LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
ssycon_rook.f
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1 *> \brief <b> SSYCON_ROOK </b>
2 *
3 * =========== DOCUMENTATION ===========
4 *
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17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE SSYCON_ROOK( UPLO, N, A, LDA, IPIV, ANORM, RCOND,
22 * WORK, IWORK, INFO )
23 *
24 * .. Scalar Arguments ..
25 * CHARACTER UPLO
26 * INTEGER INFO, LDA, N
27 * REAL ANORM, RCOND
28 * ..
29 * .. Array Arguments ..
30 * INTEGER IPIV( * ), IWORK( * )
31 * REAL A( LDA, * ), WORK( * )
32 * ..
33 *
34 *
35 *> \par Purpose:
36 * =============
37 *>
38 *> \verbatim
39 *>
40 *> SSYCON_ROOK estimates the reciprocal of the condition number (in the
41 *> 1-norm) of a real symmetric matrix A using the factorization
42 *> A = U*D*U**T or A = L*D*L**T computed by SSYTRF_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 REAL 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 SSYTRF_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 SSYTRF_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 REAL array, dimension (2*N)
103 *> \endverbatim
104 *>
105 *> \param[out] IWORK
106 *> \verbatim
107 *> IWORK is INTEGER array, dimension (N)
108 *> \endverbatim
109 *>
110 *> \param[out] INFO
111 *> \verbatim
112 *> INFO is INTEGER
113 *> = 0: successful exit
114 *> < 0: if INFO = -i, the i-th argument had an illegal value
115 *> \endverbatim
116 *
117 * Authors:
118 * ========
119 *
120 *> \author Univ. of Tennessee
121 *> \author Univ. of California Berkeley
122 *> \author Univ. of Colorado Denver
123 *> \author NAG Ltd.
124 *
125 *> \ingroup realSYcomputational
126 *
127 *> \par Contributors:
128 * ==================
129 *> \verbatim
130 *>
131 *> December 2016, Igor Kozachenko,
132 *> Computer Science Division,
133 *> University of California, Berkeley
134 *>
135 *> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
136 *> School of Mathematics,
137 *> University of Manchester
138 *>
139 *> \endverbatim
140 *
141 * =====================================================================
142  SUBROUTINE ssycon_rook( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
143  $ IWORK, INFO )
144 *
145 * -- LAPACK computational routine --
146 * -- LAPACK is a software package provided by Univ. of Tennessee, --
147 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
148 *
149 * .. Scalar Arguments ..
150  CHARACTER UPLO
151  INTEGER INFO, LDA, N
152  REAL ANORM, RCOND
153 * ..
154 * .. Array Arguments ..
155  INTEGER IPIV( * ), IWORK( * )
156  REAL A( LDA, * ), WORK( * )
157 * ..
158 *
159 * =====================================================================
160 *
161 * .. Parameters ..
162  REAL ONE, ZERO
163  parameter( one = 1.0e+0, zero = 0.0e+0 )
164 * ..
165 * .. Local Scalars ..
166  LOGICAL UPPER
167  INTEGER I, KASE
168  REAL AINVNM
169 * ..
170 * .. Local Arrays ..
171  INTEGER ISAVE( 3 )
172 * ..
173 * .. External Functions ..
174  LOGICAL LSAME
175  EXTERNAL lsame
176 * ..
177 * .. External Subroutines ..
178  EXTERNAL slacn2, ssytrs_rook, xerbla
179 * ..
180 * .. Intrinsic Functions ..
181  INTRINSIC max
182 * ..
183 * .. Executable Statements ..
184 *
185 * Test the input parameters.
186 *
187  info = 0
188  upper = lsame( uplo, 'U' )
189  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
190  info = -1
191  ELSE IF( n.LT.0 ) THEN
192  info = -2
193  ELSE IF( lda.LT.max( 1, n ) ) THEN
194  info = -4
195  ELSE IF( anorm.LT.zero ) THEN
196  info = -6
197  END IF
198  IF( info.NE.0 ) THEN
199  CALL xerbla( 'SSYCON_ROOK', -info )
200  RETURN
201  END IF
202 *
203 * Quick return if possible
204 *
205  rcond = zero
206  IF( n.EQ.0 ) THEN
207  rcond = one
208  RETURN
209  ELSE IF( anorm.LE.zero ) THEN
210  RETURN
211  END IF
212 *
213 * Check that the diagonal matrix D is nonsingular.
214 *
215  IF( upper ) THEN
216 *
217 * Upper triangular storage: examine D from bottom to top
218 *
219  DO 10 i = n, 1, -1
220  IF( ipiv( i ).GT.0 .AND. a( i, i ).EQ.zero )
221  $ RETURN
222  10 CONTINUE
223  ELSE
224 *
225 * Lower triangular storage: examine D from top to bottom.
226 *
227  DO 20 i = 1, n
228  IF( ipiv( i ).GT.0 .AND. a( i, i ).EQ.zero )
229  $ RETURN
230  20 CONTINUE
231  END IF
232 *
233 * Estimate the 1-norm of the inverse.
234 *
235  kase = 0
236  30 CONTINUE
237  CALL slacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
238  IF( kase.NE.0 ) THEN
239 *
240 * Multiply by inv(L*D*L**T) or inv(U*D*U**T).
241 *
242  CALL ssytrs_rook( uplo, n, 1, a, lda, ipiv, work, n, info )
243  GO TO 30
244  END IF
245 *
246 * Compute the estimate of the reciprocal condition number.
247 *
248  IF( ainvnm.NE.zero )
249  $ rcond = ( one / ainvnm ) / anorm
250 *
251  RETURN
252 *
253 * End of SSYCON_ROOK
254 *
255  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 ssycon_rook(UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK, IWORK, INFO)
SSYCON_ROOK
Definition: ssycon_rook.f:144
subroutine ssytrs_rook(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
SSYTRS_ROOK
Definition: ssytrs_rook.f:136