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  if the , 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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