1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256
|
*> \brief \b DGET35
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DGET35( RMAX, LMAX, NINFO, KNT )
*
* .. Scalar Arguments ..
* INTEGER KNT, LMAX, NINFO
* DOUBLE PRECISION RMAX
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> 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))
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[out] RMAX
*> \verbatim
*> RMAX is DOUBLE PRECISION
*> 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
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup double_eig
*
* =====================================================================
SUBROUTINE DGET35( RMAX, LMAX, NINFO, KNT )
*
* -- 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, NINFO
DOUBLE PRECISION RMAX
* ..
*
* =====================================================================
*
* .. 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
|