CXML
        	    
LAPACK version 3.0
dlag2(3)

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

SYNTAX
  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, * )

DESCRIPTION
  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 sufficiently
	  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
	  eigenvalues.	WI will always be non-negative.