LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
csycon_rook.f
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1 *> \brief <b> CSYCON_ROOK </b>
2 *
3 * =========== DOCUMENTATION ===========
4 *
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17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE CSYCON_ROOK( UPLO, N, A, LDA, IPIV, ANORM, RCOND,
22 * WORK, 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 *> CSYCON_ROOK estimates the reciprocal of the condition number (in the
41 *> 1-norm) of a complex symmetric matrix A using the factorization
42 *> A = U*D*U**T or A = L*D*L**T computed by CSYTRF_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**T;
57 *> = 'L': Lower triangular, form is A = L*D*L**T.
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 CSYTRF_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 CSYTRF_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 *> \ingroup complexSYcomputational
121 *
122 *> \par Contributors:
123 * ==================
124 *> \verbatim
125 *>
126 *> April 2012, Igor Kozachenko,
127 *> Computer Science Division,
128 *> University of California, Berkeley
129 *>
130 *> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
131 *> School of Mathematics,
132 *> University of Manchester
133 *>
134 *> \endverbatim
135 *
136 * =====================================================================
137  SUBROUTINE csycon_rook( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
138  $ INFO )
139 *
140 * -- LAPACK computational routine --
141 * -- LAPACK is a software package provided by Univ. of Tennessee, --
142 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
143 *
144 * .. Scalar Arguments ..
145  CHARACTER UPLO
146  INTEGER INFO, LDA, N
147  REAL ANORM, RCOND
148 * ..
149 * .. Array Arguments ..
150  INTEGER IPIV( * )
151  COMPLEX A( LDA, * ), WORK( * )
152 * ..
153 *
154 * =====================================================================
155 *
156 * .. Parameters ..
157  REAL ONE, ZERO
158  parameter( one = 1.0e+0, zero = 0.0e+0 )
159  COMPLEX CZERO
160  parameter( czero = ( 0.0e+0, 0.0e+0 ) )
161 * ..
162 * .. Local Scalars ..
163  LOGICAL UPPER
164  INTEGER I, KASE
165  REAL AINVNM
166 * ..
167 * .. Local Arrays ..
168  INTEGER ISAVE( 3 )
169 * ..
170 * .. External Functions ..
171  LOGICAL LSAME
172  EXTERNAL lsame
173 * ..
174 * .. External Subroutines ..
175  EXTERNAL clacn2, csytrs_rook, xerbla
176 * ..
177 * .. Intrinsic Functions ..
178  INTRINSIC max
179 * ..
180 * .. Executable Statements ..
181 *
182 * Test the input parameters.
183 *
184  info = 0
185  upper = lsame( uplo, 'U' )
186  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
187  info = -1
188  ELSE IF( n.LT.0 ) THEN
189  info = -2
190  ELSE IF( lda.LT.max( 1, n ) ) THEN
191  info = -4
192  ELSE IF( anorm.LT.zero ) THEN
193  info = -6
194  END IF
195  IF( info.NE.0 ) THEN
196  CALL xerbla( 'CSYCON_ROOK', -info )
197  RETURN
198  END IF
199 *
200 * Quick return if possible
201 *
202  rcond = zero
203  IF( n.EQ.0 ) THEN
204  rcond = one
205  RETURN
206  ELSE IF( anorm.LE.zero ) THEN
207  RETURN
208  END IF
209 *
210 * Check that the diagonal matrix D is nonsingular.
211 *
212  IF( upper ) THEN
213 *
214 * Upper triangular storage: examine D from bottom to top
215 *
216  DO 10 i = n, 1, -1
217  IF( ipiv( i ).GT.0 .AND. a( i, i ).EQ.czero )
218  $ RETURN
219  10 CONTINUE
220  ELSE
221 *
222 * Lower triangular storage: examine D from top to bottom.
223 *
224  DO 20 i = 1, n
225  IF( ipiv( i ).GT.0 .AND. a( i, i ).EQ.czero )
226  $ RETURN
227  20 CONTINUE
228  END IF
229 *
230 * Estimate the 1-norm of the inverse.
231 *
232  kase = 0
233  30 CONTINUE
234  CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
235  IF( kase.NE.0 ) THEN
236 *
237 * Multiply by inv(L*D*L**T) or inv(U*D*U**T).
238 *
239  CALL csytrs_rook( uplo, n, 1, a, lda, ipiv, work, n, info )
240  GO TO 30
241  END IF
242 *
243 * Compute the estimate of the reciprocal condition number.
244 *
245  IF( ainvnm.NE.zero )
246  $ rcond = ( one / ainvnm ) / anorm
247 *
248  RETURN
249 *
250 * End of CSYCON_ROOK
251 *
252  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
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:133
subroutine csycon_rook(UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK, INFO)
CSYCON_ROOK
Definition: csycon_rook.f:139
subroutine csytrs_rook(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
CSYTRS_ROOK
Definition: csytrs_rook.f:136