testdata/lapack/TESTING/EIG/sdrves.f
*> \brief \b SDRVES
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE SDRVES( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NOUNIT, A, LDA, H, HT, WR, WI, WRT, WIT, VS,
* LDVS, RESULT, WORK, NWORK, IWORK, BWORK, INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, LDA, LDVS, NOUNIT, NSIZES, NTYPES, NWORK
* REAL THRESH
* ..
* .. Array Arguments ..
* LOGICAL BWORK( * ), DOTYPE( * )
* INTEGER ISEED( 4 ), IWORK( * ), NN( * )
* REAL A( LDA, * ), H( LDA, * ), HT( LDA, * ),
* $ RESULT( 13 ), VS( LDVS, * ), WI( * ), WIT( * ),
* $ WORK( * ), WR( * ), WRT( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SDRVES checks the nonsymmetric eigenvalue (Schur form) problem
*> driver SGEES.
*>
*> When SDRVES is called, a number of matrix "sizes" ("n's") and a
*> number of matrix "types" are specified. For each size ("n")
*> and each type of matrix, one matrix will be generated and used
*> to test the nonsymmetric eigenroutines. For each matrix, 13
*> tests will be performed:
*>
*> (1) 0 if T is in Schur form, 1/ulp otherwise
*> (no sorting of eigenvalues)
*>
*> (2) | A - VS T VS' | / ( n |A| ulp )
*>
*> Here VS is the matrix of Schur eigenvectors, and T is in Schur
*> form (no sorting of eigenvalues).
*>
*> (3) | I - VS VS' | / ( n ulp ) (no sorting of eigenvalues).
*>
*> (4) 0 if WR+sqrt(-1)*WI are eigenvalues of T
*> 1/ulp otherwise
*> (no sorting of eigenvalues)
*>
*> (5) 0 if T(with VS) = T(without VS),
*> 1/ulp otherwise
*> (no sorting of eigenvalues)
*>
*> (6) 0 if eigenvalues(with VS) = eigenvalues(without VS),
*> 1/ulp otherwise
*> (no sorting of eigenvalues)
*>
*> (7) 0 if T is in Schur form, 1/ulp otherwise
*> (with sorting of eigenvalues)
*>
*> (8) | A - VS T VS' | / ( n |A| ulp )
*>
*> Here VS is the matrix of Schur eigenvectors, and T is in Schur
*> form (with sorting of eigenvalues).
*>
*> (9) | I - VS VS' | / ( n ulp ) (with sorting of eigenvalues).
*>
*> (10) 0 if WR+sqrt(-1)*WI are eigenvalues of T
*> 1/ulp otherwise
*> (with sorting of eigenvalues)
*>
*> (11) 0 if T(with VS) = T(without VS),
*> 1/ulp otherwise
*> (with sorting of eigenvalues)
*>
*> (12) 0 if eigenvalues(with VS) = eigenvalues(without VS),
*> 1/ulp otherwise
*> (with sorting of eigenvalues)
*>
*> (13) if sorting worked and SDIM is the number of
*> eigenvalues which were SELECTed
*>
*> 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 signs.
*> (ULP = (first number larger than 1) - 1 )
*> (5) A diagonal matrix with geometrically spaced entries
*> 1, ..., ULP and random signs.
*> (6) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP
*> and random signs.
*>
*> (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 orthogonal and
*> T has evenly spaced entries 1, ..., ULP with random signs
*> on the diagonal and random O(1) entries in the upper
*> triangle.
*>
*> (10) A matrix of the form U' T U, where U is orthogonal and
*> T has geometrically spaced entries 1, ..., ULP with random
*> signs on the diagonal and random O(1) entries in the upper
*> triangle.
*>
*> (11) A matrix of the form U' T U, where U is orthogonal and
*> T has "clustered" entries 1, ULP,..., ULP with random
*> signs on the diagonal and random O(1) entries in the upper
*> triangle.
*>
*> (12) A matrix of the form U' T U, where U is orthogonal and
*> T has real or complex conjugate paired eigenvalues randomly
*> chosen from ( ULP, 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 signs 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 signs 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 signs 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 real or complex conjugate paired
*> eigenvalues randomly chosen from ( ULP, 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 (-1,1).
*> 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
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> NSIZES is INTEGER
*> The number of sizes of matrices to use. If it is zero,
*> SDRVES does nothing. It must be at least zero.
*> \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. If it is zero, SDRVES
*> does nothing. It must be at least zero. 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 SDRVES to continue the same random number
*> sequence.
*> \endverbatim
*>
*> \param[in] THRESH
*> \verbatim
*> THRESH is REAL
*> 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] 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 REAL array, dimension (LDA, max(NN))
*> 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).
*> \endverbatim
*>
*> \param[out] H
*> \verbatim
*> H is REAL array, dimension (LDA, max(NN))
*> Another copy of the test matrix A, modified by SGEES.
*> \endverbatim
*>
*> \param[out] HT
*> \verbatim
*> HT is REAL array, dimension (LDA, max(NN))
*> Yet another copy of the test matrix A, modified by SGEES.
*> \endverbatim
*>
*> \param[out] WR
*> \verbatim
*> WR is REAL array, dimension (max(NN))
*> \endverbatim
*>
*> \param[out] WI
*> \verbatim
*> WI is REAL array, dimension (max(NN))
*>
*> The real and imaginary parts of the eigenvalues of A.
*> On exit, WR + WI*i are the eigenvalues of the matrix in A.
*> \endverbatim
*>
*> \param[out] WRT
*> \verbatim
*> WRT is REAL array, dimension (max(NN))
*> \endverbatim
*>
*> \param[out] WIT
*> \verbatim
*> WIT is REAL array, dimension (max(NN))
*>
*> Like WR, WI, these arrays contain the eigenvalues of A,
*> but those computed when SGEES only computes a partial
*> eigendecomposition, i.e. not Schur vectors
*> \endverbatim
*>
*> \param[out] VS
*> \verbatim
*> VS is REAL array, dimension (LDVS, max(NN))
*> VS holds the computed Schur vectors.
*> \endverbatim
*>
*> \param[in] LDVS
*> \verbatim
*> LDVS is INTEGER
*> Leading dimension of VS. Must be at least max(1,max(NN)).
*> \endverbatim
*>
*> \param[out] RESULT
*> \verbatim
*> RESULT is REAL array, dimension (13)
*> The values computed by the 13 tests described above.
*> The values are currently limited to 1/ulp, to avoid overflow.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is REAL array, dimension (NWORK)
*> \endverbatim
*>
*> \param[in] NWORK
*> \verbatim
*> NWORK is INTEGER
*> The number of entries in WORK. This must be at least
*> 5*NN(j)+2*NN(j)**2 for all j.
*> \endverbatim
*>
*> \param[out] IWORK
*> \verbatim
*> IWORK is INTEGER array, dimension (max(NN))
*> \endverbatim
*>
*> \param[out] BWORK
*> \verbatim
*> BWORK is LOGICAL array, dimension (max(NN))
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> If 0, then everything ran OK.
*> -1: NSIZES < 0
*> -2: Some NN(j) < 0
*> -3: NTYPES < 0
*> -6: THRESH < 0
*> -9: LDA < 1 or LDA < NMAX, where NMAX is max( NN(j) ).
*> -17: LDVS < 1 or LDVS < NMAX, where NMAX is max( NN(j) ).
*> -20: NWORK too small.
*> If SLATMR, SLATMS, SLATME or SGEES returns an error code,
*> the absolute value of it is returned.
*>
*>-----------------------------------------------------------------------
*>
*> Some Local Variables and Parameters:
*> ---- ----- --------- --- ----------
*>
*> ZERO, ONE Real 0 and 1.
*> MAXTYP The number of types defined.
*> NMAX Largest value in NN.
*> 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 single_eig
*
* =====================================================================
SUBROUTINE SDRVES( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
$ NOUNIT, A, LDA, H, HT, WR, WI, WRT, WIT, VS,
$ LDVS, RESULT, WORK, NWORK, IWORK, BWORK, 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, LDVS, NOUNIT, NSIZES, NTYPES, NWORK
REAL THRESH
* ..
* .. Array Arguments ..
LOGICAL BWORK( * ), DOTYPE( * )
INTEGER ISEED( 4 ), IWORK( * ), NN( * )
REAL A( LDA, * ), H( LDA, * ), HT( LDA, * ),
$ RESULT( 13 ), VS( LDVS, * ), WI( * ), WIT( * ),
$ WORK( * ), WR( * ), WRT( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 )
INTEGER MAXTYP
PARAMETER ( MAXTYP = 21 )
* ..
* .. Local Scalars ..
LOGICAL BADNN
CHARACTER SORT
CHARACTER*3 PATH
INTEGER I, IINFO, IMODE, ISORT, ITYPE, IWK, J, JCOL,
$ JSIZE, JTYPE, KNTEIG, LWORK, MTYPES, N,
$ NERRS, NFAIL, NMAX, NNWORK, NTEST, NTESTF,
$ NTESTT, RSUB, SDIM
REAL ANORM, COND, CONDS, OVFL, RTULP, RTULPI, TMP,
$ ULP, ULPINV, UNFL
* ..
* .. Local Arrays ..
CHARACTER ADUMMA( 1 )
INTEGER IDUMMA( 1 ), IOLDSD( 4 ), KCONDS( MAXTYP ),
$ KMAGN( MAXTYP ), KMODE( MAXTYP ),
$ KTYPE( MAXTYP )
REAL RES( 2 )
* ..
* .. Arrays in Common ..
LOGICAL SELVAL( 20 )
REAL SELWI( 20 ), SELWR( 20 )
* ..
* .. Scalars in Common ..
INTEGER SELDIM, SELOPT
* ..
* .. Common blocks ..
COMMON / SSLCT / SELOPT, SELDIM, SELVAL, SELWR, SELWI
* ..
* .. External Functions ..
LOGICAL SSLECT
REAL SLAMCH
EXTERNAL SSLECT, SLAMCH
* ..
* .. External Subroutines ..
EXTERNAL SGEES, SHST01, SLABAD, SLACPY, SLASUM, SLATME,
$ SLATMR, SLATMS, SLASET, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, SIGN, 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 /
* ..
* .. Executable Statements ..
*
PATH( 1: 1 ) = 'Single precision'
PATH( 2: 3 ) = 'ES'
*
* Check for errors
*
NTESTT = 0
NTESTF = 0
INFO = 0
SELOPT = 0
*
* Important constants
*
BADNN = .FALSE.
NMAX = 0
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( NOUNIT.LE.0 ) THEN
INFO = -7
ELSE IF( LDA.LT.1 .OR. LDA.LT.NMAX ) THEN
INFO = -9
ELSE IF( LDVS.LT.1 .OR. LDVS.LT.NMAX ) THEN
INFO = -17
ELSE IF( 5*NMAX+2*NMAX**2.GT.NWORK ) THEN
INFO = -20
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'SDRVES', -INFO )
RETURN
END IF
*
* Quick return if nothing to do
*
IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 )
$ RETURN
*
* More Important constants
*
UNFL = SLAMCH( 'Safe minimum' )
OVFL = ONE / UNFL
CALL SLABAD( UNFL, OVFL )
ULP = SLAMCH( 'Precision' )
ULPINV = ONE / ULP
RTULP = SQRT( ULP )
RTULPI = ONE / RTULP
*
* Loop over sizes, types
*
NERRS = 0
*
DO 270 JSIZE = 1, NSIZES
N = NN( JSIZE )
MTYPES = MAXTYP
IF( NSIZES.EQ.1 .AND. NTYPES.EQ.MAXTYP+1 )
$ MTYPES = MTYPES + 1
*
DO 260 JTYPE = 1, MTYPES
IF( .NOT.DOTYPE( JTYPE ) )
$ GO TO 260
*
* 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 SLASET( 'Full', LDA, N, ZERO, ZERO, 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 SLATMS( N, N, 'S', ISEED, 'S', WORK, IMODE, COND,
$ ANORM, 0, 0, 'N', A, LDA, WORK( N+1 ),
$ IINFO )
*
ELSE IF( ITYPE.EQ.5 ) THEN
*
* Symmetric, eigenvalues specified
*
CALL SLATMS( N, N, 'S', ISEED, 'S', WORK, 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
*
ADUMMA( 1 ) = ' '
CALL SLATME( N, 'S', ISEED, WORK, IMODE, COND, ONE,
$ ADUMMA, 'T', 'T', 'T', WORK( N+1 ), 4,
$ CONDS, N, N, ANORM, A, LDA, WORK( 2*N+1 ),
$ IINFO )
*
ELSE IF( ITYPE.EQ.7 ) THEN
*
* Diagonal, random eigenvalues
*
CALL SLATMR( N, N, 'S', ISEED, 'S', WORK, 6, ONE, ONE,
$ 'T', 'N', WORK( N+1 ), 1, ONE,
$ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, 0, 0,
$ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
*
ELSE IF( ITYPE.EQ.8 ) THEN
*
* Symmetric, random eigenvalues
*
CALL SLATMR( N, N, 'S', ISEED, 'S', WORK, 6, ONE, ONE,
$ 'T', 'N', WORK( N+1 ), 1, ONE,
$ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, N,
$ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
*
ELSE IF( ITYPE.EQ.9 ) THEN
*
* General, random eigenvalues
*
CALL SLATMR( N, N, 'S', ISEED, 'N', WORK, 6, ONE, ONE,
$ 'T', 'N', WORK( N+1 ), 1, ONE,
$ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, N,
$ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
IF( N.GE.4 ) THEN
CALL SLASET( 'Full', 2, N, ZERO, ZERO, A, LDA )
CALL SLASET( 'Full', N-3, 1, ZERO, ZERO, A( 3, 1 ),
$ LDA )
CALL SLASET( 'Full', N-3, 2, ZERO, ZERO, A( 3, N-1 ),
$ LDA )
CALL SLASET( 'Full', 1, N, ZERO, ZERO, A( N, 1 ),
$ LDA )
END IF
*
ELSE IF( ITYPE.EQ.10 ) THEN
*
* Triangular, random eigenvalues
*
CALL SLATMR( N, N, 'S', ISEED, 'N', WORK, 6, ONE, ONE,
$ 'T', 'N', WORK( N+1 ), 1, ONE,
$ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, 0,
$ ZERO, ANORM, 'NO', A, LDA, IWORK, 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 250 IWK = 1, 2
IF( IWK.EQ.1 ) THEN
NNWORK = 3*N
ELSE
NNWORK = 5*N + 2*N**2
END IF
NNWORK = MAX( NNWORK, 1 )
*
* Initialize RESULT
*
DO 100 J = 1, 13
RESULT( J ) = -ONE
100 CONTINUE
*
* Test with and without sorting of eigenvalues
*
DO 210 ISORT = 0, 1
IF( ISORT.EQ.0 ) THEN
SORT = 'N'
RSUB = 0
ELSE
SORT = 'S'
RSUB = 6
END IF
*
* Compute Schur form and Schur vectors, and test them
*
CALL SLACPY( 'F', N, N, A, LDA, H, LDA )
CALL SGEES( 'V', SORT, SSLECT, N, H, LDA, SDIM, WR,
$ WI, VS, LDVS, WORK, NNWORK, BWORK, IINFO )
IF( IINFO.NE.0 .AND. IINFO.NE.N+2 ) THEN
RESULT( 1+RSUB ) = ULPINV
WRITE( NOUNIT, FMT = 9992 )'SGEES1', IINFO, N,
$ JTYPE, IOLDSD
INFO = ABS( IINFO )
GO TO 220
END IF
*
* Do Test (1) or Test (7)
*
RESULT( 1+RSUB ) = ZERO
DO 120 J = 1, N - 2
DO 110 I = J + 2, N
IF( H( I, J ).NE.ZERO )
$ RESULT( 1+RSUB ) = ULPINV
110 CONTINUE
120 CONTINUE
DO 130 I = 1, N - 2
IF( H( I+1, I ).NE.ZERO .AND. H( I+2, I+1 ).NE.
$ ZERO )RESULT( 1+RSUB ) = ULPINV
130 CONTINUE
DO 140 I = 1, N - 1
IF( H( I+1, I ).NE.ZERO ) THEN
IF( H( I, I ).NE.H( I+1, I+1 ) .OR.
$ H( I, I+1 ).EQ.ZERO .OR.
$ SIGN( ONE, H( I+1, I ) ).EQ.
$ SIGN( ONE, H( I, I+1 ) ) )RESULT( 1+RSUB )
$ = ULPINV
END IF
140 CONTINUE
*
* Do Tests (2) and (3) or Tests (8) and (9)
*
LWORK = MAX( 1, 2*N*N )
CALL SHST01( N, 1, N, A, LDA, H, LDA, VS, LDVS, WORK,
$ LWORK, RES )
RESULT( 2+RSUB ) = RES( 1 )
RESULT( 3+RSUB ) = RES( 2 )
*
* Do Test (4) or Test (10)
*
RESULT( 4+RSUB ) = ZERO
DO 150 I = 1, N
IF( H( I, I ).NE.WR( I ) )
$ RESULT( 4+RSUB ) = ULPINV
150 CONTINUE
IF( N.GT.1 ) THEN
IF( H( 2, 1 ).EQ.ZERO .AND. WI( 1 ).NE.ZERO )
$ RESULT( 4+RSUB ) = ULPINV
IF( H( N, N-1 ).EQ.ZERO .AND. WI( N ).NE.ZERO )
$ RESULT( 4+RSUB ) = ULPINV
END IF
DO 160 I = 1, N - 1
IF( H( I+1, I ).NE.ZERO ) THEN
TMP = SQRT( ABS( H( I+1, I ) ) )*
$ SQRT( ABS( H( I, I+1 ) ) )
RESULT( 4+RSUB ) = MAX( RESULT( 4+RSUB ),
$ ABS( WI( I )-TMP ) /
$ MAX( ULP*TMP, UNFL ) )
RESULT( 4+RSUB ) = MAX( RESULT( 4+RSUB ),
$ ABS( WI( I+1 )+TMP ) /
$ MAX( ULP*TMP, UNFL ) )
ELSE IF( I.GT.1 ) THEN
IF( H( I+1, I ).EQ.ZERO .AND. H( I, I-1 ).EQ.
$ ZERO .AND. WI( I ).NE.ZERO )RESULT( 4+RSUB )
$ = ULPINV
END IF
160 CONTINUE
*
* Do Test (5) or Test (11)
*
CALL SLACPY( 'F', N, N, A, LDA, HT, LDA )
CALL SGEES( 'N', SORT, SSLECT, N, HT, LDA, SDIM, WRT,
$ WIT, VS, LDVS, WORK, NNWORK, BWORK,
$ IINFO )
IF( IINFO.NE.0 .AND. IINFO.NE.N+2 ) THEN
RESULT( 5+RSUB ) = ULPINV
WRITE( NOUNIT, FMT = 9992 )'SGEES2', IINFO, N,
$ JTYPE, IOLDSD
INFO = ABS( IINFO )
GO TO 220
END IF
*
RESULT( 5+RSUB ) = ZERO
DO 180 J = 1, N
DO 170 I = 1, N
IF( H( I, J ).NE.HT( I, J ) )
$ RESULT( 5+RSUB ) = ULPINV
170 CONTINUE
180 CONTINUE
*
* Do Test (6) or Test (12)
*
RESULT( 6+RSUB ) = ZERO
DO 190 I = 1, N
IF( WR( I ).NE.WRT( I ) .OR. WI( I ).NE.WIT( I ) )
$ RESULT( 6+RSUB ) = ULPINV
190 CONTINUE
*
* Do Test (13)
*
IF( ISORT.EQ.1 ) THEN
RESULT( 13 ) = ZERO
KNTEIG = 0
DO 200 I = 1, N
IF( SSLECT( WR( I ), WI( I ) ) .OR.
$ SSLECT( WR( I ), -WI( I ) ) )
$ KNTEIG = KNTEIG + 1
IF( I.LT.N ) THEN
IF( ( SSLECT( WR( I+1 ),
$ WI( I+1 ) ) .OR. SSLECT( WR( I+1 ),
$ -WI( I+1 ) ) ) .AND.
$ ( .NOT.( SSLECT( WR( I ),
$ WI( I ) ) .OR. SSLECT( WR( I ),
$ -WI( I ) ) ) ) .AND. IINFO.NE.N+2 )
$ RESULT( 13 ) = ULPINV
END IF
200 CONTINUE
IF( SDIM.NE.KNTEIG ) THEN
RESULT( 13 ) = ULPINV
END IF
END IF
*
210 CONTINUE
*
* End of Loop -- Check for RESULT(j) > THRESH
*
220 CONTINUE
*
NTEST = 0
NFAIL = 0
DO 230 J = 1, 13
IF( RESULT( J ).GE.ZERO )
$ NTEST = NTEST + 1
IF( RESULT( J ).GE.THRESH )
$ NFAIL = NFAIL + 1
230 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
WRITE( NOUNIT, FMT = 9994 )
NTESTF = 2
END IF
*
DO 240 J = 1, 13
IF( RESULT( J ).GE.THRESH ) THEN
WRITE( NOUNIT, FMT = 9993 )N, IWK, IOLDSD, JTYPE,
$ J, RESULT( J )
END IF
240 CONTINUE
*
NERRS = NERRS + NFAIL
NTESTT = NTESTT + NTEST
*
250 CONTINUE
260 CONTINUE
270 CONTINUE
*
* Summary
*
CALL SLASUM( PATH, NOUNIT, NERRS, NTESTT )
*
9999 FORMAT( / 1X, A3, ' -- Real Schur Form Decomposition Driver',
$ / ' Matrix types (see SDRVES 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 ', 6X, ' ',
$ ' 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. ', / )
9995 FORMAT( ' Tests performed with test threshold =', F8.2,
$ / ' ( A denotes A on input and T denotes A on output)',
$ / / ' 1 = 0 if T in Schur form (no sort), ',
$ ' 1/ulp otherwise', /
$ ' 2 = | A - VS T transpose(VS) | / ( n |A| ulp ) (no sort)',
$ / ' 3 = | I - VS transpose(VS) | / ( n ulp ) (no sort) ', /
$ ' 4 = 0 if WR+sqrt(-1)*WI are eigenvalues of T (no sort),',
$ ' 1/ulp otherwise', /
$ ' 5 = 0 if T same no matter if VS computed (no sort),',
$ ' 1/ulp otherwise', /
$ ' 6 = 0 if WR, WI same no matter if VS computed (no sort)',
$ ', 1/ulp otherwise' )
9994 FORMAT( ' 7 = 0 if T in Schur form (sort), ', ' 1/ulp otherwise',
$ / ' 8 = | A - VS T transpose(VS) | / ( n |A| ulp ) (sort)',
$ / ' 9 = | I - VS transpose(VS) | / ( n ulp ) (sort) ',
$ / ' 10 = 0 if WR+sqrt(-1)*WI are eigenvalues of T (sort),',
$ ' 1/ulp otherwise', /
$ ' 11 = 0 if T same no matter if VS computed (sort),',
$ ' 1/ulp otherwise', /
$ ' 12 = 0 if WR, WI same no matter if VS computed (sort),',
$ ' 1/ulp otherwise', /
$ ' 13 = 0 if sorting successful, 1/ulp otherwise', / )
9993 FORMAT( ' N=', I5, ', IWK=', I2, ', seed=', 4( I4, ',' ),
$ ' type ', I2, ', test(', I2, ')=', G10.3 )
9992 FORMAT( ' SDRVES: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
$ I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
*
RETURN
*
* End of SDRVES
*
END