LAPACK  3.4.2 LAPACK: Linear Algebra PACKage
dpbcon.f
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1 *> \brief \b DPBCON
2 *
3 * =========== DOCUMENTATION ===========
4 *
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17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE DPBCON( UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK,
22 * IWORK, INFO )
23 *
24 * .. Scalar Arguments ..
25 * CHARACTER UPLO
26 * INTEGER INFO, KD, LDAB, N
27 * DOUBLE PRECISION ANORM, RCOND
28 * ..
29 * .. Array Arguments ..
30 * INTEGER IWORK( * )
31 * DOUBLE PRECISION AB( LDAB, * ), WORK( * )
32 * ..
33 *
34 *
35 *> \par Purpose:
36 * =============
37 *>
38 *> \verbatim
39 *>
40 *> DPBCON estimates the reciprocal of the condition number (in the
41 *> 1-norm) of a real symmetric positive definite band matrix using the
42 *> Cholesky factorization A = U**T*U or A = L*L**T computed by DPBTRF.
43 *>
44 *> An estimate is obtained for norm(inv(A)), and the reciprocal of the
45 *> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
46 *> \endverbatim
47 *
48 * Arguments:
49 * ==========
50 *
51 *> \param[in] UPLO
52 *> \verbatim
53 *> UPLO is CHARACTER*1
54 *> = 'U': Upper triangular factor stored in AB;
55 *> = 'L': Lower triangular factor stored in AB.
56 *> \endverbatim
57 *>
58 *> \param[in] N
59 *> \verbatim
60 *> N is INTEGER
61 *> The order of the matrix A. N >= 0.
62 *> \endverbatim
63 *>
64 *> \param[in] KD
65 *> \verbatim
66 *> KD is INTEGER
67 *> The number of superdiagonals of the matrix A if UPLO = 'U',
68 *> or the number of subdiagonals if UPLO = 'L'. KD >= 0.
69 *> \endverbatim
70 *>
71 *> \param[in] AB
72 *> \verbatim
73 *> AB is DOUBLE PRECISION array, dimension (LDAB,N)
74 *> The triangular factor U or L from the Cholesky factorization
75 *> A = U**T*U or A = L*L**T of the band matrix A, stored in the
76 *> first KD+1 rows of the array. The j-th column of U or L is
77 *> stored in the j-th column of the array AB as follows:
78 *> if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
79 *> if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).
80 *> \endverbatim
81 *>
82 *> \param[in] LDAB
83 *> \verbatim
84 *> LDAB is INTEGER
85 *> The leading dimension of the array AB. LDAB >= KD+1.
86 *> \endverbatim
87 *>
88 *> \param[in] ANORM
89 *> \verbatim
90 *> ANORM is DOUBLE PRECISION
91 *> The 1-norm (or infinity-norm) of the symmetric band matrix A.
92 *> \endverbatim
93 *>
94 *> \param[out] RCOND
95 *> \verbatim
96 *> RCOND is DOUBLE PRECISION
97 *> The reciprocal of the condition number of the matrix A,
98 *> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
99 *> estimate of the 1-norm of inv(A) computed in this routine.
100 *> \endverbatim
101 *>
102 *> \param[out] WORK
103 *> \verbatim
104 *> WORK is DOUBLE PRECISION array, dimension (3*N)
105 *> \endverbatim
106 *>
107 *> \param[out] IWORK
108 *> \verbatim
109 *> IWORK is INTEGER array, dimension (N)
110 *> \endverbatim
111 *>
112 *> \param[out] INFO
113 *> \verbatim
114 *> INFO is INTEGER
115 *> = 0: successful exit
116 *> < 0: if INFO = -i, the i-th argument had an illegal value
117 *> \endverbatim
118 *
119 * Authors:
120 * ========
121 *
122 *> \author Univ. of Tennessee
123 *> \author Univ. of California Berkeley
124 *> \author Univ. of Colorado Denver
125 *> \author NAG Ltd.
126 *
127 *> \date November 2011
128 *
129 *> \ingroup doubleOTHERcomputational
130 *
131 * =====================================================================
132  SUBROUTINE dpbcon( UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK,
133  \$ iwork, info )
134 *
135 * -- LAPACK computational routine (version 3.4.0) --
136 * -- LAPACK is a software package provided by Univ. of Tennessee, --
137 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
138 * November 2011
139 *
140 * .. Scalar Arguments ..
141  CHARACTER uplo
142  INTEGER info, kd, ldab, n
143  DOUBLE PRECISION anorm, rcond
144 * ..
145 * .. Array Arguments ..
146  INTEGER iwork( * )
147  DOUBLE PRECISION ab( ldab, * ), work( * )
148 * ..
149 *
150 * =====================================================================
151 *
152 * .. Parameters ..
153  DOUBLE PRECISION one, zero
154  parameter( one = 1.0d+0, zero = 0.0d+0 )
155 * ..
156 * .. Local Scalars ..
157  LOGICAL upper
158  CHARACTER normin
159  INTEGER ix, kase
160  DOUBLE PRECISION ainvnm, scale, scalel, scaleu, smlnum
161 * ..
162 * .. Local Arrays ..
163  INTEGER isave( 3 )
164 * ..
165 * .. External Functions ..
166  LOGICAL lsame
167  INTEGER idamax
168  DOUBLE PRECISION dlamch
169  EXTERNAL lsame, idamax, dlamch
170 * ..
171 * .. External Subroutines ..
172  EXTERNAL dlacn2, dlatbs, drscl, xerbla
173 * ..
174 * .. Intrinsic Functions ..
175  INTRINSIC abs
176 * ..
177 * .. Executable Statements ..
178 *
179 * Test the input parameters.
180 *
181  info = 0
182  upper = lsame( uplo, 'U' )
183  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
184  info = -1
185  ELSE IF( n.LT.0 ) THEN
186  info = -2
187  ELSE IF( kd.LT.0 ) THEN
188  info = -3
189  ELSE IF( ldab.LT.kd+1 ) THEN
190  info = -5
191  ELSE IF( anorm.LT.zero ) THEN
192  info = -6
193  END IF
194  IF( info.NE.0 ) THEN
195  CALL xerbla( 'DPBCON', -info )
196  return
197  END IF
198 *
199 * Quick return if possible
200 *
201  rcond = zero
202  IF( n.EQ.0 ) THEN
203  rcond = one
204  return
205  ELSE IF( anorm.EQ.zero ) THEN
206  return
207  END IF
208 *
209  smlnum = dlamch( 'Safe minimum' )
210 *
211 * Estimate the 1-norm of the inverse.
212 *
213  kase = 0
214  normin = 'N'
215  10 continue
216  CALL dlacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
217  IF( kase.NE.0 ) THEN
218  IF( upper ) THEN
219 *
220 * Multiply by inv(U**T).
221 *
222  CALL dlatbs( 'Upper', 'Transpose', 'Non-unit', normin, n,
223  \$ kd, ab, ldab, work, scalel, work( 2*n+1 ),
224  \$ info )
225  normin = 'Y'
226 *
227 * Multiply by inv(U).
228 *
229  CALL dlatbs( 'Upper', 'No transpose', 'Non-unit', normin, n,
230  \$ kd, ab, ldab, work, scaleu, work( 2*n+1 ),
231  \$ info )
232  ELSE
233 *
234 * Multiply by inv(L).
235 *
236  CALL dlatbs( 'Lower', 'No transpose', 'Non-unit', normin, n,
237  \$ kd, ab, ldab, work, scalel, work( 2*n+1 ),
238  \$ info )
239  normin = 'Y'
240 *
241 * Multiply by inv(L**T).
242 *
243  CALL dlatbs( 'Lower', 'Transpose', 'Non-unit', normin, n,
244  \$ kd, ab, ldab, work, scaleu, work( 2*n+1 ),
245  \$ info )
246  END IF
247 *
248 * Multiply by 1/SCALE if doing so will not cause overflow.
249 *
250  scale = scalel*scaleu
251  IF( scale.NE.one ) THEN
252  ix = idamax( n, work, 1 )
253  IF( scale.LT.abs( work( ix ) )*smlnum .OR. scale.EQ.zero )
254  \$ go to 20
255  CALL drscl( n, scale, work, 1 )
256  END IF
257  go to 10
258  END IF
259 *
260 * Compute the estimate of the reciprocal condition number.
261 *
262  IF( ainvnm.NE.zero )
263  \$ rcond = ( one / ainvnm ) / anorm
264 *
265  20 continue
266 *
267  return
268 *
269 * End of DPBCON
270 *
271  END