testdata/lapack/TESTING/EIG/schkhs.f
*> \brief \b SCHKHS
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE SCHKHS( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NOUNIT, A, LDA, H, T1, T2, U, LDU, Z, UZ, WR1,
* WI1, WR2, WI2, WR3, WI3, EVECTL, EVECTR, EVECTY,
* EVECTX, UU, TAU, WORK, NWORK, IWORK, SELECT,
* RESULT, INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, LDA, LDU, NOUNIT, NSIZES, NTYPES, NWORK
* REAL THRESH
* ..
* .. Array Arguments ..
* LOGICAL DOTYPE( * ), SELECT( * )
* INTEGER ISEED( 4 ), IWORK( * ), NN( * )
* REAL A( LDA, * ), EVECTL( LDU, * ),
* $ EVECTR( LDU, * ), EVECTX( LDU, * ),
* $ EVECTY( LDU, * ), H( LDA, * ), RESULT( 14 ),
* $ T1( LDA, * ), T2( LDA, * ), TAU( * ),
* $ U( LDU, * ), UU( LDU, * ), UZ( LDU, * ),
* $ WI1( * ), WI2( * ), WI3( * ), WORK( * ),
* $ WR1( * ), WR2( * ), WR3( * ), Z( LDU, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SCHKHS checks the nonsymmetric eigenvalue problem routines.
*>
*> SGEHRD factors A as U H U' , where ' means transpose,
*> H is hessenberg, and U is an orthogonal matrix.
*>
*> SORGHR generates the orthogonal matrix U.
*>
*> SORMHR multiplies a matrix by the orthogonal matrix U.
*>
*> SHSEQR factors H as Z T Z' , where Z is orthogonal and
*> T is "quasi-triangular", and the eigenvalue vector W.
*>
*> STREVC computes the left and right eigenvector matrices
*> L and R for T.
*>
*> SHSEIN computes the left and right eigenvector matrices
*> Y and X for H, using inverse iteration.
*>
*> When SCHKHS 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, 14
*> tests will be performed:
*>
*> (1) | A - U H U**T | / ( |A| n ulp )
*>
*> (2) | I - UU**T | / ( n ulp )
*>
*> (3) | H - Z T Z**T | / ( |H| n ulp )
*>
*> (4) | I - ZZ**T | / ( n ulp )
*>
*> (5) | A - UZ H (UZ)**T | / ( |A| n ulp )
*>
*> (6) | I - UZ (UZ)**T | / ( 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 )
*>
*> 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 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 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 SQRT( overflow threshold )
*> (18) Same as (16), but multiplied by SQRT( underflow threshold )
*>
*> (19) Nonsymmetric matrix with random entries chosen from (-1,1).
*> (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,
*> SCHKHS 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, SCHKHS
*> 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 SCHKHS to continue the same random number
*> sequence.
*> Modified.
*>
*> THRESH - 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.
*> 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 - 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.
*> 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 - REAL array, dimension (LDA,max(NN))
*> The upper hessenberg matrix computed by SGEHRD. On exit,
*> H contains the Hessenberg form of the matrix in A.
*> Modified.
*>
*> T1 - REAL array, dimension (LDA,max(NN))
*> The Schur (="quasi-triangular") matrix computed by SHSEQR
*> if Z is computed. On exit, T1 contains the Schur form of
*> the matrix in A.
*> Modified.
*>
*> T2 - REAL array, dimension (LDA,max(NN))
*> The Schur matrix computed by SHSEQR 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 - REAL array, dimension (LDU,max(NN))
*> The orthogonal matrix computed by SGEHRD.
*> Modified.
*>
*> Z - REAL array, dimension (LDU,max(NN))
*> The orthogonal matrix computed by SHSEQR.
*> Modified.
*>
*> UZ - REAL array, dimension (LDU,max(NN))
*> The product of U times Z.
*> Modified.
*>
*> WR1 - REAL array, dimension (max(NN))
*> WI1 - REAL array, dimension (max(NN))
*> The real and imaginary parts of the eigenvalues of A,
*> as computed when Z is computed.
*> On exit, WR1 + WI1*i are the eigenvalues of the matrix in A.
*> Modified.
*>
*> WR2 - REAL array, dimension (max(NN))
*> WI2 - REAL array, dimension (max(NN))
*> The real and imaginary parts of the eigenvalues of A,
*> as computed when T is computed but not Z.
*> On exit, WR2 + WI2*i are the eigenvalues of the matrix in A.
*> Modified.
*>
*> WR3 - REAL array, dimension (max(NN))
*> WI3 - REAL array, dimension (max(NN))
*> Like WR1, WI1, these arrays contain the eigenvalues of A,
*> but those computed when SHSEQR only computes the
*> eigenvalues, i.e., not the Schur vectors and no more of the
*> Schur form than is necessary for computing the
*> eigenvalues.
*> Modified.
*>
*> EVECTL - REAL array, dimension (LDU,max(NN))
*> The (upper triangular) left eigenvector matrix for the
*> matrix in T1. For complex conjugate pairs, the real part
*> is stored in one row and the imaginary part in the next.
*> Modified.
*>
*> EVECTR - REAL array, dimension (LDU,max(NN))
*> The (upper triangular) right eigenvector matrix for the
*> matrix in T1. For complex conjugate pairs, the real part
*> is stored in one column and the imaginary part in the next.
*> Modified.
*>
*> EVECTY - REAL array, dimension (LDU,max(NN))
*> The left eigenvector matrix for the
*> matrix in H. For complex conjugate pairs, the real part
*> is stored in one row and the imaginary part in the next.
*> Modified.
*>
*> EVECTX - REAL array, dimension (LDU,max(NN))
*> The right eigenvector matrix for the
*> matrix in H. For complex conjugate pairs, the real part
*> is stored in one column and the imaginary part in the next.
*> Modified.
*>
*> UU - REAL array, dimension (LDU,max(NN))
*> Details of the orthogonal matrix computed by SGEHRD.
*> Modified.
*>
*> TAU - REAL array, dimension(max(NN))
*> Further details of the orthogonal matrix computed by SGEHRD.
*> Modified.
*>
*> WORK - REAL array, dimension (NWORK)
*> Workspace.
*> Modified.
*>
*> NWORK - INTEGER
*> The number of entries in WORK. NWORK >= 4*NN(j)*NN(j) + 2.
*>
*> IWORK - INTEGER array, dimension (max(NN))
*> Workspace.
*> Modified.
*>
*> SELECT - LOGICAL array, dimension (max(NN))
*> Workspace.
*> Modified.
*>
*> RESULT - REAL array, dimension (14)
*> 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.
*> -28: NWORK too small.
*> If SLATMR, SLATMS, or SLATME returns an error code, the
*> absolute value of it is returned.
*> If 1, then SHSEQR 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 SLAFTS).
*> 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.
*
*> \date December 2016
*
*> \ingroup single_eig
*
* =====================================================================
SUBROUTINE SCHKHS( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
$ NOUNIT, A, LDA, H, T1, T2, U, LDU, Z, UZ, WR1,
$ WI1, WR2, WI2, WR3, WI3, EVECTL, EVECTR,
$ EVECTY, EVECTX, UU, TAU, WORK, NWORK, IWORK,
$ SELECT, RESULT, 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..--
* December 2016
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, LDU, NOUNIT, NSIZES, NTYPES, NWORK
REAL THRESH
* ..
* .. Array Arguments ..
LOGICAL DOTYPE( * ), SELECT( * )
INTEGER ISEED( 4 ), IWORK( * ), NN( * )
REAL A( LDA, * ), EVECTL( LDU, * ),
$ EVECTR( LDU, * ), EVECTX( LDU, * ),
$ EVECTY( LDU, * ), H( LDA, * ), RESULT( 14 ),
$ T1( LDA, * ), T2( LDA, * ), TAU( * ),
$ U( LDU, * ), UU( LDU, * ), UZ( LDU, * ),
$ WI1( * ), WI2( * ), WI3( * ), WORK( * ),
$ WR1( * ), WR2( * ), WR3( * ), Z( LDU, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0, ONE = 1.0 )
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, NSELC, NSELR, NTEST, NTESTT
REAL ANINV, ANORM, COND, CONDS, OVFL, RTOVFL, RTULP,
$ RTULPI, RTUNFL, TEMP1, TEMP2, ULP, ULPINV, UNFL
* ..
* .. Local Arrays ..
CHARACTER ADUMMA( 1 )
INTEGER IDUMMA( 1 ), IOLDSD( 4 ), KCONDS( MAXTYP ),
$ KMAGN( MAXTYP ), KMODE( MAXTYP ),
$ KTYPE( MAXTYP )
REAL DUMMA( 6 )
* ..
* .. External Functions ..
REAL SLAMCH
EXTERNAL SLAMCH
* ..
* .. External Subroutines ..
EXTERNAL SCOPY, SGEHRD, SGEMM, SGET10, SGET22, SHSEIN,
$ SHSEQR, SHST01, SLABAD, SLACPY, SLAFTS, SLASET,
$ SLASUM, SLATME, SLATMR, SLATMS, SORGHR, SORMHR,
$ STREVC, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, MIN, REAL, 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 = -28
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'SCHKHS', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 )
$ RETURN
*
* More important constants
*
UNFL = SLAMCH( 'Safe minimum' )
OVFL = SLAMCH( 'Overflow' )
CALL SLABAD( UNFL, OVFL )
ULP = SLAMCH( 'Epsilon' )*SLAMCH( '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 270 JSIZE = 1, NSIZES
N = NN( JSIZE )
IF( N.EQ.0 )
$ GO TO 270
N1 = MAX( 1, N )
ANINV = ONE / REAL( N1 )
*
IF( NSIZES.NE.1 ) THEN
MTYPES = MIN( MAXTYP, NTYPES )
ELSE
MTYPES = MIN( MAXTYP+1, NTYPES )
END IF
*
DO 260 JTYPE = 1, MTYPES
IF( .NOT.DOTYPE( JTYPE ) )
$ GO TO 260
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 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 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 SLASET( 'Full', LDA, N, ZERO, ZERO, 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 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 )
*
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 = 9999 )'Generator', IINFO, N, JTYPE,
$ IOLDSD
INFO = ABS( IINFO )
RETURN
END IF
*
100 CONTINUE
*
* Call SGEHRD to compute H and U, do tests.
*
CALL SLACPY( ' ', N, N, A, LDA, H, LDA )
*
NTEST = 1
*
ILO = 1
IHI = N
*
CALL SGEHRD( N, ILO, IHI, H, LDA, WORK, WORK( N+1 ),
$ NWORK-N, IINFO )
*
IF( IINFO.NE.0 ) THEN
RESULT( 1 ) = ULPINV
WRITE( NOUNIT, FMT = 9999 )'SGEHRD', IINFO, N, JTYPE,
$ IOLDSD
INFO = ABS( IINFO )
GO TO 250
END IF
*
DO 120 J = 1, N - 1
UU( J+1, J ) = ZERO
DO 110 I = J + 2, N
U( I, J ) = H( I, J )
UU( I, J ) = H( I, J )
H( I, J ) = ZERO
110 CONTINUE
120 CONTINUE
CALL SCOPY( N-1, WORK, 1, TAU, 1 )
CALL SORGHR( N, ILO, IHI, U, LDU, WORK, WORK( N+1 ),
$ NWORK-N, IINFO )
NTEST = 2
*
CALL SHST01( N, ILO, IHI, A, LDA, H, LDA, U, LDU, WORK,
$ NWORK, RESULT( 1 ) )
*
* Call SHSEQR to compute T1, T2 and Z, do tests.
*
* Eigenvalues only (WR3,WI3)
*
CALL SLACPY( ' ', N, N, H, LDA, T2, LDA )
NTEST = 3
RESULT( 3 ) = ULPINV
*
CALL SHSEQR( 'E', 'N', N, ILO, IHI, T2, LDA, WR3, WI3, UZ,
$ LDU, WORK, NWORK, IINFO )
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'SHSEQR(E)', IINFO, N, JTYPE,
$ IOLDSD
IF( IINFO.LE.N+2 ) THEN
INFO = ABS( IINFO )
GO TO 250
END IF
END IF
*
* Eigenvalues (WR2,WI2) and Full Schur Form (T2)
*
CALL SLACPY( ' ', N, N, H, LDA, T2, LDA )
*
CALL SHSEQR( 'S', 'N', N, ILO, IHI, T2, LDA, WR2, WI2, UZ,
$ LDU, WORK, NWORK, IINFO )
IF( IINFO.NE.0 .AND. IINFO.LE.N+2 ) THEN
WRITE( NOUNIT, FMT = 9999 )'SHSEQR(S)', IINFO, N, JTYPE,
$ IOLDSD
INFO = ABS( IINFO )
GO TO 250
END IF
*
* Eigenvalues (WR1,WI1), Schur Form (T1), and Schur vectors
* (UZ)
*
CALL SLACPY( ' ', N, N, H, LDA, T1, LDA )
CALL SLACPY( ' ', N, N, U, LDU, UZ, LDU )
*
CALL SHSEQR( 'S', 'V', N, ILO, IHI, T1, LDA, WR1, WI1, UZ,
$ LDU, WORK, NWORK, IINFO )
IF( IINFO.NE.0 .AND. IINFO.LE.N+2 ) THEN
WRITE( NOUNIT, FMT = 9999 )'SHSEQR(V)', IINFO, N, JTYPE,
$ IOLDSD
INFO = ABS( IINFO )
GO TO 250
END IF
*
* Compute Z = U' UZ
*
CALL SGEMM( 'T', 'N', N, N, N, ONE, U, LDU, UZ, LDU, ZERO,
$ Z, LDU )
NTEST = 8
*
* Do Tests 3: | H - Z T Z' | / ( |H| n ulp )
* and 4: | I - Z Z' | / ( n ulp )
*
CALL SHST01( N, ILO, IHI, H, LDA, T1, LDA, Z, LDU, WORK,
$ NWORK, RESULT( 3 ) )
*
* Do Tests 5: | A - UZ T (UZ)' | / ( |A| n ulp )
* and 6: | I - UZ (UZ)' | / ( n ulp )
*
CALL SHST01( N, ILO, IHI, A, LDA, T1, LDA, UZ, LDU, WORK,
$ NWORK, RESULT( 5 ) )
*
* Do Test 7: | T2 - T1 | / ( |T| n ulp )
*
CALL SGET10( N, N, T2, LDA, T1, LDA, WORK, RESULT( 7 ) )
*
* Do Test 8: | W2 - W1 | / ( max(|W1|,|W2|) ulp )
*
TEMP1 = ZERO
TEMP2 = ZERO
DO 130 J = 1, N
TEMP1 = MAX( TEMP1, ABS( WR1( J ) )+ABS( WI1( J ) ),
$ ABS( WR2( J ) )+ABS( WI2( J ) ) )
TEMP2 = MAX( TEMP2, ABS( WR1( J )-WR2( J ) )+
$ ABS( WI1( J )-WI2( 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 last max(N/4,1) real, max(N/4,1) complex eigenvectors
*
NSELC = 0
NSELR = 0
J = N
140 CONTINUE
IF( WI1( J ).EQ.ZERO ) THEN
IF( NSELR.LT.MAX( N / 4, 1 ) ) THEN
NSELR = NSELR + 1
SELECT( J ) = .TRUE.
ELSE
SELECT( J ) = .FALSE.
END IF
J = J - 1
ELSE
IF( NSELC.LT.MAX( N / 4, 1 ) ) THEN
NSELC = NSELC + 1
SELECT( J ) = .TRUE.
SELECT( J-1 ) = .FALSE.
ELSE
SELECT( J ) = .FALSE.
SELECT( J-1 ) = .FALSE.
END IF
J = J - 2
END IF
IF( J.GT.0 )
$ GO TO 140
*
CALL STREVC( 'Right', 'All', SELECT, N, T1, LDA, DUMMA, LDU,
$ EVECTR, LDU, N, IN, WORK, IINFO )
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'STREVC(R,A)', IINFO, N,
$ JTYPE, IOLDSD
INFO = ABS( IINFO )
GO TO 250
END IF
*
* Test 9: | TR - RW | / ( |T| |R| ulp )
*
CALL SGET22( 'N', 'N', 'N', N, T1, LDA, EVECTR, LDU, WR1,
$ WI1, WORK, DUMMA( 1 ) )
RESULT( 9 ) = DUMMA( 1 )
IF( DUMMA( 2 ).GT.THRESH ) THEN
WRITE( NOUNIT, FMT = 9998 )'Right', 'STREVC',
$ DUMMA( 2 ), N, JTYPE, IOLDSD
END IF
*
* Compute selected right eigenvectors and confirm that
* they agree with previous right eigenvectors
*
CALL STREVC( 'Right', 'Some', SELECT, N, T1, LDA, DUMMA,
$ LDU, EVECTL, LDU, N, IN, WORK, IINFO )
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'STREVC(R,S)', IINFO, N,
$ JTYPE, IOLDSD
INFO = ABS( IINFO )
GO TO 250
END IF
*
K = 1
MATCH = .TRUE.
DO 170 J = 1, N
IF( SELECT( J ) .AND. WI1( J ).EQ.ZERO ) THEN
DO 150 JJ = 1, N
IF( EVECTR( JJ, J ).NE.EVECTL( JJ, K ) ) THEN
MATCH = .FALSE.
GO TO 180
END IF
150 CONTINUE
K = K + 1
ELSE IF( SELECT( J ) .AND. WI1( J ).NE.ZERO ) THEN
DO 160 JJ = 1, N
IF( EVECTR( JJ, J ).NE.EVECTL( JJ, K ) .OR.
$ EVECTR( JJ, J+1 ).NE.EVECTL( JJ, K+1 ) ) THEN
MATCH = .FALSE.
GO TO 180
END IF
160 CONTINUE
K = K + 2
END IF
170 CONTINUE
180 CONTINUE
IF( .NOT.MATCH )
$ WRITE( NOUNIT, FMT = 9997 )'Right', 'STREVC', N, JTYPE,
$ IOLDSD
*
* Compute the Left eigenvector Matrix:
*
NTEST = 10
RESULT( 10 ) = ULPINV
CALL STREVC( 'Left', 'All', SELECT, N, T1, LDA, EVECTL, LDU,
$ DUMMA, LDU, N, IN, WORK, IINFO )
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'STREVC(L,A)', IINFO, N,
$ JTYPE, IOLDSD
INFO = ABS( IINFO )
GO TO 250
END IF
*
* Test 10: | LT - WL | / ( |T| |L| ulp )
*
CALL SGET22( 'Trans', 'N', 'Conj', N, T1, LDA, EVECTL, LDU,
$ WR1, WI1, WORK, DUMMA( 3 ) )
RESULT( 10 ) = DUMMA( 3 )
IF( DUMMA( 4 ).GT.THRESH ) THEN
WRITE( NOUNIT, FMT = 9998 )'Left', 'STREVC', DUMMA( 4 ),
$ N, JTYPE, IOLDSD
END IF
*
* Compute selected left eigenvectors and confirm that
* they agree with previous left eigenvectors
*
CALL STREVC( 'Left', 'Some', SELECT, N, T1, LDA, EVECTR,
$ LDU, DUMMA, LDU, N, IN, WORK, IINFO )
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'STREVC(L,S)', IINFO, N,
$ JTYPE, IOLDSD
INFO = ABS( IINFO )
GO TO 250
END IF
*
K = 1
MATCH = .TRUE.
DO 210 J = 1, N
IF( SELECT( J ) .AND. WI1( J ).EQ.ZERO ) THEN
DO 190 JJ = 1, N
IF( EVECTL( JJ, J ).NE.EVECTR( JJ, K ) ) THEN
MATCH = .FALSE.
GO TO 220
END IF
190 CONTINUE
K = K + 1
ELSE IF( SELECT( J ) .AND. WI1( J ).NE.ZERO ) THEN
DO 200 JJ = 1, N
IF( EVECTL( JJ, J ).NE.EVECTR( JJ, K ) .OR.
$ EVECTL( JJ, J+1 ).NE.EVECTR( JJ, K+1 ) ) THEN
MATCH = .FALSE.
GO TO 220
END IF
200 CONTINUE
K = K + 2
END IF
210 CONTINUE
220 CONTINUE
IF( .NOT.MATCH )
$ WRITE( NOUNIT, FMT = 9997 )'Left', 'STREVC', N, JTYPE,
$ IOLDSD
*
* Call SHSEIN for Right eigenvectors of H, do test 11
*
NTEST = 11
RESULT( 11 ) = ULPINV
DO 230 J = 1, N
SELECT( J ) = .TRUE.
230 CONTINUE
*
CALL SHSEIN( 'Right', 'Qr', 'Ninitv', SELECT, N, H, LDA,
$ WR3, WI3, DUMMA, LDU, EVECTX, LDU, N1, IN,
$ WORK, IWORK, IWORK, IINFO )
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'SHSEIN(R)', IINFO, N, JTYPE,
$ IOLDSD
INFO = ABS( IINFO )
IF( IINFO.LT.0 )
$ GO TO 250
ELSE
*
* Test 11: | HX - XW | / ( |H| |X| ulp )
*
* (from inverse iteration)
*
CALL SGET22( 'N', 'N', 'N', N, H, LDA, EVECTX, LDU, WR3,
$ WI3, WORK, DUMMA( 1 ) )
IF( DUMMA( 1 ).LT.ULPINV )
$ RESULT( 11 ) = DUMMA( 1 )*ANINV
IF( DUMMA( 2 ).GT.THRESH ) THEN
WRITE( NOUNIT, FMT = 9998 )'Right', 'SHSEIN',
$ DUMMA( 2 ), N, JTYPE, IOLDSD
END IF
END IF
*
* Call SHSEIN for Left eigenvectors of H, do test 12
*
NTEST = 12
RESULT( 12 ) = ULPINV
DO 240 J = 1, N
SELECT( J ) = .TRUE.
240 CONTINUE
*
CALL SHSEIN( 'Left', 'Qr', 'Ninitv', SELECT, N, H, LDA, WR3,
$ WI3, EVECTY, LDU, DUMMA, LDU, N1, IN, WORK,
$ IWORK, IWORK, IINFO )
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'SHSEIN(L)', IINFO, N, JTYPE,
$ IOLDSD
INFO = ABS( IINFO )
IF( IINFO.LT.0 )
$ GO TO 250
ELSE
*
* Test 12: | YH - WY | / ( |H| |Y| ulp )
*
* (from inverse iteration)
*
CALL SGET22( 'C', 'N', 'C', N, H, LDA, EVECTY, LDU, WR3,
$ WI3, WORK, DUMMA( 3 ) )
IF( DUMMA( 3 ).LT.ULPINV )
$ RESULT( 12 ) = DUMMA( 3 )*ANINV
IF( DUMMA( 4 ).GT.THRESH ) THEN
WRITE( NOUNIT, FMT = 9998 )'Left', 'SHSEIN',
$ DUMMA( 4 ), N, JTYPE, IOLDSD
END IF
END IF
*
* Call SORMHR for Right eigenvectors of A, do test 13
*
NTEST = 13
RESULT( 13 ) = ULPINV
*
CALL SORMHR( 'Left', 'No transpose', N, N, ILO, IHI, UU,
$ LDU, TAU, EVECTX, LDU, WORK, NWORK, IINFO )
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'SORMHR(R)', IINFO, N, JTYPE,
$ IOLDSD
INFO = ABS( IINFO )
IF( IINFO.LT.0 )
$ GO TO 250
ELSE
*
* Test 13: | AX - XW | / ( |A| |X| ulp )
*
* (from inverse iteration)
*
CALL SGET22( 'N', 'N', 'N', N, A, LDA, EVECTX, LDU, WR3,
$ WI3, WORK, DUMMA( 1 ) )
IF( DUMMA( 1 ).LT.ULPINV )
$ RESULT( 13 ) = DUMMA( 1 )*ANINV
END IF
*
* Call SORMHR for Left eigenvectors of A, do test 14
*
NTEST = 14
RESULT( 14 ) = ULPINV
*
CALL SORMHR( 'Left', 'No transpose', N, N, ILO, IHI, UU,
$ LDU, TAU, EVECTY, LDU, WORK, NWORK, IINFO )
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'SORMHR(L)', IINFO, N, JTYPE,
$ IOLDSD
INFO = ABS( IINFO )
IF( IINFO.LT.0 )
$ GO TO 250
ELSE
*
* Test 14: | YA - WY | / ( |A| |Y| ulp )
*
* (from inverse iteration)
*
CALL SGET22( 'C', 'N', 'C', N, A, LDA, EVECTY, LDU, WR3,
$ WI3, WORK, DUMMA( 3 ) )
IF( DUMMA( 3 ).LT.ULPINV )
$ RESULT( 14 ) = DUMMA( 3 )*ANINV
END IF
*
* End of Loop -- Check for RESULT(j) > THRESH
*
250 CONTINUE
*
NTESTT = NTESTT + NTEST
CALL SLAFTS( 'SHS', N, N, JTYPE, NTEST, RESULT, IOLDSD,
$ THRESH, NOUNIT, NERRS )
*
260 CONTINUE
270 CONTINUE
*
* Summary
*
CALL SLASUM( 'SHS', NOUNIT, NERRS, NTESTT )
*
RETURN
*
9999 FORMAT( ' SCHKHS: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
$ I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
9998 FORMAT( ' SCHKHS: ', A, ' Eigenvectors from ', A, ' incorrectly ',
$ 'normalized.', / ' Bits of error=', 0P, G10.3, ',', 9X,
$ 'N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5,
$ ')' )
9997 FORMAT( ' SCHKHS: Selected ', A, ' Eigenvectors from ', A,
$ ' do not match other eigenvectors ', 9X, 'N=', I6,
$ ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
*
* End of SCHKHS
*
END