SUBROUTINE DGET35( RMAX, LMAX, NINFO, KNT ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. INTEGER KNT, LMAX, NINFO DOUBLE PRECISION RMAX * .. * * Purpose * ======= * * DGET35 tests DTRSYL, 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)) * * Arguments * ========== * * RMAX (output) DOUBLE PRECISION * Value of the largest test ratio. * * LMAX (output) INTEGER * Example number where largest test ratio achieved. * * NINFO (output) INTEGER * Number of examples where INFO is nonzero. * * KNT (output) INTEGER * Total number of examples tested. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) DOUBLE PRECISION TWO, FOUR PARAMETER ( TWO = 2.0D0, FOUR = 4.0D0 ) * .. * .. Local Scalars .. CHARACTER TRANA, TRANB INTEGER I, IMA, IMB, IMLDA1, IMLDA2, IMLDB1, IMLOFF, \$ INFO, ISGN, ITRANA, ITRANB, J, M, N DOUBLE PRECISION BIGNUM, CNRM, EPS, RES, RES1, RMUL, SCALE, \$ SMLNUM, TNRM, XNRM * .. * .. Local Arrays .. INTEGER IDIM( 8 ), IVAL( 6, 6, 8 ) DOUBLE PRECISION A( 6, 6 ), B( 6, 6 ), C( 6, 6 ), CC( 6, 6 ), \$ DUM( 1 ), VM1( 3 ), VM2( 3 ) * .. * .. External Functions .. DOUBLE PRECISION DLAMCH, DLANGE EXTERNAL DLAMCH, DLANGE * .. * .. External Subroutines .. EXTERNAL DGEMM, DLABAD, DTRSYL * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, MAX, SIN, SQRT * .. * .. Data statements .. DATA IDIM / 1, 2, 3, 4, 3, 3, 6, 4 / DATA IVAL / 1, 35*0, 1, 2, 4*0, -2, 0, 28*0, 1, 5*0, \$ 5, 1, 2, 3*0, -8, -2, 1, 21*0, 3, 4, 4*0, -5, \$ 3, 4*0, 1, 2, 1, 4, 2*0, -3, -9, -1, 1, 14*0, \$ 1, 5*0, 2, 3, 4*0, 5, 6, 7, 21*0, 1, 5*0, 1, 3, \$ -4, 3*0, 2, 5, 2, 21*0, 1, 2, 4*0, -2, 0, 4*0, \$ 5, 6, 3, 4, 2*0, -1, -9, -5, 2, 2*0, 4*8, 5, 6, \$ 4*9, -7, 5, 1, 5*0, 1, 5, 2, 3*0, 2, -21, 5, \$ 3*0, 1, 2, 3, 4, 14*0 / * .. * .. Executable Statements .. * * Get machine parameters * EPS = DLAMCH( 'P' ) SMLNUM = DLAMCH( 'S' )*FOUR / EPS BIGNUM = ONE / SMLNUM CALL DLABAD( SMLNUM, BIGNUM ) * * Set up test case parameters * VM1( 1 ) = SQRT( SMLNUM ) VM1( 2 ) = ONE VM1( 3 ) = SQRT( BIGNUM ) VM2( 1 ) = ONE VM2( 2 ) = ONE + TWO*EPS VM2( 3 ) = TWO * KNT = 0 NINFO = 0 LMAX = 0 RMAX = ZERO * * Begin test loop * DO 150 ITRANA = 1, 2 DO 140 ITRANB = 1, 2 DO 130 ISGN = -1, 1, 2 DO 120 IMA = 1, 8 DO 110 IMLDA1 = 1, 3 DO 100 IMLDA2 = 1, 3 DO 90 IMLOFF = 1, 2 DO 80 IMB = 1, 8 DO 70 IMLDB1 = 1, 3 IF( ITRANA.EQ.1 ) \$ TRANA = 'N' IF( ITRANA.EQ.2 ) \$ TRANA = 'T' IF( ITRANB.EQ.1 ) \$ TRANB = 'N' IF( ITRANB.EQ.2 ) \$ TRANB = 'T' M = IDIM( IMA ) N = IDIM( IMB ) TNRM = ZERO DO 20 I = 1, M DO 10 J = 1, M A( I, J ) = IVAL( I, J, IMA ) IF( ABS( I-J ).LE.1 ) THEN A( I, J ) = A( I, J )* \$ VM1( IMLDA1 ) A( I, J ) = A( I, J )* \$ VM2( IMLDA2 ) ELSE A( I, J ) = A( I, J )* \$ VM1( IMLOFF ) END IF TNRM = MAX( TNRM, \$ ABS( A( I, J ) ) ) 10 CONTINUE 20 CONTINUE DO 40 I = 1, N DO 30 J = 1, N B( I, J ) = IVAL( I, J, IMB ) IF( ABS( I-J ).LE.1 ) THEN B( I, J ) = B( I, J )* \$ VM1( IMLDB1 ) ELSE B( I, J ) = B( I, J )* \$ VM1( IMLOFF ) END IF TNRM = MAX( TNRM, \$ ABS( B( I, J ) ) ) 30 CONTINUE 40 CONTINUE CNRM = ZERO DO 60 I = 1, M DO 50 J = 1, N C( I, J ) = SIN( DBLE( I*J ) ) CNRM = MAX( CNRM, C( I, J ) ) CC( I, J ) = C( I, J ) 50 CONTINUE 60 CONTINUE KNT = KNT + 1 CALL DTRSYL( TRANA, TRANB, ISGN, M, N, \$ A, 6, B, 6, C, 6, SCALE, \$ INFO ) IF( INFO.NE.0 ) \$ NINFO = NINFO + 1 XNRM = DLANGE( 'M', M, N, C, 6, DUM ) RMUL = ONE IF( XNRM.GT.ONE .AND. TNRM.GT.ONE ) \$ THEN IF( XNRM.GT.BIGNUM / TNRM ) THEN RMUL = ONE / MAX( XNRM, TNRM ) END IF END IF CALL DGEMM( TRANA, 'N', M, N, M, RMUL, \$ A, 6, C, 6, -SCALE*RMUL, \$ CC, 6 ) CALL DGEMM( 'N', TRANB, M, N, N, \$ DBLE( ISGN )*RMUL, C, 6, B, \$ 6, ONE, CC, 6 ) RES1 = DLANGE( 'M', M, N, CC, 6, DUM ) RES = RES1 / MAX( SMLNUM, SMLNUM*XNRM, \$ ( ( RMUL*TNRM )*EPS )*XNRM ) IF( RES.GT.RMAX ) THEN LMAX = KNT RMAX = RES END IF 70 CONTINUE 80 CONTINUE 90 CONTINUE 100 CONTINUE 110 CONTINUE 120 CONTINUE 130 CONTINUE 140 CONTINUE 150 CONTINUE * RETURN * * End of DGET35 * END