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NAME
     slag2 - compute the eigenvalues  of  a  2  x  2  generalized
     eigenvalue  problem A-wB, with scaling as necessary to avoid
     overflow/underflow

SYNOPSIS
     SUBROUTINE SLAG2( A, LDA, B, LDB,  SAFMIN,  SCALE1,  SCALE2,
               WR1, WR2, WI )

     INTEGER LDA, LDB

     REAL SAFMIN, SCALE1, SCALE2, WI, WR1, WR2

     REAL A( LDA, * ), B( LDB, * )



     #include <sunperf.h>

     void slag2(float *sa, int lda, float  *sb,  int  ldb,  float
               safmin,  float *scale1, float *scale2, float *wr1,
               float *wr2, float *wi) ;

PURPOSE
     SLAG2 computes the eigenvalues of a 2 x 2 generalized eigen-
     value  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) REAL 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) REAL 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) REAL
               The smallest positive number  s.t.  1/SAFMIN  does
               not  overflow.  (This should always be SLAMCH('S')
               -- it is an argument in order to avoid  having  to
               call SLAMCH frequently.)

     SCALE1    (output) REAL
               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) REAL
               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) REAL
               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) REAL
               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) REAL
               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.

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