LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
dchkpt.f
Go to the documentation of this file.
00001 *> \brief \b DCHKPT
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 DCHKPT( 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   A( * ), B( * ), D( * ), E( * ), RWORK( * ),
00023 *      $                   WORK( * ), X( * ), XACT( * )
00024 *       ..
00025 *  
00026 *
00027 *> \par Purpose:
00028 *  =============
00029 *>
00030 *> \verbatim
00031 *>
00032 *> DCHKPT tests DPTTRF, -TRS, -RFS, and -CON
00033 *> \endverbatim
00034 *
00035 *  Arguments:
00036 *  ==========
00037 *
00038 *> \param[in] DOTYPE
00039 *> \verbatim
00040 *>          DOTYPE is LOGICAL array, dimension (NTYPES)
00041 *>          The matrix types to be used for testing.  Matrices of type j
00042 *>          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
00043 *>          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
00044 *> \endverbatim
00045 *>
00046 *> \param[in] NN
00047 *> \verbatim
00048 *>          NN is INTEGER
00049 *>          The number of values of N contained in the vector NVAL.
00050 *> \endverbatim
00051 *>
00052 *> \param[in] NVAL
00053 *> \verbatim
00054 *>          NVAL is INTEGER array, dimension (NN)
00055 *>          The values of the matrix dimension N.
00056 *> \endverbatim
00057 *>
00058 *> \param[in] NNS
00059 *> \verbatim
00060 *>          NNS is INTEGER
00061 *>          The number of values of NRHS contained in the vector NSVAL.
00062 *> \endverbatim
00063 *>
00064 *> \param[in] NSVAL
00065 *> \verbatim
00066 *>          NSVAL is INTEGER array, dimension (NNS)
00067 *>          The values of the number of right hand sides NRHS.
00068 *> \endverbatim
00069 *>
00070 *> \param[in] THRESH
00071 *> \verbatim
00072 *>          THRESH is DOUBLE PRECISION
00073 *>          The threshold value for the test ratios.  A result is
00074 *>          included in the output file if RESULT >= THRESH.  To have
00075 *>          every test ratio printed, use THRESH = 0.
00076 *> \endverbatim
00077 *>
00078 *> \param[in] TSTERR
00079 *> \verbatim
00080 *>          TSTERR is LOGICAL
00081 *>          Flag that indicates whether error exits are to be tested.
00082 *> \endverbatim
00083 *>
00084 *> \param[out] A
00085 *> \verbatim
00086 *>          A is DOUBLE PRECISION array, dimension (NMAX*2)
00087 *> \endverbatim
00088 *>
00089 *> \param[out] D
00090 *> \verbatim
00091 *>          D is DOUBLE PRECISION array, dimension (NMAX*2)
00092 *> \endverbatim
00093 *>
00094 *> \param[out] E
00095 *> \verbatim
00096 *>          E is DOUBLE PRECISION array, dimension (NMAX*2)
00097 *> \endverbatim
00098 *>
00099 *> \param[out] B
00100 *> \verbatim
00101 *>          B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
00102 *>          where NSMAX is the largest entry in NSVAL.
00103 *> \endverbatim
00104 *>
00105 *> \param[out] X
00106 *> \verbatim
00107 *>          X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
00108 *> \endverbatim
00109 *>
00110 *> \param[out] XACT
00111 *> \verbatim
00112 *>          XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
00113 *> \endverbatim
00114 *>
00115 *> \param[out] WORK
00116 *> \verbatim
00117 *>          WORK is DOUBLE PRECISION array, dimension
00118 *>                      (NMAX*max(3,NSMAX))
00119 *> \endverbatim
00120 *>
00121 *> \param[out] RWORK
00122 *> \verbatim
00123 *>          RWORK is DOUBLE PRECISION array, dimension
00124 *>                      (max(NMAX,2*NSMAX))
00125 *> \endverbatim
00126 *>
00127 *> \param[in] NOUT
00128 *> \verbatim
00129 *>          NOUT is INTEGER
00130 *>          The unit number for output.
00131 *> \endverbatim
00132 *
00133 *  Authors:
00134 *  ========
00135 *
00136 *> \author Univ. of Tennessee 
00137 *> \author Univ. of California Berkeley 
00138 *> \author Univ. of Colorado Denver 
00139 *> \author NAG Ltd. 
00140 *
00141 *> \date November 2011
00142 *
00143 *> \ingroup double_lin
00144 *
00145 *  =====================================================================
00146       SUBROUTINE DCHKPT( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
00147      $                   A, D, E, B, X, XACT, WORK, RWORK, NOUT )
00148 *
00149 *  -- LAPACK test routine (version 3.4.0) --
00150 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00151 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00152 *     November 2011
00153 *
00154 *     .. Scalar Arguments ..
00155       LOGICAL            TSTERR
00156       INTEGER            NN, NNS, NOUT
00157       DOUBLE PRECISION   THRESH
00158 *     ..
00159 *     .. Array Arguments ..
00160       LOGICAL            DOTYPE( * )
00161       INTEGER            NSVAL( * ), NVAL( * )
00162       DOUBLE PRECISION   A( * ), B( * ), D( * ), E( * ), RWORK( * ),
00163      $                   WORK( * ), X( * ), XACT( * )
00164 *     ..
00165 *
00166 *  =====================================================================
00167 *
00168 *     .. Parameters ..
00169       DOUBLE PRECISION   ONE, ZERO
00170       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
00171       INTEGER            NTYPES
00172       PARAMETER          ( NTYPES = 12 )
00173       INTEGER            NTESTS
00174       PARAMETER          ( NTESTS = 7 )
00175 *     ..
00176 *     .. Local Scalars ..
00177       LOGICAL            ZEROT
00178       CHARACTER          DIST, TYPE
00179       CHARACTER*3        PATH
00180       INTEGER            I, IA, IMAT, IN, INFO, IRHS, IX, IZERO, J, K,
00181      $                   KL, KU, LDA, MODE, N, NERRS, NFAIL, NIMAT,
00182      $                   NRHS, NRUN
00183       DOUBLE PRECISION   AINVNM, ANORM, COND, DMAX, RCOND, RCONDC
00184 *     ..
00185 *     .. Local Arrays ..
00186       INTEGER            ISEED( 4 ), ISEEDY( 4 )
00187       DOUBLE PRECISION   RESULT( NTESTS ), Z( 3 )
00188 *     ..
00189 *     .. External Functions ..
00190       INTEGER            IDAMAX
00191       DOUBLE PRECISION   DASUM, DGET06, DLANST
00192       EXTERNAL           IDAMAX, DASUM, DGET06, DLANST
00193 *     ..
00194 *     .. External Subroutines ..
00195       EXTERNAL           ALAERH, ALAHD, ALASUM, DCOPY, DERRGT, DGET04,
00196      $                   DLACPY, DLAPTM, DLARNV, DLATB4, DLATMS, DPTCON,
00197      $                   DPTRFS, DPTT01, DPTT02, DPTT05, DPTTRF, DPTTRS,
00198      $                   DSCAL
00199 *     ..
00200 *     .. Intrinsic Functions ..
00201       INTRINSIC          ABS, MAX
00202 *     ..
00203 *     .. Scalars in Common ..
00204       LOGICAL            LERR, OK
00205       CHARACTER*32       SRNAMT
00206       INTEGER            INFOT, NUNIT
00207 *     ..
00208 *     .. Common blocks ..
00209       COMMON             / INFOC / INFOT, NUNIT, OK, LERR
00210       COMMON             / SRNAMC / SRNAMT
00211 *     ..
00212 *     .. Data statements ..
00213       DATA               ISEEDY / 0, 0, 0, 1 /
00214 *     ..
00215 *     .. Executable Statements ..
00216 *
00217       PATH( 1: 1 ) = 'Double precision'
00218       PATH( 2: 3 ) = 'PT'
00219       NRUN = 0
00220       NFAIL = 0
00221       NERRS = 0
00222       DO 10 I = 1, 4
00223          ISEED( I ) = ISEEDY( I )
00224    10 CONTINUE
00225 *
00226 *     Test the error exits
00227 *
00228       IF( TSTERR )
00229      $   CALL DERRGT( PATH, NOUT )
00230       INFOT = 0
00231 *
00232       DO 110 IN = 1, NN
00233 *
00234 *        Do for each value of N in NVAL.
00235 *
00236          N = NVAL( IN )
00237          LDA = MAX( 1, N )
00238          NIMAT = NTYPES
00239          IF( N.LE.0 )
00240      $      NIMAT = 1
00241 *
00242          DO 100 IMAT = 1, NIMAT
00243 *
00244 *           Do the tests only if DOTYPE( IMAT ) is true.
00245 *
00246             IF( N.GT.0 .AND. .NOT.DOTYPE( IMAT ) )
00247      $         GO TO 100
00248 *
00249 *           Set up parameters with DLATB4.
00250 *
00251             CALL DLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE,
00252      $                   COND, DIST )
00253 *
00254             ZEROT = IMAT.GE.8 .AND. IMAT.LE.10
00255             IF( IMAT.LE.6 ) THEN
00256 *
00257 *              Type 1-6:  generate a symmetric tridiagonal matrix of
00258 *              known condition number in lower triangular band storage.
00259 *
00260                SRNAMT = 'DLATMS'
00261                CALL DLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE, COND,
00262      $                      ANORM, KL, KU, 'B', A, 2, WORK, INFO )
00263 *
00264 *              Check the error code from DLATMS.
00265 *
00266                IF( INFO.NE.0 ) THEN
00267                   CALL ALAERH( PATH, 'DLATMS', INFO, 0, ' ', N, N, KL,
00268      $                         KU, -1, IMAT, NFAIL, NERRS, NOUT )
00269                   GO TO 100
00270                END IF
00271                IZERO = 0
00272 *
00273 *              Copy the matrix to D and E.
00274 *
00275                IA = 1
00276                DO 20 I = 1, N - 1
00277                   D( I ) = A( IA )
00278                   E( I ) = A( IA+1 )
00279                   IA = IA + 2
00280    20          CONTINUE
00281                IF( N.GT.0 )
00282      $            D( N ) = A( IA )
00283             ELSE
00284 *
00285 *              Type 7-12:  generate a diagonally dominant matrix with
00286 *              unknown condition number in the vectors D and E.
00287 *
00288                IF( .NOT.ZEROT .OR. .NOT.DOTYPE( 7 ) ) THEN
00289 *
00290 *                 Let D and E have values from [-1,1].
00291 *
00292                   CALL DLARNV( 2, ISEED, N, D )
00293                   CALL DLARNV( 2, ISEED, N-1, E )
00294 *
00295 *                 Make the tridiagonal matrix diagonally dominant.
00296 *
00297                   IF( N.EQ.1 ) THEN
00298                      D( 1 ) = ABS( D( 1 ) )
00299                   ELSE
00300                      D( 1 ) = ABS( D( 1 ) ) + ABS( E( 1 ) )
00301                      D( N ) = ABS( D( N ) ) + ABS( E( N-1 ) )
00302                      DO 30 I = 2, N - 1
00303                         D( I ) = ABS( D( I ) ) + ABS( E( I ) ) +
00304      $                           ABS( E( I-1 ) )
00305    30                CONTINUE
00306                   END IF
00307 *
00308 *                 Scale D and E so the maximum element is ANORM.
00309 *
00310                   IX = IDAMAX( N, D, 1 )
00311                   DMAX = D( IX )
00312                   CALL DSCAL( N, ANORM / DMAX, D, 1 )
00313                   CALL DSCAL( N-1, ANORM / DMAX, E, 1 )
00314 *
00315                ELSE IF( IZERO.GT.0 ) THEN
00316 *
00317 *                 Reuse the last matrix by copying back the zeroed out
00318 *                 elements.
00319 *
00320                   IF( IZERO.EQ.1 ) THEN
00321                      D( 1 ) = Z( 2 )
00322                      IF( N.GT.1 )
00323      $                  E( 1 ) = Z( 3 )
00324                   ELSE IF( IZERO.EQ.N ) THEN
00325                      E( N-1 ) = Z( 1 )
00326                      D( N ) = Z( 2 )
00327                   ELSE
00328                      E( IZERO-1 ) = Z( 1 )
00329                      D( IZERO ) = Z( 2 )
00330                      E( IZERO ) = Z( 3 )
00331                   END IF
00332                END IF
00333 *
00334 *              For types 8-10, set one row and column of the matrix to
00335 *              zero.
00336 *
00337                IZERO = 0
00338                IF( IMAT.EQ.8 ) THEN
00339                   IZERO = 1
00340                   Z( 2 ) = D( 1 )
00341                   D( 1 ) = ZERO
00342                   IF( N.GT.1 ) THEN
00343                      Z( 3 ) = E( 1 )
00344                      E( 1 ) = ZERO
00345                   END IF
00346                ELSE IF( IMAT.EQ.9 ) THEN
00347                   IZERO = N
00348                   IF( N.GT.1 ) THEN
00349                      Z( 1 ) = E( N-1 )
00350                      E( N-1 ) = ZERO
00351                   END IF
00352                   Z( 2 ) = D( N )
00353                   D( N ) = ZERO
00354                ELSE IF( IMAT.EQ.10 ) THEN
00355                   IZERO = ( N+1 ) / 2
00356                   IF( IZERO.GT.1 ) THEN
00357                      Z( 1 ) = E( IZERO-1 )
00358                      E( IZERO-1 ) = ZERO
00359                      Z( 3 ) = E( IZERO )
00360                      E( IZERO ) = ZERO
00361                   END IF
00362                   Z( 2 ) = D( IZERO )
00363                   D( IZERO ) = ZERO
00364                END IF
00365             END IF
00366 *
00367             CALL DCOPY( N, D, 1, D( N+1 ), 1 )
00368             IF( N.GT.1 )
00369      $         CALL DCOPY( N-1, E, 1, E( N+1 ), 1 )
00370 *
00371 *+    TEST 1
00372 *           Factor A as L*D*L' and compute the ratio
00373 *              norm(L*D*L' - A) / (n * norm(A) * EPS )
00374 *
00375             CALL DPTTRF( N, D( N+1 ), E( N+1 ), INFO )
00376 *
00377 *           Check error code from DPTTRF.
00378 *
00379             IF( INFO.NE.IZERO ) THEN
00380                CALL ALAERH( PATH, 'DPTTRF', INFO, IZERO, ' ', N, N, -1,
00381      $                      -1, -1, IMAT, NFAIL, NERRS, NOUT )
00382                GO TO 100
00383             END IF
00384 *
00385             IF( INFO.GT.0 ) THEN
00386                RCONDC = ZERO
00387                GO TO 90
00388             END IF
00389 *
00390             CALL DPTT01( N, D, E, D( N+1 ), E( N+1 ), WORK,
00391      $                   RESULT( 1 ) )
00392 *
00393 *           Print the test ratio if greater than or equal to THRESH.
00394 *
00395             IF( RESULT( 1 ).GE.THRESH ) THEN
00396                IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
00397      $            CALL ALAHD( NOUT, PATH )
00398                WRITE( NOUT, FMT = 9999 )N, IMAT, 1, RESULT( 1 )
00399                NFAIL = NFAIL + 1
00400             END IF
00401             NRUN = NRUN + 1
00402 *
00403 *           Compute RCONDC = 1 / (norm(A) * norm(inv(A))
00404 *
00405 *           Compute norm(A).
00406 *
00407             ANORM = DLANST( '1', N, D, E )
00408 *
00409 *           Use DPTTRS to solve for one column at a time of inv(A),
00410 *           computing the maximum column sum as we go.
00411 *
00412             AINVNM = ZERO
00413             DO 50 I = 1, N
00414                DO 40 J = 1, N
00415                   X( J ) = ZERO
00416    40          CONTINUE
00417                X( I ) = ONE
00418                CALL DPTTRS( N, 1, D( N+1 ), E( N+1 ), X, LDA, INFO )
00419                AINVNM = MAX( AINVNM, DASUM( N, X, 1 ) )
00420    50       CONTINUE
00421             RCONDC = ONE / MAX( ONE, ANORM*AINVNM )
00422 *
00423             DO 80 IRHS = 1, NNS
00424                NRHS = NSVAL( IRHS )
00425 *
00426 *           Generate NRHS random solution vectors.
00427 *
00428                IX = 1
00429                DO 60 J = 1, NRHS
00430                   CALL DLARNV( 2, ISEED, N, XACT( IX ) )
00431                   IX = IX + LDA
00432    60          CONTINUE
00433 *
00434 *           Set the right hand side.
00435 *
00436                CALL DLAPTM( N, NRHS, ONE, D, E, XACT, LDA, ZERO, B,
00437      $                      LDA )
00438 *
00439 *+    TEST 2
00440 *           Solve A*x = b and compute the residual.
00441 *
00442                CALL DLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
00443                CALL DPTTRS( N, NRHS, D( N+1 ), E( N+1 ), X, LDA, INFO )
00444 *
00445 *           Check error code from DPTTRS.
00446 *
00447                IF( INFO.NE.0 )
00448      $            CALL ALAERH( PATH, 'DPTTRS', INFO, 0, ' ', N, N, -1,
00449      $                         -1, NRHS, IMAT, NFAIL, NERRS, NOUT )
00450 *
00451                CALL DLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
00452                CALL DPTT02( N, NRHS, D, E, X, LDA, WORK, LDA,
00453      $                      RESULT( 2 ) )
00454 *
00455 *+    TEST 3
00456 *           Check solution from generated exact solution.
00457 *
00458                CALL DGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
00459      $                      RESULT( 3 ) )
00460 *
00461 *+    TESTS 4, 5, and 6
00462 *           Use iterative refinement to improve the solution.
00463 *
00464                SRNAMT = 'DPTRFS'
00465                CALL DPTRFS( N, NRHS, D, E, D( N+1 ), E( N+1 ), B, LDA,
00466      $                      X, LDA, RWORK, RWORK( NRHS+1 ), WORK, INFO )
00467 *
00468 *           Check error code from DPTRFS.
00469 *
00470                IF( INFO.NE.0 )
00471      $            CALL ALAERH( PATH, 'DPTRFS', INFO, 0, ' ', N, N, -1,
00472      $                         -1, NRHS, IMAT, NFAIL, NERRS, NOUT )
00473 *
00474                CALL DGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
00475      $                      RESULT( 4 ) )
00476                CALL DPTT05( N, NRHS, D, E, B, LDA, X, LDA, XACT, LDA,
00477      $                      RWORK, RWORK( NRHS+1 ), RESULT( 5 ) )
00478 *
00479 *           Print information about the tests that did not pass the
00480 *           threshold.
00481 *
00482                DO 70 K = 2, 6
00483                   IF( RESULT( K ).GE.THRESH ) THEN
00484                      IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
00485      $                  CALL ALAHD( NOUT, PATH )
00486                      WRITE( NOUT, FMT = 9998 )N, NRHS, IMAT, K,
00487      $                  RESULT( K )
00488                      NFAIL = NFAIL + 1
00489                   END IF
00490    70          CONTINUE
00491                NRUN = NRUN + 5
00492    80       CONTINUE
00493 *
00494 *+    TEST 7
00495 *           Estimate the reciprocal of the condition number of the
00496 *           matrix.
00497 *
00498    90       CONTINUE
00499             SRNAMT = 'DPTCON'
00500             CALL DPTCON( N, D( N+1 ), E( N+1 ), ANORM, RCOND, RWORK,
00501      $                   INFO )
00502 *
00503 *           Check error code from DPTCON.
00504 *
00505             IF( INFO.NE.0 )
00506      $         CALL ALAERH( PATH, 'DPTCON', INFO, 0, ' ', N, N, -1, -1,
00507      $                      -1, IMAT, NFAIL, NERRS, NOUT )
00508 *
00509             RESULT( 7 ) = DGET06( RCOND, RCONDC )
00510 *
00511 *           Print the test ratio if greater than or equal to THRESH.
00512 *
00513             IF( RESULT( 7 ).GE.THRESH ) THEN
00514                IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
00515      $            CALL ALAHD( NOUT, PATH )
00516                WRITE( NOUT, FMT = 9999 )N, IMAT, 7, RESULT( 7 )
00517                NFAIL = NFAIL + 1
00518             END IF
00519             NRUN = NRUN + 1
00520   100    CONTINUE
00521   110 CONTINUE
00522 *
00523 *     Print a summary of the results.
00524 *
00525       CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
00526 *
00527  9999 FORMAT( ' N =', I5, ', type ', I2, ', test ', I2, ', ratio = ',
00528      $      G12.5 )
00529  9998 FORMAT( ' N =', I5, ', NRHS=', I3, ', type ', I2, ', test(', I2,
00530      $      ') = ', G12.5 )
00531       RETURN
00532 *
00533 *     End of DCHKPT
00534 *
00535       END
 All Files Functions