LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
checon_rook.f
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1 *> \brief <b> CHECON_ROOK estimates the reciprocal of the condition number fort HE matrices using factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges) </b>
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 CHECON_ROOK( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
22 * INFO )
23 *
24 * .. Scalar Arguments ..
25 * CHARACTER UPLO
26 * INTEGER INFO, LDA, N
27 * REAL ANORM, RCOND
28 * ..
29 * .. Array Arguments ..
30 * INTEGER IPIV( * )
31 * COMPLEX A( LDA, * ), WORK( * )
32 * ..
33 *
34 *
35 *> \par Purpose:
36 * =============
37 *>
38 *> \verbatim
39 *>
40 *> CHECON_ROOK estimates the reciprocal of the condition number of a complex
41 *> Hermitian matrix A using the factorization A = U*D*U**H or
42 *> A = L*D*L**H computed by CHETRF_ROOK.
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 *> Specifies whether the details of the factorization are stored
55 *> as an upper or lower triangular matrix.
56 *> = 'U': Upper triangular, form is A = U*D*U**H;
57 *> = 'L': Lower triangular, form is A = L*D*L**H.
58 *> \endverbatim
59 *>
60 *> \param[in] N
61 *> \verbatim
62 *> N is INTEGER
63 *> The order of the matrix A. N >= 0.
64 *> \endverbatim
65 *>
66 *> \param[in] A
67 *> \verbatim
68 *> A is COMPLEX array, dimension (LDA,N)
69 *> The block diagonal matrix D and the multipliers used to
70 *> obtain the factor U or L as computed by CHETRF_ROOK.
71 *> \endverbatim
72 *>
73 *> \param[in] LDA
74 *> \verbatim
75 *> LDA is INTEGER
76 *> The leading dimension of the array A. LDA >= max(1,N).
77 *> \endverbatim
78 *>
79 *> \param[in] IPIV
80 *> \verbatim
81 *> IPIV is INTEGER array, dimension (N)
82 *> Details of the interchanges and the block structure of D
83 *> as determined by CHETRF_ROOK.
84 *> \endverbatim
85 *>
86 *> \param[in] ANORM
87 *> \verbatim
88 *> ANORM is REAL
89 *> The 1-norm of the original matrix A.
90 *> \endverbatim
91 *>
92 *> \param[out] RCOND
93 *> \verbatim
94 *> RCOND is REAL
95 *> The reciprocal of the condition number of the matrix A,
96 *> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
97 *> estimate of the 1-norm of inv(A) computed in this routine.
98 *> \endverbatim
99 *>
100 *> \param[out] WORK
101 *> \verbatim
102 *> WORK is COMPLEX array, dimension (2*N)
103 *> \endverbatim
104 *>
105 *> \param[out] INFO
106 *> \verbatim
107 *> INFO is INTEGER
108 *> = 0: successful exit
109 *> < 0: if INFO = -i, the i-th argument had an illegal value
110 *> \endverbatim
111 *
112 * Authors:
113 * ========
114 *
115 *> \author Univ. of Tennessee
116 *> \author Univ. of California Berkeley
117 *> \author Univ. of Colorado Denver
118 *> \author NAG Ltd.
119 *
120 *> \date December 2016
121 *
122 *> \ingroup complexHEcomputational
123 *
124 *> \par Contributors:
125 * ==================
126 *> \verbatim
127 *>
128 *> December 2016, Igor Kozachenko,
129 *> Computer Science Division,
130 *> University of California, Berkeley
131 *>
132 *> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
133 *> School of Mathematics,
134 *> University of Manchester
135 *>
136 *> \endverbatim
137 *
138 * =====================================================================
139  SUBROUTINE checon_rook( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
140  $ INFO )
141 *
142 * -- LAPACK computational routine (version 3.7.0) --
143 * -- LAPACK is a software package provided by Univ. of Tennessee, --
144 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
145 * December 2016
146 *
147 * .. Scalar Arguments ..
148  CHARACTER UPLO
149  INTEGER INFO, LDA, N
150  REAL ANORM, RCOND
151 * ..
152 * .. Array Arguments ..
153  INTEGER IPIV( * )
154  COMPLEX A( lda, * ), WORK( * )
155 * ..
156 *
157 * =====================================================================
158 *
159 * .. Parameters ..
160  REAL ONE, ZERO
161  parameter( one = 1.0e+0, zero = 0.0e+0 )
162 * ..
163 * .. Local Scalars ..
164  LOGICAL UPPER
165  INTEGER I, KASE
166  REAL AINVNM
167 * ..
168 * .. Local Arrays ..
169  INTEGER ISAVE( 3 )
170 * ..
171 * .. External Functions ..
172  LOGICAL LSAME
173  EXTERNAL lsame
174 * ..
175 * .. External Subroutines ..
176  EXTERNAL chetrs_rook, clacn2, xerbla
177 * ..
178 * .. Intrinsic Functions ..
179  INTRINSIC max
180 * ..
181 * .. Executable Statements ..
182 *
183 * Test the input parameters.
184 *
185  info = 0
186  upper = lsame( uplo, 'U' )
187  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
188  info = -1
189  ELSE IF( n.LT.0 ) THEN
190  info = -2
191  ELSE IF( lda.LT.max( 1, n ) ) THEN
192  info = -4
193  ELSE IF( anorm.LT.zero ) THEN
194  info = -6
195  END IF
196  IF( info.NE.0 ) THEN
197  CALL xerbla( 'CHECON_ROOK', -info )
198  RETURN
199  END IF
200 *
201 * Quick return if possible
202 *
203  rcond = zero
204  IF( n.EQ.0 ) THEN
205  rcond = one
206  RETURN
207  ELSE IF( anorm.LE.zero ) THEN
208  RETURN
209  END IF
210 *
211 * Check that the diagonal matrix D is nonsingular.
212 *
213  IF( upper ) THEN
214 *
215 * Upper triangular storage: examine D from bottom to top
216 *
217  DO 10 i = n, 1, -1
218  IF( ipiv( i ).GT.0 .AND. a( i, i ).EQ.zero )
219  $ RETURN
220  10 CONTINUE
221  ELSE
222 *
223 * Lower triangular storage: examine D from top to bottom.
224 *
225  DO 20 i = 1, n
226  IF( ipiv( i ).GT.0 .AND. a( i, i ).EQ.zero )
227  $ RETURN
228  20 CONTINUE
229  END IF
230 *
231 * Estimate the 1-norm of the inverse.
232 *
233  kase = 0
234  30 CONTINUE
235  CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
236  IF( kase.NE.0 ) THEN
237 *
238 * Multiply by inv(L*D*L**H) or inv(U*D*U**H).
239 *
240  CALL chetrs_rook( uplo, n, 1, a, lda, ipiv, work, n, info )
241  GO TO 30
242  END IF
243 *
244 * Compute the estimate of the reciprocal condition number.
245 *
246  IF( ainvnm.NE.zero )
247  $ rcond = ( one / ainvnm ) / anorm
248 *
249  RETURN
250 *
251 * End of CHECON_ROOK
252 *
253  END
subroutine chetrs_rook(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
CHETRS_ROOK computes the solution to a system of linear equations A * X = B for HE matrices using fac...
Definition: chetrs_rook.f:138
subroutine checon_rook(UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK, INFO)
CHECON_ROOK estimates the reciprocal of the condition number fort HE matrices using factorization ob...
Definition: checon_rook.f:141
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
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