lower to upper case in ksh

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zlags2

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)

Shell Programming and Scripting