LAPACK: TESTING/LIN/zchkpb.f Source File

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00001       SUBROUTINE ZCHKPB( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
00002      $                   THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
00003      $                   XACT, WORK, RWORK, 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, NNB, NNS, NOUT
00012       DOUBLE PRECISION   THRESH
00013 *     ..
00014 *     .. Array Arguments ..
00015       LOGICAL            DOTYPE( * )
00016       INTEGER            NBVAL( * ), NSVAL( * ), NVAL( * )
00017       DOUBLE PRECISION   RWORK( * )
00018       COMPLEX*16         A( * ), AFAC( * ), AINV( * ), B( * ),
00019      $                   WORK( * ), X( * ), XACT( * )
00020 *     ..
00021 *
00022 *  Purpose
00023 *  =======
00024 *
00025 *  ZCHKPB tests ZPBTRF, -TRS, -RFS, and -CON.
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 *  NNB     (input) INTEGER
00042 *          The number of values of NB contained in the vector NBVAL.
00043 *
00044 *  NBVAL   (input) INTEGER array, dimension (NBVAL)
00045 *          The values of the blocksize NB.
00046 *
00047 *  NNS     (input) INTEGER
00048 *          The number of values of NRHS contained in the vector NSVAL.
00049 *
00050 *  NSVAL   (input) INTEGER array, dimension (NNS)
00051 *          The values of the number of right hand sides NRHS.
00052 *
00053 *  THRESH  (input) DOUBLE PRECISION
00054 *          The threshold value for the test ratios.  A result is
00055 *          included in the output file if RESULT >= THRESH.  To have
00056 *          every test ratio printed, use THRESH = 0.
00057 *
00058 *  TSTERR  (input) LOGICAL
00059 *          Flag that indicates whether error exits are to be tested.
00060 *
00061 *  NMAX    (input) INTEGER
00062 *          The maximum value permitted for N, used in dimensioning the
00063 *          work arrays.
00064 *
00065 *  A       (workspace) DOUBLE PRECISION array, dimension (NMAX*NMAX)
00066 *
00067 *  AFAC    (workspace) DOUBLE PRECISION array, dimension (NMAX*NMAX)
00068 *
00069 *  AINV    (workspace) DOUBLE PRECISION array, dimension (NMAX*NMAX)
00070 *
00071 *  B       (workspace) DOUBLE PRECISION array, dimension (NMAX*NSMAX)
00072 *          where NSMAX is the largest entry in NSVAL.
00073 *
00074 *  X       (workspace) DOUBLE PRECISION array, dimension (NMAX*NSMAX)
00075 *
00076 *  XACT    (workspace) DOUBLE PRECISION array, dimension (NMAX*NSMAX)
00077 *
00078 *  WORK    (workspace) DOUBLE PRECISION array, dimension
00079 *                      (NMAX*max(3,NSMAX))
00080 *
00081 *  RWORK   (workspace) DOUBLE PRECISION array, dimension
00082 *                      (max(NMAX,2*NSMAX))
00083 *
00084 *  NOUT    (input) INTEGER
00085 *          The unit number for output.
00086 *
00087 *  =====================================================================
00088 *
00089 *     .. Parameters ..
00090       DOUBLE PRECISION   ONE, ZERO
00091       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
00092       INTEGER            NTYPES, NTESTS
00093       PARAMETER          ( NTYPES = 8, NTESTS = 7 )
00094       INTEGER            NBW
00095       PARAMETER          ( NBW = 4 )
00096 *     ..
00097 *     .. Local Scalars ..
00098       LOGICAL            ZEROT
00099       CHARACTER          DIST, PACKIT, TYPE, UPLO, XTYPE
00100       CHARACTER*3        PATH
00101       INTEGER            I, I1, I2, IKD, IMAT, IN, INB, INFO, IOFF,
00102      $                   IRHS, IUPLO, IW, IZERO, K, KD, KL, KOFF, KU,
00103      $                   LDA, LDAB, MODE, N, NB, NERRS, NFAIL, NIMAT,
00104      $                   NKD, NRHS, NRUN
00105       DOUBLE PRECISION   AINVNM, ANORM, CNDNUM, RCOND, RCONDC
00106 *     ..
00107 *     .. Local Arrays ..
00108       INTEGER            ISEED( 4 ), ISEEDY( 4 ), KDVAL( NBW )
00109       DOUBLE PRECISION   RESULT( NTESTS )
00110 *     ..
00111 *     .. External Functions ..
00112       DOUBLE PRECISION   DGET06, ZLANGE, ZLANHB
00113       EXTERNAL           DGET06, ZLANGE, ZLANHB
00114 *     ..
00115 *     .. External Subroutines ..
00116       EXTERNAL           ALAERH, ALAHD, ALASUM, XLAENV, ZCOPY, ZERRPO,
00117      $                   ZGET04, ZLACPY, ZLAIPD, ZLARHS, ZLASET, ZLATB4,
00118      $                   ZLATMS, ZPBCON, ZPBRFS, ZPBT01, ZPBT02, ZPBT05,
00119      $                   ZPBTRF, ZPBTRS, ZSWAP
00120 *     ..
00121 *     .. Intrinsic Functions ..
00122       INTRINSIC          DCMPLX, MAX, MIN
00123 *     ..
00124 *     .. Scalars in Common ..
00125       LOGICAL            LERR, OK
00126       CHARACTER*32       SRNAMT
00127       INTEGER            INFOT, NUNIT
00128 *     ..
00129 *     .. Common blocks ..
00130       COMMON             / INFOC / INFOT, NUNIT, OK, LERR
00131       COMMON             / SRNAMC / SRNAMT
00132 *     ..
00133 *     .. Data statements ..
00134       DATA               ISEEDY / 1988, 1989, 1990, 1991 /
00135 *     ..
00136 *     .. Executable Statements ..
00137 *
00138 *     Initialize constants and the random number seed.
00139 *
00140       PATH( 1: 1 ) = 'Zomplex precision'
00141       PATH( 2: 3 ) = 'PB'
00142       NRUN = 0
00143       NFAIL = 0
00144       NERRS = 0
00145       DO 10 I = 1, 4
00146          ISEED( I ) = ISEEDY( I )
00147    10 CONTINUE
00148 *
00149 *     Test the error exits
00150 *
00151       IF( TSTERR )
00152      $   CALL ZERRPO( PATH, NOUT )
00153       INFOT = 0
00154       KDVAL( 1 ) = 0
00155 *
00156 *     Do for each value of N in NVAL
00157 *
00158       DO 90 IN = 1, NN
00159          N = NVAL( IN )
00160          LDA = MAX( N, 1 )
00161          XTYPE = 'N'
00162 *
00163 *        Set limits on the number of loop iterations.
00164 *
00165          NKD = MAX( 1, MIN( N, 4 ) )
00166          NIMAT = NTYPES
00167          IF( N.EQ.0 )
00168      $      NIMAT = 1
00169 *
00170          KDVAL( 2 ) = N + ( N+1 ) / 4
00171          KDVAL( 3 ) = ( 3*N-1 ) / 4
00172          KDVAL( 4 ) = ( N+1 ) / 4
00173 *
00174          DO 80 IKD = 1, NKD
00175 *
00176 *           Do for KD = 0, (5*N+1)/4, (3N-1)/4, and (N+1)/4. This order
00177 *           makes it easier to skip redundant values for small values
00178 *           of N.
00179 *
00180             KD = KDVAL( IKD )
00181             LDAB = KD + 1
00182 *
00183 *           Do first for UPLO = 'U', then for UPLO = 'L'
00184 *
00185             DO 70 IUPLO = 1, 2
00186                KOFF = 1
00187                IF( IUPLO.EQ.1 ) THEN
00188                   UPLO = 'U'
00189                   KOFF = MAX( 1, KD+2-N )
00190                   PACKIT = 'Q'
00191                ELSE
00192                   UPLO = 'L'
00193                   PACKIT = 'B'
00194                END IF
00195 *
00196                DO 60 IMAT = 1, NIMAT
00197 *
00198 *                 Do the tests only if DOTYPE( IMAT ) is true.
00199 *
00200                   IF( .NOT.DOTYPE( IMAT ) )
00201      $               GO TO 60
00202 *
00203 *                 Skip types 2, 3, or 4 if the matrix size is too small.
00204 *
00205                   ZEROT = IMAT.GE.2 .AND. IMAT.LE.4
00206                   IF( ZEROT .AND. N.LT.IMAT-1 )
00207      $               GO TO 60
00208 *
00209                   IF( .NOT.ZEROT .OR. .NOT.DOTYPE( 1 ) ) THEN
00210 *
00211 *                    Set up parameters with ZLATB4 and generate a test
00212 *                    matrix with ZLATMS.
00213 *
00214                      CALL ZLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM,
00215      $                            MODE, CNDNUM, DIST )
00216 *
00217                      SRNAMT = 'ZLATMS'
00218                      CALL ZLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
00219      $                            CNDNUM, ANORM, KD, KD, PACKIT,
00220      $                            A( KOFF ), LDAB, WORK, INFO )
00221 *
00222 *                    Check error code from ZLATMS.
00223 *
00224                      IF( INFO.NE.0 ) THEN
00225                         CALL ALAERH( PATH, 'ZLATMS', INFO, 0, UPLO, N,
00226      $                               N, KD, KD, -1, IMAT, NFAIL, NERRS,
00227      $                               NOUT )
00228                         GO TO 60
00229                      END IF
00230                   ELSE IF( IZERO.GT.0 ) THEN
00231 *
00232 *                    Use the same matrix for types 3 and 4 as for type
00233 *                    2 by copying back the zeroed out column,
00234 *
00235                      IW = 2*LDA + 1
00236                      IF( IUPLO.EQ.1 ) THEN
00237                         IOFF = ( IZERO-1 )*LDAB + KD + 1
00238                         CALL ZCOPY( IZERO-I1, WORK( IW ), 1,
00239      $                              A( IOFF-IZERO+I1 ), 1 )
00240                         IW = IW + IZERO - I1
00241                         CALL ZCOPY( I2-IZERO+1, WORK( IW ), 1,
00242      $                              A( IOFF ), MAX( LDAB-1, 1 ) )
00243                      ELSE
00244                         IOFF = ( I1-1 )*LDAB + 1
00245                         CALL ZCOPY( IZERO-I1, WORK( IW ), 1,
00246      $                              A( IOFF+IZERO-I1 ),
00247      $                              MAX( LDAB-1, 1 ) )
00248                         IOFF = ( IZERO-1 )*LDAB + 1
00249                         IW = IW + IZERO - I1
00250                         CALL ZCOPY( I2-IZERO+1, WORK( IW ), 1,
00251      $                              A( IOFF ), 1 )
00252                      END IF
00253                   END IF
00254 *
00255 *                 For types 2-4, zero one row and column of the matrix
00256 *                 to test that INFO is returned correctly.
00257 *
00258                   IZERO = 0
00259                   IF( ZEROT ) THEN
00260                      IF( IMAT.EQ.2 ) THEN
00261                         IZERO = 1
00262                      ELSE IF( IMAT.EQ.3 ) THEN
00263                         IZERO = N
00264                      ELSE
00265                         IZERO = N / 2 + 1
00266                      END IF
00267 *
00268 *                    Save the zeroed out row and column in WORK(*,3)
00269 *
00270                      IW = 2*LDA
00271                      DO 20 I = 1, MIN( 2*KD+1, N )
00272                         WORK( IW+I ) = ZERO
00273    20                CONTINUE
00274                      IW = IW + 1
00275                      I1 = MAX( IZERO-KD, 1 )
00276                      I2 = MIN( IZERO+KD, N )
00277 *
00278                      IF( IUPLO.EQ.1 ) THEN
00279                         IOFF = ( IZERO-1 )*LDAB + KD + 1
00280                         CALL ZSWAP( IZERO-I1, A( IOFF-IZERO+I1 ), 1,
00281      $                              WORK( IW ), 1 )
00282                         IW = IW + IZERO - I1
00283                         CALL ZSWAP( I2-IZERO+1, A( IOFF ),
00284      $                              MAX( LDAB-1, 1 ), WORK( IW ), 1 )
00285                      ELSE
00286                         IOFF = ( I1-1 )*LDAB + 1
00287                         CALL ZSWAP( IZERO-I1, A( IOFF+IZERO-I1 ),
00288      $                              MAX( LDAB-1, 1 ), WORK( IW ), 1 )
00289                         IOFF = ( IZERO-1 )*LDAB + 1
00290                         IW = IW + IZERO - I1
00291                         CALL ZSWAP( I2-IZERO+1, A( IOFF ), 1,
00292      $                              WORK( IW ), 1 )
00293                      END IF
00294                   END IF
00295 *
00296 *                 Set the imaginary part of the diagonals.
00297 *
00298                   IF( IUPLO.EQ.1 ) THEN
00299                      CALL ZLAIPD( N, A( KD+1 ), LDAB, 0 )
00300                   ELSE
00301                      CALL ZLAIPD( N, A( 1 ), LDAB, 0 )
00302                   END IF
00303 *
00304 *                 Do for each value of NB in NBVAL
00305 *
00306                   DO 50 INB = 1, NNB
00307                      NB = NBVAL( INB )
00308                      CALL XLAENV( 1, NB )
00309 *
00310 *                    Compute the L*L' or U'*U factorization of the band
00311 *                    matrix.
00312 *
00313                      CALL ZLACPY( 'Full', KD+1, N, A, LDAB, AFAC, LDAB )
00314                      SRNAMT = 'ZPBTRF'
00315                      CALL ZPBTRF( UPLO, N, KD, AFAC, LDAB, INFO )
00316 *
00317 *                    Check error code from ZPBTRF.
00318 *
00319                      IF( INFO.NE.IZERO ) THEN
00320                         CALL ALAERH( PATH, 'ZPBTRF', INFO, IZERO, UPLO,
00321      $                               N, N, KD, KD, NB, IMAT, NFAIL,
00322      $                               NERRS, NOUT )
00323                         GO TO 50
00324                      END IF
00325 *
00326 *                    Skip the tests if INFO is not 0.
00327 *
00328                      IF( INFO.NE.0 )
00329      $                  GO TO 50
00330 *
00331 *+    TEST 1
00332 *                    Reconstruct matrix from factors and compute
00333 *                    residual.
00334 *
00335                      CALL ZLACPY( 'Full', KD+1, N, AFAC, LDAB, AINV,
00336      $                            LDAB )
00337                      CALL ZPBT01( UPLO, N, KD, A, LDAB, AINV, LDAB,
00338      $                            RWORK, RESULT( 1 ) )
00339 *
00340 *                    Print the test ratio if it is .GE. THRESH.
00341 *
00342                      IF( RESULT( 1 ).GE.THRESH ) THEN
00343                         IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
00344      $                     CALL ALAHD( NOUT, PATH )
00345                         WRITE( NOUT, FMT = 9999 )UPLO, N, KD, NB, IMAT,
00346      $                     1, RESULT( 1 )
00347                         NFAIL = NFAIL + 1
00348                      END IF
00349                      NRUN = NRUN + 1
00350 *
00351 *                    Only do other tests if this is the first blocksize.
00352 *
00353                      IF( INB.GT.1 )
00354      $                  GO TO 50
00355 *
00356 *                    Form the inverse of A so we can get a good estimate
00357 *                    of RCONDC = 1/(norm(A) * norm(inv(A))).
00358 *
00359                      CALL ZLASET( 'Full', N, N, DCMPLX( ZERO ),
00360      $                            DCMPLX( ONE ), AINV, LDA )
00361                      SRNAMT = 'ZPBTRS'
00362                      CALL ZPBTRS( UPLO, N, KD, N, AFAC, LDAB, AINV, LDA,
00363      $                            INFO )
00364 *
00365 *                    Compute RCONDC = 1/(norm(A) * norm(inv(A))).
00366 *
00367                      ANORM = ZLANHB( '1', UPLO, N, KD, A, LDAB, RWORK )
00368                      AINVNM = ZLANGE( '1', N, N, AINV, LDA, RWORK )
00369                      IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
00370                         RCONDC = ONE
00371                      ELSE
00372                         RCONDC = ( ONE / ANORM ) / AINVNM
00373                      END IF
00374 *
00375                      DO 40 IRHS = 1, NNS
00376                         NRHS = NSVAL( IRHS )
00377 *
00378 *+    TEST 2
00379 *                    Solve and compute residual for A * X = B.
00380 *
00381                         SRNAMT = 'ZLARHS'
00382                         CALL ZLARHS( PATH, XTYPE, UPLO, ' ', N, N, KD,
00383      $                               KD, NRHS, A, LDAB, XACT, LDA, B,
00384      $                               LDA, ISEED, INFO )
00385                         CALL ZLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
00386 *
00387                         SRNAMT = 'ZPBTRS'
00388                         CALL ZPBTRS( UPLO, N, KD, NRHS, AFAC, LDAB, X,
00389      $                               LDA, INFO )
00390 *
00391 *                    Check error code from ZPBTRS.
00392 *
00393                         IF( INFO.NE.0 )
00394      $                     CALL ALAERH( PATH, 'ZPBTRS', INFO, 0, UPLO,
00395      $                                  N, N, KD, KD, NRHS, IMAT, NFAIL,
00396      $                                  NERRS, NOUT )
00397 *
00398                         CALL ZLACPY( 'Full', N, NRHS, B, LDA, WORK,
00399      $                               LDA )
00400                         CALL ZPBT02( UPLO, N, KD, NRHS, A, LDAB, X, LDA,
00401      $                               WORK, LDA, RWORK, RESULT( 2 ) )
00402 *
00403 *+    TEST 3
00404 *                    Check solution from generated exact solution.
00405 *
00406                         CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
00407      $                               RESULT( 3 ) )
00408 *
00409 *+    TESTS 4, 5, and 6
00410 *                    Use iterative refinement to improve the solution.
00411 *
00412                         SRNAMT = 'ZPBRFS'
00413                         CALL ZPBRFS( UPLO, N, KD, NRHS, A, LDAB, AFAC,
00414      $                               LDAB, B, LDA, X, LDA, RWORK,
00415      $                               RWORK( NRHS+1 ), WORK,
00416      $                               RWORK( 2*NRHS+1 ), INFO )
00417 *
00418 *                    Check error code from ZPBRFS.
00419 *
00420                         IF( INFO.NE.0 )
00421      $                     CALL ALAERH( PATH, 'ZPBRFS', INFO, 0, UPLO,
00422      $                                  N, N, KD, KD, NRHS, IMAT, NFAIL,
00423      $                                  NERRS, NOUT )
00424 *
00425                         CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
00426      $                               RESULT( 4 ) )
00427                         CALL ZPBT05( UPLO, N, KD, NRHS, A, LDAB, B, LDA,
00428      $                               X, LDA, XACT, LDA, RWORK,
00429      $                               RWORK( NRHS+1 ), RESULT( 5 ) )
00430 *
00431 *                       Print information about the tests that did not
00432 *                       pass the threshold.
00433 *
00434                         DO 30 K = 2, 6
00435                            IF( RESULT( K ).GE.THRESH ) THEN
00436                               IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
00437      $                           CALL ALAHD( NOUT, PATH )
00438                               WRITE( NOUT, FMT = 9998 )UPLO, N, KD,
00439      $                           NRHS, IMAT, K, RESULT( K )
00440                               NFAIL = NFAIL + 1
00441                            END IF
00442    30                   CONTINUE
00443                         NRUN = NRUN + 5
00444    40                CONTINUE
00445 *
00446 *+    TEST 7
00447 *                    Get an estimate of RCOND = 1/CNDNUM.
00448 *
00449                      SRNAMT = 'ZPBCON'
00450                      CALL ZPBCON( UPLO, N, KD, AFAC, LDAB, ANORM, RCOND,
00451      $                            WORK, RWORK, INFO )
00452 *
00453 *                    Check error code from ZPBCON.
00454 *
00455                      IF( INFO.NE.0 )
00456      $                  CALL ALAERH( PATH, 'ZPBCON', INFO, 0, UPLO, N,
00457      $                               N, KD, KD, -1, IMAT, NFAIL, NERRS,
00458      $                               NOUT )
00459 *
00460                      RESULT( 7 ) = DGET06( RCOND, RCONDC )
00461 *
00462 *                    Print the test ratio if it is .GE. THRESH.
00463 *
00464                      IF( RESULT( 7 ).GE.THRESH ) THEN
00465                         IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
00466      $                     CALL ALAHD( NOUT, PATH )
00467                         WRITE( NOUT, FMT = 9997 )UPLO, N, KD, IMAT, 7,
00468      $                     RESULT( 7 )
00469                         NFAIL = NFAIL + 1
00470                      END IF
00471                      NRUN = NRUN + 1
00472    50             CONTINUE
00473    60          CONTINUE
00474    70       CONTINUE
00475    80    CONTINUE
00476    90 CONTINUE
00477 *
00478 *     Print a summary of the results.
00479 *
00480       CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
00481 *
00482  9999 FORMAT( ' UPLO=''', A1, ''', N=', I5, ', KD=', I5, ', NB=', I4,
00483      $      ', type ', I2, ', test ', I2, ', ratio= ', G12.5 )
00484  9998 FORMAT( ' UPLO=''', A1, ''', N=', I5, ', KD=', I5, ', NRHS=', I3,
00485      $      ', type ', I2, ', test(', I2, ') = ', G12.5 )
00486  9997 FORMAT( ' UPLO=''', A1, ''', N=', I5, ', KD=', I5, ',', 10X,
00487      $      ' type ', I2, ', test(', I2, ') = ', G12.5 )
00488       RETURN
00489 *
00490 *     End of ZCHKPB
00491 *
00492       END