LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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zsysv_rook.f
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1*> \brief <b> ZSYSV_ROOK computes the solution to system of linear equations A * X = B for SY matrices</b>
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download ZSYSV_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/zsysv_rook.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsysv_rook.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE ZSYSV_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
22* LWORK, INFO )
23*
24* .. Scalar Arguments ..
25* CHARACTER UPLO
26* INTEGER INFO, LDA, LDB, LWORK, N, NRHS
27* ..
28* .. Array Arguments ..
29* INTEGER IPIV( * )
30* COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
31* ..
32*
33*
34*> \par Purpose:
35* =============
36*>
37*> \verbatim
38*>
39*> ZSYSV_ROOK computes the solution to a complex system of linear
40*> equations
41*> A * X = B,
42*> where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
43*> matrices.
44*>
45*> The diagonal pivoting method is used to factor A as
46*> A = U * D * U**T, if UPLO = 'U', or
47*> A = L * D * L**T, if UPLO = 'L',
48*> where U (or L) is a product of permutation and unit upper (lower)
49*> triangular matrices, and D is symmetric and block diagonal with
50*> 1-by-1 and 2-by-2 diagonal blocks.
51*>
52*> ZSYTRF_ROOK is called to compute the factorization of a complex
53*> symmetric matrix A using the bounded Bunch-Kaufman ("rook") diagonal
54*> pivoting method.
55*>
56*> The factored form of A is then used to solve the system
57*> of equations A * X = B by calling ZSYTRS_ROOK.
58*> \endverbatim
59*
60* Arguments:
61* ==========
62*
63*> \param[in] UPLO
64*> \verbatim
65*> UPLO is CHARACTER*1
66*> = 'U': Upper triangle of A is stored;
67*> = 'L': Lower triangle of A is stored.
68*> \endverbatim
69*>
70*> \param[in] N
71*> \verbatim
72*> N is INTEGER
73*> The number of linear equations, i.e., the order of the
74*> matrix A. N >= 0.
75*> \endverbatim
76*>
77*> \param[in] NRHS
78*> \verbatim
79*> NRHS is INTEGER
80*> The number of right hand sides, i.e., the number of columns
81*> of the matrix B. NRHS >= 0.
82*> \endverbatim
83*>
84*> \param[in,out] A
85*> \verbatim
86*> A is COMPLEX*16 array, dimension (LDA,N)
87*> On entry, the symmetric matrix A. If UPLO = 'U', the leading
88*> N-by-N upper triangular part of A contains the upper
89*> triangular part of the matrix A, and the strictly lower
90*> triangular part of A is not referenced. If UPLO = 'L', the
91*> leading N-by-N lower triangular part of A contains the lower
92*> triangular part of the matrix A, and the strictly upper
93*> triangular part of A is not referenced.
94*>
95*> On exit, if INFO = 0, the block diagonal matrix D and the
96*> multipliers used to obtain the factor U or L from the
97*> factorization A = U*D*U**T or A = L*D*L**T as computed by
98*> ZSYTRF_ROOK.
99*> \endverbatim
100*>
101*> \param[in] LDA
102*> \verbatim
103*> LDA is INTEGER
104*> The leading dimension of the array A. LDA >= max(1,N).
105*> \endverbatim
106*>
107*> \param[out] IPIV
108*> \verbatim
109*> IPIV is INTEGER array, dimension (N)
110*> Details of the interchanges and the block structure of D,
111*> as determined by ZSYTRF_ROOK.
112*>
113*> If UPLO = 'U':
114*> If IPIV(k) > 0, then rows and columns k and IPIV(k)
115*> were interchanged and D(k,k) is a 1-by-1 diagonal block.
116*>
117*> If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
118*> columns k and -IPIV(k) were interchanged and rows and
119*> columns k-1 and -IPIV(k-1) were inerchaged,
120*> D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
121*>
122*> If UPLO = 'L':
123*> If IPIV(k) > 0, then rows and columns k and IPIV(k)
124*> were interchanged and D(k,k) is a 1-by-1 diagonal block.
125*>
126*> If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
127*> columns k and -IPIV(k) were interchanged and rows and
128*> columns k+1 and -IPIV(k+1) were inerchaged,
129*> D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
130*> \endverbatim
131*>
132*> \param[in,out] B
133*> \verbatim
134*> B is COMPLEX*16 array, dimension (LDB,NRHS)
135*> On entry, the N-by-NRHS right hand side matrix B.
136*> On exit, if INFO = 0, the N-by-NRHS solution matrix X.
137*> \endverbatim
138*>
139*> \param[in] LDB
140*> \verbatim
141*> LDB is INTEGER
142*> The leading dimension of the array B. LDB >= max(1,N).
143*> \endverbatim
144*>
145*> \param[out] WORK
146*> \verbatim
147*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
148*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
149*> \endverbatim
150*>
151*> \param[in] LWORK
152*> \verbatim
153*> LWORK is INTEGER
154*> The length of WORK. LWORK >= 1, and for best performance
155*> LWORK >= max(1,N*NB), where NB is the optimal blocksize for
156*> ZSYTRF_ROOK.
157*>
158*> TRS will be done with Level 2 BLAS
159*>
160*> If LWORK = -1, then a workspace query is assumed; the routine
161*> only calculates the optimal size of the WORK array, returns
162*> this value as the first entry of the WORK array, and no error
163*> message related to LWORK is issued by XERBLA.
164*> \endverbatim
165*>
166*> \param[out] INFO
167*> \verbatim
168*> INFO is INTEGER
169*> = 0: successful exit
170*> < 0: if INFO = -i, the i-th argument had an illegal value
171*> > 0: if INFO = i, D(i,i) is exactly zero. The factorization
172*> has been completed, but the block diagonal matrix D is
173*> exactly singular, so the solution could not be computed.
174*> \endverbatim
175*
176* Authors:
177* ========
178*
179*> \author Univ. of Tennessee
180*> \author Univ. of California Berkeley
181*> \author Univ. of Colorado Denver
182*> \author NAG Ltd.
183*
184*> \ingroup complex16SYsolve
185*
186*> \par Contributors:
187* ==================
188*>
189*> \verbatim
190*>
191*> December 2016, Igor Kozachenko,
192*> Computer Science Division,
193*> University of California, Berkeley
194*>
195*> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
196*> School of Mathematics,
197*> University of Manchester
198*>
199*> \endverbatim
200*
201* =====================================================================
202 SUBROUTINE zsysv_rook( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
203 $ LWORK, INFO )
204*
205* -- LAPACK driver routine --
206* -- LAPACK is a software package provided by Univ. of Tennessee, --
207* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
208*
209* .. Scalar Arguments ..
210 CHARACTER UPLO
211 INTEGER INFO, LDA, LDB, LWORK, N, NRHS
212* ..
213* .. Array Arguments ..
214 INTEGER IPIV( * )
215 COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
216* ..
217*
218* =====================================================================
219*
220* .. Local Scalars ..
221 LOGICAL LQUERY
222 INTEGER LWKOPT
223* ..
224* .. External Functions ..
225 LOGICAL LSAME
226 EXTERNAL lsame
227* ..
228* .. External Subroutines ..
230* ..
231* .. Intrinsic Functions ..
232 INTRINSIC max
233* ..
234* .. Executable Statements ..
235*
236* Test the input parameters.
237*
238 info = 0
239 lquery = ( lwork.EQ.-1 )
240 IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
241 info = -1
242 ELSE IF( n.LT.0 ) THEN
243 info = -2
244 ELSE IF( nrhs.LT.0 ) THEN
245 info = -3
246 ELSE IF( lda.LT.max( 1, n ) ) THEN
247 info = -5
248 ELSE IF( ldb.LT.max( 1, n ) ) THEN
249 info = -8
250 ELSE IF( lwork.LT.1 .AND. .NOT.lquery ) THEN
251 info = -10
252 END IF
253*
254 IF( info.EQ.0 ) THEN
255 IF( n.EQ.0 ) THEN
256 lwkopt = 1
257 ELSE
258 CALL zsytrf_rook( uplo, n, a, lda, ipiv, work, -1, info )
259 lwkopt = int( dble( work( 1 ) ) )
260 END IF
261 work( 1 ) = lwkopt
262 END IF
263*
264 IF( info.NE.0 ) THEN
265 CALL xerbla( 'ZSYSV_ROOK ', -info )
266 RETURN
267 ELSE IF( lquery ) THEN
268 RETURN
269 END IF
270*
271* Compute the factorization A = U*D*U**T or A = L*D*L**T.
272*
273 CALL zsytrf_rook( uplo, n, a, lda, ipiv, work, lwork, info )
274 IF( info.EQ.0 ) THEN
275*
276* Solve the system A*X = B, overwriting B with X.
277*
278* Solve with TRS_ROOK ( Use Level 2 BLAS)
279*
280 CALL zsytrs_rook( uplo, n, nrhs, a, lda, ipiv, b, ldb, info )
281*
282 END IF
283*
284 work( 1 ) = lwkopt
285*
286 RETURN
287*
288* End of ZSYSV_ROOK
289*
290 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine zsytrs_rook(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
ZSYTRS_ROOK
Definition: zsytrs_rook.f:136
subroutine zsytrf_rook(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
ZSYTRF_ROOK
Definition: zsytrf_rook.f:208
subroutine zsysv_rook(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO)
ZSYSV_ROOK computes the solution to system of linear equations A * X = B for SY matrices
Definition: zsysv_rook.f:204