Loading...
Searching...
No Matches

## dlag2()

subroutine dlag2 | ( | double precision, dimension( lda, * ) | a,
|  | integer | lda,
|  | double precision, dimension( ldb, * ) | b,
|  | integer | ldb,
|  | double precision | safmin,
|  | double precision | scale1,
|  | double precision | scale2,
|  | double precision | wr1,
|  | double precision | wr2,
|  | double precision | wi )

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

Download DLAG2 + dependencies [TGZ] [ZIP] [TXT]

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  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

  [in]

  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.
      !>

  [in]

  LDA

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

  [in]

  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.
      !>

  [in]

  LDB

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

  [in]

  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.)
      !>

  [out]

  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 threshold if the exact eigenvalue
      !>          is sufficiently large.
      !>

  [out]

  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
      !>          threshold if the exact eigenvalue is sufficiently large.
      !>

  [out]

  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.
      !>

  [out]

  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.
      !>

  [out]

  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.