dchkbd.f

Go to the documentation of this file.

*> \brief \b DCHKBD
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE DCHKBD( NSIZES, MVAL, NVAL, NTYPES, DOTYPE, NRHS,
*                          ISEED, THRESH, A, LDA, BD, BE, S1, S2, X, LDX,
*                          Y, Z, Q, LDQ, PT, LDPT, U, VT, WORK, LWORK,
*                          IWORK, NOUT, INFO )
*
*       .. Scalar Arguments ..
*       INTEGER            INFO, LDA, LDPT, LDQ, LDX, LWORK, NOUT, NRHS,
*      $                   NSIZES, NTYPES
*       DOUBLE PRECISION   THRESH
*       ..
*       .. Array Arguments ..
*       LOGICAL            DOTYPE( * )
*       INTEGER            ISEED( 4 ), IWORK( * ), MVAL( * ), NVAL( * )
*       DOUBLE PRECISION   A( LDA, * ), BD( * ), BE( * ), PT( LDPT, * ),
*      $                   Q( LDQ, * ), S1( * ), S2( * ), U( LDPT, * ),
*      $                   VT( LDPT, * ), WORK( * ), X( LDX, * ),
*      $                   Y( LDX, * ), Z( LDX, * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DCHKBD checks the singular value decomposition (SVD) routines.
*>
*> DGEBRD reduces a real general m by n matrix A to upper or lower
*> bidiagonal form B by an orthogonal transformation:  Q' * A * P = B
*> (or A = Q * B * P').  The matrix B is upper bidiagonal if m >= n
*> and lower bidiagonal if m < n.
*>
*> DORGBR generates the orthogonal matrices Q and P' from DGEBRD.
*> Note that Q and P are not necessarily square.
*>
*> DBDSQR computes the singular value decomposition of the bidiagonal
*> matrix B as B = U S V'.  It is called three times to compute
*>    1)  B = U S1 V', where S1 is the diagonal matrix of singular
*>        values and the columns of the matrices U and V are the left
*>        and right singular vectors, respectively, of B.
*>    2)  Same as 1), but the singular values are stored in S2 and the
*>        singular vectors are not computed.
*>    3)  A = (UQ) S (P'V'), the SVD of the original matrix A.
*> In addition, DBDSQR has an option to apply the left orthogonal matrix
*> U to a matrix X, useful in least squares applications.
*>
*> DBDSDC computes the singular value decomposition of the bidiagonal
*> matrix B as B = U S V' using divide-and-conquer. It is called twice
*> to compute
*>    1) B = U S1 V', where S1 is the diagonal matrix of singular
*>        values and the columns of the matrices U and V are the left
*>        and right singular vectors, respectively, of B.
*>    2) Same as 1), but the singular values are stored in S2 and the
*>        singular vectors are not computed.
*>
*>  DBDSVDX computes the singular value decomposition of the bidiagonal
*>  matrix B as B = U S V' using bisection and inverse iteration. It is
*>  called six times to compute
*>     1) B = U S1 V', RANGE='A', where S1 is the diagonal matrix of singular
*>         values and the columns of the matrices U and V are the left
*>         and right singular vectors, respectively, of B.
*>     2) Same as 1), but the singular values are stored in S2 and the
*>         singular vectors are not computed.
*>     3) B = U S1 V', RANGE='I', with where S1 is the diagonal matrix of singular
*>         values and the columns of the matrices U and V are the left
*>         and right singular vectors, respectively, of B
*>     4) Same as 3), but the singular values are stored in S2 and the
*>         singular vectors are not computed.
*>     5) B = U S1 V', RANGE='V', with where S1 is the diagonal matrix of singular
*>         values and the columns of the matrices U and V are the left
*>         and right singular vectors, respectively, of B
*>     6) Same as 5), but the singular values are stored in S2 and the
*>         singular vectors are not computed.
*>
*> 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 X are generated.
*> The problem dimensions are as follows
*>    A:          M x N
*>    Q:          M x min(M,N) (but M x M if NRHS > 0)
*>    P:          min(M,N) x N
*>    B:          min(M,N) x min(M,N)
*>    U, V:       min(M,N) x min(M,N)
*>    S1, S2      diagonal, order min(M,N)
*>    X:          M x NRHS
*>
*> For each generated matrix, 14 tests are performed:
*>
*> Test DGEBRD and DORGBR
*>
*> (1)   | A - Q B PT | / ( |A| max(M,N) ulp ), PT = P'
*>
*> (2)   | I - Q' Q | / ( M ulp )
*>
*> (3)   | I - PT PT' | / ( N ulp )
*>
*> Test DBDSQR on bidiagonal matrix B
*>
*> (4)   | B - U S1 VT | / ( |B| min(M,N) ulp ), VT = V'
*>
*> (5)   | Y - U Z | / ( |Y| max(min(M,N),k) ulp ), where Y = Q' X
*>                                                  and   Z = U' Y.
*> (6)   | I - U' U | / ( min(M,N) ulp )
*>
*> (7)   | I - VT VT' | / ( min(M,N) ulp )
*>
*> (8)   S1 contains min(M,N) nonnegative values in decreasing order.
*>       (Return 0 if true, 1/ULP if false.)
*>
*> (9)   | S1 - S2 | / ( |S1| ulp ), where S2 is computed without
*>                                   computing U and V.
*>
*> (10)  0 if the true singular values of B are within THRESH of
*>       those in S1.  2*THRESH if they are not.  (Tested using
*>       DSVDCH)
*>
*> Test DBDSQR on matrix A
*>
*> (11)  | A - (QU) S (VT PT) | / ( |A| max(M,N) ulp )
*>
*> (12)  | X - (QU) Z | / ( |X| max(M,k) ulp )
*>
*> (13)  | I - (QU)'(QU) | / ( M ulp )
*>
*> (14)  | I - (VT PT) (PT'VT') | / ( N ulp )
*>
*> Test DBDSDC on bidiagonal matrix B
*>
*> (15)  | B - U S1 VT | / ( |B| min(M,N) ulp ), VT = V'
*>
*> (16)  | I - U' U | / ( min(M,N) ulp )
*>
*> (17)  | I - VT VT' | / ( min(M,N) ulp )
*>
*> (18)  S1 contains min(M,N) nonnegative values in decreasing order.
*>       (Return 0 if true, 1/ULP if false.)
*>
*> (19)  | S1 - S2 | / ( |S1| ulp ), where S2 is computed without
*>                                   computing U and V.
*>  Test DBDSVDX on bidiagonal matrix B
*>
*>  (20)  | B - U S1 VT | / ( |B| min(M,N) ulp ), VT = V'
*>
*>  (21)  | I - U' U | / ( min(M,N) ulp )
*>
*>  (22)  | I - VT VT' | / ( min(M,N) ulp )
*>
*>  (23)  S1 contains min(M,N) nonnegative values in decreasing order.
*>        (Return 0 if true, 1/ULP if false.)
*>
*>  (24)  | S1 - S2 | / ( |S1| ulp ), where S2 is computed without
*>                                    computing U and V.
*>
*>  (25)  | S1 - U' B VT' | / ( |S| n ulp )    DBDSVDX('V', 'I')
*>
*>  (26)  | I - U' U | / ( min(M,N) ulp )
*>
*>  (27)  | I - VT VT' | / ( min(M,N) ulp )
*>
*>  (28)  S1 contains min(M,N) nonnegative values in decreasing order.
*>        (Return 0 if true, 1/ULP if false.)
*>
*>  (29)  | S1 - S2 | / ( |S1| ulp ), where S2 is computed without
*>                                    computing U and V.
*>
*>  (30)  | S1 - U' B VT' | / ( |S1| n ulp )   DBDSVDX('V', 'V')
*>
*>  (31)  | I - U' U | / ( min(M,N) ulp )
*>
*>  (32)  | I - VT VT' | / ( min(M,N) ulp )
*>
*>  (33)  S1 contains min(M,N) nonnegative values in decreasing order.
*>        (Return 0 if true, 1/ULP if false.)
*>
*>  (34)  | S1 - S2 | / ( |S1| ulp ), where S2 is computed without
*>                                    computing U and V.
*>
*> 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 )
*>
*> Special case:
*> (16) A bidiagonal matrix with random entries chosen from a
*>      logarithmic distribution on [ulp^2,ulp^(-2)]  (I.e., each
*>      entry is  e^x, where x is chosen uniformly on
*>      [ 2 log(ulp), -2 log(ulp) ] .)  For *this* type:
*>      (a) DGEBRD is not called to reduce it to bidiagonal form.
*>      (b) the bidiagonal is  min(M,N) x min(M,N); if M<N, the
*>          matrix will be lower bidiagonal, otherwise upper.
*>      (c) only tests 5--8 and 14 are performed.
*>
*> A subset of the full set of matrix types may be selected through
*> the logical array DOTYPE.
*> \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).
*> \endverbatim
*>
*> \param[in] MVAL
*> \verbatim
*>          MVAL is INTEGER array, dimension (NM)
*>          The values of the matrix row dimension M.
*> \endverbatim
*>
*> \param[in] NVAL
*> \verbatim
*>          NVAL is INTEGER array, dimension (NM)
*>          The values of the matrix column dimension N.
*> \endverbatim
*>
*> \param[in] NTYPES
*> \verbatim
*>          NTYPES is INTEGER
*>          The number of elements in DOTYPE.   If it is zero, DCHKBD
*>          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 matrices are in A and B.
*>          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 (m,n), a matrix
*>          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" matrices X, Y,
*>          and Z, used in testing DBDSQR.  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 values of ISEED are changed on exit, and can be
*>          used in the next call to DCHKBD to continue the same random
*>          number sequence.
*> \endverbatim
*>
*> \param[in] THRESH
*> \verbatim
*>          THRESH is DOUBLE PRECISION
*>          The threshold value for the test ratios.  A result is
*>          included in the output file if RESULT >= THRESH.  To have
*>          every test ratio printed, use THRESH = 0.  Note that the
*>          expected value of the test ratios is O(1), so THRESH should
*>          be a reasonably small multiple of 1, e.g., 10 or 100.
*> \endverbatim
*>
*> \param[out] A
*> \verbatim
*>          A is DOUBLE PRECISION array, dimension (LDA,NMAX)
*>          where NMAX is the maximum value of N in NVAL.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.  LDA >= max(1,MMAX),
*>          where MMAX is the maximum value of M in MVAL.
*> \endverbatim
*>
*> \param[out] BD
*> \verbatim
*>          BD is DOUBLE PRECISION array, dimension
*>                      (max(min(MVAL(j),NVAL(j))))
*> \endverbatim
*>
*> \param[out] BE
*> \verbatim
*>          BE is DOUBLE PRECISION array, dimension
*>                      (max(min(MVAL(j),NVAL(j))))
*> \endverbatim
*>
*> \param[out] S1
*> \verbatim
*>          S1 is DOUBLE PRECISION array, dimension
*>                      (max(min(MVAL(j),NVAL(j))))
*> \endverbatim
*>
*> \param[out] S2
*> \verbatim
*>          S2 is DOUBLE PRECISION array, dimension
*>                      (max(min(MVAL(j),NVAL(j))))
*> \endverbatim
*>
*> \param[out] X
*> \verbatim
*>          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
*> \endverbatim
*>
*> \param[in] LDX
*> \verbatim
*>          LDX is INTEGER
*>          The leading dimension of the arrays X, Y, and Z.
*>          LDX >= max(1,MMAX)
*> \endverbatim
*>
*> \param[out] Y
*> \verbatim
*>          Y is DOUBLE PRECISION array, dimension (LDX,NRHS)
*> \endverbatim
*>
*> \param[out] Z
*> \verbatim
*>          Z is DOUBLE PRECISION array, dimension (LDX,NRHS)
*> \endverbatim
*>
*> \param[out] Q
*> \verbatim
*>          Q is DOUBLE PRECISION array, dimension (LDQ,MMAX)
*> \endverbatim
*>
*> \param[in] LDQ
*> \verbatim
*>          LDQ is INTEGER
*>          The leading dimension of the array Q.  LDQ >= max(1,MMAX).
*> \endverbatim
*>
*> \param[out] PT
*> \verbatim
*>          PT is DOUBLE PRECISION array, dimension (LDPT,NMAX)
*> \endverbatim
*>
*> \param[in] LDPT
*> \verbatim
*>          LDPT is INTEGER
*>          The leading dimension of the arrays PT, U, and V.
*>          LDPT >= max(1, max(min(MVAL(j),NVAL(j)))).
*> \endverbatim
*>
*> \param[out] U
*> \verbatim
*>          U is DOUBLE PRECISION array, dimension
*>                      (LDPT,max(min(MVAL(j),NVAL(j))))
*> \endverbatim
*>
*> \param[out] VT
*> \verbatim
*>          VT is DOUBLE PRECISION array, dimension
*>                      (LDPT,max(min(MVAL(j),NVAL(j))))
*> \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
*>          3(M+N) and  M(M + max(M,N,k) + 1) + N*min(M,N)  for all
*>          pairs  (M,N)=(MM(j),NN(j))
*> \endverbatim
*>
*> \param[out] IWORK
*> \verbatim
*>          IWORK is INTEGER array, dimension at least 8*min(M,N)
*> \endverbatim
*>
*> \param[in] NOUT
*> \verbatim
*>          NOUT is INTEGER
*>          The FORTRAN unit number for printing out error messages
*>          (e.g., if a routine returns IINFO not equal to 0.)
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          INFO is INTEGER
*>          If 0, then everything ran OK.
*>           -1: NSIZES < 0
*>           -2: Some MM(j) < 0
*>           -3: Some NN(j) < 0
*>           -4: NTYPES < 0
*>           -6: NRHS  < 0
*>           -8: THRESH < 0
*>          -11: LDA < 1 or LDA < MMAX, where MMAX is max( MM(j) ).
*>          -17: LDB < 1 or LDB < MMAX.
*>          -21: LDQ < 1 or LDQ < MMAX.
*>          -23: LDPT< 1 or LDPT< MNMAX.
*>          -27: LWORK too small.
*>          If  DLATMR, SLATMS, DGEBRD, DORGBR, or DBDSQR,
*>              returns an error code, the
*>              absolute value of it is returned.
*>
*>-----------------------------------------------------------------------
*>
*>     Some Local Variables and Parameters:
*>     ---- ----- --------- --- ----------
*>
*>     ZERO, ONE       Real 0 and 1.
*>     MAXTYP          The number of types defined.
*>     NTEST           The number of tests performed, or which can
*>                     be performed so far, for the current matrix.
*>     MMAX            Largest value in NN.
*>     NMAX            Largest value in NN.
*>     MNMIN           min(MM(j), NN(j)) (the dimension of the bidiagonal
*>                     matrix.)
*>     MNMAX           The maximum value of MNMIN for j=1,...,NSIZES.
*>     NFAIL           The number of tests which have exceeded THRESH
*>     COND, IMODE     Values to be passed to the matrix generators.
*>     ANORM           Norm of A; passed to matrix generators.
*>
*>     OVFL, UNFL      Overflow and underflow thresholds.
*>     RTOVFL, RTUNFL  Square roots of the previous 2 values.
*>     ULP, ULPINV     Finest relative precision and its inverse.
*>
*>             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 dchkbd( NSIZES, MVAL, NVAL, NTYPES, DOTYPE, NRHS,
     $                   ISEED, THRESH, A, LDA, BD, BE, S1, S2, X, LDX,
     $                   Y, Z, Q, LDQ, PT, LDPT, U, VT, WORK, LWORK,
     $                   IWORK, NOUT, 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, LDPT, LDQ, LDX, LWORK, NOUT, NRHS,
     $                   NSIZES, NTYPES
      DOUBLE PRECISION   THRESH
*     ..
*     .. Array Arguments ..
      LOGICAL            DOTYPE( * )
      INTEGER            ISEED( 4 ), IWORK( * ), MVAL( * ), NVAL( * )
      DOUBLE PRECISION   A( LDA, * ), BD( * ), BE( * ), PT( LDPT, * ),
     $                   q( ldq, * ), s1( * ), s2( * ), u( ldpt, * ),
     $                   vt( ldpt, * ), work( * ), x( ldx, * ),
     $                   y( ldx, * ), z( ldx, * )
*     ..
*
* ======================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE, TWO, HALF
      PARAMETER          ( ZERO = 0.0d0, one = 1.0d0, two = 2.0d0,
     $                   half = 0.5d0 )
      INTEGER            MAXTYP
      parameter( maxtyp = 16 )
*     ..
*     .. Local Scalars ..
      LOGICAL            BADMM, BADNN, BIDIAG
      CHARACTER          UPLO
      CHARACTER*3        PATH
      INTEGER            I, IINFO, IL, IMODE, ITEMP, ITYPE, IU, IWBD,
     $                   iwbe, iwbs, iwbz, iwwork, j, jcol, jsize,
     $                   jtype, log2ui, m, minwrk, mmax, mnmax, mnmin,
     $                   mnmin2, mq, mtypes, n, nfail, nmax,
     $                   ns1, ns2, ntest
      DOUBLE PRECISION   ABSTOL, AMNINV, ANORM, COND, OVFL, RTOVFL,
     $                   RTUNFL, TEMP1, TEMP2, ULP, ULPINV, UNFL,
     $                   VL, VU
*     ..
*     .. Local Arrays ..
      INTEGER            IDUM( 1 ), IOLDSD( 4 ), ISEED2( 4 ),
     $                   KMAGN( MAXTYP ), KMODE( MAXTYP ),
     $                   KTYPE( MAXTYP )
      DOUBLE PRECISION   DUM( 1 ), DUMMA( 1 ), RESULT( 40 )
*     ..
*     .. External Functions ..
      DOUBLE PRECISION   DLAMCH, DLARND, DSXT1
      EXTERNAL           DLAMCH, DLARND, DSXT1
*     ..
*     .. External Subroutines ..
      EXTERNAL           alasum, dbdsdc, dbdsqr, dbdsvdx, dbdt01,
     $                   dbdt02, dbdt03, dbdt04, dcopy, dgebrd,
     $                   dgemm, dlabad, dlacpy, dlahd2, dlaset,
     $                   dlatmr, dlatms, dorgbr, dort01, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, exp, int, log, max, min, sqrt
*     ..
*     .. Scalars in Common ..
      LOGICAL            LERR, OK
      CHARACTER*32       SRNAMT
      INTEGER            INFOT, NUNIT
*     ..
*     .. Common blocks ..
      COMMON             / infoc / infot, nunit, ok, lerr
      COMMON             / srnamc / srnamt
*     ..
*     .. Data statements ..
      DATA            ktype / 1, 2, 5*4, 5*6, 3*9, 10 /
      DATA            kmagn / 2*1, 3*1, 2, 3, 3*1, 2, 3, 1, 2, 3, 0 /
      DATA            kmode / 2*0, 4, 3, 1, 4, 4, 4, 3, 1, 4, 4, 0,
     $                0, 0, 0 /
*     ..
*     .. Executable Statements ..
*
*     Check for errors
*
      info = 0
*
      badmm = .false.
      badnn = .false.
      mmax = 1
      nmax = 1
      mnmax = 1
      minwrk = 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 ) ) )
         minwrk = max( minwrk, 3*( mval( j )+nval( j ) ),
     $            mval( j )*( mval( j )+max( mval( j ), nval( j ),
     $            nrhs )+1 )+nval( j )*min( nval( j ), mval( j ) ) )
   10 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( ntypes.LT.0 ) THEN
         info = -4
      ELSE IF( nrhs.LT.0 ) THEN
         info = -6
      ELSE IF( lda.LT.mmax ) THEN
         info = -11
      ELSE IF( ldx.LT.mmax ) THEN
         info = -17
      ELSE IF( ldq.LT.mmax ) THEN
         info = -21
      ELSE IF( ldpt.LT.mnmax ) THEN
         info = -23
      ELSE IF( minwrk.GT.lwork ) THEN
         info = -27
      END IF
*
      IF( info.NE.0 ) THEN
         CALL xerbla( 'DCHKBD', -info )
         RETURN
      END IF
*
*     Initialize constants
*
      path( 1: 1 ) = 'Double precision'
      path( 2: 3 ) = 'BD'
      nfail = 0
      ntest = 0
      unfl = dlamch( 'Safe minimum' )
      ovfl = dlamch( 'Overflow' )
      CALL dlabad( unfl, ovfl )
      ulp = dlamch( 'Precision' )
      ulpinv = one / ulp
      log2ui = int( log( ulpinv ) / log( two ) )
      rtunfl = sqrt( unfl )
      rtovfl = sqrt( ovfl )
      infot = 0
      abstol = 2*unfl
*
*     Loop over sizes, types
*
      DO 300 jsize = 1, nsizes
         m = mval( jsize )
         n = nval( jsize )
         mnmin = min( m, n )
         amninv = one / max( m, n, 1 )
*
         IF( nsizes.NE.1 ) THEN
            mtypes = min( maxtyp, ntypes )
         ELSE
            mtypes = min( maxtyp+1, ntypes )
         END IF
*
         DO 290 jtype = 1, mtypes
            IF( .NOT.dotype( jtype ) )
     $         GO TO 290
*
            DO 20 j = 1, 4
               ioldsd( j ) = iseed( j )
   20       CONTINUE
*
            DO 30 j = 1, 34
               result( j ) = -one
   30       CONTINUE
*
            uplo = ' '
*
*           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/ eigenvalues)
*       =5         random       symmetric, w/ eigenvalues
*       =6                      nonsymmetric, w/ singular values
*       =7                      random diagonal
*       =8                      random symmetric
*       =9                      random nonsymmetric
*       =10                     random bidiagonal (log. distrib.)
*
            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 )*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 )
            iinfo = 0
            cond = ulpinv
*
            bidiag = .false.
            IF( itype.EQ.1 ) THEN
*
*              Zero matrix
*
               iinfo = 0
*
            ELSE IF( itype.EQ.2 ) THEN
*
*              Identity
*
               DO 80 jcol = 1, mnmin
                  a( jcol, jcol ) = anorm
   80          CONTINUE
*
            ELSE IF( itype.EQ.4 ) THEN
*
*              Diagonal Matrix, [Eigen]values Specified
*
               CALL dlatms( mnmin, mnmin, 'S', iseed, 'N', work, imode,
     $                      cond, anorm, 0, 0, 'N', a, lda,
     $                      work( mnmin+1 ), iinfo )
*
            ELSE IF( itype.EQ.5 ) THEN
*
*              Symmetric, eigenvalues specified
*
               CALL dlatms( mnmin, mnmin, 'S', iseed, 'S', work, imode,
     $                      cond, anorm, m, n, 'N', a, lda,
     $                      work( mnmin+1 ), iinfo )
*
            ELSE IF( itype.EQ.6 ) THEN
*
*              Nonsymmetric, singular values specified
*
               CALL dlatms( m, n, 'S', iseed, 'N', work, imode, cond,
     $                      anorm, m, n, 'N', a, lda, work( mnmin+1 ),
     $                      iinfo )
*
            ELSE IF( itype.EQ.7 ) THEN
*
*              Diagonal, random entries
*
               CALL dlatmr( mnmin, mnmin, 'S', iseed, 'N', work, 6, one,
     $                      one, 'T', 'N', work( mnmin+1 ), 1, one,
     $                      work( 2*mnmin+1 ), 1, one, 'N', iwork, 0, 0,
     $                      zero, anorm, 'NO', a, lda, iwork, iinfo )
*
            ELSE IF( itype.EQ.8 ) THEN
*
*              Symmetric, random entries
*
               CALL dlatmr( mnmin, mnmin, 'S', iseed, 'S', work, 6, one,
     $                      one, 'T', 'N', work( mnmin+1 ), 1, one,
     $                      work( m+mnmin+1 ), 1, one, 'N', iwork, m, n,
     $                      zero, anorm, 'NO', a, lda, iwork, iinfo )
*
            ELSE IF( itype.EQ.9 ) THEN
*
*              Nonsymmetric, random entries
*
               CALL dlatmr( m, n, 'S', iseed, 'N', work, 6, one, one,
     $                      'T', 'N', work( mnmin+1 ), 1, one,
     $                      work( m+mnmin+1 ), 1, one, 'N', iwork, m, n,
     $                      zero, anorm, 'NO', a, lda, iwork, iinfo )
*
            ELSE IF( itype.EQ.10 ) THEN
*
*              Bidiagonal, random entries
*
               temp1 = -two*log( ulp )
               DO 90 j = 1, mnmin
                  bd( j ) = exp( temp1*dlarnd( 2, iseed ) )
                  IF( j.LT.mnmin )
     $               be( j ) = exp( temp1*dlarnd( 2, iseed ) )
   90          CONTINUE
*
               iinfo = 0
               bidiag = .true.
               IF( m.GE.n ) THEN
                  uplo = 'U'
               ELSE
                  uplo = 'L'
               END IF
            ELSE
               iinfo = 1
            END IF
*
            IF( iinfo.EQ.0 ) THEN
*
*              Generate Right-Hand Side
*
               IF( bidiag ) THEN
                  CALL dlatmr( mnmin, nrhs, 'S', iseed, 'N', work, 6,
     $                         one, one, 'T', 'N', work( mnmin+1 ), 1,
     $                         one, work( 2*mnmin+1 ), 1, one, 'N',
     $                         iwork, mnmin, nrhs, zero, one, 'NO', y,
     $                         ldx, iwork, iinfo )
               ELSE
                  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', iwork, m,
     $                         nrhs, zero, one, 'NO', x, ldx, iwork,
     $                         iinfo )
               END IF
            END IF
*
*           Error Exit
*
            IF( iinfo.NE.0 ) THEN
               WRITE( nout, fmt = 9998 )'Generator', iinfo, m, n,
     $            jtype, ioldsd
               info = abs( iinfo )
               RETURN
            END IF
*
  100       CONTINUE
*
*           Call DGEBRD and DORGBR to compute B, Q, and P, do tests.
*
            IF( .NOT.bidiag ) THEN
*
*              Compute transformations to reduce A to bidiagonal form:
*              B := Q' * A * P.
*
               CALL dlacpy( ' ', m, n, a, lda, q, ldq )
               CALL dgebrd( m, n, q, ldq, bd, be, work, work( mnmin+1 ),
     $                      work( 2*mnmin+1 ), lwork-2*mnmin, iinfo )
*
*              Check error code from DGEBRD.
*
               IF( iinfo.NE.0 ) THEN
                  WRITE( nout, fmt = 9998 )'dgebrd', IINFO, M, N,
     $               JTYPE, IOLDSD
                  INFO = ABS( IINFO )
                  RETURN
               END IF
*
               CALL DLACPY( ' ', M, N, Q, LDQ, PT, LDPT )
.GE.               IF( MN ) THEN
                  UPLO = 'u'
               ELSE
                  UPLO = 'l'
               END IF
*
*              Generate Q
*
               MQ = M
.LE.               IF( NRHS0 )
     $            MQ = MNMIN
               CALL DORGBR( 'q', M, MQ, N, Q, LDQ, WORK,
     $                      WORK( 2*MNMIN+1 ), LWORK-2*MNMIN, IINFO )
*
*              Check error code from DORGBR.
*
.NE.               IF( IINFO0 ) THEN
                  WRITE( NOUT, FMT = 9998 )'dorgbr(q)', IINFO, M, N,
     $               JTYPE, IOLDSD
                  INFO = ABS( IINFO )
                  RETURN
               END IF
*
*              Generate P'
*
               CALL DORGBR( 'p', MNMIN, N, M, PT, LDPT, WORK( MNMIN+1 ),
     $                      WORK( 2*MNMIN+1 ), LWORK-2*MNMIN, IINFO )
*
*              Check error code from DORGBR.
*
.NE.               IF( IINFO0 ) THEN
                  WRITE( NOUT, FMT = 9998 )'dorgbr(p)', IINFO, M, N,
     $               JTYPE, IOLDSD
                  INFO = ABS( IINFO )
                  RETURN
               END IF
*
*              Apply Q' to an M by NRHS matrix X:  Y := Q' * X.
*
               CALL DGEMM( 'transpose', 'no transpose', M, NRHS, M, ONE,
     $                     Q, LDQ, X, LDX, ZERO, Y, LDX )
*
*              Test 1:  Check the decomposition A := Q * B * PT
*                   2:  Check the orthogonality of Q
*                   3:  Check the orthogonality of PT
*
               CALL DBDT01( M, N, 1, A, LDA, Q, LDQ, BD, BE, PT, LDPT,
     $                      WORK, RESULT( 1 ) )
               CALL DORT01( 'columns', M, MQ, Q, LDQ, WORK, LWORK,
     $                      RESULT( 2 ) )
               CALL DORT01( 'rows', MNMIN, N, PT, LDPT, WORK, LWORK,
     $                      RESULT( 3 ) )
            END IF
*
*           Use DBDSQR to form the SVD of the bidiagonal matrix B:
*           B := U * S1 * VT, and compute Z = U' * Y.
*
            CALL DCOPY( MNMIN, BD, 1, S1, 1 )
.GT.            IF( MNMIN0 )
     $         CALL DCOPY( MNMIN-1, BE, 1, WORK, 1 )
            CALL DLACPY( ' ', M, NRHS, Y, LDX, Z, LDX )
            CALL DLASET( 'full', MNMIN, MNMIN, ZERO, ONE, U, LDPT )
            CALL DLASET( 'full', MNMIN, MNMIN, ZERO, ONE, VT, LDPT )
*
            CALL DBDSQR( UPLO, MNMIN, MNMIN, MNMIN, NRHS, S1, WORK, VT,
     $                   LDPT, U, LDPT, Z, LDX, WORK( MNMIN+1 ), IINFO )
*
*           Check error code from DBDSQR.
*
.NE.            IF( IINFO0 ) THEN
               WRITE( NOUT, FMT = 9998 )'dbdsqr(vects)', IINFO, M, N,
     $            JTYPE, IOLDSD
               INFO = ABS( IINFO )
.LT.               IF( IINFO0 ) THEN
                  RETURN
               ELSE
                  RESULT( 4 ) = ULPINV
                  GO TO 270
               END IF
            END IF
*
*           Use DBDSQR to compute only the singular values of the
*           bidiagonal matrix B;  U, VT, and Z should not be modified.
*
            CALL DCOPY( MNMIN, BD, 1, S2, 1 )
.GT.            IF( MNMIN0 )
     $         CALL DCOPY( MNMIN-1, BE, 1, WORK, 1 )
*
            CALL DBDSQR( UPLO, MNMIN, 0, 0, 0, S2, WORK, VT, LDPT, U,
     $                   LDPT, Z, LDX, WORK( MNMIN+1 ), IINFO )
*
*           Check error code from DBDSQR.
*
.NE.            IF( IINFO0 ) THEN
               WRITE( NOUT, FMT = 9998 )'dbdsqr(values)', IINFO, M, N,
     $            JTYPE, IOLDSD
               INFO = ABS( IINFO )
.LT.               IF( IINFO0 ) THEN
                  RETURN
               ELSE
                  RESULT( 9 ) = ULPINV
                  GO TO 270
               END IF
            END IF
*
*           Test 4:  Check the decomposition B := U * S1 * VT
*                5:  Check the computation Z := U' * Y
*                6:  Check the orthogonality of U
*                7:  Check the orthogonality of VT
*
            CALL DBDT03( UPLO, MNMIN, 1, BD, BE, U, LDPT, S1, VT, LDPT,
     $                   WORK, RESULT( 4 ) )
            CALL DBDT02( MNMIN, NRHS, Y, LDX, Z, LDX, U, LDPT, WORK,
     $                   RESULT( 5 ) )
            CALL DORT01( 'columns', MNMIN, MNMIN, U, LDPT, WORK, LWORK,
     $                   RESULT( 6 ) )
            CALL DORT01( 'rows', MNMIN, MNMIN, VT, LDPT, WORK, LWORK,
     $                   RESULT( 7 ) )
*
*           Test 8:  Check that the singular values are sorted in
*                    non-increasing order and are non-negative
*
            RESULT( 8 ) = ZERO
            DO 110 I = 1, MNMIN - 1
.LT.               IF( S1( I )S1( I+1 ) )
     $            RESULT( 8 ) = ULPINV
.LT.               IF( S1( I )ZERO )
     $            RESULT( 8 ) = ULPINV
  110       CONTINUE
.GE.            IF( MNMIN1 ) THEN
.LT.               IF( S1( MNMIN )ZERO )
     $            RESULT( 8 ) = ULPINV
            END IF
*
*           Test 9:  Compare DBDSQR with and without singular vectors
*
            TEMP2 = ZERO
*
            DO 120 J = 1, MNMIN
               TEMP1 = ABS( S1( J )-S2( J ) ) /
     $                 MAX( SQRT( UNFL )*MAX( S1( 1 ), ONE ),
     $                 ULP*MAX( ABS( S1( J ) ), ABS( S2( J ) ) ) )
               TEMP2 = MAX( TEMP1, TEMP2 )
  120       CONTINUE
*
            RESULT( 9 ) = TEMP2
*
*           Test 10:  Sturm sequence test of singular values
*                     Go up by factors of two until it succeeds
*
            TEMP1 = THRESH*( HALF-ULP )
*
            DO 130 J = 0, LOG2UI
*               CALL DSVDCH( MNMIN, BD, BE, S1, TEMP1, IINFO )
.EQ.               IF( IINFO0 )
     $            GO TO 140
               TEMP1 = TEMP1*TWO
  130       CONTINUE
*
  140       CONTINUE
            RESULT( 10 ) = TEMP1
*
*           Use DBDSQR to form the decomposition A := (QU) S (VT PT)
*           from the bidiagonal form A := Q B PT.
*
.NOT.            IF( BIDIAG ) THEN
               CALL DCOPY( MNMIN, BD, 1, S2, 1 )
.GT.               IF( MNMIN0 )
     $            CALL DCOPY( MNMIN-1, BE, 1, WORK, 1 )
*
               CALL DBDSQR( UPLO, MNMIN, N, M, NRHS, S2, WORK, PT, LDPT,
     $                      Q, LDQ, Y, LDX, WORK( MNMIN+1 ), IINFO )
*
*              Test 11:  Check the decomposition A := Q*U * S2 * VT*PT
*                   12:  Check the computation Z := U' * Q' * X
*                   13:  Check the orthogonality of Q*U
*                   14:  Check the orthogonality of VT*PT
*
               CALL DBDT01( M, N, 0, A, LDA, Q, LDQ, S2, DUMMA, PT,
     $                      LDPT, WORK, RESULT( 11 ) )
               CALL DBDT02( M, NRHS, X, LDX, Y, LDX, Q, LDQ, WORK,
     $                      RESULT( 12 ) )
               CALL DORT01( 'columns', M, MQ, Q, LDQ, WORK, LWORK,
     $                      RESULT( 13 ) )
               CALL DORT01( 'rows', MNMIN, N, PT, LDPT, WORK, LWORK,
     $                      RESULT( 14 ) )
            END IF
*
*           Use DBDSDC to form the SVD of the bidiagonal matrix B:
*           B := U * S1 * VT
*
            CALL DCOPY( MNMIN, BD, 1, S1, 1 )
.GT.            IF( MNMIN0 )
     $         CALL DCOPY( MNMIN-1, BE, 1, WORK, 1 )
            CALL DLASET( 'full', MNMIN, MNMIN, ZERO, ONE, U, LDPT )
            CALL DLASET( 'full', MNMIN, MNMIN, ZERO, ONE, VT, LDPT )
*
            CALL DBDSDC( UPLO, 'i', MNMIN, S1, WORK, U, LDPT, VT, LDPT,
     $                   DUM, IDUM, WORK( MNMIN+1 ), IWORK, IINFO )
*
*           Check error code from DBDSDC.
*
.NE.            IF( IINFO0 ) THEN
               WRITE( NOUT, FMT = 9998 )'dbdsdc(vects)', IINFO, M, N,
     $            JTYPE, IOLDSD
               INFO = ABS( IINFO )
.LT.               IF( IINFO0 ) THEN
                  RETURN
               ELSE
                  RESULT( 15 ) = ULPINV
                  GO TO 270
               END IF
            END IF
*
*           Use DBDSDC to compute only the singular values of the
*           bidiagonal matrix B;  U and VT should not be modified.
*
            CALL DCOPY( MNMIN, BD, 1, S2, 1 )
.GT.            IF( MNMIN0 )
     $         CALL DCOPY( MNMIN-1, BE, 1, WORK, 1 )
*
            CALL DBDSDC( UPLO, 'n', MNMIN, S2, WORK, DUM, 1, DUM, 1,
     $                   DUM, IDUM, WORK( MNMIN+1 ), IWORK, IINFO )
*
*           Check error code from DBDSDC.
*
.NE.            IF( IINFO0 ) THEN
               WRITE( NOUT, FMT = 9998 )'dbdsdc(values)', IINFO, M, N,
     $            JTYPE, IOLDSD
               INFO = ABS( IINFO )
.LT.               IF( IINFO0 ) THEN
                  RETURN
               ELSE
                  RESULT( 18 ) = ULPINV
                  GO TO 270
               END IF
            END IF
*
*           Test 15:  Check the decomposition B := U * S1 * VT
*                16:  Check the orthogonality of U
*                17:  Check the orthogonality of VT
*
            CALL DBDT03( UPLO, MNMIN, 1, BD, BE, U, LDPT, S1, VT, LDPT,
     $                   WORK, RESULT( 15 ) )
            CALL DORT01( 'columns', MNMIN, MNMIN, U, LDPT, WORK, LWORK,
     $                   RESULT( 16 ) )
            CALL DORT01( 'rows', MNMIN, MNMIN, VT, LDPT, WORK, LWORK,
     $                   RESULT( 17 ) )
*
*           Test 18:  Check that the singular values are sorted in
*                     non-increasing order and are non-negative
*
            RESULT( 18 ) = ZERO
            DO 150 I = 1, MNMIN - 1
.LT.               IF( S1( I )S1( I+1 ) )
     $            RESULT( 18 ) = ULPINV
.LT.               IF( S1( I )ZERO )
     $            RESULT( 18 ) = ULPINV
  150       CONTINUE
.GE.            IF( MNMIN1 ) THEN
.LT.               IF( S1( MNMIN )ZERO )
     $            RESULT( 18 ) = ULPINV
            END IF
*
*           Test 19:  Compare DBDSQR with and without singular vectors
*
            TEMP2 = ZERO
*
            DO 160 J = 1, MNMIN
               TEMP1 = ABS( S1( J )-S2( J ) ) /
     $                 MAX( SQRT( UNFL )*MAX( S1( 1 ), ONE ),
     $                 ULP*MAX( ABS( S1( 1 ) ), ABS( S2( 1 ) ) ) )
               TEMP2 = MAX( TEMP1, TEMP2 )
  160       CONTINUE
*
            RESULT( 19 ) = TEMP2
*
*
*           Use DBDSVDX to compute the SVD of the bidiagonal matrix B:
*           B := U * S1 * VT
*
.EQ..OR..EQ.            IF( JTYPE10  JTYPE16 ) THEN
*              =================================
*              Matrix types temporarily disabled
*              =================================
               RESULT( 20:34 ) = ZERO
               GO TO 270
            END IF
*
            IWBS = 1
            IWBD = IWBS + MNMIN
            IWBE = IWBD + MNMIN
            IWBZ = IWBE + MNMIN
            IWWORK = IWBZ + 2*MNMIN*(MNMIN+1)
            MNMIN2 = MAX( 1,MNMIN*2 )
*
            CALL DCOPY( MNMIN, BD, 1, WORK( IWBD ), 1 )
.GT.            IF( MNMIN0 )
     $         CALL DCOPY( MNMIN-1, BE, 1, WORK( IWBE ), 1 )
*
            CALL DBDSVDX( UPLO, 'v', 'a', MNMIN, WORK( IWBD ),
     $                    WORK( IWBE ), ZERO, ZERO, 0, 0, NS1, S1,
     $                    WORK( IWBZ ), MNMIN2, WORK( IWWORK ),
     $                    IWORK, IINFO)
*
*           Check error code from DBDSVDX.
*
.NE.            IF( IINFO0 ) THEN
               WRITE( NOUT, FMT = 9998 )'dbdsvdx(vects,a)', IINFO, M, N,
     $            JTYPE, IOLDSD
               INFO = ABS( IINFO )
.LT.               IF( IINFO0 ) THEN
                  RETURN
               ELSE
                  RESULT( 20 ) = ULPINV
                  GO TO 270
               END IF
            END IF
*
            J = IWBZ
            DO 170 I = 1, NS1
               CALL DCOPY( MNMIN, WORK( J ), 1, U( 1,I ), 1 )
               J = J + MNMIN
               CALL DCOPY( MNMIN, WORK( J ), 1, VT( I,1 ), LDPT )
               J = J + MNMIN
  170       CONTINUE
*
*           Use DBDSVDX to compute only the singular values of the
*           bidiagonal matrix B;  U and VT should not be modified.
*
.EQ.            IF( JTYPE9 ) THEN
*              =================================
*              Matrix types temporarily disabled
*              =================================
               RESULT( 24 ) = ZERO
               GO TO 270
            END IF
*
            CALL DCOPY( MNMIN, BD, 1, WORK( IWBD ), 1 )
.GT.            IF( MNMIN0 )
     $         CALL DCOPY( MNMIN-1, BE, 1, WORK( IWBE ), 1 )
*
            CALL DBDSVDX( UPLO, 'n', 'a', MNMIN, WORK( IWBD ),
     $                    WORK( IWBE ), ZERO, ZERO, 0, 0, NS2, S2,
     $                    WORK( IWBZ ), MNMIN2, WORK( IWWORK ),
     $                    IWORK, IINFO )
*
*           Check error code from DBDSVDX.
*
.NE.            IF( IINFO0 ) THEN
               WRITE( NOUT, FMT = 9998 )'dbdsvdx(values,a)', IINFO,
     $            M, N, JTYPE, IOLDSD
               INFO = ABS( IINFO )
.LT.               IF( IINFO0 ) THEN
                  RETURN
               ELSE
                  RESULT( 24 ) = ULPINV
                  GO TO 270
               END IF
            END IF
*
*           Save S1 for tests 30-34.
*
            CALL DCOPY( MNMIN, S1, 1, WORK( IWBS ), 1 )
*
*           Test 20:  Check the decomposition B := U * S1 * VT
*                21:  Check the orthogonality of U
*                22:  Check the orthogonality of VT
*                23:  Check that the singular values are sorted in
*                     non-increasing order and are non-negative
*                24:  Compare DBDSVDX with and without singular vectors
*
            CALL DBDT03( UPLO, MNMIN, 1, BD, BE, U, LDPT, S1, VT,
     $                   LDPT, WORK( IWBS+MNMIN ), RESULT( 20 ) )
            CALL DORT01( 'columns', MNMIN, MNMIN, U, LDPT,
     $                   WORK( IWBS+MNMIN ), LWORK-MNMIN,
     $                   RESULT( 21 ) )
            CALL DORT01( 'rows', MNMIN, MNMIN, VT, LDPT,
     $                   WORK( IWBS+MNMIN ), LWORK-MNMIN,
     $                   RESULT( 22) )
*
            RESULT( 23 ) = ZERO
            DO 180 I = 1, MNMIN - 1
.LT.               IF( S1( I )S1( I+1 ) )
     $            RESULT( 23 ) = ULPINV
.LT.               IF( S1( I )ZERO )
     $            RESULT( 23 ) = ULPINV
  180       CONTINUE
.GE.            IF( MNMIN1 ) THEN
.LT.               IF( S1( MNMIN )ZERO )
     $            RESULT( 23 ) = ULPINV
            END IF
*
            TEMP2 = ZERO
            DO 190 J = 1, MNMIN
               TEMP1 = ABS( S1( J )-S2( J ) ) /
     $                 MAX( SQRT( UNFL )*MAX( S1( 1 ), ONE ),
     $                 ULP*MAX( ABS( S1( 1 ) ), ABS( S2( 1 ) ) ) )
               TEMP2 = MAX( TEMP1, TEMP2 )
  190       CONTINUE
            RESULT( 24 ) = TEMP2
            ANORM = S1( 1 )
*
*           Use DBDSVDX with RANGE='I': choose random values for IL and
*           IU, and ask for the IL-th through IU-th singular values
*           and corresponding vectors.
*
            DO 200 I = 1, 4
               ISEED2( I ) = ISEED( I )
  200       CONTINUE
.LE.            IF( MNMIN1 ) THEN
               IL = 1
               IU = MNMIN
            ELSE
               IL = 1 + INT( ( MNMIN-1 )*DLARND( 1, ISEED2 ) )
               IU = 1 + INT( ( MNMIN-1 )*DLARND( 1, ISEED2 ) )
.LT.               IF( IUIL ) THEN
                  ITEMP = IU
                  IU = IL
                  IL = ITEMP
               END IF
            END IF
*
            CALL DCOPY( MNMIN, BD, 1, WORK( IWBD ), 1 )
.GT.            IF( MNMIN0 )
     $         CALL DCOPY( MNMIN-1, BE, 1, WORK( IWBE ), 1 )
*
            CALL DBDSVDX( UPLO, 'v', 'i', MNMIN, WORK( IWBD ),
     $                    WORK( IWBE ), ZERO, ZERO, IL, IU, NS1, S1,
     $                    WORK( IWBZ ), MNMIN2, WORK( IWWORK ),
     $                    IWORK, IINFO)
*
*           Check error code from DBDSVDX.
*
.NE.            IF( IINFO0 ) THEN
               WRITE( NOUT, FMT = 9998 )'dbdsvdx(vects,i)', IINFO,
     $            M, N, JTYPE, IOLDSD
               INFO = ABS( IINFO )
.LT.               IF( IINFO0 ) THEN
                  RETURN
               ELSE
                  RESULT( 25 ) = ULPINV
                  GO TO 270
               END IF
            END IF
*
            J = IWBZ
            DO 210 I = 1, NS1
               CALL DCOPY( MNMIN, WORK( J ), 1, U( 1,I ), 1 )
               J = J + MNMIN
               CALL DCOPY( MNMIN, WORK( J ), 1, VT( I,1 ), LDPT )
               J = J + MNMIN
  210       CONTINUE
*
*           Use DBDSVDX to compute only the singular values of the
*           bidiagonal matrix B;  U and VT should not be modified.
*
            CALL DCOPY( MNMIN, BD, 1, WORK( IWBD ), 1 )
.GT.            IF( MNMIN0 )
     $         CALL DCOPY( MNMIN-1, BE, 1, WORK( IWBE ), 1 )
*
            CALL DBDSVDX( UPLO, 'n', 'i', MNMIN, WORK( IWBD ),
     $                    WORK( IWBE ), ZERO, ZERO, IL, IU, NS2, S2,
     $                    WORK( IWBZ ), MNMIN2, WORK( IWWORK ),
     $                    IWORK, IINFO )
*
*           Check error code from DBDSVDX.
*
.NE.            IF( IINFO0 ) THEN
               WRITE( NOUT, FMT = 9998 )'dbdsvdx(values,i)', IINFO,
     $            M, N, JTYPE, IOLDSD
               INFO = ABS( IINFO )
.LT.               IF( IINFO0 ) THEN
                  RETURN
               ELSE
                  RESULT( 29 ) = ULPINV
                  GO TO 270
               END IF
            END IF
*
*           Test 25:  Check S1 - U' * B * VT'
*                26:  Check the orthogonality of U
*                27:  Check the orthogonality of VT
*                28:  Check that the singular values are sorted in
*                     non-increasing order and are non-negative
*                29:  Compare DBDSVDX with and without singular vectors
*
            CALL DBDT04( UPLO, MNMIN, BD, BE, S1, NS1, U,
     $                   LDPT, VT, LDPT, WORK( IWBS+MNMIN ),
     $                   RESULT( 25 ) )
            CALL DORT01( 'columns', MNMIN, NS1, U, LDPT,
     $                   WORK( IWBS+MNMIN ), LWORK-MNMIN,
     $                   RESULT( 26 ) )
            CALL DORT01( 'rows', NS1, MNMIN, VT, LDPT,
     $                   WORK( IWBS+MNMIN ), LWORK-MNMIN,
     $                   RESULT( 27 ) )
*
            RESULT( 28 ) = ZERO
            DO 220 I = 1, NS1 - 1
.LT.               IF( S1( I )S1( I+1 ) )
     $            RESULT( 28 ) = ULPINV
.LT.               IF( S1( I )ZERO )
     $            RESULT( 28 ) = ULPINV
  220       CONTINUE
.GE.            IF( NS11 ) THEN
.LT.               IF( S1( NS1 )ZERO )
     $            RESULT( 28 ) = ULPINV
            END IF
*
            TEMP2 = ZERO
            DO 230 J = 1, NS1
               TEMP1 = ABS( S1( J )-S2( J ) ) /
     $                 MAX( SQRT( UNFL )*MAX( S1( 1 ), ONE ),
     $                 ULP*MAX( ABS( S1( 1 ) ), ABS( S2( 1 ) ) ) )
               TEMP2 = MAX( TEMP1, TEMP2 )
  230       CONTINUE
            RESULT( 29 ) = TEMP2
*
*           Use DBDSVDX with RANGE='V': determine the values VL and VU
*           of the IL-th and IU-th singular values and ask for all
*           singular values in this range.
*
            CALL DCOPY( MNMIN, WORK( IWBS ), 1, S1, 1 )
*
.GT.            IF( MNMIN0 ) THEN
.NE.               IF( IL1 ) THEN
                  VU = S1( IL ) + MAX( HALF*ABS( S1( IL )-S1( IL-1 ) ),
     $                 ULP*ANORM, TWO*RTUNFL )
               ELSE
                  VU = S1( 1 ) + MAX( HALF*ABS( S1( MNMIN )-S1( 1 ) ),
     $                 ULP*ANORM, TWO*RTUNFL )
               END IF
.NE.               IF( IUNS1 ) THEN
                  VL = S1( IU ) - MAX( ULP*ANORM, TWO*RTUNFL,
     $                 HALF*ABS( S1( IU+1 )-S1( IU ) ) )
               ELSE
                  VL = S1( NS1 ) - MAX( ULP*ANORM, TWO*RTUNFL,
     $                 HALF*ABS( S1( MNMIN )-S1( 1 ) ) )
               END IF
               VL = MAX( VL,ZERO )
               VU = MAX( VU,ZERO )
.GE.               IF( VLVU ) VU = MAX( VU*2, VU+VL+HALF )
            ELSE
               VL = ZERO
               VU = ONE
            END IF
*
            CALL DCOPY( MNMIN, BD, 1, WORK( IWBD ), 1 )
.GT.            IF( MNMIN0 )
     $         CALL DCOPY( MNMIN-1, BE, 1, WORK( IWBE ), 1 )
*
            CALL DBDSVDX( UPLO, 'v', 'v', MNMIN, WORK( IWBD ),
     $                    WORK( IWBE ), VL, VU, 0, 0, NS1, S1,
     $                    WORK( IWBZ ), MNMIN2, WORK( IWWORK ),
     $                    IWORK, IINFO )
*
*           Check error code from DBDSVDX.
*
.NE.            IF( IINFO0 ) THEN
               WRITE( NOUT, FMT = 9998 )'dbdsvdx(vects,v)', IINFO,
     $            M, N, JTYPE, IOLDSD
               INFO = ABS( IINFO )
.LT.               IF( IINFO0 ) THEN
                  RETURN
               ELSE
                  RESULT( 30 ) = ULPINV
                  GO TO 270
               END IF
            END IF
*
            J = IWBZ
            DO 240 I = 1, NS1
               CALL DCOPY( MNMIN, WORK( J ), 1, U( 1,I ), 1 )
               J = J + MNMIN
               CALL DCOPY( MNMIN, WORK( J ), 1, VT( I,1 ), LDPT )
               J = J + MNMIN
  240       CONTINUE
*
*           Use DBDSVDX to compute only the singular values of the
*           bidiagonal matrix B;  U and VT should not be modified.
*
            CALL DCOPY( MNMIN, BD, 1, WORK( IWBD ), 1 )
.GT.            IF( MNMIN0 )
     $         CALL DCOPY( MNMIN-1, BE, 1, WORK( IWBE ), 1 )
*
            CALL DBDSVDX( UPLO, 'n', 'v', MNMIN, WORK( IWBD ),
     $                    WORK( IWBE ), VL, VU, 0, 0, NS2, S2,
     $                    WORK( IWBZ ), MNMIN2, WORK( IWWORK ),
     $                    IWORK, IINFO )
*
*           Check error code from DBDSVDX.
*
.NE.            IF( IINFO0 ) THEN
               WRITE( NOUT, FMT = 9998 )'dbdsvdx(values,v)', IINFO,
     $            M, N, JTYPE, IOLDSD
               INFO = ABS( IINFO )
.LT.               IF( IINFO0 ) THEN
                  RETURN
               ELSE
                  RESULT( 34 ) = ULPINV
                  GO TO 270
               END IF
            END IF
*
*           Test 30:  Check S1 - U' * B * VT'
*                31:  Check the orthogonality of U
*                32:  Check the orthogonality of VT
*                33:  Check that the singular values are sorted in
*                     non-increasing order and are non-negative
*                34:  Compare DBDSVDX with and without singular vectors
*
            CALL DBDT04( UPLO, MNMIN, BD, BE, S1, NS1, U,
     $                   LDPT, VT, LDPT, WORK( IWBS+MNMIN ),
     $                   RESULT( 30 ) )
            CALL DORT01( 'columns', MNMIN, NS1, U, LDPT,
     $                   WORK( IWBS+MNMIN ), LWORK-MNMIN,
     $                   RESULT( 31 ) )
            CALL DORT01( 'rows', NS1, MNMIN, VT, LDPT,
     $                   WORK( IWBS+MNMIN ), LWORK-MNMIN,
     $                   RESULT( 32 ) )
*
            RESULT( 33 ) = ZERO
            DO 250 I = 1, NS1 - 1
.LT.               IF( S1( I )S1( I+1 ) )
     $            RESULT( 28 ) = ULPINV
.LT.               IF( S1( I )ZERO )
     $            RESULT( 28 ) = ULPINV
  250       CONTINUE
.GE.            IF( NS11 ) THEN
.LT.               IF( S1( NS1 )ZERO )
     $            RESULT( 28 ) = ULPINV
            END IF
*
            TEMP2 = ZERO
            DO 260 J = 1, NS1
               TEMP1 = ABS( S1( J )-S2( J ) ) /
     $                 MAX( SQRT( UNFL )*MAX( S1( 1 ), ONE ),
     $                 ULP*MAX( ABS( S1( 1 ) ), ABS( S2( 1 ) ) ) )
               TEMP2 = MAX( TEMP1, TEMP2 )
  260       CONTINUE
            RESULT( 34 ) = TEMP2
*
*           End of Loop -- Check for RESULT(j) > THRESH
*
  270       CONTINUE
*
            DO 280 J = 1, 34
.GE.               IF( RESULT( J )THRESH ) THEN
.EQ.                  IF( NFAIL0 )
     $               CALL DLAHD2( NOUT, PATH )
                  WRITE( NOUT, FMT = 9999 )M, N, JTYPE, IOLDSD, J,
     $               RESULT( J )
                  NFAIL = NFAIL + 1
               END IF
  280       CONTINUE
.NOT.            IF( BIDIAG ) THEN
               NTEST = NTEST + 34
            ELSE
               NTEST = NTEST + 30
            END IF
*
  290    CONTINUE
  300 CONTINUE
*
*     Summary
*
      CALL ALASUM( PATH, NOUT, NFAIL, NTEST, 0 )
*
      RETURN
*
*     End of DCHKBD
*
 9999 FORMAT( ' m=', I5, ', n=', I5, ', type ', i2, ', seed=',
     $      4( i4, ',' ), ' test(', i2, ')=', g11.4 )
 9998 FORMAT( ' DCHKBD: ', a, ' returned INFO=', i6, '.', / 9x, 'M=',
     $      i6, ', N=', i6, ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ),
     $      i5, ')' )
*
      END