DLAG2(l)								 )								  DLAG2(l)

NAME

       DLAG2 - compute the eigenvalues of a 2 x 2 generalized eigenvalue problem A - w B, with scaling as necessary to avoid over-/underflow

SYNOPSIS

       SUBROUTINE DLAG2( A, LDA, B, LDB, SAFMIN, SCALE1, SCALE2, WR1, WR2, WI )

	   INTEGER	 LDA, LDB

	   DOUBLE	 PRECISION SAFMIN, SCALE1, SCALE2, WI, WR1, WR2

	   DOUBLE	 PRECISION A( LDA, * ), B( LDB, * )

PURPOSE

       DLAG2  computes the eigenvalues of a 2 x 2 generalized eigenvalue problem A - w B, with scaling as necessary to avoid over-/underflow.  The
       scaling factor "s" results in a modified eigenvalue equation

	   s A - w B

       where  s  is a non-negative scaling factor chosen so that  w,  w B, and	s A  do not overflow and, if possible, do not underflow, either.

ARGUMENTS

       A       (input) DOUBLE PRECISION array, dimension (LDA, 2)
	       On entry, the 2 x 2 matrix A.  It is assumed that its 1-norm is less than 1/SAFMIN.  Entries  less  than  sqrt(SAFMIN)*norm(A)  are
	       subject to being treated as zero.

       LDA     (input) INTEGER
	       The leading dimension of the array A.  LDA >= 2.

       B       (input) DOUBLE PRECISION array, dimension (LDB, 2)
	       On  entry,  the 2 x 2 upper triangular matrix B.  It is assumed that the one-norm of B is less than 1/SAFMIN.  The diagonals should
	       be at least sqrt(SAFMIN) times the largest element of B (in absolute value);  if  a  diagonal  is  smaller  than  that,	then   +/-
	       sqrt(SAFMIN) will be used instead of that diagonal.

       LDB     (input) INTEGER
	       The leading dimension of the array B.  LDB >= 2.

       SAFMIN  (input) DOUBLE PRECISION
	       The  smallest positive number s.t. 1/SAFMIN does not overflow.  (This should always be DLAMCH('S') -- it is an argument in order to
	       avoid having to call DLAMCH frequently.)

       SCALE1  (output) DOUBLE PRECISION
	       A scaling factor used to avoid over-/underflow in the eigenvalue equation which defines the first eigenvalue.  If  the  eigenvalues
	       are  complex,  then  the  eigenvalues  are  ( WR1  +/-  WI i ) / SCALE1	(which may lie outside the exponent range of the machine),
	       SCALE1=SCALE2, and SCALE1 will always be positive.  If the eigenvalues are real, then the first (real) eigenvalue is  WR1 /  SCALE1
	       , but this may overflow or underflow, and in fact, SCALE1 may be zero or less than the underflow threshhold if the exact eigenvalue
	       is sufficiently large.

       SCALE2  (output) DOUBLE PRECISION
	       A scaling factor used to avoid over-/underflow in the eigenvalue equation which defines the second eigenvalue.  If the  eigenvalues
	       are  complex,  then  SCALE2=SCALE1.   If the eigenvalues are real, then the second (real) eigenvalue is WR2 / SCALE2 , but this may
	       overflow or underflow, and in fact, SCALE2 may be zero or less than the underflow threshhold if	the  exact  eigenvalue	is  suffi-
	       ciently large.

       WR1     (output) DOUBLE PRECISION
	       If the eigenvalue is real, then WR1 is SCALE1 times the eigenvalue closest to the (2,2) element of A B**(-1).  If the eigenvalue is
	       complex, then WR1=WR2 is SCALE1 times the real part of the eigenvalues.

       WR2     (output) DOUBLE PRECISION
	       If the eigenvalue is real, then WR2 is SCALE2 times the other eigenvalue.  If the eigenvalue is complex,  then  WR1=WR2	is  SCALE1
	       times the real part of the eigenvalues.

       WI      (output) DOUBLE PRECISION
	       If the eigenvalue is real, then WI is zero.  If the eigenvalue is complex, then WI is SCALE1 times the imaginary part of the eigen-
	       values.	WI will always be non-negative.

LAPACK version 3.0						   15 June 2000 							  DLAG2(l)