LAPACK: TESTING/LIN/zdrvsy.f Source File

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00001       SUBROUTINE ZDRVSY( 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       DOUBLE PRECISION   THRESH
00013 *     ..
00014 *     .. Array Arguments ..
00015       LOGICAL            DOTYPE( * )
00016       INTEGER            IWORK( * ), NVAL( * )
00017       DOUBLE PRECISION   RWORK( * )
00018       COMPLEX*16         A( * ), AFAC( * ), AINV( * ), B( * ),
00019      $                   WORK( * ), X( * ), XACT( * )
00020 *     ..
00021 *
00022 *  Purpose
00023 *  =======
00024 *
00025 *  ZDRVSY tests the driver routines ZSYSV 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) DOUBLE PRECISION
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) COMPLEX*16 array, dimension (NMAX*NMAX)
00058 *
00059 *  AFAC    (workspace) COMPLEX*16 array, dimension (NMAX*NMAX)
00060 *
00061 *  AINV    (workspace) COMPLEX*16 array, dimension (NMAX*NMAX)
00062 *
00063 *  B       (workspace) COMPLEX*16 array, dimension (NMAX*NRHS)
00064 *
00065 *  X       (workspace) COMPLEX*16 array, dimension (NMAX*NRHS)
00066 *
00067 *  XACT    (workspace) COMPLEX*16 array, dimension (NMAX*NRHS)
00068 *
00069 *  WORK    (workspace) COMPLEX*16 array, dimension
00070 *                      (NMAX*max(2,NRHS))
00071 *
00072 *  RWORK   (workspace) DOUBLE PRECISION array, dimension (NMAX+2*NRHS)
00073 *
00074 *  IWORK   (workspace) INTEGER array, dimension (NMAX)
00075 *
00076 *  NOUT    (input) INTEGER
00077 *          The unit number for output.
00078 *
00079 *  =====================================================================
00080 *
00081 *     .. Parameters ..
00082       DOUBLE PRECISION   ONE, ZERO
00083       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
00084       INTEGER            NTYPES, NTESTS
00085       PARAMETER          ( NTYPES = 11, NTESTS = 6 )
00086       INTEGER            NFACT
00087       PARAMETER          ( NFACT = 2 )
00088 *     ..
00089 *     .. Local Scalars ..
00090       LOGICAL            ZEROT
00091       CHARACTER          DIST, FACT, TYPE, UPLO, XTYPE
00092       CHARACTER*3        PATH
00093       INTEGER            I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
00094      $                   IZERO, J, K, K1, KL, KU, LDA, LWORK, MODE, N,
00095      $                   NB, NBMIN, NERRS, NFAIL, NIMAT, NRUN, NT
00096       DOUBLE PRECISION   AINVNM, ANORM, CNDNUM, RCOND, RCONDC
00097 *     ..
00098 *     .. Local Arrays ..
00099       CHARACTER          FACTS( NFACT ), UPLOS( 2 )
00100       INTEGER            ISEED( 4 ), ISEEDY( 4 )
00101       DOUBLE PRECISION   RESULT( NTESTS )
00102 *     ..
00103 *     .. External Functions ..
00104       DOUBLE PRECISION   DGET06, ZLANSY
00105       EXTERNAL           DGET06, ZLANSY
00106 *     ..
00107 *     .. External Subroutines ..
00108       EXTERNAL           ALADHD, ALAERH, ALASVM, XLAENV, ZERRVX, ZGET04,
00109      $                   ZLACPY, ZLARHS, ZLASET, ZLATB4, ZLATMS, ZLATSY,
00110      $                   ZPOT05, ZSYSV, ZSYSVX, ZSYT01, ZSYT02, ZSYTRF,
00111      $                   ZSYTRI2
00112 *     ..
00113 *     .. Scalars in Common ..
00114       LOGICAL            LERR, OK
00115       CHARACTER*32       SRNAMT
00116       INTEGER            INFOT, NUNIT
00117 *     ..
00118 *     .. Common blocks ..
00119       COMMON             / INFOC / INFOT, NUNIT, OK, LERR
00120       COMMON             / SRNAMC / SRNAMT
00121 *     ..
00122 *     .. Intrinsic Functions ..
00123       INTRINSIC          DCMPLX, MAX, MIN
00124 *     ..
00125 *     .. Data statements ..
00126       DATA               ISEEDY / 1988, 1989, 1990, 1991 /
00127       DATA               UPLOS / 'U', 'L' / , FACTS / 'F', 'N' /
00128 *     ..
00129 *     .. Executable Statements ..
00130 *
00131 *     Initialize constants and the random number seed.
00132 *
00133       PATH( 1: 1 ) = 'Zomplex precision'
00134       PATH( 2: 3 ) = 'SY'
00135       NRUN = 0
00136       NFAIL = 0
00137       NERRS = 0
00138       DO 10 I = 1, 4
00139          ISEED( I ) = ISEEDY( I )
00140    10 CONTINUE
00141       LWORK = MAX( 2*NMAX, NMAX*NRHS )
00142 *
00143 *     Test the error exits
00144 *
00145       IF( TSTERR )
00146      $   CALL ZERRVX( PATH, NOUT )
00147       INFOT = 0
00148 *
00149 *     Set the block size and minimum block size for testing.
00150 *
00151       NB = 1
00152       NBMIN = 2
00153       CALL XLAENV( 1, NB )
00154       CALL XLAENV( 2, NBMIN )
00155 *
00156 *     Do for each value of N in NVAL
00157 *
00158       DO 180 IN = 1, NN
00159          N = NVAL( IN )
00160          LDA = MAX( N, 1 )
00161          XTYPE = 'N'
00162          NIMAT = NTYPES
00163          IF( N.LE.0 )
00164      $      NIMAT = 1
00165 *
00166          DO 170 IMAT = 1, NIMAT
00167 *
00168 *           Do the tests only if DOTYPE( IMAT ) is true.
00169 *
00170             IF( .NOT.DOTYPE( IMAT ) )
00171      $         GO TO 170
00172 *
00173 *           Skip types 3, 4, 5, or 6 if the matrix size is too small.
00174 *
00175             ZEROT = IMAT.GE.3 .AND. IMAT.LE.6
00176             IF( ZEROT .AND. N.LT.IMAT-2 )
00177      $         GO TO 170
00178 *
00179 *           Do first for UPLO = 'U', then for UPLO = 'L'
00180 *
00181             DO 160 IUPLO = 1, 2
00182                UPLO = UPLOS( IUPLO )
00183 *
00184                IF( IMAT.NE.NTYPES ) THEN
00185 *
00186 *                 Set up parameters with ZLATB4 and generate a test
00187 *                 matrix with ZLATMS.
00188 *
00189                   CALL ZLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM,
00190      $                         MODE, CNDNUM, DIST )
00191 *
00192                   SRNAMT = 'ZLATMS'
00193                   CALL ZLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
00194      $                         CNDNUM, ANORM, KL, KU, UPLO, A, LDA,
00195      $                         WORK, INFO )
00196 *
00197 *                 Check error code from ZLATMS.
00198 *
00199                   IF( INFO.NE.0 ) THEN
00200                      CALL ALAERH( PATH, 'ZLATMS', INFO, 0, UPLO, N, N,
00201      $                            -1, -1, -1, IMAT, NFAIL, NERRS, NOUT )
00202                      GO TO 160
00203                   END IF
00204 *
00205 *                 For types 3-6, zero one or more rows and columns of
00206 *                 the matrix to test that INFO is returned correctly.
00207 *
00208                   IF( ZEROT ) THEN
00209                      IF( IMAT.EQ.3 ) THEN
00210                         IZERO = 1
00211                      ELSE IF( IMAT.EQ.4 ) THEN
00212                         IZERO = N
00213                      ELSE
00214                         IZERO = N / 2 + 1
00215                      END IF
00216 *
00217                      IF( IMAT.LT.6 ) THEN
00218 *
00219 *                       Set row and column IZERO to zero.
00220 *
00221                         IF( IUPLO.EQ.1 ) THEN
00222                            IOFF = ( IZERO-1 )*LDA
00223                            DO 20 I = 1, IZERO - 1
00224                               A( IOFF+I ) = ZERO
00225    20                      CONTINUE
00226                            IOFF = IOFF + IZERO
00227                            DO 30 I = IZERO, N
00228                               A( IOFF ) = ZERO
00229                               IOFF = IOFF + LDA
00230    30                      CONTINUE
00231                         ELSE
00232                            IOFF = IZERO
00233                            DO 40 I = 1, IZERO - 1
00234                               A( IOFF ) = ZERO
00235                               IOFF = IOFF + LDA
00236    40                      CONTINUE
00237                            IOFF = IOFF - IZERO
00238                            DO 50 I = IZERO, N
00239                               A( IOFF+I ) = ZERO
00240    50                      CONTINUE
00241                         END IF
00242                      ELSE
00243                         IF( IUPLO.EQ.1 ) THEN
00244 *
00245 *                          Set the first IZERO rows to zero.
00246 *
00247                            IOFF = 0
00248                            DO 70 J = 1, N
00249                               I2 = MIN( J, IZERO )
00250                               DO 60 I = 1, I2
00251                                  A( IOFF+I ) = ZERO
00252    60                         CONTINUE
00253                               IOFF = IOFF + LDA
00254    70                      CONTINUE
00255                         ELSE
00256 *
00257 *                          Set the last IZERO rows to zero.
00258 *
00259                            IOFF = 0
00260                            DO 90 J = 1, N
00261                               I1 = MAX( J, IZERO )
00262                               DO 80 I = I1, N
00263                                  A( IOFF+I ) = ZERO
00264    80                         CONTINUE
00265                               IOFF = IOFF + LDA
00266    90                      CONTINUE
00267                         END IF
00268                      END IF
00269                   ELSE
00270                      IZERO = 0
00271                   END IF
00272                ELSE
00273 *
00274 *                 IMAT = NTYPES:  Use a special block diagonal matrix to
00275 *                 test alternate code for the 2-by-2 blocks.
00276 *
00277                   CALL ZLATSY( UPLO, N, A, LDA, ISEED )
00278                END IF
00279 *
00280                DO 150 IFACT = 1, NFACT
00281 *
00282 *                 Do first for FACT = 'F', then for other values.
00283 *
00284                   FACT = FACTS( IFACT )
00285 *
00286 *                 Compute the condition number for comparison with
00287 *                 the value returned by ZSYSVX.
00288 *
00289                   IF( ZEROT ) THEN
00290                      IF( IFACT.EQ.1 )
00291      $                  GO TO 150
00292                      RCONDC = ZERO
00293 *
00294                   ELSE IF( IFACT.EQ.1 ) THEN
00295 *
00296 *                    Compute the 1-norm of A.
00297 *
00298                      ANORM = ZLANSY( '1', UPLO, N, A, LDA, RWORK )
00299 *
00300 *                    Factor the matrix A.
00301 *
00302                      CALL ZLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
00303                      CALL ZSYTRF( UPLO, N, AFAC, LDA, IWORK, WORK,
00304      $                            LWORK, INFO )
00305 *
00306 *                    Compute inv(A) and take its norm.
00307 *
00308                      CALL ZLACPY( UPLO, N, N, AFAC, LDA, AINV, LDA )
00309                      LWORK = (N+NB+1)*(NB+3)
00310                      CALL ZSYTRI2( UPLO, N, AINV, LDA, IWORK, WORK,
00311      $                            LWORK, INFO )
00312                      AINVNM = ZLANSY( '1', UPLO, N, AINV, LDA, RWORK )
00313 *
00314 *                    Compute the 1-norm condition number of A.
00315 *
00316                      IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
00317                         RCONDC = ONE
00318                      ELSE
00319                         RCONDC = ( ONE / ANORM ) / AINVNM
00320                      END IF
00321                   END IF
00322 *
00323 *                 Form an exact solution and set the right hand side.
00324 *
00325                   SRNAMT = 'ZLARHS'
00326                   CALL ZLARHS( PATH, XTYPE, UPLO, ' ', N, N, KL, KU,
00327      $                         NRHS, A, LDA, XACT, LDA, B, LDA, ISEED,
00328      $                         INFO )
00329                   XTYPE = 'C'
00330 *
00331 *                 --- Test ZSYSV  ---
00332 *
00333                   IF( IFACT.EQ.2 ) THEN
00334                      CALL ZLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
00335                      CALL ZLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
00336 *
00337 *                    Factor the matrix and solve the system using ZSYSV.
00338 *
00339                      SRNAMT = 'ZSYSV '
00340                      CALL ZSYSV( UPLO, N, NRHS, AFAC, LDA, IWORK, X,
00341      $                           LDA, WORK, LWORK, INFO )
00342 *
00343 *                    Adjust the expected value of INFO to account for
00344 *                    pivoting.
00345 *
00346                      K = IZERO
00347                      IF( K.GT.0 ) THEN
00348   100                   CONTINUE
00349                         IF( IWORK( K ).LT.0 ) THEN
00350                            IF( IWORK( K ).NE.-K ) THEN
00351                               K = -IWORK( K )
00352                               GO TO 100
00353                            END IF
00354                         ELSE IF( IWORK( K ).NE.K ) THEN
00355                            K = IWORK( K )
00356                            GO TO 100
00357                         END IF
00358                      END IF
00359 *
00360 *                    Check error code from ZSYSV .
00361 *
00362                      IF( INFO.NE.K ) THEN
00363                         CALL ALAERH( PATH, 'ZSYSV ', INFO, K, UPLO, N,
00364      $                               N, -1, -1, NRHS, IMAT, NFAIL,
00365      $                               NERRS, NOUT )
00366                         GO TO 120
00367                      ELSE IF( INFO.NE.0 ) THEN
00368                         GO TO 120
00369                      END IF
00370 *
00371 *                    Reconstruct matrix from factors and compute
00372 *                    residual.
00373 *
00374                      CALL ZSYT01( UPLO, N, A, LDA, AFAC, LDA, IWORK,
00375      $                            AINV, LDA, RWORK, RESULT( 1 ) )
00376 *
00377 *                    Compute residual of the computed solution.
00378 *
00379                      CALL ZLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
00380                      CALL ZSYT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
00381      $                            LDA, RWORK, RESULT( 2 ) )
00382 *
00383 *                    Check solution from generated exact solution.
00384 *
00385                      CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
00386      $                            RESULT( 3 ) )
00387                      NT = 3
00388 *
00389 *                    Print information about the tests that did not pass
00390 *                    the threshold.
00391 *
00392                      DO 110 K = 1, NT
00393                         IF( RESULT( K ).GE.THRESH ) THEN
00394                            IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
00395      $                        CALL ALADHD( NOUT, PATH )
00396                            WRITE( NOUT, FMT = 9999 )'ZSYSV ', UPLO, N,
00397      $                        IMAT, K, RESULT( K )
00398                            NFAIL = NFAIL + 1
00399                         END IF
00400   110                CONTINUE
00401                      NRUN = NRUN + NT
00402   120                CONTINUE
00403                   END IF
00404 *
00405 *                 --- Test ZSYSVX ---
00406 *
00407                   IF( IFACT.EQ.2 )
00408      $               CALL ZLASET( UPLO, N, N, DCMPLX( ZERO ),
00409      $                            DCMPLX( ZERO ), AFAC, LDA )
00410                   CALL ZLASET( 'Full', N, NRHS, DCMPLX( ZERO ),
00411      $                         DCMPLX( ZERO ), X, LDA )
00412 *
00413 *                 Solve the system and compute the condition number and
00414 *                 error bounds using ZSYSVX.
00415 *
00416                   SRNAMT = 'ZSYSVX'
00417                   CALL ZSYSVX( FACT, UPLO, N, NRHS, A, LDA, AFAC, LDA,
00418      $                         IWORK, B, LDA, X, LDA, RCOND, RWORK,
00419      $                         RWORK( NRHS+1 ), WORK, LWORK,
00420      $                         RWORK( 2*NRHS+1 ), INFO )
00421 *
00422 *                 Adjust the expected value of INFO to account for
00423 *                 pivoting.
00424 *
00425                   K = IZERO
00426                   IF( K.GT.0 ) THEN
00427   130                CONTINUE
00428                      IF( IWORK( K ).LT.0 ) THEN
00429                         IF( IWORK( K ).NE.-K ) THEN
00430                            K = -IWORK( K )
00431                            GO TO 130
00432                         END IF
00433                      ELSE IF( IWORK( K ).NE.K ) THEN
00434                         K = IWORK( K )
00435                         GO TO 130
00436                      END IF
00437                   END IF
00438 *
00439 *                 Check the error code from ZSYSVX.
00440 *
00441                   IF( INFO.NE.K ) THEN
00442                      CALL ALAERH( PATH, 'ZSYSVX', INFO, K, FACT // UPLO,
00443      $                            N, N, -1, -1, NRHS, IMAT, NFAIL,
00444      $                            NERRS, NOUT )
00445                      GO TO 150
00446                   END IF
00447 *
00448                   IF( INFO.EQ.0 ) THEN
00449                      IF( IFACT.GE.2 ) THEN
00450 *
00451 *                       Reconstruct matrix from factors and compute
00452 *                       residual.
00453 *
00454                         CALL ZSYT01( UPLO, N, A, LDA, AFAC, LDA, IWORK,
00455      $                               AINV, LDA, RWORK( 2*NRHS+1 ),
00456      $                               RESULT( 1 ) )
00457                         K1 = 1
00458                      ELSE
00459                         K1 = 2
00460                      END IF
00461 *
00462 *                    Compute residual of the computed solution.
00463 *
00464                      CALL ZLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
00465                      CALL ZSYT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
00466      $                            LDA, RWORK( 2*NRHS+1 ), RESULT( 2 ) )
00467 *
00468 *                    Check solution from generated exact solution.
00469 *
00470                      CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
00471      $                            RESULT( 3 ) )
00472 *
00473 *                    Check the error bounds from iterative refinement.
00474 *
00475                      CALL ZPOT05( UPLO, N, NRHS, A, LDA, B, LDA, X, LDA,
00476      $                            XACT, LDA, RWORK, RWORK( NRHS+1 ),
00477      $                            RESULT( 4 ) )
00478                   ELSE
00479                      K1 = 6
00480                   END IF
00481 *
00482 *                 Compare RCOND from ZSYSVX with the computed value
00483 *                 in RCONDC.
00484 *
00485                   RESULT( 6 ) = DGET06( RCOND, RCONDC )
00486 *
00487 *                 Print information about the tests that did not pass
00488 *                 the threshold.
00489 *
00490                   DO 140 K = K1, 6
00491                      IF( RESULT( K ).GE.THRESH ) THEN
00492                         IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
00493      $                     CALL ALADHD( NOUT, PATH )
00494                         WRITE( NOUT, FMT = 9998 )'ZSYSVX', FACT, UPLO,
00495      $                     N, IMAT, K, RESULT( K )
00496                         NFAIL = NFAIL + 1
00497                      END IF
00498   140             CONTINUE
00499                   NRUN = NRUN + 7 - K1
00500 *
00501   150          CONTINUE
00502 *
00503   160       CONTINUE
00504   170    CONTINUE
00505   180 CONTINUE
00506 *
00507 *     Print a summary of the results.
00508 *
00509       CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
00510 *
00511  9999 FORMAT( 1X, A, ', UPLO=''', A1, ''', N =', I5, ', type ', I2,
00512      $      ', test ', I2, ', ratio =', G12.5 )
00513  9998 FORMAT( 1X, A, ', FACT=''', A1, ''', UPLO=''', A1, ''', N =', I5,
00514      $      ', type ', I2, ', test ', I2, ', ratio =', G12.5 )
00515       RETURN
00516 *
00517 *     End of ZDRVSY
00518 *
00519       END