LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
sdrvsp.f
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00001 *> \brief \b SDRVSP
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 SDRVSP( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
00012 *                          A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
00013 *                          NOUT )
00014 * 
00015 *       .. Scalar Arguments ..
00016 *       LOGICAL            TSTERR
00017 *       INTEGER            NMAX, NN, NOUT, NRHS
00018 *       REAL               THRESH
00019 *       ..
00020 *       .. Array Arguments ..
00021 *       LOGICAL            DOTYPE( * )
00022 *       INTEGER            IWORK( * ), NVAL( * )
00023 *       REAL               A( * ), AFAC( * ), AINV( * ), B( * ),
00024 *      $                   RWORK( * ), WORK( * ), X( * ), XACT( * )
00025 *       ..
00026 *  
00027 *
00028 *> \par Purpose:
00029 *  =============
00030 *>
00031 *> \verbatim
00032 *>
00033 *> SDRVSP tests the driver routines SSPSV and -SVX.
00034 *> \endverbatim
00035 *
00036 *  Arguments:
00037 *  ==========
00038 *
00039 *> \param[in] DOTYPE
00040 *> \verbatim
00041 *>          DOTYPE is LOGICAL array, dimension (NTYPES)
00042 *>          The matrix types to be used for testing.  Matrices of type j
00043 *>          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
00044 *>          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
00045 *> \endverbatim
00046 *>
00047 *> \param[in] NN
00048 *> \verbatim
00049 *>          NN is INTEGER
00050 *>          The number of values of N contained in the vector NVAL.
00051 *> \endverbatim
00052 *>
00053 *> \param[in] NVAL
00054 *> \verbatim
00055 *>          NVAL is INTEGER array, dimension (NN)
00056 *>          The values of the matrix dimension N.
00057 *> \endverbatim
00058 *>
00059 *> \param[in] NRHS
00060 *> \verbatim
00061 *>          NRHS is INTEGER
00062 *>          The number of right hand side vectors to be generated for
00063 *>          each linear system.
00064 *> \endverbatim
00065 *>
00066 *> \param[in] THRESH
00067 *> \verbatim
00068 *>          THRESH is REAL
00069 *>          The threshold value for the test ratios.  A result is
00070 *>          included in the output file if RESULT >= THRESH.  To have
00071 *>          every test ratio printed, use THRESH = 0.
00072 *> \endverbatim
00073 *>
00074 *> \param[in] TSTERR
00075 *> \verbatim
00076 *>          TSTERR is LOGICAL
00077 *>          Flag that indicates whether error exits are to be tested.
00078 *> \endverbatim
00079 *>
00080 *> \param[in] NMAX
00081 *> \verbatim
00082 *>          NMAX is INTEGER
00083 *>          The maximum value permitted for N, used in dimensioning the
00084 *>          work arrays.
00085 *> \endverbatim
00086 *>
00087 *> \param[out] A
00088 *> \verbatim
00089 *>          A is REAL array, dimension
00090 *>                      (NMAX*(NMAX+1)/2)
00091 *> \endverbatim
00092 *>
00093 *> \param[out] AFAC
00094 *> \verbatim
00095 *>          AFAC is REAL array, dimension
00096 *>                      (NMAX*(NMAX+1)/2)
00097 *> \endverbatim
00098 *>
00099 *> \param[out] AINV
00100 *> \verbatim
00101 *>          AINV is REAL array, dimension
00102 *>                      (NMAX*(NMAX+1)/2)
00103 *> \endverbatim
00104 *>
00105 *> \param[out] B
00106 *> \verbatim
00107 *>          B is REAL array, dimension (NMAX*NRHS)
00108 *> \endverbatim
00109 *>
00110 *> \param[out] X
00111 *> \verbatim
00112 *>          X is REAL array, dimension (NMAX*NRHS)
00113 *> \endverbatim
00114 *>
00115 *> \param[out] XACT
00116 *> \verbatim
00117 *>          XACT is REAL array, dimension (NMAX*NRHS)
00118 *> \endverbatim
00119 *>
00120 *> \param[out] WORK
00121 *> \verbatim
00122 *>          WORK is REAL array, dimension
00123 *>                      (NMAX*max(2,NRHS))
00124 *> \endverbatim
00125 *>
00126 *> \param[out] RWORK
00127 *> \verbatim
00128 *>          RWORK is REAL array, dimension (NMAX+2*NRHS)
00129 *> \endverbatim
00130 *>
00131 *> \param[out] IWORK
00132 *> \verbatim
00133 *>          IWORK is INTEGER array, dimension (2*NMAX)
00134 *> \endverbatim
00135 *>
00136 *> \param[in] NOUT
00137 *> \verbatim
00138 *>          NOUT is INTEGER
00139 *>          The unit number for output.
00140 *> \endverbatim
00141 *
00142 *  Authors:
00143 *  ========
00144 *
00145 *> \author Univ. of Tennessee 
00146 *> \author Univ. of California Berkeley 
00147 *> \author Univ. of Colorado Denver 
00148 *> \author NAG Ltd. 
00149 *
00150 *> \date November 2011
00151 *
00152 *> \ingroup single_lin
00153 *
00154 *  =====================================================================
00155       SUBROUTINE SDRVSP( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
00156      $                   A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
00157      $                   NOUT )
00158 *
00159 *  -- LAPACK test routine (version 3.4.0) --
00160 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00161 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00162 *     November 2011
00163 *
00164 *     .. Scalar Arguments ..
00165       LOGICAL            TSTERR
00166       INTEGER            NMAX, NN, NOUT, NRHS
00167       REAL               THRESH
00168 *     ..
00169 *     .. Array Arguments ..
00170       LOGICAL            DOTYPE( * )
00171       INTEGER            IWORK( * ), NVAL( * )
00172       REAL               A( * ), AFAC( * ), AINV( * ), B( * ),
00173      $                   RWORK( * ), WORK( * ), X( * ), XACT( * )
00174 *     ..
00175 *
00176 *  =====================================================================
00177 *
00178 *     .. Parameters ..
00179       REAL               ONE, ZERO
00180       PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
00181       INTEGER            NTYPES, NTESTS
00182       PARAMETER          ( NTYPES = 10, NTESTS = 6 )
00183       INTEGER            NFACT
00184       PARAMETER          ( NFACT = 2 )
00185 *     ..
00186 *     .. Local Scalars ..
00187       LOGICAL            ZEROT
00188       CHARACTER          DIST, FACT, PACKIT, TYPE, UPLO, XTYPE
00189       CHARACTER*3        PATH
00190       INTEGER            I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
00191      $                   IZERO, J, K, K1, KL, KU, LDA, LWORK, MODE, N,
00192      $                   NERRS, NFAIL, NIMAT, NPP, NRUN, NT
00193       REAL               AINVNM, ANORM, CNDNUM, RCOND, RCONDC
00194 *     ..
00195 *     .. Local Arrays ..
00196       CHARACTER          FACTS( NFACT )
00197       INTEGER            ISEED( 4 ), ISEEDY( 4 )
00198       REAL               RESULT( NTESTS )
00199 *     ..
00200 *     .. External Functions ..
00201       REAL               SGET06, SLANSP
00202       EXTERNAL           SGET06, SLANSP
00203 *     ..
00204 *     .. External Subroutines ..
00205       EXTERNAL           ALADHD, ALAERH, ALASVM, SCOPY, SERRVX, SGET04,
00206      $                   SLACPY, SLARHS, SLASET, SLATB4, SLATMS, SPPT02,
00207      $                   SPPT05, SSPSV, SSPSVX, SSPT01, SSPTRF, SSPTRI
00208 *     ..
00209 *     .. Scalars in Common ..
00210       LOGICAL            LERR, OK
00211       CHARACTER*32       SRNAMT
00212       INTEGER            INFOT, NUNIT
00213 *     ..
00214 *     .. Common blocks ..
00215       COMMON             / INFOC / INFOT, NUNIT, OK, LERR
00216       COMMON             / SRNAMC / SRNAMT
00217 *     ..
00218 *     .. Intrinsic Functions ..
00219       INTRINSIC          MAX, MIN
00220 *     ..
00221 *     .. Data statements ..
00222       DATA               ISEEDY / 1988, 1989, 1990, 1991 /
00223       DATA               FACTS / 'F', 'N' /
00224 *     ..
00225 *     .. Executable Statements ..
00226 *
00227 *     Initialize constants and the random number seed.
00228 *
00229       PATH( 1: 1 ) = 'Single precision'
00230       PATH( 2: 3 ) = 'SP'
00231       NRUN = 0
00232       NFAIL = 0
00233       NERRS = 0
00234       DO 10 I = 1, 4
00235          ISEED( I ) = ISEEDY( I )
00236    10 CONTINUE
00237       LWORK = MAX( 2*NMAX, NMAX*NRHS )
00238 *
00239 *     Test the error exits
00240 *
00241       IF( TSTERR )
00242      $   CALL SERRVX( PATH, NOUT )
00243       INFOT = 0
00244 *
00245 *     Do for each value of N in NVAL
00246 *
00247       DO 180 IN = 1, NN
00248          N = NVAL( IN )
00249          LDA = MAX( N, 1 )
00250          NPP = N*( N+1 ) / 2
00251          XTYPE = 'N'
00252          NIMAT = NTYPES
00253          IF( N.LE.0 )
00254      $      NIMAT = 1
00255 *
00256          DO 170 IMAT = 1, NIMAT
00257 *
00258 *           Do the tests only if DOTYPE( IMAT ) is true.
00259 *
00260             IF( .NOT.DOTYPE( IMAT ) )
00261      $         GO TO 170
00262 *
00263 *           Skip types 3, 4, 5, or 6 if the matrix size is too small.
00264 *
00265             ZEROT = IMAT.GE.3 .AND. IMAT.LE.6
00266             IF( ZEROT .AND. N.LT.IMAT-2 )
00267      $         GO TO 170
00268 *
00269 *           Do first for UPLO = 'U', then for UPLO = 'L'
00270 *
00271             DO 160 IUPLO = 1, 2
00272                IF( IUPLO.EQ.1 ) THEN
00273                   UPLO = 'U'
00274                   PACKIT = 'C'
00275                ELSE
00276                   UPLO = 'L'
00277                   PACKIT = 'R'
00278                END IF
00279 *
00280 *              Set up parameters with SLATB4 and generate a test matrix
00281 *              with SLATMS.
00282 *
00283                CALL SLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE,
00284      $                      CNDNUM, DIST )
00285 *
00286                SRNAMT = 'SLATMS'
00287                CALL SLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
00288      $                      CNDNUM, ANORM, KL, KU, PACKIT, A, LDA, WORK,
00289      $                      INFO )
00290 *
00291 *              Check error code from SLATMS.
00292 *
00293                IF( INFO.NE.0 ) THEN
00294                   CALL ALAERH( PATH, 'SLATMS', INFO, 0, UPLO, N, N, -1,
00295      $                         -1, -1, IMAT, NFAIL, NERRS, NOUT )
00296                   GO TO 160
00297                END IF
00298 *
00299 *              For types 3-6, zero one or more rows and columns of the
00300 *              matrix to test that INFO is returned correctly.
00301 *
00302                IF( ZEROT ) THEN
00303                   IF( IMAT.EQ.3 ) THEN
00304                      IZERO = 1
00305                   ELSE IF( IMAT.EQ.4 ) THEN
00306                      IZERO = N
00307                   ELSE
00308                      IZERO = N / 2 + 1
00309                   END IF
00310 *
00311                   IF( IMAT.LT.6 ) THEN
00312 *
00313 *                    Set row and column IZERO to zero.
00314 *
00315                      IF( IUPLO.EQ.1 ) THEN
00316                         IOFF = ( IZERO-1 )*IZERO / 2
00317                         DO 20 I = 1, IZERO - 1
00318                            A( IOFF+I ) = ZERO
00319    20                   CONTINUE
00320                         IOFF = IOFF + IZERO
00321                         DO 30 I = IZERO, N
00322                            A( IOFF ) = ZERO
00323                            IOFF = IOFF + I
00324    30                   CONTINUE
00325                      ELSE
00326                         IOFF = IZERO
00327                         DO 40 I = 1, IZERO - 1
00328                            A( IOFF ) = ZERO
00329                            IOFF = IOFF + N - I
00330    40                   CONTINUE
00331                         IOFF = IOFF - IZERO
00332                         DO 50 I = IZERO, N
00333                            A( IOFF+I ) = ZERO
00334    50                   CONTINUE
00335                      END IF
00336                   ELSE
00337                      IOFF = 0
00338                      IF( IUPLO.EQ.1 ) THEN
00339 *
00340 *                       Set the first IZERO rows and columns to zero.
00341 *
00342                         DO 70 J = 1, N
00343                            I2 = MIN( J, IZERO )
00344                            DO 60 I = 1, I2
00345                               A( IOFF+I ) = ZERO
00346    60                      CONTINUE
00347                            IOFF = IOFF + J
00348    70                   CONTINUE
00349                      ELSE
00350 *
00351 *                       Set the last IZERO rows and columns to zero.
00352 *
00353                         DO 90 J = 1, N
00354                            I1 = MAX( J, IZERO )
00355                            DO 80 I = I1, N
00356                               A( IOFF+I ) = ZERO
00357    80                      CONTINUE
00358                            IOFF = IOFF + N - J
00359    90                   CONTINUE
00360                      END IF
00361                   END IF
00362                ELSE
00363                   IZERO = 0
00364                END IF
00365 *
00366                DO 150 IFACT = 1, NFACT
00367 *
00368 *                 Do first for FACT = 'F', then for other values.
00369 *
00370                   FACT = FACTS( IFACT )
00371 *
00372 *                 Compute the condition number for comparison with
00373 *                 the value returned by SSPSVX.
00374 *
00375                   IF( ZEROT ) THEN
00376                      IF( IFACT.EQ.1 )
00377      $                  GO TO 150
00378                      RCONDC = ZERO
00379 *
00380                   ELSE IF( IFACT.EQ.1 ) THEN
00381 *
00382 *                    Compute the 1-norm of A.
00383 *
00384                      ANORM = SLANSP( '1', UPLO, N, A, RWORK )
00385 *
00386 *                    Factor the matrix A.
00387 *
00388                      CALL SCOPY( NPP, A, 1, AFAC, 1 )
00389                      CALL SSPTRF( UPLO, N, AFAC, IWORK, INFO )
00390 *
00391 *                    Compute inv(A) and take its norm.
00392 *
00393                      CALL SCOPY( NPP, AFAC, 1, AINV, 1 )
00394                      CALL SSPTRI( UPLO, N, AINV, IWORK, WORK, INFO )
00395                      AINVNM = SLANSP( '1', UPLO, N, AINV, RWORK )
00396 *
00397 *                    Compute the 1-norm condition number of A.
00398 *
00399                      IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
00400                         RCONDC = ONE
00401                      ELSE
00402                         RCONDC = ( ONE / ANORM ) / AINVNM
00403                      END IF
00404                   END IF
00405 *
00406 *                 Form an exact solution and set the right hand side.
00407 *
00408                   SRNAMT = 'SLARHS'
00409                   CALL SLARHS( PATH, XTYPE, UPLO, ' ', N, N, KL, KU,
00410      $                         NRHS, A, LDA, XACT, LDA, B, LDA, ISEED,
00411      $                         INFO )
00412                   XTYPE = 'C'
00413 *
00414 *                 --- Test SSPSV  ---
00415 *
00416                   IF( IFACT.EQ.2 ) THEN
00417                      CALL SCOPY( NPP, A, 1, AFAC, 1 )
00418                      CALL SLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
00419 *
00420 *                    Factor the matrix and solve the system using SSPSV.
00421 *
00422                      SRNAMT = 'SSPSV '
00423                      CALL SSPSV( UPLO, N, NRHS, AFAC, IWORK, X, LDA,
00424      $                           INFO )
00425 *
00426 *                    Adjust the expected value of INFO to account for
00427 *                    pivoting.
00428 *
00429                      K = IZERO
00430                      IF( K.GT.0 ) THEN
00431   100                   CONTINUE
00432                         IF( IWORK( K ).LT.0 ) THEN
00433                            IF( IWORK( K ).NE.-K ) THEN
00434                               K = -IWORK( K )
00435                               GO TO 100
00436                            END IF
00437                         ELSE IF( IWORK( K ).NE.K ) THEN
00438                            K = IWORK( K )
00439                            GO TO 100
00440                         END IF
00441                      END IF
00442 *
00443 *                    Check error code from SSPSV .
00444 *
00445                      IF( INFO.NE.K ) THEN
00446                         CALL ALAERH( PATH, 'SSPSV ', INFO, K, UPLO, N,
00447      $                               N, -1, -1, NRHS, IMAT, NFAIL,
00448      $                               NERRS, NOUT )
00449                         GO TO 120
00450                      ELSE IF( INFO.NE.0 ) THEN
00451                         GO TO 120
00452                      END IF
00453 *
00454 *                    Reconstruct matrix from factors and compute
00455 *                    residual.
00456 *
00457                      CALL SSPT01( UPLO, N, A, AFAC, IWORK, AINV, LDA,
00458      $                            RWORK, RESULT( 1 ) )
00459 *
00460 *                    Compute residual of the computed solution.
00461 *
00462                      CALL SLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
00463                      CALL SPPT02( UPLO, N, NRHS, A, X, LDA, WORK, LDA,
00464      $                            RWORK, RESULT( 2 ) )
00465 *
00466 *                    Check solution from generated exact solution.
00467 *
00468                      CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
00469      $                            RESULT( 3 ) )
00470                      NT = 3
00471 *
00472 *                    Print information about the tests that did not pass
00473 *                    the threshold.
00474 *
00475                      DO 110 K = 1, NT
00476                         IF( RESULT( K ).GE.THRESH ) THEN
00477                            IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
00478      $                        CALL ALADHD( NOUT, PATH )
00479                            WRITE( NOUT, FMT = 9999 )'SSPSV ', UPLO, N,
00480      $                        IMAT, K, RESULT( K )
00481                            NFAIL = NFAIL + 1
00482                         END IF
00483   110                CONTINUE
00484                      NRUN = NRUN + NT
00485   120                CONTINUE
00486                   END IF
00487 *
00488 *                 --- Test SSPSVX ---
00489 *
00490                   IF( IFACT.EQ.2 .AND. NPP.GT.0 )
00491      $               CALL SLASET( 'Full', NPP, 1, ZERO, ZERO, AFAC,
00492      $                            NPP )
00493                   CALL SLASET( 'Full', N, NRHS, ZERO, ZERO, X, LDA )
00494 *
00495 *                 Solve the system and compute the condition number and
00496 *                 error bounds using SSPSVX.
00497 *
00498                   SRNAMT = 'SSPSVX'
00499                   CALL SSPSVX( FACT, UPLO, N, NRHS, A, AFAC, IWORK, B,
00500      $                         LDA, X, LDA, RCOND, RWORK,
00501      $                         RWORK( NRHS+1 ), WORK, IWORK( N+1 ),
00502      $                         INFO )
00503 *
00504 *                 Adjust the expected value of INFO to account for
00505 *                 pivoting.
00506 *
00507                   K = IZERO
00508                   IF( K.GT.0 ) THEN
00509   130                CONTINUE
00510                      IF( IWORK( K ).LT.0 ) THEN
00511                         IF( IWORK( K ).NE.-K ) THEN
00512                            K = -IWORK( K )
00513                            GO TO 130
00514                         END IF
00515                      ELSE IF( IWORK( K ).NE.K ) THEN
00516                         K = IWORK( K )
00517                         GO TO 130
00518                      END IF
00519                   END IF
00520 *
00521 *                 Check the error code from SSPSVX.
00522 *
00523                   IF( INFO.NE.K ) THEN
00524                      CALL ALAERH( PATH, 'SSPSVX', INFO, K, FACT // UPLO,
00525      $                            N, N, -1, -1, NRHS, IMAT, NFAIL,
00526      $                            NERRS, NOUT )
00527                      GO TO 150
00528                   END IF
00529 *
00530                   IF( INFO.EQ.0 ) THEN
00531                      IF( IFACT.GE.2 ) THEN
00532 *
00533 *                       Reconstruct matrix from factors and compute
00534 *                       residual.
00535 *
00536                         CALL SSPT01( UPLO, N, A, AFAC, IWORK, AINV, LDA,
00537      $                               RWORK( 2*NRHS+1 ), RESULT( 1 ) )
00538                         K1 = 1
00539                      ELSE
00540                         K1 = 2
00541                      END IF
00542 *
00543 *                    Compute residual of the computed solution.
00544 *
00545                      CALL SLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
00546                      CALL SPPT02( UPLO, N, NRHS, A, X, LDA, WORK, LDA,
00547      $                            RWORK( 2*NRHS+1 ), RESULT( 2 ) )
00548 *
00549 *                    Check solution from generated exact solution.
00550 *
00551                      CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
00552      $                            RESULT( 3 ) )
00553 *
00554 *                    Check the error bounds from iterative refinement.
00555 *
00556                      CALL SPPT05( UPLO, N, NRHS, A, B, LDA, X, LDA,
00557      $                            XACT, LDA, RWORK, RWORK( NRHS+1 ),
00558      $                            RESULT( 4 ) )
00559                   ELSE
00560                      K1 = 6
00561                   END IF
00562 *
00563 *                 Compare RCOND from SSPSVX with the computed value
00564 *                 in RCONDC.
00565 *
00566                   RESULT( 6 ) = SGET06( RCOND, RCONDC )
00567 *
00568 *                 Print information about the tests that did not pass
00569 *                 the threshold.
00570 *
00571                   DO 140 K = K1, 6
00572                      IF( RESULT( K ).GE.THRESH ) THEN
00573                         IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
00574      $                     CALL ALADHD( NOUT, PATH )
00575                         WRITE( NOUT, FMT = 9998 )'SSPSVX', FACT, UPLO,
00576      $                     N, IMAT, K, RESULT( K )
00577                         NFAIL = NFAIL + 1
00578                      END IF
00579   140             CONTINUE
00580                   NRUN = NRUN + 7 - K1
00581 *
00582   150          CONTINUE
00583 *
00584   160       CONTINUE
00585   170    CONTINUE
00586   180 CONTINUE
00587 *
00588 *     Print a summary of the results.
00589 *
00590       CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
00591 *
00592  9999 FORMAT( 1X, A, ', UPLO=''', A1, ''', N =', I5, ', type ', I2,
00593      $      ', test ', I2, ', ratio =', G12.5 )
00594  9998 FORMAT( 1X, A, ', FACT=''', A1, ''', UPLO=''', A1, ''', N =', I5,
00595      $      ', type ', I2, ', test ', I2, ', ratio =', G12.5 )
00596       RETURN
00597 *
00598 *     End of SDRVSP
00599 *
00600       END
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