LAPACK 3.3.1 Linear Algebra PACKage

# schktb.f

Go to the documentation of this file.
```00001       SUBROUTINE SCHKTB( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
00002      \$                   NMAX, AB, 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, NNS, NOUT
00012       REAL               THRESH
00013 *     ..
00014 *     .. Array Arguments ..
00015       LOGICAL            DOTYPE( * )
00016       INTEGER            IWORK( * ), NSVAL( * ), NVAL( * )
00017       REAL               AB( * ), AINV( * ), B( * ), RWORK( * ),
00018      \$                   WORK( * ), X( * ), XACT( * )
00019 *     ..
00020 *
00021 *  Purpose
00022 *  =======
00023 *
00024 *  SCHKTB tests STBTRS, -RFS, and -CON, and SLATBS.
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 column dimension N.
00039 *
00040 *  NNS     (input) INTEGER
00041 *          The number of values of NRHS contained in the vector NSVAL.
00042 *
00043 *  NSVAL   (input) INTEGER array, dimension (NNS)
00044 *          The values of the number of right hand sides NRHS.
00045 *
00046 *  THRESH  (input) REAL
00047 *          The threshold value for the test ratios.  A result is
00048 *          included in the output file if RESULT >= THRESH.  To have
00049 *          every test ratio printed, use THRESH = 0.
00050 *
00051 *  TSTERR  (input) LOGICAL
00052 *          Flag that indicates whether error exits are to be tested.
00053 *
00054 *  NMAX    (input) INTEGER
00055 *          The leading dimension of the work arrays.
00056 *          NMAX >= the maximum value of N in NVAL.
00057 *
00058 *  AB      (workspace) REAL array, dimension (NMAX*NMAX)
00059 *
00060 *  AINV    (workspace) REAL array, dimension (NMAX*NMAX)
00061 *
00062 *  B       (workspace) REAL array, dimension (NMAX*NSMAX)
00063 *          where NSMAX is the largest entry in NSVAL.
00064 *
00065 *  X       (workspace) REAL array, dimension (NMAX*NSMAX)
00066 *
00067 *  XACT    (workspace) REAL array, dimension (NMAX*NSMAX)
00068 *
00069 *  WORK    (workspace) REAL array, dimension
00070 *                      (NMAX*max(3,NSMAX))
00071 *
00072 *  RWORK   (workspace) REAL array, dimension
00073 *                      (max(NMAX,2*NSMAX))
00074 *
00075 *  IWORK   (workspace) INTEGER array, dimension (NMAX)
00076 *
00077 *  NOUT    (input) INTEGER
00078 *          The unit number for output.
00079 *
00080 *  =====================================================================
00081 *
00082 *     .. Parameters ..
00083       INTEGER            NTYPE1, NTYPES
00084       PARAMETER          ( NTYPE1 = 9, NTYPES = 17 )
00085       INTEGER            NTESTS
00086       PARAMETER          ( NTESTS = 8 )
00087       INTEGER            NTRAN
00088       PARAMETER          ( NTRAN = 3 )
00089       REAL               ONE, ZERO
00090       PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
00091 *     ..
00092 *     .. Local Scalars ..
00093       CHARACTER          DIAG, NORM, TRANS, UPLO, XTYPE
00094       CHARACTER*3        PATH
00095       INTEGER            I, IDIAG, IK, IMAT, IN, INFO, IRHS, ITRAN,
00096      \$                   IUPLO, J, K, KD, LDA, LDAB, N, NERRS, NFAIL,
00097      \$                   NIMAT, NIMAT2, NK, NRHS, NRUN
00098       REAL               AINVNM, ANORM, RCOND, RCONDC, RCONDI, RCONDO,
00099      \$                   SCALE
00100 *     ..
00101 *     .. Local Arrays ..
00102       CHARACTER          TRANSS( NTRAN ), UPLOS( 2 )
00103       INTEGER            ISEED( 4 ), ISEEDY( 4 )
00104       REAL               RESULT( NTESTS )
00105 *     ..
00106 *     .. External Functions ..
00107       LOGICAL            LSAME
00108       REAL               SLANTB, SLANTR
00109       EXTERNAL           LSAME, SLANTB, SLANTR
00110 *     ..
00111 *     .. External Subroutines ..
00112       EXTERNAL           ALAERH, ALAHD, ALASUM, SCOPY, SERRTR, SGET04,
00113      \$                   SLACPY, SLARHS, SLASET, SLATBS, SLATTB, STBCON,
00114      \$                   STBRFS, STBSV, STBT02, STBT03, STBT05, STBT06,
00115      \$                   STBTRS
00116 *     ..
00117 *     .. Scalars in Common ..
00118       LOGICAL            LERR, OK
00119       CHARACTER*32       SRNAMT
00120       INTEGER            INFOT, IOUNIT
00121 *     ..
00122 *     .. Common blocks ..
00123       COMMON             / INFOC / INFOT, IOUNIT, OK, LERR
00124       COMMON             / SRNAMC / SRNAMT
00125 *     ..
00126 *     .. Intrinsic Functions ..
00127       INTRINSIC          MAX, MIN
00128 *     ..
00129 *     .. Data statements ..
00130       DATA               ISEEDY / 1988, 1989, 1990, 1991 /
00131       DATA               UPLOS / 'U', 'L' / , TRANSS / 'N', 'T', 'C' /
00132 *     ..
00133 *     .. Executable Statements ..
00134 *
00135 *     Initialize constants and the random number seed.
00136 *
00137       PATH( 1: 1 ) = 'Single precision'
00138       PATH( 2: 3 ) = 'TB'
00139       NRUN = 0
00140       NFAIL = 0
00141       NERRS = 0
00142       DO 10 I = 1, 4
00143          ISEED( I ) = ISEEDY( I )
00144    10 CONTINUE
00145 *
00146 *     Test the error exits
00147 *
00148       IF( TSTERR )
00149      \$   CALL SERRTR( PATH, NOUT )
00150       INFOT = 0
00151 *
00152       DO 140 IN = 1, NN
00153 *
00154 *        Do for each value of N in NVAL
00155 *
00156          N = NVAL( IN )
00157          LDA = MAX( 1, N )
00158          XTYPE = 'N'
00159          NIMAT = NTYPE1
00160          NIMAT2 = NTYPES
00161          IF( N.LE.0 ) THEN
00162             NIMAT = 1
00163             NIMAT2 = NTYPE1 + 1
00164          END IF
00165 *
00166          NK = MIN( N+1, 4 )
00167          DO 130 IK = 1, NK
00168 *
00169 *           Do for KD = 0, N, (3N-1)/4, and (N+1)/4. This order makes
00170 *           it easier to skip redundant values for small values of N.
00171 *
00172             IF( IK.EQ.1 ) THEN
00173                KD = 0
00174             ELSE IF( IK.EQ.2 ) THEN
00175                KD = MAX( N, 0 )
00176             ELSE IF( IK.EQ.3 ) THEN
00177                KD = ( 3*N-1 ) / 4
00178             ELSE IF( IK.EQ.4 ) THEN
00179                KD = ( N+1 ) / 4
00180             END IF
00181             LDAB = KD + 1
00182 *
00183             DO 90 IMAT = 1, NIMAT
00184 *
00185 *              Do the tests only if DOTYPE( IMAT ) is true.
00186 *
00187                IF( .NOT.DOTYPE( IMAT ) )
00188      \$            GO TO 90
00189 *
00190                DO 80 IUPLO = 1, 2
00191 *
00192 *                 Do first for UPLO = 'U', then for UPLO = 'L'
00193 *
00194                   UPLO = UPLOS( IUPLO )
00195 *
00196 *                 Call SLATTB to generate a triangular test matrix.
00197 *
00198                   SRNAMT = 'SLATTB'
00199                   CALL SLATTB( IMAT, UPLO, 'No transpose', DIAG, ISEED,
00200      \$                         N, KD, AB, LDAB, X, WORK, INFO )
00201 *
00202 *                 Set IDIAG = 1 for non-unit matrices, 2 for unit.
00203 *
00204                   IF( LSAME( DIAG, 'N' ) ) THEN
00205                      IDIAG = 1
00206                   ELSE
00207                      IDIAG = 2
00208                   END IF
00209 *
00210 *                 Form the inverse of A so we can get a good estimate
00211 *                 of RCONDC = 1/(norm(A) * norm(inv(A))).
00212 *
00213                   CALL SLASET( 'Full', N, N, ZERO, ONE, AINV, LDA )
00214                   IF( LSAME( UPLO, 'U' ) ) THEN
00215                      DO 20 J = 1, N
00216                         CALL STBSV( UPLO, 'No transpose', DIAG, J, KD,
00217      \$                              AB, LDAB, AINV( ( J-1 )*LDA+1 ), 1 )
00218    20                CONTINUE
00219                   ELSE
00220                      DO 30 J = 1, N
00221                         CALL STBSV( UPLO, 'No transpose', DIAG, N-J+1,
00222      \$                              KD, AB( ( J-1 )*LDAB+1 ), LDAB,
00223      \$                              AINV( ( J-1 )*LDA+J ), 1 )
00224    30                CONTINUE
00225                   END IF
00226 *
00227 *                 Compute the 1-norm condition number of A.
00228 *
00229                   ANORM = SLANTB( '1', UPLO, DIAG, N, KD, AB, LDAB,
00230      \$                    RWORK )
00231                   AINVNM = SLANTR( '1', UPLO, DIAG, N, N, AINV, LDA,
00232      \$                     RWORK )
00233                   IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
00234                      RCONDO = ONE
00235                   ELSE
00236                      RCONDO = ( ONE / ANORM ) / AINVNM
00237                   END IF
00238 *
00239 *                 Compute the infinity-norm condition number of A.
00240 *
00241                   ANORM = SLANTB( 'I', UPLO, DIAG, N, KD, AB, LDAB,
00242      \$                    RWORK )
00243                   AINVNM = SLANTR( 'I', UPLO, DIAG, N, N, AINV, LDA,
00244      \$                     RWORK )
00245                   IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
00246                      RCONDI = ONE
00247                   ELSE
00248                      RCONDI = ( ONE / ANORM ) / AINVNM
00249                   END IF
00250 *
00251                   DO 60 IRHS = 1, NNS
00252                      NRHS = NSVAL( IRHS )
00253                      XTYPE = 'N'
00254 *
00255                      DO 50 ITRAN = 1, NTRAN
00256 *
00257 *                    Do for op(A) = A, A**T, or A**H.
00258 *
00259                         TRANS = TRANSS( ITRAN )
00260                         IF( ITRAN.EQ.1 ) THEN
00261                            NORM = 'O'
00262                            RCONDC = RCONDO
00263                         ELSE
00264                            NORM = 'I'
00265                            RCONDC = RCONDI
00266                         END IF
00267 *
00268 *+    TEST 1
00269 *                    Solve and compute residual for op(A)*x = b.
00270 *
00271                         SRNAMT = 'SLARHS'
00272                         CALL SLARHS( PATH, XTYPE, UPLO, TRANS, N, N, KD,
00273      \$                               IDIAG, NRHS, AB, LDAB, XACT, LDA,
00274      \$                               B, LDA, ISEED, INFO )
00275                         XTYPE = 'C'
00276                         CALL SLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
00277 *
00278                         SRNAMT = 'STBTRS'
00279                         CALL STBTRS( UPLO, TRANS, DIAG, N, KD, NRHS, AB,
00280      \$                               LDAB, X, LDA, INFO )
00281 *
00282 *                    Check error code from STBTRS.
00283 *
00284                         IF( INFO.NE.0 )
00285      \$                     CALL ALAERH( PATH, 'STBTRS', INFO, 0,
00286      \$                                  UPLO // TRANS // DIAG, N, N, KD,
00287      \$                                  KD, NRHS, IMAT, NFAIL, NERRS,
00288      \$                                  NOUT )
00289 *
00290                         CALL STBT02( UPLO, TRANS, DIAG, N, KD, NRHS, AB,
00291      \$                               LDAB, X, LDA, B, LDA, WORK,
00292      \$                               RESULT( 1 ) )
00293 *
00294 *+    TEST 2
00295 *                    Check solution from generated exact solution.
00296 *
00297                         CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
00298      \$                               RESULT( 2 ) )
00299 *
00300 *+    TESTS 3, 4, and 5
00301 *                    Use iterative refinement to improve the solution
00302 *                    and compute error bounds.
00303 *
00304                         SRNAMT = 'STBRFS'
00305                         CALL STBRFS( UPLO, TRANS, DIAG, N, KD, NRHS, AB,
00306      \$                               LDAB, B, LDA, X, LDA, RWORK,
00307      \$                               RWORK( NRHS+1 ), WORK, IWORK,
00308      \$                               INFO )
00309 *
00310 *                    Check error code from STBRFS.
00311 *
00312                         IF( INFO.NE.0 )
00313      \$                     CALL ALAERH( PATH, 'STBRFS', INFO, 0,
00314      \$                                  UPLO // TRANS // DIAG, N, N, KD,
00315      \$                                  KD, NRHS, IMAT, NFAIL, NERRS,
00316      \$                                  NOUT )
00317 *
00318                         CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
00319      \$                               RESULT( 3 ) )
00320                         CALL STBT05( UPLO, TRANS, DIAG, N, KD, NRHS, AB,
00321      \$                               LDAB, B, LDA, X, LDA, XACT, LDA,
00322      \$                               RWORK, RWORK( NRHS+1 ),
00323      \$                               RESULT( 4 ) )
00324 *
00325 *                       Print information about the tests that did not
00326 *                       pass the threshold.
00327 *
00328                         DO 40 K = 1, 5
00329                            IF( RESULT( K ).GE.THRESH ) THEN
00330                               IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
00331      \$                           CALL ALAHD( NOUT, PATH )
00332                               WRITE( NOUT, FMT = 9999 )UPLO, TRANS,
00333      \$                           DIAG, N, KD, NRHS, IMAT, K, RESULT( K )
00334                               NFAIL = NFAIL + 1
00335                            END IF
00336    40                   CONTINUE
00337                         NRUN = NRUN + 5
00338    50                CONTINUE
00339    60             CONTINUE
00340 *
00341 *+    TEST 6
00342 *                    Get an estimate of RCOND = 1/CNDNUM.
00343 *
00344                   DO 70 ITRAN = 1, 2
00345                      IF( ITRAN.EQ.1 ) THEN
00346                         NORM = 'O'
00347                         RCONDC = RCONDO
00348                      ELSE
00349                         NORM = 'I'
00350                         RCONDC = RCONDI
00351                      END IF
00352                      SRNAMT = 'STBCON'
00353                      CALL STBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB,
00354      \$                            RCOND, WORK, IWORK, INFO )
00355 *
00356 *                    Check error code from STBCON.
00357 *
00358                      IF( INFO.NE.0 )
00359      \$                  CALL ALAERH( PATH, 'STBCON', INFO, 0,
00360      \$                               NORM // UPLO // DIAG, N, N, KD, KD,
00361      \$                               -1, IMAT, NFAIL, NERRS, NOUT )
00362 *
00363                      CALL STBT06( RCOND, RCONDC, UPLO, DIAG, N, KD, AB,
00364      \$                            LDAB, RWORK, RESULT( 6 ) )
00365 *
00366 *                    Print information about the tests that did not pass
00367 *                    the threshold.
00368 *
00369                      IF( RESULT( 6 ).GE.THRESH ) THEN
00370                         IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
00371      \$                     CALL ALAHD( NOUT, PATH )
00372                         WRITE( NOUT, FMT = 9998 ) 'STBCON', NORM, UPLO,
00373      \$                     DIAG, N, KD, IMAT, 6, RESULT( 6 )
00374                         NFAIL = NFAIL + 1
00375                      END IF
00376                      NRUN = NRUN + 1
00377    70             CONTINUE
00378    80          CONTINUE
00379    90       CONTINUE
00380 *
00381 *           Use pathological test matrices to test SLATBS.
00382 *
00383             DO 120 IMAT = NTYPE1 + 1, NIMAT2
00384 *
00385 *              Do the tests only if DOTYPE( IMAT ) is true.
00386 *
00387                IF( .NOT.DOTYPE( IMAT ) )
00388      \$            GO TO 120
00389 *
00390                DO 110 IUPLO = 1, 2
00391 *
00392 *                 Do first for UPLO = 'U', then for UPLO = 'L'
00393 *
00394                   UPLO = UPLOS( IUPLO )
00395                   DO 100 ITRAN = 1, NTRAN
00396 *
00397 *                    Do for op(A) = A, A**T, and A**H.
00398 *
00399                      TRANS = TRANSS( ITRAN )
00400 *
00401 *                    Call SLATTB to generate a triangular test matrix.
00402 *
00403                      SRNAMT = 'SLATTB'
00404                      CALL SLATTB( IMAT, UPLO, TRANS, DIAG, ISEED, N, KD,
00405      \$                            AB, LDAB, X, WORK, INFO )
00406 *
00407 *+    TEST 7
00408 *                    Solve the system op(A)*x = b
00409 *
00410                      SRNAMT = 'SLATBS'
00411                      CALL SCOPY( N, X, 1, B, 1 )
00412                      CALL SLATBS( UPLO, TRANS, DIAG, 'N', N, KD, AB,
00413      \$                            LDAB, B, SCALE, RWORK, INFO )
00414 *
00415 *                    Check error code from SLATBS.
00416 *
00417                      IF( INFO.NE.0 )
00418      \$                  CALL ALAERH( PATH, 'SLATBS', INFO, 0,
00419      \$                               UPLO // TRANS // DIAG // 'N', N, N,
00420      \$                               KD, KD, -1, IMAT, NFAIL, NERRS,
00421      \$                               NOUT )
00422 *
00423                      CALL STBT03( UPLO, TRANS, DIAG, N, KD, 1, AB, LDAB,
00424      \$                            SCALE, RWORK, ONE, B, LDA, X, LDA,
00425      \$                            WORK, RESULT( 7 ) )
00426 *
00427 *+    TEST 8
00428 *                    Solve op(A)*x = b again with NORMIN = 'Y'.
00429 *
00430                      CALL SCOPY( N, X, 1, B, 1 )
00431                      CALL SLATBS( UPLO, TRANS, DIAG, 'Y', N, KD, AB,
00432      \$                            LDAB, B, SCALE, RWORK, INFO )
00433 *
00434 *                    Check error code from SLATBS.
00435 *
00436                      IF( INFO.NE.0 )
00437      \$                  CALL ALAERH( PATH, 'SLATBS', INFO, 0,
00438      \$                               UPLO // TRANS // DIAG // 'Y', N, N,
00439      \$                               KD, KD, -1, IMAT, NFAIL, NERRS,
00440      \$                               NOUT )
00441 *
00442                      CALL STBT03( UPLO, TRANS, DIAG, N, KD, 1, AB, LDAB,
00443      \$                            SCALE, RWORK, ONE, B, LDA, X, LDA,
00444      \$                            WORK, RESULT( 8 ) )
00445 *
00446 *                    Print information about the tests that did not pass
00447 *                    the threshold.
00448 *
00449                      IF( RESULT( 7 ).GE.THRESH ) THEN
00450                         IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
00451      \$                     CALL ALAHD( NOUT, PATH )
00452                         WRITE( NOUT, FMT = 9997 )'SLATBS', UPLO, TRANS,
00453      \$                     DIAG, 'N', N, KD, IMAT, 7, RESULT( 7 )
00454                         NFAIL = NFAIL + 1
00455                      END IF
00456                      IF( RESULT( 8 ).GE.THRESH ) THEN
00457                         IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
00458      \$                     CALL ALAHD( NOUT, PATH )
00459                         WRITE( NOUT, FMT = 9997 )'SLATBS', UPLO, TRANS,
00460      \$                     DIAG, 'Y', N, KD, IMAT, 8, RESULT( 8 )
00461                         NFAIL = NFAIL + 1
00462                      END IF
00463                      NRUN = NRUN + 2
00464   100             CONTINUE
00465   110          CONTINUE
00466   120       CONTINUE
00467   130    CONTINUE
00468   140 CONTINUE
00469 *
00470 *     Print a summary of the results.
00471 *
00472       CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
00473 *
00474  9999 FORMAT( ' UPLO=''', A1, ''', TRANS=''', A1, ''
00475 ',     \$      DIAG=''', A1, ''', N=', I5, ', KD=', I5, ', NRHS=', I5,
00476      \$      ', type ', I2, ', test(', I2, ')=', G12.5 )
00477  9998 FORMAT( 1X, A, '( ''', A1, ''', ''', A1, ''', ''', A1, ''',',
00478      \$      I5, ',', I5, ',  ... ), type ', I2, ', test(', I2, ')=',
00479      \$      G12.5 )
00480  9997 FORMAT( 1X, A, '( ''', A1, ''', ''', A1, ''', ''', A1, ''', ''',
00481      \$      A1, ''',', I5, ',', I5, ', ...  ),  type ', I2, ', test(',
00482      \$      I1, ')=', G12.5 )
00483       RETURN
00484 *
00485 *     End of SCHKTB
00486 *
00487       END
```