dchksp.f

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*> \brief \b DCHKSP
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE DCHKSP( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
*                          NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK,
*                          IWORK, NOUT )
*
*       .. Scalar Arguments ..
*       LOGICAL            TSTERR
*       INTEGER            NMAX, NN, NNS, NOUT
*       DOUBLE PRECISION   THRESH
*       ..
*       .. Array Arguments ..
*       LOGICAL            DOTYPE( * )
*       INTEGER            IWORK( * ), NSVAL( * ), NVAL( * )
*       DOUBLE PRECISION   A( * ), AFAC( * ), AINV( * ), B( * ),
*      $                   RWORK( * ), WORK( * ), X( * ), XACT( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DCHKSP tests DSPTRF, -TRI, -TRS, -RFS, and -CON
*> \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] NNS
*> \verbatim
*>          NNS is INTEGER
*>          The number of values of NRHS contained in the vector NSVAL.
*> \endverbatim
*>
*> \param[in] NSVAL
*> \verbatim
*>          NSVAL is INTEGER array, dimension (NNS)
*>          The values of the number of right hand sides NRHS.
*> \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 DOUBLE PRECISION array, dimension
*>                      (NMAX*(NMAX+1)/2)
*> \endverbatim
*>
*> \param[out] AFAC
*> \verbatim
*>          AFAC is DOUBLE PRECISION array, dimension
*>                      (NMAX*(NMAX+1)/2)
*> \endverbatim
*>
*> \param[out] AINV
*> \verbatim
*>          AINV is DOUBLE PRECISION array, dimension
*>                      (NMAX*(NMAX+1)/2)
*> \endverbatim
*>
*> \param[out] B
*> \verbatim
*>          B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
*>          where NSMAX is the largest entry in NSVAL.
*> \endverbatim
*>
*> \param[out] X
*> \verbatim
*>          X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
*> \endverbatim
*>
*> \param[out] XACT
*> \verbatim
*>          XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is DOUBLE PRECISION array, dimension
*>                      (NMAX*max(2,NSMAX))
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*>          RWORK is DOUBLE PRECISION array,
*>                                 dimension (NMAX+2*NSMAX)
*> \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 dchksp( DOTYPE, NN, NVAL, NNS, NSVAL, 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, NNS, NOUT
      DOUBLE PRECISION   THRESH
*     ..
*     .. Array Arguments ..
      LOGICAL            DOTYPE( * )
      INTEGER            IWORK( * ), NSVAL( * ), NVAL( * )
      DOUBLE PRECISION   A( * ), AFAC( * ), AINV( * ), B( * ),
     $                   rwork( * ), work( * ), x( * ), xact( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO
      PARAMETER          ( ZERO = 0.0d+0 )
      INTEGER            NTYPES
      parameter( ntypes = 10 )
      INTEGER            NTESTS
      parameter( ntests = 8 )
*     ..
*     .. Local Scalars ..
      LOGICAL            TRFCON, ZEROT
      CHARACTER          DIST, PACKIT, TYPE, UPLO, XTYPE
      CHARACTER*3        PATH
      INTEGER            I, I1, I2, IMAT, IN, INFO, IOFF, IRHS, IUPLO,
     $                   izero, j, k, kl, ku, lda, mode, n, nerrs,
     $                   nfail, nimat, npp, nrhs, nrun, nt
      DOUBLE PRECISION   ANORM, CNDNUM, RCOND, RCONDC
*     ..
*     .. Local Arrays ..
      CHARACTER          UPLOS( 2 )
      INTEGER            ISEED( 4 ), ISEEDY( 4 )
      DOUBLE PRECISION   RESULT( NTESTS )
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      DOUBLE PRECISION   DGET06, DLANSP
      EXTERNAL           lsame, dget06, dlansp
*     ..
*     .. External Subroutines ..
      EXTERNAL           alaerh, alahd, alasum, dcopy, derrsy, dget04,
     $                   dlacpy, dlarhs, dlatb4, dlatms, dppt02, dppt03,
     $                   dppt05, dspcon, dsprfs, dspt01, dsptrf, dsptri,
     $                   dsptrs
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max, min
*     ..
*     .. Scalars in Common ..
      LOGICAL            LERR, OK
      CHARACTER*32       SRNAMT
      INTEGER            INFOT, NUNIT
*     ..
*     .. Common blocks ..
      COMMON             / infoc / infot, nunit, ok, lerr
      COMMON             / srnamc / srnamt
*     ..
*     .. Data statements ..
      DATA               iseedy / 1988, 1989, 1990, 1991 /
      DATA               uplos / 'U', 'L' /
*     ..
*     .. Executable Statements ..
*
*     Initialize constants and the random number seed.
*
      path( 1: 1 ) = 'Double precision'
      path( 2: 3 ) = 'SP'
      nrun = 0
      nfail = 0
      nerrs = 0
      DO 10 i = 1, 4
         iseed( i ) = iseedy( i )
   10 CONTINUE
*
*     Test the error exits
*
      IF( tsterr )
     $   CALL derrsy( path, nout )
      infot = 0
*
*     Do for each value of N in NVAL
*
      DO 170 in = 1, nn
         n = nval( in )
         lda = max( n, 1 )
         xtype = 'N'
         nimat = ntypes
         IF( n.LE.0 )
     $      nimat = 1
*
         izero = 0
         DO 160 imat = 1, nimat
*
*           Do the tests only if DOTYPE( IMAT ) is true.
*
            IF( .NOT.dotype( imat ) )
     $         GO TO 160
*
*           Skip types 3, 4, 5, or 6 if the matrix size is too small.
*
            zerot = imat.GE.3 .AND. imat.LE.6
            IF( zerot .AND. n.LT.imat-2 )
     $         GO TO 160
*
*           Do first for UPLO = 'U', then for UPLO = 'L'
*
            DO 150 iuplo = 1, 2
               uplo = uplos( iuplo )
               IF( lsame( uplo, 'U' ) ) THEN
                  packit = 'C'
               ELSE
                  packit = 'R'
               END IF
*
*              Set up parameters with DLATB4 and generate a test matrix
*              with DLATMS.
*
               CALL dlatb4( path, imat, n, n, TYPE, KL, ku, anorm, mode,
     $                      cndnum, dist )
*
               srnamt = 'dlatms'
               CALL DLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
     $                      CNDNUM, ANORM, KL, KU, PACKIT, A, LDA, WORK,
     $                      INFO )
*
*              Check error code from DLATMS.
*
.NE.               IF( INFO0 ) THEN
                  CALL ALAERH( PATH, 'dlatms', INFO, 0, UPLO, N, N, -1,
     $                         -1, -1, IMAT, NFAIL, NERRS, NOUT )
                  GO TO 150
               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 )*IZERO / 2
                        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 + I
   30                   CONTINUE
                     ELSE
                        IOFF = IZERO
                        DO 40 I = 1, IZERO - 1
                           A( IOFF ) = ZERO
                           IOFF = IOFF + N - I
   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 + J
   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 + N - J
   90                   CONTINUE
                     END IF
                  END IF
               ELSE
                  IZERO = 0
               END IF
*
*              Compute the L*D*L' or U*D*U' factorization of the matrix.
*
               NPP = N*( N+1 ) / 2
               CALL DCOPY( NPP, A, 1, AFAC, 1 )
               SRNAMT = 'dsptrf'
               CALL DSPTRF( UPLO, N, AFAC, IWORK, 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 DSPTRF.
*
.NE.               IF( INFOK )
     $            CALL ALAERH( PATH, 'dsptrf', INFO, K, UPLO, N, N, -1,
     $                         -1, -1, IMAT, NFAIL, NERRS, NOUT )
.NE.               IF( INFO0 ) THEN
                  TRFCON = .TRUE.
               ELSE
                  TRFCON = .FALSE.
               END IF
*
*+    TEST 1
*              Reconstruct matrix from factors and compute residual.
*
               CALL DSPT01( UPLO, N, A, AFAC, IWORK, AINV, LDA, RWORK,
     $                      RESULT( 1 ) )
               NT = 1
*
*+    TEST 2
*              Form the inverse and compute the residual.
*
.NOT.               IF( TRFCON ) THEN
                  CALL DCOPY( NPP, AFAC, 1, AINV, 1 )
                  SRNAMT = 'dsptri'
                  CALL DSPTRI( UPLO, N, AINV, IWORK, WORK, INFO )
*
*              Check error code from DSPTRI.
*
.NE.                  IF( INFO0 )
     $               CALL ALAERH( PATH, 'dsptri', INFO, 0, UPLO, N, N,
     $                            -1, -1, -1, IMAT, NFAIL, NERRS, NOUT )
*
                  CALL DPPT03( UPLO, N, A, AINV, WORK, LDA, RWORK,
     $                         RCONDC, RESULT( 2 ) )
                  NT = 2
               END IF
*
*              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 ALAHD( NOUT, PATH )
                     WRITE( NOUT, FMT = 9999 )UPLO, N, IMAT, K,
     $                  RESULT( K )
                     NFAIL = NFAIL + 1
                  END IF
  110          CONTINUE
               NRUN = NRUN + NT
*
*              Do only the condition estimate if INFO is not 0.
*
               IF( TRFCON ) THEN
                  RCONDC = ZERO
                  GO TO 140
               END IF
*
               DO 130 IRHS = 1, NNS
                  NRHS = NSVAL( IRHS )
*
*+    TEST 3
*              Solve and compute residual for  A * X = B.
*
                  SRNAMT = 'dlarhs'
                  CALL DLARHS( PATH, XTYPE, UPLO, ' ', N, N, KL, KU,
     $                         NRHS, A, LDA, XACT, LDA, B, LDA, ISEED,
     $                         INFO )
                  CALL DLACPY( 'full', N, NRHS, B, LDA, X, LDA )
*
                  SRNAMT = 'dsptrs'
                  CALL DSPTRS( UPLO, N, NRHS, AFAC, IWORK, X, LDA,
     $                         INFO )
*
*              Check error code from DSPTRS.
*
.NE.                  IF( INFO0 )
     $               CALL ALAERH( PATH, 'dsptrs', INFO, 0, UPLO, N, N,
     $                            -1, -1, NRHS, IMAT, NFAIL, NERRS,
     $                            NOUT )
*
                  CALL DLACPY( 'full', n, nrhs, b, lda, work, lda )
                  CALL dppt02( uplo, n, nrhs, a, x, lda, work, lda,
     $                         rwork, result( 3 ) )
*
*+    TEST 4
*              Check solution from generated exact solution.
*
                  CALL dget04( n, nrhs, x, lda, xact, lda, rcondc,
     $                         result( 4 ) )
*
*+    TESTS 5, 6, and 7
*              Use iterative refinement to improve the solution.
*
                  srnamt = 'DSPRFS'
                  CALL dsprfs( uplo, n, nrhs, a, afac, iwork, b, lda, x,
     $                         lda, rwork, rwork( nrhs+1 ), work,
     $                         iwork( n+1 ), info )
*
*              Check error code from DSPRFS.
*
                  IF( info.NE.0 )
     $               CALL alaerh( path, 'DSPRFS', info, 0, uplo, n, n,
     $                            -1, -1, nrhs, imat, nfail, nerrs,
     $                            nout )
*
                  CALL dget04( n, nrhs, x, lda, xact, lda, rcondc,
     $                         result( 5 ) )
                  CALL dppt05( uplo, n, nrhs, a, b, lda, x, lda, xact,
     $                         lda, rwork, rwork( nrhs+1 ),
     $                         result( 6 ) )
*
*                 Print information about the tests that did not pass
*                 the threshold.
*
                  DO 120 k = 3, 7
                     IF( result( k ).GE.thresh ) THEN
                        IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
     $                     CALL alahd( nout, path )
                        WRITE( nout, fmt = 9998 )uplo, n, nrhs, imat,
     $                     k, result( k )
                        nfail = nfail + 1
                     END IF
  120             CONTINUE
                  nrun = nrun + 5
  130          CONTINUE
*
*+    TEST 8
*              Get an estimate of RCOND = 1/CNDNUM.
*
  140          CONTINUE
               anorm = dlansp( '1', uplo, n, a, rwork )
               srnamt = 'DSPCON'
               CALL dspcon( uplo, n, afac, iwork, anorm, rcond, work,
     $                      iwork( n+1 ), info )
*
*              Check error code from DSPCON.
*
               IF( info.NE.0 )
     $            CALL alaerh( path, 'DSPCON', info, 0, uplo, n, n, -1,
     $                         -1, -1, imat, nfail, nerrs, nout )
*
               result( 8 ) = dget06( rcond, rcondc )
*
*              Print the test ratio if it is .GE. THRESH.
*
               IF( result( 8 ).GE.thresh ) THEN
                  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
     $               CALL alahd( nout, path )
                  WRITE( nout, fmt = 9999 )uplo, n, imat, 8,
     $               result( 8 )
                  nfail = nfail + 1
               END IF
               nrun = nrun + 1
  150       CONTINUE
  160    CONTINUE
  170 CONTINUE
*
*     Print a summary of the results.
*
      CALL alasum( path, nout, nfail, nrun, nerrs )
*
 9999 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', type ', i2, ', test ',
     $      i2, ', ratio =', g12.5 )
 9998 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', NRHS=', i3, ', type ',
     $      i2, ', test(', i2, ') =', g12.5 )
      RETURN
*
*     End of DCHKSP
*
      END