LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ zget35()

subroutine zget35 ( double precision  rmax,
integer  lmax,
integer  ninfo,
integer  knt,
integer  nin 
)

ZGET35

Purpose:
 ZGET35 tests ZTRSYL, 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.
[in]NIN
          NIN is INTEGER
          Input logical unit number.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 83 of file zget35.f.

84*
85* -- LAPACK test routine --
86* -- LAPACK is a software package provided by Univ. of Tennessee, --
87* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
88*
89* .. Scalar Arguments ..
90 INTEGER KNT, LMAX, NIN, NINFO
91 DOUBLE PRECISION RMAX
92* ..
93*
94* =====================================================================
95*
96* .. Parameters ..
97 INTEGER LDT
98 parameter( ldt = 10 )
99 DOUBLE PRECISION ZERO, ONE, TWO
100 parameter( zero = 0.0d0, one = 1.0d0, two = 2.0d0 )
101 DOUBLE PRECISION LARGE
102 parameter( large = 1.0d6 )
103 COMPLEX*16 CONE
104 parameter( cone = 1.0d0 )
105* ..
106* .. Local Scalars ..
107 CHARACTER TRANA, TRANB
108 INTEGER I, IMLA, IMLAD, IMLB, IMLC, INFO, ISGN, ITRANA,
109 $ ITRANB, J, M, N
110 DOUBLE PRECISION BIGNUM, EPS, RES, RES1, SCALE, SMLNUM, TNRM,
111 $ XNRM
112 COMPLEX*16 RMUL
113* ..
114* .. Local Arrays ..
115 DOUBLE PRECISION DUM( 1 ), VM1( 3 ), VM2( 3 )
116 COMPLEX*16 A( LDT, LDT ), ATMP( LDT, LDT ), B( LDT, LDT ),
117 $ BTMP( LDT, LDT ), C( LDT, LDT ),
118 $ CSAV( LDT, LDT ), CTMP( LDT, LDT )
119* ..
120* .. External Functions ..
121 DOUBLE PRECISION DLAMCH, ZLANGE
122 EXTERNAL dlamch, zlange
123* ..
124* .. External Subroutines ..
125 EXTERNAL zgemm, ztrsyl
126* ..
127* .. Intrinsic Functions ..
128 INTRINSIC abs, dble, max, sqrt
129* ..
130* .. Executable Statements ..
131*
132* Get machine parameters
133*
134 eps = dlamch( 'P' )
135 smlnum = dlamch( 'S' ) / eps
136 bignum = one / smlnum
137*
138* Set up test case parameters
139*
140 vm1( 1 ) = sqrt( smlnum )
141 vm1( 2 ) = one
142 vm1( 3 ) = large
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 10 CONTINUE
155 READ( nin, fmt = * )m, n
156 IF( n.EQ.0 )
157 $ RETURN
158 DO 20 i = 1, m
159 READ( nin, fmt = * )( atmp( i, j ), j = 1, m )
160 20 CONTINUE
161 DO 30 i = 1, n
162 READ( nin, fmt = * )( btmp( i, j ), j = 1, n )
163 30 CONTINUE
164 DO 40 i = 1, m
165 READ( nin, fmt = * )( ctmp( i, j ), j = 1, n )
166 40 CONTINUE
167 DO 170 imla = 1, 3
168 DO 160 imlad = 1, 3
169 DO 150 imlb = 1, 3
170 DO 140 imlc = 1, 3
171 DO 130 itrana = 1, 2
172 DO 120 itranb = 1, 2
173 DO 110 isgn = -1, 1, 2
174 IF( itrana.EQ.1 )
175 $ trana = 'N'
176 IF( itrana.EQ.2 )
177 $ trana = 'C'
178 IF( itranb.EQ.1 )
179 $ tranb = 'N'
180 IF( itranb.EQ.2 )
181 $ tranb = 'C'
182 tnrm = zero
183 DO 60 i = 1, m
184 DO 50 j = 1, m
185 a( i, j ) = atmp( i, j )*vm1( imla )
186 tnrm = max( tnrm, abs( a( i, j ) ) )
187 50 CONTINUE
188 a( i, i ) = a( i, i )*vm2( imlad )
189 tnrm = max( tnrm, abs( a( i, i ) ) )
190 60 CONTINUE
191 DO 80 i = 1, n
192 DO 70 j = 1, n
193 b( i, j ) = btmp( i, j )*vm1( imlb )
194 tnrm = max( tnrm, abs( b( i, j ) ) )
195 70 CONTINUE
196 80 CONTINUE
197 IF( tnrm.EQ.zero )
198 $ tnrm = one
199 DO 100 i = 1, m
200 DO 90 j = 1, n
201 c( i, j ) = ctmp( i, j )*vm1( imlc )
202 csav( i, j ) = c( i, j )
203 90 CONTINUE
204 100 CONTINUE
205 knt = knt + 1
206 CALL ztrsyl( trana, tranb, isgn, m, n, a,
207 $ ldt, b, ldt, c, ldt, scale,
208 $ info )
209 IF( info.NE.0 )
210 $ ninfo = ninfo + 1
211 xnrm = zlange( 'M', m, n, c, ldt, dum )
212 rmul = cone
213 IF( xnrm.GT.one .AND. tnrm.GT.one ) THEN
214 IF( xnrm.GT.bignum / tnrm ) THEN
215 rmul = max( xnrm, tnrm )
216 rmul = cone / rmul
217 END IF
218 END IF
219 CALL zgemm( trana, 'N', m, n, m, rmul, a,
220 $ ldt, c, ldt, -scale*rmul, csav,
221 $ ldt )
222 CALL zgemm( 'N', tranb, m, n, n,
223 $ dble( isgn )*rmul, c, ldt, b,
224 $ ldt, cone, csav, ldt )
225 res1 = zlange( 'M', m, n, csav, ldt, dum )
226 res = res1 / max( smlnum, smlnum*xnrm,
227 $ ( ( abs( rmul )*tnrm )*eps )*xnrm )
228 IF( res.GT.rmax ) THEN
229 lmax = knt
230 rmax = res
231 END IF
232 110 CONTINUE
233 120 CONTINUE
234 130 CONTINUE
235 140 CONTINUE
236 150 CONTINUE
237 160 CONTINUE
238 170 CONTINUE
239 GO TO 10
240*
241* End of ZGET35
242*
zgemm
subroutine zgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
ZGEMM
Definition zgemm.f:188
dlamch
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
zlange
double precision function zlange(norm, m, n, a, lda, work)
ZLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition zlange.f:115
ztrsyl
subroutine ztrsyl(trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, info)
ZTRSYL
Definition ztrsyl.f:157
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