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Cloned library LAPACK-3.11.0 with extra build files for internal package management.
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LAPACK-3.11.0/TESTING/EIG/zchkhs.f

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*> \brief \b ZCHKHS
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZCHKHS( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NOUNIT, A, LDA, H, T1, T2, U, LDU, Z, UZ, W1,
* W3, EVECTL, EVECTR, EVECTY, EVECTX, UU, TAU,
* WORK, NWORK, RWORK, IWORK, SELECT, RESULT,
* INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, LDA, LDU, NOUNIT, NSIZES, NTYPES, NWORK
* DOUBLE PRECISION THRESH
* ..
* .. Array Arguments ..
* LOGICAL DOTYPE( * ), SELECT( * )
* INTEGER ISEED( 4 ), IWORK( * ), NN( * )
* DOUBLE PRECISION RESULT( 16 ), RWORK( * )
* COMPLEX*16 A( LDA, * ), EVECTL( LDU, * ),
* $ EVECTR( LDU, * ), EVECTX( LDU, * ),
* $ EVECTY( LDU, * ), H( LDA, * ), T1( LDA, * ),
* $ T2( LDA, * ), TAU( * ), U( LDU, * ),
* $ UU( LDU, * ), UZ( LDU, * ), W1( * ), W3( * ),
* $ WORK( * ), Z( LDU, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZCHKHS checks the nonsymmetric eigenvalue problem routines.
*>
*> ZGEHRD factors A as U H U' , where ' means conjugate
*> transpose, H is hessenberg, and U is unitary.
*>
*> ZUNGHR generates the unitary matrix U.
*>
*> ZUNMHR multiplies a matrix by the unitary matrix U.
*>
*> ZHSEQR factors H as Z T Z' , where Z is unitary and T
*> is upper triangular. It also computes the eigenvalues,
*> w(1), ..., w(n); we define a diagonal matrix W whose
*> (diagonal) entries are the eigenvalues.
*>
*> ZTREVC computes the left eigenvector matrix L and the
*> right eigenvector matrix R for the matrix T. The
*> columns of L are the complex conjugates of the left
*> eigenvectors of T. The columns of R are the right
*> eigenvectors of T. L is lower triangular, and R is
*> upper triangular.
*>
*> ZHSEIN computes the left eigenvector matrix Y and the
*> right eigenvector matrix X for the matrix H. The
*> columns of Y are the complex conjugates of the left
*> eigenvectors of H. The columns of X are the right
*> eigenvectors of H. Y is lower triangular, and X is
*> upper triangular.
*>
*> ZTREVC3 computes left and right eigenvector matrices
*> from a Schur matrix T and backtransforms them with Z
*> to eigenvector matrices L and R for A. L and R are
*> GE matrices.
*>
*> When ZCHKHS 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, 16
*> tests will be performed:
*>
*> (1) | A - U H U**H | / ( |A| n ulp )
*>
*> (2) | I - UU**H | / ( n ulp )
*>
*> (3) | H - Z T Z**H | / ( |H| n ulp )
*>
*> (4) | I - ZZ**H | / ( n ulp )
*>
*> (5) | A - UZ H (UZ)**H | / ( |A| n ulp )
*>
*> (6) | I - UZ (UZ)**H | / ( n ulp )
*>
*> (7) | T(Z computed) - T(Z not computed) | / ( |T| ulp )
*>
*> (8) | W(Z computed) - W(Z not computed) | / ( |W| ulp )
*>
*> (9) | TR - RW | / ( |T| |R| ulp )
*>
*> (10) | L**H T - W**H L | / ( |T| |L| ulp )
*>
*> (11) | HX - XW | / ( |H| |X| ulp )
*>
*> (12) | Y**H H - W**H Y | / ( |H| |Y| ulp )
*>
*> (13) | AX - XW | / ( |A| |X| ulp )
*>
*> (14) | Y**H A - W**H Y | / ( |A| |Y| ulp )
*>
*> (15) | AR - RW | / ( |A| |R| ulp )
*>
*> (16) | LA - WL | / ( |A| |L| ulp )
*>
*> 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 SQRT( overflow threshold )
*> (8) Same as (4), but multiplied by SQRT( 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 SQRT( overflow threshold )
*> (18) Same as (16), but multiplied by SQRT( underflow threshold )
*>
*> (19) Nonsymmetric matrix with random entries chosen from |z| < 1
*> (20) Same as (19), but multiplied by SQRT( overflow threshold )
*> (21) Same as (19), but multiplied by SQRT( underflow threshold )
*> \endverbatim
*
* Arguments:
* ==========
*
*> \verbatim
*> NSIZES - INTEGER
*> The number of sizes of matrices to use. If it is zero,
*> ZCHKHS does nothing. It must be at least zero.
*> Not modified.
*>
*> NN - 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.
*> Not modified.
*>
*> NTYPES - INTEGER
*> The number of elements in DOTYPE. If it is zero, ZCHKHS
*> 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. .
*> Not modified.
*>
*> DOTYPE - 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.
*> Not modified.
*>
*> ISEED - 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 ZCHKHS to continue the same random number
*> sequence.
*> Modified.
*>
*> THRESH - 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.
*> Not modified.
*>
*> NOUNIT - INTEGER
*> The FORTRAN unit number for printing out error messages
*> (e.g., if a routine returns IINFO not equal to 0.)
*> Not modified.
*>
*> A - COMPLEX*16 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.
*> Modified.
*>
*> LDA - INTEGER
*> The leading dimension of A, H, T1 and T2. It must be at
*> least 1 and at least max( NN ).
*> Not modified.
*>
*> H - COMPLEX*16 array, dimension (LDA,max(NN))
*> The upper hessenberg matrix computed by ZGEHRD. On exit,
*> H contains the Hessenberg form of the matrix in A.
*> Modified.
*>
*> T1 - COMPLEX*16 array, dimension (LDA,max(NN))
*> The Schur (="quasi-triangular") matrix computed by ZHSEQR
*> if Z is computed. On exit, T1 contains the Schur form of
*> the matrix in A.
*> Modified.
*>
*> T2 - COMPLEX*16 array, dimension (LDA,max(NN))
*> The Schur matrix computed by ZHSEQR when Z is not computed.
*> This should be identical to T1.
*> Modified.
*>
*> LDU - INTEGER
*> The leading dimension of U, Z, UZ and UU. It must be at
*> least 1 and at least max( NN ).
*> Not modified.
*>
*> U - COMPLEX*16 array, dimension (LDU,max(NN))
*> The unitary matrix computed by ZGEHRD.
*> Modified.
*>
*> Z - COMPLEX*16 array, dimension (LDU,max(NN))
*> The unitary matrix computed by ZHSEQR.
*> Modified.
*>
*> UZ - COMPLEX*16 array, dimension (LDU,max(NN))
*> The product of U times Z.
*> Modified.
*>
*> W1 - COMPLEX*16 array, dimension (max(NN))
*> The eigenvalues of A, as computed by a full Schur
*> decomposition H = Z T Z'. On exit, W1 contains the
*> eigenvalues of the matrix in A.
*> Modified.
*>
*> W3 - COMPLEX*16 array, dimension (max(NN))
*> The eigenvalues of A, as computed by a partial Schur
*> decomposition (Z not computed, T only computed as much
*> as is necessary for determining eigenvalues). On exit,
*> W3 contains the eigenvalues of the matrix in A, possibly
*> perturbed by ZHSEIN.
*> Modified.
*>
*> EVECTL - COMPLEX*16 array, dimension (LDU,max(NN))
*> The conjugate transpose of the (upper triangular) left
*> eigenvector matrix for the matrix in T1.
*> Modified.
*>
*> EVEZTR - COMPLEX*16 array, dimension (LDU,max(NN))
*> The (upper triangular) right eigenvector matrix for the
*> matrix in T1.
*> Modified.
*>
*> EVECTY - COMPLEX*16 array, dimension (LDU,max(NN))
*> The conjugate transpose of the left eigenvector matrix
*> for the matrix in H.
*> Modified.
*>
*> EVECTX - COMPLEX*16 array, dimension (LDU,max(NN))
*> The right eigenvector matrix for the matrix in H.
*> Modified.
*>
*> UU - COMPLEX*16 array, dimension (LDU,max(NN))
*> Details of the unitary matrix computed by ZGEHRD.
*> Modified.
*>
*> TAU - COMPLEX*16 array, dimension (max(NN))
*> Further details of the unitary matrix computed by ZGEHRD.
*> Modified.
*>
*> WORK - COMPLEX*16 array, dimension (NWORK)
*> Workspace.
*> Modified.
*>
*> NWORK - INTEGER
*> The number of entries in WORK. NWORK >= 4*NN(j)*NN(j) + 2.
*>
*> RWORK - DOUBLE PRECISION array, dimension (max(NN))
*> Workspace. Could be equivalenced to IWORK, but not SELECT.
*> Modified.
*>
*> IWORK - INTEGER array, dimension (max(NN))
*> Workspace.
*> Modified.
*>
*> SELECT - LOGICAL array, dimension (max(NN))
*> Workspace. Could be equivalenced to IWORK, but not RWORK.
*> Modified.
*>
*> RESULT - DOUBLE PRECISION array, dimension (16)
*> The values computed by the fourteen tests described above.
*> The values are currently limited to 1/ulp, to avoid
*> overflow.
*> Modified.
*>
*> INFO - 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) ).
*> -14: LDU < 1 or LDU < NMAX.
*> -26: NWORK too small.
*> If ZLATMR, CLATMS, or CLATME returns an error code, the
*> absolute value of it is returned.
*> If 1, then ZHSEQR could not find all the shifts.
*> If 2, then the EISPACK code (for small blocks) failed.
*> If >2, then 30*N iterations were not enough to find an
*> eigenvalue or to decompose the problem.
*> Modified.
*>
*>-----------------------------------------------------------------------
*>
*> Some Local Variables and Parameters:
*> ---- ----- --------- --- ----------
*>
*> ZERO, ONE Real 0 and 1.
*> MAXTYP The number of types defined.
*> MTEST The number of tests defined: care must be taken
*> that (1) the size of RESULT, (2) the number of
*> tests actually performed, and (3) MTEST agree.
*> NTEST The number of tests performed on this matrix
*> so far. This should be less than MTEST, and
*> equal to it by the last test. It will be less
*> if any of the routines being tested indicates
*> that it could not compute the matrices that
*> would be tested.
*> NMAX Largest value in NN.
*> NMATS The number of matrices generated so far.
*> NERRS The number of tests which have exceeded THRESH
*> so far (computed by DLAFTS).
*> 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.
*> RTOVFL, RTUNFL,
*> 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) Selects 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.
*
*> \ingroup complex16_eig
*
* =====================================================================
SUBROUTINE ZCHKHS( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
$ NOUNIT, A, LDA, H, T1, T2, U, LDU, Z, UZ, W1,
$ W3, EVECTL, EVECTR, EVECTY, EVECTX, UU, TAU,
$ WORK, NWORK, RWORK, IWORK, SELECT, RESULT,
$ INFO )
*
* -- LAPACK test routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, LDU, NOUNIT, NSIZES, NTYPES, NWORK
DOUBLE PRECISION THRESH
* ..
* .. Array Arguments ..
LOGICAL DOTYPE( * ), SELECT( * )
INTEGER ISEED( 4 ), IWORK( * ), NN( * )
DOUBLE PRECISION RESULT( 16 ), RWORK( * )
COMPLEX*16 A( LDA, * ), EVECTL( LDU, * ),
$ EVECTR( LDU, * ), EVECTX( LDU, * ),
$ EVECTY( LDU, * ), H( LDA, * ), T1( LDA, * ),
$ T2( LDA, * ), TAU( * ), U( LDU, * ),
$ UU( LDU, * ), UZ( LDU, * ), W1( * ), W3( * ),
$ WORK( * ), Z( LDU, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
COMPLEX*16 CZERO, CONE
PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
$ CONE = ( 1.0D+0, 0.0D+0 ) )
INTEGER MAXTYP
PARAMETER ( MAXTYP = 21 )
* ..
* .. Local Scalars ..
LOGICAL BADNN, MATCH
INTEGER I, IHI, IINFO, ILO, IMODE, IN, ITYPE, J, JCOL,
$ JJ, JSIZE, JTYPE, K, MTYPES, N, N1, NERRS,
$ NMATS, NMAX, NTEST, NTESTT
DOUBLE PRECISION ANINV, ANORM, COND, CONDS, OVFL, RTOVFL, RTULP,
$ RTULPI, RTUNFL, TEMP1, TEMP2, ULP, ULPINV, UNFL
* ..
* .. Local Arrays ..
INTEGER IDUMMA( 1 ), IOLDSD( 4 ), KCONDS( MAXTYP ),
$ KMAGN( MAXTYP ), KMODE( MAXTYP ),
$ KTYPE( MAXTYP )
DOUBLE PRECISION DUMMA( 4 )
COMPLEX*16 CDUMMA( 4 )
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH
EXTERNAL DLAMCH
* ..
* .. External Subroutines ..
EXTERNAL DLAFTS, DLASUM, XERBLA, ZCOPY, ZGEHRD, ZGEMM,
$ ZGET10, ZGET22, ZHSEIN, ZHSEQR, ZHST01, ZLACPY,
$ ZLASET, ZLATME, ZLATMR, ZLATMS, ZTREVC, ZTREVC3,
$ ZUNGHR, ZUNMHR
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DBLE, 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 /
* ..
* .. Executable Statements ..
*
* Check for errors
*
NTESTT = 0
INFO = 0
*
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( LDA.LE.1 .OR. LDA.LT.NMAX ) THEN
INFO = -9
ELSE IF( LDU.LE.1 .OR. LDU.LT.NMAX ) THEN
INFO = -14
ELSE IF( 4*NMAX*NMAX+2.GT.NWORK ) THEN
INFO = -26
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZCHKHS', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 )
$ RETURN
*
* More important constants
*
UNFL = DLAMCH( 'Safe minimum' )
OVFL = DLAMCH( 'Overflow' )
ULP = DLAMCH( 'Epsilon' )*DLAMCH( 'Base' )
ULPINV = ONE / ULP
RTUNFL = SQRT( UNFL )
RTOVFL = SQRT( OVFL )
RTULP = SQRT( ULP )
RTULPI = ONE / RTULP
*
* Loop over sizes, types
*
NERRS = 0
NMATS = 0
*
DO 260 JSIZE = 1, NSIZES
N = NN( JSIZE )
IF( N.EQ.0 )
$ GO TO 260
N1 = MAX( 1, N )
ANINV = ONE / DBLE( N1 )
*
IF( NSIZES.NE.1 ) THEN
MTYPES = MIN( MAXTYP, NTYPES )
ELSE
MTYPES = MIN( MAXTYP+1, NTYPES )
END IF
*
DO 250 JTYPE = 1, MTYPES
IF( .NOT.DOTYPE( JTYPE ) )
$ GO TO 250
NMATS = NMATS + 1
NTEST = 0
*
* Save ISEED in case of an error.
*
DO 20 J = 1, 4
IOLDSD( J ) = ISEED( J )
20 CONTINUE
*
* Initialize RESULT
*
DO 30 J = 1, 14
RESULT( J ) = ZERO
30 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 hermitian, w/ eigenvalues
* =6 random general, w/ eigenvalues
* =7 random diagonal
* =8 random hermitian
* =9 random general
* =10 random triangular
*
IF( MTYPES.GT.MAXTYP )
$ GO TO 100
*
ITYPE = KTYPE( JTYPE )
IMODE = KMODE( JTYPE )
*
* Compute norm
*
GO TO ( 40, 50, 60 )KMAGN( JTYPE )
*
40 CONTINUE
ANORM = ONE
GO TO 70
*
50 CONTINUE
ANORM = ( RTOVFL*ULP )*ANINV
GO TO 70
*
60 CONTINUE
ANORM = RTUNFL*N*ULPINV
GO TO 70
*
70 CONTINUE
*
CALL ZLASET( 'Full', LDA, N, CZERO, CZERO, A, LDA )
IINFO = 0
COND = ULPINV
*
* Special Matrices
*
IF( ITYPE.EQ.1 ) THEN
*
* Zero
*
IINFO = 0
ELSE IF( ITYPE.EQ.2 ) THEN
*
* Identity
*
DO 80 JCOL = 1, N
A( JCOL, JCOL ) = ANORM
80 CONTINUE
*
ELSE IF( ITYPE.EQ.3 ) THEN
*
* Jordan Block
*
DO 90 JCOL = 1, N
A( JCOL, JCOL ) = ANORM
IF( JCOL.GT.1 )
$ A( JCOL, JCOL-1 ) = ONE
90 CONTINUE
*
ELSE IF( ITYPE.EQ.4 ) THEN
*
* Diagonal Matrix, [Eigen]values Specified
*
CALL ZLATMR( N, N, 'D', ISEED, 'N', WORK, IMODE, COND,
$ CONE, '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.5 ) THEN
*
* Hermitian, eigenvalues specified
*
CALL ZLATMS( N, N, 'D', ISEED, 'H', RWORK, IMODE, COND,
$ ANORM, N, N, 'N', A, LDA, WORK, 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( N+1 ), IINFO )
*
ELSE IF( ITYPE.EQ.7 ) THEN
*
* Diagonal, 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, 0, 0,
$ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
*
ELSE IF( ITYPE.EQ.8 ) THEN
*
* Hermitian, 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, IWORK, 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, IWORK, IINFO )
*
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, IWORK, IINFO )
*
ELSE
*
IINFO = 1
END IF
*
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'Generator', IINFO, N, JTYPE,
$ IOLDSD
INFO = ABS( IINFO )
RETURN
END IF
*
100 CONTINUE
*
* Call ZGEHRD to compute H and U, do tests.
*
CALL ZLACPY( ' ', N, N, A, LDA, H, LDA )
NTEST = 1
*
ILO = 1
IHI = N
*
CALL ZGEHRD( N, ILO, IHI, H, LDA, WORK, WORK( N+1 ),
$ NWORK-N, IINFO )
*
IF( IINFO.NE.0 ) THEN
RESULT( 1 ) = ULPINV
WRITE( NOUNIT, FMT = 9999 )'ZGEHRD', IINFO, N, JTYPE,
$ IOLDSD
INFO = ABS( IINFO )
GO TO 240
END IF
*
DO 120 J = 1, N - 1
UU( J+1, J ) = CZERO
DO 110 I = J + 2, N
U( I, J ) = H( I, J )
UU( I, J ) = H( I, J )
H( I, J ) = CZERO
110 CONTINUE
120 CONTINUE
CALL ZCOPY( N-1, WORK, 1, TAU, 1 )
CALL ZUNGHR( N, ILO, IHI, U, LDU, WORK, WORK( N+1 ),
$ NWORK-N, IINFO )
NTEST = 2
*
CALL ZHST01( N, ILO, IHI, A, LDA, H, LDA, U, LDU, WORK,
$ NWORK, RWORK, RESULT( 1 ) )
*
* Call ZHSEQR to compute T1, T2 and Z, do tests.
*
* Eigenvalues only (W3)
*
CALL ZLACPY( ' ', N, N, H, LDA, T2, LDA )
NTEST = 3
RESULT( 3 ) = ULPINV
*
CALL ZHSEQR( 'E', 'N', N, ILO, IHI, T2, LDA, W3, UZ, LDU,
$ WORK, NWORK, IINFO )
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'ZHSEQR(E)', IINFO, N, JTYPE,
$ IOLDSD
IF( IINFO.LE.N+2 ) THEN
INFO = ABS( IINFO )
GO TO 240
END IF
END IF
*
* Eigenvalues (W1) and Full Schur Form (T2)
*
CALL ZLACPY( ' ', N, N, H, LDA, T2, LDA )
*
CALL ZHSEQR( 'S', 'N', N, ILO, IHI, T2, LDA, W1, UZ, LDU,
$ WORK, NWORK, IINFO )
IF( IINFO.NE.0 .AND. IINFO.LE.N+2 ) THEN
WRITE( NOUNIT, FMT = 9999 )'ZHSEQR(S)', IINFO, N, JTYPE,
$ IOLDSD
INFO = ABS( IINFO )
GO TO 240
END IF
*
* Eigenvalues (W1), Schur Form (T1), and Schur Vectors (UZ)
*
CALL ZLACPY( ' ', N, N, H, LDA, T1, LDA )
CALL ZLACPY( ' ', N, N, U, LDU, UZ, LDU )
*
CALL ZHSEQR( 'S', 'V', N, ILO, IHI, T1, LDA, W1, UZ, LDU,
$ WORK, NWORK, IINFO )
IF( IINFO.NE.0 .AND. IINFO.LE.N+2 ) THEN
WRITE( NOUNIT, FMT = 9999 )'ZHSEQR(V)', IINFO, N, JTYPE,
$ IOLDSD
INFO = ABS( IINFO )
GO TO 240
END IF
*
* Compute Z = U' UZ
*
CALL ZGEMM( 'C', 'N', N, N, N, CONE, U, LDU, UZ, LDU, CZERO,
$ Z, LDU )
NTEST = 8
*
* Do Tests 3: | H - Z T Z' | / ( |H| n ulp )
* and 4: | I - Z Z' | / ( n ulp )
*
CALL ZHST01( N, ILO, IHI, H, LDA, T1, LDA, Z, LDU, WORK,
$ NWORK, RWORK, RESULT( 3 ) )
*
* Do Tests 5: | A - UZ T (UZ)' | / ( |A| n ulp )
* and 6: | I - UZ (UZ)' | / ( n ulp )
*
CALL ZHST01( N, ILO, IHI, A, LDA, T1, LDA, UZ, LDU, WORK,
$ NWORK, RWORK, RESULT( 5 ) )
*
* Do Test 7: | T2 - T1 | / ( |T| n ulp )
*
CALL ZGET10( N, N, T2, LDA, T1, LDA, WORK, RWORK,
$ RESULT( 7 ) )
*
* Do Test 8: | W3 - W1 | / ( max(|W1|,|W3|) ulp )
*
TEMP1 = ZERO
TEMP2 = ZERO
DO 130 J = 1, N
TEMP1 = MAX( TEMP1, ABS( W1( J ) ), ABS( W3( J ) ) )
TEMP2 = MAX( TEMP2, ABS( W1( J )-W3( J ) ) )
130 CONTINUE
*
RESULT( 8 ) = TEMP2 / MAX( UNFL, ULP*MAX( TEMP1, TEMP2 ) )
*
* Compute the Left and Right Eigenvectors of T
*
* Compute the Right eigenvector Matrix:
*
NTEST = 9
RESULT( 9 ) = ULPINV
*
* Select every other eigenvector
*
DO 140 J = 1, N
SELECT( J ) = .FALSE.
140 CONTINUE
DO 150 J = 1, N, 2
SELECT( J ) = .TRUE.
150 CONTINUE
CALL ZTREVC( 'Right', 'All', SELECT, N, T1, LDA, CDUMMA,
$ LDU, EVECTR, LDU, N, IN, WORK, RWORK, IINFO )
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'ZTREVC(R,A)', IINFO, N,
$ JTYPE, IOLDSD
INFO = ABS( IINFO )
GO TO 240
END IF
*
* Test 9: | TR - RW | / ( |T| |R| ulp )
*
CALL ZGET22( 'N', 'N', 'N', N, T1, LDA, EVECTR, LDU, W1,
$ WORK, RWORK, DUMMA( 1 ) )
RESULT( 9 ) = DUMMA( 1 )
IF( DUMMA( 2 ).GT.THRESH ) THEN
WRITE( NOUNIT, FMT = 9998 )'Right', 'ZTREVC',
$ DUMMA( 2 ), N, JTYPE, IOLDSD
END IF
*
* Compute selected right eigenvectors and confirm that
* they agree with previous right eigenvectors
*
CALL ZTREVC( 'Right', 'Some', SELECT, N, T1, LDA, CDUMMA,
$ LDU, EVECTL, LDU, N, IN, WORK, RWORK, IINFO )
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'ZTREVC(R,S)', IINFO, N,
$ JTYPE, IOLDSD
INFO = ABS( IINFO )
GO TO 240
END IF
*
K = 1
MATCH = .TRUE.
DO 170 J = 1, N
IF( SELECT( J ) ) THEN
DO 160 JJ = 1, N
IF( EVECTR( JJ, J ).NE.EVECTL( JJ, K ) ) THEN
MATCH = .FALSE.
GO TO 180
END IF
160 CONTINUE
K = K + 1
END IF
170 CONTINUE
180 CONTINUE
IF( .NOT.MATCH )
$ WRITE( NOUNIT, FMT = 9997 )'Right', 'ZTREVC', N, JTYPE,
$ IOLDSD
*
* Compute the Left eigenvector Matrix:
*
NTEST = 10
RESULT( 10 ) = ULPINV
CALL ZTREVC( 'Left', 'All', SELECT, N, T1, LDA, EVECTL, LDU,
$ CDUMMA, LDU, N, IN, WORK, RWORK, IINFO )
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'ZTREVC(L,A)', IINFO, N,
$ JTYPE, IOLDSD
INFO = ABS( IINFO )
GO TO 240
END IF
*
* Test 10: | LT - WL | / ( |T| |L| ulp )
*
CALL ZGET22( 'C', 'N', 'C', N, T1, LDA, EVECTL, LDU, W1,
$ WORK, RWORK, DUMMA( 3 ) )
RESULT( 10 ) = DUMMA( 3 )
IF( DUMMA( 4 ).GT.THRESH ) THEN
WRITE( NOUNIT, FMT = 9998 )'Left', 'ZTREVC', DUMMA( 4 ),
$ N, JTYPE, IOLDSD
END IF
*
* Compute selected left eigenvectors and confirm that
* they agree with previous left eigenvectors
*
CALL ZTREVC( 'Left', 'Some', SELECT, N, T1, LDA, EVECTR,
$ LDU, CDUMMA, LDU, N, IN, WORK, RWORK, IINFO )
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'ZTREVC(L,S)', IINFO, N,
$ JTYPE, IOLDSD
INFO = ABS( IINFO )
GO TO 240
END IF
*
K = 1
MATCH = .TRUE.
DO 200 J = 1, N
IF( SELECT( J ) ) THEN
DO 190 JJ = 1, N
IF( EVECTL( JJ, J ).NE.EVECTR( JJ, K ) ) THEN
MATCH = .FALSE.
GO TO 210
END IF
190 CONTINUE
K = K + 1
END IF
200 CONTINUE
210 CONTINUE
IF( .NOT.MATCH )
$ WRITE( NOUNIT, FMT = 9997 )'Left', 'ZTREVC', N, JTYPE,
$ IOLDSD
*
* Call ZHSEIN for Right eigenvectors of H, do test 11
*
NTEST = 11
RESULT( 11 ) = ULPINV
DO 220 J = 1, N
SELECT( J ) = .TRUE.
220 CONTINUE
*
CALL ZHSEIN( 'Right', 'Qr', 'Ninitv', SELECT, N, H, LDA, W3,
$ CDUMMA, LDU, EVECTX, LDU, N1, IN, WORK, RWORK,
$ IWORK, IWORK, IINFO )
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'ZHSEIN(R)', IINFO, N, JTYPE,
$ IOLDSD
INFO = ABS( IINFO )
IF( IINFO.LT.0 )
$ GO TO 240
ELSE
*
* Test 11: | HX - XW | / ( |H| |X| ulp )
*
* (from inverse iteration)
*
CALL ZGET22( 'N', 'N', 'N', N, H, LDA, EVECTX, LDU, W3,
$ WORK, RWORK, DUMMA( 1 ) )
IF( DUMMA( 1 ).LT.ULPINV )
$ RESULT( 11 ) = DUMMA( 1 )*ANINV
IF( DUMMA( 2 ).GT.THRESH ) THEN
WRITE( NOUNIT, FMT = 9998 )'Right', 'ZHSEIN',
$ DUMMA( 2 ), N, JTYPE, IOLDSD
END IF
END IF
*
* Call ZHSEIN for Left eigenvectors of H, do test 12
*
NTEST = 12
RESULT( 12 ) = ULPINV
DO 230 J = 1, N
SELECT( J ) = .TRUE.
230 CONTINUE
*
CALL ZHSEIN( 'Left', 'Qr', 'Ninitv', SELECT, N, H, LDA, W3,
$ EVECTY, LDU, CDUMMA, LDU, N1, IN, WORK, RWORK,
$ IWORK, IWORK, IINFO )
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'ZHSEIN(L)', IINFO, N, JTYPE,
$ IOLDSD
INFO = ABS( IINFO )
IF( IINFO.LT.0 )
$ GO TO 240
ELSE
*
* Test 12: | YH - WY | / ( |H| |Y| ulp )
*
* (from inverse iteration)
*
CALL ZGET22( 'C', 'N', 'C', N, H, LDA, EVECTY, LDU, W3,
$ WORK, RWORK, DUMMA( 3 ) )
IF( DUMMA( 3 ).LT.ULPINV )
$ RESULT( 12 ) = DUMMA( 3 )*ANINV
IF( DUMMA( 4 ).GT.THRESH ) THEN
WRITE( NOUNIT, FMT = 9998 )'Left', 'ZHSEIN',
$ DUMMA( 4 ), N, JTYPE, IOLDSD
END IF
END IF
*
* Call ZUNMHR for Right eigenvectors of A, do test 13
*
NTEST = 13
RESULT( 13 ) = ULPINV
*
CALL ZUNMHR( 'Left', 'No transpose', N, N, ILO, IHI, UU,
$ LDU, TAU, EVECTX, LDU, WORK, NWORK, IINFO )
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'ZUNMHR(L)', IINFO, N, JTYPE,
$ IOLDSD
INFO = ABS( IINFO )
IF( IINFO.LT.0 )
$ GO TO 240
ELSE
*
* Test 13: | AX - XW | / ( |A| |X| ulp )
*
* (from inverse iteration)
*
CALL ZGET22( 'N', 'N', 'N', N, A, LDA, EVECTX, LDU, W3,
$ WORK, RWORK, DUMMA( 1 ) )
IF( DUMMA( 1 ).LT.ULPINV )
$ RESULT( 13 ) = DUMMA( 1 )*ANINV
END IF
*
* Call ZUNMHR for Left eigenvectors of A, do test 14
*
NTEST = 14
RESULT( 14 ) = ULPINV
*
CALL ZUNMHR( 'Left', 'No transpose', N, N, ILO, IHI, UU,
$ LDU, TAU, EVECTY, LDU, WORK, NWORK, IINFO )
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'ZUNMHR(L)', IINFO, N, JTYPE,
$ IOLDSD
INFO = ABS( IINFO )
IF( IINFO.LT.0 )
$ GO TO 240
ELSE
*
* Test 14: | YA - WY | / ( |A| |Y| ulp )
*
* (from inverse iteration)
*
CALL ZGET22( 'C', 'N', 'C', N, A, LDA, EVECTY, LDU, W3,
$ WORK, RWORK, DUMMA( 3 ) )
IF( DUMMA( 3 ).LT.ULPINV )
$ RESULT( 14 ) = DUMMA( 3 )*ANINV
END IF
*
* Compute Left and Right Eigenvectors of A
*
* Compute a Right eigenvector matrix:
*
NTEST = 15
RESULT( 15 ) = ULPINV
*
CALL ZLACPY( ' ', N, N, UZ, LDU, EVECTR, LDU )
*
CALL ZTREVC3( 'Right', 'Back', SELECT, N, T1, LDA, CDUMMA,
$ LDU, EVECTR, LDU, N, IN, WORK, NWORK, RWORK,
$ N, IINFO )
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'ZTREVC3(R,B)', IINFO, N,
$ JTYPE, IOLDSD
INFO = ABS( IINFO )
GO TO 250
END IF
*
* Test 15: | AR - RW | / ( |A| |R| ulp )
*
* (from Schur decomposition)
*
CALL ZGET22( 'N', 'N', 'N', N, A, LDA, EVECTR, LDU, W1,
$ WORK, RWORK, DUMMA( 1 ) )
RESULT( 15 ) = DUMMA( 1 )
IF( DUMMA( 2 ).GT.THRESH ) THEN
WRITE( NOUNIT, FMT = 9998 )'Right', 'ZTREVC3',
$ DUMMA( 2 ), N, JTYPE, IOLDSD
END IF
*
* Compute a Left eigenvector matrix:
*
NTEST = 16
RESULT( 16 ) = ULPINV
*
CALL ZLACPY( ' ', N, N, UZ, LDU, EVECTL, LDU )
*
CALL ZTREVC3( 'Left', 'Back', SELECT, N, T1, LDA, EVECTL,
$ LDU, CDUMMA, LDU, N, IN, WORK, NWORK, RWORK,
$ N, IINFO )
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'ZTREVC3(L,B)', IINFO, N,
$ JTYPE, IOLDSD
INFO = ABS( IINFO )
GO TO 250
END IF
*
* Test 16: | LA - WL | / ( |A| |L| ulp )
*
* (from Schur decomposition)
*
CALL ZGET22( 'Conj', 'N', 'Conj', N, A, LDA, EVECTL, LDU,
$ W1, WORK, RWORK, DUMMA( 3 ) )
RESULT( 16 ) = DUMMA( 3 )
IF( DUMMA( 4 ).GT.THRESH ) THEN
WRITE( NOUNIT, FMT = 9998 )'Left', 'ZTREVC3', DUMMA( 4 ),
$ N, JTYPE, IOLDSD
END IF
*
* End of Loop -- Check for RESULT(j) > THRESH
*
240 CONTINUE
*
NTESTT = NTESTT + NTEST
CALL DLAFTS( 'ZHS', N, N, JTYPE, NTEST, RESULT, IOLDSD,
$ THRESH, NOUNIT, NERRS )
*
250 CONTINUE
260 CONTINUE
*
* Summary
*
CALL DLASUM( 'ZHS', NOUNIT, NERRS, NTESTT )
*
RETURN
*
9999 FORMAT( ' ZCHKHS: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
$ I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
9998 FORMAT( ' ZCHKHS: ', A, ' Eigenvectors from ', A, ' incorrectly ',
$ 'normalized.', / ' Bits of error=', 0P, G10.3, ',', 9X,
$ 'N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5,
$ ')' )
9997 FORMAT( ' ZCHKHS: Selected ', A, ' Eigenvectors from ', A,
$ ' do not match other eigenvectors ', 9X, 'N=', I6,
$ ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
*
* End of ZCHKHS
*
END