NAME

       slag2.f -

SYNOPSIS

   Functions/Subroutines
       subroutine slag2 (A, LDA, B, LDB, SAFMIN, SCALE1, SCALE2, WR1, WR2, WI)
           SLAG2 computes the eigenvalues of a 2-by-2 generalized eigenvalue problem, with
           scaling as necessary to avoid over-/underflow.

Function/Subroutine Documentation

   subroutine slag2 (real, dimension( lda, * )A, integerLDA, real, dimension( ldb, * )B,
       integerLDB, realSAFMIN, realSCALE1, realSCALE2, realWR1, realWR2, realWI)
       SLAG2 computes the eigenvalues of a 2-by-2 generalized eigenvalue problem, with scaling as
       necessary to avoid over-/underflow.

       Purpose:

            SLAG2 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 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

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

           B

                     B is 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

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

           SAFMIN

                     SAFMIN is 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

                     SCALE1 is 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

                     SCALE2 is 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

                     WR1 is 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

                     WR2 is 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

                     WI is 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.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           September 2012

       Definition at line 156 of file slag2.f.

Author

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