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*> \brief \b CSYL01
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE CSYL01( THRESH, NFAIL, RMAX, NINFO, KNT )
*
* .. Scalar Arguments ..
* INTEGER KNT
* REAL THRESH
* ..
* .. Array Arguments ..
* INTEGER NFAIL( 3 ), NINFO( 2 )
* REAL RMAX( 2 )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CSYL01 tests CTRSYL and CTRSYL3, routines for solving the Sylvester matrix
*> equation
*>
*> op(A)*X + ISGN*X*op(B) = scale*C,
*>
*> where op(A) and op(B) are both upper triangular form, op() represents an
*> optional conjugate transpose, and ISGN can be -1 or +1. Scale is an output
*> less than or equal to 1, chosen to avoid overflow in X.
*>
*> The test code verifies that the following residual does not exceed
*> the provided threshold:
*>
*> norm(op(A)*X + ISGN*X*op(B) - scale*C) /
*> (EPS*max(norm(A),norm(B))*norm(X))
*>
*> This routine complements CGET35 by testing with larger,
*> random matrices, of which some require rescaling of X to avoid overflow.
*>
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] THRESH
*> \verbatim
*> THRESH is REAL
*> A test will count as "failed" if the residual, computed as
*> described above, exceeds THRESH.
*> \endverbatim
*>
*> \param[out] NFAIL
*> \verbatim
*> NFAIL is INTEGER array, dimension (3)
*> NFAIL(1) = No. of times residual CTRSYL exceeds threshold THRESH
*> NFAIL(2) = No. of times residual CTRSYL3 exceeds threshold THRESH
*> NFAIL(3) = No. of times CTRSYL3 and CTRSYL deviate
*> \endverbatim
*>
*> \param[out] RMAX
*> \verbatim
*> RMAX is DOUBLE PRECISION array, dimension (2)
*> RMAX(1) = Value of the largest test ratio of CTRSYL
*> RMAX(2) = Value of the largest test ratio of CTRSYL3
*> \endverbatim
*>
*> \param[out] NINFO
*> \verbatim
*> NINFO is INTEGER array, dimension (2)
*> NINFO(1) = No. of times CTRSYL where INFO is nonzero
*> NINFO(2) = No. of times CTRSYL3 where INFO is nonzero
*> \endverbatim
*>
*> \param[out] KNT
*> \verbatim
*> KNT is INTEGER
*> Total number of examples tested.
*> \endverbatim
*
* -- LAPACK test routine --
SUBROUTINE CSYL01( THRESH, NFAIL, RMAX, NINFO, KNT )
IMPLICIT NONE
*
* -- 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 ..
INTEGER KNT
REAL THRESH
* ..
* .. Array Arguments ..
INTEGER NFAIL( 3 ), NINFO( 2 )
REAL RMAX( 2 )
* ..
*
* =====================================================================
* ..
* .. Parameters ..
COMPLEX CONE
PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ) )
REAL ONE, ZERO
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
INTEGER MAXM, MAXN, LDSWORK
PARAMETER ( MAXM = 101, MAXN = 138, LDSWORK = 18 )
* ..
* .. Local Scalars ..
CHARACTER TRANA, TRANB
INTEGER I, INFO, IINFO, ISGN, ITRANA, ITRANB, J, KLA,
$ KUA, KLB, KUB, M, N
REAL ANRM, BNRM, BIGNUM, EPS, RES, RES1,
$ SCALE, SCALE3, SMLNUM, TNRM, XNRM
COMPLEX RMUL
* ..
* .. Local Arrays ..
COMPLEX A( MAXM, MAXM ), B( MAXN, MAXN ),
$ C( MAXM, MAXN ), CC( MAXM, MAXN ),
$ X( MAXM, MAXN ),
$ DUML( MAXM ), DUMR( MAXN ),
$ D( MIN( MAXM, MAXN ) )
REAL SWORK( LDSWORK, 54 ), DUM( MAXN ), VM( 2 )
INTEGER ISEED( 4 ), IWORK( MAXM + MAXN + 2 )
* ..
* .. External Functions ..
LOGICAL SISNAN
REAL SLAMCH, CLANGE
EXTERNAL SISNAN, SLAMCH, CLANGE
* ..
* .. External Subroutines ..
EXTERNAL CLATMR, CLACPY, CGEMM, CTRSYL, CTRSYL3
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, REAL, MAX
* ..
* .. Executable Statements ..
*
* Get machine parameters
*
EPS = SLAMCH( 'P' )
SMLNUM = SLAMCH( 'S' ) / EPS
BIGNUM = ONE / SMLNUM
*
* Expect INFO = 0
VM( 1 ) = ONE
* Expect INFO = 1
VM( 2 ) = 0.5E+0
*
* Begin test loop
*
NINFO( 1 ) = 0
NINFO( 2 ) = 0
NFAIL( 1 ) = 0
NFAIL( 2 ) = 0
NFAIL( 3 ) = 0
RMAX( 1 ) = ZERO
RMAX( 2 ) = ZERO
KNT = 0
ISEED( 1 ) = 1
ISEED( 2 ) = 1
ISEED( 3 ) = 1
ISEED( 4 ) = 1
SCALE = ONE
SCALE3 = ONE
DO J = 1, 2
DO ISGN = -1, 1, 2
* Reset seed (overwritten by LATMR)
ISEED( 1 ) = 1
ISEED( 2 ) = 1
ISEED( 3 ) = 1
ISEED( 4 ) = 1
DO M = 32, MAXM, 23
KLA = 0
KUA = M - 1
CALL CLATMR( M, M, 'S', ISEED, 'N', D,
$ 6, ONE, CONE, 'T', 'N',
$ DUML, 1, ONE, DUMR, 1, ONE,
$ 'N', IWORK, KLA, KUA, ZERO,
$ ONE, 'NO', A, MAXM, IWORK,
$ IINFO )
DO I = 1, M
A( I, I ) = A( I, I ) * VM( J )
END DO
ANRM = CLANGE( 'M', M, M, A, MAXM, DUM )
DO N = 51, MAXN, 29
KLB = 0
KUB = N - 1
CALL CLATMR( N, N, 'S', ISEED, 'N', D,
$ 6, ONE, CONE, 'T', 'N',
$ DUML, 1, ONE, DUMR, 1, ONE,
$ 'N', IWORK, KLB, KUB, ZERO,
$ ONE, 'NO', B, MAXN, IWORK,
$ IINFO )
DO I = 1, N
B( I, I ) = B( I, I ) * VM ( J )
END DO
BNRM = CLANGE( 'M', N, N, B, MAXN, DUM )
TNRM = MAX( ANRM, BNRM )
CALL CLATMR( M, N, 'S', ISEED, 'N', D,
$ 6, ONE, CONE, 'T', 'N',
$ DUML, 1, ONE, DUMR, 1, ONE,
$ 'N', IWORK, M, N, ZERO, ONE,
$ 'NO', C, MAXM, IWORK, IINFO )
DO ITRANA = 1, 2
IF( ITRANA.EQ.1 )
$ TRANA = 'N'
IF( ITRANA.EQ.2 )
$ TRANA = 'C'
DO ITRANB = 1, 2
IF( ITRANB.EQ.1 )
$ TRANB = 'N'
IF( ITRANB.EQ.2 )
$ TRANB = 'C'
KNT = KNT + 1
*
CALL CLACPY( 'All', M, N, C, MAXM, X, MAXM)
CALL CLACPY( 'All', M, N, C, MAXM, CC, MAXM)
CALL CTRSYL( TRANA, TRANB, ISGN, M, N,
$ A, MAXM, B, MAXN, X, MAXM,
$ SCALE, IINFO )
IF( IINFO.NE.0 )
$ NINFO( 1 ) = NINFO( 1 ) + 1
XNRM = CLANGE( 'M', M, N, X, MAXM, DUM )
RMUL = CONE
IF( XNRM.GT.ONE .AND. TNRM.GT.ONE ) THEN
IF( XNRM.GT.BIGNUM / TNRM ) THEN
RMUL = CONE / MAX( XNRM, TNRM )
END IF
END IF
CALL CGEMM( TRANA, 'N', M, N, M, RMUL,
$ A, MAXM, X, MAXM, -SCALE*RMUL,
$ CC, MAXM )
CALL CGEMM( 'N', TRANB, M, N, N,
$ REAL( ISGN )*RMUL, X, MAXM, B,
$ MAXN, CONE, CC, MAXM )
RES1 = CLANGE( 'M', M, N, CC, MAXM, DUM )
RES = RES1 / MAX( SMLNUM, SMLNUM*XNRM,
$ ( ( ABS( RMUL )*TNRM )*EPS )*XNRM )
IF( RES.GT.THRESH )
$ NFAIL( 1 ) = NFAIL( 1 ) + 1
IF( RES.GT.RMAX( 1 ) )
$ RMAX( 1 ) = RES
*
CALL CLACPY( 'All', M, N, C, MAXM, X, MAXM )
CALL CLACPY( 'All', M, N, C, MAXM, CC, MAXM )
CALL CTRSYL3( TRANA, TRANB, ISGN, M, N,
$ A, MAXM, B, MAXN, X, MAXM,
$ SCALE3, SWORK, LDSWORK, INFO)
IF( INFO.NE.0 )
$ NINFO( 2 ) = NINFO( 2 ) + 1
XNRM = CLANGE( 'M', M, N, X, MAXM, DUM )
RMUL = CONE
IF( XNRM.GT.ONE .AND. TNRM.GT.ONE ) THEN
IF( XNRM.GT.BIGNUM / TNRM ) THEN
RMUL = CONE / MAX( XNRM, TNRM )
END IF
END IF
CALL CGEMM( TRANA, 'N', M, N, M, RMUL,
$ A, MAXM, X, MAXM, -SCALE3*RMUL,
$ CC, MAXM )
CALL CGEMM( 'N', TRANB, M, N, N,
$ REAL( ISGN )*RMUL, X, MAXM, B,
$ MAXN, CONE, CC, MAXM )
RES1 = CLANGE( 'M', M, N, CC, MAXM, DUM )
RES = RES1 / MAX( SMLNUM, SMLNUM*XNRM,
$ ( ( ABS( RMUL )*TNRM )*EPS )*XNRM )
* Verify that TRSYL3 only flushes if TRSYL flushes (but
* there may be cases where TRSYL3 avoid flushing).
IF( SCALE3.EQ.ZERO .AND. SCALE.GT.ZERO .OR.
$ IINFO.NE.INFO ) THEN
NFAIL( 3 ) = NFAIL( 3 ) + 1
END IF
IF( RES.GT.THRESH .OR. SISNAN( RES ) )
$ NFAIL( 2 ) = NFAIL( 2 ) + 1
IF( RES.GT.RMAX( 2 ) )
$ RMAX( 2 ) = RES
END DO
END DO
END DO
END DO
END DO
END DO
*
RETURN
*
* End of CSYL01
*
END
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