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RedHat 9 (Linux i386) - man page for dlag2 (redhat section l)

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 modi-
       fied 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 over-
       flow 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 fre-
	       quently.)

       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 eigenval-
	       ues 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 eigenval-
	       ues 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 eigenval-
	       ues.

       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-neg-
	       ative.

LAPACK version 3.0			   15 June 2000 				 DLAG2(l)


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