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SUBROUTINE ZDRVGE( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
$ A, AFAC, ASAV, B, BSAV, X, XACT, S, 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 NMAX, NN, NOUT, NRHS
DOUBLE PRECISION THRESH
* ..
* .. Array Arguments ..
LOGICAL DOTYPE( * )
INTEGER IWORK( * ), NVAL( * )
DOUBLE PRECISION RWORK( * ), S( * )
COMPLEX*16 A( * ), AFAC( * ), ASAV( * ), B( * ),
$ BSAV( * ), WORK( * ), X( * ), XACT( * )
* ..
*
* Purpose
* =======
*
* ZDRVGE tests the driver routines ZGESV 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 column dimension N.
*
* NRHS (input) INTEGER
* The number of right hand side vectors to be generated for
* each linear system.
*
* 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.
*
* NMAX (input) INTEGER
* The maximum value permitted for N, used in dimensioning the
* work arrays.
*
* A (workspace) COMPLEX*16 array, dimension (NMAX*NMAX)
*
* AFAC (workspace) COMPLEX*16 array, dimension (NMAX*NMAX)
*
* ASAV (workspace) COMPLEX*16 array, dimension (NMAX*NMAX)
*
* B (workspace) COMPLEX*16 array, dimension (NMAX*NRHS)
*
* BSAV (workspace) COMPLEX*16 array, dimension (NMAX*NRHS)
*
* X (workspace) COMPLEX*16 array, dimension (NMAX*NRHS)
*
* XACT (workspace) COMPLEX*16 array, dimension (NMAX*NRHS)
*
* S (workspace) DOUBLE PRECISION array, dimension (2*NMAX)
*
* WORK (workspace) COMPLEX*16 array, dimension
* (NMAX*max(3,NRHS))
*
* RWORK (workspace) DOUBLE PRECISION array, dimension (2*NRHS+NMAX)
*
* IWORK (workspace) INTEGER array, dimension (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 = 11 )
INTEGER NTESTS
PARAMETER ( NTESTS = 7 )
INTEGER NTRAN
PARAMETER ( NTRAN = 3 )
* ..
* .. Local Scalars ..
LOGICAL EQUIL, NOFACT, PREFAC, TRFCON, ZEROT
CHARACTER DIST, EQUED, FACT, TRANS, TYPE, XTYPE
CHARACTER*3 PATH
INTEGER I, IEQUED, IFACT, IMAT, IN, INFO, IOFF, ITRAN,
$ IZERO, K, K1, KL, KU, LDA, LWORK, MODE, N, NB,
$ NBMIN, NERRS, NFACT, NFAIL, NIMAT, NRUN, NT
DOUBLE PRECISION AINVNM, AMAX, ANORM, ANORMI, ANORMO, CNDNUM,
$ COLCND, RCOND, RCONDC, RCONDI, RCONDO, ROLDC,
$ ROLDI, ROLDO, ROWCND, RPVGRW
* ..
* .. Local Arrays ..
CHARACTER EQUEDS( 4 ), FACTS( 3 ), TRANSS( NTRAN )
INTEGER ISEED( 4 ), ISEEDY( 4 )
DOUBLE PRECISION RDUM( 1 ), RESULT( NTESTS )
* ..
* .. External Functions ..
LOGICAL LSAME
DOUBLE PRECISION DGET06, DLAMCH, ZLANGE, ZLANTR
EXTERNAL LSAME, DGET06, DLAMCH, ZLANGE, ZLANTR
* ..
* .. External Subroutines ..
EXTERNAL ALADHD, ALAERH, ALASVM, XLAENV, ZERRVX, ZGEEQU,
$ ZGESV, ZGESVX, ZGET01, ZGET02, ZGET04, ZGET07,
$ ZGETRF, ZGETRI, ZLACPY, ZLAQGE, ZLARHS, ZLASET,
$ ZLATB4, ZLATMS
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DCMPLX, 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 / 1988, 1989, 1990, 1991 /
DATA TRANSS / 'N', 'T', 'C' /
DATA FACTS / 'F', 'N', 'E' /
DATA EQUEDS / 'N', 'R', 'C', 'B' /
* ..
* .. Executable Statements ..
*
* Initialize constants and the random number seed.
*
PATH( 1: 1 ) = 'Zomplex precision'
PATH( 2: 3 ) = 'GE'
NRUN = 0
NFAIL = 0
NERRS = 0
DO 10 I = 1, 4
ISEED( I ) = ISEEDY( I )
10 CONTINUE
*
* Test the error exits
*
IF( TSTERR )
$ CALL ZERRVX( PATH, NOUT )
INFOT = 0
*
* Set the block size and minimum block size for testing.
*
NB = 1
NBMIN = 2
CALL XLAENV( 1, NB )
CALL XLAENV( 2, NBMIN )
*
* Do for each value of N in NVAL
*
DO 90 IN = 1, NN
N = NVAL( IN )
LDA = MAX( N, 1 )
XTYPE = 'N'
NIMAT = NTYPES
IF( N.LE.0 )
$ NIMAT = 1
*
DO 80 IMAT = 1, NIMAT
*
* Do the tests only if DOTYPE( IMAT ) is true.
*
IF( .NOT.DOTYPE( IMAT ) )
$ GO TO 80
*
* Skip types 5, 6, or 7 if the matrix size is too small.
*
ZEROT = IMAT.GE.5 .AND. IMAT.LE.7
IF( ZEROT .AND. N.LT.IMAT-4 )
$ GO TO 80
*
* Set up parameters with ZLATB4 and generate a test matrix
* with ZLATMS.
*
CALL ZLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE,
$ CNDNUM, DIST )
RCONDC = ONE / CNDNUM
*
SRNAMT = 'ZLATMS'
CALL ZLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE, CNDNUM,
$ ANORM, KL, KU, 'No packing', A, LDA, WORK,
$ INFO )
*
* Check error code from ZLATMS.
*
IF( INFO.NE.0 ) THEN
CALL ALAERH( PATH, 'ZLATMS', INFO, 0, ' ', N, N, -1, -1,
$ -1, IMAT, NFAIL, NERRS, NOUT )
GO TO 80
END IF
*
* For types 5-7, zero one or more columns of the matrix to
* test that INFO is returned correctly.
*
IF( ZEROT ) THEN
IF( IMAT.EQ.5 ) THEN
IZERO = 1
ELSE IF( IMAT.EQ.6 ) THEN
IZERO = N
ELSE
IZERO = N / 2 + 1
END IF
IOFF = ( IZERO-1 )*LDA
IF( IMAT.LT.7 ) THEN
DO 20 I = 1, N
A( IOFF+I ) = ZERO
20 CONTINUE
ELSE
CALL ZLASET( 'Full', N, N-IZERO+1, DCMPLX( ZERO ),
$ DCMPLX( ZERO ), A( IOFF+1 ), LDA )
END IF
ELSE
IZERO = 0
END IF
*
* Save a copy of the matrix A in ASAV.
*
CALL ZLACPY( 'Full', N, N, A, LDA, ASAV, LDA )
*
DO 70 IEQUED = 1, 4
EQUED = EQUEDS( IEQUED )
IF( IEQUED.EQ.1 ) THEN
NFACT = 3
ELSE
NFACT = 1
END IF
*
DO 60 IFACT = 1, NFACT
FACT = FACTS( IFACT )
PREFAC = LSAME( FACT, 'F' )
NOFACT = LSAME( FACT, 'N' )
EQUIL = LSAME( FACT, 'E' )
*
IF( ZEROT ) THEN
IF( PREFAC )
$ GO TO 60
RCONDO = ZERO
RCONDI = ZERO
*
ELSE IF( .NOT.NOFACT ) THEN
*
* Compute the condition number for comparison with
* the value returned by ZGESVX (FACT = 'N' reuses
* the condition number from the previous iteration
* with FACT = 'F').
*
CALL ZLACPY( 'Full', N, N, ASAV, LDA, AFAC, LDA )
IF( EQUIL .OR. IEQUED.GT.1 ) THEN
*
* Compute row and column scale factors to
* equilibrate the matrix A.
*
CALL ZGEEQU( N, N, AFAC, LDA, S, S( N+1 ),
$ ROWCND, COLCND, AMAX, INFO )
IF( INFO.EQ.0 .AND. N.GT.0 ) THEN
IF( LSAME( EQUED, 'R' ) ) THEN
ROWCND = ZERO
COLCND = ONE
ELSE IF( LSAME( EQUED, 'C' ) ) THEN
ROWCND = ONE
COLCND = ZERO
ELSE IF( LSAME( EQUED, 'B' ) ) THEN
ROWCND = ZERO
COLCND = ZERO
END IF
*
* Equilibrate the matrix.
*
CALL ZLAQGE( N, N, AFAC, LDA, S, S( N+1 ),
$ ROWCND, COLCND, AMAX, EQUED )
END IF
END IF
*
* Save the condition number of the non-equilibrated
* system for use in ZGET04.
*
IF( EQUIL ) THEN
ROLDO = RCONDO
ROLDI = RCONDI
END IF
*
* Compute the 1-norm and infinity-norm of A.
*
ANORMO = ZLANGE( '1', N, N, AFAC, LDA, RWORK )
ANORMI = ZLANGE( 'I', N, N, AFAC, LDA, RWORK )
*
* Factor the matrix A.
*
CALL ZGETRF( N, N, AFAC, LDA, IWORK, INFO )
*
* Form the inverse of A.
*
CALL ZLACPY( 'Full', N, N, AFAC, LDA, A, LDA )
LWORK = NMAX*MAX( 3, NRHS )
CALL ZGETRI( N, A, LDA, IWORK, WORK, LWORK, INFO )
*
* Compute the 1-norm condition number of A.
*
AINVNM = ZLANGE( '1', N, N, A, LDA, RWORK )
IF( ANORMO.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
RCONDO = ONE
ELSE
RCONDO = ( ONE / ANORMO ) / AINVNM
END IF
*
* Compute the infinity-norm condition number of A.
*
AINVNM = ZLANGE( 'I', N, N, A, LDA, RWORK )
IF( ANORMI.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
RCONDI = ONE
ELSE
RCONDI = ( ONE / ANORMI ) / AINVNM
END IF
END IF
*
DO 50 ITRAN = 1, NTRAN
*
* Do for each value of TRANS.
*
TRANS = TRANSS( ITRAN )
IF( ITRAN.EQ.1 ) THEN
RCONDC = RCONDO
ELSE
RCONDC = RCONDI
END IF
*
* Restore the matrix A.
*
CALL ZLACPY( 'Full', N, N, ASAV, LDA, A, LDA )
*
* Form an exact solution and set the right hand side.
*
SRNAMT = 'ZLARHS'
CALL ZLARHS( PATH, XTYPE, 'Full', TRANS, N, N, KL,
$ KU, NRHS, A, LDA, XACT, LDA, B, LDA,
$ ISEED, INFO )
XTYPE = 'C'
CALL ZLACPY( 'Full', N, NRHS, B, LDA, BSAV, LDA )
*
IF( NOFACT .AND. ITRAN.EQ.1 ) THEN
*
* --- Test ZGESV ---
*
* Compute the LU factorization of the matrix and
* solve the system.
*
CALL ZLACPY( 'Full', N, N, A, LDA, AFAC, LDA )
CALL ZLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
*
SRNAMT = 'ZGESV '
CALL ZGESV( N, NRHS, AFAC, LDA, IWORK, X, LDA,
$ INFO )
*
* Check error code from ZGESV .
*
IF( INFO.NE.IZERO )
$ CALL ALAERH( PATH, 'ZGESV ', INFO, IZERO,
$ ' ', N, N, -1, -1, NRHS, IMAT,
$ NFAIL, NERRS, NOUT )
*
* Reconstruct matrix from factors and compute
* residual.
*
CALL ZGET01( N, N, A, LDA, AFAC, LDA, IWORK,
$ RWORK, RESULT( 1 ) )
NT = 1
IF( IZERO.EQ.0 ) THEN
*
* Compute residual of the computed solution.
*
CALL ZLACPY( 'Full', N, NRHS, B, LDA, WORK,
$ LDA )
CALL ZGET02( 'No transpose', N, N, NRHS, A,
$ LDA, X, LDA, WORK, LDA, RWORK,
$ RESULT( 2 ) )
*
* Check solution from generated exact solution.
*
CALL ZGET04( 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 30 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 )'ZGESV ', N,
$ IMAT, K, RESULT( K )
NFAIL = NFAIL + 1
END IF
30 CONTINUE
NRUN = NRUN + NT
END IF
*
* --- Test ZGESVX ---
*
IF( .NOT.PREFAC )
$ CALL ZLASET( 'Full', N, N, DCMPLX( ZERO ),
$ DCMPLX( ZERO ), AFAC, LDA )
CALL ZLASET( 'Full', N, NRHS, DCMPLX( ZERO ),
$ DCMPLX( ZERO ), X, LDA )
IF( IEQUED.GT.1 .AND. N.GT.0 ) THEN
*
* Equilibrate the matrix if FACT = 'F' and
* EQUED = 'R', 'C', or 'B'.
*
CALL ZLAQGE( N, N, A, LDA, S, S( N+1 ), ROWCND,
$ COLCND, AMAX, EQUED )
END IF
*
* Solve the system and compute the condition number
* and error bounds using ZGESVX.
*
SRNAMT = 'ZGESVX'
CALL ZGESVX( FACT, TRANS, N, NRHS, A, LDA, AFAC,
$ LDA, IWORK, EQUED, S, S( N+1 ), B,
$ LDA, X, LDA, RCOND, RWORK,
$ RWORK( NRHS+1 ), WORK,
$ RWORK( 2*NRHS+1 ), INFO )
*
* Check the error code from ZGESVX.
*
IF( INFO.NE.IZERO )
$ CALL ALAERH( PATH, 'ZGESVX', INFO, IZERO,
$ FACT // TRANS, N, N, -1, -1, NRHS,
$ IMAT, NFAIL, NERRS, NOUT )
*
* Compare RWORK(2*NRHS+1) from ZGESVX with the
* computed reciprocal pivot growth factor RPVGRW
*
IF( INFO.NE.0 ) THEN
RPVGRW = ZLANTR( 'M', 'U', 'N', INFO, INFO,
$ AFAC, LDA, RDUM )
IF( RPVGRW.EQ.ZERO ) THEN
RPVGRW = ONE
ELSE
RPVGRW = ZLANGE( 'M', N, INFO, A, LDA,
$ RDUM ) / RPVGRW
END IF
ELSE
RPVGRW = ZLANTR( 'M', 'U', 'N', N, N, AFAC, LDA,
$ RDUM )
IF( RPVGRW.EQ.ZERO ) THEN
RPVGRW = ONE
ELSE
RPVGRW = ZLANGE( 'M', N, N, A, LDA, RDUM ) /
$ RPVGRW
END IF
END IF
RESULT( 7 ) = ABS( RPVGRW-RWORK( 2*NRHS+1 ) ) /
$ MAX( RWORK( 2*NRHS+1 ), RPVGRW ) /
$ DLAMCH( 'E' )
*
IF( .NOT.PREFAC ) THEN
*
* Reconstruct matrix from factors and compute
* residual.
*
CALL ZGET01( N, N, A, LDA, AFAC, LDA, IWORK,
$ RWORK( 2*NRHS+1 ), RESULT( 1 ) )
K1 = 1
ELSE
K1 = 2
END IF
*
IF( INFO.EQ.0 ) THEN
TRFCON = .FALSE.
*
* Compute residual of the computed solution.
*
CALL ZLACPY( 'Full', N, NRHS, BSAV, LDA, WORK,
$ LDA )
CALL ZGET02( TRANS, N, N, NRHS, ASAV, LDA, X,
$ LDA, WORK, LDA, RWORK( 2*NRHS+1 ),
$ RESULT( 2 ) )
*
* Check solution from generated exact solution.
*
IF( NOFACT .OR. ( PREFAC .AND. LSAME( EQUED,
$ 'N' ) ) ) THEN
CALL ZGET04( N, NRHS, X, LDA, XACT, LDA,
$ RCONDC, RESULT( 3 ) )
ELSE
IF( ITRAN.EQ.1 ) THEN
ROLDC = ROLDO
ELSE
ROLDC = ROLDI
END IF
CALL ZGET04( N, NRHS, X, LDA, XACT, LDA,
$ ROLDC, RESULT( 3 ) )
END IF
*
* Check the error bounds from iterative
* refinement.
*
CALL ZGET07( TRANS, N, NRHS, ASAV, LDA, B, LDA,
$ X, LDA, XACT, LDA, RWORK, .TRUE.,
$ RWORK( NRHS+1 ), RESULT( 4 ) )
ELSE
TRFCON = .TRUE.
END IF
*
* Compare RCOND from ZGESVX with the computed value
* in RCONDC.
*
RESULT( 6 ) = DGET06( RCOND, RCONDC )
*
* Print information about the tests that did not pass
* the threshold.
*
IF( .NOT.TRFCON ) THEN
DO 40 K = K1, NTESTS
IF( RESULT( K ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALADHD( NOUT, PATH )
IF( PREFAC ) THEN
WRITE( NOUT, FMT = 9997 )'ZGESVX',
$ FACT, TRANS, N, EQUED, IMAT, K,
$ RESULT( K )
ELSE
WRITE( NOUT, FMT = 9998 )'ZGESVX',
$ FACT, TRANS, N, IMAT, K, RESULT( K )
END IF
NFAIL = NFAIL + 1
END IF
40 CONTINUE
NRUN = NRUN + 7 - K1
ELSE
IF( RESULT( 1 ).GE.THRESH .AND. .NOT.PREFAC )
$ THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALADHD( NOUT, PATH )
IF( PREFAC ) THEN
WRITE( NOUT, FMT = 9997 )'ZGESVX', FACT,
$ TRANS, N, EQUED, IMAT, 1, RESULT( 1 )
ELSE
WRITE( NOUT, FMT = 9998 )'ZGESVX', FACT,
$ TRANS, N, IMAT, 1, RESULT( 1 )
END IF
NFAIL = NFAIL + 1
NRUN = NRUN + 1
END IF
IF( RESULT( 6 ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALADHD( NOUT, PATH )
IF( PREFAC ) THEN
WRITE( NOUT, FMT = 9997 )'ZGESVX', FACT,
$ TRANS, N, EQUED, IMAT, 6, RESULT( 6 )
ELSE
WRITE( NOUT, FMT = 9998 )'ZGESVX', FACT,
$ TRANS, N, IMAT, 6, RESULT( 6 )
END IF
NFAIL = NFAIL + 1
NRUN = NRUN + 1
END IF
IF( RESULT( 7 ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALADHD( NOUT, PATH )
IF( PREFAC ) THEN
WRITE( NOUT, FMT = 9997 )'ZGESVX', FACT,
$ TRANS, N, EQUED, IMAT, 7, RESULT( 7 )
ELSE
WRITE( NOUT, FMT = 9998 )'ZGESVX', FACT,
$ TRANS, N, IMAT, 7, RESULT( 7 )
END IF
NFAIL = NFAIL + 1
NRUN = NRUN + 1
END IF
*
END IF
*
50 CONTINUE
60 CONTINUE
70 CONTINUE
80 CONTINUE
90 CONTINUE
*
* Print a summary of the results.
*
CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
*
9999 FORMAT( 1X, A, ', N =', I5, ', type ', I2, ', test(', I2, ') =',
$ G12.5 )
9998 FORMAT( 1X, A, ', FACT=''', A1, ''', TRANS=''', A1, ''', N=', I5,
$ ', type ', I2, ', test(', I1, ')=', G12.5 )
9997 FORMAT( 1X, A, ', FACT=''', A1, ''', TRANS=''', A1, ''', N=', I5,
$ ', EQUED=''', A1, ''', type ', I2, ', test(', I1, ')=',
$ G12.5 )
RETURN
*
* End of ZDRVGE
*
END
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