TESTING/EIG/dget23.f(3)

NAME
TESTING/EIG/dget23.f

SYNOPSIS

  Functions/Subroutines
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

Function/Subroutine Documentation

  subroutine dget23 (logical comp, character balanc, integer jtype, double precision thresh, integer, dimension( 4 ) iseed, integer nounit, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( lda, * ) h, double precision, dimension( * ) wr, double precision, dimension( * ) wi, double precision, dimension( * ) wr1, double precision, dimension( * ) wi1, double precision, dimension( ldvl, * ) vl, integer ldvl, double precision, dimension( ldvr, * ) vr, integer ldvr, double precision, dimension( ldlre, * ) lre, integer ldlre, double precision, dimension( * ) rcondv, double precision, dimension( * ) rcndv1, double precision, dimension( * ) rcdvin, double precision, dimension( * ) rconde, double precision, dimension( * ) rcnde1, double precision, dimension( * ) rcdein, double precision, dimension( * ) scale, double precision, dimension( * ) scale1, double precision, dimension( 11 ) result, double precision, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer info)

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.

Author

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