LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
sdrvls.f
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00001 *> \brief \b SDRVLS
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *  Definition:
00009 *  ===========
00010 *
00011 *       SUBROUTINE SDRVLS( DOTYPE, NM, MVAL, NN, NVAL, NNS, NSVAL, NNB,
00012 *                          NBVAL, NXVAL, THRESH, TSTERR, A, COPYA, B,
00013 *                          COPYB, C, S, COPYS, WORK, IWORK, NOUT )
00014 * 
00015 *       .. Scalar Arguments ..
00016 *       LOGICAL            TSTERR
00017 *       INTEGER            NM, NN, NNB, NNS, NOUT
00018 *       REAL               THRESH
00019 *       ..
00020 *       .. Array Arguments ..
00021 *       LOGICAL            DOTYPE( * )
00022 *       INTEGER            IWORK( * ), MVAL( * ), NBVAL( * ), NSVAL( * ),
00023 *      $                   NVAL( * ), NXVAL( * )
00024 *       REAL               A( * ), B( * ), C( * ), COPYA( * ), COPYB( * ),
00025 *      $                   COPYS( * ), S( * ), WORK( * )
00026 *       ..
00027 *  
00028 *
00029 *> \par Purpose:
00030 *  =============
00031 *>
00032 *> \verbatim
00033 *>
00034 *> SDRVLS tests the least squares driver routines SGELS, SGELSS, SGELSX,
00035 *> SGELSY and SGELSD.
00036 *> \endverbatim
00037 *
00038 *  Arguments:
00039 *  ==========
00040 *
00041 *> \param[in] DOTYPE
00042 *> \verbatim
00043 *>          DOTYPE is LOGICAL array, dimension (NTYPES)
00044 *>          The matrix types to be used for testing.  Matrices of type j
00045 *>          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
00046 *>          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
00047 *>          The matrix of type j is generated as follows:
00048 *>          j=1: A = U*D*V where U and V are random orthogonal matrices
00049 *>               and D has random entries (> 0.1) taken from a uniform 
00050 *>               distribution (0,1). A is full rank.
00051 *>          j=2: The same of 1, but A is scaled up.
00052 *>          j=3: The same of 1, but A is scaled down.
00053 *>          j=4: A = U*D*V where U and V are random orthogonal matrices
00054 *>               and D has 3*min(M,N)/4 random entries (> 0.1) taken
00055 *>               from a uniform distribution (0,1) and the remaining
00056 *>               entries set to 0. A is rank-deficient. 
00057 *>          j=5: The same of 4, but A is scaled up.
00058 *>          j=6: The same of 5, but A is scaled down.
00059 *> \endverbatim
00060 *>
00061 *> \param[in] NM
00062 *> \verbatim
00063 *>          NM is INTEGER
00064 *>          The number of values of M contained in the vector MVAL.
00065 *> \endverbatim
00066 *>
00067 *> \param[in] MVAL
00068 *> \verbatim
00069 *>          MVAL is INTEGER array, dimension (NM)
00070 *>          The values of the matrix row dimension M.
00071 *> \endverbatim
00072 *>
00073 *> \param[in] NN
00074 *> \verbatim
00075 *>          NN is INTEGER
00076 *>          The number of values of N contained in the vector NVAL.
00077 *> \endverbatim
00078 *>
00079 *> \param[in] NVAL
00080 *> \verbatim
00081 *>          NVAL is INTEGER array, dimension (NN)
00082 *>          The values of the matrix column dimension N.
00083 *> \endverbatim
00084 *>
00085 *> \param[in] NNS
00086 *> \verbatim
00087 *>          NNS is INTEGER
00088 *>          The number of values of NRHS contained in the vector NSVAL.
00089 *> \endverbatim
00090 *>
00091 *> \param[in] NSVAL
00092 *> \verbatim
00093 *>          NSVAL is INTEGER array, dimension (NNS)
00094 *>          The values of the number of right hand sides NRHS.
00095 *> \endverbatim
00096 *>
00097 *> \param[in] NNB
00098 *> \verbatim
00099 *>          NNB is INTEGER
00100 *>          The number of values of NB and NX contained in the
00101 *>          vectors NBVAL and NXVAL.  The blocking parameters are used
00102 *>          in pairs (NB,NX).
00103 *> \endverbatim
00104 *>
00105 *> \param[in] NBVAL
00106 *> \verbatim
00107 *>          NBVAL is INTEGER array, dimension (NNB)
00108 *>          The values of the blocksize NB.
00109 *> \endverbatim
00110 *>
00111 *> \param[in] NXVAL
00112 *> \verbatim
00113 *>          NXVAL is INTEGER array, dimension (NNB)
00114 *>          The values of the crossover point NX.
00115 *> \endverbatim
00116 *>
00117 *> \param[in] THRESH
00118 *> \verbatim
00119 *>          THRESH is REAL
00120 *>          The threshold value for the test ratios.  A result is
00121 *>          included in the output file if RESULT >= THRESH.  To have
00122 *>          every test ratio printed, use THRESH = 0.
00123 *> \endverbatim
00124 *>
00125 *> \param[in] TSTERR
00126 *> \verbatim
00127 *>          TSTERR is LOGICAL
00128 *>          Flag that indicates whether error exits are to be tested.
00129 *> \endverbatim
00130 *>
00131 *> \param[out] A
00132 *> \verbatim
00133 *>          A is REAL array, dimension (MMAX*NMAX)
00134 *>          where MMAX is the maximum value of M in MVAL and NMAX is the
00135 *>          maximum value of N in NVAL.
00136 *> \endverbatim
00137 *>
00138 *> \param[out] COPYA
00139 *> \verbatim
00140 *>          COPYA is REAL array, dimension (MMAX*NMAX)
00141 *> \endverbatim
00142 *>
00143 *> \param[out] B
00144 *> \verbatim
00145 *>          B is REAL array, dimension (MMAX*NSMAX)
00146 *>          where MMAX is the maximum value of M in MVAL and NSMAX is the
00147 *>          maximum value of NRHS in NSVAL.
00148 *> \endverbatim
00149 *>
00150 *> \param[out] COPYB
00151 *> \verbatim
00152 *>          COPYB is REAL array, dimension (MMAX*NSMAX)
00153 *> \endverbatim
00154 *>
00155 *> \param[out] C
00156 *> \verbatim
00157 *>          C is REAL array, dimension (MMAX*NSMAX)
00158 *> \endverbatim
00159 *>
00160 *> \param[out] S
00161 *> \verbatim
00162 *>          S is REAL array, dimension
00163 *>                      (min(MMAX,NMAX))
00164 *> \endverbatim
00165 *>
00166 *> \param[out] COPYS
00167 *> \verbatim
00168 *>          COPYS is REAL array, dimension
00169 *>                      (min(MMAX,NMAX))
00170 *> \endverbatim
00171 *>
00172 *> \param[out] WORK
00173 *> \verbatim
00174 *>          WORK is REAL array,
00175 *>                      dimension (MMAX*NMAX + 4*NMAX + MMAX).
00176 *> \endverbatim
00177 *>
00178 *> \param[out] IWORK
00179 *> \verbatim
00180 *>          IWORK is INTEGER array, dimension (15*NMAX)
00181 *> \endverbatim
00182 *>
00183 *> \param[in] NOUT
00184 *> \verbatim
00185 *>          NOUT is INTEGER
00186 *>          The unit number for output.
00187 *> \endverbatim
00188 *
00189 *  Authors:
00190 *  ========
00191 *
00192 *> \author Univ. of Tennessee 
00193 *> \author Univ. of California Berkeley 
00194 *> \author Univ. of Colorado Denver 
00195 *> \author NAG Ltd. 
00196 *
00197 *> \date November 2011
00198 *
00199 *> \ingroup single_lin
00200 *
00201 *  =====================================================================
00202       SUBROUTINE SDRVLS( DOTYPE, NM, MVAL, NN, NVAL, NNS, NSVAL, NNB,
00203      $                   NBVAL, NXVAL, THRESH, TSTERR, A, COPYA, B,
00204      $                   COPYB, C, S, COPYS, WORK, IWORK, NOUT )
00205 *
00206 *  -- LAPACK test routine (version 3.4.0) --
00207 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00208 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00209 *     November 2011
00210 *
00211 *     .. Scalar Arguments ..
00212       LOGICAL            TSTERR
00213       INTEGER            NM, NN, NNB, NNS, NOUT
00214       REAL               THRESH
00215 *     ..
00216 *     .. Array Arguments ..
00217       LOGICAL            DOTYPE( * )
00218       INTEGER            IWORK( * ), MVAL( * ), NBVAL( * ), NSVAL( * ),
00219      $                   NVAL( * ), NXVAL( * )
00220       REAL               A( * ), B( * ), C( * ), COPYA( * ), COPYB( * ),
00221      $                   COPYS( * ), S( * ), WORK( * )
00222 *     ..
00223 *
00224 *  =====================================================================
00225 *
00226 *     .. Parameters ..
00227       INTEGER            NTESTS
00228       PARAMETER          ( NTESTS = 18 )
00229       INTEGER            SMLSIZ
00230       PARAMETER          ( SMLSIZ = 25 )
00231       REAL               ONE, TWO, ZERO
00232       PARAMETER          ( ONE = 1.0E0, TWO = 2.0E0, ZERO = 0.0E0 )
00233 *     ..
00234 *     .. Local Scalars ..
00235       CHARACTER          TRANS
00236       CHARACTER*3        PATH
00237       INTEGER            CRANK, I, IM, IN, INB, INFO, INS, IRANK, 
00238      $                   ISCALE, ITRAN, ITYPE, J, K, LDA, LDB, LDWORK, 
00239      $                   LWLSY, LWORK, M, MNMIN, N, NB, NCOLS, NERRS, 
00240      $                   NFAIL, NLVL, NRHS, NROWS, NRUN, RANK
00241       REAL               EPS, NORMA, NORMB, RCOND
00242 *     ..
00243 *     .. Local Arrays ..
00244       INTEGER            ISEED( 4 ), ISEEDY( 4 )
00245       REAL               RESULT( NTESTS )
00246 *     ..
00247 *     .. External Functions ..
00248       REAL               SASUM, SLAMCH, SQRT12, SQRT14, SQRT17
00249       EXTERNAL           SASUM, SLAMCH, SQRT12, SQRT14, SQRT17
00250 *     ..
00251 *     .. External Subroutines ..
00252       EXTERNAL           ALAERH, ALAHD, ALASVM, SAXPY, SERRLS, SGELS,
00253      $                   SGELSD, SGELSS, SGELSX, SGELSY, SGEMM, SLACPY,
00254      $                   SLARNV, SQRT13, SQRT15, SQRT16, SSCAL,
00255      $                   XLAENV
00256 *     ..
00257 *     .. Intrinsic Functions ..
00258       INTRINSIC          INT, LOG, MAX, MIN, REAL, SQRT
00259 *     ..
00260 *     .. Scalars in Common ..
00261       LOGICAL            LERR, OK
00262       CHARACTER*32       SRNAMT
00263       INTEGER            INFOT, IOUNIT
00264 *     ..
00265 *     .. Common blocks ..
00266       COMMON             / INFOC / INFOT, IOUNIT, OK, LERR
00267       COMMON             / SRNAMC / SRNAMT
00268 *     ..
00269 *     .. Data statements ..
00270       DATA               ISEEDY / 1988, 1989, 1990, 1991 /
00271 *     ..
00272 *     .. Executable Statements ..
00273 *
00274 *     Initialize constants and the random number seed.
00275 *
00276       PATH( 1: 1 ) = 'Single precision'
00277       PATH( 2: 3 ) = 'LS'
00278       NRUN = 0
00279       NFAIL = 0
00280       NERRS = 0
00281       DO 10 I = 1, 4
00282          ISEED( I ) = ISEEDY( I )
00283    10 CONTINUE
00284       EPS = SLAMCH( 'Epsilon' )
00285 *
00286 *     Threshold for rank estimation
00287 *
00288       RCOND = SQRT( EPS ) - ( SQRT( EPS )-EPS ) / 2
00289 *
00290 *     Test the error exits
00291 *
00292       CALL XLAENV( 2, 2 )
00293       CALL XLAENV( 9, SMLSIZ )
00294       IF( TSTERR )
00295      $   CALL SERRLS( PATH, NOUT )
00296 *
00297 *     Print the header if NM = 0 or NN = 0 and THRESH = 0.
00298 *
00299       IF( ( NM.EQ.0 .OR. NN.EQ.0 ) .AND. THRESH.EQ.ZERO )
00300      $   CALL ALAHD( NOUT, PATH )
00301       INFOT = 0
00302 *
00303       DO 150 IM = 1, NM
00304          M = MVAL( IM )
00305          LDA = MAX( 1, M )
00306 *
00307          DO 140 IN = 1, NN
00308             N = NVAL( IN )
00309             MNMIN = MIN( M, N )
00310             LDB = MAX( 1, M, N )
00311 *
00312             DO 130 INS = 1, NNS
00313                NRHS = NSVAL( INS )
00314                NLVL = MAX( INT( LOG( MAX( ONE, REAL( MNMIN ) ) /
00315      $                REAL( SMLSIZ+1 ) ) / LOG( TWO ) ) + 1, 0 )
00316                LWORK = MAX( 1, ( M+NRHS )*( N+2 ), ( N+NRHS )*( M+2 ),
00317      $                 M*N+4*MNMIN+MAX( M, N ), 12*MNMIN+2*MNMIN*SMLSIZ+
00318      $                 8*MNMIN*NLVL+MNMIN*NRHS+(SMLSIZ+1)**2 )
00319 *
00320                DO 120 IRANK = 1, 2
00321                   DO 110 ISCALE = 1, 3
00322                      ITYPE = ( IRANK-1 )*3 + ISCALE
00323                      IF( .NOT.DOTYPE( ITYPE ) )
00324      $                  GO TO 110
00325 *
00326                      IF( IRANK.EQ.1 ) THEN
00327 *
00328 *                       Test SGELS
00329 *
00330 *                       Generate a matrix of scaling type ISCALE
00331 *
00332                         CALL SQRT13( ISCALE, M, N, COPYA, LDA, NORMA,
00333      $                               ISEED )
00334                         DO 40 INB = 1, NNB
00335                            NB = NBVAL( INB )
00336                            CALL XLAENV( 1, NB )
00337                            CALL XLAENV( 3, NXVAL( INB ) )
00338 *
00339                            DO 30 ITRAN = 1, 2
00340                               IF( ITRAN.EQ.1 ) THEN
00341                                  TRANS = 'N'
00342                                  NROWS = M
00343                                  NCOLS = N
00344                               ELSE
00345                                  TRANS = 'T'
00346                                  NROWS = N
00347                                  NCOLS = M
00348                               END IF
00349                               LDWORK = MAX( 1, NCOLS )
00350 *
00351 *                             Set up a consistent rhs
00352 *
00353                               IF( NCOLS.GT.0 ) THEN
00354                                  CALL SLARNV( 2, ISEED, NCOLS*NRHS,
00355      $                                        WORK )
00356                                  CALL SSCAL( NCOLS*NRHS,
00357      $                                       ONE / REAL( NCOLS ), WORK,
00358      $                                       1 )
00359                               END IF
00360                               CALL SGEMM( TRANS, 'No transpose', NROWS,
00361      $                                    NRHS, NCOLS, ONE, COPYA, LDA,
00362      $                                    WORK, LDWORK, ZERO, B, LDB )
00363                               CALL SLACPY( 'Full', NROWS, NRHS, B, LDB,
00364      $                                     COPYB, LDB )
00365 *
00366 *                             Solve LS or overdetermined system
00367 *
00368                               IF( M.GT.0 .AND. N.GT.0 ) THEN
00369                                  CALL SLACPY( 'Full', M, N, COPYA, LDA,
00370      $                                        A, LDA )
00371                                  CALL SLACPY( 'Full', NROWS, NRHS,
00372      $                                        COPYB, LDB, B, LDB )
00373                               END IF
00374                               SRNAMT = 'SGELS '
00375                               CALL SGELS( TRANS, M, N, NRHS, A, LDA, B,
00376      $                                    LDB, WORK, LWORK, INFO )
00377                               IF( INFO.NE.0 )
00378      $                           CALL ALAERH( PATH, 'SGELS ', INFO, 0,
00379      $                                        TRANS, M, N, NRHS, -1, NB,
00380      $                                        ITYPE, NFAIL, NERRS,
00381      $                                        NOUT )
00382 *
00383 *                             Check correctness of results
00384 *
00385                               LDWORK = MAX( 1, NROWS )
00386                               IF( NROWS.GT.0 .AND. NRHS.GT.0 )
00387      $                           CALL SLACPY( 'Full', NROWS, NRHS,
00388      $                                        COPYB, LDB, C, LDB )
00389                               CALL SQRT16( TRANS, M, N, NRHS, COPYA,
00390      $                                     LDA, B, LDB, C, LDB, WORK,
00391      $                                     RESULT( 1 ) )
00392 *
00393                               IF( ( ITRAN.EQ.1 .AND. M.GE.N ) .OR.
00394      $                            ( ITRAN.EQ.2 .AND. M.LT.N ) ) THEN
00395 *
00396 *                                Solving LS system
00397 *
00398                                  RESULT( 2 ) = SQRT17( TRANS, 1, M, N,
00399      $                                         NRHS, COPYA, LDA, B, LDB,
00400      $                                         COPYB, LDB, C, WORK,
00401      $                                         LWORK )
00402                               ELSE
00403 *
00404 *                                Solving overdetermined system
00405 *
00406                                  RESULT( 2 ) = SQRT14( TRANS, M, N,
00407      $                                         NRHS, COPYA, LDA, B, LDB,
00408      $                                         WORK, LWORK )
00409                               END IF
00410 *
00411 *                             Print information about the tests that
00412 *                             did not pass the threshold.
00413 *
00414                               DO 20 K = 1, 2
00415                                  IF( RESULT( K ).GE.THRESH ) THEN
00416                                     IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
00417      $                                 CALL ALAHD( NOUT, PATH )
00418                                     WRITE( NOUT, FMT = 9999 )TRANS, M,
00419      $                                 N, NRHS, NB, ITYPE, K,
00420      $                                 RESULT( K )
00421                                     NFAIL = NFAIL + 1
00422                                  END IF
00423    20                         CONTINUE
00424                               NRUN = NRUN + 2
00425    30                      CONTINUE
00426    40                   CONTINUE
00427                      END IF
00428 *
00429 *                    Generate a matrix of scaling type ISCALE and rank
00430 *                    type IRANK.
00431 *
00432                      CALL SQRT15( ISCALE, IRANK, M, N, NRHS, COPYA, LDA,
00433      $                            COPYB, LDB, COPYS, RANK, NORMA, NORMB,
00434      $                            ISEED, WORK, LWORK )
00435 *
00436 *                    workspace used: MAX(M+MIN(M,N),NRHS*MIN(M,N),2*N+M)
00437 *
00438 *                    Initialize vector IWORK.
00439 *
00440                      DO 50 J = 1, N
00441                         IWORK( J ) = 0
00442    50                CONTINUE
00443                      LDWORK = MAX( 1, M )
00444 *
00445 *                    Test SGELSX
00446 *
00447 *                    SGELSX:  Compute the minimum-norm solution X
00448 *                    to min( norm( A * X - B ) ) using a complete
00449 *                    orthogonal factorization.
00450 *
00451                      CALL SLACPY( 'Full', M, N, COPYA, LDA, A, LDA )
00452                      CALL SLACPY( 'Full', M, NRHS, COPYB, LDB, B, LDB )
00453 *
00454                      SRNAMT = 'SGELSX'
00455                      CALL SGELSX( M, N, NRHS, A, LDA, B, LDB, IWORK,
00456      $                            RCOND, CRANK, WORK, INFO )
00457                      IF( INFO.NE.0 )
00458      $                  CALL ALAERH( PATH, 'SGELSX', INFO, 0, ' ', M, N,
00459      $                               NRHS, -1, NB, ITYPE, NFAIL, NERRS,
00460      $                               NOUT )
00461 *
00462 *                    workspace used: MAX( MNMIN+3*N, 2*MNMIN+NRHS )
00463 *
00464 *                    Test 3:  Compute relative error in svd
00465 *                             workspace: M*N + 4*MIN(M,N) + MAX(M,N)
00466 *
00467                      RESULT( 3 ) = SQRT12( CRANK, CRANK, A, LDA, COPYS,
00468      $                             WORK, LWORK )
00469 *
00470 *                    Test 4:  Compute error in solution
00471 *                             workspace:  M*NRHS + M
00472 *
00473                      CALL SLACPY( 'Full', M, NRHS, COPYB, LDB, WORK,
00474      $                            LDWORK )
00475                      CALL SQRT16( 'No transpose', M, N, NRHS, COPYA,
00476      $                            LDA, B, LDB, WORK, LDWORK,
00477      $                            WORK( M*NRHS+1 ), RESULT( 4 ) )
00478 *
00479 *                    Test 5:  Check norm of r'*A
00480 *                             workspace: NRHS*(M+N)
00481 *
00482                      RESULT( 5 ) = ZERO
00483                      IF( M.GT.CRANK )
00484      $                  RESULT( 5 ) = SQRT17( 'No transpose', 1, M, N,
00485      $                                NRHS, COPYA, LDA, B, LDB, COPYB,
00486      $                                LDB, C, WORK, LWORK )
00487 *
00488 *                    Test 6:  Check if x is in the rowspace of A
00489 *                             workspace: (M+NRHS)*(N+2)
00490 *
00491                      RESULT( 6 ) = ZERO
00492 *
00493                      IF( N.GT.CRANK )
00494      $                  RESULT( 6 ) = SQRT14( 'No transpose', M, N,
00495      $                                NRHS, COPYA, LDA, B, LDB, WORK,
00496      $                                LWORK )
00497 *
00498 *                    Print information about the tests that did not
00499 *                    pass the threshold.
00500 *
00501                      DO 60 K = 3, 6
00502                         IF( RESULT( K ).GE.THRESH ) THEN
00503                            IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
00504      $                        CALL ALAHD( NOUT, PATH )
00505                            WRITE( NOUT, FMT = 9998 )M, N, NRHS, NB,
00506      $                        ITYPE, K, RESULT( K )
00507                            NFAIL = NFAIL + 1
00508                         END IF
00509    60                CONTINUE
00510                      NRUN = NRUN + 4
00511 *
00512 *                    Loop for testing different block sizes.
00513 *
00514                      DO 100 INB = 1, NNB
00515                         NB = NBVAL( INB )
00516                         CALL XLAENV( 1, NB )
00517                         CALL XLAENV( 3, NXVAL( INB ) )
00518 *
00519 *                       Test SGELSY
00520 *
00521 *                       SGELSY:  Compute the minimum-norm solution X
00522 *                       to min( norm( A * X - B ) )
00523 *                       using the rank-revealing orthogonal
00524 *                       factorization.
00525 *
00526 *                       Initialize vector IWORK.
00527 *
00528                         DO 70 J = 1, N
00529                            IWORK( J ) = 0
00530    70                   CONTINUE
00531 *
00532 *                       Set LWLSY to the adequate value.
00533 *
00534                         LWLSY = MAX( 1, MNMIN+2*N+NB*( N+1 ),
00535      $                          2*MNMIN+NB*NRHS )
00536 *
00537                         CALL SLACPY( 'Full', M, N, COPYA, LDA, A, LDA )
00538                         CALL SLACPY( 'Full', M, NRHS, COPYB, LDB, B,
00539      $                               LDB )
00540 *
00541                         SRNAMT = 'SGELSY'
00542                         CALL SGELSY( M, N, NRHS, A, LDA, B, LDB, IWORK,
00543      $                               RCOND, CRANK, WORK, LWLSY, INFO )
00544                         IF( INFO.NE.0 )
00545      $                     CALL ALAERH( PATH, 'SGELSY', INFO, 0, ' ', M,
00546      $                                  N, NRHS, -1, NB, ITYPE, NFAIL,
00547      $                                  NERRS, NOUT )
00548 *
00549 *                       Test 7:  Compute relative error in svd
00550 *                                workspace: M*N + 4*MIN(M,N) + MAX(M,N)
00551 *
00552                         RESULT( 7 ) = SQRT12( CRANK, CRANK, A, LDA,
00553      $                                COPYS, WORK, LWORK )
00554 *
00555 *                       Test 8:  Compute error in solution
00556 *                                workspace:  M*NRHS + M
00557 *
00558                         CALL SLACPY( 'Full', M, NRHS, COPYB, LDB, WORK,
00559      $                               LDWORK )
00560                         CALL SQRT16( 'No transpose', M, N, NRHS, COPYA,
00561      $                               LDA, B, LDB, WORK, LDWORK,
00562      $                               WORK( M*NRHS+1 ), RESULT( 8 ) )
00563 *
00564 *                       Test 9:  Check norm of r'*A
00565 *                                workspace: NRHS*(M+N)
00566 *
00567                         RESULT( 9 ) = ZERO
00568                         IF( M.GT.CRANK )
00569      $                     RESULT( 9 ) = SQRT17( 'No transpose', 1, M,
00570      $                                   N, NRHS, COPYA, LDA, B, LDB,
00571      $                                   COPYB, LDB, C, WORK, LWORK )
00572 *
00573 *                       Test 10:  Check if x is in the rowspace of A
00574 *                                workspace: (M+NRHS)*(N+2)
00575 *
00576                         RESULT( 10 ) = ZERO
00577 *
00578                         IF( N.GT.CRANK )
00579      $                     RESULT( 10 ) = SQRT14( 'No transpose', M, N,
00580      $                                    NRHS, COPYA, LDA, B, LDB,
00581      $                                    WORK, LWORK )
00582 *
00583 *                       Test SGELSS
00584 *
00585 *                       SGELSS:  Compute the minimum-norm solution X
00586 *                       to min( norm( A * X - B ) )
00587 *                       using the SVD.
00588 *
00589                         CALL SLACPY( 'Full', M, N, COPYA, LDA, A, LDA )
00590                         CALL SLACPY( 'Full', M, NRHS, COPYB, LDB, B,
00591      $                               LDB )
00592                         SRNAMT = 'SGELSS'
00593                         CALL SGELSS( M, N, NRHS, A, LDA, B, LDB, S,
00594      $                               RCOND, CRANK, WORK, LWORK, INFO )
00595                         IF( INFO.NE.0 )
00596      $                     CALL ALAERH( PATH, 'SGELSS', INFO, 0, ' ', M,
00597      $                                  N, NRHS, -1, NB, ITYPE, NFAIL,
00598      $                                  NERRS, NOUT )
00599 *
00600 *                       workspace used: 3*min(m,n) +
00601 *                                       max(2*min(m,n),nrhs,max(m,n))
00602 *
00603 *                       Test 11:  Compute relative error in svd
00604 *
00605                         IF( RANK.GT.0 ) THEN
00606                            CALL SAXPY( MNMIN, -ONE, COPYS, 1, S, 1 )
00607                            RESULT( 11 ) = SASUM( MNMIN, S, 1 ) /
00608      $                                    SASUM( MNMIN, COPYS, 1 ) /
00609      $                                    ( EPS*REAL( MNMIN ) )
00610                         ELSE
00611                            RESULT( 11 ) = ZERO
00612                         END IF
00613 *
00614 *                       Test 12:  Compute error in solution
00615 *
00616                         CALL SLACPY( 'Full', M, NRHS, COPYB, LDB, WORK,
00617      $                               LDWORK )
00618                         CALL SQRT16( 'No transpose', M, N, NRHS, COPYA,
00619      $                               LDA, B, LDB, WORK, LDWORK,
00620      $                               WORK( M*NRHS+1 ), RESULT( 12 ) )
00621 *
00622 *                       Test 13:  Check norm of r'*A
00623 *
00624                         RESULT( 13 ) = ZERO
00625                         IF( M.GT.CRANK )
00626      $                     RESULT( 13 ) = SQRT17( 'No transpose', 1, M,
00627      $                                    N, NRHS, COPYA, LDA, B, LDB,
00628      $                                    COPYB, LDB, C, WORK, LWORK )
00629 *
00630 *                       Test 14:  Check if x is in the rowspace of A
00631 *
00632                         RESULT( 14 ) = ZERO
00633                         IF( N.GT.CRANK )
00634      $                     RESULT( 14 ) = SQRT14( 'No transpose', M, N,
00635      $                                    NRHS, COPYA, LDA, B, LDB,
00636      $                                    WORK, LWORK )
00637 *
00638 *                       Test SGELSD
00639 *
00640 *                       SGELSD:  Compute the minimum-norm solution X
00641 *                       to min( norm( A * X - B ) ) using a
00642 *                       divide and conquer SVD.
00643 *
00644 *                       Initialize vector IWORK.
00645 *
00646                         DO 80 J = 1, N
00647                            IWORK( J ) = 0
00648    80                   CONTINUE
00649 *
00650                         CALL SLACPY( 'Full', M, N, COPYA, LDA, A, LDA )
00651                         CALL SLACPY( 'Full', M, NRHS, COPYB, LDB, B,
00652      $                               LDB )
00653 *
00654                         SRNAMT = 'SGELSD'
00655                         CALL SGELSD( M, N, NRHS, A, LDA, B, LDB, S,
00656      $                               RCOND, CRANK, WORK, LWORK, IWORK,
00657      $                               INFO )
00658                         IF( INFO.NE.0 )
00659      $                     CALL ALAERH( PATH, 'SGELSD', INFO, 0, ' ', M,
00660      $                                  N, NRHS, -1, NB, ITYPE, NFAIL,
00661      $                                  NERRS, NOUT )
00662 *
00663 *                       Test 15:  Compute relative error in svd
00664 *
00665                         IF( RANK.GT.0 ) THEN
00666                            CALL SAXPY( MNMIN, -ONE, COPYS, 1, S, 1 )
00667                            RESULT( 15 ) = SASUM( MNMIN, S, 1 ) /
00668      $                                    SASUM( MNMIN, COPYS, 1 ) /
00669      $                                    ( EPS*REAL( MNMIN ) )
00670                         ELSE
00671                            RESULT( 15 ) = ZERO
00672                         END IF
00673 *
00674 *                       Test 16:  Compute error in solution
00675 *
00676                         CALL SLACPY( 'Full', M, NRHS, COPYB, LDB, WORK,
00677      $                               LDWORK )
00678                         CALL SQRT16( 'No transpose', M, N, NRHS, COPYA,
00679      $                               LDA, B, LDB, WORK, LDWORK,
00680      $                               WORK( M*NRHS+1 ), RESULT( 16 ) )
00681 *
00682 *                       Test 17:  Check norm of r'*A
00683 *
00684                         RESULT( 17 ) = ZERO
00685                         IF( M.GT.CRANK )
00686      $                     RESULT( 17 ) = SQRT17( 'No transpose', 1, M,
00687      $                                    N, NRHS, COPYA, LDA, B, LDB,
00688      $                                    COPYB, LDB, C, WORK, LWORK )
00689 *
00690 *                       Test 18:  Check if x is in the rowspace of A
00691 *
00692                         RESULT( 18 ) = ZERO
00693                         IF( N.GT.CRANK )
00694      $                     RESULT( 18 ) = SQRT14( 'No transpose', M, N,
00695      $                                    NRHS, COPYA, LDA, B, LDB,
00696      $                                    WORK, LWORK )
00697 *
00698 *                       Print information about the tests that did not
00699 *                       pass the threshold.
00700 *
00701                         DO 90 K = 7, NTESTS
00702                            IF( RESULT( K ).GE.THRESH ) THEN
00703                               IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
00704      $                           CALL ALAHD( NOUT, PATH )
00705                               WRITE( NOUT, FMT = 9998 )M, N, NRHS, NB,
00706      $                           ITYPE, K, RESULT( K )
00707                               NFAIL = NFAIL + 1
00708                            END IF
00709    90                   CONTINUE
00710                         NRUN = NRUN + 12 
00711 *
00712   100                CONTINUE
00713   110             CONTINUE
00714   120          CONTINUE
00715   130       CONTINUE
00716   140    CONTINUE
00717   150 CONTINUE
00718 *
00719 *     Print a summary of the results.
00720 *
00721       CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
00722 *
00723  9999 FORMAT( ' TRANS=''', A1, ''', M=', I5, ', N=', I5, ', NRHS=', I4,
00724      $      ', NB=', I4, ', type', I2, ', test(', I2, ')=', G12.5 )
00725  9998 FORMAT( ' M=', I5, ', N=', I5, ', NRHS=', I4, ', NB=', I4,
00726      $      ', type', I2, ', test(', I2, ')=', G12.5 )
00727       RETURN
00728 *
00729 *     End of SDRVLS
00730 *
00731       END
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