Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3  -  computes  the  eigenvalues of a 2 x 2 generalized eigenvalue problem A - w B,
       with scaling as necessary to avoid over-/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, * )

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.

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.

 LAPACK auxiliary routine (version 3.2)     April 2011                             SLAG2(3lapack)