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DLAG2(1)	    LAPACK auxiliary routine (version 3.2)	      DLAG2(1)

NAME
       DLAG2  -	 computes  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 prob‐
       lem  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 eigenval‐
	       ue  equation which defines the first eigenvalue.	 If the eigen‐
	       values 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 eigenval‐
	       ue equation which defines the second eigenvalue.	 If the eigen‐
	       values 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 sufficiently large.

       WR1     (output) DOUBLE PRECISION
	       If the eigenvalue is real, then WR1 is SCALE1 times the	eigen‐
	       value closest to the (2,2) element of A B**(-1).	 If the eigen‐
	       value 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
	       eigenvalues.  WI will always be non-negative.

 LAPACK auxiliary routine (versioNovember 2008			      DLAG2(1)
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