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SUBROUTINE DDRVGT( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, AF,
$ B, X, XACT, WORK, RWORK, IWORK, NOUT )
*
* -- LAPACK test routine (version 3.1) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* November 2006
*
* .. Scalar Arguments ..
LOGICAL TSTERR
INTEGER NN, NOUT, NRHS
DOUBLE PRECISION THRESH
* ..
* .. Array Arguments ..
LOGICAL DOTYPE( * )
INTEGER IWORK( * ), NVAL( * )
DOUBLE PRECISION A( * ), AF( * ), B( * ), RWORK( * ), WORK( * ),
$ X( * ), XACT( * )
* ..
*
* Purpose
* =======
*
* DDRVGT tests DGTSV and -SVX.
*
* Arguments
* =========
*
* DOTYPE (input) 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.
*
* NN (input) INTEGER
* The number of values of N contained in the vector NVAL.
*
* NVAL (input) INTEGER array, dimension (NN)
* The values of the matrix dimension N.
*
* THRESH (input) 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.
*
* TSTERR (input) LOGICAL
* Flag that indicates whether error exits are to be tested.
*
* A (workspace) DOUBLE PRECISION array, dimension (NMAX*4)
*
* AF (workspace) DOUBLE PRECISION array, dimension (NMAX*4)
*
* B (workspace) DOUBLE PRECISION array, dimension (NMAX*NRHS)
*
* X (workspace) DOUBLE PRECISION array, dimension (NMAX*NRHS)
*
* XACT (workspace) DOUBLE PRECISION array, dimension (NMAX*NRHS)
*
* WORK (workspace) DOUBLE PRECISION array, dimension
* (NMAX*max(3,NRHS))
*
* RWORK (workspace) DOUBLE PRECISION array, dimension
* (max(NMAX,2*NRHS))
*
* IWORK (workspace) INTEGER array, dimension (2*NMAX)
*
* NOUT (input) INTEGER
* The unit number for output.
*
* =====================================================================
*
* .. 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 TRFCON, ZEROT
CHARACTER DIST, FACT, TRANS, TYPE
CHARACTER*3 PATH
INTEGER I, IFACT, IMAT, IN, INFO, ITRAN, IX, IZERO, J,
$ K, K1, KL, KOFF, KU, LDA, M, MODE, N, NERRS,
$ NFAIL, NIMAT, NRUN, NT
DOUBLE PRECISION AINVNM, ANORM, ANORMI, ANORMO, COND, RCOND,
$ RCONDC, RCONDI, RCONDO
* ..
* .. Local Arrays ..
CHARACTER TRANSS( 3 )
INTEGER ISEED( 4 ), ISEEDY( 4 )
DOUBLE PRECISION RESULT( NTESTS ), Z( 3 )
* ..
* .. External Functions ..
DOUBLE PRECISION DASUM, DGET06, DLANGT
EXTERNAL DASUM, DGET06, DLANGT
* ..
* .. External Subroutines ..
EXTERNAL ALADHD, ALAERH, ALASVM, DCOPY, DERRVX, DGET04,
$ DGTSV, DGTSVX, DGTT01, DGTT02, DGTT05, DGTTRF,
$ DGTTRS, DLACPY, DLAGTM, DLARNV, DLASET, DLATB4,
$ DLATMS, DSCAL
* ..
* .. Intrinsic Functions ..
INTRINSIC 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 / , TRANSS / 'N', 'T',
$ 'C' /
* ..
* .. Executable Statements ..
*
PATH( 1: 1 ) = 'Double precision'
PATH( 2: 3 ) = 'GT'
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 140 IN = 1, NN
*
* Do for each value of N in NVAL.
*
N = NVAL( IN )
M = MAX( N-1, 0 )
LDA = MAX( 1, N )
NIMAT = NTYPES
IF( N.LE.0 )
$ NIMAT = 1
*
DO 130 IMAT = 1, NIMAT
*
* Do the tests only if DOTYPE( IMAT ) is true.
*
IF( .NOT.DOTYPE( IMAT ) )
$ GO TO 130
*
* 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
*
* Types 1-6: generate matrices of known condition number.
*
KOFF = MAX( 2-KU, 3-MAX( 1, N ) )
SRNAMT = 'DLATMS'
CALL DLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE, COND,
$ ANORM, KL, KU, 'Z', AF( KOFF ), 3, 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 130
END IF
IZERO = 0
*
IF( N.GT.1 ) THEN
CALL DCOPY( N-1, AF( 4 ), 3, A, 1 )
CALL DCOPY( N-1, AF( 3 ), 3, A( N+M+1 ), 1 )
END IF
CALL DCOPY( N, AF( 2 ), 3, A( M+1 ), 1 )
ELSE
*
* Types 7-12: generate tridiagonal matrices with
* unknown condition numbers.
*
IF( .NOT.ZEROT .OR. .NOT.DOTYPE( 7 ) ) THEN
*
* Generate a matrix with elements from [-1,1].
*
CALL DLARNV( 2, ISEED, N+2*M, A )
IF( ANORM.NE.ONE )
$ CALL DSCAL( N+2*M, ANORM, A, 1 )
ELSE IF( IZERO.GT.0 ) THEN
*
* Reuse the last matrix by copying back the zeroed out
* elements.
*
IF( IZERO.EQ.1 ) THEN
A( N ) = Z( 2 )
IF( N.GT.1 )
$ A( 1 ) = Z( 3 )
ELSE IF( IZERO.EQ.N ) THEN
A( 3*N-2 ) = Z( 1 )
A( 2*N-1 ) = Z( 2 )
ELSE
A( 2*N-2+IZERO ) = Z( 1 )
A( N-1+IZERO ) = Z( 2 )
A( IZERO ) = Z( 3 )
END IF
END IF
*
* If IMAT > 7, set one column of the matrix to 0.
*
IF( .NOT.ZEROT ) THEN
IZERO = 0
ELSE IF( IMAT.EQ.8 ) THEN
IZERO = 1
Z( 2 ) = A( N )
A( N ) = ZERO
IF( N.GT.1 ) THEN
Z( 3 ) = A( 1 )
A( 1 ) = ZERO
END IF
ELSE IF( IMAT.EQ.9 ) THEN
IZERO = N
Z( 1 ) = A( 3*N-2 )
Z( 2 ) = A( 2*N-1 )
A( 3*N-2 ) = ZERO
A( 2*N-1 ) = ZERO
ELSE
IZERO = ( N+1 ) / 2
DO 20 I = IZERO, N - 1
A( 2*N-2+I ) = ZERO
A( N-1+I ) = ZERO
A( I ) = ZERO
20 CONTINUE
A( 3*N-2 ) = ZERO
A( 2*N-1 ) = ZERO
END IF
END IF
*
DO 120 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 DGTSVX.
*
IF( ZEROT ) THEN
IF( IFACT.EQ.1 )
$ GO TO 120
RCONDO = ZERO
RCONDI = ZERO
*
ELSE IF( IFACT.EQ.1 ) THEN
CALL DCOPY( N+2*M, A, 1, AF, 1 )
*
* Compute the 1-norm and infinity-norm of A.
*
ANORMO = DLANGT( '1', N, A, A( M+1 ), A( N+M+1 ) )
ANORMI = DLANGT( 'I', N, A, A( M+1 ), A( N+M+1 ) )
*
* Factor the matrix A.
*
CALL DGTTRF( N, AF, AF( M+1 ), AF( N+M+1 ),
$ AF( N+2*M+1 ), IWORK, INFO )
*
* Use DGTTRS to solve for one column at a time of
* inv(A), computing the maximum column sum as we go.
*
AINVNM = ZERO
DO 40 I = 1, N
DO 30 J = 1, N
X( J ) = ZERO
30 CONTINUE
X( I ) = ONE
CALL DGTTRS( 'No transpose', N, 1, AF, AF( M+1 ),
$ AF( N+M+1 ), AF( N+2*M+1 ), IWORK, X,
$ LDA, INFO )
AINVNM = MAX( AINVNM, DASUM( N, X, 1 ) )
40 CONTINUE
*
* Compute the 1-norm condition number of A.
*
IF( ANORMO.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
RCONDO = ONE
ELSE
RCONDO = ( ONE / ANORMO ) / AINVNM
END IF
*
* Use DGTTRS 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 DGTTRS( 'Transpose', N, 1, AF, AF( M+1 ),
$ AF( N+M+1 ), AF( N+2*M+1 ), IWORK, X,
$ LDA, INFO )
AINVNM = MAX( AINVNM, DASUM( N, X, 1 ) )
60 CONTINUE
*
* Compute the infinity-norm condition number of A.
*
IF( ANORMI.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
RCONDI = ONE
ELSE
RCONDI = ( ONE / ANORMI ) / AINVNM
END IF
END IF
*
DO 110 ITRAN = 1, 3
TRANS = TRANSS( ITRAN )
IF( ITRAN.EQ.1 ) THEN
RCONDC = RCONDO
ELSE
RCONDC = RCONDI
END IF
*
* Generate NRHS random solution vectors.
*
IX = 1
DO 70 J = 1, NRHS
CALL DLARNV( 2, ISEED, N, XACT( IX ) )
IX = IX + LDA
70 CONTINUE
*
* Set the right hand side.
*
CALL DLAGTM( TRANS, N, NRHS, ONE, A, A( M+1 ),
$ A( N+M+1 ), XACT, LDA, ZERO, B, LDA )
*
IF( IFACT.EQ.2 .AND. ITRAN.EQ.1 ) THEN
*
* --- Test DGTSV ---
*
* Solve the system using Gaussian elimination with
* partial pivoting.
*
CALL DCOPY( N+2*M, A, 1, AF, 1 )
CALL DLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
*
SRNAMT = 'DGTSV '
CALL DGTSV( N, NRHS, AF, AF( M+1 ), AF( N+M+1 ), X,
$ LDA, INFO )
*
* Check error code from DGTSV .
*
IF( INFO.NE.IZERO )
$ CALL ALAERH( PATH, 'DGTSV ', INFO, IZERO, ' ',
$ N, N, 1, 1, NRHS, IMAT, NFAIL,
$ NERRS, NOUT )
NT = 1
IF( IZERO.EQ.0 ) THEN
*
* Check residual of computed solution.
*
CALL DLACPY( 'Full', N, NRHS, B, LDA, WORK,
$ LDA )
CALL DGTT02( TRANS, N, NRHS, A, A( M+1 ),
$ A( N+M+1 ), X, LDA, WORK, LDA,
$ RWORK, 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 80 K = 2, NT
IF( RESULT( K ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALADHD( NOUT, PATH )
WRITE( NOUT, FMT = 9999 )'DGTSV ', N, IMAT,
$ K, RESULT( K )
NFAIL = NFAIL + 1
END IF
80 CONTINUE
NRUN = NRUN + NT - 1
END IF
*
* --- Test DGTSVX ---
*
IF( IFACT.GT.1 ) THEN
*
* Initialize AF to zero.
*
DO 90 I = 1, 3*N - 2
AF( I ) = ZERO
90 CONTINUE
END IF
CALL DLASET( 'Full', N, NRHS, ZERO, ZERO, X, LDA )
*
* Solve the system and compute the condition number and
* error bounds using DGTSVX.
*
SRNAMT = 'DGTSVX'
CALL DGTSVX( FACT, TRANS, N, NRHS, A, A( M+1 ),
$ A( N+M+1 ), AF, AF( M+1 ), AF( N+M+1 ),
$ AF( N+2*M+1 ), IWORK, B, LDA, X, LDA,
$ RCOND, RWORK, RWORK( NRHS+1 ), WORK,
$ IWORK( N+1 ), INFO )
*
* Check the error code from DGTSVX.
*
IF( INFO.NE.IZERO )
$ CALL ALAERH( PATH, 'DGTSVX', INFO, IZERO,
$ FACT // TRANS, N, N, 1, 1, NRHS, IMAT,
$ NFAIL, NERRS, NOUT )
*
IF( IFACT.GE.2 ) THEN
*
* Reconstruct matrix from factors and compute
* residual.
*
CALL DGTT01( N, A, A( M+1 ), A( N+M+1 ), AF,
$ AF( M+1 ), AF( N+M+1 ), AF( N+2*M+1 ),
$ IWORK, WORK, LDA, RWORK, RESULT( 1 ) )
K1 = 1
ELSE
K1 = 2
END IF
*
IF( INFO.EQ.0 ) THEN
TRFCON = .FALSE.
*
* Check residual of computed solution.
*
CALL DLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
CALL DGTT02( TRANS, N, NRHS, A, A( M+1 ),
$ A( N+M+1 ), X, LDA, WORK, LDA, RWORK,
$ RESULT( 2 ) )
*
* Check solution from generated exact solution.
*
CALL DGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
$ RESULT( 3 ) )
*
* Check the error bounds from iterative refinement.
*
CALL DGTT05( TRANS, N, NRHS, A, A( M+1 ),
$ A( N+M+1 ), B, LDA, X, LDA, XACT, LDA,
$ RWORK, RWORK( NRHS+1 ), RESULT( 4 ) )
NT = 5
END IF
*
* Print information about the tests that did not pass
* the threshold.
*
DO 100 K = K1, NT
IF( RESULT( K ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALADHD( NOUT, PATH )
WRITE( NOUT, FMT = 9998 )'DGTSVX', FACT, TRANS,
$ N, IMAT, K, RESULT( K )
NFAIL = NFAIL + 1
END IF
100 CONTINUE
*
* Check the reciprocal of the condition number.
*
RESULT( 6 ) = DGET06( RCOND, RCONDC )
IF( RESULT( 6 ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALADHD( NOUT, PATH )
WRITE( NOUT, FMT = 9998 )'DGTSVX', FACT, TRANS, N,
$ IMAT, K, RESULT( K )
NFAIL = NFAIL + 1
END IF
NRUN = NRUN + NT - K1 + 2
*
110 CONTINUE
120 CONTINUE
130 CONTINUE
140 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, ''', TRANS=''', A1, ''', N =',
$ I5, ', type ', I2, ', test ', I2, ', ratio = ', G12.5 )
RETURN
*
* End of DDRVGT
*
END
|
