LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
zpocon.f
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1 *> \brief \b ZPOCON
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
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15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE ZPOCON( UPLO, N, A, LDA, ANORM, RCOND, WORK, RWORK,
22 * INFO )
23 *
24 * .. Scalar Arguments ..
25 * CHARACTER UPLO
26 * INTEGER INFO, LDA, N
27 * DOUBLE PRECISION ANORM, RCOND
28 * ..
29 * .. Array Arguments ..
30 * DOUBLE PRECISION RWORK( * )
31 * COMPLEX*16 A( LDA, * ), WORK( * )
32 * ..
33 *
34 *
35 *> \par Purpose:
36 * =============
37 *>
38 *> \verbatim
39 *>
40 *> ZPOCON estimates the reciprocal of the condition number (in the
41 *> 1-norm) of a complex Hermitian positive definite matrix using the
42 *> Cholesky factorization A = U**H*U or A = L*L**H computed by ZPOTRF.
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 triangle of A is stored;
55 *> = 'L': Lower triangle of A is stored.
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] A
65 *> \verbatim
66 *> A is COMPLEX*16 array, dimension (LDA,N)
67 *> The triangular factor U or L from the Cholesky factorization
68 *> A = U**H*U or A = L*L**H, as computed by ZPOTRF.
69 *> \endverbatim
70 *>
71 *> \param[in] LDA
72 *> \verbatim
73 *> LDA is INTEGER
74 *> The leading dimension of the array A. LDA >= max(1,N).
75 *> \endverbatim
76 *>
77 *> \param[in] ANORM
78 *> \verbatim
79 *> ANORM is DOUBLE PRECISION
80 *> The 1-norm (or infinity-norm) of the Hermitian matrix A.
81 *> \endverbatim
82 *>
83 *> \param[out] RCOND
84 *> \verbatim
85 *> RCOND is DOUBLE PRECISION
86 *> The reciprocal of the condition number of the matrix A,
87 *> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
88 *> estimate of the 1-norm of inv(A) computed in this routine.
89 *> \endverbatim
90 *>
91 *> \param[out] WORK
92 *> \verbatim
93 *> WORK is COMPLEX*16 array, dimension (2*N)
94 *> \endverbatim
95 *>
96 *> \param[out] RWORK
97 *> \verbatim
98 *> RWORK is DOUBLE PRECISION array, dimension (N)
99 *> \endverbatim
100 *>
101 *> \param[out] INFO
102 *> \verbatim
103 *> INFO is INTEGER
104 *> = 0: successful exit
105 *> < 0: if INFO = -i, the i-th argument had an illegal value
106 *> \endverbatim
107 *
108 * Authors:
109 * ========
110 *
111 *> \author Univ. of Tennessee
112 *> \author Univ. of California Berkeley
113 *> \author Univ. of Colorado Denver
114 *> \author NAG Ltd.
115 *
116 *> \ingroup complex16POcomputational
117 *
118 * =====================================================================
119  SUBROUTINE zpocon( UPLO, N, A, LDA, ANORM, RCOND, WORK, RWORK,
120  $ INFO )
121 *
122 * -- LAPACK computational routine --
123 * -- LAPACK is a software package provided by Univ. of Tennessee, --
124 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
125 *
126 * .. Scalar Arguments ..
127  CHARACTER UPLO
128  INTEGER INFO, LDA, N
129  DOUBLE PRECISION ANORM, RCOND
130 * ..
131 * .. Array Arguments ..
132  DOUBLE PRECISION RWORK( * )
133  COMPLEX*16 A( LDA, * ), WORK( * )
134 * ..
135 *
136 * =====================================================================
137 *
138 * .. Parameters ..
139  DOUBLE PRECISION ONE, ZERO
140  parameter( one = 1.0d+0, zero = 0.0d+0 )
141 * ..
142 * .. Local Scalars ..
143  LOGICAL UPPER
144  CHARACTER NORMIN
145  INTEGER IX, KASE
146  DOUBLE PRECISION AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
147  COMPLEX*16 ZDUM
148 * ..
149 * .. Local Arrays ..
150  INTEGER ISAVE( 3 )
151 * ..
152 * .. External Functions ..
153  LOGICAL LSAME
154  INTEGER IZAMAX
155  DOUBLE PRECISION DLAMCH
156  EXTERNAL lsame, izamax, dlamch
157 * ..
158 * .. External Subroutines ..
159  EXTERNAL xerbla, zdrscl, zlacn2, zlatrs
160 * ..
161 * .. Intrinsic Functions ..
162  INTRINSIC abs, dble, dimag, max
163 * ..
164 * .. Statement Functions ..
165  DOUBLE PRECISION CABS1
166 * ..
167 * .. Statement Function definitions ..
168  cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
169 * ..
170 * .. Executable Statements ..
171 *
172 * Test the input parameters.
173 *
174  info = 0
175  upper = lsame( uplo, 'U' )
176  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
177  info = -1
178  ELSE IF( n.LT.0 ) THEN
179  info = -2
180  ELSE IF( lda.LT.max( 1, n ) ) THEN
181  info = -4
182  ELSE IF( anorm.LT.zero ) THEN
183  info = -5
184  END IF
185  IF( info.NE.0 ) THEN
186  CALL xerbla( 'ZPOCON', -info )
187  RETURN
188  END IF
189 *
190 * Quick return if possible
191 *
192  rcond = zero
193  IF( n.EQ.0 ) THEN
194  rcond = one
195  RETURN
196  ELSE IF( anorm.EQ.zero ) THEN
197  RETURN
198  END IF
199 *
200  smlnum = dlamch( 'Safe minimum' )
201 *
202 * Estimate the 1-norm of inv(A).
203 *
204  kase = 0
205  normin = 'N'
206  10 CONTINUE
207  CALL zlacn2( n, work( n+1 ), work, ainvnm, kase, isave )
208  IF( kase.NE.0 ) THEN
209  IF( upper ) THEN
210 *
211 * Multiply by inv(U**H).
212 *
213  CALL zlatrs( 'Upper', 'Conjugate transpose', 'Non-unit',
214  $ normin, n, a, lda, work, scalel, rwork, info )
215  normin = 'Y'
216 *
217 * Multiply by inv(U).
218 *
219  CALL zlatrs( 'Upper', 'No transpose', 'Non-unit', normin, n,
220  $ a, lda, work, scaleu, rwork, info )
221  ELSE
222 *
223 * Multiply by inv(L).
224 *
225  CALL zlatrs( 'Lower', 'No transpose', 'Non-unit', normin, n,
226  $ a, lda, work, scalel, rwork, info )
227  normin = 'Y'
228 *
229 * Multiply by inv(L**H).
230 *
231  CALL zlatrs( 'Lower', 'Conjugate transpose', 'Non-unit',
232  $ normin, n, a, lda, work, scaleu, rwork, info )
233  END IF
234 *
235 * Multiply by 1/SCALE if doing so will not cause overflow.
236 *
237  scale = scalel*scaleu
238  IF( scale.NE.one ) THEN
239  ix = izamax( n, work, 1 )
240  IF( scale.LT.cabs1( work( ix ) )*smlnum .OR. scale.EQ.zero )
241  $ GO TO 20
242  CALL zdrscl( n, scale, work, 1 )
243  END IF
244  GO TO 10
245  END IF
246 *
247 * Compute the estimate of the reciprocal condition number.
248 *
249  IF( ainvnm.NE.zero )
250  $ rcond = ( one / ainvnm ) / anorm
251 *
252  20 CONTINUE
253  RETURN
254 *
255 * End of ZPOCON
256 *
257  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine zlacn2(N, V, X, EST, KASE, ISAVE)
ZLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition: zlacn2.f:133
subroutine zlatrs(UPLO, TRANS, DIAG, NORMIN, N, A, LDA, X, SCALE, CNORM, INFO)
ZLATRS solves a triangular system of equations with the scale factor set to prevent overflow.
Definition: zlatrs.f:239
subroutine zdrscl(N, SA, SX, INCX)
ZDRSCL multiplies a vector by the reciprocal of a real scalar.
Definition: zdrscl.f:84
subroutine zpocon(UPLO, N, A, LDA, ANORM, RCOND, WORK, RWORK, INFO)
ZPOCON
Definition: zpocon.f:121