dlag2.f(3)

NAME
dlag2.f -

SYNOPSIS

  Functions/Subroutines

subroutine dlag2 (A, LDA, B, LDB, SAFMIN, SCALE1, SCALE2, WR1, WR2, WI)
DLAG2 computes the eigenvalues of a 2-by-2 generalized eigenvalue problem, with scaling as necessary to avoid over-/underflow.

Function/Subroutine Documentation

  subroutine dlag2 (double precision, dimension( lda, * )A, integerLDA, double precision, dimension( ldb, * )B, integerLDB, double precisionSAFMIN, double precisionSCALE1, double precisionSCALE2, double precisionWR1, double precisionWR2, double precisionWI)

DLAG2 computes the eigenvalues of a 2-by-2 generalized eigenvalue problem, with scaling as necessary to avoid over-/underflow.

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 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 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 frequently.)

    SCALE1

              SCALE1 is 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 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 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

              WR1 is 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

              WR2 is 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 eigenvalues.

    WI

              WI is 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 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 dlag2.f.

Author

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