sdrvsy_rook.f

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*> \brief \b SDRVSY_ROOK
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*     SUBROUTINE SDRVSY_ROOK( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR,
*    $                        NMAX, A, AFAC, AINV, B, X, XACT, WORK,
*    $                        RWORK, IWORK, NOUT )
*
*       .. Scalar Arguments ..
*       LOGICAL            TSTERR
*       INTEGER            NMAX, NN, NOUT, NRHS
*       REAL               THRESH
*       ..
*       .. Array Arguments ..
*       LOGICAL            DOTYPE( * )
*       INTEGER            IWORK( * ), NVAL( * )
*       REAL               A( * ), AFAC( * ), AINV( * ), B( * ),
*      $                   RWORK( * ), WORK( * ), X( * ), XACT( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> SDRVSY_ROOK tests the driver routines SSYSV_ROOK.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] DOTYPE
*> \verbatim
*>          DOTYPE is LOGICAL array, dimension (NTYPES)
*>          The matrix types to be used for testing.  Matrices of type j
*>          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
*>          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
*> \endverbatim
*>
*> \param[in] NN
*> \verbatim
*>          NN is INTEGER
*>          The number of values of N contained in the vector NVAL.
*> \endverbatim
*>
*> \param[in] NVAL
*> \verbatim
*>          NVAL is INTEGER array, dimension (NN)
*>          The values of the matrix dimension N.
*> \endverbatim
*>
*> \param[in] NRHS
*> \verbatim
*>          NRHS is INTEGER
*>          The number of right hand side vectors to be generated for
*>          each linear system.
*> \endverbatim
*>
*> \param[in] THRESH
*> \verbatim
*>          THRESH is DOUBLE PRECISION
*>          The threshold value for the test ratios.  A result is
*>          included in the output file if RESULT >= THRESH.  To have
*>          every test ratio printed, use THRESH = 0.
*> \endverbatim
*>
*> \param[in] TSTERR
*> \verbatim
*>          TSTERR is LOGICAL
*>          Flag that indicates whether error exits are to be tested.
*> \endverbatim
*>
*> \param[in] NMAX
*> \verbatim
*>          NMAX is INTEGER
*>          The maximum value permitted for N, used in dimensioning the
*>          work arrays.
*> \endverbatim
*>
*> \param[out] A
*> \verbatim
*>          A is REAL array, dimension (NMAX*NMAX)
*> \endverbatim
*>
*> \param[out] AFAC
*> \verbatim
*>          AFAC is REAL array, dimension (NMAX*NMAX)
*> \endverbatim
*>
*> \param[out] AINV
*> \verbatim
*>          AINV is REAL array, dimension (NMAX*NMAX)
*> \endverbatim
*>
*> \param[out] B
*> \verbatim
*>          B is REAL array, dimension (NMAX*NRHS)
*> \endverbatim
*>
*> \param[out] X
*> \verbatim
*>          X is REAL array, dimension (NMAX*NRHS)
*> \endverbatim
*>
*> \param[out] XACT
*> \verbatim
*>          XACT is REAL array, dimension (NMAX*NRHS)
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is REAL array, dimension
*>                      (NMAX*max(2,NRHS))
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*>          RWORK is REAL array, dimension (NMAX+2*NRHS)
*> \endverbatim
*>
*> \param[out] IWORK
*> \verbatim
*>          IWORK is INTEGER array, dimension (2*NMAX)
*> \endverbatim
*>
*> \param[in] NOUT
*> \verbatim
*>          NOUT is INTEGER
*>          The unit number for output.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup double_lin
*
*  =====================================================================
      SUBROUTINE sdrvsy_rook( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR,
     $                        NMAX, A, AFAC, AINV, B, X, XACT, WORK,
     $                        RWORK, IWORK, NOUT )
*
*  -- LAPACK test routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      LOGICAL            TSTERR
      INTEGER            NMAX, NN, NOUT, NRHS
      REAL               THRESH
*     ..
*     .. Array Arguments ..
      LOGICAL            DOTYPE( * )
      INTEGER            IWORK( * ), NVAL( * )
      REAL               A( * ), AFAC( * ), AINV( * ), B( * ),
     $                   rwork( * ), work( * ), x( * ), xact( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ONE, ZERO
      PARAMETER          ( ONE = 1.0e+0, zero = 0.0e+0 )
      INTEGER            NTYPES, NTESTS
      parameter( ntypes = 10, ntests = 3 )
      INTEGER            NFACT
      parameter( nfact = 2 )
*     ..
*     .. Local Scalars ..
      LOGICAL            ZEROT
      CHARACTER          DIST, FACT, TYPE, UPLO, XTYPE
      CHARACTER*3        PATH, MATPATH
      INTEGER            I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
     $                   izero, j, k, kl, ku, lda, lwork, mode, n,
     $                   nb, nbmin, nerrs, nfail, nimat, nrun, nt
      REAL               AINVNM, ANORM, CNDNUM, RCONDC
*     ..
*     .. Local Arrays ..
      CHARACTER          FACTS( NFACT ), UPLOS( 2 )
      INTEGER            ISEED( 4 ), ISEEDY( 4 )
      REAL               RESULT( NTESTS )
*     ..
*     .. External Functions ..
      REAL               SLANSY
      EXTERNAL           SLANSY
*     ..
*     .. External Subroutines ..
      EXTERNAL           aladhd, alaerh, alasvm, serrvx, sget04, slacpy,
     $                   slarhs, slaset, slatb4, slatms, spot02, spot05,
     $                   ssysv_rook, ssyt01_rook, ssytrf_rook,
     $                   ssytri_rook,
     $                   xlaenv
*     ..
*     .. Scalars in Common ..
      LOGICAL            LERR, OK
      CHARACTER*32       SRNAMT
      INTEGER            INFOT, NUNIT
*     ..
*     .. Common blocks ..
      COMMON             / infoc / infot, nunit, ok, lerr
      COMMON             / srnamc / srnamt
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max, min
*     ..
*     .. Data statements ..
      DATA               iseedy / 1988, 1989, 1990, 1991 /
      DATA               uplos / 'u', 'l' / , FACTS / 'f', 'n' /
*     ..
*     .. Executable Statements ..
*
*     Initialize constants and the random number seed.
*
*     Test path
*
      PATH( 1: 1 ) = 'single precision'
      PATH( 2: 3 ) = 'sr'
*
*     Path to generate matrices
*
      MATPATH( 1: 1 ) = 'single precision'
      MATPATH( 2: 3 ) = 'sy'
*
      NRUN = 0
      NFAIL = 0
      NERRS = 0
      DO 10 I = 1, 4
         ISEED( I ) = ISEEDY( I )
   10 CONTINUE
      LWORK = MAX( 2*NMAX, NMAX*NRHS )
*
*     Test the error exits
*
      IF( TSTERR )
     $   CALL SERRVX( PATH, NOUT )
      INFOT = 0
*
*     Set the block size and minimum block size for which the block
*     routine should be used, which will be later returned by ILAENV.
*
      NB = 1
      NBMIN = 2
      CALL XLAENV( 1, NB )
      CALL XLAENV( 2, NBMIN )
*
*     Do for each value of N in NVAL
*
      DO 180 IN = 1, NN
         N = NVAL( IN )
         LDA = MAX( N, 1 )
         XTYPE = 'n'
         NIMAT = NTYPES
.LE.         IF( N0 )
     $      NIMAT = 1
*
         DO 170 IMAT = 1, NIMAT
*
*           Do the tests only if DOTYPE( IMAT ) is true.
*
.NOT.            IF( DOTYPE( IMAT ) )
     $         GO TO 170
*
*           Skip types 3, 4, 5, or 6 if the matrix size is too small.
*
.GE..AND..LE.            ZEROT = IMAT3  IMAT6
.AND..LT.            IF( ZEROT  NIMAT-2 )
     $         GO TO 170
*
*           Do first for UPLO = 'U', then for UPLO = 'L'
*
            DO 160 IUPLO = 1, 2
               UPLO = UPLOS( IUPLO )
*
*              Begin generate the test matrix A.
*
*              Set up parameters with SLATB4 for the matrix generator
*              based on the type of matrix to be generated.
*
               CALL SLATB4( MATPATH, IMAT, N, N, TYPE, KL, KU, ANORM,
     $                      MODE, CNDNUM, DIST )
*
*              Generate a matrix with SLATMS.
*
               SRNAMT = 'slatms'
               CALL SLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
     $                      CNDNUM, ANORM, KL, KU, UPLO, A, LDA, WORK,
     $                      INFO )
*
*              Check error code from SLATMS and handle error.
*
.NE.               IF( INFO0 ) THEN
                  CALL ALAERH( PATH, 'slatms', INFO, 0, UPLO, N, N, -1,
     $                         -1, -1, IMAT, NFAIL, NERRS, NOUT )
*
*                 Skip all tests for this generated matrix
*
                  GO TO 160
               END IF
*
*              For types 3-6, zero one or more rows and columns of the
*              matrix to test that INFO is returned correctly.
*
               IF( ZEROT ) THEN
.EQ.                  IF( IMAT3 ) THEN
                     IZERO = 1
.EQ.                  ELSE IF( IMAT4 ) THEN
                     IZERO = N
                  ELSE
                     IZERO = N / 2 + 1
                  END IF
*
.LT.                  IF( IMAT6 ) THEN
*
*                    Set row and column IZERO to zero.
*
.EQ.                     IF( IUPLO1 ) THEN
                        IOFF = ( IZERO-1 )*LDA
                        DO 20 I = 1, IZERO - 1
                           A( IOFF+I ) = ZERO
   20                   CONTINUE
                        IOFF = IOFF + IZERO
                        DO 30 I = IZERO, N
                           A( IOFF ) = ZERO
                           IOFF = IOFF + LDA
   30                   CONTINUE
                     ELSE
                        IOFF = IZERO
                        DO 40 I = 1, IZERO - 1
                           A( IOFF ) = ZERO
                           IOFF = IOFF + LDA
   40                   CONTINUE
                        IOFF = IOFF - IZERO
                        DO 50 I = IZERO, N
                           A( IOFF+I ) = ZERO
   50                   CONTINUE
                     END IF
                  ELSE
                     IOFF = 0
.EQ.                     IF( IUPLO1 ) THEN
*
*                       Set the first IZERO rows and columns to zero.
*
                        DO 70 J = 1, N
                           I2 = MIN( J, IZERO )
                           DO 60 I = 1, I2
                              A( IOFF+I ) = ZERO
   60                      CONTINUE
                           IOFF = IOFF + LDA
   70                   CONTINUE
                     ELSE
*
*                       Set the last IZERO rows and columns to zero.
*
                        DO 90 J = 1, N
                           I1 = MAX( J, IZERO )
                           DO 80 I = I1, N
                              A( IOFF+I ) = ZERO
   80                      CONTINUE
                           IOFF = IOFF + LDA
   90                   CONTINUE
                     END IF
                  END IF
               ELSE
                  IZERO = 0
               END IF
*
*              End generate the test matrix A.
*
               DO 150 IFACT = 1, NFACT
*
*                 Do first for FACT = 'F', then for other values.
*
                  FACT = FACTS( IFACT )
*
*                 Compute the condition number for comparison with
*                 the value returned by DSYSVX_ROOK.
*
                  IF( ZEROT ) THEN
.EQ.                     IF( IFACT1 )
     $                  GO TO 150
                     RCONDC = ZERO
*
.EQ.                  ELSE IF( IFACT1 ) THEN
*
*                    Compute the 1-norm of A.
*
                     ANORM = SLANSY( '1', UPLO, N, A, LDA, RWORK )
*
*                    Factor the matrix A.
*
                     CALL SLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
                     CALL SSYTRF_ROOK( UPLO, N, AFAC, LDA, IWORK, WORK,
     $                            LWORK, INFO )
*
*                    Compute inv(A) and take its norm.
*
                     CALL SLACPY( UPLO, N, N, AFAC, LDA, AINV, LDA )
                     LWORK = (N+NB+1)*(NB+3)
                     CALL SSYTRI_ROOK( UPLO, N, AINV, LDA, IWORK,
     $                                 WORK, INFO )
                     AINVNM = SLANSY( '1', UPLO, N, AINV, LDA, RWORK )
*
*                    Compute the 1-norm condition number of A.
*
.LE..OR..LE.                     IF( ANORMZERO  AINVNMZERO ) THEN
                        RCONDC = ONE
                     ELSE
                        RCONDC = ( ONE / ANORM ) / AINVNM
                     END IF
                  END IF
*
*                 Form an exact solution and set the right hand side.
*
                  SRNAMT = 'slarhs'
                  CALL SLARHS( MATPATH, XTYPE, UPLO, ' ', N, N, KL, KU,
     $                         NRHS, A, LDA, XACT, LDA, B, LDA, ISEED,
     $                         INFO )
                  XTYPE = 'c'
*
*                 --- Test SSYSV_ROOK  ---
*
.EQ.                  IF( IFACT2 ) THEN
                     CALL SLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
                     CALL SLACPY( 'full', N, NRHS, B, LDA, X, LDA )
*
*                    Factor the matrix and solve the system using
*                    SSYSV_ROOK.
*
                     SRNAMT = 'ssysv_rook'
                     CALL SSYSV_ROOK( UPLO, N, NRHS, AFAC, LDA, IWORK,
     $                                X, LDA, WORK, LWORK, INFO )
*
*                    Adjust the expected value of INFO to account for
*                    pivoting.
*
                     K = IZERO
.GT.                     IF( K0 ) THEN
  100                   CONTINUE
.LT.                        IF( IWORK( K )0 ) THEN
.NE.                           IF( IWORK( K )-K ) THEN
                              K = -IWORK( K )
                              GO TO 100
                           END IF
.NE.                        ELSE IF( IWORK( K )K ) THEN
                           K = IWORK( K )
                           GO TO 100
                        END IF
                     END IF
*
*                    Check error code from SSYSV_ROOK and handle error.
*
.NE.                     IF( INFOK ) THEN
                        CALL ALAERH( PATH, 'ssysv_rook', INFO, K, UPLO,
     $                               N, N, -1, -1, NRHS, IMAT, NFAIL,
     $                               NERRS, NOUT )
                        GO TO 120
.NE.                     ELSE IF( INFO0 ) THEN
                        GO TO 120
                     END IF
*
*+    TEST 1      Reconstruct matrix from factors and compute
*                 residual.
*
                     CALL SSYT01_ROOK( UPLO, N, A, LDA, AFAC, LDA,
     $                                 IWORK, AINV, LDA, RWORK,
     $                                 RESULT( 1 ) )
*
*+    TEST 2      Compute residual of the computed solution.
*
                     CALL SLACPY( 'full', N, NRHS, B, LDA, WORK, LDA )
                     CALL SPOT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
     $                            LDA, RWORK, RESULT( 2 ) )
*
*+    TEST 3
*                 Check solution from generated exact solution.
*
                     CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
     $                            RESULT( 3 ) )
                     NT = 3
*
*                    Print information about the tests that did not pass
*                    the threshold.
*
                     DO 110 K = 1, NT
.GE.                        IF( RESULT( K )THRESH ) THEN
.EQ..AND..EQ.                           IF( NFAIL0  NERRS0 )
     $                        CALL ALADHD( NOUT, PATH )
                           WRITE( NOUT, FMT = 9999 )'ssysv_rook', UPLO,
     $                           N, IMAT, K, RESULT( K )
                           NFAIL = NFAIL + 1
                        END IF
  110                CONTINUE
                     NRUN = NRUN + NT
  120                CONTINUE
                  END IF
*
  150          CONTINUE
*
  160       CONTINUE
  170    CONTINUE
  180 CONTINUE
*
*     Print a summary of the results.
*
      CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
*
 9999 FORMAT( 1X, A, ', uplo=''', A1, ''', n =', I5, ', type ', I2,
     $      ', test ', I2, ', ratio =', G12.5 )
      RETURN
*
*     End of SDRVSY_ROOK
*
      END