LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
cdrvpt.f
Go to the documentation of this file.
00001 *> \brief \b CDRVPT
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 CDRVPT( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, D,
00012 *                          E, B, X, XACT, WORK, RWORK, NOUT )
00013 * 
00014 *       .. Scalar Arguments ..
00015 *       LOGICAL            TSTERR
00016 *       INTEGER            NN, NOUT, NRHS
00017 *       REAL               THRESH
00018 *       ..
00019 *       .. Array Arguments ..
00020 *       LOGICAL            DOTYPE( * )
00021 *       INTEGER            NVAL( * )
00022 *       REAL               D( * ), RWORK( * )
00023 *       COMPLEX            A( * ), B( * ), E( * ), WORK( * ), X( * ),
00024 *      $                   XACT( * )
00025 *       ..
00026 *  
00027 *
00028 *> \par Purpose:
00029 *  =============
00030 *>
00031 *> \verbatim
00032 *>
00033 *> CDRVPT tests CPTSV and -SVX.
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] NRHS
00060 *> \verbatim
00061 *>          NRHS is INTEGER
00062 *>          The number of right hand side vectors to be generated for
00063 *>          each linear system.
00064 *> \endverbatim
00065 *>
00066 *> \param[in] THRESH
00067 *> \verbatim
00068 *>          THRESH is REAL
00069 *>          The threshold value for the test ratios.  A result is
00070 *>          included in the output file if RESULT >= THRESH.  To have
00071 *>          every test ratio printed, use THRESH = 0.
00072 *> \endverbatim
00073 *>
00074 *> \param[in] TSTERR
00075 *> \verbatim
00076 *>          TSTERR is LOGICAL
00077 *>          Flag that indicates whether error exits are to be tested.
00078 *> \endverbatim
00079 *>
00080 *> \param[out] A
00081 *> \verbatim
00082 *>          A is COMPLEX array, dimension (NMAX*2)
00083 *> \endverbatim
00084 *>
00085 *> \param[out] D
00086 *> \verbatim
00087 *>          D is REAL array, dimension (NMAX*2)
00088 *> \endverbatim
00089 *>
00090 *> \param[out] E
00091 *> \verbatim
00092 *>          E is COMPLEX array, dimension (NMAX*2)
00093 *> \endverbatim
00094 *>
00095 *> \param[out] B
00096 *> \verbatim
00097 *>          B is COMPLEX array, dimension (NMAX*NRHS)
00098 *> \endverbatim
00099 *>
00100 *> \param[out] X
00101 *> \verbatim
00102 *>          X is COMPLEX array, dimension (NMAX*NRHS)
00103 *> \endverbatim
00104 *>
00105 *> \param[out] XACT
00106 *> \verbatim
00107 *>          XACT is COMPLEX array, dimension (NMAX*NRHS)
00108 *> \endverbatim
00109 *>
00110 *> \param[out] WORK
00111 *> \verbatim
00112 *>          WORK is COMPLEX array, dimension
00113 *>                      (NMAX*max(3,NRHS))
00114 *> \endverbatim
00115 *>
00116 *> \param[out] RWORK
00117 *> \verbatim
00118 *>          RWORK is REAL array, dimension (NMAX+2*NRHS)
00119 *> \endverbatim
00120 *>
00121 *> \param[in] NOUT
00122 *> \verbatim
00123 *>          NOUT is INTEGER
00124 *>          The unit number for output.
00125 *> \endverbatim
00126 *
00127 *  Authors:
00128 *  ========
00129 *
00130 *> \author Univ. of Tennessee 
00131 *> \author Univ. of California Berkeley 
00132 *> \author Univ. of Colorado Denver 
00133 *> \author NAG Ltd. 
00134 *
00135 *> \date November 2011
00136 *
00137 *> \ingroup complex_lin
00138 *
00139 *  =====================================================================
00140       SUBROUTINE CDRVPT( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, D,
00141      $                   E, B, X, XACT, WORK, RWORK, NOUT )
00142 *
00143 *  -- LAPACK test routine (version 3.4.0) --
00144 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00145 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00146 *     November 2011
00147 *
00148 *     .. Scalar Arguments ..
00149       LOGICAL            TSTERR
00150       INTEGER            NN, NOUT, NRHS
00151       REAL               THRESH
00152 *     ..
00153 *     .. Array Arguments ..
00154       LOGICAL            DOTYPE( * )
00155       INTEGER            NVAL( * )
00156       REAL               D( * ), RWORK( * )
00157       COMPLEX            A( * ), B( * ), E( * ), WORK( * ), X( * ),
00158      $                   XACT( * )
00159 *     ..
00160 *
00161 *  =====================================================================
00162 *
00163 *     .. Parameters ..
00164       REAL               ONE, ZERO
00165       PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
00166       INTEGER            NTYPES
00167       PARAMETER          ( NTYPES = 12 )
00168       INTEGER            NTESTS
00169       PARAMETER          ( NTESTS = 6 )
00170 *     ..
00171 *     .. Local Scalars ..
00172       LOGICAL            ZEROT
00173       CHARACTER          DIST, FACT, TYPE
00174       CHARACTER*3        PATH
00175       INTEGER            I, IA, IFACT, IMAT, IN, INFO, IX, IZERO, J, K,
00176      $                   K1, KL, KU, LDA, MODE, N, NERRS, NFAIL, NIMAT,
00177      $                   NRUN, NT
00178       REAL               AINVNM, ANORM, COND, DMAX, RCOND, RCONDC
00179 *     ..
00180 *     .. Local Arrays ..
00181       INTEGER            ISEED( 4 ), ISEEDY( 4 )
00182       REAL               RESULT( NTESTS ), Z( 3 )
00183 *     ..
00184 *     .. External Functions ..
00185       INTEGER            ISAMAX
00186       REAL               CLANHT, SCASUM, SGET06
00187       EXTERNAL           ISAMAX, CLANHT, SCASUM, SGET06
00188 *     ..
00189 *     .. External Subroutines ..
00190       EXTERNAL           ALADHD, ALAERH, ALASVM, CCOPY, CERRVX, CGET04,
00191      $                   CLACPY, CLAPTM, CLARNV, CLASET, CLATB4, CLATMS,
00192      $                   CPTSV, CPTSVX, CPTT01, CPTT02, CPTT05, CPTTRF,
00193      $                   CPTTRS, CSSCAL, SCOPY, SLARNV, SSCAL
00194 *     ..
00195 *     .. Intrinsic Functions ..
00196       INTRINSIC          ABS, CMPLX, MAX
00197 *     ..
00198 *     .. Scalars in Common ..
00199       LOGICAL            LERR, OK
00200       CHARACTER*32       SRNAMT
00201       INTEGER            INFOT, NUNIT
00202 *     ..
00203 *     .. Common blocks ..
00204       COMMON             / INFOC / INFOT, NUNIT, OK, LERR
00205       COMMON             / SRNAMC / SRNAMT
00206 *     ..
00207 *     .. Data statements ..
00208       DATA               ISEEDY / 0, 0, 0, 1 /
00209 *     ..
00210 *     .. Executable Statements ..
00211 *
00212       PATH( 1: 1 ) = 'Complex precision'
00213       PATH( 2: 3 ) = 'PT'
00214       NRUN = 0
00215       NFAIL = 0
00216       NERRS = 0
00217       DO 10 I = 1, 4
00218          ISEED( I ) = ISEEDY( I )
00219    10 CONTINUE
00220 *
00221 *     Test the error exits
00222 *
00223       IF( TSTERR )
00224      $   CALL CERRVX( PATH, NOUT )
00225       INFOT = 0
00226 *
00227       DO 120 IN = 1, NN
00228 *
00229 *        Do for each value of N in NVAL.
00230 *
00231          N = NVAL( IN )
00232          LDA = MAX( 1, N )
00233          NIMAT = NTYPES
00234          IF( N.LE.0 )
00235      $      NIMAT = 1
00236 *
00237          DO 110 IMAT = 1, NIMAT
00238 *
00239 *           Do the tests only if DOTYPE( IMAT ) is true.
00240 *
00241             IF( N.GT.0 .AND. .NOT.DOTYPE( IMAT ) )
00242      $         GO TO 110
00243 *
00244 *           Set up parameters with CLATB4.
00245 *
00246             CALL CLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE,
00247      $                   COND, DIST )
00248 *
00249             ZEROT = IMAT.GE.8 .AND. IMAT.LE.10
00250             IF( IMAT.LE.6 ) THEN
00251 *
00252 *              Type 1-6:  generate a symmetric tridiagonal matrix of
00253 *              known condition number in lower triangular band storage.
00254 *
00255                SRNAMT = 'CLATMS'
00256                CALL CLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE, COND,
00257      $                      ANORM, KL, KU, 'B', A, 2, WORK, INFO )
00258 *
00259 *              Check the error code from CLATMS.
00260 *
00261                IF( INFO.NE.0 ) THEN
00262                   CALL ALAERH( PATH, 'CLATMS', INFO, 0, ' ', N, N, KL,
00263      $                         KU, -1, IMAT, NFAIL, NERRS, NOUT )
00264                   GO TO 110
00265                END IF
00266                IZERO = 0
00267 *
00268 *              Copy the matrix to D and E.
00269 *
00270                IA = 1
00271                DO 20 I = 1, N - 1
00272                   D( I ) = A( IA )
00273                   E( I ) = A( IA+1 )
00274                   IA = IA + 2
00275    20          CONTINUE
00276                IF( N.GT.0 )
00277      $            D( N ) = A( IA )
00278             ELSE
00279 *
00280 *              Type 7-12:  generate a diagonally dominant matrix with
00281 *              unknown condition number in the vectors D and E.
00282 *
00283                IF( .NOT.ZEROT .OR. .NOT.DOTYPE( 7 ) ) THEN
00284 *
00285 *                 Let D and E have values from [-1,1].
00286 *
00287                   CALL SLARNV( 2, ISEED, N, D )
00288                   CALL CLARNV( 2, ISEED, N-1, E )
00289 *
00290 *                 Make the tridiagonal matrix diagonally dominant.
00291 *
00292                   IF( N.EQ.1 ) THEN
00293                      D( 1 ) = ABS( D( 1 ) )
00294                   ELSE
00295                      D( 1 ) = ABS( D( 1 ) ) + ABS( E( 1 ) )
00296                      D( N ) = ABS( D( N ) ) + ABS( E( N-1 ) )
00297                      DO 30 I = 2, N - 1
00298                         D( I ) = ABS( D( I ) ) + ABS( E( I ) ) +
00299      $                           ABS( E( I-1 ) )
00300    30                CONTINUE
00301                   END IF
00302 *
00303 *                 Scale D and E so the maximum element is ANORM.
00304 *
00305                   IX = ISAMAX( N, D, 1 )
00306                   DMAX = D( IX )
00307                   CALL SSCAL( N, ANORM / DMAX, D, 1 )
00308                   IF( N.GT.1 )
00309      $               CALL CSSCAL( N-1, ANORM / DMAX, E, 1 )
00310 *
00311                ELSE IF( IZERO.GT.0 ) THEN
00312 *
00313 *                 Reuse the last matrix by copying back the zeroed out
00314 *                 elements.
00315 *
00316                   IF( IZERO.EQ.1 ) THEN
00317                      D( 1 ) = Z( 2 )
00318                      IF( N.GT.1 )
00319      $                  E( 1 ) = Z( 3 )
00320                   ELSE IF( IZERO.EQ.N ) THEN
00321                      E( N-1 ) = Z( 1 )
00322                      D( N ) = Z( 2 )
00323                   ELSE
00324                      E( IZERO-1 ) = Z( 1 )
00325                      D( IZERO ) = Z( 2 )
00326                      E( IZERO ) = Z( 3 )
00327                   END IF
00328                END IF
00329 *
00330 *              For types 8-10, set one row and column of the matrix to
00331 *              zero.
00332 *
00333                IZERO = 0
00334                IF( IMAT.EQ.8 ) THEN
00335                   IZERO = 1
00336                   Z( 2 ) = D( 1 )
00337                   D( 1 ) = ZERO
00338                   IF( N.GT.1 ) THEN
00339                      Z( 3 ) = E( 1 )
00340                      E( 1 ) = ZERO
00341                   END IF
00342                ELSE IF( IMAT.EQ.9 ) THEN
00343                   IZERO = N
00344                   IF( N.GT.1 ) THEN
00345                      Z( 1 ) = E( N-1 )
00346                      E( N-1 ) = ZERO
00347                   END IF
00348                   Z( 2 ) = D( N )
00349                   D( N ) = ZERO
00350                ELSE IF( IMAT.EQ.10 ) THEN
00351                   IZERO = ( N+1 ) / 2
00352                   IF( IZERO.GT.1 ) THEN
00353                      Z( 1 ) = E( IZERO-1 )
00354                      E( IZERO-1 ) = ZERO
00355                      Z( 3 ) = E( IZERO )
00356                      E( IZERO ) = ZERO
00357                   END IF
00358                   Z( 2 ) = D( IZERO )
00359                   D( IZERO ) = ZERO
00360                END IF
00361             END IF
00362 *
00363 *           Generate NRHS random solution vectors.
00364 *
00365             IX = 1
00366             DO 40 J = 1, NRHS
00367                CALL CLARNV( 2, ISEED, N, XACT( IX ) )
00368                IX = IX + LDA
00369    40       CONTINUE
00370 *
00371 *           Set the right hand side.
00372 *
00373             CALL CLAPTM( 'Lower', N, NRHS, ONE, D, E, XACT, LDA, ZERO,
00374      $                   B, LDA )
00375 *
00376             DO 100 IFACT = 1, 2
00377                IF( IFACT.EQ.1 ) THEN
00378                   FACT = 'F'
00379                ELSE
00380                   FACT = 'N'
00381                END IF
00382 *
00383 *              Compute the condition number for comparison with
00384 *              the value returned by CPTSVX.
00385 *
00386                IF( ZEROT ) THEN
00387                   IF( IFACT.EQ.1 )
00388      $               GO TO 100
00389                   RCONDC = ZERO
00390 *
00391                ELSE IF( IFACT.EQ.1 ) THEN
00392 *
00393 *                 Compute the 1-norm of A.
00394 *
00395                   ANORM = CLANHT( '1', N, D, E )
00396 *
00397                   CALL SCOPY( N, D, 1, D( N+1 ), 1 )
00398                   IF( N.GT.1 )
00399      $               CALL CCOPY( N-1, E, 1, E( N+1 ), 1 )
00400 *
00401 *                 Factor the matrix A.
00402 *
00403                   CALL CPTTRF( N, D( N+1 ), E( N+1 ), INFO )
00404 *
00405 *                 Use CPTTRS to solve for one column at a time of
00406 *                 inv(A), computing the maximum column sum as we go.
00407 *
00408                   AINVNM = ZERO
00409                   DO 60 I = 1, N
00410                      DO 50 J = 1, N
00411                         X( J ) = ZERO
00412    50                CONTINUE
00413                      X( I ) = ONE
00414                      CALL CPTTRS( 'Lower', N, 1, D( N+1 ), E( N+1 ), X,
00415      $                            LDA, INFO )
00416                      AINVNM = MAX( AINVNM, SCASUM( N, X, 1 ) )
00417    60             CONTINUE
00418 *
00419 *                 Compute the 1-norm condition number of A.
00420 *
00421                   IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
00422                      RCONDC = ONE
00423                   ELSE
00424                      RCONDC = ( ONE / ANORM ) / AINVNM
00425                   END IF
00426                END IF
00427 *
00428                IF( IFACT.EQ.2 ) THEN
00429 *
00430 *                 --- Test CPTSV --
00431 *
00432                   CALL SCOPY( N, D, 1, D( N+1 ), 1 )
00433                   IF( N.GT.1 )
00434      $               CALL CCOPY( N-1, E, 1, E( N+1 ), 1 )
00435                   CALL CLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
00436 *
00437 *                 Factor A as L*D*L' and solve the system A*X = B.
00438 *
00439                   SRNAMT = 'CPTSV '
00440                   CALL CPTSV( N, NRHS, D( N+1 ), E( N+1 ), X, LDA,
00441      $                        INFO )
00442 *
00443 *                 Check error code from CPTSV .
00444 *
00445                   IF( INFO.NE.IZERO )
00446      $               CALL ALAERH( PATH, 'CPTSV ', INFO, IZERO, ' ', N,
00447      $                            N, 1, 1, NRHS, IMAT, NFAIL, NERRS,
00448      $                            NOUT )
00449                   NT = 0
00450                   IF( IZERO.EQ.0 ) THEN
00451 *
00452 *                    Check the factorization by computing the ratio
00453 *                       norm(L*D*L' - A) / (n * norm(A) * EPS )
00454 *
00455                      CALL CPTT01( N, D, E, D( N+1 ), E( N+1 ), WORK,
00456      $                            RESULT( 1 ) )
00457 *
00458 *                    Compute the residual in the solution.
00459 *
00460                      CALL CLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
00461                      CALL CPTT02( 'Lower', N, NRHS, D, E, X, LDA, WORK,
00462      $                            LDA, RESULT( 2 ) )
00463 *
00464 *                    Check solution from generated exact solution.
00465 *
00466                      CALL CGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
00467      $                            RESULT( 3 ) )
00468                      NT = 3
00469                   END IF
00470 *
00471 *                 Print information about the tests that did not pass
00472 *                 the threshold.
00473 *
00474                   DO 70 K = 1, NT
00475                      IF( RESULT( K ).GE.THRESH ) THEN
00476                         IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
00477      $                     CALL ALADHD( NOUT, PATH )
00478                         WRITE( NOUT, FMT = 9999 )'CPTSV ', N, IMAT, K,
00479      $                     RESULT( K )
00480                         NFAIL = NFAIL + 1
00481                      END IF
00482    70             CONTINUE
00483                   NRUN = NRUN + NT
00484                END IF
00485 *
00486 *              --- Test CPTSVX ---
00487 *
00488                IF( IFACT.GT.1 ) THEN
00489 *
00490 *                 Initialize D( N+1:2*N ) and E( N+1:2*N ) to zero.
00491 *
00492                   DO 80 I = 1, N - 1
00493                      D( N+I ) = ZERO
00494                      E( N+I ) = ZERO
00495    80             CONTINUE
00496                   IF( N.GT.0 )
00497      $               D( N+N ) = ZERO
00498                END IF
00499 *
00500                CALL CLASET( 'Full', N, NRHS, CMPLX( ZERO ),
00501      $                      CMPLX( ZERO ), X, LDA )
00502 *
00503 *              Solve the system and compute the condition number and
00504 *              error bounds using CPTSVX.
00505 *
00506                SRNAMT = 'CPTSVX'
00507                CALL CPTSVX( FACT, N, NRHS, D, E, D( N+1 ), E( N+1 ), B,
00508      $                      LDA, X, LDA, RCOND, RWORK, RWORK( NRHS+1 ),
00509      $                      WORK, RWORK( 2*NRHS+1 ), INFO )
00510 *
00511 *              Check the error code from CPTSVX.
00512 *
00513                IF( INFO.NE.IZERO )
00514      $            CALL ALAERH( PATH, 'CPTSVX', INFO, IZERO, FACT, N, N,
00515      $                         1, 1, NRHS, IMAT, NFAIL, NERRS, NOUT )
00516                IF( IZERO.EQ.0 ) THEN
00517                   IF( IFACT.EQ.2 ) THEN
00518 *
00519 *                    Check the factorization by computing the ratio
00520 *                       norm(L*D*L' - A) / (n * norm(A) * EPS )
00521 *
00522                      K1 = 1
00523                      CALL CPTT01( N, D, E, D( N+1 ), E( N+1 ), WORK,
00524      $                            RESULT( 1 ) )
00525                   ELSE
00526                      K1 = 2
00527                   END IF
00528 *
00529 *                 Compute the residual in the solution.
00530 *
00531                   CALL CLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
00532                   CALL CPTT02( 'Lower', N, NRHS, D, E, X, LDA, WORK,
00533      $                         LDA, RESULT( 2 ) )
00534 *
00535 *                 Check solution from generated exact solution.
00536 *
00537                   CALL CGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
00538      $                         RESULT( 3 ) )
00539 *
00540 *                 Check error bounds from iterative refinement.
00541 *
00542                   CALL CPTT05( N, NRHS, D, E, B, LDA, X, LDA, XACT, LDA,
00543      $                         RWORK, RWORK( NRHS+1 ), RESULT( 4 ) )
00544                ELSE
00545                   K1 = 6
00546                END IF
00547 *
00548 *              Check the reciprocal of the condition number.
00549 *
00550                RESULT( 6 ) = SGET06( RCOND, RCONDC )
00551 *
00552 *              Print information about the tests that did not pass
00553 *              the threshold.
00554 *
00555                DO 90 K = K1, 6
00556                   IF( RESULT( K ).GE.THRESH ) THEN
00557                      IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
00558      $                  CALL ALADHD( NOUT, PATH )
00559                      WRITE( NOUT, FMT = 9998 )'CPTSVX', FACT, N, IMAT,
00560      $                  K, RESULT( K )
00561                      NFAIL = NFAIL + 1
00562                   END IF
00563    90          CONTINUE
00564                NRUN = NRUN + 7 - K1
00565   100       CONTINUE
00566   110    CONTINUE
00567   120 CONTINUE
00568 *
00569 *     Print a summary of the results.
00570 *
00571       CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
00572 *
00573  9999 FORMAT( 1X, A, ', N =', I5, ', type ', I2, ', test ', I2,
00574      $      ', ratio = ', G12.5 )
00575  9998 FORMAT( 1X, A, ', FACT=''', A1, ''', N =', I5, ', type ', I2,
00576      $      ', test ', I2, ', ratio = ', G12.5 )
00577       RETURN
00578 *
00579 *     End of CDRVPT
00580 *
00581       END
 All Files Functions