LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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zsycon_rook.f
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1*> \brief \b ZSYCON_ROOK
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download ZSYCON_ROOK + dependencies
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11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zsycon_rook.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsycon_rook.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE ZSYCON_ROOK( UPLO, N, A, LDA, IPIV, ANORM, RCOND,
22* WORK, INFO )
23*
24* .. Scalar Arguments ..
25* CHARACTER UPLO
26* INTEGER INFO, LDA, N
27* DOUBLE PRECISION ANORM, RCOND
28* ..
29* .. Array Arguments ..
30* INTEGER IPIV( * )
31* COMPLEX*16 A( LDA, * ), WORK( * )
32* ..
33*
34*
35*> \par Purpose:
36* =============
37*>
38*> \verbatim
39*>
40*> ZSYCON_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 ZSYTRF_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*16 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 ZSYTRF_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 ZSYTRF_ROOK.
84*> \endverbatim
85*>
86*> \param[in] ANORM
87*> \verbatim
88*> ANORM is DOUBLE PRECISION
89*> The 1-norm of the original matrix A.
90*> \endverbatim
91*>
92*> \param[out] RCOND
93*> \verbatim
94*> RCOND is DOUBLE PRECISION
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*16 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 complex16SYcomputational
121*
122*> \par Contributors:
123* ==================
124*> \verbatim
125*>
126*> December 2016, 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 zsycon_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 DOUBLE PRECISION ANORM, RCOND
148* ..
149* .. Array Arguments ..
150 INTEGER IPIV( * )
151 COMPLEX*16 A( LDA, * ), WORK( * )
152* ..
153*
154* =====================================================================
155*
156* .. Parameters ..
157 DOUBLE PRECISION ONE, ZERO
158 parameter( one = 1.0d+0, zero = 0.0d+0 )
159 COMPLEX*16 CZERO
160 parameter( czero = ( 0.0d+0, 0.0d+0 ) )
161* ..
162* .. Local Scalars ..
163 LOGICAL UPPER
164 INTEGER I, KASE
165 DOUBLE PRECISION 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 zlacn2, zsytrs_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( 'ZSYCON_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 zlacn2( 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 zsytrs_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 ZSYCON_ROOK
251*
252 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 zsycon_rook(UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK, INFO)
ZSYCON_ROOK
Definition: zsycon_rook.f:139
subroutine zsytrs_rook(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
ZSYTRS_ROOK
Definition: zsytrs_rook.f:136