slag2.f - Man Page

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.

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 threshold 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
          threshold 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.

Definition at line 154 of file slag2.f.