LAPACK: TESTING/LIN/sdrvpo.f Source File

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00001       SUBROUTINE SDRVPO( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
00002      $                   A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK,
00003      $                   RWORK, IWORK, NOUT )
00004 *
00005 *  -- LAPACK test routine (version 3.1) --
00006 *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
00007 *     November 2006
00008 *
00009 *     .. Scalar Arguments ..
00010       LOGICAL            TSTERR
00011       INTEGER            NMAX, NN, NOUT, NRHS
00012       REAL               THRESH
00013 *     ..
00014 *     .. Array Arguments ..
00015       LOGICAL            DOTYPE( * )
00016       INTEGER            IWORK( * ), NVAL( * )
00017       REAL               A( * ), AFAC( * ), ASAV( * ), B( * ),
00018      $                   BSAV( * ), RWORK( * ), S( * ), WORK( * ),
00019      $                   X( * ), XACT( * )
00020 *     ..
00021 *
00022 *  Purpose
00023 *  =======
00024 *
00025 *  SDRVPO tests the driver routines SPOSV and -SVX.
00026 *
00027 *  Arguments
00028 *  =========
00029 *
00030 *  DOTYPE  (input) LOGICAL array, dimension (NTYPES)
00031 *          The matrix types to be used for testing.  Matrices of type j
00032 *          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
00033 *          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
00034 *
00035 *  NN      (input) INTEGER
00036 *          The number of values of N contained in the vector NVAL.
00037 *
00038 *  NVAL    (input) INTEGER array, dimension (NN)
00039 *          The values of the matrix dimension N.
00040 *
00041 *  NRHS    (input) INTEGER
00042 *          The number of right hand side vectors to be generated for
00043 *          each linear system.
00044 *
00045 *  THRESH  (input) REAL
00046 *          The threshold value for the test ratios.  A result is
00047 *          included in the output file if RESULT >= THRESH.  To have
00048 *          every test ratio printed, use THRESH = 0.
00049 *
00050 *  TSTERR  (input) LOGICAL
00051 *          Flag that indicates whether error exits are to be tested.
00052 *
00053 *  NMAX    (input) INTEGER
00054 *          The maximum value permitted for N, used in dimensioning the
00055 *          work arrays.
00056 *
00057 *  A       (workspace) REAL array, dimension (NMAX*NMAX)
00058 *
00059 *  AFAC    (workspace) REAL array, dimension (NMAX*NMAX)
00060 *
00061 *  ASAV    (workspace) REAL array, dimension (NMAX*NMAX)
00062 *
00063 *  B       (workspace) REAL array, dimension (NMAX*NRHS)
00064 *
00065 *  BSAV    (workspace) REAL array, dimension (NMAX*NRHS)
00066 *
00067 *  X       (workspace) REAL array, dimension (NMAX*NRHS)
00068 *
00069 *  XACT    (workspace) REAL array, dimension (NMAX*NRHS)
00070 *
00071 *  S       (workspace) REAL array, dimension (NMAX)
00072 *
00073 *  WORK    (workspace) REAL array, dimension
00074 *                      (NMAX*max(3,NRHS))
00075 *
00076 *  RWORK   (workspace) REAL array, dimension (NMAX+2*NRHS)
00077 *
00078 *  IWORK   (workspace) INTEGER array, dimension (NMAX)
00079 *
00080 *  NOUT    (input) INTEGER
00081 *          The unit number for output.
00082 *
00083 *  =====================================================================
00084 *
00085 *     .. Parameters ..
00086       REAL               ONE, ZERO
00087       PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
00088       INTEGER            NTYPES
00089       PARAMETER          ( NTYPES = 9 )
00090       INTEGER            NTESTS
00091       PARAMETER          ( NTESTS = 6 )
00092 *     ..
00093 *     .. Local Scalars ..
00094       LOGICAL            EQUIL, NOFACT, PREFAC, ZEROT
00095       CHARACTER          DIST, EQUED, FACT, TYPE, UPLO, XTYPE
00096       CHARACTER*3        PATH
00097       INTEGER            I, IEQUED, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
00098      $                   IZERO, K, K1, KL, KU, LDA, MODE, N, NB, NBMIN,
00099      $                   NERRS, NFACT, NFAIL, NIMAT, NRUN, NT
00100       REAL               AINVNM, AMAX, ANORM, CNDNUM, RCOND, RCONDC,
00101      $                   ROLDC, SCOND
00102 *     ..
00103 *     .. Local Arrays ..
00104       CHARACTER          EQUEDS( 2 ), FACTS( 3 ), UPLOS( 2 )
00105       INTEGER            ISEED( 4 ), ISEEDY( 4 )
00106       REAL               RESULT( NTESTS )
00107 *     ..
00108 *     .. External Functions ..
00109       LOGICAL            LSAME
00110       REAL               SGET06, SLANSY
00111       EXTERNAL           LSAME, SGET06, SLANSY
00112 *     ..
00113 *     .. External Subroutines ..
00114       EXTERNAL           ALADHD, ALAERH, ALASVM, SERRVX, SGET04, SLACPY,
00115      $                   SLAQSY, SLARHS, SLASET, SLATB4, SLATMS, SPOEQU,
00116      $                   SPOSV, SPOSVX, SPOT01, SPOT02, SPOT05, SPOTRF,
00117      $                   SPOTRI, XLAENV
00118 *     ..
00119 *     .. Intrinsic Functions ..
00120       INTRINSIC          MAX
00121 *     ..
00122 *     .. Scalars in Common ..
00123       LOGICAL            LERR, OK
00124       CHARACTER*32       SRNAMT
00125       INTEGER            INFOT, NUNIT
00126 *     ..
00127 *     .. Common blocks ..
00128       COMMON             / INFOC / INFOT, NUNIT, OK, LERR
00129       COMMON             / SRNAMC / SRNAMT
00130 *     ..
00131 *     .. Data statements ..
00132       DATA               ISEEDY / 1988, 1989, 1990, 1991 /
00133       DATA               UPLOS / 'U', 'L' /
00134       DATA               FACTS / 'F', 'N', 'E' /
00135       DATA               EQUEDS / 'N', 'Y' /
00136 *     ..
00137 *     .. Executable Statements ..
00138 *
00139 *     Initialize constants and the random number seed.
00140 *
00141       PATH( 1: 1 ) = 'Single precision'
00142       PATH( 2: 3 ) = 'PO'
00143       NRUN = 0
00144       NFAIL = 0
00145       NERRS = 0
00146       DO 10 I = 1, 4
00147          ISEED( I ) = ISEEDY( I )
00148    10 CONTINUE
00149 *
00150 *     Test the error exits
00151 *
00152       IF( TSTERR )
00153      $   CALL SERRVX( PATH, NOUT )
00154       INFOT = 0
00155 *
00156 *     Set the block size and minimum block size for testing.
00157 *
00158       NB = 1
00159       NBMIN = 2
00160       CALL XLAENV( 1, NB )
00161       CALL XLAENV( 2, NBMIN )
00162 *
00163 *     Do for each value of N in NVAL
00164 *
00165       DO 130 IN = 1, NN
00166          N = NVAL( IN )
00167          LDA = MAX( N, 1 )
00168          XTYPE = 'N'
00169          NIMAT = NTYPES
00170          IF( N.LE.0 )
00171      $      NIMAT = 1
00172 *
00173          DO 120 IMAT = 1, NIMAT
00174 *
00175 *           Do the tests only if DOTYPE( IMAT ) is true.
00176 *
00177             IF( .NOT.DOTYPE( IMAT ) )
00178      $         GO TO 120
00179 *
00180 *           Skip types 3, 4, or 5 if the matrix size is too small.
00181 *
00182             ZEROT = IMAT.GE.3 .AND. IMAT.LE.5
00183             IF( ZEROT .AND. N.LT.IMAT-2 )
00184      $         GO TO 120
00185 *
00186 *           Do first for UPLO = 'U', then for UPLO = 'L'
00187 *
00188             DO 110 IUPLO = 1, 2
00189                UPLO = UPLOS( IUPLO )
00190 *
00191 *              Set up parameters with SLATB4 and generate a test matrix
00192 *              with SLATMS.
00193 *
00194                CALL SLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE,
00195      $                      CNDNUM, DIST )
00196 *
00197                SRNAMT = 'SLATMS'
00198                CALL SLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
00199      $                      CNDNUM, ANORM, KL, KU, UPLO, A, LDA, WORK,
00200      $                      INFO )
00201 *
00202 *              Check error code from SLATMS.
00203 *
00204                IF( INFO.NE.0 ) THEN
00205                   CALL ALAERH( PATH, 'SLATMS', INFO, 0, UPLO, N, N, -1,
00206      $                         -1, -1, IMAT, NFAIL, NERRS, NOUT )
00207                   GO TO 110
00208                END IF
00209 *
00210 *              For types 3-5, zero one row and column of the matrix to
00211 *              test that INFO is returned correctly.
00212 *
00213                IF( ZEROT ) THEN
00214                   IF( IMAT.EQ.3 ) THEN
00215                      IZERO = 1
00216                   ELSE IF( IMAT.EQ.4 ) THEN
00217                      IZERO = N
00218                   ELSE
00219                      IZERO = N / 2 + 1
00220                   END IF
00221                   IOFF = ( IZERO-1 )*LDA
00222 *
00223 *                 Set row and column IZERO of A to 0.
00224 *
00225                   IF( IUPLO.EQ.1 ) THEN
00226                      DO 20 I = 1, IZERO - 1
00227                         A( IOFF+I ) = ZERO
00228    20                CONTINUE
00229                      IOFF = IOFF + IZERO
00230                      DO 30 I = IZERO, N
00231                         A( IOFF ) = ZERO
00232                         IOFF = IOFF + LDA
00233    30                CONTINUE
00234                   ELSE
00235                      IOFF = IZERO
00236                      DO 40 I = 1, IZERO - 1
00237                         A( IOFF ) = ZERO
00238                         IOFF = IOFF + LDA
00239    40                CONTINUE
00240                      IOFF = IOFF - IZERO
00241                      DO 50 I = IZERO, N
00242                         A( IOFF+I ) = ZERO
00243    50                CONTINUE
00244                   END IF
00245                ELSE
00246                   IZERO = 0
00247                END IF
00248 *
00249 *              Save a copy of the matrix A in ASAV.
00250 *
00251                CALL SLACPY( UPLO, N, N, A, LDA, ASAV, LDA )
00252 *
00253                DO 100 IEQUED = 1, 2
00254                   EQUED = EQUEDS( IEQUED )
00255                   IF( IEQUED.EQ.1 ) THEN
00256                      NFACT = 3
00257                   ELSE
00258                      NFACT = 1
00259                   END IF
00260 *
00261                   DO 90 IFACT = 1, NFACT
00262                      FACT = FACTS( IFACT )
00263                      PREFAC = LSAME( FACT, 'F' )
00264                      NOFACT = LSAME( FACT, 'N' )
00265                      EQUIL = LSAME( FACT, 'E' )
00266 *
00267                      IF( ZEROT ) THEN
00268                         IF( PREFAC )
00269      $                     GO TO 90
00270                         RCONDC = ZERO
00271 *
00272                      ELSE IF( .NOT.LSAME( FACT, 'N' ) ) THEN
00273 *
00274 *                       Compute the condition number for comparison with
00275 *                       the value returned by SPOSVX (FACT = 'N' reuses
00276 *                       the condition number from the previous iteration
00277 *                       with FACT = 'F').
00278 *
00279                         CALL SLACPY( UPLO, N, N, ASAV, LDA, AFAC, LDA )
00280                         IF( EQUIL .OR. IEQUED.GT.1 ) THEN
00281 *
00282 *                          Compute row and column scale factors to
00283 *                          equilibrate the matrix A.
00284 *
00285                            CALL SPOEQU( N, AFAC, LDA, S, SCOND, AMAX,
00286      $                                  INFO )
00287                            IF( INFO.EQ.0 .AND. N.GT.0 ) THEN
00288                               IF( IEQUED.GT.1 )
00289      $                           SCOND = ZERO
00290 *
00291 *                             Equilibrate the matrix.
00292 *
00293                               CALL SLAQSY( UPLO, N, AFAC, LDA, S, SCOND,
00294      $                                     AMAX, EQUED )
00295                            END IF
00296                         END IF
00297 *
00298 *                       Save the condition number of the
00299 *                       non-equilibrated system for use in SGET04.
00300 *
00301                         IF( EQUIL )
00302      $                     ROLDC = RCONDC
00303 *
00304 *                       Compute the 1-norm of A.
00305 *
00306                         ANORM = SLANSY( '1', UPLO, N, AFAC, LDA, RWORK )
00307 *
00308 *                       Factor the matrix A.
00309 *
00310                         CALL SPOTRF( UPLO, N, AFAC, LDA, INFO )
00311 *
00312 *                       Form the inverse of A.
00313 *
00314                         CALL SLACPY( UPLO, N, N, AFAC, LDA, A, LDA )
00315                         CALL SPOTRI( UPLO, N, A, LDA, INFO )
00316 *
00317 *                       Compute the 1-norm condition number of A.
00318 *
00319                         AINVNM = SLANSY( '1', UPLO, N, A, LDA, RWORK )
00320                         IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
00321                            RCONDC = ONE
00322                         ELSE
00323                            RCONDC = ( ONE / ANORM ) / AINVNM
00324                         END IF
00325                      END IF
00326 *
00327 *                    Restore the matrix A.
00328 *
00329                      CALL SLACPY( UPLO, N, N, ASAV, LDA, A, LDA )
00330 *
00331 *                    Form an exact solution and set the right hand side.
00332 *
00333                      SRNAMT = 'SLARHS'
00334                      CALL SLARHS( PATH, XTYPE, UPLO, ' ', N, N, KL, KU,
00335      $                            NRHS, A, LDA, XACT, LDA, B, LDA,
00336      $                            ISEED, INFO )
00337                      XTYPE = 'C'
00338                      CALL SLACPY( 'Full', N, NRHS, B, LDA, BSAV, LDA )
00339 *
00340                      IF( NOFACT ) THEN
00341 *
00342 *                       --- Test SPOSV  ---
00343 *
00344 *                       Compute the L*L' or U'*U factorization of the
00345 *                       matrix and solve the system.
00346 *
00347                         CALL SLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
00348                         CALL SLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
00349 *
00350                         SRNAMT = 'SPOSV '
00351                         CALL SPOSV( UPLO, N, NRHS, AFAC, LDA, X, LDA,
00352      $                              INFO )
00353 *
00354 *                       Check error code from SPOSV .
00355 *
00356                         IF( INFO.NE.IZERO ) THEN
00357                            CALL ALAERH( PATH, 'SPOSV ', INFO, IZERO,
00358      $                                  UPLO, N, N, -1, -1, NRHS, IMAT,
00359      $                                  NFAIL, NERRS, NOUT )
00360                            GO TO 70
00361                         ELSE IF( INFO.NE.0 ) THEN
00362                            GO TO 70
00363                         END IF
00364 *
00365 *                       Reconstruct matrix from factors and compute
00366 *                       residual.
00367 *
00368                         CALL SPOT01( UPLO, N, A, LDA, AFAC, LDA, RWORK,
00369      $                               RESULT( 1 ) )
00370 *
00371 *                       Compute residual of the computed solution.
00372 *
00373                         CALL SLACPY( 'Full', N, NRHS, B, LDA, WORK,
00374      $                               LDA )
00375                         CALL SPOT02( UPLO, N, NRHS, A, LDA, X, LDA,
00376      $                               WORK, LDA, RWORK, RESULT( 2 ) )
00377 *
00378 *                       Check solution from generated exact solution.
00379 *
00380                         CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
00381      $                               RESULT( 3 ) )
00382                         NT = 3
00383 *
00384 *                       Print information about the tests that did not
00385 *                       pass the threshold.
00386 *
00387                         DO 60 K = 1, NT
00388                            IF( RESULT( K ).GE.THRESH ) THEN
00389                               IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
00390      $                           CALL ALADHD( NOUT, PATH )
00391                               WRITE( NOUT, FMT = 9999 )'SPOSV ', UPLO,
00392      $                           N, IMAT, K, RESULT( K )
00393                               NFAIL = NFAIL + 1
00394                            END IF
00395    60                   CONTINUE
00396                         NRUN = NRUN + NT
00397    70                   CONTINUE
00398                      END IF
00399 *
00400 *                    --- Test SPOSVX ---
00401 *
00402                      IF( .NOT.PREFAC )
00403      $                  CALL SLASET( UPLO, N, N, ZERO, ZERO, AFAC, LDA )
00404                      CALL SLASET( 'Full', N, NRHS, ZERO, ZERO, X, LDA )
00405                      IF( IEQUED.GT.1 .AND. N.GT.0 ) THEN
00406 *
00407 *                       Equilibrate the matrix if FACT='F' and
00408 *                       EQUED='Y'.
00409 *
00410                         CALL SLAQSY( UPLO, N, A, LDA, S, SCOND, AMAX,
00411      $                               EQUED )
00412                      END IF
00413 *
00414 *                    Solve the system and compute the condition number
00415 *                    and error bounds using SPOSVX.
00416 *
00417                      SRNAMT = 'SPOSVX'
00418                      CALL SPOSVX( FACT, UPLO, N, NRHS, A, LDA, AFAC,
00419      $                            LDA, EQUED, S, B, LDA, X, LDA, RCOND,
00420      $                            RWORK, RWORK( NRHS+1 ), WORK, IWORK,
00421      $                            INFO )
00422 *
00423 *                    Check the error code from SPOSVX.
00424 *
00425                      IF( INFO.NE.IZERO ) THEN
00426                         CALL ALAERH( PATH, 'SPOSVX', INFO, IZERO,
00427      $                               FACT // UPLO, N, N, -1, -1, NRHS,
00428      $                               IMAT, NFAIL, NERRS, NOUT )
00429                         GO TO 90
00430                      END IF
00431 *
00432                      IF( INFO.EQ.0 ) THEN
00433                         IF( .NOT.PREFAC ) THEN
00434 *
00435 *                          Reconstruct matrix from factors and compute
00436 *                          residual.
00437 *
00438                            CALL SPOT01( UPLO, N, A, LDA, AFAC, LDA,
00439      $                                  RWORK( 2*NRHS+1 ), RESULT( 1 ) )
00440                            K1 = 1
00441                         ELSE
00442                            K1 = 2
00443                         END IF
00444 *
00445 *                       Compute residual of the computed solution.
00446 *
00447                         CALL SLACPY( 'Full', N, NRHS, BSAV, LDA, WORK,
00448      $                               LDA )
00449                         CALL SPOT02( UPLO, N, NRHS, ASAV, LDA, X, LDA,
00450      $                               WORK, LDA, RWORK( 2*NRHS+1 ),
00451      $                               RESULT( 2 ) )
00452 *
00453 *                       Check solution from generated exact solution.
00454 *
00455                         IF( NOFACT .OR. ( PREFAC .AND. LSAME( EQUED,
00456      $                      'N' ) ) ) THEN
00457                            CALL SGET04( N, NRHS, X, LDA, XACT, LDA,
00458      $                                  RCONDC, RESULT( 3 ) )
00459                         ELSE
00460                            CALL SGET04( N, NRHS, X, LDA, XACT, LDA,
00461      $                                  ROLDC, RESULT( 3 ) )
00462                         END IF
00463 *
00464 *                       Check the error bounds from iterative
00465 *                       refinement.
00466 *
00467                         CALL SPOT05( UPLO, N, NRHS, ASAV, LDA, B, LDA,
00468      $                               X, LDA, XACT, LDA, RWORK,
00469      $                               RWORK( NRHS+1 ), RESULT( 4 ) )
00470                      ELSE
00471                         K1 = 6
00472                      END IF
00473 *
00474 *                    Compare RCOND from SPOSVX with the computed value
00475 *                    in RCONDC.
00476 *
00477                      RESULT( 6 ) = SGET06( RCOND, RCONDC )
00478 *
00479 *                    Print information about the tests that did not pass
00480 *                    the threshold.
00481 *
00482                      DO 80 K = K1, 6
00483                         IF( RESULT( K ).GE.THRESH ) THEN
00484                            IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
00485      $                        CALL ALADHD( NOUT, PATH )
00486                            IF( PREFAC ) THEN
00487                               WRITE( NOUT, FMT = 9997 )'SPOSVX', FACT,
00488      $                           UPLO, N, EQUED, IMAT, K, RESULT( K )
00489                            ELSE
00490                               WRITE( NOUT, FMT = 9998 )'SPOSVX', FACT,
00491      $                           UPLO, N, IMAT, K, RESULT( K )
00492                            END IF
00493                            NFAIL = NFAIL + 1
00494                         END IF
00495    80                CONTINUE
00496                      NRUN = NRUN + 7 - K1
00497    90             CONTINUE
00498   100          CONTINUE
00499   110       CONTINUE
00500   120    CONTINUE
00501   130 CONTINUE
00502 *
00503 *     Print a summary of the results.
00504 *
00505       CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
00506 *
00507  9999 FORMAT( 1X, A, ', UPLO=''', A1, ''', N =', I5, ', type ', I1,
00508      $      ', test(', I1, ')=', G12.5 )
00509  9998 FORMAT( 1X, A, ', FACT=''', A1, ''', UPLO=''', A1, ''', N=', I5,
00510      $      ', type ', I1, ', test(', I1, ')=', G12.5 )
00511  9997 FORMAT( 1X, A, ', FACT=''', A1, ''', UPLO=''', A1, ''', N=', I5,
00512      $      ', EQUED=''', A1, ''', type ', I1, ', test(', I1, ') =',
00513      $      G12.5 )
00514       RETURN
00515 *
00516 *     End of SDRVPO
00517 *
00518       END