LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
zsysv_aa.f
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1 *> \brief <b> ZSYSV_AA computes the solution to system of linear equations A * X = B for SY matrices</b>
2 *
3 * =========== DOCUMENTATION ===========
4 *
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17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE ZSYSV_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
22 * LWORK, INFO )
23 *
24 * .. Scalar Arguments ..
25 * CHARACTER UPLO
26 * INTEGER N, NRHS, LDA, LDB, LWORK, INFO
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 computes the solution to a complex system of linear equations
40 *> A * X = B,
41 *> where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
42 *> matrices.
43 *>
44 *> Aasen's algorithm is used to factor A as
45 *> A = U**T * T * U, if UPLO = 'U', or
46 *> A = L * T * L**T, if UPLO = 'L',
47 *> where U (or L) is a product of permutation and unit upper (lower)
48 *> triangular matrices, and T is symmetric tridiagonal. The factored
49 *> form of A is then used to solve the system of equations A * X = B.
50 *> \endverbatim
51 *
52 * Arguments:
53 * ==========
54 *
55 *> \param[in] UPLO
56 *> \verbatim
57 *> UPLO is CHARACTER*1
58 *> = 'U': Upper triangle of A is stored;
59 *> = 'L': Lower triangle of A is stored.
60 *> \endverbatim
61 *>
62 *> \param[in] N
63 *> \verbatim
64 *> N is INTEGER
65 *> The number of linear equations, i.e., the order of the
66 *> matrix A. N >= 0.
67 *> \endverbatim
68 *>
69 *> \param[in] NRHS
70 *> \verbatim
71 *> NRHS is INTEGER
72 *> The number of right hand sides, i.e., the number of columns
73 *> of the matrix B. NRHS >= 0.
74 *> \endverbatim
75 *>
76 *> \param[in,out] A
77 *> \verbatim
78 *> A is COMPLEX*16 array, dimension (LDA,N)
79 *> On entry, the symmetric matrix A. If UPLO = 'U', the leading
80 *> N-by-N upper triangular part of A contains the upper
81 *> triangular part of the matrix A, and the strictly lower
82 *> triangular part of A is not referenced. If UPLO = 'L', the
83 *> leading N-by-N lower triangular part of A contains the lower
84 *> triangular part of the matrix A, and the strictly upper
85 *> triangular part of A is not referenced.
86 *>
87 *> On exit, if INFO = 0, the tridiagonal matrix T and the
88 *> multipliers used to obtain the factor U or L from the
89 *> factorization A = U**T*T*U or A = L*T*L**T as computed by
90 *> ZSYTRF.
91 *> \endverbatim
92 *>
93 *> \param[in] LDA
94 *> \verbatim
95 *> LDA is INTEGER
96 *> The leading dimension of the array A. LDA >= max(1,N).
97 *> \endverbatim
98 *>
99 *> \param[out] IPIV
100 *> \verbatim
101 *> IPIV is INTEGER array, dimension (N)
102 *> On exit, it contains the details of the interchanges, i.e.,
103 *> the row and column k of A were interchanged with the
104 *> row and column IPIV(k).
105 *> \endverbatim
106 *>
107 *> \param[in,out] B
108 *> \verbatim
109 *> B is COMPLEX*16 array, dimension (LDB,NRHS)
110 *> On entry, the N-by-NRHS right hand side matrix B.
111 *> On exit, if INFO = 0, the N-by-NRHS solution matrix X.
112 *> \endverbatim
113 *>
114 *> \param[in] LDB
115 *> \verbatim
116 *> LDB is INTEGER
117 *> The leading dimension of the array B. LDB >= max(1,N).
118 *> \endverbatim
119 *>
120 *> \param[out] WORK
121 *> \verbatim
122 *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
123 *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
124 *> \endverbatim
125 *>
126 *> \param[in] LWORK
127 *> \verbatim
128 *> LWORK is INTEGER
129 *> The length of WORK. LWORK >= MAX(1,2*N,3*N-2), and for
130 *> the best performance, LWORK >= MAX(1,N*NB), where NB is
131 *> the optimal blocksize for ZSYTRF_AA.
132 *>
133 *> If LWORK = -1, then a workspace query is assumed; the routine
134 *> only calculates the optimal size of the WORK array, returns
135 *> this value as the first entry of the WORK array, and no error
136 *> message related to LWORK is issued by XERBLA.
137 *> \endverbatim
138 *>
139 *> \param[out] INFO
140 *> \verbatim
141 *> INFO is INTEGER
142 *> = 0: successful exit
143 *> < 0: if INFO = -i, the i-th argument had an illegal value
144 *> > 0: if INFO = i, D(i,i) is exactly zero. The factorization
145 *> has been completed, but the block diagonal matrix D is
146 *> exactly singular, so the solution could not be computed.
147 *> \endverbatim
148 *
149 * Authors:
150 * ========
151 *
152 *> \author Univ. of Tennessee
153 *> \author Univ. of California Berkeley
154 *> \author Univ. of Colorado Denver
155 *> \author NAG Ltd.
156 *
157 *> \ingroup complex16SYsolve
158 *
159 * =====================================================================
160  SUBROUTINE zsysv_aa( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
161  $ LWORK, INFO )
162 *
163 * -- LAPACK driver routine --
164 * -- LAPACK is a software package provided by Univ. of Tennessee, --
165 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
166 *
167 * .. Scalar Arguments ..
168  CHARACTER UPLO
169  INTEGER INFO, LDA, LDB, LWORK, N, NRHS
170 * ..
171 * .. Array Arguments ..
172  INTEGER IPIV( * )
173  COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
174 * ..
175 *
176 * =====================================================================
177 *
178 * .. Local Scalars ..
179  LOGICAL LQUERY
180  INTEGER LWKOPT, LWKOPT_SYTRF, LWKOPT_SYTRS
181 * ..
182 * .. External Functions ..
183  LOGICAL LSAME
184  INTEGER ILAENV
185  EXTERNAL ilaenv, lsame
186 * ..
187 * .. External Subroutines ..
188  EXTERNAL xerbla, zsytrf_aa, zsytrs_aa
189 * ..
190 * .. Intrinsic Functions ..
191  INTRINSIC max
192 * ..
193 * .. Executable Statements ..
194 *
195 * Test the input parameters.
196 *
197  info = 0
198  lquery = ( lwork.EQ.-1 )
199  IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
200  info = -1
201  ELSE IF( n.LT.0 ) THEN
202  info = -2
203  ELSE IF( nrhs.LT.0 ) THEN
204  info = -3
205  ELSE IF( lda.LT.max( 1, n ) ) THEN
206  info = -5
207  ELSE IF( ldb.LT.max( 1, n ) ) THEN
208  info = -8
209  ELSE IF( lwork.LT.max(2*n, 3*n-2) .AND. .NOT.lquery ) THEN
210  info = -10
211  END IF
212 *
213  IF( info.EQ.0 ) THEN
214  CALL zsytrf_aa( uplo, n, a, lda, ipiv, work, -1, info )
215  lwkopt_sytrf = int( work(1) )
216  CALL zsytrs_aa( uplo, n, nrhs, a, lda, ipiv, b, ldb, work,
217  $ -1, info )
218  lwkopt_sytrs = int( work(1) )
219  lwkopt = max( lwkopt_sytrf, lwkopt_sytrs )
220  work( 1 ) = lwkopt
221  END IF
222 *
223  IF( info.NE.0 ) THEN
224  CALL xerbla( 'ZSYSV_AA ', -info )
225  RETURN
226  ELSE IF( lquery ) THEN
227  RETURN
228  END IF
229 *
230 * Compute the factorization A = U**T*T*U or A = L*T*L**T.
231 *
232  CALL zsytrf_aa( uplo, n, a, lda, ipiv, work, lwork, info )
233  IF( info.EQ.0 ) THEN
234 *
235 * Solve the system A*X = B, overwriting B with X.
236 *
237  CALL zsytrs_aa( uplo, n, nrhs, a, lda, ipiv, b, ldb, work,
238  $ lwork, info )
239 *
240  END IF
241 *
242  work( 1 ) = lwkopt
243 *
244  RETURN
245 *
246 * End of ZSYSV_AA
247 *
248  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine zsytrs_aa(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO)
ZSYTRS_AA
Definition: zsytrs_aa.f:131
subroutine zsytrf_aa(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
ZSYTRF_AA
Definition: zsytrf_aa.f:132
subroutine zsysv_aa(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO)
ZSYSV_AA computes the solution to system of linear equations A * X = B for SY matrices
Definition: zsysv_aa.f:162