LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ schkgk()

 subroutine schkgk ( integer NIN, integer NOUT )

SCHKGK

Purpose:
``` SCHKGK tests SGGBAK, a routine for backward balancing  of
a matrix pair (A, B).```
Parameters
 [in] NIN ``` NIN is INTEGER The logical unit number for input. NIN > 0.``` [in] NOUT ``` NOUT is INTEGER The logical unit number for output. NOUT > 0.```

Definition at line 53 of file schkgk.f.

54 *
55 * -- LAPACK test routine --
56 * -- LAPACK is a software package provided by Univ. of Tennessee, --
57 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
58 *
59 * .. Scalar Arguments ..
60  INTEGER NIN, NOUT
61 * ..
62 *
63 * =====================================================================
64 *
65 * .. Parameters ..
66  INTEGER LDA, LDB, LDVL, LDVR
67  parameter( lda = 50, ldb = 50, ldvl = 50, ldvr = 50 )
68  INTEGER LDE, LDF, LDWORK
69  parameter( lde = 50, ldf = 50, ldwork = 50 )
70  REAL ZERO, ONE
71  parameter( zero = 0.0e+0, one = 1.0e+0 )
72 * ..
73 * .. Local Scalars ..
74  INTEGER I, IHI, ILO, INFO, J, KNT, M, N, NINFO
75  REAL ANORM, BNORM, EPS, RMAX, VMAX
76 * ..
77 * .. Local Arrays ..
78  INTEGER LMAX( 4 )
79  REAL A( LDA, LDA ), AF( LDA, LDA ), B( LDB, LDB ),
80  \$ BF( LDB, LDB ), E( LDE, LDE ), F( LDF, LDF ),
81  \$ LSCALE( LDA ), RSCALE( LDA ), VL( LDVL, LDVL ),
82  \$ VLF( LDVL, LDVL ), VR( LDVR, LDVR ),
83  \$ VRF( LDVR, LDVR ), WORK( LDWORK, LDWORK )
84 * ..
85 * .. External Functions ..
86  REAL SLAMCH, SLANGE
87  EXTERNAL slamch, slange
88 * ..
89 * .. External Subroutines ..
90  EXTERNAL sgemm, sggbak, sggbal, slacpy
91 * ..
92 * .. Intrinsic Functions ..
93  INTRINSIC abs, max
94 * ..
95 * .. Executable Statements ..
96 *
97 * Initialization
98 *
99  lmax( 1 ) = 0
100  lmax( 2 ) = 0
101  lmax( 3 ) = 0
102  lmax( 4 ) = 0
103  ninfo = 0
104  knt = 0
105  rmax = zero
106 *
107  eps = slamch( 'Precision' )
108 *
109  10 CONTINUE
110  READ( nin, fmt = * )n, m
111  IF( n.EQ.0 )
112  \$ GO TO 100
113 *
114  DO 20 i = 1, n
115  READ( nin, fmt = * )( a( i, j ), j = 1, n )
116  20 CONTINUE
117 *
118  DO 30 i = 1, n
119  READ( nin, fmt = * )( b( i, j ), j = 1, n )
120  30 CONTINUE
121 *
122  DO 40 i = 1, n
123  READ( nin, fmt = * )( vl( i, j ), j = 1, m )
124  40 CONTINUE
125 *
126  DO 50 i = 1, n
127  READ( nin, fmt = * )( vr( i, j ), j = 1, m )
128  50 CONTINUE
129 *
130  knt = knt + 1
131 *
132  anorm = slange( 'M', n, n, a, lda, work )
133  bnorm = slange( 'M', n, n, b, ldb, work )
134 *
135  CALL slacpy( 'FULL', n, n, a, lda, af, lda )
136  CALL slacpy( 'FULL', n, n, b, ldb, bf, ldb )
137 *
138  CALL sggbal( 'B', n, a, lda, b, ldb, ilo, ihi, lscale, rscale,
139  \$ work, info )
140  IF( info.NE.0 ) THEN
141  ninfo = ninfo + 1
142  lmax( 1 ) = knt
143  END IF
144 *
145  CALL slacpy( 'FULL', n, m, vl, ldvl, vlf, ldvl )
146  CALL slacpy( 'FULL', n, m, vr, ldvr, vrf, ldvr )
147 *
148  CALL sggbak( 'B', 'L', n, ilo, ihi, lscale, rscale, m, vl, ldvl,
149  \$ info )
150  IF( info.NE.0 ) THEN
151  ninfo = ninfo + 1
152  lmax( 2 ) = knt
153  END IF
154 *
155  CALL sggbak( 'B', 'R', n, ilo, ihi, lscale, rscale, m, vr, ldvr,
156  \$ info )
157  IF( info.NE.0 ) THEN
158  ninfo = ninfo + 1
159  lmax( 3 ) = knt
160  END IF
161 *
162 * Test of SGGBAK
163 *
164 * Check tilde(VL)'*A*tilde(VR) - VL'*tilde(A)*VR
165 * where tilde(A) denotes the transformed matrix.
166 *
167  CALL sgemm( 'N', 'N', n, m, n, one, af, lda, vr, ldvr, zero, work,
168  \$ ldwork )
169  CALL sgemm( 'T', 'N', m, m, n, one, vl, ldvl, work, ldwork, zero,
170  \$ e, lde )
171 *
172  CALL sgemm( 'N', 'N', n, m, n, one, a, lda, vrf, ldvr, zero, work,
173  \$ ldwork )
174  CALL sgemm( 'T', 'N', m, m, n, one, vlf, ldvl, work, ldwork, zero,
175  \$ f, ldf )
176 *
177  vmax = zero
178  DO 70 j = 1, m
179  DO 60 i = 1, m
180  vmax = max( vmax, abs( e( i, j )-f( i, j ) ) )
181  60 CONTINUE
182  70 CONTINUE
183  vmax = vmax / ( eps*max( anorm, bnorm ) )
184  IF( vmax.GT.rmax ) THEN
185  lmax( 4 ) = knt
186  rmax = vmax
187  END IF
188 *
189 * Check tilde(VL)'*B*tilde(VR) - VL'*tilde(B)*VR
190 *
191  CALL sgemm( 'N', 'N', n, m, n, one, bf, ldb, vr, ldvr, zero, work,
192  \$ ldwork )
193  CALL sgemm( 'T', 'N', m, m, n, one, vl, ldvl, work, ldwork, zero,
194  \$ e, lde )
195 *
196  CALL sgemm( 'N', 'N', n, m, n, one, b, ldb, vrf, ldvr, zero, work,
197  \$ ldwork )
198  CALL sgemm( 'T', 'N', m, m, n, one, vlf, ldvl, work, ldwork, zero,
199  \$ f, ldf )
200 *
201  vmax = zero
202  DO 90 j = 1, m
203  DO 80 i = 1, m
204  vmax = max( vmax, abs( e( i, j )-f( i, j ) ) )
205  80 CONTINUE
206  90 CONTINUE
207  vmax = vmax / ( eps*max( anorm, bnorm ) )
208  IF( vmax.GT.rmax ) THEN
209  lmax( 4 ) = knt
210  rmax = vmax
211  END IF
212 *
213  GO TO 10
214 *
215  100 CONTINUE
216 *
217  WRITE( nout, fmt = 9999 )
218  9999 FORMAT( 1x, '.. test output of SGGBAK .. ' )
219 *
220  WRITE( nout, fmt = 9998 )rmax
221  9998 FORMAT( ' value of largest test error =', e12.3 )
222  WRITE( nout, fmt = 9997 )lmax( 1 )
223  9997 FORMAT( ' example number where SGGBAL info is not 0 =', i4 )
224  WRITE( nout, fmt = 9996 )lmax( 2 )
225  9996 FORMAT( ' example number where SGGBAK(L) info is not 0 =', i4 )
226  WRITE( nout, fmt = 9995 )lmax( 3 )
227  9995 FORMAT( ' example number where SGGBAK(R) info is not 0 =', i4 )
228  WRITE( nout, fmt = 9994 )lmax( 4 )
229  9994 FORMAT( ' example number having largest error =', i4 )
230  WRITE( nout, fmt = 9992 )ninfo
231  9992 FORMAT( ' number of examples where info is not 0 =', i4 )
232  WRITE( nout, fmt = 9991 )knt
233  9991 FORMAT( ' total number of examples tested =', i4 )
234 *
235  RETURN
236 *
237 * End of SCHKGK
238 *
logical function lde(RI, RJ, LR)
Definition: dblat2.f:2942
subroutine slacpy(UPLO, M, N, A, LDA, B, LDB)
SLACPY copies all or part of one two-dimensional array to another.
Definition: slacpy.f:103
subroutine sggbak(JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, M, V, LDV, INFO)
SGGBAK
Definition: sggbak.f:147
subroutine sggbal(JOB, N, A, LDA, B, LDB, ILO, IHI, LSCALE, RSCALE, WORK, INFO)
SGGBAL
Definition: sggbal.f:177
real function slange(NORM, M, N, A, LDA, WORK)
SLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: slange.f:114
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
Definition: sgemm.f:187
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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