LAPACK 3.3.1 Linear Algebra PACKage

# zchkpt.f

Go to the documentation of this file.
```00001       SUBROUTINE ZCHKPT( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
00002      \$                   A, D, E, B, X, XACT, WORK, RWORK, NOUT )
00003 *
00004 *  -- LAPACK test routine (version 3.1) --
00005 *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
00006 *     November 2006
00007 *
00008 *     .. Scalar Arguments ..
00009       LOGICAL            TSTERR
00010       INTEGER            NN, NNS, NOUT
00011       DOUBLE PRECISION   THRESH
00012 *     ..
00013 *     .. Array Arguments ..
00014       LOGICAL            DOTYPE( * )
00015       INTEGER            NSVAL( * ), NVAL( * )
00016       DOUBLE PRECISION   D( * ), RWORK( * )
00017       COMPLEX*16         A( * ), B( * ), E( * ), WORK( * ), X( * ),
00018      \$                   XACT( * )
00019 *     ..
00020 *
00021 *  Purpose
00022 *  =======
00023 *
00024 *  ZCHKPT tests ZPTTRF, -TRS, -RFS, and -CON
00025 *
00026 *  Arguments
00027 *  =========
00028 *
00029 *  DOTYPE  (input) LOGICAL array, dimension (NTYPES)
00030 *          The matrix types to be used for testing.  Matrices of type j
00031 *          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
00032 *          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
00033 *
00034 *  NN      (input) INTEGER
00035 *          The number of values of N contained in the vector NVAL.
00036 *
00037 *  NVAL    (input) INTEGER array, dimension (NN)
00038 *          The values of the matrix dimension N.
00039 *
00040 *  NNS     (input) INTEGER
00041 *          The number of values of NRHS contained in the vector NSVAL.
00042 *
00043 *  NSVAL   (input) INTEGER array, dimension (NNS)
00044 *          The values of the number of right hand sides NRHS.
00045 *
00046 *  THRESH  (input) DOUBLE PRECISION
00047 *          The threshold value for the test ratios.  A result is
00048 *          included in the output file if RESULT >= THRESH.  To have
00049 *          every test ratio printed, use THRESH = 0.
00050 *
00051 *  TSTERR  (input) LOGICAL
00052 *          Flag that indicates whether error exits are to be tested.
00053 *
00054 *  A       (workspace) COMPLEX*16 array, dimension (NMAX*2)
00055 *
00056 *  D       (workspace) DOUBLE PRECISION array, dimension (NMAX*2)
00057 *
00058 *  E       (workspace) COMPLEX*16 array, dimension (NMAX*2)
00059 *
00060 *  B       (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX)
00061 *          where NSMAX is the largest entry in NSVAL.
00062 *
00063 *  X       (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX)
00064 *
00065 *  XACT    (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX)
00066 *
00067 *  WORK    (workspace) COMPLEX*16 array, dimension
00068 *                      (NMAX*max(3,NSMAX))
00069 *
00070 *  RWORK   (workspace) DOUBLE PRECISION array, dimension
00071 *                      (max(NMAX,2*NSMAX))
00072 *
00073 *  NOUT    (input) INTEGER
00074 *          The unit number for output.
00075 *
00076 *  =====================================================================
00077 *
00078 *     .. Parameters ..
00079       DOUBLE PRECISION   ONE, ZERO
00080       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
00081       INTEGER            NTYPES
00082       PARAMETER          ( NTYPES = 12 )
00083       INTEGER            NTESTS
00084       PARAMETER          ( NTESTS = 7 )
00085 *     ..
00086 *     .. Local Scalars ..
00087       LOGICAL            ZEROT
00088       CHARACTER          DIST, TYPE, UPLO
00089       CHARACTER*3        PATH
00090       INTEGER            I, IA, IMAT, IN, INFO, IRHS, IUPLO, IX, IZERO,
00091      \$                   J, K, KL, KU, LDA, MODE, N, NERRS, NFAIL,
00092      \$                   NIMAT, NRHS, NRUN
00093       DOUBLE PRECISION   AINVNM, ANORM, COND, DMAX, RCOND, RCONDC
00094 *     ..
00095 *     .. Local Arrays ..
00096       CHARACTER          UPLOS( 2 )
00097       INTEGER            ISEED( 4 ), ISEEDY( 4 )
00098       DOUBLE PRECISION   RESULT( NTESTS )
00099       COMPLEX*16         Z( 3 )
00100 *     ..
00101 *     .. External Functions ..
00102       INTEGER            IDAMAX
00103       DOUBLE PRECISION   DGET06, DZASUM, ZLANHT
00104       EXTERNAL           IDAMAX, DGET06, DZASUM, ZLANHT
00105 *     ..
00106 *     .. External Subroutines ..
00107       EXTERNAL           ALAERH, ALAHD, ALASUM, DCOPY, DLARNV, DSCAL,
00108      \$                   ZCOPY, ZDSCAL, ZERRGT, ZGET04, ZLACPY, ZLAPTM,
00109      \$                   ZLARNV, ZLATB4, ZLATMS, ZPTCON, ZPTRFS, ZPTT01,
00110      \$                   ZPTT02, ZPTT05, ZPTTRF, ZPTTRS
00111 *     ..
00112 *     .. Intrinsic Functions ..
00113       INTRINSIC          ABS, DBLE, MAX
00114 *     ..
00115 *     .. Scalars in Common ..
00116       LOGICAL            LERR, OK
00117       CHARACTER*32       SRNAMT
00118       INTEGER            INFOT, NUNIT
00119 *     ..
00120 *     .. Common blocks ..
00121       COMMON             / INFOC / INFOT, NUNIT, OK, LERR
00122       COMMON             / SRNAMC / SRNAMT
00123 *     ..
00124 *     .. Data statements ..
00125       DATA               ISEEDY / 0, 0, 0, 1 / , UPLOS / 'U', 'L' /
00126 *     ..
00127 *     .. Executable Statements ..
00128 *
00129       PATH( 1: 1 ) = 'Zomplex precision'
00130       PATH( 2: 3 ) = 'PT'
00131       NRUN = 0
00132       NFAIL = 0
00133       NERRS = 0
00134       DO 10 I = 1, 4
00135          ISEED( I ) = ISEEDY( I )
00136    10 CONTINUE
00137 *
00138 *     Test the error exits
00139 *
00140       IF( TSTERR )
00141      \$   CALL ZERRGT( PATH, NOUT )
00142       INFOT = 0
00143 *
00144       DO 120 IN = 1, NN
00145 *
00146 *        Do for each value of N in NVAL.
00147 *
00148          N = NVAL( IN )
00149          LDA = MAX( 1, N )
00150          NIMAT = NTYPES
00151          IF( N.LE.0 )
00152      \$      NIMAT = 1
00153 *
00154          DO 110 IMAT = 1, NIMAT
00155 *
00156 *           Do the tests only if DOTYPE( IMAT ) is true.
00157 *
00158             IF( N.GT.0 .AND. .NOT.DOTYPE( IMAT ) )
00159      \$         GO TO 110
00160 *
00161 *           Set up parameters with ZLATB4.
00162 *
00163             CALL ZLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE,
00164      \$                   COND, DIST )
00165 *
00166             ZEROT = IMAT.GE.8 .AND. IMAT.LE.10
00167             IF( IMAT.LE.6 ) THEN
00168 *
00169 *              Type 1-6:  generate a Hermitian tridiagonal matrix of
00170 *              known condition number in lower triangular band storage.
00171 *
00172                SRNAMT = 'ZLATMS'
00173                CALL ZLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE, COND,
00174      \$                      ANORM, KL, KU, 'B', A, 2, WORK, INFO )
00175 *
00176 *              Check the error code from ZLATMS.
00177 *
00178                IF( INFO.NE.0 ) THEN
00179                   CALL ALAERH( PATH, 'ZLATMS', INFO, 0, ' ', N, N, KL,
00180      \$                         KU, -1, IMAT, NFAIL, NERRS, NOUT )
00181                   GO TO 110
00182                END IF
00183                IZERO = 0
00184 *
00185 *              Copy the matrix to D and E.
00186 *
00187                IA = 1
00188                DO 20 I = 1, N - 1
00189                   D( I ) = DBLE( A( IA ) )
00190                   E( I ) = A( IA+1 )
00191                   IA = IA + 2
00192    20          CONTINUE
00193                IF( N.GT.0 )
00194      \$            D( N ) = DBLE( A( IA ) )
00195             ELSE
00196 *
00197 *              Type 7-12:  generate a diagonally dominant matrix with
00198 *              unknown condition number in the vectors D and E.
00199 *
00200                IF( .NOT.ZEROT .OR. .NOT.DOTYPE( 7 ) ) THEN
00201 *
00202 *                 Let E be complex, D real, with values from [-1,1].
00203 *
00204                   CALL DLARNV( 2, ISEED, N, D )
00205                   CALL ZLARNV( 2, ISEED, N-1, E )
00206 *
00207 *                 Make the tridiagonal matrix diagonally dominant.
00208 *
00209                   IF( N.EQ.1 ) THEN
00210                      D( 1 ) = ABS( D( 1 ) )
00211                   ELSE
00212                      D( 1 ) = ABS( D( 1 ) ) + ABS( E( 1 ) )
00213                      D( N ) = ABS( D( N ) ) + ABS( E( N-1 ) )
00214                      DO 30 I = 2, N - 1
00215                         D( I ) = ABS( D( I ) ) + ABS( E( I ) ) +
00216      \$                           ABS( E( I-1 ) )
00217    30                CONTINUE
00218                   END IF
00219 *
00220 *                 Scale D and E so the maximum element is ANORM.
00221 *
00222                   IX = IDAMAX( N, D, 1 )
00223                   DMAX = D( IX )
00224                   CALL DSCAL( N, ANORM / DMAX, D, 1 )
00225                   CALL ZDSCAL( N-1, ANORM / DMAX, E, 1 )
00226 *
00227                ELSE IF( IZERO.GT.0 ) THEN
00228 *
00229 *                 Reuse the last matrix by copying back the zeroed out
00230 *                 elements.
00231 *
00232                   IF( IZERO.EQ.1 ) THEN
00233                      D( 1 ) = Z( 2 )
00234                      IF( N.GT.1 )
00235      \$                  E( 1 ) = Z( 3 )
00236                   ELSE IF( IZERO.EQ.N ) THEN
00237                      E( N-1 ) = Z( 1 )
00238                      D( N ) = Z( 2 )
00239                   ELSE
00240                      E( IZERO-1 ) = Z( 1 )
00241                      D( IZERO ) = Z( 2 )
00242                      E( IZERO ) = Z( 3 )
00243                   END IF
00244                END IF
00245 *
00246 *              For types 8-10, set one row and column of the matrix to
00247 *              zero.
00248 *
00249                IZERO = 0
00250                IF( IMAT.EQ.8 ) THEN
00251                   IZERO = 1
00252                   Z( 2 ) = D( 1 )
00253                   D( 1 ) = ZERO
00254                   IF( N.GT.1 ) THEN
00255                      Z( 3 ) = E( 1 )
00256                      E( 1 ) = ZERO
00257                   END IF
00258                ELSE IF( IMAT.EQ.9 ) THEN
00259                   IZERO = N
00260                   IF( N.GT.1 ) THEN
00261                      Z( 1 ) = E( N-1 )
00262                      E( N-1 ) = ZERO
00263                   END IF
00264                   Z( 2 ) = D( N )
00265                   D( N ) = ZERO
00266                ELSE IF( IMAT.EQ.10 ) THEN
00267                   IZERO = ( N+1 ) / 2
00268                   IF( IZERO.GT.1 ) THEN
00269                      Z( 1 ) = E( IZERO-1 )
00270                      Z( 3 ) = E( IZERO )
00271                      E( IZERO-1 ) = ZERO
00272                      E( IZERO ) = ZERO
00273                   END IF
00274                   Z( 2 ) = D( IZERO )
00275                   D( IZERO ) = ZERO
00276                END IF
00277             END IF
00278 *
00279             CALL DCOPY( N, D, 1, D( N+1 ), 1 )
00280             IF( N.GT.1 )
00281      \$         CALL ZCOPY( N-1, E, 1, E( N+1 ), 1 )
00282 *
00283 *+    TEST 1
00284 *           Factor A as L*D*L' and compute the ratio
00285 *              norm(L*D*L' - A) / (n * norm(A) * EPS )
00286 *
00287             CALL ZPTTRF( N, D( N+1 ), E( N+1 ), INFO )
00288 *
00289 *           Check error code from ZPTTRF.
00290 *
00291             IF( INFO.NE.IZERO ) THEN
00292                CALL ALAERH( PATH, 'ZPTTRF', INFO, IZERO, ' ', N, N, -1,
00293      \$                      -1, -1, IMAT, NFAIL, NERRS, NOUT )
00294                GO TO 110
00295             END IF
00296 *
00297             IF( INFO.GT.0 ) THEN
00298                RCONDC = ZERO
00299                GO TO 100
00300             END IF
00301 *
00302             CALL ZPTT01( N, D, E, D( N+1 ), E( N+1 ), WORK,
00303      \$                   RESULT( 1 ) )
00304 *
00305 *           Print the test ratio if greater than or equal to THRESH.
00306 *
00307             IF( RESULT( 1 ).GE.THRESH ) THEN
00308                IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
00309      \$            CALL ALAHD( NOUT, PATH )
00310                WRITE( NOUT, FMT = 9999 )N, IMAT, 1, RESULT( 1 )
00311                NFAIL = NFAIL + 1
00312             END IF
00313             NRUN = NRUN + 1
00314 *
00315 *           Compute RCONDC = 1 / (norm(A) * norm(inv(A))
00316 *
00317 *           Compute norm(A).
00318 *
00319             ANORM = ZLANHT( '1', N, D, E )
00320 *
00321 *           Use ZPTTRS to solve for one column at a time of inv(A),
00322 *           computing the maximum column sum as we go.
00323 *
00324             AINVNM = ZERO
00325             DO 50 I = 1, N
00326                DO 40 J = 1, N
00327                   X( J ) = ZERO
00328    40          CONTINUE
00329                X( I ) = ONE
00330                CALL ZPTTRS( 'Lower', N, 1, D( N+1 ), E( N+1 ), X, LDA,
00331      \$                      INFO )
00332                AINVNM = MAX( AINVNM, DZASUM( N, X, 1 ) )
00333    50       CONTINUE
00334             RCONDC = ONE / MAX( ONE, ANORM*AINVNM )
00335 *
00336             DO 90 IRHS = 1, NNS
00337                NRHS = NSVAL( IRHS )
00338 *
00339 *           Generate NRHS random solution vectors.
00340 *
00341                IX = 1
00342                DO 60 J = 1, NRHS
00343                   CALL ZLARNV( 2, ISEED, N, XACT( IX ) )
00344                   IX = IX + LDA
00345    60          CONTINUE
00346 *
00347                DO 80 IUPLO = 1, 2
00348 *
00349 *              Do first for UPLO = 'U', then for UPLO = 'L'.
00350 *
00351                   UPLO = UPLOS( IUPLO )
00352 *
00353 *              Set the right hand side.
00354 *
00355                   CALL ZLAPTM( UPLO, N, NRHS, ONE, D, E, XACT, LDA,
00356      \$                         ZERO, B, LDA )
00357 *
00358 *+    TEST 2
00359 *              Solve A*x = b and compute the residual.
00360 *
00361                   CALL ZLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
00362                   CALL ZPTTRS( UPLO, N, NRHS, D( N+1 ), E( N+1 ), X,
00363      \$                         LDA, INFO )
00364 *
00365 *              Check error code from ZPTTRS.
00366 *
00367                   IF( INFO.NE.0 )
00368      \$               CALL ALAERH( PATH, 'ZPTTRS', INFO, 0, UPLO, N, N,
00369      \$                            -1, -1, NRHS, IMAT, NFAIL, NERRS,
00370      \$                            NOUT )
00371 *
00372                   CALL ZLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
00373                   CALL ZPTT02( UPLO, N, NRHS, D, E, X, LDA, WORK, LDA,
00374      \$                         RESULT( 2 ) )
00375 *
00376 *+    TEST 3
00377 *              Check solution from generated exact solution.
00378 *
00379                   CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
00380      \$                         RESULT( 3 ) )
00381 *
00382 *+    TESTS 4, 5, and 6
00383 *              Use iterative refinement to improve the solution.
00384 *
00385                   SRNAMT = 'ZPTRFS'
00386                   CALL ZPTRFS( UPLO, N, NRHS, D, E, D( N+1 ), E( N+1 ),
00387      \$                         B, LDA, X, LDA, RWORK, RWORK( NRHS+1 ),
00388      \$                         WORK, RWORK( 2*NRHS+1 ), INFO )
00389 *
00390 *              Check error code from ZPTRFS.
00391 *
00392                   IF( INFO.NE.0 )
00393      \$               CALL ALAERH( PATH, 'ZPTRFS', INFO, 0, UPLO, N, N,
00394      \$                            -1, -1, NRHS, IMAT, NFAIL, NERRS,
00395      \$                            NOUT )
00396 *
00397                   CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
00398      \$                         RESULT( 4 ) )
00399                   CALL ZPTT05( N, NRHS, D, E, B, LDA, X, LDA, XACT, LDA,
00400      \$                         RWORK, RWORK( NRHS+1 ), RESULT( 5 ) )
00401 *
00402 *              Print information about the tests that did not pass the
00403 *              threshold.
00404 *
00405                   DO 70 K = 2, 6
00406                      IF( RESULT( K ).GE.THRESH ) THEN
00407                         IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
00408      \$                     CALL ALAHD( NOUT, PATH )
00409                         WRITE( NOUT, FMT = 9998 )UPLO, N, NRHS, IMAT,
00410      \$                     K, RESULT( K )
00411                         NFAIL = NFAIL + 1
00412                      END IF
00413    70             CONTINUE
00414                   NRUN = NRUN + 5
00415 *
00416    80          CONTINUE
00417    90       CONTINUE
00418 *
00419 *+    TEST 7
00420 *           Estimate the reciprocal of the condition number of the
00421 *           matrix.
00422 *
00423   100       CONTINUE
00424             SRNAMT = 'ZPTCON'
00425             CALL ZPTCON( N, D( N+1 ), E( N+1 ), ANORM, RCOND, RWORK,
00426      \$                   INFO )
00427 *
00428 *           Check error code from ZPTCON.
00429 *
00430             IF( INFO.NE.0 )
00431      \$         CALL ALAERH( PATH, 'ZPTCON', INFO, 0, ' ', N, N, -1, -1,
00432      \$                      -1, IMAT, NFAIL, NERRS, NOUT )
00433 *
00434             RESULT( 7 ) = DGET06( RCOND, RCONDC )
00435 *
00436 *           Print the test ratio if greater than or equal to THRESH.
00437 *
00438             IF( RESULT( 7 ).GE.THRESH ) THEN
00439                IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
00440      \$            CALL ALAHD( NOUT, PATH )
00441                WRITE( NOUT, FMT = 9999 )N, IMAT, 7, RESULT( 7 )
00442                NFAIL = NFAIL + 1
00443             END IF
00444             NRUN = NRUN + 1
00445   110    CONTINUE
00446   120 CONTINUE
00447 *
00448 *     Print a summary of the results.
00449 *
00450       CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
00451 *
00452  9999 FORMAT( ' N =', I5, ', type ', I2, ', test ', I2, ', ratio = ',
00453      \$      G12.5 )
00454  9998 FORMAT( ' UPLO = ''', A1, ''', N =', I5, ', NRHS =', I3,
00455      \$        ', type ', I2, ', test ', I2, ', ratio = ', G12.5 )
00456       RETURN
00457 *
00458 *     End of ZCHKPT
00459 *
00460       END
```