dlag2.f(3)							      LAPACK								dlag2.f(3)

NAME

       dlag2.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dlag2 (A, LDA, B, LDB, SAFMIN, SCALE1, SCALE2, WR1, WR2, WI)
	   DLAG2 computes the eigenvalues of a 2-by-2 generalized eigenvalue problem, with scaling as necessary to avoid over-/underflow.

Function/Subroutine Documentation
   subroutine dlag2 (double precision, dimension( lda, * )A, integerLDA, double precision, dimension( ldb, * )B, integerLDB, double
       precisionSAFMIN, double precisionSCALE1, double precisionSCALE2, double precisionWR1, double precisionWR2, double precisionWI)
       DLAG2 computes the eigenvalues of a 2-by-2 generalized eigenvalue problem, with scaling as necessary to avoid over-/underflow.

       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.

       Parameters:
	   A

		     A is 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

		     LDA is INTEGER
		     The leading dimension of the array A.  LDA >= 2.

	   B

		     B is 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

		     LDB is INTEGER
		     The leading dimension of the array B.  LDB >= 2.

	   SAFMIN

		     SAFMIN is 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

		     SCALE1 is 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

		     SCALE2 is 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

		     WR1 is 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

		     WR2 is 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

		     WI is 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.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   September 2012

       Definition at line 156 of file dlag2.f.

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

Version 3.4.2							  Tue Sep 25 2012							dlag2.f(3)