LAPACK 3.3.1 Linear Algebra PACKage

# zchkpp.f

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```00001       SUBROUTINE ZCHKPP( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
00002      \$                   NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK,
00003      \$                   NOUT )
00004 *
00005 *  -- LAPACK test routine (version 3.1) --
00006 *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
00007 *     November 2006
00008 *
00009 *     .. Scalar Arguments ..
00010       LOGICAL            TSTERR
00011       INTEGER            NMAX, NN, NNS, NOUT
00012       DOUBLE PRECISION   THRESH
00013 *     ..
00014 *     .. Array Arguments ..
00015       LOGICAL            DOTYPE( * )
00016       INTEGER            NSVAL( * ), NVAL( * )
00017       DOUBLE PRECISION   RWORK( * )
00018       COMPLEX*16         A( * ), AFAC( * ), AINV( * ), B( * ),
00019      \$                   WORK( * ), X( * ), XACT( * )
00020 *     ..
00021 *
00022 *  Purpose
00023 *  =======
00024 *
00025 *  ZCHKPP tests ZPPTRF, -TRI, -TRS, -RFS, and -CON
00026 *
00027 *  Arguments
00028 *  =========
00029 *
00030 *  DOTYPE  (input) LOGICAL array, dimension (NTYPES)
00031 *          The matrix types to be used for testing.  Matrices of type j
00032 *          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
00033 *          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
00034 *
00035 *  NN      (input) INTEGER
00036 *          The number of values of N contained in the vector NVAL.
00037 *
00038 *  NVAL    (input) INTEGER array, dimension (NN)
00039 *          The values of the matrix dimension N.
00040 *
00041 *  NNS     (input) INTEGER
00042 *          The number of values of NRHS contained in the vector NSVAL.
00043 *
00044 *  NSVAL   (input) INTEGER array, dimension (NNS)
00045 *          The values of the number of right hand sides NRHS.
00046 *
00047 *  THRESH  (input) DOUBLE PRECISION
00048 *          The threshold value for the test ratios.  A result is
00049 *          included in the output file if RESULT >= THRESH.  To have
00050 *          every test ratio printed, use THRESH = 0.
00051 *
00052 *  TSTERR  (input) LOGICAL
00053 *          Flag that indicates whether error exits are to be tested.
00054 *
00055 *  NMAX    (input) INTEGER
00056 *          The maximum value permitted for N, used in dimensioning the
00057 *          work arrays.
00058 *
00059 *  A       (workspace) COMPLEX*16 array, dimension
00060 *                      (NMAX*(NMAX+1)/2)
00061 *
00062 *  AFAC    (workspace) COMPLEX*16 array, dimension
00063 *                      (NMAX*(NMAX+1)/2)
00064 *
00065 *  AINV    (workspace) COMPLEX*16 array, dimension
00066 *                      (NMAX*(NMAX+1)/2)
00067 *
00068 *  B       (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX)
00069 *          where NSMAX is the largest entry in NSVAL.
00070 *
00071 *  X       (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX)
00072 *
00073 *  XACT    (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX)
00074 *
00075 *  WORK    (workspace) COMPLEX*16 array, dimension
00076 *                      (NMAX*max(3,NSMAX))
00077 *
00078 *  RWORK   (workspace) DOUBLE PRECISION array, dimension
00079 *                      (max(NMAX,2*NSMAX))
00080 *
00081 *  NOUT    (input) INTEGER
00082 *          The unit number for output.
00083 *
00084 *  =====================================================================
00085 *
00086 *     .. Parameters ..
00087       DOUBLE PRECISION   ZERO
00088       PARAMETER          ( ZERO = 0.0D+0 )
00089       INTEGER            NTYPES
00090       PARAMETER          ( NTYPES = 9 )
00091       INTEGER            NTESTS
00092       PARAMETER          ( NTESTS = 8 )
00093 *     ..
00094 *     .. Local Scalars ..
00095       LOGICAL            ZEROT
00096       CHARACTER          DIST, PACKIT, TYPE, UPLO, XTYPE
00097       CHARACTER*3        PATH
00098       INTEGER            I, IMAT, IN, INFO, IOFF, IRHS, IUPLO, IZERO, K,
00099      \$                   KL, KU, LDA, MODE, N, NERRS, NFAIL, NIMAT, NPP,
00100      \$                   NRHS, NRUN
00101       DOUBLE PRECISION   ANORM, CNDNUM, RCOND, RCONDC
00102 *     ..
00103 *     .. Local Arrays ..
00104       CHARACTER          PACKS( 2 ), UPLOS( 2 )
00105       INTEGER            ISEED( 4 ), ISEEDY( 4 )
00106       DOUBLE PRECISION   RESULT( NTESTS )
00107 *     ..
00108 *     .. External Functions ..
00109       DOUBLE PRECISION   DGET06, ZLANHP
00110       EXTERNAL           DGET06, ZLANHP
00111 *     ..
00112 *     .. External Subroutines ..
00113       EXTERNAL           ALAERH, ALAHD, ALASUM, ZCOPY, ZERRPO, ZGET04,
00114      \$                   ZLACPY, ZLAIPD, ZLARHS, ZLATB4, ZLATMS, ZPPCON,
00115      \$                   ZPPRFS, ZPPT01, ZPPT02, ZPPT03, ZPPT05, ZPPTRF,
00116      \$                   ZPPTRI, ZPPTRS
00117 *     ..
00118 *     .. Scalars in Common ..
00119       LOGICAL            LERR, OK
00120       CHARACTER*32       SRNAMT
00121       INTEGER            INFOT, NUNIT
00122 *     ..
00123 *     .. Common blocks ..
00124       COMMON             / INFOC / INFOT, NUNIT, OK, LERR
00125       COMMON             / SRNAMC / SRNAMT
00126 *     ..
00127 *     .. Intrinsic Functions ..
00128       INTRINSIC          MAX
00129 *     ..
00130 *     .. Data statements ..
00131       DATA               ISEEDY / 1988, 1989, 1990, 1991 /
00132       DATA               UPLOS / 'U', 'L' / , PACKS / 'C', 'R' /
00133 *     ..
00134 *     .. Executable Statements ..
00135 *
00136 *     Initialize constants and the random number seed.
00137 *
00138       PATH( 1: 1 ) = 'Zomplex precision'
00139       PATH( 2: 3 ) = 'PP'
00140       NRUN = 0
00141       NFAIL = 0
00142       NERRS = 0
00143       DO 10 I = 1, 4
00144          ISEED( I ) = ISEEDY( I )
00145    10 CONTINUE
00146 *
00147 *     Test the error exits
00148 *
00149       IF( TSTERR )
00150      \$   CALL ZERRPO( PATH, NOUT )
00151       INFOT = 0
00152 *
00153 *     Do for each value of N in NVAL
00154 *
00155       DO 110 IN = 1, NN
00156          N = NVAL( IN )
00157          LDA = MAX( N, 1 )
00158          XTYPE = 'N'
00159          NIMAT = NTYPES
00160          IF( N.LE.0 )
00161      \$      NIMAT = 1
00162 *
00163          DO 100 IMAT = 1, NIMAT
00164 *
00165 *           Do the tests only if DOTYPE( IMAT ) is true.
00166 *
00167             IF( .NOT.DOTYPE( IMAT ) )
00168      \$         GO TO 100
00169 *
00170 *           Skip types 3, 4, or 5 if the matrix size is too small.
00171 *
00172             ZEROT = IMAT.GE.3 .AND. IMAT.LE.5
00173             IF( ZEROT .AND. N.LT.IMAT-2 )
00174      \$         GO TO 100
00175 *
00176 *           Do first for UPLO = 'U', then for UPLO = 'L'
00177 *
00178             DO 90 IUPLO = 1, 2
00179                UPLO = UPLOS( IUPLO )
00180                PACKIT = PACKS( IUPLO )
00181 *
00182 *              Set up parameters with ZLATB4 and generate a test matrix
00183 *              with ZLATMS.
00184 *
00185                CALL ZLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE,
00186      \$                      CNDNUM, DIST )
00187 *
00188                SRNAMT = 'ZLATMS'
00189                CALL ZLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
00190      \$                      CNDNUM, ANORM, KL, KU, PACKIT, A, LDA, WORK,
00191      \$                      INFO )
00192 *
00193 *              Check error code from ZLATMS.
00194 *
00195                IF( INFO.NE.0 ) THEN
00196                   CALL ALAERH( PATH, 'ZLATMS', INFO, 0, UPLO, N, N, -1,
00197      \$                         -1, -1, IMAT, NFAIL, NERRS, NOUT )
00198                   GO TO 90
00199                END IF
00200 *
00201 *              For types 3-5, zero one row and column of the matrix to
00202 *              test that INFO is returned correctly.
00203 *
00204                IF( ZEROT ) THEN
00205                   IF( IMAT.EQ.3 ) THEN
00206                      IZERO = 1
00207                   ELSE IF( IMAT.EQ.4 ) THEN
00208                      IZERO = N
00209                   ELSE
00210                      IZERO = N / 2 + 1
00211                   END IF
00212 *
00213 *                 Set row and column IZERO of A to 0.
00214 *
00215                   IF( IUPLO.EQ.1 ) THEN
00216                      IOFF = ( IZERO-1 )*IZERO / 2
00217                      DO 20 I = 1, IZERO - 1
00218                         A( IOFF+I ) = ZERO
00219    20                CONTINUE
00220                      IOFF = IOFF + IZERO
00221                      DO 30 I = IZERO, N
00222                         A( IOFF ) = ZERO
00223                         IOFF = IOFF + I
00224    30                CONTINUE
00225                   ELSE
00226                      IOFF = IZERO
00227                      DO 40 I = 1, IZERO - 1
00228                         A( IOFF ) = ZERO
00229                         IOFF = IOFF + N - I
00230    40                CONTINUE
00231                      IOFF = IOFF - IZERO
00232                      DO 50 I = IZERO, N
00233                         A( IOFF+I ) = ZERO
00234    50                CONTINUE
00235                   END IF
00236                ELSE
00237                   IZERO = 0
00238                END IF
00239 *
00240 *              Set the imaginary part of the diagonals.
00241 *
00242                IF( IUPLO.EQ.1 ) THEN
00243                   CALL ZLAIPD( N, A, 2, 1 )
00244                ELSE
00245                   CALL ZLAIPD( N, A, N, -1 )
00246                END IF
00247 *
00248 *              Compute the L*L' or U'*U factorization of the matrix.
00249 *
00250                NPP = N*( N+1 ) / 2
00251                CALL ZCOPY( NPP, A, 1, AFAC, 1 )
00252                SRNAMT = 'ZPPTRF'
00253                CALL ZPPTRF( UPLO, N, AFAC, INFO )
00254 *
00255 *              Check error code from ZPPTRF.
00256 *
00257                IF( INFO.NE.IZERO ) THEN
00258                   CALL ALAERH( PATH, 'ZPPTRF', INFO, IZERO, UPLO, N, N,
00259      \$                         -1, -1, -1, IMAT, NFAIL, NERRS, NOUT )
00260                   GO TO 90
00261                END IF
00262 *
00263 *              Skip the tests if INFO is not 0.
00264 *
00265                IF( INFO.NE.0 )
00266      \$            GO TO 90
00267 *
00268 *+    TEST 1
00269 *              Reconstruct matrix from factors and compute residual.
00270 *
00271                CALL ZCOPY( NPP, AFAC, 1, AINV, 1 )
00272                CALL ZPPT01( UPLO, N, A, AINV, RWORK, RESULT( 1 ) )
00273 *
00274 *+    TEST 2
00275 *              Form the inverse and compute the residual.
00276 *
00277                CALL ZCOPY( NPP, AFAC, 1, AINV, 1 )
00278                SRNAMT = 'ZPPTRI'
00279                CALL ZPPTRI( UPLO, N, AINV, INFO )
00280 *
00281 *              Check error code from ZPPTRI.
00282 *
00283                IF( INFO.NE.0 )
00284      \$            CALL ALAERH( PATH, 'ZPPTRI', INFO, 0, UPLO, N, N, -1,
00285      \$                         -1, -1, IMAT, NFAIL, NERRS, NOUT )
00286 *
00287                CALL ZPPT03( UPLO, N, A, AINV, WORK, LDA, RWORK, RCONDC,
00288      \$                      RESULT( 2 ) )
00289 *
00290 *              Print information about the tests that did not pass
00291 *              the threshold.
00292 *
00293                DO 60 K = 1, 2
00294                   IF( RESULT( K ).GE.THRESH ) THEN
00295                      IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
00296      \$                  CALL ALAHD( NOUT, PATH )
00297                      WRITE( NOUT, FMT = 9999 )UPLO, N, IMAT, K,
00298      \$                  RESULT( K )
00299                      NFAIL = NFAIL + 1
00300                   END IF
00301    60          CONTINUE
00302                NRUN = NRUN + 2
00303 *
00304                DO 80 IRHS = 1, NNS
00305                   NRHS = NSVAL( IRHS )
00306 *
00307 *+    TEST 3
00308 *              Solve and compute residual for  A * X = B.
00309 *
00310                   SRNAMT = 'ZLARHS'
00311                   CALL ZLARHS( PATH, XTYPE, UPLO, ' ', N, N, KL, KU,
00312      \$                         NRHS, A, LDA, XACT, LDA, B, LDA, ISEED,
00313      \$                         INFO )
00314                   CALL ZLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
00315 *
00316                   SRNAMT = 'ZPPTRS'
00317                   CALL ZPPTRS( UPLO, N, NRHS, AFAC, X, LDA, INFO )
00318 *
00319 *              Check error code from ZPPTRS.
00320 *
00321                   IF( INFO.NE.0 )
00322      \$               CALL ALAERH( PATH, 'ZPPTRS', INFO, 0, UPLO, N, N,
00323      \$                            -1, -1, NRHS, IMAT, NFAIL, NERRS,
00324      \$                            NOUT )
00325 *
00326                   CALL ZLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
00327                   CALL ZPPT02( UPLO, N, NRHS, A, X, LDA, WORK, LDA,
00328      \$                         RWORK, RESULT( 3 ) )
00329 *
00330 *+    TEST 4
00331 *              Check solution from generated exact solution.
00332 *
00333                   CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
00334      \$                         RESULT( 4 ) )
00335 *
00336 *+    TESTS 5, 6, and 7
00337 *              Use iterative refinement to improve the solution.
00338 *
00339                   SRNAMT = 'ZPPRFS'
00340                   CALL ZPPRFS( UPLO, N, NRHS, A, AFAC, B, LDA, X, LDA,
00341      \$                         RWORK, RWORK( NRHS+1 ), WORK,
00342      \$                         RWORK( 2*NRHS+1 ), INFO )
00343 *
00344 *              Check error code from ZPPRFS.
00345 *
00346                   IF( INFO.NE.0 )
00347      \$               CALL ALAERH( PATH, 'ZPPRFS', INFO, 0, UPLO, N, N,
00348      \$                            -1, -1, NRHS, IMAT, NFAIL, NERRS,
00349      \$                            NOUT )
00350 *
00351                   CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
00352      \$                         RESULT( 5 ) )
00353                   CALL ZPPT05( UPLO, N, NRHS, A, B, LDA, X, LDA, XACT,
00354      \$                         LDA, RWORK, RWORK( NRHS+1 ),
00355      \$                         RESULT( 6 ) )
00356 *
00357 *                 Print information about the tests that did not pass
00358 *                 the threshold.
00359 *
00360                   DO 70 K = 3, 7
00361                      IF( RESULT( K ).GE.THRESH ) THEN
00362                         IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
00363      \$                     CALL ALAHD( NOUT, PATH )
00364                         WRITE( NOUT, FMT = 9998 )UPLO, N, NRHS, IMAT,
00365      \$                     K, RESULT( K )
00366                         NFAIL = NFAIL + 1
00367                      END IF
00368    70             CONTINUE
00369                   NRUN = NRUN + 5
00370    80          CONTINUE
00371 *
00372 *+    TEST 8
00373 *              Get an estimate of RCOND = 1/CNDNUM.
00374 *
00375                ANORM = ZLANHP( '1', UPLO, N, A, RWORK )
00376                SRNAMT = 'ZPPCON'
00377                CALL ZPPCON( UPLO, N, AFAC, ANORM, RCOND, WORK, RWORK,
00378      \$                      INFO )
00379 *
00380 *              Check error code from ZPPCON.
00381 *
00382                IF( INFO.NE.0 )
00383      \$            CALL ALAERH( PATH, 'ZPPCON', INFO, 0, UPLO, N, N, -1,
00384      \$                         -1, -1, IMAT, NFAIL, NERRS, NOUT )
00385 *
00386                RESULT( 8 ) = DGET06( RCOND, RCONDC )
00387 *
00388 *              Print the test ratio if greater than or equal to THRESH.
00389 *
00390                IF( RESULT( 8 ).GE.THRESH ) THEN
00391                   IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
00392      \$               CALL ALAHD( NOUT, PATH )
00393                   WRITE( NOUT, FMT = 9999 )UPLO, N, IMAT, 8,
00394      \$               RESULT( 8 )
00395                   NFAIL = NFAIL + 1
00396                END IF
00397                NRUN = NRUN + 1
00398 *
00399    90       CONTINUE
00400   100    CONTINUE
00401   110 CONTINUE
00402 *
00403 *     Print a summary of the results.
00404 *
00405       CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
00406 *
00407  9999 FORMAT( ' UPLO = ''', A1, ''', N =', I5, ', type ', I2, ', test ',
00408      \$      I2, ', ratio =', G12.5 )
00409  9998 FORMAT( ' UPLO = ''', A1, ''', N =', I5, ', NRHS=', I3, ', type ',
00410      \$      I2, ', test(', I2, ') =', G12.5 )
00411       RETURN
00412 *
00413 *     End of ZCHKPP
00414 *
00415       END
```