LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
sdrvpt.f
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00001 *> \brief \b SDRVPT
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 SDRVPT( 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               A( * ), B( * ), D( * ), E( * ), RWORK( * ),
00023 *      $                   WORK( * ), X( * ), XACT( * )
00024 *       ..
00025 *  
00026 *
00027 *> \par Purpose:
00028 *  =============
00029 *>
00030 *> \verbatim
00031 *>
00032 *> SDRVPT tests SPTSV and -SVX.
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] NRHS
00059 *> \verbatim
00060 *>          NRHS is INTEGER
00061 *>          The number of right hand side vectors to be generated for
00062 *>          each linear system.
00063 *> \endverbatim
00064 *>
00065 *> \param[in] THRESH
00066 *> \verbatim
00067 *>          THRESH is REAL
00068 *>          The threshold value for the test ratios.  A result is
00069 *>          included in the output file if RESULT >= THRESH.  To have
00070 *>          every test ratio printed, use THRESH = 0.
00071 *> \endverbatim
00072 *>
00073 *> \param[in] TSTERR
00074 *> \verbatim
00075 *>          TSTERR is LOGICAL
00076 *>          Flag that indicates whether error exits are to be tested.
00077 *> \endverbatim
00078 *>
00079 *> \param[out] A
00080 *> \verbatim
00081 *>          A is REAL array, dimension (NMAX*2)
00082 *> \endverbatim
00083 *>
00084 *> \param[out] D
00085 *> \verbatim
00086 *>          D is REAL array, dimension (NMAX*2)
00087 *> \endverbatim
00088 *>
00089 *> \param[out] E
00090 *> \verbatim
00091 *>          E is REAL array, dimension (NMAX*2)
00092 *> \endverbatim
00093 *>
00094 *> \param[out] B
00095 *> \verbatim
00096 *>          B is REAL array, dimension (NMAX*NRHS)
00097 *> \endverbatim
00098 *>
00099 *> \param[out] X
00100 *> \verbatim
00101 *>          X is REAL array, dimension (NMAX*NRHS)
00102 *> \endverbatim
00103 *>
00104 *> \param[out] XACT
00105 *> \verbatim
00106 *>          XACT is REAL array, dimension (NMAX*NRHS)
00107 *> \endverbatim
00108 *>
00109 *> \param[out] WORK
00110 *> \verbatim
00111 *>          WORK is REAL array, dimension
00112 *>                      (NMAX*max(3,NRHS))
00113 *> \endverbatim
00114 *>
00115 *> \param[out] RWORK
00116 *> \verbatim
00117 *>          RWORK is REAL array, dimension
00118 *>                      (max(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 single_lin
00138 *
00139 *  =====================================================================
00140       SUBROUTINE SDRVPT( 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               A( * ), B( * ), D( * ), E( * ), RWORK( * ),
00157      $                   WORK( * ), X( * ), XACT( * )
00158 *     ..
00159 *
00160 *  =====================================================================
00161 *
00162 *     .. Parameters ..
00163       REAL               ONE, ZERO
00164       PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
00165       INTEGER            NTYPES
00166       PARAMETER          ( NTYPES = 12 )
00167       INTEGER            NTESTS
00168       PARAMETER          ( NTESTS = 6 )
00169 *     ..
00170 *     .. Local Scalars ..
00171       LOGICAL            ZEROT
00172       CHARACTER          DIST, FACT, TYPE
00173       CHARACTER*3        PATH
00174       INTEGER            I, IA, IFACT, IMAT, IN, INFO, IX, IZERO, J, K,
00175      $                   K1, KL, KU, LDA, MODE, N, NERRS, NFAIL, NIMAT,
00176      $                   NRUN, NT
00177       REAL               AINVNM, ANORM, COND, DMAX, RCOND, RCONDC
00178 *     ..
00179 *     .. Local Arrays ..
00180       INTEGER            ISEED( 4 ), ISEEDY( 4 )
00181       REAL               RESULT( NTESTS ), Z( 3 )
00182 *     ..
00183 *     .. External Functions ..
00184       INTEGER            ISAMAX
00185       REAL               SASUM, SGET06, SLANST
00186       EXTERNAL           ISAMAX, SASUM, SGET06, SLANST
00187 *     ..
00188 *     .. External Subroutines ..
00189       EXTERNAL           ALADHD, ALAERH, ALASVM, SCOPY, SERRVX, SGET04,
00190      $                   SLACPY, SLAPTM, SLARNV, SLASET, SLATB4, SLATMS,
00191      $                   SPTSV, SPTSVX, SPTT01, SPTT02, SPTT05, SPTTRF,
00192      $                   SPTTRS, SSCAL
00193 *     ..
00194 *     .. Intrinsic Functions ..
00195       INTRINSIC          ABS, MAX
00196 *     ..
00197 *     .. Scalars in Common ..
00198       LOGICAL            LERR, OK
00199       CHARACTER*32       SRNAMT
00200       INTEGER            INFOT, NUNIT
00201 *     ..
00202 *     .. Common blocks ..
00203       COMMON             / INFOC / INFOT, NUNIT, OK, LERR
00204       COMMON             / SRNAMC / SRNAMT
00205 *     ..
00206 *     .. Data statements ..
00207       DATA               ISEEDY / 0, 0, 0, 1 /
00208 *     ..
00209 *     .. Executable Statements ..
00210 *
00211       PATH( 1: 1 ) = 'Single precision'
00212       PATH( 2: 3 ) = 'PT'
00213       NRUN = 0
00214       NFAIL = 0
00215       NERRS = 0
00216       DO 10 I = 1, 4
00217          ISEED( I ) = ISEEDY( I )
00218    10 CONTINUE
00219 *
00220 *     Test the error exits
00221 *
00222       IF( TSTERR )
00223      $   CALL SERRVX( PATH, NOUT )
00224       INFOT = 0
00225 *
00226       DO 120 IN = 1, NN
00227 *
00228 *        Do for each value of N in NVAL.
00229 *
00230          N = NVAL( IN )
00231          LDA = MAX( 1, N )
00232          NIMAT = NTYPES
00233          IF( N.LE.0 )
00234      $      NIMAT = 1
00235 *
00236          DO 110 IMAT = 1, NIMAT
00237 *
00238 *           Do the tests only if DOTYPE( IMAT ) is true.
00239 *
00240             IF( N.GT.0 .AND. .NOT.DOTYPE( IMAT ) )
00241      $         GO TO 110
00242 *
00243 *           Set up parameters with SLATB4.
00244 *
00245             CALL SLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE,
00246      $                   COND, DIST )
00247 *
00248             ZEROT = IMAT.GE.8 .AND. IMAT.LE.10
00249             IF( IMAT.LE.6 ) THEN
00250 *
00251 *              Type 1-6:  generate a symmetric tridiagonal matrix of
00252 *              known condition number in lower triangular band storage.
00253 *
00254                SRNAMT = 'SLATMS'
00255                CALL SLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE, COND,
00256      $                      ANORM, KL, KU, 'B', A, 2, WORK, INFO )
00257 *
00258 *              Check the error code from SLATMS.
00259 *
00260                IF( INFO.NE.0 ) THEN
00261                   CALL ALAERH( PATH, 'SLATMS', INFO, 0, ' ', N, N, KL,
00262      $                         KU, -1, IMAT, NFAIL, NERRS, NOUT )
00263                   GO TO 110
00264                END IF
00265                IZERO = 0
00266 *
00267 *              Copy the matrix to D and E.
00268 *
00269                IA = 1
00270                DO 20 I = 1, N - 1
00271                   D( I ) = A( IA )
00272                   E( I ) = A( IA+1 )
00273                   IA = IA + 2
00274    20          CONTINUE
00275                IF( N.GT.0 )
00276      $            D( N ) = A( IA )
00277             ELSE
00278 *
00279 *              Type 7-12:  generate a diagonally dominant matrix with
00280 *              unknown condition number in the vectors D and E.
00281 *
00282                IF( .NOT.ZEROT .OR. .NOT.DOTYPE( 7 ) ) THEN
00283 *
00284 *                 Let D and E have values from [-1,1].
00285 *
00286                   CALL SLARNV( 2, ISEED, N, D )
00287                   CALL SLARNV( 2, ISEED, N-1, E )
00288 *
00289 *                 Make the tridiagonal matrix diagonally dominant.
00290 *
00291                   IF( N.EQ.1 ) THEN
00292                      D( 1 ) = ABS( D( 1 ) )
00293                   ELSE
00294                      D( 1 ) = ABS( D( 1 ) ) + ABS( E( 1 ) )
00295                      D( N ) = ABS( D( N ) ) + ABS( E( N-1 ) )
00296                      DO 30 I = 2, N - 1
00297                         D( I ) = ABS( D( I ) ) + ABS( E( I ) ) +
00298      $                           ABS( E( I-1 ) )
00299    30                CONTINUE
00300                   END IF
00301 *
00302 *                 Scale D and E so the maximum element is ANORM.
00303 *
00304                   IX = ISAMAX( N, D, 1 )
00305                   DMAX = D( IX )
00306                   CALL SSCAL( N, ANORM / DMAX, D, 1 )
00307                   IF( N.GT.1 )
00308      $               CALL SSCAL( N-1, ANORM / DMAX, E, 1 )
00309 *
00310                ELSE IF( IZERO.GT.0 ) THEN
00311 *
00312 *                 Reuse the last matrix by copying back the zeroed out
00313 *                 elements.
00314 *
00315                   IF( IZERO.EQ.1 ) THEN
00316                      D( 1 ) = Z( 2 )
00317                      IF( N.GT.1 )
00318      $                  E( 1 ) = Z( 3 )
00319                   ELSE IF( IZERO.EQ.N ) THEN
00320                      E( N-1 ) = Z( 1 )
00321                      D( N ) = Z( 2 )
00322                   ELSE
00323                      E( IZERO-1 ) = Z( 1 )
00324                      D( IZERO ) = Z( 2 )
00325                      E( IZERO ) = Z( 3 )
00326                   END IF
00327                END IF
00328 *
00329 *              For types 8-10, set one row and column of the matrix to
00330 *              zero.
00331 *
00332                IZERO = 0
00333                IF( IMAT.EQ.8 ) THEN
00334                   IZERO = 1
00335                   Z( 2 ) = D( 1 )
00336                   D( 1 ) = ZERO
00337                   IF( N.GT.1 ) THEN
00338                      Z( 3 ) = E( 1 )
00339                      E( 1 ) = ZERO
00340                   END IF
00341                ELSE IF( IMAT.EQ.9 ) THEN
00342                   IZERO = N
00343                   IF( N.GT.1 ) THEN
00344                      Z( 1 ) = E( N-1 )
00345                      E( N-1 ) = ZERO
00346                   END IF
00347                   Z( 2 ) = D( N )
00348                   D( N ) = ZERO
00349                ELSE IF( IMAT.EQ.10 ) THEN
00350                   IZERO = ( N+1 ) / 2
00351                   IF( IZERO.GT.1 ) THEN
00352                      Z( 1 ) = E( IZERO-1 )
00353                      Z( 3 ) = E( IZERO )
00354                      E( IZERO-1 ) = ZERO
00355                      E( IZERO ) = ZERO
00356                   END IF
00357                   Z( 2 ) = D( IZERO )
00358                   D( IZERO ) = ZERO
00359                END IF
00360             END IF
00361 *
00362 *           Generate NRHS random solution vectors.
00363 *
00364             IX = 1
00365             DO 40 J = 1, NRHS
00366                CALL SLARNV( 2, ISEED, N, XACT( IX ) )
00367                IX = IX + LDA
00368    40       CONTINUE
00369 *
00370 *           Set the right hand side.
00371 *
00372             CALL SLAPTM( N, NRHS, ONE, D, E, XACT, LDA, ZERO, B, LDA )
00373 *
00374             DO 100 IFACT = 1, 2
00375                IF( IFACT.EQ.1 ) THEN
00376                   FACT = 'F'
00377                ELSE
00378                   FACT = 'N'
00379                END IF
00380 *
00381 *              Compute the condition number for comparison with
00382 *              the value returned by SPTSVX.
00383 *
00384                IF( ZEROT ) THEN
00385                   IF( IFACT.EQ.1 )
00386      $               GO TO 100
00387                   RCONDC = ZERO
00388 *
00389                ELSE IF( IFACT.EQ.1 ) THEN
00390 *
00391 *                 Compute the 1-norm of A.
00392 *
00393                   ANORM = SLANST( '1', N, D, E )
00394 *
00395                   CALL SCOPY( N, D, 1, D( N+1 ), 1 )
00396                   IF( N.GT.1 )
00397      $               CALL SCOPY( N-1, E, 1, E( N+1 ), 1 )
00398 *
00399 *                 Factor the matrix A.
00400 *
00401                   CALL SPTTRF( N, D( N+1 ), E( N+1 ), INFO )
00402 *
00403 *                 Use SPTTRS to solve for one column at a time of
00404 *                 inv(A), computing the maximum column sum as we go.
00405 *
00406                   AINVNM = ZERO
00407                   DO 60 I = 1, N
00408                      DO 50 J = 1, N
00409                         X( J ) = ZERO
00410    50                CONTINUE
00411                      X( I ) = ONE
00412                      CALL SPTTRS( N, 1, D( N+1 ), E( N+1 ), X, LDA,
00413      $                            INFO )
00414                      AINVNM = MAX( AINVNM, SASUM( N, X, 1 ) )
00415    60             CONTINUE
00416 *
00417 *                 Compute the 1-norm condition number of A.
00418 *
00419                   IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
00420                      RCONDC = ONE
00421                   ELSE
00422                      RCONDC = ( ONE / ANORM ) / AINVNM
00423                   END IF
00424                END IF
00425 *
00426                IF( IFACT.EQ.2 ) THEN
00427 *
00428 *                 --- Test SPTSV --
00429 *
00430                   CALL SCOPY( N, D, 1, D( N+1 ), 1 )
00431                   IF( N.GT.1 )
00432      $               CALL SCOPY( N-1, E, 1, E( N+1 ), 1 )
00433                   CALL SLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
00434 *
00435 *                 Factor A as L*D*L' and solve the system A*X = B.
00436 *
00437                   SRNAMT = 'SPTSV '
00438                   CALL SPTSV( N, NRHS, D( N+1 ), E( N+1 ), X, LDA,
00439      $                        INFO )
00440 *
00441 *                 Check error code from SPTSV .
00442 *
00443                   IF( INFO.NE.IZERO )
00444      $               CALL ALAERH( PATH, 'SPTSV ', INFO, IZERO, ' ', N,
00445      $                            N, 1, 1, NRHS, IMAT, NFAIL, NERRS,
00446      $                            NOUT )
00447                   NT = 0
00448                   IF( IZERO.EQ.0 ) THEN
00449 *
00450 *                    Check the factorization by computing the ratio
00451 *                       norm(L*D*L' - A) / (n * norm(A) * EPS )
00452 *
00453                      CALL SPTT01( N, D, E, D( N+1 ), E( N+1 ), WORK,
00454      $                            RESULT( 1 ) )
00455 *
00456 *                    Compute the residual in the solution.
00457 *
00458                      CALL SLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
00459                      CALL SPTT02( N, NRHS, D, E, X, LDA, WORK, LDA,
00460      $                            RESULT( 2 ) )
00461 *
00462 *                    Check solution from generated exact solution.
00463 *
00464                      CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
00465      $                            RESULT( 3 ) )
00466                      NT = 3
00467                   END IF
00468 *
00469 *                 Print information about the tests that did not pass
00470 *                 the threshold.
00471 *
00472                   DO 70 K = 1, NT
00473                      IF( RESULT( K ).GE.THRESH ) THEN
00474                         IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
00475      $                     CALL ALADHD( NOUT, PATH )
00476                         WRITE( NOUT, FMT = 9999 )'SPTSV ', N, IMAT, K,
00477      $                     RESULT( K )
00478                         NFAIL = NFAIL + 1
00479                      END IF
00480    70             CONTINUE
00481                   NRUN = NRUN + NT
00482                END IF
00483 *
00484 *              --- Test SPTSVX ---
00485 *
00486                IF( IFACT.GT.1 ) THEN
00487 *
00488 *                 Initialize D( N+1:2*N ) and E( N+1:2*N ) to zero.
00489 *
00490                   DO 80 I = 1, N - 1
00491                      D( N+I ) = ZERO
00492                      E( N+I ) = ZERO
00493    80             CONTINUE
00494                   IF( N.GT.0 )
00495      $               D( N+N ) = ZERO
00496                END IF
00497 *
00498                CALL SLASET( 'Full', N, NRHS, ZERO, ZERO, X, LDA )
00499 *
00500 *              Solve the system and compute the condition number and
00501 *              error bounds using SPTSVX.
00502 *
00503                SRNAMT = 'SPTSVX'
00504                CALL SPTSVX( FACT, N, NRHS, D, E, D( N+1 ), E( N+1 ), B,
00505      $                      LDA, X, LDA, RCOND, RWORK, RWORK( NRHS+1 ),
00506      $                      WORK, INFO )
00507 *
00508 *              Check the error code from SPTSVX.
00509 *
00510                IF( INFO.NE.IZERO )
00511      $            CALL ALAERH( PATH, 'SPTSVX', INFO, IZERO, FACT, N, N,
00512      $                         1, 1, NRHS, IMAT, NFAIL, NERRS, NOUT )
00513                IF( IZERO.EQ.0 ) THEN
00514                   IF( IFACT.EQ.2 ) THEN
00515 *
00516 *                    Check the factorization by computing the ratio
00517 *                       norm(L*D*L' - A) / (n * norm(A) * EPS )
00518 *
00519                      K1 = 1
00520                      CALL SPTT01( N, D, E, D( N+1 ), E( N+1 ), WORK,
00521      $                            RESULT( 1 ) )
00522                   ELSE
00523                      K1 = 2
00524                   END IF
00525 *
00526 *                 Compute the residual in the solution.
00527 *
00528                   CALL SLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
00529                   CALL SPTT02( N, NRHS, D, E, X, LDA, WORK, LDA,
00530      $                         RESULT( 2 ) )
00531 *
00532 *                 Check solution from generated exact solution.
00533 *
00534                   CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
00535      $                         RESULT( 3 ) )
00536 *
00537 *                 Check error bounds from iterative refinement.
00538 *
00539                   CALL SPTT05( N, NRHS, D, E, B, LDA, X, LDA, XACT, LDA,
00540      $                         RWORK, RWORK( NRHS+1 ), RESULT( 4 ) )
00541                ELSE
00542                   K1 = 6
00543                END IF
00544 *
00545 *              Check the reciprocal of the condition number.
00546 *
00547                RESULT( 6 ) = SGET06( RCOND, RCONDC )
00548 *
00549 *              Print information about the tests that did not pass
00550 *              the threshold.
00551 *
00552                DO 90 K = K1, 6
00553                   IF( RESULT( K ).GE.THRESH ) THEN
00554                      IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
00555      $                  CALL ALADHD( NOUT, PATH )
00556                      WRITE( NOUT, FMT = 9998 )'SPTSVX', FACT, N, IMAT,
00557      $                  K, RESULT( K )
00558                      NFAIL = NFAIL + 1
00559                   END IF
00560    90          CONTINUE
00561                NRUN = NRUN + 7 - K1
00562   100       CONTINUE
00563   110    CONTINUE
00564   120 CONTINUE
00565 *
00566 *     Print a summary of the results.
00567 *
00568       CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
00569 *
00570  9999 FORMAT( 1X, A, ', N =', I5, ', type ', I2, ', test ', I2,
00571      $      ', ratio = ', G12.5 )
00572  9998 FORMAT( 1X, A, ', FACT=''', A1, ''', N =', I5, ', type ', I2,
00573      $      ', test ', I2, ', ratio = ', G12.5 )
00574       RETURN
00575 *
00576 *     End of SDRVPT
00577 *
00578       END
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