testdata/lapack/TESTING/EIG/zdrvvx.f
*> \brief \b ZDRVVX
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZDRVVX( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NIUNIT, NOUNIT, A, LDA, H, W, W1, VL, LDVL, VR,
* LDVR, LRE, LDLRE, RCONDV, RCNDV1, RCDVIN,
* RCONDE, RCNDE1, RCDEIN, SCALE, SCALE1, RESULT,
* WORK, NWORK, RWORK, INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, LDA, LDLRE, LDVL, LDVR, NIUNIT, NOUNIT,
* $ NSIZES, NTYPES, NWORK
* DOUBLE PRECISION THRESH
* ..
* .. Array Arguments ..
* LOGICAL DOTYPE( * )
* INTEGER ISEED( 4 ), NN( * )
* DOUBLE PRECISION RCDEIN( * ), RCDVIN( * ), RCNDE1( * ),
* $ RCNDV1( * ), RCONDE( * ), RCONDV( * ),
* $ RESULT( 11 ), RWORK( * ), SCALE( * ),
* $ SCALE1( * )
* COMPLEX*16 A( LDA, * ), H( LDA, * ), LRE( LDLRE, * ),
* $ VL( LDVL, * ), VR( LDVR, * ), W( * ), W1( * ),
* $ WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZDRVVX checks the nonsymmetric eigenvalue problem expert driver
*> ZGEEVX.
*>
*> ZDRVVX uses both test matrices generated randomly depending on
*> data supplied in the calling sequence, as well as on data
*> read from an input file and including precomputed condition
*> numbers to which it compares the ones it computes.
*>
*> When ZDRVVX is called, a number of matrix "sizes" ("n's") and a
*> number of matrix "types" are specified in the calling sequence.
*> For each size ("n") and each type of matrix, one matrix will be
*> generated and used to test the nonsymmetric eigenroutines. For
*> each matrix, 9 tests will be performed:
*>
*> (1) | A * VR - VR * W | / ( n |A| ulp )
*>
*> Here VR is the matrix of unit right eigenvectors.
*> W is a diagonal matrix with diagonal entries W(j).
*>
*> (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) W(full) = W(partial)
*>
*> 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) VR(full) = VR(partial)
*>
*> 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) VL(full) = VL(partial)
*>
*> 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) RCONDV(full) = RCONDV(partial)
*>
*> 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.
*>
*> The "sizes" are specified by an array NN(1:NSIZES); the value of
*> each element NN(j) specifies one size.
*> The "types" are specified by a logical array DOTYPE( 1:NTYPES );
*> if DOTYPE(j) is .TRUE., then matrix type "j" will be generated.
*> Currently, the list of possible types is:
*>
*> (1) The zero matrix.
*> (2) The identity matrix.
*> (3) A (transposed) Jordan block, with 1's on the diagonal.
*>
*> (4) A diagonal matrix with evenly spaced entries
*> 1, ..., ULP and random complex angles.
*> (ULP = (first number larger than 1) - 1 )
*> (5) A diagonal matrix with geometrically spaced entries
*> 1, ..., ULP and random complex angles.
*> (6) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP
*> and random complex angles.
*>
*> (7) Same as (4), but multiplied by a constant near
*> the overflow threshold
*> (8) Same as (4), but multiplied by a constant near
*> the underflow threshold
*>
*> (9) A matrix of the form U' T U, where U is unitary and
*> T has evenly spaced entries 1, ..., ULP with random complex
*> angles on the diagonal and random O(1) entries in the upper
*> triangle.
*>
*> (10) A matrix of the form U' T U, where U is unitary and
*> T has geometrically spaced entries 1, ..., ULP with random
*> complex angles on the diagonal and random O(1) entries in
*> the upper triangle.
*>
*> (11) A matrix of the form U' T U, where U is unitary and
*> T has "clustered" entries 1, ULP,..., ULP with random
*> complex angles on the diagonal and random O(1) entries in
*> the upper triangle.
*>
*> (12) A matrix of the form U' T U, where U is unitary and
*> T has complex eigenvalues randomly chosen from
*> ULP < |z| < 1 and random O(1) entries in the upper
*> triangle.
*>
*> (13) A matrix of the form X' T X, where X has condition
*> SQRT( ULP ) and T has evenly spaced entries 1, ..., ULP
*> with random complex angles on the diagonal and random O(1)
*> entries in the upper triangle.
*>
*> (14) A matrix of the form X' T X, where X has condition
*> SQRT( ULP ) and T has geometrically spaced entries
*> 1, ..., ULP with random complex angles on the diagonal
*> and random O(1) entries in the upper triangle.
*>
*> (15) A matrix of the form X' T X, where X has condition
*> SQRT( ULP ) and T has "clustered" entries 1, ULP,..., ULP
*> with random complex angles on the diagonal and random O(1)
*> entries in the upper triangle.
*>
*> (16) A matrix of the form X' T X, where X has condition
*> SQRT( ULP ) and T has complex eigenvalues randomly chosen
*> from ULP < |z| < 1 and random O(1) entries in the upper
*> triangle.
*>
*> (17) Same as (16), but multiplied by a constant
*> near the overflow threshold
*> (18) Same as (16), but multiplied by a constant
*> near the underflow threshold
*>
*> (19) Nonsymmetric matrix with random entries chosen from |z| < 1
*> If N is at least 4, all entries in first two rows and last
*> row, and first column and last two columns are zero.
*> (20) Same as (19), but multiplied by a constant
*> near the overflow threshold
*> (21) Same as (19), but multiplied by a constant
*> near the underflow threshold
*>
*> In addition, an input file will be read from logical unit number
*> NIUNIT. The file contains matrices along with precomputed
*> eigenvalues and reciprocal condition numbers for the eigenvalues
*> and right eigenvectors. For these matrices, in addition to tests
*> (1) to (9) we will compute the following two tests:
*>
*> (10) |RCONDV - RCDVIN| / cond(RCONDV)
*>
*> RCONDV is the reciprocal right eigenvector condition number
*> computed by ZGEEVX 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 ZGEEVX 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.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> NSIZES is INTEGER
*> The number of sizes of matrices to use. NSIZES must be at
*> least zero. If it is zero, no randomly generated matrices
*> are tested, but any test matrices read from NIUNIT will be
*> tested.
*> \endverbatim
*>
*> \param[in] NN
*> \verbatim
*> NN is INTEGER array, dimension (NSIZES)
*> An array containing the sizes to be used for the matrices.
*> Zero values will be skipped. The values must be at least
*> zero.
*> \endverbatim
*>
*> \param[in] NTYPES
*> \verbatim
*> NTYPES is INTEGER
*> The number of elements in DOTYPE. NTYPES must be at least
*> zero. If it is zero, no randomly generated test matrices
*> are tested, but and test matrices read from NIUNIT will be
*> tested. If it is MAXTYP+1 and NSIZES is 1, then an
*> additional type, MAXTYP+1 is defined, which is to use
*> whatever matrix is in A. This is only useful if
*> DOTYPE(1:MAXTYP) is .FALSE. and DOTYPE(MAXTYP+1) is .TRUE. .
*> \endverbatim
*>
*> \param[in] DOTYPE
*> \verbatim
*> DOTYPE is LOGICAL array, dimension (NTYPES)
*> If DOTYPE(j) is .TRUE., then for each size in NN a
*> matrix of that size and of type j will be generated.
*> If NTYPES is smaller than the maximum number of types
*> defined (PARAMETER MAXTYP), then types NTYPES+1 through
*> MAXTYP will not be generated. If NTYPES is larger
*> than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
*> will be ignored.
*> \endverbatim
*>
*> \param[in,out] ISEED
*> \verbatim
*> ISEED is INTEGER array, dimension (4)
*> On entry ISEED specifies the seed of the random number
*> generator. The array elements should be between 0 and 4095;
*> if not they will be reduced mod 4096. Also, ISEED(4) must
*> be odd. The random number generator uses a linear
*> congruential sequence limited to small integers, and so
*> should produce machine independent random numbers. The
*> values of ISEED are changed on exit, and can be used in the
*> next call to ZDRVVX to continue the same random number
*> sequence.
*> \endverbatim
*>
*> \param[in] THRESH
*> \verbatim
*> 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.
*> \endverbatim
*>
*> \param[in] NIUNIT
*> \verbatim
*> NIUNIT is INTEGER
*> The FORTRAN unit number for reading in the data file of
*> problems to solve.
*> \endverbatim
*>
*> \param[in] NOUNIT
*> \verbatim
*> NOUNIT is INTEGER
*> The FORTRAN unit number for printing out error messages
*> (e.g., if a routine returns INFO not equal to 0.)
*> \endverbatim
*>
*> \param[out] A
*> \verbatim
*> A is COMPLEX*16 array, dimension (LDA, max(NN,12))
*> Used to hold the matrix whose eigenvalues are to be
*> computed. On exit, A contains the last matrix actually used.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of A, and H. LDA must be at
*> least 1 and at least max( NN, 12 ). (12 is the
*> dimension of the largest matrix on the precomputed
*> input file.)
*> \endverbatim
*>
*> \param[out] H
*> \verbatim
*> H is COMPLEX*16 array, dimension (LDA, max(NN,12))
*> Another copy of the test matrix A, modified by ZGEEVX.
*> \endverbatim
*>
*> \param[out] W
*> \verbatim
*> W is COMPLEX*16 array, dimension (max(NN,12))
*> Contains the eigenvalues of A.
*> \endverbatim
*>
*> \param[out] W1
*> \verbatim
*> W1 is COMPLEX*16 array, dimension (max(NN,12))
*> Like W, this array contains the eigenvalues of A,
*> but those computed when ZGEEVX only computes a partial
*> eigendecomposition, i.e. not the eigenvalues and left
*> and right eigenvectors.
*> \endverbatim
*>
*> \param[out] VL
*> \verbatim
*> VL is COMPLEX*16 array, dimension (LDVL, max(NN,12))
*> VL holds the computed left eigenvectors.
*> \endverbatim
*>
*> \param[in] LDVL
*> \verbatim
*> LDVL is INTEGER
*> Leading dimension of VL. Must be at least max(1,max(NN,12)).
*> \endverbatim
*>
*> \param[out] VR
*> \verbatim
*> VR is COMPLEX*16 array, dimension (LDVR, max(NN,12))
*> VR holds the computed right eigenvectors.
*> \endverbatim
*>
*> \param[in] LDVR
*> \verbatim
*> LDVR is INTEGER
*> Leading dimension of VR. Must be at least max(1,max(NN,12)).
*> \endverbatim
*>
*> \param[out] LRE
*> \verbatim
*> LRE is COMPLEX*16 array, dimension (LDLRE, max(NN,12))
*> LRE holds the computed right or left eigenvectors.
*> \endverbatim
*>
*> \param[in] LDLRE
*> \verbatim
*> LDLRE is INTEGER
*> Leading dimension of LRE. Must be at least max(1,max(NN,12))
*> \endverbatim
*>
*> \param[out] RCONDV
*> \verbatim
*> RCONDV is DOUBLE PRECISION array, dimension (N)
*> RCONDV holds the computed reciprocal condition numbers
*> for eigenvectors.
*> \endverbatim
*>
*> \param[out] RCNDV1
*> \verbatim
*> RCNDV1 is DOUBLE PRECISION array, dimension (N)
*> RCNDV1 holds more computed reciprocal condition numbers
*> for eigenvectors.
*> \endverbatim
*>
*> \param[in] RCDVIN
*> \verbatim
*> RCDVIN is DOUBLE PRECISION array, dimension (N)
*> When COMP = .TRUE. RCDVIN holds the precomputed reciprocal
*> condition numbers for eigenvectors to be compared with
*> RCONDV.
*> \endverbatim
*>
*> \param[out] RCONDE
*> \verbatim
*> RCONDE is DOUBLE PRECISION array, dimension (N)
*> RCONDE holds the computed reciprocal condition numbers
*> for eigenvalues.
*> \endverbatim
*>
*> \param[out] RCNDE1
*> \verbatim
*> RCNDE1 is DOUBLE PRECISION array, dimension (N)
*> RCNDE1 holds more computed reciprocal condition numbers
*> for eigenvalues.
*> \endverbatim
*>
*> \param[in] RCDEIN
*> \verbatim
*> RCDEIN is DOUBLE PRECISION array, dimension (N)
*> When COMP = .TRUE. RCDEIN holds the precomputed reciprocal
*> condition numbers for eigenvalues to be compared with
*> RCONDE.
*> \endverbatim
*>
*> \param[out] SCALE
*> \verbatim
*> SCALE is DOUBLE PRECISION array, dimension (N)
*> Holds information describing balancing of matrix.
*> \endverbatim
*>
*> \param[out] SCALE1
*> \verbatim
*> SCALE1 is DOUBLE PRECISION array, dimension (N)
*> Holds information describing balancing of matrix.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX*16 array, dimension (NWORK)
*> \endverbatim
*>
*> \param[out] RESULT
*> \verbatim
*> RESULT is DOUBLE PRECISION array, dimension (11)
*> The values computed by the seven tests described above.
*> The values are currently limited to 1/ulp, to avoid
*> overflow.
*> \endverbatim
*>
*> \param[in] NWORK
*> \verbatim
*> NWORK is INTEGER
*> The number of entries in WORK. This must be at least
*> max(6*12+2*12**2,6*NN(j)+2*NN(j)**2) =
*> max( 360 ,6*NN(j)+2*NN(j)**2) for all j.
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is DOUBLE PRECISION array, dimension (2*max(NN,12))
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> If 0, then successful exit.
*> If <0, then input parameter -INFO is incorrect.
*> If >0, ZLATMR, CLATMS, CLATME or ZGET23 returned an error
*> code, and INFO is its absolute value.
*>
*>-----------------------------------------------------------------------
*>
*> Some Local Variables and Parameters:
*> ---- ----- --------- --- ----------
*>
*> ZERO, ONE Real 0 and 1.
*> MAXTYP The number of types defined.
*> NMAX Largest value in NN or 12.
*> NERRS The number of tests which have exceeded THRESH
*> COND, CONDS,
*> IMODE Values to be passed to the matrix generators.
*> ANORM Norm of A; passed to matrix generators.
*>
*> OVFL, UNFL Overflow and underflow thresholds.
*> ULP, ULPINV Finest relative precision and its inverse.
*> RTULP, RTULPI Square roots of the previous 4 values.
*>
*> The following four arrays decode JTYPE:
*> KTYPE(j) The general type (1-10) for type "j".
*> KMODE(j) The MODE value to be passed to the matrix
*> generator for type "j".
*> KMAGN(j) The order of magnitude ( O(1),
*> O(overflow^(1/2) ), O(underflow^(1/2) )
*> KCONDS(j) Selectw whether CONDS is to be 1 or
*> 1/sqrt(ulp). (0 means irrelevant.)
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date June 2016
*
*> \ingroup complex16_eig
*
* =====================================================================
SUBROUTINE ZDRVVX( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
$ NIUNIT, NOUNIT, A, LDA, H, W, W1, VL, LDVL, VR,
$ LDVR, LRE, LDLRE, RCONDV, RCNDV1, RCDVIN,
$ RCONDE, RCNDE1, RCDEIN, SCALE, SCALE1, RESULT,
$ WORK, NWORK, RWORK, INFO )
*
* -- LAPACK test routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* June 2016
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, LDLRE, LDVL, LDVR, NIUNIT, NOUNIT,
$ NSIZES, NTYPES, NWORK
DOUBLE PRECISION THRESH
* ..
* .. Array Arguments ..
LOGICAL DOTYPE( * )
INTEGER ISEED( 4 ), NN( * )
DOUBLE PRECISION RCDEIN( * ), RCDVIN( * ), RCNDE1( * ),
$ RCNDV1( * ), RCONDE( * ), RCONDV( * ),
$ RESULT( 11 ), RWORK( * ), SCALE( * ),
$ SCALE1( * )
COMPLEX*16 A( LDA, * ), H( LDA, * ), LRE( LDLRE, * ),
$ VL( LDVL, * ), VR( LDVR, * ), W( * ), W1( * ),
$ WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
COMPLEX*16 CZERO
PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ) )
COMPLEX*16 CONE
PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) )
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
INTEGER MAXTYP
PARAMETER ( MAXTYP = 21 )
* ..
* .. Local Scalars ..
LOGICAL BADNN
CHARACTER BALANC
CHARACTER*3 PATH
INTEGER I, IBAL, IINFO, IMODE, ISRT, ITYPE, IWK, J,
$ JCOL, JSIZE, JTYPE, MTYPES, N, NERRS, NFAIL,
$ NMAX, NNWORK, NTEST, NTESTF, NTESTT
DOUBLE PRECISION ANORM, COND, CONDS, OVFL, RTULP, RTULPI, ULP,
$ ULPINV, UNFL, WI, WR
* ..
* .. Local Arrays ..
CHARACTER BAL( 4 )
INTEGER IDUMMA( 1 ), IOLDSD( 4 ), KCONDS( MAXTYP ),
$ KMAGN( MAXTYP ), KMODE( MAXTYP ),
$ KTYPE( MAXTYP )
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH
EXTERNAL DLAMCH
* ..
* .. External Subroutines ..
EXTERNAL DLABAD, DLASUM, XERBLA, ZGET23, ZLASET, ZLATME,
$ ZLATMR, ZLATMS
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DCMPLX, MAX, MIN, SQRT
* ..
* .. Data statements ..
DATA KTYPE / 1, 2, 3, 5*4, 4*6, 6*6, 3*9 /
DATA KMAGN / 3*1, 1, 1, 1, 2, 3, 4*1, 1, 1, 1, 1, 2,
$ 3, 1, 2, 3 /
DATA KMODE / 3*0, 4, 3, 1, 4, 4, 4, 3, 1, 5, 4, 3,
$ 1, 5, 5, 5, 4, 3, 1 /
DATA KCONDS / 3*0, 5*0, 4*1, 6*2, 3*0 /
DATA BAL / 'N', 'P', 'S', 'B' /
* ..
* .. Executable Statements ..
*
PATH( 1: 1 ) = 'Zomplex precision'
PATH( 2: 3 ) = 'VX'
*
* Check for errors
*
NTESTT = 0
NTESTF = 0
INFO = 0
*
* Important constants
*
BADNN = .FALSE.
*
* 7 is the largest dimension in the input file of precomputed
* problems
*
NMAX = 7
DO 10 J = 1, NSIZES
NMAX = MAX( NMAX, NN( J ) )
IF( NN( J ).LT.0 )
$ BADNN = .TRUE.
10 CONTINUE
*
* Check for errors
*
IF( NSIZES.LT.0 ) THEN
INFO = -1
ELSE IF( BADNN ) THEN
INFO = -2
ELSE IF( NTYPES.LT.0 ) THEN
INFO = -3
ELSE IF( THRESH.LT.ZERO ) THEN
INFO = -6
ELSE IF( LDA.LT.1 .OR. LDA.LT.NMAX ) THEN
INFO = -10
ELSE IF( LDVL.LT.1 .OR. LDVL.LT.NMAX ) THEN
INFO = -15
ELSE IF( LDVR.LT.1 .OR. LDVR.LT.NMAX ) THEN
INFO = -17
ELSE IF( LDLRE.LT.1 .OR. LDLRE.LT.NMAX ) THEN
INFO = -19
ELSE IF( 6*NMAX+2*NMAX**2.GT.NWORK ) THEN
INFO = -30
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZDRVVX', -INFO )
RETURN
END IF
*
* If nothing to do check on NIUNIT
*
IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 )
$ GO TO 160
*
* More Important constants
*
UNFL = DLAMCH( 'Safe minimum' )
OVFL = ONE / UNFL
CALL DLABAD( UNFL, OVFL )
ULP = DLAMCH( 'Precision' )
ULPINV = ONE / ULP
RTULP = SQRT( ULP )
RTULPI = ONE / RTULP
*
* Loop over sizes, types
*
NERRS = 0
*
DO 150 JSIZE = 1, NSIZES
N = NN( JSIZE )
IF( NSIZES.NE.1 ) THEN
MTYPES = MIN( MAXTYP, NTYPES )
ELSE
MTYPES = MIN( MAXTYP+1, NTYPES )
END IF
*
DO 140 JTYPE = 1, MTYPES
IF( .NOT.DOTYPE( JTYPE ) )
$ GO TO 140
*
* Save ISEED in case of an error.
*
DO 20 J = 1, 4
IOLDSD( J ) = ISEED( J )
20 CONTINUE
*
* Compute "A"
*
* Control parameters:
*
* KMAGN KCONDS KMODE KTYPE
* =1 O(1) 1 clustered 1 zero
* =2 large large clustered 2 identity
* =3 small exponential Jordan
* =4 arithmetic diagonal, (w/ eigenvalues)
* =5 random log symmetric, w/ eigenvalues
* =6 random general, w/ eigenvalues
* =7 random diagonal
* =8 random symmetric
* =9 random general
* =10 random triangular
*
IF( MTYPES.GT.MAXTYP )
$ GO TO 90
*
ITYPE = KTYPE( JTYPE )
IMODE = KMODE( JTYPE )
*
* Compute norm
*
GO TO ( 30, 40, 50 )KMAGN( JTYPE )
*
30 CONTINUE
ANORM = ONE
GO TO 60
*
40 CONTINUE
ANORM = OVFL*ULP
GO TO 60
*
50 CONTINUE
ANORM = UNFL*ULPINV
GO TO 60
*
60 CONTINUE
*
CALL ZLASET( 'Full', LDA, N, CZERO, CZERO, A, LDA )
IINFO = 0
COND = ULPINV
*
* Special Matrices -- Identity & Jordan block
*
* Zero
*
IF( ITYPE.EQ.1 ) THEN
IINFO = 0
*
ELSE IF( ITYPE.EQ.2 ) THEN
*
* Identity
*
DO 70 JCOL = 1, N
A( JCOL, JCOL ) = ANORM
70 CONTINUE
*
ELSE IF( ITYPE.EQ.3 ) THEN
*
* Jordan Block
*
DO 80 JCOL = 1, N
A( JCOL, JCOL ) = ANORM
IF( JCOL.GT.1 )
$ A( JCOL, JCOL-1 ) = ONE
80 CONTINUE
*
ELSE IF( ITYPE.EQ.4 ) THEN
*
* Diagonal Matrix, [Eigen]values Specified
*
CALL ZLATMS( N, N, 'S', ISEED, 'H', RWORK, IMODE, COND,
$ ANORM, 0, 0, 'N', A, LDA, WORK( N+1 ),
$ IINFO )
*
ELSE IF( ITYPE.EQ.5 ) THEN
*
* Symmetric, eigenvalues specified
*
CALL ZLATMS( N, N, 'S', ISEED, 'H', RWORK, IMODE, COND,
$ ANORM, N, N, 'N', A, LDA, WORK( N+1 ),
$ IINFO )
*
ELSE IF( ITYPE.EQ.6 ) THEN
*
* General, eigenvalues specified
*
IF( KCONDS( JTYPE ).EQ.1 ) THEN
CONDS = ONE
ELSE IF( KCONDS( JTYPE ).EQ.2 ) THEN
CONDS = RTULPI
ELSE
CONDS = ZERO
END IF
*
CALL ZLATME( N, 'D', ISEED, WORK, IMODE, COND, CONE,
$ 'T', 'T', 'T', RWORK, 4, CONDS, N, N, ANORM,
$ A, LDA, WORK( 2*N+1 ), IINFO )
*
ELSE IF( ITYPE.EQ.7 ) THEN
*
* Diagonal, random eigenvalues
*
CALL ZLATMR( N, N, 'D', ISEED, 'S', WORK, 6, ONE, CONE,
$ 'T', 'N', WORK( N+1 ), 1, ONE,
$ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, 0, 0,
$ ZERO, ANORM, 'NO', A, LDA, IDUMMA, IINFO )
*
ELSE IF( ITYPE.EQ.8 ) THEN
*
* Symmetric, random eigenvalues
*
CALL ZLATMR( N, N, 'D', ISEED, 'H', WORK, 6, ONE, CONE,
$ 'T', 'N', WORK( N+1 ), 1, ONE,
$ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, N,
$ ZERO, ANORM, 'NO', A, LDA, IDUMMA, IINFO )
*
ELSE IF( ITYPE.EQ.9 ) THEN
*
* General, random eigenvalues
*
CALL ZLATMR( N, N, 'D', ISEED, 'N', WORK, 6, ONE, CONE,
$ 'T', 'N', WORK( N+1 ), 1, ONE,
$ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, N,
$ ZERO, ANORM, 'NO', A, LDA, IDUMMA, IINFO )
IF( N.GE.4 ) THEN
CALL ZLASET( 'Full', 2, N, CZERO, CZERO, A, LDA )
CALL ZLASET( 'Full', N-3, 1, CZERO, CZERO, A( 3, 1 ),
$ LDA )
CALL ZLASET( 'Full', N-3, 2, CZERO, CZERO,
$ A( 3, N-1 ), LDA )
CALL ZLASET( 'Full', 1, N, CZERO, CZERO, A( N, 1 ),
$ LDA )
END IF
*
ELSE IF( ITYPE.EQ.10 ) THEN
*
* Triangular, random eigenvalues
*
CALL ZLATMR( N, N, 'D', ISEED, 'N', WORK, 6, ONE, CONE,
$ 'T', 'N', WORK( N+1 ), 1, ONE,
$ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, 0,
$ ZERO, ANORM, 'NO', A, LDA, IDUMMA, IINFO )
*
ELSE
*
IINFO = 1
END IF
*
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9992 )'Generator', IINFO, N, JTYPE,
$ IOLDSD
INFO = ABS( IINFO )
RETURN
END IF
*
90 CONTINUE
*
* Test for minimal and generous workspace
*
DO 130 IWK = 1, 3
IF( IWK.EQ.1 ) THEN
NNWORK = 2*N
ELSE IF( IWK.EQ.2 ) THEN
NNWORK = 2*N + N**2
ELSE
NNWORK = 6*N + 2*N**2
END IF
NNWORK = MAX( NNWORK, 1 )
*
* Test for all balancing options
*
DO 120 IBAL = 1, 4
BALANC = BAL( IBAL )
*
* Perform tests
*
CALL ZGET23( .FALSE., 0, BALANC, JTYPE, THRESH,
$ IOLDSD, NOUNIT, N, A, LDA, H, W, W1, VL,
$ LDVL, VR, LDVR, LRE, LDLRE, RCONDV,
$ RCNDV1, RCDVIN, RCONDE, RCNDE1, RCDEIN,
$ SCALE, SCALE1, RESULT, WORK, NNWORK,
$ RWORK, INFO )
*
* Check for RESULT(j) > THRESH
*
NTEST = 0
NFAIL = 0
DO 100 J = 1, 9
IF( RESULT( J ).GE.ZERO )
$ NTEST = NTEST + 1
IF( RESULT( J ).GE.THRESH )
$ NFAIL = NFAIL + 1
100 CONTINUE
*
IF( NFAIL.GT.0 )
$ NTESTF = NTESTF + 1
IF( NTESTF.EQ.1 ) THEN
WRITE( NOUNIT, FMT = 9999 )PATH
WRITE( NOUNIT, FMT = 9998 )
WRITE( NOUNIT, FMT = 9997 )
WRITE( NOUNIT, FMT = 9996 )
WRITE( NOUNIT, FMT = 9995 )THRESH
NTESTF = 2
END IF
*
DO 110 J = 1, 9
IF( RESULT( J ).GE.THRESH ) THEN
WRITE( NOUNIT, FMT = 9994 )BALANC, N, IWK,
$ IOLDSD, JTYPE, J, RESULT( J )
END IF
110 CONTINUE
*
NERRS = NERRS + NFAIL
NTESTT = NTESTT + NTEST
*
120 CONTINUE
130 CONTINUE
140 CONTINUE
150 CONTINUE
*
160 CONTINUE
*
* Read in data from file to check accuracy of condition estimation.
* Assume input eigenvalues are sorted lexicographically (increasing
* by real part, then decreasing by imaginary part)
*
JTYPE = 0
170 CONTINUE
READ( NIUNIT, FMT = *, END = 220 )N, ISRT
*
* Read input data until N=0
*
IF( N.EQ.0 )
$ GO TO 220
JTYPE = JTYPE + 1
ISEED( 1 ) = JTYPE
DO 180 I = 1, N
READ( NIUNIT, FMT = * )( A( I, J ), J = 1, N )
180 CONTINUE
DO 190 I = 1, N
READ( NIUNIT, FMT = * )WR, WI, RCDEIN( I ), RCDVIN( I )
W1( I ) = DCMPLX( WR, WI )
190 CONTINUE
CALL ZGET23( .TRUE., ISRT, 'N', 22, THRESH, ISEED, NOUNIT, N, A,
$ LDA, H, W, W1, VL, LDVL, VR, LDVR, LRE, LDLRE,
$ RCONDV, RCNDV1, RCDVIN, RCONDE, RCNDE1, RCDEIN,
$ SCALE, SCALE1, RESULT, WORK, 6*N+2*N**2, RWORK,
$ INFO )
*
* Check for RESULT(j) > THRESH
*
NTEST = 0
NFAIL = 0
DO 200 J = 1, 11
IF( RESULT( J ).GE.ZERO )
$ NTEST = NTEST + 1
IF( RESULT( J ).GE.THRESH )
$ NFAIL = NFAIL + 1
200 CONTINUE
*
IF( NFAIL.GT.0 )
$ NTESTF = NTESTF + 1
IF( NTESTF.EQ.1 ) THEN
WRITE( NOUNIT, FMT = 9999 )PATH
WRITE( NOUNIT, FMT = 9998 )
WRITE( NOUNIT, FMT = 9997 )
WRITE( NOUNIT, FMT = 9996 )
WRITE( NOUNIT, FMT = 9995 )THRESH
NTESTF = 2
END IF
*
DO 210 J = 1, 11
IF( RESULT( J ).GE.THRESH ) THEN
WRITE( NOUNIT, FMT = 9993 )N, JTYPE, J, RESULT( J )
END IF
210 CONTINUE
*
NERRS = NERRS + NFAIL
NTESTT = NTESTT + NTEST
GO TO 170
220 CONTINUE
*
* Summary
*
CALL DLASUM( PATH, NOUNIT, NERRS, NTESTT )
*
9999 FORMAT( / 1X, A3, ' -- Complex Eigenvalue-Eigenvector ',
$ 'Decomposition Expert Driver',
$ / ' Matrix types (see ZDRVVX for details): ' )
*
9998 FORMAT( / ' Special Matrices:', / ' 1=Zero matrix. ',
$ ' ', ' 5=Diagonal: geometr. spaced entries.',
$ / ' 2=Identity matrix. ', ' 6=Diagona',
$ 'l: clustered entries.', / ' 3=Transposed Jordan block. ',
$ ' ', ' 7=Diagonal: large, evenly spaced.', / ' ',
$ '4=Diagonal: evenly spaced entries. ', ' 8=Diagonal: s',
$ 'mall, evenly spaced.' )
9997 FORMAT( ' Dense, Non-Symmetric Matrices:', / ' 9=Well-cond., ev',
$ 'enly spaced eigenvals.', ' 14=Ill-cond., geomet. spaced e',
$ 'igenals.', / ' 10=Well-cond., geom. spaced eigenvals. ',
$ ' 15=Ill-conditioned, clustered e.vals.', / ' 11=Well-cond',
$ 'itioned, clustered e.vals. ', ' 16=Ill-cond., random comp',
$ 'lex ', / ' 12=Well-cond., random complex ', ' ',
$ ' 17=Ill-cond., large rand. complx ', / ' 13=Ill-condi',
$ 'tioned, evenly spaced. ', ' 18=Ill-cond., small rand.',
$ ' complx ' )
9996 FORMAT( ' 19=Matrix with random O(1) entries. ', ' 21=Matrix ',
$ 'with small random entries.', / ' 20=Matrix with large ran',
$ 'dom entries. ', ' 22=Matrix read from input file', / )
9995 FORMAT( ' Tests performed with test threshold =', F8.2,
$ / / ' 1 = | A VR - VR W | / ( n |A| ulp ) ',
$ / ' 2 = | transpose(A) VL - VL W | / ( n |A| ulp ) ',
$ / ' 3 = | |VR(i)| - 1 | / ulp ',
$ / ' 4 = | |VL(i)| - 1 | / ulp ',
$ / ' 5 = 0 if W same no matter if VR or VL computed,',
$ ' 1/ulp otherwise', /
$ ' 6 = 0 if VR same no matter what else computed,',
$ ' 1/ulp otherwise', /
$ ' 7 = 0 if VL same no matter what else computed,',
$ ' 1/ulp otherwise', /
$ ' 8 = 0 if RCONDV same no matter what else computed,',
$ ' 1/ulp otherwise', /
$ ' 9 = 0 if SCALE, ILO, IHI, ABNRM same no matter what else',
$ ' computed, 1/ulp otherwise',
$ / ' 10 = | RCONDV - RCONDV(precomputed) | / cond(RCONDV),',
$ / ' 11 = | RCONDE - RCONDE(precomputed) | / cond(RCONDE),' )
9994 FORMAT( ' BALANC=''', A1, ''',N=', I4, ',IWK=', I1, ', seed=',
$ 4( I4, ',' ), ' type ', I2, ', test(', I2, ')=', G10.3 )
9993 FORMAT( ' N=', I5, ', input example =', I3, ', test(', I2, ')=',
$ G10.3 )
9992 FORMAT( ' ZDRVVX: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
$ I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
*
RETURN
*
* End of ZDRVVX
*
END