zlags2(3) [debian man page]

zlags2.f(3)							      LAPACK							       zlags2.f(3)

NAME

       zlags2.f -

SYNOPSIS

   Functions/Subroutines
       subroutine zlags2 (UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV, SNV, CSQ, SNQ)
	   ZLAGS2

Function/Subroutine Documentation
   subroutine zlags2 (logicalUPPER, double precisionA1, complex*16A2, double precisionA3, double precisionB1, complex*16B2, double precisionB3,
       double precisionCSU, complex*16SNU, double precisionCSV, complex*16SNV, double precisionCSQ, complex*16SNQ)
       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.

       Date:
	   November 2011

       Definition at line 158 of file zlags2.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.1							  Sun May 26 2013						       zlags2.f(3)

Check Out this Related Man Page

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)

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