LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ 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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

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, 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*
137* Set up test case parameters
138*
139 vm1( 1 ) = sqrt( smlnum )
140 vm1( 2 ) = one
141 vm1( 3 ) = sqrt( bignum )
142 vm2( 1 ) = one
143 vm2( 2 ) = one + two*eps
144 vm2( 3 ) = two
145*
146 knt = 0
147 ninfo = 0
148 lmax = 0
149 rmax = zero
150*
151* Begin test loop
152*
153 DO 150 itrana = 1, 2
154 DO 140 itranb = 1, 2
155 DO 130 isgn = -1, 1, 2
156 DO 120 ima = 1, 8
157 DO 110 imlda1 = 1, 3
158 DO 100 imlda2 = 1, 3
159 DO 90 imloff = 1, 2
160 DO 80 imb = 1, 8
161 DO 70 imldb1 = 1, 3
162 IF( itrana.EQ.1 )
163 $ trana = 'N'
164 IF( itrana.EQ.2 )
165 $ trana = 'T'
166 IF( itranb.EQ.1 )
167 $ tranb = 'N'
168 IF( itranb.EQ.2 )
169 $ tranb = 'T'
170 m = idim( ima )
171 n = idim( imb )
172 tnrm = zero
173 DO 20 i = 1, m
174 DO 10 j = 1, m
175 a( i, j ) = ival( i, j, ima )
176 IF( abs( i-j ).LE.1 ) THEN
177 a( i, j ) = a( i, j )*
178 $ vm1( imlda1 )
179 a( i, j ) = a( i, j )*
180 $ vm2( imlda2 )
181 ELSE
182 a( i, j ) = a( i, j )*
183 $ vm1( imloff )
184 END IF
185 tnrm = max( tnrm,
186 $ abs( a( i, j ) ) )
187 10 CONTINUE
188 20 CONTINUE
189 DO 40 i = 1, n
190 DO 30 j = 1, n
191 b( i, j ) = ival( i, j, imb )
192 IF( abs( i-j ).LE.1 ) THEN
193 b( i, j ) = b( i, j )*
194 $ vm1( imldb1 )
195 ELSE
196 b( i, j ) = b( i, j )*
197 $ vm1( imloff )
198 END IF
199 tnrm = max( tnrm,
200 $ abs( b( i, j ) ) )
201 30 CONTINUE
202 40 CONTINUE
203 cnrm = zero
204 DO 60 i = 1, m
205 DO 50 j = 1, n
206 c( i, j ) = sin( dble( i*j ) )
207 cnrm = max( cnrm, c( i, j ) )
208 cc( i, j ) = c( i, j )
209 50 CONTINUE
210 60 CONTINUE
211 knt = knt + 1
212 CALL dtrsyl( trana, tranb, isgn, m, n,
213 $ a, 6, b, 6, c, 6, scale,
214 $ info )
215 IF( info.NE.0 )
216 $ ninfo = ninfo + 1
217 xnrm = dlange( 'M', m, n, c, 6, dum )
218 rmul = one
219 IF( xnrm.GT.one .AND. tnrm.GT.one )
220 $ THEN
221 IF( xnrm.GT.bignum / tnrm ) THEN
222 rmul = one / max( xnrm, tnrm )
223 END IF
224 END IF
225 CALL dgemm( trana, 'N', m, n, m, rmul,
226 $ a, 6, c, 6, -scale*rmul,
227 $ cc, 6 )
228 CALL dgemm( 'N', tranb, m, n, n,
229 $ dble( isgn )*rmul, c, 6, b,
230 $ 6, one, cc, 6 )
231 res1 = dlange( 'M', m, n, cc, 6, dum )
232 res = res1 / max( smlnum, smlnum*xnrm,
233 $ ( ( rmul*tnrm )*eps )*xnrm )
234 IF( res.GT.rmax ) THEN
235 lmax = knt
236 rmax = res
237 END IF
238 70 CONTINUE
239 80 CONTINUE
240 90 CONTINUE
241 100 CONTINUE
242 110 CONTINUE
243 120 CONTINUE
244 130 CONTINUE
245 140 CONTINUE
246 150 CONTINUE
247*
248 RETURN
249*
250* End of DGET35
251*
dgemm
subroutine dgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
DGEMM
Definition dgemm.f:188
dlamch
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
dlange
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
dtrsyl
subroutine dtrsyl(trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, info)
DTRSYL
Definition dtrsyl.f:164
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