dget23.f - Man Page

subroutine dget23 (comp, balanc, jtype, thresh, iseed, nounit, n, a, lda, h, wr, wi, wr1, wi1, vl, ldvl, vr, ldvr, lre, ldlre, rcondv, rcndv1, rcdvin, rconde, rcnde1, rcdein, scale, scale1, result, work, lwork, iwork, info)
DGET23

DGET23

Purpose:

    DGET23  checks the nonsymmetric eigenvalue problem driver SGEEVX.
    If COMP = .FALSE., the first 8 of the following tests will be
    performed on the input matrix A, and also test 9 if LWORK is
    sufficiently large.
    if COMP is .TRUE. all 11 tests will be performed.

    (1)     | A * VR - VR * W | / ( n |A| ulp )

      Here VR is the matrix of unit right eigenvectors.
      W is a block diagonal matrix, with a 1x1 block for each
      real eigenvalue and a 2x2 block for each complex conjugate
      pair.  If eigenvalues j and j+1 are a complex conjugate pair,
      so WR(j) = WR(j+1) = wr and WI(j) = - WI(j+1) = wi, then the
      2 x 2 block corresponding to the pair will be:

              (  wr  wi  )
              ( -wi  wr  )

      Such a block multiplying an n x 2 matrix  ( ur ui ) on the
      right will be the same as multiplying  ur + i*ui  by  wr + i*wi.

    (2)     | A**H * VL - VL * W**H | / ( n |A| ulp )

      Here VL is the matrix of unit left eigenvectors, A**H is the
      conjugate transpose of A, and W is as above.

    (3)     | |VR(i)| - 1 | / ulp and largest component real

      VR(i) denotes the i-th column of VR.

    (4)     | |VL(i)| - 1 | / ulp and largest component real

      VL(i) denotes the i-th column of VL.

    (5)     0 if W(full) = W(partial), 1/ulp otherwise

      W(full) denotes the eigenvalues computed when VR, VL, RCONDV
      and RCONDE are also computed, and W(partial) denotes the
      eigenvalues computed when only some of VR, VL, RCONDV, and
      RCONDE are computed.

    (6)     0 if VR(full) = VR(partial), 1/ulp otherwise

      VR(full) denotes the right eigenvectors computed when VL, RCONDV
      and RCONDE are computed, and VR(partial) denotes the result
      when only some of VL and RCONDV are computed.

    (7)     0 if VL(full) = VL(partial), 1/ulp otherwise

      VL(full) denotes the left eigenvectors computed when VR, RCONDV
      and RCONDE are computed, and VL(partial) denotes the result
      when only some of VR and RCONDV are computed.

    (8)     0 if SCALE, ILO, IHI, ABNRM (full) =
                 SCALE, ILO, IHI, ABNRM (partial)
            1/ulp otherwise

      SCALE, ILO, IHI and ABNRM describe how the matrix is balanced.
      (full) is when VR, VL, RCONDE and RCONDV are also computed, and
      (partial) is when some are not computed.

    (9)     0 if RCONDV(full) = RCONDV(partial), 1/ulp otherwise

      RCONDV(full) denotes the reciprocal condition numbers of the
      right eigenvectors computed when VR, VL and RCONDE are also
      computed. RCONDV(partial) denotes the reciprocal condition
      numbers when only some of VR, VL and RCONDE are computed.

   (10)     |RCONDV - RCDVIN| / cond(RCONDV)

      RCONDV is the reciprocal right eigenvector condition number
      computed by DGEEVX and RCDVIN (the precomputed true value)
      is supplied as input. cond(RCONDV) is the condition number of
      RCONDV, and takes errors in computing RCONDV into account, so
      that the resulting quantity should be O(ULP). cond(RCONDV) is
      essentially given by norm(A)/RCONDE.

   (11)     |RCONDE - RCDEIN| / cond(RCONDE)

      RCONDE is the reciprocal eigenvalue condition number
      computed by DGEEVX and RCDEIN (the precomputed true value)
      is supplied as input.  cond(RCONDE) is the condition number
      of RCONDE, and takes errors in computing RCONDE into account,
      so that the resulting quantity should be O(ULP). cond(RCONDE)
      is essentially given by norm(A)/RCONDV.

Parameters

COMP

          COMP is LOGICAL
          COMP describes which input tests to perform:
            = .FALSE. if the computed condition numbers are not to
                      be tested against RCDVIN and RCDEIN
            = .TRUE.  if they are to be compared

BALANC

          BALANC is CHARACTER
          Describes the balancing option to be tested.
            = 'N' for no permuting or diagonal scaling
            = 'P' for permuting but no diagonal scaling
            = 'S' for no permuting but diagonal scaling
            = 'B' for permuting and diagonal scaling

JTYPE

          JTYPE is INTEGER
          Type of input matrix. Used to label output if error occurs.

THRESH

          THRESH is DOUBLE PRECISION
          A test will count as 'failed' if the 'error', computed as
          described above, exceeds THRESH.  Note that the error
          is scaled to be O(1), so THRESH should be a reasonably
          small multiple of 1, e.g., 10 or 100.  In particular,
          it should not depend on the precision (single vs. double)
          or the size of the matrix.  It must be at least zero.

ISEED

          ISEED is INTEGER array, dimension (4)
          If COMP = .FALSE., the random number generator seed
          used to produce matrix.
          If COMP = .TRUE., ISEED(1) = the number of the example.
          Used to label output if error occurs.

NOUNIT

          NOUNIT is INTEGER
          The FORTRAN unit number for printing out error messages
          (e.g., if a routine returns INFO not equal to 0.)

N

          N is INTEGER
          The dimension of A. N must be at least 0.

A

          A is DOUBLE PRECISION array, dimension (LDA,N)
          Used to hold the matrix whose eigenvalues are to be
          computed.

LDA

          LDA is INTEGER
          The leading dimension of A, and H. LDA must be at
          least 1 and at least N.

H

          H is DOUBLE PRECISION array, dimension (LDA,N)
          Another copy of the test matrix A, modified by DGEEVX.

WR

          WR is DOUBLE PRECISION array, dimension (N)

WI

          WI is DOUBLE PRECISION array, dimension (N)

          The real and imaginary parts of the eigenvalues of A.
          On exit, WR + WI*i are the eigenvalues of the matrix in A.

WR1

          WR1 is DOUBLE PRECISION array, dimension (N)

WI1

          WI1 is DOUBLE PRECISION array, dimension (N)

          Like WR, WI, these arrays contain the eigenvalues of A,
          but those computed when DGEEVX only computes a partial
          eigendecomposition, i.e. not the eigenvalues and left
          and right eigenvectors.

VL

          VL is DOUBLE PRECISION array, dimension (LDVL,N)
          VL holds the computed left eigenvectors.

LDVL

          LDVL is INTEGER
          Leading dimension of VL. Must be at least max(1,N).

VR

          VR is DOUBLE PRECISION array, dimension (LDVR,N)
          VR holds the computed right eigenvectors.

LDVR

          LDVR is INTEGER
          Leading dimension of VR. Must be at least max(1,N).

LRE

          LRE is DOUBLE PRECISION array, dimension (LDLRE,N)
          LRE holds the computed right or left eigenvectors.

LDLRE

          LDLRE is INTEGER
          Leading dimension of LRE. Must be at least max(1,N).

RCONDV

          RCONDV is DOUBLE PRECISION array, dimension (N)
          RCONDV holds the computed reciprocal condition numbers
          for eigenvectors.

RCNDV1

          RCNDV1 is DOUBLE PRECISION array, dimension (N)
          RCNDV1 holds more computed reciprocal condition numbers
          for eigenvectors.

RCDVIN

          RCDVIN is DOUBLE PRECISION array, dimension (N)
          When COMP = .TRUE. RCDVIN holds the precomputed reciprocal
          condition numbers for eigenvectors to be compared with
          RCONDV.

RCONDE

          RCONDE is DOUBLE PRECISION array, dimension (N)
          RCONDE holds the computed reciprocal condition numbers
          for eigenvalues.

RCNDE1

          RCNDE1 is DOUBLE PRECISION array, dimension (N)
          RCNDE1 holds more computed reciprocal condition numbers
          for eigenvalues.

RCDEIN

          RCDEIN is DOUBLE PRECISION array, dimension (N)
          When COMP = .TRUE. RCDEIN holds the precomputed reciprocal
          condition numbers for eigenvalues to be compared with
          RCONDE.

SCALE

          SCALE is DOUBLE PRECISION array, dimension (N)
          Holds information describing balancing of matrix.

SCALE1

          SCALE1 is DOUBLE PRECISION array, dimension (N)
          Holds information describing balancing of matrix.

RESULT

          RESULT is DOUBLE PRECISION array, dimension (11)
          The values computed by the 11 tests described above.
          The values are currently limited to 1/ulp, to avoid
          overflow.

WORK

          WORK is DOUBLE PRECISION array, dimension (LWORK)

LWORK

          LWORK is INTEGER
          The number of entries in WORK.  This must be at least
          3*N, and 6*N+N**2 if tests 9, 10 or 11 are to be performed.

IWORK

          IWORK is INTEGER array, dimension (2*N)

INFO

          INFO is INTEGER
          If 0,  successful exit.
          If <0, input parameter -INFO had an incorrect value.
          If >0, DGEEVX returned an error code, the absolute
                 value of which is returned.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 373 of file dget23.f.