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*> \brief \b CGET35
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE CGET35( RMAX, LMAX, NINFO, KNT, NIN )
*
* .. Scalar Arguments ..
* INTEGER KNT, LMAX, NIN, NINFO
* REAL RMAX
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CGET35 tests CTRSYL, a routine for solving the Sylvester matrix
*> equation
*>
*> op(A)*X + ISGN*X*op(B) = scale*C,
*>
*> A and B are assumed to be in Schur canonical form, op() represents an
*> optional 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 is order 1:
*>
*> norm(op(A)*X + ISGN*X*op(B) - scale*C) /
*> (EPS*max(norm(A),norm(B))*norm(X))
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[out] RMAX
*> \verbatim
*> RMAX is REAL
*> Value of the largest test ratio.
*> \endverbatim
*>
*> \param[out] LMAX
*> \verbatim
*> LMAX is INTEGER
*> Example number where largest test ratio achieved.
*> \endverbatim
*>
*> \param[out] NINFO
*> \verbatim
*> NINFO is INTEGER
*> Number of examples where INFO is nonzero.
*> \endverbatim
*>
*> \param[out] KNT
*> \verbatim
*> KNT is INTEGER
*> Total number of examples tested.
*> \endverbatim
*>
*> \param[in] NIN
*> \verbatim
*> NIN is INTEGER
*> Input logical unit number.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup complex_eig
*
* =====================================================================
SUBROUTINE CGET35( RMAX, LMAX, NINFO, KNT, NIN )
*
* -- 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 ..
INTEGER KNT, LMAX, NIN, NINFO
REAL RMAX
* ..
*
* =====================================================================
*
* .. Parameters ..
INTEGER LDT
PARAMETER ( LDT = 10 )
REAL ZERO, ONE, TWO
PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0, TWO = 2.0E0 )
REAL LARGE
PARAMETER ( LARGE = 1.0E6 )
COMPLEX CONE
PARAMETER ( CONE = 1.0E0 )
* ..
* .. Local Scalars ..
CHARACTER TRANA, TRANB
INTEGER I, IMLA, IMLAD, IMLB, IMLC, INFO, ISGN, ITRANA,
$ ITRANB, J, M, N
REAL BIGNUM, EPS, RES, RES1, SCALE, SMLNUM, TNRM,
$ XNRM
COMPLEX RMUL
* ..
* .. Local Arrays ..
REAL DUM( 1 ), VM1( 3 ), VM2( 3 )
COMPLEX A( LDT, LDT ), ATMP( LDT, LDT ), B( LDT, LDT ),
$ BTMP( LDT, LDT ), C( LDT, LDT ),
$ CSAV( LDT, LDT ), CTMP( LDT, LDT )
* ..
* .. External Functions ..
REAL CLANGE, SLAMCH
EXTERNAL CLANGE, SLAMCH
* ..
* .. External Subroutines ..
EXTERNAL CGEMM, CTRSYL
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, REAL, SQRT
* ..
* .. Executable Statements ..
*
* Get machine parameters
*
EPS = SLAMCH( 'P' )
SMLNUM = SLAMCH( 'S' ) / EPS
BIGNUM = ONE / SMLNUM
CALL SLABAD( SMLNUM, BIGNUM )
*
* Set up test case parameters
*
VM1( 1 ) = SQRT( SMLNUM )
VM1( 2 ) = ONE
VM1( 3 ) = LARGE
VM2( 1 ) = ONE
VM2( 2 ) = ONE + TWO*EPS
VM2( 3 ) = TWO
*
KNT = 0
NINFO = 0
LMAX = 0
RMAX = ZERO
*
* Begin test loop
*
10 CONTINUE
READ( NIN, FMT = * )M, N
IF( N.EQ.0 )
$ RETURN
DO 20 I = 1, M
READ( NIN, FMT = * )( ATMP( I, J ), J = 1, M )
20 CONTINUE
DO 30 I = 1, N
READ( NIN, FMT = * )( BTMP( I, J ), J = 1, N )
30 CONTINUE
DO 40 I = 1, M
READ( NIN, FMT = * )( CTMP( I, J ), J = 1, N )
40 CONTINUE
DO 170 IMLA = 1, 3
DO 160 IMLAD = 1, 3
DO 150 IMLB = 1, 3
DO 140 IMLC = 1, 3
DO 130 ITRANA = 1, 2
DO 120 ITRANB = 1, 2
DO 110 ISGN = -1, 1, 2
IF( ITRANA.EQ.1 )
$ TRANA = 'N'
IF( ITRANA.EQ.2 )
$ TRANA = 'C'
IF( ITRANB.EQ.1 )
$ TRANB = 'N'
IF( ITRANB.EQ.2 )
$ TRANB = 'C'
TNRM = ZERO
DO 60 I = 1, M
DO 50 J = 1, M
A( I, J ) = ATMP( I, J )*VM1( IMLA )
TNRM = MAX( TNRM, ABS( A( I, J ) ) )
50 CONTINUE
A( I, I ) = A( I, I )*VM2( IMLAD )
TNRM = MAX( TNRM, ABS( A( I, I ) ) )
60 CONTINUE
DO 80 I = 1, N
DO 70 J = 1, N
B( I, J ) = BTMP( I, J )*VM1( IMLB )
TNRM = MAX( TNRM, ABS( B( I, J ) ) )
70 CONTINUE
80 CONTINUE
IF( TNRM.EQ.ZERO )
$ TNRM = ONE
DO 100 I = 1, M
DO 90 J = 1, N
C( I, J ) = CTMP( I, J )*VM1( IMLC )
CSAV( I, J ) = C( I, J )
90 CONTINUE
100 CONTINUE
KNT = KNT + 1
CALL CTRSYL( TRANA, TRANB, ISGN, M, N, A,
$ LDT, B, LDT, C, LDT, SCALE,
$ INFO )
IF( INFO.NE.0 )
$ NINFO = NINFO + 1
XNRM = CLANGE( 'M', M, N, C, LDT, DUM )
RMUL = CONE
IF( XNRM.GT.ONE .AND. TNRM.GT.ONE ) THEN
IF( XNRM.GT.BIGNUM / TNRM ) THEN
RMUL = MAX( XNRM, TNRM )
RMUL = CONE / RMUL
END IF
END IF
CALL CGEMM( TRANA, 'N', M, N, M, RMUL, A,
$ LDT, C, LDT, -SCALE*RMUL, CSAV,
$ LDT )
CALL CGEMM( 'N', TRANB, M, N, N,
$ REAL( ISGN )*RMUL, C, LDT, B,
$ LDT, CONE, CSAV, LDT )
RES1 = CLANGE( 'M', M, N, CSAV, LDT, DUM )
RES = RES1 / MAX( SMLNUM, SMLNUM*XNRM,
$ ( ( ABS( RMUL )*TNRM )*EPS )*XNRM )
IF( RES.GT.RMAX ) THEN
LMAX = KNT
RMAX = RES
END IF
110 CONTINUE
120 CONTINUE
130 CONTINUE
140 CONTINUE
150 CONTINUE
160 CONTINUE
170 CONTINUE
GO TO 10
*
* End of CGET35
*
END
|
