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|
*> \brief \b DDRVPT
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DDRVPT( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, D,
* E, B, X, XACT, WORK, RWORK, NOUT )
*
* .. Scalar Arguments ..
* LOGICAL TSTERR
* INTEGER NN, NOUT, NRHS
* DOUBLE PRECISION THRESH
* ..
* .. Array Arguments ..
* LOGICAL DOTYPE( * )
* INTEGER NVAL( * )
* DOUBLE PRECISION A( * ), B( * ), D( * ), E( * ), RWORK( * ),
* $ WORK( * ), X( * ), XACT( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DDRVPT tests DPTSV and -SVX.
*> \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[out] A
*> \verbatim
*> A is DOUBLE PRECISION array, dimension (NMAX*2)
*> \endverbatim
*>
*> \param[out] D
*> \verbatim
*> D is DOUBLE PRECISION array, dimension (NMAX*2)
*> \endverbatim
*>
*> \param[out] E
*> \verbatim
*> E is DOUBLE PRECISION array, dimension (NMAX*2)
*> \endverbatim
*>
*> \param[out] B
*> \verbatim
*> B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
*> \endverbatim
*>
*> \param[out] X
*> \verbatim
*> X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
*> \endverbatim
*>
*> \param[out] XACT
*> \verbatim
*> XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension
*> (NMAX*max(3,NRHS))
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is DOUBLE PRECISION array, dimension
*> (max(NMAX,2*NRHS))
*> \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.
*
*> \date November 2011
*
*> \ingroup double_lin
*
* =====================================================================
SUBROUTINE DDRVPT( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, D,
$ E, B, X, XACT, WORK, RWORK, NOUT )
*
* -- LAPACK test routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
LOGICAL TSTERR
INTEGER NN, NOUT, NRHS
DOUBLE PRECISION THRESH
* ..
* .. Array Arguments ..
LOGICAL DOTYPE( * )
INTEGER NVAL( * )
DOUBLE PRECISION A( * ), B( * ), D( * ), E( * ), RWORK( * ),
$ WORK( * ), X( * ), XACT( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
INTEGER NTYPES
PARAMETER ( NTYPES = 12 )
INTEGER NTESTS
PARAMETER ( NTESTS = 6 )
* ..
* .. Local Scalars ..
LOGICAL ZEROT
CHARACTER DIST, FACT, TYPE
CHARACTER*3 PATH
INTEGER I, IA, IFACT, IMAT, IN, INFO, IX, IZERO, J, K,
$ K1, KL, KU, LDA, MODE, N, NERRS, NFAIL, NIMAT,
$ NRUN, NT
DOUBLE PRECISION AINVNM, ANORM, COND, DMAX, RCOND, RCONDC
* ..
* .. Local Arrays ..
INTEGER ISEED( 4 ), ISEEDY( 4 )
DOUBLE PRECISION RESULT( NTESTS ), Z( 3 )
* ..
* .. External Functions ..
INTEGER IDAMAX
DOUBLE PRECISION DASUM, DGET06, DLANST
EXTERNAL IDAMAX, DASUM, DGET06, DLANST
* ..
* .. External Subroutines ..
EXTERNAL ALADHD, ALAERH, ALASVM, DCOPY, DERRVX, DGET04,
$ DLACPY, DLAPTM, DLARNV, DLASET, DLATB4, DLATMS,
$ DPTSV, DPTSVX, DPTT01, DPTT02, DPTT05, DPTTRF,
$ DPTTRS, DSCAL
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX
* ..
* .. 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 / 0, 0, 0, 1 /
* ..
* .. Executable Statements ..
*
PATH( 1: 1 ) = 'Double precision'
PATH( 2: 3 ) = 'PT'
NRUN = 0
NFAIL = 0
NERRS = 0
DO 10 I = 1, 4
ISEED( I ) = ISEEDY( I )
10 CONTINUE
*
* Test the error exits
*
IF( TSTERR )
$ CALL DERRVX( PATH, NOUT )
INFOT = 0
*
DO 120 IN = 1, NN
*
* Do for each value of N in NVAL.
*
N = NVAL( IN )
LDA = MAX( 1, N )
NIMAT = NTYPES
IF( N.LE.0 )
$ NIMAT = 1
*
DO 110 IMAT = 1, NIMAT
*
* Do the tests only if DOTYPE( IMAT ) is true.
*
IF( N.GT.0 .AND. .NOT.DOTYPE( IMAT ) )
$ GO TO 110
*
* Set up parameters with DLATB4.
*
CALL DLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE,
$ COND, DIST )
*
ZEROT = IMAT.GE.8 .AND. IMAT.LE.10
IF( IMAT.LE.6 ) THEN
*
* Type 1-6: generate a symmetric tridiagonal matrix of
* known condition number in lower triangular band storage.
*
SRNAMT = 'DLATMS'
CALL DLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE, COND,
$ ANORM, KL, KU, 'B', A, 2, WORK, INFO )
*
* Check the error code from DLATMS.
*
IF( INFO.NE.0 ) THEN
CALL ALAERH( PATH, 'DLATMS', INFO, 0, ' ', N, N, KL,
$ KU, -1, IMAT, NFAIL, NERRS, NOUT )
GO TO 110
END IF
IZERO = 0
*
* Copy the matrix to D and E.
*
IA = 1
DO 20 I = 1, N - 1
D( I ) = A( IA )
E( I ) = A( IA+1 )
IA = IA + 2
20 CONTINUE
IF( N.GT.0 )
$ D( N ) = A( IA )
ELSE
*
* Type 7-12: generate a diagonally dominant matrix with
* unknown condition number in the vectors D and E.
*
IF( .NOT.ZEROT .OR. .NOT.DOTYPE( 7 ) ) THEN
*
* Let D and E have values from [-1,1].
*
CALL DLARNV( 2, ISEED, N, D )
CALL DLARNV( 2, ISEED, N-1, E )
*
* Make the tridiagonal matrix diagonally dominant.
*
IF( N.EQ.1 ) THEN
D( 1 ) = ABS( D( 1 ) )
ELSE
D( 1 ) = ABS( D( 1 ) ) + ABS( E( 1 ) )
D( N ) = ABS( D( N ) ) + ABS( E( N-1 ) )
DO 30 I = 2, N - 1
D( I ) = ABS( D( I ) ) + ABS( E( I ) ) +
$ ABS( E( I-1 ) )
30 CONTINUE
END IF
*
* Scale D and E so the maximum element is ANORM.
*
IX = IDAMAX( N, D, 1 )
DMAX = D( IX )
CALL DSCAL( N, ANORM / DMAX, D, 1 )
IF( N.GT.1 )
$ CALL DSCAL( N-1, ANORM / DMAX, E, 1 )
*
ELSE IF( IZERO.GT.0 ) THEN
*
* Reuse the last matrix by copying back the zeroed out
* elements.
*
IF( IZERO.EQ.1 ) THEN
D( 1 ) = Z( 2 )
IF( N.GT.1 )
$ E( 1 ) = Z( 3 )
ELSE IF( IZERO.EQ.N ) THEN
E( N-1 ) = Z( 1 )
D( N ) = Z( 2 )
ELSE
E( IZERO-1 ) = Z( 1 )
D( IZERO ) = Z( 2 )
E( IZERO ) = Z( 3 )
END IF
END IF
*
* For types 8-10, set one row and column of the matrix to
* zero.
*
IZERO = 0
IF( IMAT.EQ.8 ) THEN
IZERO = 1
Z( 2 ) = D( 1 )
D( 1 ) = ZERO
IF( N.GT.1 ) THEN
Z( 3 ) = E( 1 )
E( 1 ) = ZERO
END IF
ELSE IF( IMAT.EQ.9 ) THEN
IZERO = N
IF( N.GT.1 ) THEN
Z( 1 ) = E( N-1 )
E( N-1 ) = ZERO
END IF
Z( 2 ) = D( N )
D( N ) = ZERO
ELSE IF( IMAT.EQ.10 ) THEN
IZERO = ( N+1 ) / 2
IF( IZERO.GT.1 ) THEN
Z( 1 ) = E( IZERO-1 )
Z( 3 ) = E( IZERO )
E( IZERO-1 ) = ZERO
E( IZERO ) = ZERO
END IF
Z( 2 ) = D( IZERO )
D( IZERO ) = ZERO
END IF
END IF
*
* Generate NRHS random solution vectors.
*
IX = 1
DO 40 J = 1, NRHS
CALL DLARNV( 2, ISEED, N, XACT( IX ) )
IX = IX + LDA
40 CONTINUE
*
* Set the right hand side.
*
CALL DLAPTM( N, NRHS, ONE, D, E, XACT, LDA, ZERO, B, LDA )
*
DO 100 IFACT = 1, 2
IF( IFACT.EQ.1 ) THEN
FACT = 'F'
ELSE
FACT = 'N'
END IF
*
* Compute the condition number for comparison with
* the value returned by DPTSVX.
*
IF( ZEROT ) THEN
IF( IFACT.EQ.1 )
$ GO TO 100
RCONDC = ZERO
*
ELSE IF( IFACT.EQ.1 ) THEN
*
* Compute the 1-norm of A.
*
ANORM = DLANST( '1', N, D, E )
*
CALL DCOPY( N, D, 1, D( N+1 ), 1 )
IF( N.GT.1 )
$ CALL DCOPY( N-1, E, 1, E( N+1 ), 1 )
*
* Factor the matrix A.
*
CALL DPTTRF( N, D( N+1 ), E( N+1 ), INFO )
*
* Use DPTTRS to solve for one column at a time of
* inv(A), computing the maximum column sum as we go.
*
AINVNM = ZERO
DO 60 I = 1, N
DO 50 J = 1, N
X( J ) = ZERO
50 CONTINUE
X( I ) = ONE
CALL DPTTRS( N, 1, D( N+1 ), E( N+1 ), X, LDA,
$ INFO )
AINVNM = MAX( AINVNM, DASUM( N, X, 1 ) )
60 CONTINUE
*
* Compute the 1-norm condition number of A.
*
IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
RCONDC = ONE
ELSE
RCONDC = ( ONE / ANORM ) / AINVNM
END IF
END IF
*
IF( IFACT.EQ.2 ) THEN
*
* --- Test DPTSV --
*
CALL DCOPY( N, D, 1, D( N+1 ), 1 )
IF( N.GT.1 )
$ CALL DCOPY( N-1, E, 1, E( N+1 ), 1 )
CALL DLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
*
* Factor A as L*D*L' and solve the system A*X = B.
*
SRNAMT = 'DPTSV '
CALL DPTSV( N, NRHS, D( N+1 ), E( N+1 ), X, LDA,
$ INFO )
*
* Check error code from DPTSV .
*
IF( INFO.NE.IZERO )
$ CALL ALAERH( PATH, 'DPTSV ', INFO, IZERO, ' ', N,
$ N, 1, 1, NRHS, IMAT, NFAIL, NERRS,
$ NOUT )
NT = 0
IF( IZERO.EQ.0 ) THEN
*
* Check the factorization by computing the ratio
* norm(L*D*L' - A) / (n * norm(A) * EPS )
*
CALL DPTT01( N, D, E, D( N+1 ), E( N+1 ), WORK,
$ RESULT( 1 ) )
*
* Compute the residual in the solution.
*
CALL DLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
CALL DPTT02( N, NRHS, D, E, X, LDA, WORK, LDA,
$ RESULT( 2 ) )
*
* Check solution from generated exact solution.
*
CALL DGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
$ RESULT( 3 ) )
NT = 3
END IF
*
* Print information about the tests that did not pass
* the threshold.
*
DO 70 K = 1, NT
IF( RESULT( K ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALADHD( NOUT, PATH )
WRITE( NOUT, FMT = 9999 )'DPTSV ', N, IMAT, K,
$ RESULT( K )
NFAIL = NFAIL + 1
END IF
70 CONTINUE
NRUN = NRUN + NT
END IF
*
* --- Test DPTSVX ---
*
IF( IFACT.GT.1 ) THEN
*
* Initialize D( N+1:2*N ) and E( N+1:2*N ) to zero.
*
DO 80 I = 1, N - 1
D( N+I ) = ZERO
E( N+I ) = ZERO
80 CONTINUE
IF( N.GT.0 )
$ D( N+N ) = ZERO
END IF
*
CALL DLASET( 'Full', N, NRHS, ZERO, ZERO, X, LDA )
*
* Solve the system and compute the condition number and
* error bounds using DPTSVX.
*
SRNAMT = 'DPTSVX'
CALL DPTSVX( FACT, N, NRHS, D, E, D( N+1 ), E( N+1 ), B,
$ LDA, X, LDA, RCOND, RWORK, RWORK( NRHS+1 ),
$ WORK, INFO )
*
* Check the error code from DPTSVX.
*
IF( INFO.NE.IZERO )
$ CALL ALAERH( PATH, 'DPTSVX', INFO, IZERO, FACT, N, N,
$ 1, 1, NRHS, IMAT, NFAIL, NERRS, NOUT )
IF( IZERO.EQ.0 ) THEN
IF( IFACT.EQ.2 ) THEN
*
* Check the factorization by computing the ratio
* norm(L*D*L' - A) / (n * norm(A) * EPS )
*
K1 = 1
CALL DPTT01( N, D, E, D( N+1 ), E( N+1 ), WORK,
$ RESULT( 1 ) )
ELSE
K1 = 2
END IF
*
* Compute the residual in the solution.
*
CALL DLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
CALL DPTT02( N, NRHS, D, E, X, LDA, WORK, LDA,
$ RESULT( 2 ) )
*
* Check solution from generated exact solution.
*
CALL DGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
$ RESULT( 3 ) )
*
* Check error bounds from iterative refinement.
*
CALL DPTT05( N, NRHS, D, E, B, LDA, X, LDA, XACT, LDA,
$ RWORK, RWORK( NRHS+1 ), RESULT( 4 ) )
ELSE
K1 = 6
END IF
*
* Check the reciprocal of the condition number.
*
RESULT( 6 ) = DGET06( RCOND, RCONDC )
*
* Print information about the tests that did not pass
* the threshold.
*
DO 90 K = K1, 6
IF( RESULT( K ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALADHD( NOUT, PATH )
WRITE( NOUT, FMT = 9998 )'DPTSVX', FACT, N, IMAT,
$ K, RESULT( K )
NFAIL = NFAIL + 1
END IF
90 CONTINUE
NRUN = NRUN + 7 - K1
100 CONTINUE
110 CONTINUE
120 CONTINUE
*
* Print a summary of the results.
*
CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
*
9999 FORMAT( 1X, A, ', N =', I5, ', type ', I2, ', test ', I2,
$ ', ratio = ', G12.5 )
9998 FORMAT( 1X, A, ', FACT=''', A1, ''', N =', I5, ', type ', I2,
$ ', test ', I2, ', ratio = ', G12.5 )
RETURN
*
* End of DDRVPT
*
END
|
