LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
zchkpt.f
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00001 *> \brief \b ZCHKPT
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 ZCHKPT( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
00012 *                          A, D, E, B, X, XACT, WORK, RWORK, NOUT )
00013 * 
00014 *       .. Scalar Arguments ..
00015 *       LOGICAL            TSTERR
00016 *       INTEGER            NN, NNS, NOUT
00017 *       DOUBLE PRECISION   THRESH
00018 *       ..
00019 *       .. Array Arguments ..
00020 *       LOGICAL            DOTYPE( * )
00021 *       INTEGER            NSVAL( * ), NVAL( * )
00022 *       DOUBLE PRECISION   D( * ), RWORK( * )
00023 *       COMPLEX*16         A( * ), B( * ), E( * ), WORK( * ), X( * ),
00024 *      $                   XACT( * )
00025 *       ..
00026 *  
00027 *
00028 *> \par Purpose:
00029 *  =============
00030 *>
00031 *> \verbatim
00032 *>
00033 *> ZCHKPT tests ZPTTRF, -TRS, -RFS, and -CON
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] NNS
00060 *> \verbatim
00061 *>          NNS is INTEGER
00062 *>          The number of values of NRHS contained in the vector NSVAL.
00063 *> \endverbatim
00064 *>
00065 *> \param[in] NSVAL
00066 *> \verbatim
00067 *>          NSVAL is INTEGER array, dimension (NNS)
00068 *>          The values of the number of right hand sides NRHS.
00069 *> \endverbatim
00070 *>
00071 *> \param[in] THRESH
00072 *> \verbatim
00073 *>          THRESH is DOUBLE PRECISION
00074 *>          The threshold value for the test ratios.  A result is
00075 *>          included in the output file if RESULT >= THRESH.  To have
00076 *>          every test ratio printed, use THRESH = 0.
00077 *> \endverbatim
00078 *>
00079 *> \param[in] TSTERR
00080 *> \verbatim
00081 *>          TSTERR is LOGICAL
00082 *>          Flag that indicates whether error exits are to be tested.
00083 *> \endverbatim
00084 *>
00085 *> \param[out] A
00086 *> \verbatim
00087 *>          A is COMPLEX*16 array, dimension (NMAX*2)
00088 *> \endverbatim
00089 *>
00090 *> \param[out] D
00091 *> \verbatim
00092 *>          D is DOUBLE PRECISION array, dimension (NMAX*2)
00093 *> \endverbatim
00094 *>
00095 *> \param[out] E
00096 *> \verbatim
00097 *>          E is COMPLEX*16 array, dimension (NMAX*2)
00098 *> \endverbatim
00099 *>
00100 *> \param[out] B
00101 *> \verbatim
00102 *>          B is COMPLEX*16 array, dimension (NMAX*NSMAX)
00103 *>          where NSMAX is the largest entry in NSVAL.
00104 *> \endverbatim
00105 *>
00106 *> \param[out] X
00107 *> \verbatim
00108 *>          X is COMPLEX*16 array, dimension (NMAX*NSMAX)
00109 *> \endverbatim
00110 *>
00111 *> \param[out] XACT
00112 *> \verbatim
00113 *>          XACT is COMPLEX*16 array, dimension (NMAX*NSMAX)
00114 *> \endverbatim
00115 *>
00116 *> \param[out] WORK
00117 *> \verbatim
00118 *>          WORK is COMPLEX*16 array, dimension
00119 *>                      (NMAX*max(3,NSMAX))
00120 *> \endverbatim
00121 *>
00122 *> \param[out] RWORK
00123 *> \verbatim
00124 *>          RWORK is DOUBLE PRECISION array, dimension
00125 *>                      (max(NMAX,2*NSMAX))
00126 *> \endverbatim
00127 *>
00128 *> \param[in] NOUT
00129 *> \verbatim
00130 *>          NOUT is INTEGER
00131 *>          The unit number for output.
00132 *> \endverbatim
00133 *
00134 *  Authors:
00135 *  ========
00136 *
00137 *> \author Univ. of Tennessee 
00138 *> \author Univ. of California Berkeley 
00139 *> \author Univ. of Colorado Denver 
00140 *> \author NAG Ltd. 
00141 *
00142 *> \date November 2011
00143 *
00144 *> \ingroup complex16_lin
00145 *
00146 *  =====================================================================
00147       SUBROUTINE ZCHKPT( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
00148      $                   A, D, E, B, X, XACT, WORK, RWORK, NOUT )
00149 *
00150 *  -- LAPACK test routine (version 3.4.0) --
00151 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00152 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00153 *     November 2011
00154 *
00155 *     .. Scalar Arguments ..
00156       LOGICAL            TSTERR
00157       INTEGER            NN, NNS, NOUT
00158       DOUBLE PRECISION   THRESH
00159 *     ..
00160 *     .. Array Arguments ..
00161       LOGICAL            DOTYPE( * )
00162       INTEGER            NSVAL( * ), NVAL( * )
00163       DOUBLE PRECISION   D( * ), RWORK( * )
00164       COMPLEX*16         A( * ), B( * ), E( * ), WORK( * ), X( * ),
00165      $                   XACT( * )
00166 *     ..
00167 *
00168 *  =====================================================================
00169 *
00170 *     .. Parameters ..
00171       DOUBLE PRECISION   ONE, ZERO
00172       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
00173       INTEGER            NTYPES
00174       PARAMETER          ( NTYPES = 12 )
00175       INTEGER            NTESTS
00176       PARAMETER          ( NTESTS = 7 )
00177 *     ..
00178 *     .. Local Scalars ..
00179       LOGICAL            ZEROT
00180       CHARACTER          DIST, TYPE, UPLO
00181       CHARACTER*3        PATH
00182       INTEGER            I, IA, IMAT, IN, INFO, IRHS, IUPLO, IX, IZERO,
00183      $                   J, K, KL, KU, LDA, MODE, N, NERRS, NFAIL,
00184      $                   NIMAT, NRHS, NRUN
00185       DOUBLE PRECISION   AINVNM, ANORM, COND, DMAX, RCOND, RCONDC
00186 *     ..
00187 *     .. Local Arrays ..
00188       CHARACTER          UPLOS( 2 )
00189       INTEGER            ISEED( 4 ), ISEEDY( 4 )
00190       DOUBLE PRECISION   RESULT( NTESTS )
00191       COMPLEX*16         Z( 3 )
00192 *     ..
00193 *     .. External Functions ..
00194       INTEGER            IDAMAX
00195       DOUBLE PRECISION   DGET06, DZASUM, ZLANHT
00196       EXTERNAL           IDAMAX, DGET06, DZASUM, ZLANHT
00197 *     ..
00198 *     .. External Subroutines ..
00199       EXTERNAL           ALAERH, ALAHD, ALASUM, DCOPY, DLARNV, DSCAL,
00200      $                   ZCOPY, ZDSCAL, ZERRGT, ZGET04, ZLACPY, ZLAPTM,
00201      $                   ZLARNV, ZLATB4, ZLATMS, ZPTCON, ZPTRFS, ZPTT01,
00202      $                   ZPTT02, ZPTT05, ZPTTRF, ZPTTRS
00203 *     ..
00204 *     .. Intrinsic Functions ..
00205       INTRINSIC          ABS, DBLE, MAX
00206 *     ..
00207 *     .. Scalars in Common ..
00208       LOGICAL            LERR, OK
00209       CHARACTER*32       SRNAMT
00210       INTEGER            INFOT, NUNIT
00211 *     ..
00212 *     .. Common blocks ..
00213       COMMON             / INFOC / INFOT, NUNIT, OK, LERR
00214       COMMON             / SRNAMC / SRNAMT
00215 *     ..
00216 *     .. Data statements ..
00217       DATA               ISEEDY / 0, 0, 0, 1 / , UPLOS / 'U', 'L' /
00218 *     ..
00219 *     .. Executable Statements ..
00220 *
00221       PATH( 1: 1 ) = 'Zomplex precision'
00222       PATH( 2: 3 ) = 'PT'
00223       NRUN = 0
00224       NFAIL = 0
00225       NERRS = 0
00226       DO 10 I = 1, 4
00227          ISEED( I ) = ISEEDY( I )
00228    10 CONTINUE
00229 *
00230 *     Test the error exits
00231 *
00232       IF( TSTERR )
00233      $   CALL ZERRGT( PATH, NOUT )
00234       INFOT = 0
00235 *
00236       DO 120 IN = 1, NN
00237 *
00238 *        Do for each value of N in NVAL.
00239 *
00240          N = NVAL( IN )
00241          LDA = MAX( 1, N )
00242          NIMAT = NTYPES
00243          IF( N.LE.0 )
00244      $      NIMAT = 1
00245 *
00246          DO 110 IMAT = 1, NIMAT
00247 *
00248 *           Do the tests only if DOTYPE( IMAT ) is true.
00249 *
00250             IF( N.GT.0 .AND. .NOT.DOTYPE( IMAT ) )
00251      $         GO TO 110
00252 *
00253 *           Set up parameters with ZLATB4.
00254 *
00255             CALL ZLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE,
00256      $                   COND, DIST )
00257 *
00258             ZEROT = IMAT.GE.8 .AND. IMAT.LE.10
00259             IF( IMAT.LE.6 ) THEN
00260 *
00261 *              Type 1-6:  generate a Hermitian tridiagonal matrix of
00262 *              known condition number in lower triangular band storage.
00263 *
00264                SRNAMT = 'ZLATMS'
00265                CALL ZLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE, COND,
00266      $                      ANORM, KL, KU, 'B', A, 2, WORK, INFO )
00267 *
00268 *              Check the error code from ZLATMS.
00269 *
00270                IF( INFO.NE.0 ) THEN
00271                   CALL ALAERH( PATH, 'ZLATMS', INFO, 0, ' ', N, N, KL,
00272      $                         KU, -1, IMAT, NFAIL, NERRS, NOUT )
00273                   GO TO 110
00274                END IF
00275                IZERO = 0
00276 *
00277 *              Copy the matrix to D and E.
00278 *
00279                IA = 1
00280                DO 20 I = 1, N - 1
00281                   D( I ) = DBLE( A( IA ) )
00282                   E( I ) = A( IA+1 )
00283                   IA = IA + 2
00284    20          CONTINUE
00285                IF( N.GT.0 )
00286      $            D( N ) = DBLE( A( IA ) )
00287             ELSE
00288 *
00289 *              Type 7-12:  generate a diagonally dominant matrix with
00290 *              unknown condition number in the vectors D and E.
00291 *
00292                IF( .NOT.ZEROT .OR. .NOT.DOTYPE( 7 ) ) THEN
00293 *
00294 *                 Let E be complex, D real, with values from [-1,1].
00295 *
00296                   CALL DLARNV( 2, ISEED, N, D )
00297                   CALL ZLARNV( 2, ISEED, N-1, E )
00298 *
00299 *                 Make the tridiagonal matrix diagonally dominant.
00300 *
00301                   IF( N.EQ.1 ) THEN
00302                      D( 1 ) = ABS( D( 1 ) )
00303                   ELSE
00304                      D( 1 ) = ABS( D( 1 ) ) + ABS( E( 1 ) )
00305                      D( N ) = ABS( D( N ) ) + ABS( E( N-1 ) )
00306                      DO 30 I = 2, N - 1
00307                         D( I ) = ABS( D( I ) ) + ABS( E( I ) ) +
00308      $                           ABS( E( I-1 ) )
00309    30                CONTINUE
00310                   END IF
00311 *
00312 *                 Scale D and E so the maximum element is ANORM.
00313 *
00314                   IX = IDAMAX( N, D, 1 )
00315                   DMAX = D( IX )
00316                   CALL DSCAL( N, ANORM / DMAX, D, 1 )
00317                   CALL ZDSCAL( N-1, ANORM / DMAX, E, 1 )
00318 *
00319                ELSE IF( IZERO.GT.0 ) THEN
00320 *
00321 *                 Reuse the last matrix by copying back the zeroed out
00322 *                 elements.
00323 *
00324                   IF( IZERO.EQ.1 ) THEN
00325                      D( 1 ) = Z( 2 )
00326                      IF( N.GT.1 )
00327      $                  E( 1 ) = Z( 3 )
00328                   ELSE IF( IZERO.EQ.N ) THEN
00329                      E( N-1 ) = Z( 1 )
00330                      D( N ) = Z( 2 )
00331                   ELSE
00332                      E( IZERO-1 ) = Z( 1 )
00333                      D( IZERO ) = Z( 2 )
00334                      E( IZERO ) = Z( 3 )
00335                   END IF
00336                END IF
00337 *
00338 *              For types 8-10, set one row and column of the matrix to
00339 *              zero.
00340 *
00341                IZERO = 0
00342                IF( IMAT.EQ.8 ) THEN
00343                   IZERO = 1
00344                   Z( 2 ) = D( 1 )
00345                   D( 1 ) = ZERO
00346                   IF( N.GT.1 ) THEN
00347                      Z( 3 ) = E( 1 )
00348                      E( 1 ) = ZERO
00349                   END IF
00350                ELSE IF( IMAT.EQ.9 ) THEN
00351                   IZERO = N
00352                   IF( N.GT.1 ) THEN
00353                      Z( 1 ) = E( N-1 )
00354                      E( N-1 ) = ZERO
00355                   END IF
00356                   Z( 2 ) = D( N )
00357                   D( N ) = ZERO
00358                ELSE IF( IMAT.EQ.10 ) THEN
00359                   IZERO = ( N+1 ) / 2
00360                   IF( IZERO.GT.1 ) THEN
00361                      Z( 1 ) = E( IZERO-1 )
00362                      Z( 3 ) = E( IZERO )
00363                      E( IZERO-1 ) = ZERO
00364                      E( IZERO ) = ZERO
00365                   END IF
00366                   Z( 2 ) = D( IZERO )
00367                   D( IZERO ) = ZERO
00368                END IF
00369             END IF
00370 *
00371             CALL DCOPY( N, D, 1, D( N+1 ), 1 )
00372             IF( N.GT.1 )
00373      $         CALL ZCOPY( N-1, E, 1, E( N+1 ), 1 )
00374 *
00375 *+    TEST 1
00376 *           Factor A as L*D*L' and compute the ratio
00377 *              norm(L*D*L' - A) / (n * norm(A) * EPS )
00378 *
00379             CALL ZPTTRF( N, D( N+1 ), E( N+1 ), INFO )
00380 *
00381 *           Check error code from ZPTTRF.
00382 *
00383             IF( INFO.NE.IZERO ) THEN
00384                CALL ALAERH( PATH, 'ZPTTRF', INFO, IZERO, ' ', N, N, -1,
00385      $                      -1, -1, IMAT, NFAIL, NERRS, NOUT )
00386                GO TO 110
00387             END IF
00388 *
00389             IF( INFO.GT.0 ) THEN
00390                RCONDC = ZERO
00391                GO TO 100
00392             END IF
00393 *
00394             CALL ZPTT01( N, D, E, D( N+1 ), E( N+1 ), WORK,
00395      $                   RESULT( 1 ) )
00396 *
00397 *           Print the test ratio if greater than or equal to THRESH.
00398 *
00399             IF( RESULT( 1 ).GE.THRESH ) THEN
00400                IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
00401      $            CALL ALAHD( NOUT, PATH )
00402                WRITE( NOUT, FMT = 9999 )N, IMAT, 1, RESULT( 1 )
00403                NFAIL = NFAIL + 1
00404             END IF
00405             NRUN = NRUN + 1
00406 *
00407 *           Compute RCONDC = 1 / (norm(A) * norm(inv(A))
00408 *
00409 *           Compute norm(A).
00410 *
00411             ANORM = ZLANHT( '1', N, D, E )
00412 *
00413 *           Use ZPTTRS to solve for one column at a time of inv(A),
00414 *           computing the maximum column sum as we go.
00415 *
00416             AINVNM = ZERO
00417             DO 50 I = 1, N
00418                DO 40 J = 1, N
00419                   X( J ) = ZERO
00420    40          CONTINUE
00421                X( I ) = ONE
00422                CALL ZPTTRS( 'Lower', N, 1, D( N+1 ), E( N+1 ), X, LDA,
00423      $                      INFO )
00424                AINVNM = MAX( AINVNM, DZASUM( N, X, 1 ) )
00425    50       CONTINUE
00426             RCONDC = ONE / MAX( ONE, ANORM*AINVNM )
00427 *
00428             DO 90 IRHS = 1, NNS
00429                NRHS = NSVAL( IRHS )
00430 *
00431 *           Generate NRHS random solution vectors.
00432 *
00433                IX = 1
00434                DO 60 J = 1, NRHS
00435                   CALL ZLARNV( 2, ISEED, N, XACT( IX ) )
00436                   IX = IX + LDA
00437    60          CONTINUE
00438 *
00439                DO 80 IUPLO = 1, 2
00440 *
00441 *              Do first for UPLO = 'U', then for UPLO = 'L'.
00442 *
00443                   UPLO = UPLOS( IUPLO )
00444 *
00445 *              Set the right hand side.
00446 *
00447                   CALL ZLAPTM( UPLO, N, NRHS, ONE, D, E, XACT, LDA,
00448      $                         ZERO, B, LDA )
00449 *
00450 *+    TEST 2
00451 *              Solve A*x = b and compute the residual.
00452 *
00453                   CALL ZLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
00454                   CALL ZPTTRS( UPLO, N, NRHS, D( N+1 ), E( N+1 ), X,
00455      $                         LDA, INFO )
00456 *
00457 *              Check error code from ZPTTRS.
00458 *
00459                   IF( INFO.NE.0 )
00460      $               CALL ALAERH( PATH, 'ZPTTRS', INFO, 0, UPLO, N, N,
00461      $                            -1, -1, NRHS, IMAT, NFAIL, NERRS,
00462      $                            NOUT )
00463 *
00464                   CALL ZLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
00465                   CALL ZPTT02( UPLO, N, NRHS, D, E, X, LDA, WORK, LDA,
00466      $                         RESULT( 2 ) )
00467 *
00468 *+    TEST 3
00469 *              Check solution from generated exact solution.
00470 *
00471                   CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
00472      $                         RESULT( 3 ) )
00473 *
00474 *+    TESTS 4, 5, and 6
00475 *              Use iterative refinement to improve the solution.
00476 *
00477                   SRNAMT = 'ZPTRFS'
00478                   CALL ZPTRFS( UPLO, N, NRHS, D, E, D( N+1 ), E( N+1 ),
00479      $                         B, LDA, X, LDA, RWORK, RWORK( NRHS+1 ),
00480      $                         WORK, RWORK( 2*NRHS+1 ), INFO )
00481 *
00482 *              Check error code from ZPTRFS.
00483 *
00484                   IF( INFO.NE.0 )
00485      $               CALL ALAERH( PATH, 'ZPTRFS', INFO, 0, UPLO, N, N,
00486      $                            -1, -1, NRHS, IMAT, NFAIL, NERRS,
00487      $                            NOUT )
00488 *
00489                   CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
00490      $                         RESULT( 4 ) )
00491                   CALL ZPTT05( N, NRHS, D, E, B, LDA, X, LDA, XACT, LDA,
00492      $                         RWORK, RWORK( NRHS+1 ), RESULT( 5 ) )
00493 *
00494 *              Print information about the tests that did not pass the
00495 *              threshold.
00496 *
00497                   DO 70 K = 2, 6
00498                      IF( RESULT( K ).GE.THRESH ) THEN
00499                         IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
00500      $                     CALL ALAHD( NOUT, PATH )
00501                         WRITE( NOUT, FMT = 9998 )UPLO, N, NRHS, IMAT,
00502      $                     K, RESULT( K )
00503                         NFAIL = NFAIL + 1
00504                      END IF
00505    70             CONTINUE
00506                   NRUN = NRUN + 5
00507 *
00508    80          CONTINUE
00509    90       CONTINUE
00510 *
00511 *+    TEST 7
00512 *           Estimate the reciprocal of the condition number of the
00513 *           matrix.
00514 *
00515   100       CONTINUE
00516             SRNAMT = 'ZPTCON'
00517             CALL ZPTCON( N, D( N+1 ), E( N+1 ), ANORM, RCOND, RWORK,
00518      $                   INFO )
00519 *
00520 *           Check error code from ZPTCON.
00521 *
00522             IF( INFO.NE.0 )
00523      $         CALL ALAERH( PATH, 'ZPTCON', INFO, 0, ' ', N, N, -1, -1,
00524      $                      -1, IMAT, NFAIL, NERRS, NOUT )
00525 *
00526             RESULT( 7 ) = DGET06( RCOND, RCONDC )
00527 *
00528 *           Print the test ratio if greater than or equal to THRESH.
00529 *
00530             IF( RESULT( 7 ).GE.THRESH ) THEN
00531                IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
00532      $            CALL ALAHD( NOUT, PATH )
00533                WRITE( NOUT, FMT = 9999 )N, IMAT, 7, RESULT( 7 )
00534                NFAIL = NFAIL + 1
00535             END IF
00536             NRUN = NRUN + 1
00537   110    CONTINUE
00538   120 CONTINUE
00539 *
00540 *     Print a summary of the results.
00541 *
00542       CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
00543 *
00544  9999 FORMAT( ' N =', I5, ', type ', I2, ', test ', I2, ', ratio = ',
00545      $      G12.5 )
00546  9998 FORMAT( ' UPLO = ''', A1, ''', N =', I5, ', NRHS =', I3,
00547      $        ', type ', I2, ', test ', I2, ', ratio = ', G12.5 )
00548       RETURN
00549 *
00550 *     End of ZCHKPT
00551 *
00552       END
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