OpenBLAS/lapack-netlib/TESTING/EIG/dchkbb.f

*> \brief \b DCHKBB
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE DCHKBB( NSIZES, MVAL, NVAL, NWDTHS, KK, NTYPES, DOTYPE,
*                          NRHS, ISEED, THRESH, NOUNIT, A, LDA, AB, LDAB,
*                          BD, BE, Q, LDQ, P, LDP, C, LDC, CC, WORK,
*                          LWORK, RESULT, INFO )
*
*       .. Scalar Arguments ..
*       INTEGER            INFO, LDA, LDAB, LDC, LDP, LDQ, LWORK, NOUNIT,
*      $                   NRHS, NSIZES, NTYPES, NWDTHS
*       DOUBLE PRECISION   THRESH
*       ..
*       .. Array Arguments ..
*       LOGICAL            DOTYPE( * )
*       INTEGER            ISEED( 4 ), KK( * ), MVAL( * ), NVAL( * )
*       DOUBLE PRECISION   A( LDA, * ), AB( LDAB, * ), BD( * ), BE( * ),
*      $                   C( LDC, * ), CC( LDC, * ), P( LDP, * ),
*      $                   Q( LDQ, * ), RESULT( * ), WORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DCHKBB tests the reduction of a general real rectangular band
*> matrix to bidiagonal form.
*>
*> DGBBRD factors a general band matrix A as  Q B P* , where * means
*> transpose, B is upper bidiagonal, and Q and P are orthogonal;
*> DGBBRD can also overwrite a given matrix C with Q* C .
*>
*> For each pair of matrix dimensions (M,N) and each selected matrix
*> type, an M by N matrix A and an M by NRHS matrix C are generated.
*> The problem dimensions are as follows
*>    A:          M x N
*>    Q:          M x M
*>    P:          N x N
*>    B:          min(M,N) x min(M,N)
*>    C:          M x NRHS
*>
*> For each generated matrix, 4 tests are performed:
*>
*> (1)   | A - Q B PT | / ( |A| max(M,N) ulp ), PT = P'
*>
*> (2)   | I - Q' Q | / ( M ulp )
*>
*> (3)   | I - PT PT' | / ( N ulp )
*>
*> (4)   | Y - Q' C | / ( |Y| max(M,NRHS) ulp ), where Y = Q' C.
*>
*> 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:
*>
*> The possible matrix types are
*>
*> (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 (3), but multiplied by SQRT( overflow threshold )
*> (7)  Same as (3), but multiplied by SQRT( underflow threshold )
*>
*> (8)  A matrix of the form  U D V, where U and V are orthogonal and
*>      D has evenly spaced entries 1, ..., ULP with random signs
*>      on the diagonal.
*>
*> (9)  A matrix of the form  U D V, where U and V are orthogonal and
*>      D has geometrically spaced entries 1, ..., ULP with random
*>      signs on the diagonal.
*>
*> (10) A matrix of the form  U D V, where U and V are orthogonal 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) Rectangular 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 values of M and N contained in the vectors
*>          MVAL and NVAL.  The matrix sizes are used in pairs (M,N).
*>          If NSIZES is zero, DCHKBB does nothing.  NSIZES must be at
*>          least zero.
*> \endverbatim
*>
*> \param[in] MVAL
*> \verbatim
*>          MVAL is INTEGER array, dimension (NSIZES)
*>          The values of the matrix row dimension M.
*> \endverbatim
*>
*> \param[in] NVAL
*> \verbatim
*>          NVAL is INTEGER array, dimension (NSIZES)
*>          The values of the matrix column dimension N.
*> \endverbatim
*>
*> \param[in] NWDTHS
*> \verbatim
*>          NWDTHS is INTEGER
*>          The number of bandwidths to use.  If it is zero,
*>          DCHKBB 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, DCHKBB
*>          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] NRHS
*> \verbatim
*>          NRHS is INTEGER
*>          The number of columns in the "right-hand side" matrix C.
*>          If NRHS = 0, then the operations on the right-hand side will
*>          not be tested. NRHS must be at least 0.
*> \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 DCHKBB 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 DOUBLE PRECISION array, dimension
*>                            (LDA, max(NN))
*>          Used to hold the matrix A.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of A.  It must be at least 1
*>          and at least max( NN ).
*> \endverbatim
*>
*> \param[out] AB
*> \verbatim
*>          AB is DOUBLE PRECISION array, dimension (LDAB, max(NN))
*>          Used to hold A in band storage format.
*> \endverbatim
*>
*> \param[in] LDAB
*> \verbatim
*>          LDAB is INTEGER
*>          The leading dimension of AB.  It must be at least 2 (not 1!)
*>          and at least max( KK )+1.
*> \endverbatim
*>
*> \param[out] BD
*> \verbatim
*>          BD is DOUBLE PRECISION array, dimension (max(NN))
*>          Used to hold the diagonal of the bidiagonal matrix computed
*>          by DGBBRD.
*> \endverbatim
*>
*> \param[out] BE
*> \verbatim
*>          BE is DOUBLE PRECISION array, dimension (max(NN))
*>          Used to hold the off-diagonal of the bidiagonal matrix
*>          computed by DGBBRD.
*> \endverbatim
*>
*> \param[out] Q
*> \verbatim
*>          Q is DOUBLE PRECISION array, dimension (LDQ, max(NN))
*>          Used to hold the orthogonal matrix Q computed by DGBBRD.
*> \endverbatim
*>
*> \param[in] LDQ
*> \verbatim
*>          LDQ is INTEGER
*>          The leading dimension of Q.  It must be at least 1
*>          and at least max( NN ).
*> \endverbatim
*>
*> \param[out] P
*> \verbatim
*>          P is DOUBLE PRECISION array, dimension (LDP, max(NN))
*>          Used to hold the orthogonal matrix P computed by DGBBRD.
*> \endverbatim
*>
*> \param[in] LDP
*> \verbatim
*>          LDP is INTEGER
*>          The leading dimension of P.  It must be at least 1
*>          and at least max( NN ).
*> \endverbatim
*>
*> \param[out] C
*> \verbatim
*>          C is DOUBLE PRECISION array, dimension (LDC, max(NN))
*>          Used to hold the matrix C updated by DGBBRD.
*> \endverbatim
*>
*> \param[in] LDC
*> \verbatim
*>          LDC is INTEGER
*>          The leading dimension of U.  It must be at least 1
*>          and at least max( NN ).
*> \endverbatim
*>
*> \param[out] CC
*> \verbatim
*>          CC is DOUBLE PRECISION array, dimension (LDC, max(NN))
*>          Used to hold a copy of the matrix C.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is DOUBLE PRECISION 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] 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.
*
*> \ingroup double_eig
*
*  =====================================================================
      SUBROUTINE DCHKBB( NSIZES, MVAL, NVAL, NWDTHS, KK, NTYPES, DOTYPE,
     $                   NRHS, ISEED, THRESH, NOUNIT, A, LDA, AB, LDAB,
     $                   BD, BE, Q, LDQ, P, LDP, C, LDC, CC, WORK,
     $                   LWORK, RESULT, INFO )
*
*  -- LAPACK test routine (input) --
*  -- 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, LDAB, LDC, LDP, LDQ, LWORK, NOUNIT,
     $                   NRHS, NSIZES, NTYPES, NWDTHS
      DOUBLE PRECISION   THRESH
*     ..
*     .. Array Arguments ..
      LOGICAL            DOTYPE( * )
      INTEGER            ISEED( 4 ), KK( * ), MVAL( * ), NVAL( * )
      DOUBLE PRECISION   A( LDA, * ), AB( LDAB, * ), BD( * ), BE( * ),
     $                   C( LDC, * ), CC( LDC, * ), P( LDP, * ),
     $                   Q( LDQ, * ), RESULT( * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
      INTEGER            MAXTYP
      PARAMETER          ( MAXTYP = 15 )
*     ..
*     .. Local Scalars ..
      LOGICAL            BADMM, BADNN, BADNNB
      INTEGER            I, IINFO, IMODE, ITYPE, J, JCOL, JR, JSIZE,
     $                   JTYPE, JWIDTH, K, KL, KMAX, KU, M, MMAX, MNMAX,
     $                   MNMIN, MTYPES, N, NERRS, NMATS, NMAX, NTEST,
     $                   NTESTT
      DOUBLE PRECISION   AMNINV, ANORM, COND, OVFL, RTOVFL, RTUNFL, 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           DBDT01, DBDT02, DGBBRD, DLACPY, DLAHD2, DLASET,
     $                   DLASUM, DLATMR, DLATMS, DORT01, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          ABS, DBLE, MAX, MIN, SQRT
*     ..
*     .. Data statements ..
      DATA               KTYPE / 1, 2, 5*4, 5*6, 3*9 /
      DATA               KMAGN / 2*1, 3*1, 2, 3, 3*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
*
      BADMM = .FALSE.
      BADNN = .FALSE.
      MMAX = 1
      NMAX = 1
      MNMAX = 1
      DO 10 J = 1, NSIZES
         MMAX = MAX( MMAX, MVAL( J ) )
         IF( MVAL( J ).LT.0 )
     $      BADMM = .TRUE.
         NMAX = MAX( NMAX, NVAL( J ) )
         IF( NVAL( J ).LT.0 )
     $      BADNN = .TRUE.
         MNMAX = MAX( MNMAX, MIN( MVAL( J ), NVAL( J ) ) )
   10 CONTINUE
*
      BADNNB = .FALSE.
      KMAX = 0
      DO 20 J = 1, NWDTHS
         KMAX = MAX( KMAX, KK( J ) )
         IF( KK( J ).LT.0 )
     $      BADNNB = .TRUE.
   20 CONTINUE
*
*     Check for errors
*
      IF( NSIZES.LT.0 ) THEN
         INFO = -1
      ELSE IF( BADMM ) THEN
         INFO = -2
      ELSE IF( BADNN ) THEN
         INFO = -3
      ELSE IF( NWDTHS.LT.0 ) THEN
         INFO = -4
      ELSE IF( BADNNB ) THEN
         INFO = -5
      ELSE IF( NTYPES.LT.0 ) THEN
         INFO = -6
      ELSE IF( NRHS.LT.0 ) THEN
         INFO = -8
      ELSE IF( LDA.LT.NMAX ) THEN
         INFO = -13
      ELSE IF( LDAB.LT.2*KMAX+1 ) THEN
         INFO = -15
      ELSE IF( LDQ.LT.NMAX ) THEN
         INFO = -19
      ELSE IF( LDP.LT.NMAX ) THEN
         INFO = -21
      ELSE IF( LDC.LT.NMAX ) THEN
         INFO = -23
      ELSE IF( ( MAX( LDA, NMAX )+1 )*NMAX.GT.LWORK ) THEN
         INFO = -26
      END IF
*
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'DCHKBB', -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, widths, types
*
      NERRS = 0
      NMATS = 0
*
      DO 160 JSIZE = 1, NSIZES
         M = MVAL( JSIZE )
         N = NVAL( JSIZE )
         MNMIN = MIN( M, N )
         AMNINV = ONE / DBLE( MAX( 1, M, N ) )
*
         DO 150 JWIDTH = 1, NWDTHS
            K = KK( JWIDTH )
            IF( K.GE.M .AND. K.GE.N )
     $         GO TO 150
            KL = MAX( 0, MIN( M-1, K ) )
            KU = MAX( 0, MIN( N-1, K ) )
*
            IF( NSIZES.NE.1 ) THEN
               MTYPES = MIN( MAXTYP, NTYPES )
            ELSE
               MTYPES = MIN( MAXTYP+1, NTYPES )
            END IF
*
            DO 140 JTYPE = 1, MTYPES
               IF( .NOT.DOTYPE( JTYPE ) )
     $            GO TO 140
               NMATS = NMATS + 1
               NTEST = 0
*
               DO 30 J = 1, 4
                  IOLDSD( J ) = ISEED( J )
   30          CONTINUE
*
*              Compute "A".
*
*              Control parameters:
*
*                  KMAGN  KMODE        KTYPE
*              =1  O(1)   clustered 1  zero
*              =2  large  clustered 2  identity
*              =3  small  exponential  (none)
*              =4         arithmetic   diagonal, (w/ singular values)
*              =5         random log   (none)
*              =6         random       nonhermitian, w/ singular values
*              =7                      (none)
*              =8                      (none)
*              =9                      random nonhermitian
*
               IF( MTYPES.GT.MAXTYP )
     $            GO TO 90
*
               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 )*AMNINV
               GO TO 70
*
   60          CONTINUE
               ANORM = RTUNFL*MAX( M, N )*ULPINV
               GO TO 70
*
   70          CONTINUE
*
               CALL DLASET( 'Full', LDA, N, ZERO, ZERO, A, LDA )
               CALL DLASET( 'Full', LDAB, N, ZERO, ZERO, AB, LDAB )
               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 80 JCOL = 1, N
                     A( JCOL, JCOL ) = ANORM
   80             CONTINUE
*
               ELSE IF( ITYPE.EQ.4 ) THEN
*
*                 Diagonal Matrix, singular values specified
*
                  CALL DLATMS( M, N, 'S', ISEED, 'N', WORK, IMODE, COND,
     $                         ANORM, 0, 0, 'N', A, LDA, WORK( M+1 ),
     $                         IINFO )
*
               ELSE IF( ITYPE.EQ.6 ) THEN
*
*                 Nonhermitian, singular values specified
*
                  CALL DLATMS( M, N, 'S', ISEED, 'N', WORK, IMODE, COND,
     $                         ANORM, KL, KU, 'N', A, LDA, WORK( M+1 ),
     $                         IINFO )
*
               ELSE IF( ITYPE.EQ.9 ) THEN
*
*                 Nonhermitian, random entries
*
                  CALL DLATMR( M, N, 'S', ISEED, 'N', WORK, 6, ONE, ONE,
     $                         'T', 'N', WORK( N+1 ), 1, ONE,
     $                         WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, KL,
     $                         KU, ZERO, ANORM, 'N', A, LDA, IDUMMA,
     $                         IINFO )
*
               ELSE
*
                  IINFO = 1
               END IF
*
*              Generate Right-Hand Side
*
               CALL DLATMR( M, NRHS, 'S', ISEED, 'N', WORK, 6, ONE, ONE,
     $                      'T', 'N', WORK( M+1 ), 1, ONE,
     $                      WORK( 2*M+1 ), 1, ONE, 'N', IDUMMA, M, NRHS,
     $                      ZERO, ONE, 'NO', C, LDC, IDUMMA, IINFO )
*
               IF( IINFO.NE.0 ) THEN
                  WRITE( NOUNIT, FMT = 9999 )'Generator', IINFO, N,
     $               JTYPE, IOLDSD
                  INFO = ABS( IINFO )
                  RETURN
               END IF
*
   90          CONTINUE
*
*              Copy A to band storage.
*
               DO 110 J = 1, N
                  DO 100 I = MAX( 1, J-KU ), MIN( M, J+KL )
                     AB( KU+1+I-J, J ) = A( I, J )
  100             CONTINUE
  110          CONTINUE
*
*              Copy C
*
               CALL DLACPY( 'Full', M, NRHS, C, LDC, CC, LDC )
*
*              Call DGBBRD to compute B, Q and P, and to update C.
*
               CALL DGBBRD( 'B', M, N, NRHS, KL, KU, AB, LDAB, BD, BE,
     $                      Q, LDQ, P, LDP, CC, LDC, WORK, IINFO )
*
               IF( IINFO.NE.0 ) THEN
                  WRITE( NOUNIT, FMT = 9999 )'DGBBRD', IINFO, N, JTYPE,
     $               IOLDSD
                  INFO = ABS( IINFO )
                  IF( IINFO.LT.0 ) THEN
                     RETURN
                  ELSE
                     RESULT( 1 ) = ULPINV
                     GO TO 120
                  END IF
               END IF
*
*              Test 1:  Check the decomposition A := Q * B * P'
*                   2:  Check the orthogonality of Q
*                   3:  Check the orthogonality of P
*                   4:  Check the computation of Q' * C
*
               CALL DBDT01( M, N, -1, A, LDA, Q, LDQ, BD, BE, P, LDP,
     $                      WORK, RESULT( 1 ) )
               CALL DORT01( 'Columns', M, M, Q, LDQ, WORK, LWORK,
     $                      RESULT( 2 ) )
               CALL DORT01( 'Rows', N, N, P, LDP, WORK, LWORK,
     $                      RESULT( 3 ) )
               CALL DBDT02( M, NRHS, C, LDC, CC, LDC, Q, LDQ, WORK,
     $                      RESULT( 4 ) )
*
*              End of Loop -- Check for RESULT(j) > THRESH
*
               NTEST = 4
  120          CONTINUE
               NTESTT = NTESTT + NTEST
*
*              Print out tests which fail.
*
               DO 130 JR = 1, NTEST
                  IF( RESULT( JR ).GE.THRESH ) THEN
                     IF( NERRS.EQ.0 )
     $                  CALL DLAHD2( NOUNIT, 'DBB' )
                     NERRS = NERRS + 1
                     WRITE( NOUNIT, FMT = 9998 )M, N, K, IOLDSD, JTYPE,
     $                  JR, RESULT( JR )
                  END IF
  130          CONTINUE
*
  140       CONTINUE
  150    CONTINUE
  160 CONTINUE
*
*     Summary
*
      CALL DLASUM( 'DBB', NOUNIT, NERRS, NTESTT )
      RETURN
*
 9999 FORMAT( ' DCHKBB: ', A, ' returned INFO=', I5, '.', / 9X, 'M=',
     $      I5, ' N=', I5, ' K=', I5, ', JTYPE=', I5, ', ISEED=(',
     $      3( I5, ',' ), I5, ')' )
 9998 FORMAT( ' M =', I4, ' N=', I4, ', K=', I3, ', seed=',
     $      4( I4, ',' ), ' type ', I2, ', test(', I2, ')=', G10.3 )
*
*     End of DCHKBB
*
      END