LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
spbcon.f
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1 *> \brief \b SPBCON
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
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15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE SPBCON( 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 * REAL ANORM, RCOND
28 * ..
29 * .. Array Arguments ..
30 * INTEGER IWORK( * )
31 * REAL AB( LDAB, * ), WORK( * )
32 * ..
33 *
34 *
35 *> \par Purpose:
36 * =============
37 *>
38 *> \verbatim
39 *>
40 *> SPBCON 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 SPBTRF.
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 REAL 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 REAL
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 REAL
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 REAL 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 *> \ingroup realOTHERcomputational
128 *
129 * =====================================================================
130  SUBROUTINE spbcon( UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK,
131  $ IWORK, INFO )
132 *
133 * -- LAPACK computational routine --
134 * -- LAPACK is a software package provided by Univ. of Tennessee, --
135 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
136 *
137 * .. Scalar Arguments ..
138  CHARACTER UPLO
139  INTEGER INFO, KD, LDAB, N
140  REAL ANORM, RCOND
141 * ..
142 * .. Array Arguments ..
143  INTEGER IWORK( * )
144  REAL AB( LDAB, * ), WORK( * )
145 * ..
146 *
147 * =====================================================================
148 *
149 * .. Parameters ..
150  REAL ONE, ZERO
151  parameter( one = 1.0e+0, zero = 0.0e+0 )
152 * ..
153 * .. Local Scalars ..
154  LOGICAL UPPER
155  CHARACTER NORMIN
156  INTEGER IX, KASE
157  REAL AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
158 * ..
159 * .. Local Arrays ..
160  INTEGER ISAVE( 3 )
161 * ..
162 * .. External Functions ..
163  LOGICAL LSAME
164  INTEGER ISAMAX
165  REAL SLAMCH
166  EXTERNAL lsame, isamax, slamch
167 * ..
168 * .. External Subroutines ..
169  EXTERNAL slacn2, slatbs, srscl, xerbla
170 * ..
171 * .. Intrinsic Functions ..
172  INTRINSIC abs
173 * ..
174 * .. Executable Statements ..
175 *
176 * Test the input parameters.
177 *
178  info = 0
179  upper = lsame( uplo, 'U' )
180  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
181  info = -1
182  ELSE IF( n.LT.0 ) THEN
183  info = -2
184  ELSE IF( kd.LT.0 ) THEN
185  info = -3
186  ELSE IF( ldab.LT.kd+1 ) THEN
187  info = -5
188  ELSE IF( anorm.LT.zero ) THEN
189  info = -6
190  END IF
191  IF( info.NE.0 ) THEN
192  CALL xerbla( 'SPBCON', -info )
193  RETURN
194  END IF
195 *
196 * Quick return if possible
197 *
198  rcond = zero
199  IF( n.EQ.0 ) THEN
200  rcond = one
201  RETURN
202  ELSE IF( anorm.EQ.zero ) THEN
203  RETURN
204  END IF
205 *
206  smlnum = slamch( 'Safe minimum' )
207 *
208 * Estimate the 1-norm of the inverse.
209 *
210  kase = 0
211  normin = 'N'
212  10 CONTINUE
213  CALL slacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
214  IF( kase.NE.0 ) THEN
215  IF( upper ) THEN
216 *
217 * Multiply by inv(U**T).
218 *
219  CALL slatbs( 'Upper', 'Transpose', 'Non-unit', normin, n,
220  $ kd, ab, ldab, work, scalel, work( 2*n+1 ),
221  $ info )
222  normin = 'Y'
223 *
224 * Multiply by inv(U).
225 *
226  CALL slatbs( 'Upper', 'No transpose', 'Non-unit', normin, n,
227  $ kd, ab, ldab, work, scaleu, work( 2*n+1 ),
228  $ info )
229  ELSE
230 *
231 * Multiply by inv(L).
232 *
233  CALL slatbs( 'Lower', 'No transpose', 'Non-unit', normin, n,
234  $ kd, ab, ldab, work, scalel, work( 2*n+1 ),
235  $ info )
236  normin = 'Y'
237 *
238 * Multiply by inv(L**T).
239 *
240  CALL slatbs( 'Lower', 'Transpose', 'Non-unit', normin, n,
241  $ kd, ab, ldab, work, scaleu, work( 2*n+1 ),
242  $ info )
243  END IF
244 *
245 * Multiply by 1/SCALE if doing so will not cause overflow.
246 *
247  scale = scalel*scaleu
248  IF( scale.NE.one ) THEN
249  ix = isamax( n, work, 1 )
250  IF( scale.LT.abs( work( ix ) )*smlnum .OR. scale.EQ.zero )
251  $ GO TO 20
252  CALL srscl( n, scale, work, 1 )
253  END IF
254  GO TO 10
255  END IF
256 *
257 * Compute the estimate of the reciprocal condition number.
258 *
259  IF( ainvnm.NE.zero )
260  $ rcond = ( one / ainvnm ) / anorm
261 *
262  20 CONTINUE
263 *
264  RETURN
265 *
266 * End of SPBCON
267 *
268  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine slacn2(N, V, X, ISGN, EST, KASE, ISAVE)
SLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition: slacn2.f:136
subroutine slatbs(UPLO, TRANS, DIAG, NORMIN, N, KD, AB, LDAB, X, SCALE, CNORM, INFO)
SLATBS solves a triangular banded system of equations.
Definition: slatbs.f:242
subroutine srscl(N, SA, SX, INCX)
SRSCL multiplies a vector by the reciprocal of a real scalar.
Definition: srscl.f:84
subroutine spbcon(UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK, IWORK, INFO)
SPBCON
Definition: spbcon.f:132