LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ cget35()

subroutine cget35 ( real  RMAX,
integer  LMAX,
integer  NINFO,
integer  KNT,
integer  NIN 
)

CGET35

Purpose:
 CGET35 tests CTRSYL, 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 REAL
          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 cget35.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  REAL RMAX
92 * ..
93 *
94 * =====================================================================
95 *
96 * .. Parameters ..
97  INTEGER LDT
98  parameter( ldt = 10 )
99  REAL ZERO, ONE, TWO
100  parameter( zero = 0.0e0, one = 1.0e0, two = 2.0e0 )
101  REAL LARGE
102  parameter( large = 1.0e6 )
103  COMPLEX CONE
104  parameter( cone = 1.0e0 )
105 * ..
106 * .. Local Scalars ..
107  CHARACTER TRANA, TRANB
108  INTEGER I, IMLA, IMLAD, IMLB, IMLC, INFO, ISGN, ITRANA,
109  $ ITRANB, J, M, N
110  REAL BIGNUM, EPS, RES, RES1, SCALE, SMLNUM, TNRM,
111  $ XNRM
112  COMPLEX RMUL
113 * ..
114 * .. Local Arrays ..
115  REAL DUM( 1 ), VM1( 3 ), VM2( 3 )
116  COMPLEX 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  REAL CLANGE, SLAMCH
122  EXTERNAL clange, slamch
123 * ..
124 * .. External Subroutines ..
125  EXTERNAL cgemm, ctrsyl
126 * ..
127 * .. Intrinsic Functions ..
128  INTRINSIC abs, max, real, sqrt
129 * ..
130 * .. Executable Statements ..
131 *
132 * Get machine parameters
133 *
134  eps = slamch( 'P' )
135  smlnum = slamch( 'S' ) / eps
136  bignum = one / smlnum
137  CALL slabad( smlnum, bignum )
138 *
139 * Set up test case parameters
140 *
141  vm1( 1 ) = sqrt( smlnum )
142  vm1( 2 ) = one
143  vm1( 3 ) = large
144  vm2( 1 ) = one
145  vm2( 2 ) = one + two*eps
146  vm2( 3 ) = two
147 *
148  knt = 0
149  ninfo = 0
150  lmax = 0
151  rmax = zero
152 *
153 * Begin test loop
154 *
155  10 CONTINUE
156  READ( nin, fmt = * )m, n
157  IF( n.EQ.0 )
158  $ RETURN
159  DO 20 i = 1, m
160  READ( nin, fmt = * )( atmp( i, j ), j = 1, m )
161  20 CONTINUE
162  DO 30 i = 1, n
163  READ( nin, fmt = * )( btmp( i, j ), j = 1, n )
164  30 CONTINUE
165  DO 40 i = 1, m
166  READ( nin, fmt = * )( ctmp( i, j ), j = 1, n )
167  40 CONTINUE
168  DO 170 imla = 1, 3
169  DO 160 imlad = 1, 3
170  DO 150 imlb = 1, 3
171  DO 140 imlc = 1, 3
172  DO 130 itrana = 1, 2
173  DO 120 itranb = 1, 2
174  DO 110 isgn = -1, 1, 2
175  IF( itrana.EQ.1 )
176  $ trana = 'N'
177  IF( itrana.EQ.2 )
178  $ trana = 'C'
179  IF( itranb.EQ.1 )
180  $ tranb = 'N'
181  IF( itranb.EQ.2 )
182  $ tranb = 'C'
183  tnrm = zero
184  DO 60 i = 1, m
185  DO 50 j = 1, m
186  a( i, j ) = atmp( i, j )*vm1( imla )
187  tnrm = max( tnrm, abs( a( i, j ) ) )
188  50 CONTINUE
189  a( i, i ) = a( i, i )*vm2( imlad )
190  tnrm = max( tnrm, abs( a( i, i ) ) )
191  60 CONTINUE
192  DO 80 i = 1, n
193  DO 70 j = 1, n
194  b( i, j ) = btmp( i, j )*vm1( imlb )
195  tnrm = max( tnrm, abs( b( i, j ) ) )
196  70 CONTINUE
197  80 CONTINUE
198  IF( tnrm.EQ.zero )
199  $ tnrm = one
200  DO 100 i = 1, m
201  DO 90 j = 1, n
202  c( i, j ) = ctmp( i, j )*vm1( imlc )
203  csav( i, j ) = c( i, j )
204  90 CONTINUE
205  100 CONTINUE
206  knt = knt + 1
207  CALL ctrsyl( trana, tranb, isgn, m, n, a,
208  $ ldt, b, ldt, c, ldt, scale,
209  $ info )
210  IF( info.NE.0 )
211  $ ninfo = ninfo + 1
212  xnrm = clange( 'M', m, n, c, ldt, dum )
213  rmul = cone
214  IF( xnrm.GT.one .AND. tnrm.GT.one ) THEN
215  IF( xnrm.GT.bignum / tnrm ) THEN
216  rmul = max( xnrm, tnrm )
217  rmul = cone / rmul
218  END IF
219  END IF
220  CALL cgemm( trana, 'N', m, n, m, rmul, a,
221  $ ldt, c, ldt, -scale*rmul, csav,
222  $ ldt )
223  CALL cgemm( 'N', tranb, m, n, n,
224  $ real( isgn )*rmul, c, ldt, b,
225  $ ldt, cone, csav, ldt )
226  res1 = clange( 'M', m, n, csav, ldt, dum )
227  res = res1 / max( smlnum, smlnum*xnrm,
228  $ ( ( abs( rmul )*tnrm )*eps )*xnrm )
229  IF( res.GT.rmax ) THEN
230  lmax = knt
231  rmax = res
232  END IF
233  110 CONTINUE
234  120 CONTINUE
235  130 CONTINUE
236  140 CONTINUE
237  150 CONTINUE
238  160 CONTINUE
239  170 CONTINUE
240  GO TO 10
241 *
242 * End of CGET35
243 *
subroutine slabad(SMALL, LARGE)
SLABAD
Definition: slabad.f:74
subroutine cgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CGEMM
Definition: cgemm.f:187
real function clange(NORM, M, N, A, LDA, WORK)
CLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: clange.f:115
subroutine ctrsyl(TRANA, TRANB, ISGN, M, N, A, LDA, B, LDB, C, LDC, SCALE, INFO)
CTRSYL
Definition: ctrsyl.f:157
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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