LAPACK 3.3.1 Linear Algebra PACKage

# sdrvsy.f

Go to the documentation of this file.
```00001       SUBROUTINE SDRVSY( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
00002      \$                   A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
00003      \$                   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( * ), AINV( * ), B( * ),
00018      \$                   RWORK( * ), WORK( * ), X( * ), XACT( * )
00019 *     ..
00020 *
00021 *  Purpose
00022 *  =======
00023 *
00024 *  SDRVSY tests the driver routines SSYSV and -SVX.
00025 *
00026 *  Arguments
00027 *  =========
00028 *
00029 *  DOTYPE  (input) LOGICAL array, dimension (NTYPES)
00030 *          The matrix types to be used for testing.  Matrices of type j
00031 *          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
00032 *          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
00033 *
00034 *  NN      (input) INTEGER
00035 *          The number of values of N contained in the vector NVAL.
00036 *
00037 *  NVAL    (input) INTEGER array, dimension (NN)
00038 *          The values of the matrix dimension N.
00039 *
00040 *  NRHS    (input) INTEGER
00041 *          The number of right hand side vectors to be generated for
00042 *          each linear system.
00043 *
00044 *  THRESH  (input) REAL
00045 *          The threshold value for the test ratios.  A result is
00046 *          included in the output file if RESULT >= THRESH.  To have
00047 *          every test ratio printed, use THRESH = 0.
00048 *
00049 *  TSTERR  (input) LOGICAL
00050 *          Flag that indicates whether error exits are to be tested.
00051 *
00052 *  NMAX    (input) INTEGER
00053 *          The maximum value permitted for N, used in dimensioning the
00054 *          work arrays.
00055 *
00056 *  A       (workspace) REAL array, dimension (NMAX*NMAX)
00057 *
00058 *  AFAC    (workspace) REAL array, dimension (NMAX*NMAX)
00059 *
00060 *  AINV    (workspace) REAL array, dimension (NMAX*NMAX)
00061 *
00062 *  B       (workspace) REAL array, dimension (NMAX*NRHS)
00063 *
00064 *  X       (workspace) REAL array, dimension (NMAX*NRHS)
00065 *
00066 *  XACT    (workspace) REAL array, dimension (NMAX*NRHS)
00067 *
00068 *  WORK    (workspace) REAL array, dimension
00069 *                      (NMAX*max(2,NRHS))
00070 *
00071 *  RWORK   (workspace) REAL array, dimension (NMAX+2*NRHS)
00072 *
00073 *  IWORK   (workspace) INTEGER array, dimension (2*NMAX)
00074 *
00075 *  NOUT    (input) INTEGER
00076 *          The unit number for output.
00077 *
00078 *  =====================================================================
00079 *
00080 *     .. Parameters ..
00081       REAL               ONE, ZERO
00082       PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
00083       INTEGER            NTYPES, NTESTS
00084       PARAMETER          ( NTYPES = 10, NTESTS = 6 )
00085       INTEGER            NFACT
00086       PARAMETER          ( NFACT = 2 )
00087 *     ..
00088 *     .. Local Scalars ..
00089       LOGICAL            ZEROT
00090       CHARACTER          DIST, FACT, TYPE, UPLO, XTYPE
00091       CHARACTER*3        PATH
00092       INTEGER            I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
00093      \$                   IZERO, J, K, K1, KL, KU, LDA, LWORK, MODE, N,
00094      \$                   NB, NBMIN, NERRS, NFAIL, NIMAT, NRUN, NT
00095       REAL               AINVNM, ANORM, CNDNUM, RCOND, RCONDC
00096 *     ..
00097 *     .. Local Arrays ..
00098       CHARACTER          FACTS( NFACT ), UPLOS( 2 )
00099       INTEGER            ISEED( 4 ), ISEEDY( 4 )
00100       REAL               RESULT( NTESTS )
00101 *     ..
00102 *     .. External Functions ..
00103       REAL               SGET06, SLANSY
00104       EXTERNAL           SGET06, SLANSY
00105 *     ..
00106 *     .. External Subroutines ..
00107       EXTERNAL           ALADHD, ALAERH, ALASVM, SERRVX, SGET04, SLACPY,
00108      \$                   SLARHS, SLASET, SLATB4, SLATMS, SPOT02, SPOT05,
00109      \$                   SSYSV, SSYSVX, SSYT01, SSYTRF, SSYTRI2, XLAENV
00110 *     ..
00111 *     .. Scalars in Common ..
00112       LOGICAL            LERR, OK
00113       CHARACTER*32       SRNAMT
00114       INTEGER            INFOT, NUNIT
00115 *     ..
00116 *     .. Common blocks ..
00117       COMMON             / INFOC / INFOT, NUNIT, OK, LERR
00118       COMMON             / SRNAMC / SRNAMT
00119 *     ..
00120 *     .. Intrinsic Functions ..
00121       INTRINSIC          MAX, MIN
00122 *     ..
00123 *     .. Data statements ..
00124       DATA               ISEEDY / 1988, 1989, 1990, 1991 /
00125       DATA               UPLOS / 'U', 'L' / , FACTS / 'F', 'N' /
00126 *     ..
00127 *     .. Executable Statements ..
00128 *
00129 *     Initialize constants and the random number seed.
00130 *
00131       PATH( 1: 1 ) = 'Single precision'
00132       PATH( 2: 3 ) = 'SY'
00133       NRUN = 0
00134       NFAIL = 0
00135       NERRS = 0
00136       DO 10 I = 1, 4
00137          ISEED( I ) = ISEEDY( I )
00138    10 CONTINUE
00139       LWORK = MAX( 2*NMAX, NMAX*NRHS )
00140 *
00141 *     Test the error exits
00142 *
00143       IF( TSTERR )
00144      \$   CALL SERRVX( PATH, NOUT )
00145       INFOT = 0
00146 *
00147 *     Set the block size and minimum block size for testing.
00148 *
00149       NB = 1
00150       NBMIN = 2
00151       CALL XLAENV( 1, NB )
00152       CALL XLAENV( 2, NBMIN )
00153 *
00154 *     Do for each value of N in NVAL
00155 *
00156       DO 180 IN = 1, NN
00157          N = NVAL( IN )
00158          LDA = MAX( N, 1 )
00159          XTYPE = 'N'
00160          NIMAT = NTYPES
00161          IF( N.LE.0 )
00162      \$      NIMAT = 1
00163 *
00164          DO 170 IMAT = 1, NIMAT
00165 *
00166 *           Do the tests only if DOTYPE( IMAT ) is true.
00167 *
00168             IF( .NOT.DOTYPE( IMAT ) )
00169      \$         GO TO 170
00170 *
00171 *           Skip types 3, 4, 5, or 6 if the matrix size is too small.
00172 *
00173             ZEROT = IMAT.GE.3 .AND. IMAT.LE.6
00174             IF( ZEROT .AND. N.LT.IMAT-2 )
00175      \$         GO TO 170
00176 *
00177 *           Do first for UPLO = 'U', then for UPLO = 'L'
00178 *
00179             DO 160 IUPLO = 1, 2
00180                UPLO = UPLOS( IUPLO )
00181 *
00182 *              Set up parameters with SLATB4 and generate a test matrix
00183 *              with SLATMS.
00184 *
00185                CALL SLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE,
00186      \$                      CNDNUM, DIST )
00187 *
00188                SRNAMT = 'SLATMS'
00189                CALL SLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
00190      \$                      CNDNUM, ANORM, KL, KU, UPLO, A, LDA, WORK,
00191      \$                      INFO )
00192 *
00193 *              Check error code from SLATMS.
00194 *
00195                IF( INFO.NE.0 ) THEN
00196                   CALL ALAERH( PATH, 'SLATMS', INFO, 0, UPLO, N, N, -1,
00197      \$                         -1, -1, IMAT, NFAIL, NERRS, NOUT )
00198                   GO TO 160
00199                END IF
00200 *
00201 *              For types 3-6, zero one or more rows and columns of the
00202 *              matrix to test that INFO is returned correctly.
00203 *
00204                IF( ZEROT ) THEN
00205                   IF( IMAT.EQ.3 ) THEN
00206                      IZERO = 1
00207                   ELSE IF( IMAT.EQ.4 ) THEN
00208                      IZERO = N
00209                   ELSE
00210                      IZERO = N / 2 + 1
00211                   END IF
00212 *
00213                   IF( IMAT.LT.6 ) THEN
00214 *
00215 *                    Set row and column IZERO to zero.
00216 *
00217                      IF( IUPLO.EQ.1 ) THEN
00218                         IOFF = ( IZERO-1 )*LDA
00219                         DO 20 I = 1, IZERO - 1
00220                            A( IOFF+I ) = ZERO
00221    20                   CONTINUE
00222                         IOFF = IOFF + IZERO
00223                         DO 30 I = IZERO, N
00224                            A( IOFF ) = ZERO
00225                            IOFF = IOFF + LDA
00226    30                   CONTINUE
00227                      ELSE
00228                         IOFF = IZERO
00229                         DO 40 I = 1, IZERO - 1
00230                            A( IOFF ) = ZERO
00231                            IOFF = IOFF + LDA
00232    40                   CONTINUE
00233                         IOFF = IOFF - IZERO
00234                         DO 50 I = IZERO, N
00235                            A( IOFF+I ) = ZERO
00236    50                   CONTINUE
00237                      END IF
00238                   ELSE
00239                      IOFF = 0
00240                      IF( IUPLO.EQ.1 ) THEN
00241 *
00242 *                       Set the first IZERO rows and columns to zero.
00243 *
00244                         DO 70 J = 1, N
00245                            I2 = MIN( J, IZERO )
00246                            DO 60 I = 1, I2
00247                               A( IOFF+I ) = ZERO
00248    60                      CONTINUE
00249                            IOFF = IOFF + LDA
00250    70                   CONTINUE
00251                      ELSE
00252 *
00253 *                       Set the last IZERO rows and columns to zero.
00254 *
00255                         DO 90 J = 1, N
00256                            I1 = MAX( J, IZERO )
00257                            DO 80 I = I1, N
00258                               A( IOFF+I ) = ZERO
00259    80                      CONTINUE
00260                            IOFF = IOFF + LDA
00261    90                   CONTINUE
00262                      END IF
00263                   END IF
00264                ELSE
00265                   IZERO = 0
00266                END IF
00267 *
00268                DO 150 IFACT = 1, NFACT
00269 *
00270 *                 Do first for FACT = 'F', then for other values.
00271 *
00272                   FACT = FACTS( IFACT )
00273 *
00274 *                 Compute the condition number for comparison with
00275 *                 the value returned by SSYSVX.
00276 *
00277                   IF( ZEROT ) THEN
00278                      IF( IFACT.EQ.1 )
00279      \$                  GO TO 150
00280                      RCONDC = ZERO
00281 *
00282                   ELSE IF( IFACT.EQ.1 ) THEN
00283 *
00284 *                    Compute the 1-norm of A.
00285 *
00286                      ANORM = SLANSY( '1', UPLO, N, A, LDA, RWORK )
00287 *
00288 *                    Factor the matrix A.
00289 *
00290                      CALL SLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
00291                      CALL SSYTRF( UPLO, N, AFAC, LDA, IWORK, WORK,
00292      \$                            LWORK, INFO )
00293 *
00294 *                    Compute inv(A) and take its norm.
00295 *
00296                      CALL SLACPY( UPLO, N, N, AFAC, LDA, AINV, LDA )
00297                      LWORK = (N+NB+1)*(NB+3)
00298                      CALL SSYTRI2( UPLO, N, AINV, LDA, IWORK, WORK,
00299      \$                            LWORK, INFO )
00300                      AINVNM = SLANSY( '1', UPLO, N, AINV, LDA, RWORK )
00301 *
00302 *                    Compute the 1-norm condition number of A.
00303 *
00304                      IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
00305                         RCONDC = ONE
00306                      ELSE
00307                         RCONDC = ( ONE / ANORM ) / AINVNM
00308                      END IF
00309                   END IF
00310 *
00311 *                 Form an exact solution and set the right hand side.
00312 *
00313                   SRNAMT = 'SLARHS'
00314                   CALL SLARHS( PATH, XTYPE, UPLO, ' ', N, N, KL, KU,
00315      \$                         NRHS, A, LDA, XACT, LDA, B, LDA, ISEED,
00316      \$                         INFO )
00317                   XTYPE = 'C'
00318 *
00319 *                 --- Test SSYSV  ---
00320 *
00321                   IF( IFACT.EQ.2 ) THEN
00322                      CALL SLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
00323                      CALL SLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
00324 *
00325 *                    Factor the matrix and solve the system using SSYSV.
00326 *
00327                      SRNAMT = 'SSYSV '
00328                      CALL SSYSV( UPLO, N, NRHS, AFAC, LDA, IWORK, X,
00329      \$                           LDA, WORK, LWORK, INFO )
00330 *
00331 *                    Adjust the expected value of INFO to account for
00332 *                    pivoting.
00333 *
00334                      K = IZERO
00335                      IF( K.GT.0 ) THEN
00336   100                   CONTINUE
00337                         IF( IWORK( K ).LT.0 ) THEN
00338                            IF( IWORK( K ).NE.-K ) THEN
00339                               K = -IWORK( K )
00340                               GO TO 100
00341                            END IF
00342                         ELSE IF( IWORK( K ).NE.K ) THEN
00343                            K = IWORK( K )
00344                            GO TO 100
00345                         END IF
00346                      END IF
00347 *
00348 *                    Check error code from SSYSV .
00349 *
00350                      IF( INFO.NE.K ) THEN
00351                         CALL ALAERH( PATH, 'SSYSV ', INFO, K, UPLO, N,
00352      \$                               N, -1, -1, NRHS, IMAT, NFAIL,
00353      \$                               NERRS, NOUT )
00354                         GO TO 120
00355                      ELSE IF( INFO.NE.0 ) THEN
00356                         GO TO 120
00357                      END IF
00358 *
00359 *                    Reconstruct matrix from factors and compute
00360 *                    residual.
00361 *
00362                      CALL SSYT01( UPLO, N, A, LDA, AFAC, LDA, IWORK,
00363      \$                            AINV, LDA, RWORK, RESULT( 1 ) )
00364 *
00365 *                    Compute residual of the computed solution.
00366 *
00367                      CALL SLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
00368                      CALL SPOT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
00369      \$                            LDA, RWORK, RESULT( 2 ) )
00370 *
00371 *                    Check solution from generated exact solution.
00372 *
00373                      CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
00374      \$                            RESULT( 3 ) )
00375                      NT = 3
00376 *
00377 *                    Print information about the tests that did not pass
00378 *                    the threshold.
00379 *
00380                      DO 110 K = 1, NT
00381                         IF( RESULT( K ).GE.THRESH ) THEN
00382                            IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
00383      \$                        CALL ALADHD( NOUT, PATH )
00384                            WRITE( NOUT, FMT = 9999 )'SSYSV ', UPLO, N,
00385      \$                        IMAT, K, RESULT( K )
00386                            NFAIL = NFAIL + 1
00387                         END IF
00388   110                CONTINUE
00389                      NRUN = NRUN + NT
00390   120                CONTINUE
00391                   END IF
00392 *
00393 *                 --- Test SSYSVX ---
00394 *
00395                   IF( IFACT.EQ.2 )
00396      \$               CALL SLASET( UPLO, N, N, ZERO, ZERO, AFAC, LDA )
00397                   CALL SLASET( 'Full', N, NRHS, ZERO, ZERO, X, LDA )
00398 *
00399 *                 Solve the system and compute the condition number and
00400 *                 error bounds using SSYSVX.
00401 *
00402                   SRNAMT = 'SSYSVX'
00403                   CALL SSYSVX( FACT, UPLO, N, NRHS, A, LDA, AFAC, LDA,
00404      \$                         IWORK, B, LDA, X, LDA, RCOND, RWORK,
00405      \$                         RWORK( NRHS+1 ), WORK, LWORK,
00406      \$                         IWORK( N+1 ), INFO )
00407 *
00408 *                 Adjust the expected value of INFO to account for
00409 *                 pivoting.
00410 *
00411                   K = IZERO
00412                   IF( K.GT.0 ) THEN
00413   130                CONTINUE
00414                      IF( IWORK( K ).LT.0 ) THEN
00415                         IF( IWORK( K ).NE.-K ) THEN
00416                            K = -IWORK( K )
00417                            GO TO 130
00418                         END IF
00419                      ELSE IF( IWORK( K ).NE.K ) THEN
00420                         K = IWORK( K )
00421                         GO TO 130
00422                      END IF
00423                   END IF
00424 *
00425 *                 Check the error code from SSYSVX.
00426 *
00427                   IF( INFO.NE.K ) THEN
00428                      CALL ALAERH( PATH, 'SSYSVX', INFO, K, FACT // UPLO,
00429      \$                            N, N, -1, -1, NRHS, IMAT, NFAIL,
00430      \$                            NERRS, NOUT )
00431                      GO TO 150
00432                   END IF
00433 *
00434                   IF( INFO.EQ.0 ) THEN
00435                      IF( IFACT.GE.2 ) THEN
00436 *
00437 *                       Reconstruct matrix from factors and compute
00438 *                       residual.
00439 *
00440                         CALL SSYT01( UPLO, N, A, LDA, AFAC, LDA, IWORK,
00441      \$                               AINV, LDA, RWORK( 2*NRHS+1 ),
00442      \$                               RESULT( 1 ) )
00443                         K1 = 1
00444                      ELSE
00445                         K1 = 2
00446                      END IF
00447 *
00448 *                    Compute residual of the computed solution.
00449 *
00450                      CALL SLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
00451                      CALL SPOT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
00452      \$                            LDA, RWORK( 2*NRHS+1 ), RESULT( 2 ) )
00453 *
00454 *                    Check solution from generated exact solution.
00455 *
00456                      CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
00457      \$                            RESULT( 3 ) )
00458 *
00459 *                    Check the error bounds from iterative refinement.
00460 *
00461                      CALL SPOT05( UPLO, N, NRHS, A, LDA, B, LDA, X, LDA,
00462      \$                            XACT, LDA, RWORK, RWORK( NRHS+1 ),
00463      \$                            RESULT( 4 ) )
00464                   ELSE
00465                      K1 = 6
00466                   END IF
00467 *
00468 *                 Compare RCOND from SSYSVX with the computed value
00469 *                 in RCONDC.
00470 *
00471                   RESULT( 6 ) = SGET06( RCOND, RCONDC )
00472 *
00473 *                 Print information about the tests that did not pass
00474 *                 the threshold.
00475 *
00476                   DO 140 K = K1, 6
00477                      IF( RESULT( K ).GE.THRESH ) THEN
00478                         IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
00479      \$                     CALL ALADHD( NOUT, PATH )
00480                         WRITE( NOUT, FMT = 9998 )'SSYSVX', FACT, UPLO,
00481      \$                     N, IMAT, K, RESULT( K )
00482                         NFAIL = NFAIL + 1
00483                      END IF
00484   140             CONTINUE
00485                   NRUN = NRUN + 7 - K1
00486 *
00487   150          CONTINUE
00488 *
00489   160       CONTINUE
00490   170    CONTINUE
00491   180 CONTINUE
00492 *
00493 *     Print a summary of the results.
00494 *
00495       CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
00496 *
00497  9999 FORMAT( 1X, A, ', UPLO=''', A1, ''', N =', I5, ', type ', I2,
00498      \$      ', test ', I2, ', ratio =', G12.5 )
00499  9998 FORMAT( 1X, A, ', FACT=''', A1, ''', UPLO=''', A1, ''', N =', I5,
00500      \$      ', type ', I2, ', test ', I2, ', ratio =', G12.5 )
00501       RETURN
00502 *
00503 *     End of SDRVSY
00504 *
00505       END
```