LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
cla_gbrcond_c.f
Go to the documentation of this file.
1 *> \brief \b CLA_GBRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general banded matrices.
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
9 *> Download CLA_GBRCOND_C + dependencies
10 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cla_gbrcond_c.f">
11 *> [TGZ]</a>
12 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cla_gbrcond_c.f">
13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cla_gbrcond_c.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * REAL FUNCTION CLA_GBRCOND_C( TRANS, N, KL, KU, AB, LDAB, AFB,
22 * LDAFB, IPIV, C, CAPPLY, INFO, WORK,
23 * RWORK )
24 *
25 * .. Scalar Arguments ..
26 * CHARACTER TRANS
27 * LOGICAL CAPPLY
28 * INTEGER N, KL, KU, KD, KE, LDAB, LDAFB, INFO
29 * ..
30 * .. Array Arguments ..
31 * INTEGER IPIV( * )
32 * COMPLEX AB( LDAB, * ), AFB( LDAFB, * ), WORK( * )
33 * REAL C( * ), RWORK( * )
34 * ..
35 *
36 *
37 *> \par Purpose:
38 * =============
39 *>
40 *> \verbatim
41 *>
42 *> CLA_GBRCOND_C Computes the infinity norm condition number of
43 *> op(A) * inv(diag(C)) where C is a REAL vector.
44 *> \endverbatim
45 *
46 * Arguments:
47 * ==========
48 *
49 *> \param[in] TRANS
50 *> \verbatim
51 *> TRANS is CHARACTER*1
52 *> Specifies the form of the system of equations:
53 *> = 'N': A * X = B (No transpose)
54 *> = 'T': A**T * X = B (Transpose)
55 *> = 'C': A**H * X = B (Conjugate Transpose = Transpose)
56 *> \endverbatim
57 *>
58 *> \param[in] N
59 *> \verbatim
60 *> N is INTEGER
61 *> The number of linear equations, i.e., the order of the
62 *> matrix A. N >= 0.
63 *> \endverbatim
64 *>
65 *> \param[in] KL
66 *> \verbatim
67 *> KL is INTEGER
68 *> The number of subdiagonals within the band of A. KL >= 0.
69 *> \endverbatim
70 *>
71 *> \param[in] KU
72 *> \verbatim
73 *> KU is INTEGER
74 *> The number of superdiagonals within the band of A. KU >= 0.
75 *> \endverbatim
76 *>
77 *> \param[in] AB
78 *> \verbatim
79 *> AB is COMPLEX array, dimension (LDAB,N)
80 *> On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
81 *> The j-th column of A is stored in the j-th column of the
82 *> array AB as follows:
83 *> AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
84 *> \endverbatim
85 *>
86 *> \param[in] LDAB
87 *> \verbatim
88 *> LDAB is INTEGER
89 *> The leading dimension of the array AB. LDAB >= KL+KU+1.
90 *> \endverbatim
91 *>
92 *> \param[in] AFB
93 *> \verbatim
94 *> AFB is COMPLEX array, dimension (LDAFB,N)
95 *> Details of the LU factorization of the band matrix A, as
96 *> computed by CGBTRF. U is stored as an upper triangular
97 *> band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1,
98 *> and the multipliers used during the factorization are stored
99 *> in rows KL+KU+2 to 2*KL+KU+1.
100 *> \endverbatim
101 *>
102 *> \param[in] LDAFB
103 *> \verbatim
104 *> LDAFB is INTEGER
105 *> The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.
106 *> \endverbatim
107 *>
108 *> \param[in] IPIV
109 *> \verbatim
110 *> IPIV is INTEGER array, dimension (N)
111 *> The pivot indices from the factorization A = P*L*U
112 *> as computed by CGBTRF; row i of the matrix was interchanged
113 *> with row IPIV(i).
114 *> \endverbatim
115 *>
116 *> \param[in] C
117 *> \verbatim
118 *> C is REAL array, dimension (N)
119 *> The vector C in the formula op(A) * inv(diag(C)).
120 *> \endverbatim
121 *>
122 *> \param[in] CAPPLY
123 *> \verbatim
124 *> CAPPLY is LOGICAL
125 *> If .TRUE. then access the vector C in the formula above.
126 *> \endverbatim
127 *>
128 *> \param[out] INFO
129 *> \verbatim
130 *> INFO is INTEGER
131 *> = 0: Successful exit.
132 *> i > 0: The ith argument is invalid.
133 *> \endverbatim
134 *>
135 *> \param[out] WORK
136 *> \verbatim
137 *> WORK is COMPLEX array, dimension (2*N).
138 *> Workspace.
139 *> \endverbatim
140 *>
141 *> \param[out] RWORK
142 *> \verbatim
143 *> RWORK is REAL array, dimension (N).
144 *> Workspace.
145 *> \endverbatim
146 *
147 * Authors:
148 * ========
149 *
150 *> \author Univ. of Tennessee
151 *> \author Univ. of California Berkeley
152 *> \author Univ. of Colorado Denver
153 *> \author NAG Ltd.
154 *
155 *> \ingroup complexGBcomputational
156 *
157 * =====================================================================
158  REAL function cla_gbrcond_c( trans, n, kl, ku, ab, ldab, afb,
159  $ ldafb, ipiv, c, capply, info, work,
160  $ rwork )
161 *
162 * -- LAPACK computational routine --
163 * -- LAPACK is a software package provided by Univ. of Tennessee, --
164 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
165 *
166 * .. Scalar Arguments ..
167  CHARACTER trans
168  LOGICAL capply
169  INTEGER n, kl, ku, kd, ke, ldab, ldafb, info
170 * ..
171 * .. Array Arguments ..
172  INTEGER ipiv( * )
173  COMPLEX ab( ldab, * ), afb( ldafb, * ), work( * )
174  REAL c( * ), rwork( * )
175 * ..
176 *
177 * =====================================================================
178 *
179 * .. Local Scalars ..
180  LOGICAL notrans
181  INTEGER kase, i, j
182  REAL ainvnm, anorm, tmp
183  COMPLEX zdum
184 * ..
185 * .. Local Arrays ..
186  INTEGER isave( 3 )
187 * ..
188 * .. External Functions ..
189  LOGICAL lsame
190  EXTERNAL lsame
191 * ..
192 * .. External Subroutines ..
193  EXTERNAL clacn2, cgbtrs, xerbla
194 * ..
195 * .. Intrinsic Functions ..
196  INTRINSIC abs, max
197 * ..
198 * .. Statement Functions ..
199  REAL cabs1
200 * ..
201 * .. Statement Function Definitions ..
202  cabs1( zdum ) = abs( real( zdum ) ) + abs( aimag( zdum ) )
203 * ..
204 * .. Executable Statements ..
205  cla_gbrcond_c = 0.0e+0
206 *
207  info = 0
208  notrans = lsame( trans, 'N' )
209  IF ( .NOT. notrans .AND. .NOT. lsame( trans, 'T' ) .AND. .NOT.
210  $ lsame( trans, 'C' ) ) THEN
211  info = -1
212  ELSE IF( n.LT.0 ) THEN
213  info = -2
214  ELSE IF( kl.LT.0 .OR. kl.GT.n-1 ) THEN
215  info = -3
216  ELSE IF( ku.LT.0 .OR. ku.GT.n-1 ) THEN
217  info = -4
218  ELSE IF( ldab.LT.kl+ku+1 ) THEN
219  info = -6
220  ELSE IF( ldafb.LT.2*kl+ku+1 ) THEN
221  info = -8
222  END IF
223  IF( info.NE.0 ) THEN
224  CALL xerbla( 'CLA_GBRCOND_C', -info )
225  RETURN
226  END IF
227 *
228 * Compute norm of op(A)*op2(C).
229 *
230  anorm = 0.0e+0
231  kd = ku + 1
232  ke = kl + 1
233  IF ( notrans ) THEN
234  DO i = 1, n
235  tmp = 0.0e+0
236  IF ( capply ) THEN
237  DO j = max( i-kl, 1 ), min( i+ku, n )
238  tmp = tmp + cabs1( ab( kd+i-j, j ) ) / c( j )
239  END DO
240  ELSE
241  DO j = max( i-kl, 1 ), min( i+ku, n )
242  tmp = tmp + cabs1( ab( kd+i-j, j ) )
243  END DO
244  END IF
245  rwork( i ) = tmp
246  anorm = max( anorm, tmp )
247  END DO
248  ELSE
249  DO i = 1, n
250  tmp = 0.0e+0
251  IF ( capply ) THEN
252  DO j = max( i-kl, 1 ), min( i+ku, n )
253  tmp = tmp + cabs1( ab( ke-i+j, i ) ) / c( j )
254  END DO
255  ELSE
256  DO j = max( i-kl, 1 ), min( i+ku, n )
257  tmp = tmp + cabs1( ab( ke-i+j, i ) )
258  END DO
259  END IF
260  rwork( i ) = tmp
261  anorm = max( anorm, tmp )
262  END DO
263  END IF
264 *
265 * Quick return if possible.
266 *
267  IF( n.EQ.0 ) THEN
268  cla_gbrcond_c = 1.0e+0
269  RETURN
270  ELSE IF( anorm .EQ. 0.0e+0 ) THEN
271  RETURN
272  END IF
273 *
274 * Estimate the norm of inv(op(A)).
275 *
276  ainvnm = 0.0e+0
277 *
278  kase = 0
279  10 CONTINUE
280  CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
281  IF( kase.NE.0 ) THEN
282  IF( kase.EQ.2 ) THEN
283 *
284 * Multiply by R.
285 *
286  DO i = 1, n
287  work( i ) = work( i ) * rwork( i )
288  END DO
289 *
290  IF ( notrans ) THEN
291  CALL cgbtrs( 'No transpose', n, kl, ku, 1, afb, ldafb,
292  $ ipiv, work, n, info )
293  ELSE
294  CALL cgbtrs( 'Conjugate transpose', n, kl, ku, 1, afb,
295  $ ldafb, ipiv, work, n, info )
296  ENDIF
297 *
298 * Multiply by inv(C).
299 *
300  IF ( capply ) THEN
301  DO i = 1, n
302  work( i ) = work( i ) * c( i )
303  END DO
304  END IF
305  ELSE
306 *
307 * Multiply by inv(C**H).
308 *
309  IF ( capply ) THEN
310  DO i = 1, n
311  work( i ) = work( i ) * c( i )
312  END DO
313  END IF
314 *
315  IF ( notrans ) THEN
316  CALL cgbtrs( 'Conjugate transpose', n, kl, ku, 1, afb,
317  $ ldafb, ipiv, work, n, info )
318  ELSE
319  CALL cgbtrs( 'No transpose', n, kl, ku, 1, afb, ldafb,
320  $ ipiv, work, n, info )
321  END IF
322 *
323 * Multiply by R.
324 *
325  DO i = 1, n
326  work( i ) = work( i ) * rwork( i )
327  END DO
328  END IF
329  GO TO 10
330  END IF
331 *
332 * Compute the estimate of the reciprocal condition number.
333 *
334  IF( ainvnm .NE. 0.0e+0 )
335  $ cla_gbrcond_c = 1.0e+0 / ainvnm
336 *
337  RETURN
338 *
339 * End of CLA_GBRCOND_C
340 *
341  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine cgbtrs(TRANS, N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO)
CGBTRS
Definition: cgbtrs.f:138
real function cla_gbrcond_c(TRANS, N, KL, KU, AB, LDAB, AFB, LDAFB, IPIV, C, CAPPLY, INFO, WORK, RWORK)
CLA_GBRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general banded ma...
subroutine clacn2(N, V, X, EST, KASE, ISAVE)
CLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition: clacn2.f:133