testdata/lapack/TESTING/EIG/zchkhb2stg.f
*> \brief \b ZCHKHBSTG
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZCHKHBSTG( NSIZES, NN, NWDTHS, KK, NTYPES, DOTYPE,
* ISEED, THRESH, NOUNIT, A, LDA, SD, SE, D1,
* D2, D3, U, LDU, WORK, LWORK, RWORK RESULT,
* INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, LDA, LDU, LWORK, NOUNIT, NSIZES, NTYPES,
* $ NWDTHS
* DOUBLE PRECISION THRESH
* ..
* .. Array Arguments ..
* LOGICAL DOTYPE( * )
* INTEGER ISEED( 4 ), KK( * ), NN( * )
* DOUBLE PRECISION RESULT( * ), RWORK( * ), SD( * ), SE( * )
* COMPLEX*16 A( LDA, * ), U( LDU, * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZCHKHBSTG tests the reduction of a Hermitian band matrix to tridiagonal
*> from, used with the Hermitian eigenvalue problem.
*>
*> ZHBTRD factors a Hermitian band matrix A as U S U* , where * means
*> conjugate transpose, S is symmetric tridiagonal, and U is unitary.
*> ZHBTRD can use either just the lower or just the upper triangle
*> of A; ZCHKHBSTG checks both cases.
*>
*> ZHETRD_HB2ST factors a Hermitian band matrix A as U S U* ,
*> where * means conjugate transpose, S is symmetric tridiagonal, and U is
*> unitary. ZHETRD_HB2ST can use either just the lower or just
*> the upper triangle of A; ZCHKHBSTG checks both cases.
*>
*> DSTEQR factors S as Z D1 Z'.
*> D1 is the matrix of eigenvalues computed when Z is not computed
*> and from the S resulting of DSBTRD "U" (used as reference for DSYTRD_SB2ST)
*> D2 is the matrix of eigenvalues computed when Z is not computed
*> and from the S resulting of DSYTRD_SB2ST "U".
*> D3 is the matrix of eigenvalues computed when Z is not computed
*> and from the S resulting of DSYTRD_SB2ST "L".
*>
*> When ZCHKHBSTG is called, a number of matrix "sizes" ("n's"), a number
*> of bandwidths ("k's"), and a number of matrix "types" are
*> specified. For each size ("n"), each bandwidth ("k") less than or
*> equal to "n", and each type of matrix, one matrix will be generated
*> and used to test the hermitian banded reduction routine. For each
*> matrix, a number of tests will be performed:
*>
*> (1) | A - V S V* | / ( |A| n ulp ) computed by ZHBTRD with
*> UPLO='U'
*>
*> (2) | I - UU* | / ( n ulp )
*>
*> (3) | A - V S V* | / ( |A| n ulp ) computed by ZHBTRD with
*> UPLO='L'
*>
*> (4) | I - UU* | / ( n ulp )
*>
*> (5) | D1 - D2 | / ( |D1| ulp ) where D1 is computed by
*> DSBTRD with UPLO='U' and
*> D2 is computed by
*> ZHETRD_HB2ST with UPLO='U'
*>
*> (6) | D1 - D3 | / ( |D1| ulp ) where D1 is computed by
*> DSBTRD with UPLO='U' and
*> D3 is computed by
*> ZHETRD_HB2ST with UPLO='L'
*>
*> 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 diagonal matrix with evenly spaced entries
*> 1, ..., ULP and random signs.
*> (ULP = (first number larger than 1) - 1 )
*> (4) A diagonal matrix with geometrically spaced entries
*> 1, ..., ULP and random signs.
*> (5) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP
*> and random signs.
*>
*> (6) Same as (4), but multiplied by SQRT( overflow threshold )
*> (7) Same as (4), but multiplied by SQRT( underflow threshold )
*>
*> (8) A matrix of the form U* D U, where U is unitary and
*> D has evenly spaced entries 1, ..., ULP with random signs
*> on the diagonal.
*>
*> (9) A matrix of the form U* D U, where U is unitary and
*> D has geometrically spaced entries 1, ..., ULP with random
*> signs on the diagonal.
*>
*> (10) A matrix of the form U* D U, where U is unitary and
*> D has "clustered" entries 1, ULP,..., ULP with random
*> signs on the diagonal.
*>
*> (11) Same as (8), but multiplied by SQRT( overflow threshold )
*> (12) Same as (8), but multiplied by SQRT( underflow threshold )
*>
*> (13) Hermitian matrix with random entries chosen from (-1,1).
*> (14) Same as (13), but multiplied by SQRT( overflow threshold )
*> (15) Same as (13), but multiplied by SQRT( underflow threshold )
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> NSIZES is INTEGER
*> The number of sizes of matrices to use. If it is zero,
*> ZCHKHBSTG 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] NWDTHS
*> \verbatim
*> NWDTHS is INTEGER
*> The number of bandwidths to use. If it is zero,
*> ZCHKHBSTG does nothing. It must be at least zero.
*> \endverbatim
*>
*> \param[in] KK
*> \verbatim
*> KK is INTEGER array, dimension (NWDTHS)
*> An array containing the bandwidths to be used for the band
*> matrices. 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, ZCHKHBSTG
*> 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 ZCHKHBSTG 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] NOUNIT
*> \verbatim
*> NOUNIT is INTEGER
*> The FORTRAN unit number for printing out error messages
*> (e.g., if a routine returns IINFO not equal to 0.)
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*> A is COMPLEX*16 array, dimension
*> (LDA, max(NN))
*> Used to hold the matrix whose eigenvalues are to be
*> computed.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of A. It must be at least 2 (not 1!)
*> and at least max( KK )+1.
*> \endverbatim
*>
*> \param[out] SD
*> \verbatim
*> SD is DOUBLE PRECISION array, dimension (max(NN))
*> Used to hold the diagonal of the tridiagonal matrix computed
*> by ZHBTRD.
*> \endverbatim
*>
*> \param[out] SE
*> \verbatim
*> SE is DOUBLE PRECISION array, dimension (max(NN))
*> Used to hold the off-diagonal of the tridiagonal matrix
*> computed by ZHBTRD.
*> \endverbatim
*>
*> \param[out] U
*> \verbatim
*> U is COMPLEX*16 array, dimension (LDU, max(NN))
*> Used to hold the unitary matrix computed by ZHBTRD.
*> \endverbatim
*>
*> \param[in] LDU
*> \verbatim
*> LDU is INTEGER
*> The leading dimension of U. It must be at least 1
*> and at least max( NN ).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX*16 array, dimension (LWORK)
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> The number of entries in WORK. This must be at least
*> max( LDA+1, max(NN)+1 )*max(NN).
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is DOUBLE PRECISION array
*> \endverbatim
*>
*> \param[out] RESULT
*> \verbatim
*> RESULT is DOUBLE PRECISION array, dimension (4)
*> The values computed by the tests described above.
*> The values are currently limited to 1/ulp, to avoid
*> overflow.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> If 0, then everything ran OK.
*>
*>-----------------------------------------------------------------------
*>
*> Some Local Variables and Parameters:
*> ---- ----- --------- --- ----------
*> ZERO, ONE Real 0 and 1.
*> MAXTYP The number of types defined.
*> NTEST The number of tests performed, or which can
*> be performed so far, for the current matrix.
*> NTESTT The total number of tests performed so far.
*> NMAX Largest value in NN.
*> NMATS The number of matrices generated so far.
*> NERRS The number of tests which have exceeded THRESH
*> so far.
*> COND, 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 Square roots of the previous 2 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) )
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date June 2017
*
*> \ingroup complex16_eig
*
* =====================================================================
SUBROUTINE ZCHKHB2STG( NSIZES, NN, NWDTHS, KK, NTYPES, DOTYPE,
$ ISEED, THRESH, NOUNIT, A, LDA, SD, SE, D1,
$ D2, D3, U, LDU, WORK, LWORK, RWORK, RESULT,
$ INFO )
*
* -- LAPACK test routine (version 3.7.1) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* June 2017
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, LDU, LWORK, NOUNIT, NSIZES, NTYPES,
$ NWDTHS
DOUBLE PRECISION THRESH
* ..
* .. Array Arguments ..
LOGICAL DOTYPE( * )
INTEGER ISEED( 4 ), KK( * ), NN( * )
DOUBLE PRECISION RESULT( * ), RWORK( * ), SD( * ), SE( * ),
$ D1( * ), D2( * ), D3( * )
COMPLEX*16 A( LDA, * ), U( LDU, * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
COMPLEX*16 CZERO, CONE
PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
$ CONE = ( 1.0D+0, 0.0D+0 ) )
DOUBLE PRECISION ZERO, ONE, TWO, TEN
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0,
$ TEN = 10.0D+0 )
DOUBLE PRECISION HALF
PARAMETER ( HALF = ONE / TWO )
INTEGER MAXTYP
PARAMETER ( MAXTYP = 15 )
* ..
* .. Local Scalars ..
LOGICAL BADNN, BADNNB
INTEGER I, IINFO, IMODE, ITYPE, J, JC, JCOL, JR, JSIZE,
$ JTYPE, JWIDTH, K, KMAX, LH, LW, MTYPES, N,
$ NERRS, NMATS, NMAX, NTEST, NTESTT
DOUBLE PRECISION ANINV, ANORM, COND, OVFL, RTOVFL, RTUNFL,
$ TEMP1, TEMP2, TEMP3, TEMP4, ULP, ULPINV, UNFL
* ..
* .. Local Arrays ..
INTEGER IDUMMA( 1 ), IOLDSD( 4 ), KMAGN( MAXTYP ),
$ KMODE( MAXTYP ), KTYPE( MAXTYP )
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH
EXTERNAL DLAMCH
* ..
* .. External Subroutines ..
EXTERNAL DLASUM, XERBLA, ZHBT21, ZHBTRD, ZLACPY, ZLASET,
$ ZLATMR, ZLATMS, ZHETRD_HB2ST, ZSTEQR
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DBLE, DCONJG, MAX, MIN, SQRT
* ..
* .. Data statements ..
DATA KTYPE / 1, 2, 5*4, 5*5, 3*8 /
DATA KMAGN / 2*1, 1, 1, 1, 2, 3, 1, 1, 1, 2, 3, 1,
$ 2, 3 /
DATA KMODE / 2*0, 4, 3, 1, 4, 4, 4, 3, 1, 4, 4, 0,
$ 0, 0 /
* ..
* .. Executable Statements ..
*
* Check for errors
*
NTESTT = 0
INFO = 0
*
* Important constants
*
BADNN = .FALSE.
NMAX = 1
DO 10 J = 1, NSIZES
NMAX = MAX( NMAX, NN( J ) )
IF( NN( J ).LT.0 )
$ BADNN = .TRUE.
10 CONTINUE
*
BADNNB = .FALSE.
KMAX = 0
DO 20 J = 1, NSIZES
KMAX = MAX( KMAX, KK( J ) )
IF( KK( J ).LT.0 )
$ BADNNB = .TRUE.
20 CONTINUE
KMAX = MIN( NMAX-1, KMAX )
*
* Check for errors
*
IF( NSIZES.LT.0 ) THEN
INFO = -1
ELSE IF( BADNN ) THEN
INFO = -2
ELSE IF( NWDTHS.LT.0 ) THEN
INFO = -3
ELSE IF( BADNNB ) THEN
INFO = -4
ELSE IF( NTYPES.LT.0 ) THEN
INFO = -5
ELSE IF( LDA.LT.KMAX+1 ) THEN
INFO = -11
ELSE IF( LDU.LT.NMAX ) THEN
INFO = -15
ELSE IF( ( MAX( LDA, NMAX )+1 )*NMAX.GT.LWORK ) THEN
INFO = -17
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZCHKHBSTG', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 .OR. NWDTHS.EQ.0 )
$ RETURN
*
* More Important constants
*
UNFL = DLAMCH( 'Safe minimum' )
OVFL = ONE / UNFL
ULP = DLAMCH( 'Epsilon' )*DLAMCH( 'Base' )
ULPINV = ONE / ULP
RTUNFL = SQRT( UNFL )
RTOVFL = SQRT( OVFL )
*
* Loop over sizes, types
*
NERRS = 0
NMATS = 0
*
DO 190 JSIZE = 1, NSIZES
N = NN( JSIZE )
ANINV = ONE / DBLE( MAX( 1, N ) )
*
DO 180 JWIDTH = 1, NWDTHS
K = KK( JWIDTH )
IF( K.GT.N )
$ GO TO 180
K = MAX( 0, MIN( N-1, K ) )
*
IF( NSIZES.NE.1 ) THEN
MTYPES = MIN( MAXTYP, NTYPES )
ELSE
MTYPES = MIN( MAXTYP+1, NTYPES )
END IF
*
DO 170 JTYPE = 1, MTYPES
IF( .NOT.DOTYPE( JTYPE ) )
$ GO TO 170
NMATS = NMATS + 1
NTEST = 0
*
DO 30 J = 1, 4
IOLDSD( J ) = ISEED( J )
30 CONTINUE
*
* Compute "A".
* Store as "Upper"; later, we will copy to other format.
*
* Control parameters:
*
* KMAGN KMODE KTYPE
* =1 O(1) clustered 1 zero
* =2 large clustered 2 identity
* =3 small exponential (none)
* =4 arithmetic diagonal, (w/ eigenvalues)
* =5 random log hermitian, w/ eigenvalues
* =6 random (none)
* =7 random diagonal
* =8 random hermitian
* =9 positive definite
* =10 diagonally dominant tridiagonal
*
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
IF( JTYPE.LE.15 ) THEN
COND = ULPINV
ELSE
COND = ULPINV*ANINV / TEN
END IF
*
* Special Matrices -- Identity & Jordan block
*
* Zero
*
IF( ITYPE.EQ.1 ) THEN
IINFO = 0
*
ELSE IF( ITYPE.EQ.2 ) THEN
*
* Identity
*
DO 80 JCOL = 1, N
A( K+1, JCOL ) = ANORM
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, 'Q', A( K+1, 1 ), LDA,
$ WORK, IINFO )
*
ELSE IF( ITYPE.EQ.5 ) THEN
*
* Hermitian, eigenvalues specified
*
CALL ZLATMS( N, N, 'S', ISEED, 'H', RWORK, IMODE,
$ COND, ANORM, K, K, 'Q', A, LDA, WORK,
$ IINFO )
*
ELSE IF( ITYPE.EQ.7 ) THEN
*
* Diagonal, random eigenvalues
*
CALL ZLATMR( N, N, 'S', ISEED, 'H', WORK, 6, ONE,
$ CONE, 'T', 'N', WORK( N+1 ), 1, ONE,
$ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, 0, 0,
$ ZERO, ANORM, 'Q', A( K+1, 1 ), LDA,
$ IDUMMA, IINFO )
*
ELSE IF( ITYPE.EQ.8 ) THEN
*
* Hermitian, random eigenvalues
*
CALL ZLATMR( N, N, 'S', ISEED, 'H', WORK, 6, ONE,
$ CONE, 'T', 'N', WORK( N+1 ), 1, ONE,
$ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, K, K,
$ ZERO, ANORM, 'Q', A, LDA, IDUMMA, IINFO )
*
ELSE IF( ITYPE.EQ.9 ) THEN
*
* Positive definite, eigenvalues specified.
*
CALL ZLATMS( N, N, 'S', ISEED, 'P', RWORK, IMODE,
$ COND, ANORM, K, K, 'Q', A, LDA,
$ WORK( N+1 ), IINFO )
*
ELSE IF( ITYPE.EQ.10 ) THEN
*
* Positive definite tridiagonal, eigenvalues specified.
*
IF( N.GT.1 )
$ K = MAX( 1, K )
CALL ZLATMS( N, N, 'S', ISEED, 'P', RWORK, IMODE,
$ COND, ANORM, 1, 1, 'Q', A( K, 1 ), LDA,
$ WORK, IINFO )
DO 90 I = 2, N
TEMP1 = ABS( A( K, I ) ) /
$ SQRT( ABS( A( K+1, I-1 )*A( K+1, I ) ) )
IF( TEMP1.GT.HALF ) THEN
A( K, I ) = HALF*SQRT( ABS( A( K+1,
$ I-1 )*A( K+1, I ) ) )
END IF
90 CONTINUE
*
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 ZHBTRD to compute S and U from upper triangle.
*
CALL ZLACPY( ' ', K+1, N, A, LDA, WORK, LDA )
*
NTEST = 1
CALL ZHBTRD( 'V', 'U', N, K, WORK, LDA, SD, SE, U, LDU,
$ WORK( LDA*N+1 ), IINFO )
*
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'ZHBTRD(U)', IINFO, N,
$ JTYPE, IOLDSD
INFO = ABS( IINFO )
IF( IINFO.LT.0 ) THEN
RETURN
ELSE
RESULT( 1 ) = ULPINV
GO TO 150
END IF
END IF
*
* Do tests 1 and 2
*
CALL ZHBT21( 'Upper', N, K, 1, A, LDA, SD, SE, U, LDU,
$ WORK, RWORK, RESULT( 1 ) )
*
* Before converting A into lower for DSBTRD, run DSYTRD_SB2ST
* otherwise matrix A will be converted to lower and then need
* to be converted back to upper in order to run the upper case
* ofDSYTRD_SB2ST
*
* Compute D1 the eigenvalues resulting from the tridiagonal
* form using the DSBTRD and used as reference to compare
* with the DSYTRD_SB2ST routine
*
* Compute D1 from the DSBTRD and used as reference for the
* DSYTRD_SB2ST
*
CALL DCOPY( N, SD, 1, D1, 1 )
IF( N.GT.0 )
$ CALL DCOPY( N-1, SE, 1, RWORK, 1 )
*
CALL ZSTEQR( 'N', N, D1, RWORK, WORK, LDU,
$ RWORK( N+1 ), IINFO )
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'ZSTEQR(N)', IINFO, N,
$ JTYPE, IOLDSD
INFO = ABS( IINFO )
IF( IINFO.LT.0 ) THEN
RETURN
ELSE
RESULT( 5 ) = ULPINV
GO TO 150
END IF
END IF
*
* DSYTRD_SB2ST Upper case is used to compute D2.
* Note to set SD and SE to zero to be sure not reusing
* the one from above. Compare it with D1 computed
* using the DSBTRD.
*
CALL DLASET( 'Full', N, 1, ZERO, ZERO, SD, 1 )
CALL DLASET( 'Full', N, 1, ZERO, ZERO, SE, 1 )
CALL ZLACPY( ' ', K+1, N, A, LDA, U, LDU )
LH = MAX(1, 4*N)
LW = LWORK - LH
CALL ZHETRD_HB2ST( 'N', 'N', "U", N, K, U, LDU, SD, SE,
$ WORK, LH, WORK( LH+1 ), LW, IINFO )
*
* Compute D2 from the DSYTRD_SB2ST Upper case
*
CALL DCOPY( N, SD, 1, D2, 1 )
IF( N.GT.0 )
$ CALL DCOPY( N-1, SE, 1, RWORK, 1 )
*
CALL ZSTEQR( 'N', N, D2, RWORK, WORK, LDU,
$ RWORK( N+1 ), IINFO )
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'ZSTEQR(N)', IINFO, N,
$ JTYPE, IOLDSD
INFO = ABS( IINFO )
IF( IINFO.LT.0 ) THEN
RETURN
ELSE
RESULT( 5 ) = ULPINV
GO TO 150
END IF
END IF
*
* Convert A from Upper-Triangle-Only storage to
* Lower-Triangle-Only storage.
*
DO 120 JC = 1, N
DO 110 JR = 0, MIN( K, N-JC )
A( JR+1, JC ) = DCONJG( A( K+1-JR, JC+JR ) )
110 CONTINUE
120 CONTINUE
DO 140 JC = N + 1 - K, N
DO 130 JR = MIN( K, N-JC ) + 1, K
A( JR+1, JC ) = ZERO
130 CONTINUE
140 CONTINUE
*
* Call ZHBTRD to compute S and U from lower triangle
*
CALL ZLACPY( ' ', K+1, N, A, LDA, WORK, LDA )
*
NTEST = 3
CALL ZHBTRD( 'V', 'L', N, K, WORK, LDA, SD, SE, U, LDU,
$ WORK( LDA*N+1 ), IINFO )
*
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'ZHBTRD(L)', IINFO, N,
$ JTYPE, IOLDSD
INFO = ABS( IINFO )
IF( IINFO.LT.0 ) THEN
RETURN
ELSE
RESULT( 3 ) = ULPINV
GO TO 150
END IF
END IF
NTEST = 4
*
* Do tests 3 and 4
*
CALL ZHBT21( 'Lower', N, K, 1, A, LDA, SD, SE, U, LDU,
$ WORK, RWORK, RESULT( 3 ) )
*
* DSYTRD_SB2ST Lower case is used to compute D3.
* Note to set SD and SE to zero to be sure not reusing
* the one from above. Compare it with D1 computed
* using the DSBTRD.
*
CALL DLASET( 'Full', N, 1, ZERO, ZERO, SD, 1 )
CALL DLASET( 'Full', N, 1, ZERO, ZERO, SE, 1 )
CALL ZLACPY( ' ', K+1, N, A, LDA, U, LDU )
LH = MAX(1, 4*N)
LW = LWORK - LH
CALL ZHETRD_HB2ST( 'N', 'N', "L", N, K, U, LDU, SD, SE,
$ WORK, LH, WORK( LH+1 ), LW, IINFO )
*
* Compute D3 from the 2-stage Upper case
*
CALL DCOPY( N, SD, 1, D3, 1 )
IF( N.GT.0 )
$ CALL DCOPY( N-1, SE, 1, RWORK, 1 )
*
CALL ZSTEQR( 'N', N, D3, RWORK, WORK, LDU,
$ RWORK( N+1 ), IINFO )
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'ZSTEQR(N)', IINFO, N,
$ JTYPE, IOLDSD
INFO = ABS( IINFO )
IF( IINFO.LT.0 ) THEN
RETURN
ELSE
RESULT( 6 ) = ULPINV
GO TO 150
END IF
END IF
*
*
* Do Tests 3 and 4 which are similar to 11 and 12 but with the
* D1 computed using the standard 1-stage reduction as reference
*
NTEST = 6
TEMP1 = ZERO
TEMP2 = ZERO
TEMP3 = ZERO
TEMP4 = ZERO
*
DO 151 J = 1, N
TEMP1 = MAX( TEMP1, ABS( D1( J ) ), ABS( D2( J ) ) )
TEMP2 = MAX( TEMP2, ABS( D1( J )-D2( J ) ) )
TEMP3 = MAX( TEMP3, ABS( D1( J ) ), ABS( D3( J ) ) )
TEMP4 = MAX( TEMP4, ABS( D1( J )-D3( J ) ) )
151 CONTINUE
*
RESULT(5) = TEMP2 / MAX( UNFL, ULP*MAX( TEMP1, TEMP2 ) )
RESULT(6) = TEMP4 / MAX( UNFL, ULP*MAX( TEMP3, TEMP4 ) )
*
* End of Loop -- Check for RESULT(j) > THRESH
*
150 CONTINUE
NTESTT = NTESTT + NTEST
*
* Print out tests which fail.
*
DO 160 JR = 1, NTEST
IF( RESULT( JR ).GE.THRESH ) THEN
*
* If this is the first test to fail,
* print a header to the data file.
*
IF( NERRS.EQ.0 ) THEN
WRITE( NOUNIT, FMT = 9998 )'ZHB'
WRITE( NOUNIT, FMT = 9997 )
WRITE( NOUNIT, FMT = 9996 )
WRITE( NOUNIT, FMT = 9995 )'Hermitian'
WRITE( NOUNIT, FMT = 9994 )'unitary', '*',
$ 'conjugate transpose', ( '*', J = 1, 6 )
END IF
NERRS = NERRS + 1
WRITE( NOUNIT, FMT = 9993 )N, K, IOLDSD, JTYPE,
$ JR, RESULT( JR )
END IF
160 CONTINUE
*
170 CONTINUE
180 CONTINUE
190 CONTINUE
*
* Summary
*
CALL DLASUM( 'ZHB', NOUNIT, NERRS, NTESTT )
RETURN
*
9999 FORMAT( ' ZCHKHBSTG: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
$ I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
9998 FORMAT( / 1X, A3,
$ ' -- Complex Hermitian Banded Tridiagonal Reduction Routines'
$ )
9997 FORMAT( ' Matrix types (see DCHK23 for details): ' )
*
9996 FORMAT( / ' Special Matrices:',
$ / ' 1=Zero matrix. ',
$ ' 5=Diagonal: clustered entries.',
$ / ' 2=Identity matrix. ',
$ ' 6=Diagonal: large, evenly spaced.',
$ / ' 3=Diagonal: evenly spaced entries. ',
$ ' 7=Diagonal: small, evenly spaced.',
$ / ' 4=Diagonal: geometr. spaced entries.' )
9995 FORMAT( ' Dense ', A, ' Banded Matrices:',
$ / ' 8=Evenly spaced eigenvals. ',
$ ' 12=Small, evenly spaced eigenvals.',
$ / ' 9=Geometrically spaced eigenvals. ',
$ ' 13=Matrix with random O(1) entries.',
$ / ' 10=Clustered eigenvalues. ',
$ ' 14=Matrix with large random entries.',
$ / ' 11=Large, evenly spaced eigenvals. ',
$ ' 15=Matrix with small random entries.' )
*
9994 FORMAT( / ' Tests performed: (S is Tridiag, U is ', A, ',',
$ / 20X, A, ' means ', A, '.', / ' UPLO=''U'':',
$ / ' 1= | A - U S U', A1, ' | / ( |A| n ulp ) ',
$ ' 2= | I - U U', A1, ' | / ( n ulp )', / ' UPLO=''L'':',
$ / ' 3= | A - U S U', A1, ' | / ( |A| n ulp ) ',
$ ' 4= | I - U U', A1, ' | / ( n ulp )' / ' Eig check:',
$ /' 5= | D1 - D2', '', ' | / ( |D1| ulp ) ',
$ ' 6= | D1 - D3', '', ' | / ( |D1| ulp ) ' )
9993 FORMAT( ' N=', I5, ', K=', I4, ', seed=', 4( I4, ',' ), ' type ',
$ I2, ', test(', I2, ')=', G10.3 )
*
* End of ZCHKHBSTG
*
END