LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ dget35()

 subroutine dget35 ( double precision RMAX, integer LMAX, integer NINFO, integer KNT )

DGET35

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))```
Parameters
 [out] RMAX ``` RMAX is DOUBLE PRECISION Value of the largest test ratio.``` [out] LMAX ``` LMAX is INTEGER Example number where largest test ratio achieved.``` [out] NINFO ``` NINFO is INTEGER Number of examples where INFO is nonzero.``` [out] KNT ``` KNT is INTEGER Total number of examples tested.```

Definition at line 77 of file dget35.f.

78 *
79 * -- LAPACK test routine --
80 * -- LAPACK is a software package provided by Univ. of Tennessee, --
81 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
82 *
83 * .. Scalar Arguments ..
84  INTEGER KNT, LMAX, NINFO
85  DOUBLE PRECISION RMAX
86 * ..
87 *
88 * =====================================================================
89 *
90 * .. Parameters ..
91  DOUBLE PRECISION ZERO, ONE
92  parameter( zero = 0.0d0, one = 1.0d0 )
93  DOUBLE PRECISION TWO, FOUR
94  parameter( two = 2.0d0, four = 4.0d0 )
95 * ..
96 * .. Local Scalars ..
97  CHARACTER TRANA, TRANB
98  INTEGER I, IMA, IMB, IMLDA1, IMLDA2, IMLDB1, IMLOFF,
99  \$ INFO, ISGN, ITRANA, ITRANB, J, M, N
100  DOUBLE PRECISION BIGNUM, CNRM, EPS, RES, RES1, RMUL, SCALE,
101  \$ SMLNUM, TNRM, XNRM
102 * ..
103 * .. Local Arrays ..
104  INTEGER IDIM( 8 ), IVAL( 6, 6, 8 )
105  DOUBLE PRECISION A( 6, 6 ), B( 6, 6 ), C( 6, 6 ), CC( 6, 6 ),
106  \$ DUM( 1 ), VM1( 3 ), VM2( 3 )
107 * ..
108 * .. External Functions ..
109  DOUBLE PRECISION DLAMCH, DLANGE
110  EXTERNAL dlamch, dlange
111 * ..
112 * .. External Subroutines ..
113  EXTERNAL dgemm, dlabad, dtrsyl
114 * ..
115 * .. Intrinsic Functions ..
116  INTRINSIC abs, dble, max, sin, sqrt
117 * ..
118 * .. Data statements ..
119  DATA idim / 1, 2, 3, 4, 3, 3, 6, 4 /
120  DATA ival / 1, 35*0, 1, 2, 4*0, -2, 0, 28*0, 1, 5*0,
121  \$ 5, 1, 2, 3*0, -8, -2, 1, 21*0, 3, 4, 4*0, -5,
122  \$ 3, 4*0, 1, 2, 1, 4, 2*0, -3, -9, -1, 1, 14*0,
123  \$ 1, 5*0, 2, 3, 4*0, 5, 6, 7, 21*0, 1, 5*0, 1, 3,
124  \$ -4, 3*0, 2, 5, 2, 21*0, 1, 2, 4*0, -2, 0, 4*0,
125  \$ 5, 6, 3, 4, 2*0, -1, -9, -5, 2, 2*0, 4*8, 5, 6,
126  \$ 4*9, -7, 5, 1, 5*0, 1, 5, 2, 3*0, 2, -21, 5,
127  \$ 3*0, 1, 2, 3, 4, 14*0 /
128 * ..
129 * .. Executable Statements ..
130 *
131 * Get machine parameters
132 *
133  eps = dlamch( 'P' )
134  smlnum = dlamch( 'S' )*four / eps
135  bignum = one / smlnum
136  CALL dlabad( smlnum, bignum )
137 *
138 * Set up test case parameters
139 *
140  vm1( 1 ) = sqrt( smlnum )
141  vm1( 2 ) = one
142  vm1( 3 ) = sqrt( bignum )
143  vm2( 1 ) = one
144  vm2( 2 ) = one + two*eps
145  vm2( 3 ) = two
146 *
147  knt = 0
148  ninfo = 0
149  lmax = 0
150  rmax = zero
151 *
152 * Begin test loop
153 *
154  DO 150 itrana = 1, 2
155  DO 140 itranb = 1, 2
156  DO 130 isgn = -1, 1, 2
157  DO 120 ima = 1, 8
158  DO 110 imlda1 = 1, 3
159  DO 100 imlda2 = 1, 3
160  DO 90 imloff = 1, 2
161  DO 80 imb = 1, 8
162  DO 70 imldb1 = 1, 3
163  IF( itrana.EQ.1 )
164  \$ trana = 'N'
165  IF( itrana.EQ.2 )
166  \$ trana = 'T'
167  IF( itranb.EQ.1 )
168  \$ tranb = 'N'
169  IF( itranb.EQ.2 )
170  \$ tranb = 'T'
171  m = idim( ima )
172  n = idim( imb )
173  tnrm = zero
174  DO 20 i = 1, m
175  DO 10 j = 1, m
176  a( i, j ) = ival( i, j, ima )
177  IF( abs( i-j ).LE.1 ) THEN
178  a( i, j ) = a( i, j )*
179  \$ vm1( imlda1 )
180  a( i, j ) = a( i, j )*
181  \$ vm2( imlda2 )
182  ELSE
183  a( i, j ) = a( i, j )*
184  \$ vm1( imloff )
185  END IF
186  tnrm = max( tnrm,
187  \$ abs( a( i, j ) ) )
188  10 CONTINUE
189  20 CONTINUE
190  DO 40 i = 1, n
191  DO 30 j = 1, n
192  b( i, j ) = ival( i, j, imb )
193  IF( abs( i-j ).LE.1 ) THEN
194  b( i, j ) = b( i, j )*
195  \$ vm1( imldb1 )
196  ELSE
197  b( i, j ) = b( i, j )*
198  \$ vm1( imloff )
199  END IF
200  tnrm = max( tnrm,
201  \$ abs( b( i, j ) ) )
202  30 CONTINUE
203  40 CONTINUE
204  cnrm = zero
205  DO 60 i = 1, m
206  DO 50 j = 1, n
207  c( i, j ) = sin( dble( i*j ) )
208  cnrm = max( cnrm, c( i, j ) )
209  cc( i, j ) = c( i, j )
210  50 CONTINUE
211  60 CONTINUE
212  knt = knt + 1
213  CALL dtrsyl( trana, tranb, isgn, m, n,
214  \$ a, 6, b, 6, c, 6, scale,
215  \$ info )
216  IF( info.NE.0 )
217  \$ ninfo = ninfo + 1
218  xnrm = dlange( 'M', m, n, c, 6, dum )
219  rmul = one
220  IF( xnrm.GT.one .AND. tnrm.GT.one )
221  \$ THEN
222  IF( xnrm.GT.bignum / tnrm ) THEN
223  rmul = one / max( xnrm, tnrm )
224  END IF
225  END IF
226  CALL dgemm( trana, 'N', m, n, m, rmul,
227  \$ a, 6, c, 6, -scale*rmul,
228  \$ cc, 6 )
229  CALL dgemm( 'N', tranb, m, n, n,
230  \$ dble( isgn )*rmul, c, 6, b,
231  \$ 6, one, cc, 6 )
232  res1 = dlange( 'M', m, n, cc, 6, dum )
233  res = res1 / max( smlnum, smlnum*xnrm,
234  \$ ( ( rmul*tnrm )*eps )*xnrm )
235  IF( res.GT.rmax ) THEN
236  lmax = knt
237  rmax = res
238  END IF
239  70 CONTINUE
240  80 CONTINUE
241  90 CONTINUE
242  100 CONTINUE
243  110 CONTINUE
244  120 CONTINUE
245  130 CONTINUE
246  140 CONTINUE
247  150 CONTINUE
248 *
249  RETURN
250 *
251 * End of DGET35
252 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine dlabad(SMALL, LARGE)
DLABAD
Definition: dlabad.f:74
subroutine dgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DGEMM
Definition: dgemm.f:187
double precision function dlange(NORM, M, N, A, LDA, WORK)
DLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: dlange.f:114
subroutine dtrsyl(TRANA, TRANB, ISGN, M, N, A, LDA, B, LDB, C, LDC, SCALE, INFO)
DTRSYL
Definition: dtrsyl.f:164
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