME

       ZLAGS2  -  compute  2-by-2 unitary matrices U, V and Q, such that if ( UPPER ) then  U'*A*Q = U'*( A1 A2 )*Q = ( x 0 ) ( 0 A3 ) ( x x ) and
       V'*B*Q = V'*( B1 B2 )*Q = ( x 0 ) ( 0 B3 ) ( x x )  or if ( .NOT.UPPER ) then  U'*A*Q = U'*( A1 0 )*Q = ( x x ) ( A2 A3	)  (  0  x  )  and
       V'*B*Q = V'*( B1 0 )*Q = ( x x ) ( B2 B3 ) ( 0 x ) where  U = ( CSU SNU ), V = ( CSV SNV ),

SYNOPSIS

       SUBROUTINE ZLAGS2( UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV, SNV, CSQ, SNQ )

	   LOGICAL	  UPPER

	   DOUBLE	  PRECISION A1, A3, B1, B3, CSQ, CSU, CSV

	   COMPLEX*16	  A2, B2, SNQ, SNU, SNV

PURPOSE

       ZLAGS2  computes  2-by-2  unitary  matrices  U, V and Q, such that if ( UPPER ) then U'*A*Q = U'*( A1 A2 )*Q = ( x 0 ) ( 0 A3 ) ( x x ) and
       V'*B*Q = V'*( B1 B2 )*Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then U'*A*Q = U'*( A1 0 )*Q = ( x x ) ( A2 A3 ) ( 0 x ) and  V'*B*Q
       = V'*( B1 0 )*Q = ( x x ) ( B2 B3 ) ( 0 x ) where U = ( CSU SNU ), V = ( CSV SNV ),	 ( -CONJG(SNU)	CSU )	   ( -CONJG(SNV) CSV )

	 Q = (	   CSQ	    SNQ )
	     ( -CONJG(SNQ)  CSQ )

       Z' denotes the conjugate transpose of Z.

       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.

ARGUMENTS

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

       A1      (input) DOUBLE PRECISION
	       A2	(input) COMPLEX*16 A3	   (input) DOUBLE PRECISION On entry, A1, A2 and A3 are elements of the input 2-by-2 upper (lower)
	       triangular matrix A.

       B1      (input) DOUBLE PRECISION
	       B2      (input) COMPLEX*16 B3	  (input) DOUBLE PRECISION On entry, B1, B2 and B3 are elements of the input 2-by-2 upper  (lower)
	       triangular matrix B.

       CSU     (output) DOUBLE PRECISION
	       SNU     (output) COMPLEX*16 The desired unitary matrix U.

       CSV     (output) DOUBLE PRECISION
	       SNV     (output) COMPLEX*16 The desired unitary matrix V.

       CSQ     (output) DOUBLE PRECISION
	       SNQ     (output) COMPLEX*16 The desired unitary matrix Q.

LAPACK version 3.0						   15 June 2000 							 ZLAGS2(l)