LAPACK  3.7.0 LAPACK: Linear Algebra PACKage
cla_gbrcond_c.f
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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 *
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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[in] WORK
136 *> \verbatim
137 *> WORK is COMPLEX array, dimension (2*N).
138 *> Workspace.
139 *> \endverbatim
140 *>
141 *> \param[in] 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 *> \date December 2016
156 *
157 *> \ingroup complexGBcomputational
158 *
159 * =====================================================================
160  REAL FUNCTION cla_gbrcond_c( TRANS, N, KL, KU, AB, LDAB, AFB,
161  \$ ldafb, ipiv, c, capply, info, work,
162  \$ rwork )
163 *
164 * -- LAPACK computational routine (version 3.7.0) --
165 * -- LAPACK is a software package provided by Univ. of Tennessee, --
166 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
167 * December 2016
168 *
169 * .. Scalar Arguments ..
170  CHARACTER TRANS
171  LOGICAL CAPPLY
172  INTEGER N, KL, KU, KD, KE, LDAB, LDAFB, INFO
173 * ..
174 * .. Array Arguments ..
175  INTEGER IPIV( * )
176  COMPLEX AB( ldab, * ), AFB( ldafb, * ), WORK( * )
177  REAL C( * ), RWORK( * )
178 * ..
179 *
180 * =====================================================================
181 *
182 * .. Local Scalars ..
183  LOGICAL NOTRANS
184  INTEGER KASE, I, J
185  REAL AINVNM, ANORM, TMP
186  COMPLEX ZDUM
187 * ..
188 * .. Local Arrays ..
189  INTEGER ISAVE( 3 )
190 * ..
191 * .. External Functions ..
192  LOGICAL LSAME
193  EXTERNAL lsame
194 * ..
195 * .. External Subroutines ..
196  EXTERNAL clacn2, cgbtrs, xerbla
197 * ..
198 * .. Intrinsic Functions ..
199  INTRINSIC abs, max
200 * ..
201 * .. Statement Functions ..
202  REAL CABS1
203 * ..
204 * .. Statement Function Definitions ..
205  cabs1( zdum ) = abs( REAL( ZDUM ) ) + abs( AIMAG( zdum ) )
206 * ..
207 * .. Executable Statements ..
208  cla_gbrcond_c = 0.0e+0
209 *
210  info = 0
211  notrans = lsame( trans, 'N' )
212  IF ( .NOT. notrans .AND. .NOT. lsame( trans, 'T' ) .AND. .NOT.
213  \$ lsame( trans, 'C' ) ) THEN
214  info = -1
215  ELSE IF( n.LT.0 ) THEN
216  info = -2
217  ELSE IF( kl.LT.0 .OR. kl.GT.n-1 ) THEN
218  info = -3
219  ELSE IF( ku.LT.0 .OR. ku.GT.n-1 ) THEN
220  info = -4
221  ELSE IF( ldab.LT.kl+ku+1 ) THEN
222  info = -6
223  ELSE IF( ldafb.LT.2*kl+ku+1 ) THEN
224  info = -8
225  END IF
226  IF( info.NE.0 ) THEN
227  CALL xerbla( 'CLA_GBRCOND_C', -info )
228  RETURN
229  END IF
230 *
231 * Compute norm of op(A)*op2(C).
232 *
233  anorm = 0.0e+0
234  kd = ku + 1
235  ke = kl + 1
236  IF ( notrans ) THEN
237  DO i = 1, n
238  tmp = 0.0e+0
239  IF ( capply ) THEN
240  DO j = max( i-kl, 1 ), min( i+ku, n )
241  tmp = tmp + cabs1( ab( kd+i-j, j ) ) / c( j )
242  END DO
243  ELSE
244  DO j = max( i-kl, 1 ), min( i+ku, n )
245  tmp = tmp + cabs1( ab( kd+i-j, j ) )
246  END DO
247  END IF
248  rwork( i ) = tmp
249  anorm = max( anorm, tmp )
250  END DO
251  ELSE
252  DO i = 1, n
253  tmp = 0.0e+0
254  IF ( capply ) THEN
255  DO j = max( i-kl, 1 ), min( i+ku, n )
256  tmp = tmp + cabs1( ab( ke-i+j, i ) ) / c( j )
257  END DO
258  ELSE
259  DO j = max( i-kl, 1 ), min( i+ku, n )
260  tmp = tmp + cabs1( ab( ke-i+j, i ) )
261  END DO
262  END IF
263  rwork( i ) = tmp
264  anorm = max( anorm, tmp )
265  END DO
266  END IF
267 *
268 * Quick return if possible.
269 *
270  IF( n.EQ.0 ) THEN
271  cla_gbrcond_c = 1.0e+0
272  RETURN
273  ELSE IF( anorm .EQ. 0.0e+0 ) THEN
274  RETURN
275  END IF
276 *
277 * Estimate the norm of inv(op(A)).
278 *
279  ainvnm = 0.0e+0
280 *
281  kase = 0
282  10 CONTINUE
283  CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
284  IF( kase.NE.0 ) THEN
285  IF( kase.EQ.2 ) THEN
286 *
287 * Multiply by R.
288 *
289  DO i = 1, n
290  work( i ) = work( i ) * rwork( i )
291  END DO
292 *
293  IF ( notrans ) THEN
294  CALL cgbtrs( 'No transpose', n, kl, ku, 1, afb, ldafb,
295  \$ ipiv, work, n, info )
296  ELSE
297  CALL cgbtrs( 'Conjugate transpose', n, kl, ku, 1, afb,
298  \$ ldafb, ipiv, work, n, info )
299  ENDIF
300 *
301 * Multiply by inv(C).
302 *
303  IF ( capply ) THEN
304  DO i = 1, n
305  work( i ) = work( i ) * c( i )
306  END DO
307  END IF
308  ELSE
309 *
310 * Multiply by inv(C**H).
311 *
312  IF ( capply ) THEN
313  DO i = 1, n
314  work( i ) = work( i ) * c( i )
315  END DO
316  END IF
317 *
318  IF ( notrans ) THEN
319  CALL cgbtrs( 'Conjugate transpose', n, kl, ku, 1, afb,
320  \$ ldafb, ipiv, work, n, info )
321  ELSE
322  CALL cgbtrs( 'No transpose', n, kl, ku, 1, afb, ldafb,
323  \$ ipiv, work, n, info )
324  END IF
325 *
326 * Multiply by R.
327 *
328  DO i = 1, n
329  work( i ) = work( i ) * rwork( i )
330  END DO
331  END IF
332  GO TO 10
333  END IF
334 *
335 * Compute the estimate of the reciprocal condition number.
336 *
337  IF( ainvnm .NE. 0.0e+0 )
338  \$ cla_gbrcond_c = 1.0e+0 / ainvnm
339 *
340  RETURN
341 *
342  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
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:135
subroutine cgbtrs(TRANS, N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO)
CGBTRS
Definition: cgbtrs.f:140