
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 nonnegative 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 1norm 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 onenorm 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 nonneg
ative.
LAPACK version 3.0 15 June 2000 DLAG2(l) 
