LAPACK  3.8.0 LAPACK: Linear Algebra PACKage
zhesv_aa.f
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1 *> \brief <b> ZHESV_AA computes the solution to system of linear equations A * X = B for HE matrices</b>
2 *
3 * =========== DOCUMENTATION ===========
4 *
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17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE ZHESV_AA( 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 *> ZHESV_AA computes the solution to a complex system of linear equations
40 *> A * X = B,
41 *> where A is an N-by-N Hermitian 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 * U**H, if UPLO = 'U', or
46 *> A = L * T * L**H, if UPLO = 'L',
47 *> where U (or L) is a product of permutation and unit upper (lower)
48 *> triangular matrices, and T is Hermitian and tridiagonal. The factored form
49 *> 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 Hermitian 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*U**H or A = L*T*L**H as computed by
90 *> ZHETRF_AA.
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 best
130 *> performance LWORK >= max(1,N*NB), where NB is the optimal
131 *> blocksize for ZHETRF.
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 *> \date November 2017
158 *
159 *> \ingroup complex16HEsolve
160 *
161 * =====================================================================
162  SUBROUTINE zhesv_aa( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
163  \$ LWORK, INFO )
164 *
165 * -- LAPACK driver routine (version 3.8.0) --
166 * -- LAPACK is a software package provided by Univ. of Tennessee, --
167 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
168 * November 2017
169 *
170 * .. Scalar Arguments ..
171  CHARACTER UPLO
172  INTEGER INFO, LDA, LDB, LWORK, N, NRHS
173 * ..
174 * .. Array Arguments ..
175  INTEGER IPIV( * )
176  COMPLEX*16 A( lda, * ), B( ldb, * ), WORK( * )
177 * ..
178 *
179 * =====================================================================
180 *
181 * .. Local Scalars ..
182  LOGICAL LQUERY
183  INTEGER LWKOPT, LWKOPT_HETRF, LWKOPT_HETRS
184 * ..
185 * .. External Functions ..
186  LOGICAL LSAME
187  INTEGER ILAENV
188  EXTERNAL lsame, ilaenv
189 * ..
190 * .. External Subroutines ..
191  EXTERNAL xerbla, zhetrf_aa, zhetrs_aa
192 * ..
193 * .. Intrinsic Functions ..
194  INTRINSIC max
195 * ..
196 * .. Executable Statements ..
197 *
198 * Test the input parameters.
199 *
200  info = 0
201  lquery = ( lwork.EQ.-1 )
202  IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
203  info = -1
204  ELSE IF( n.LT.0 ) THEN
205  info = -2
206  ELSE IF( nrhs.LT.0 ) THEN
207  info = -3
208  ELSE IF( lda.LT.max( 1, n ) ) THEN
209  info = -5
210  ELSE IF( ldb.LT.max( 1, n ) ) THEN
211  info = -8
212  END IF
213 *
214  IF( info.EQ.0 ) THEN
215  CALL zhetrf_aa( uplo, n, a, lda, ipiv, work, -1, info )
216  lwkopt_hetrf = int( work(1) )
217  CALL zhetrs_aa( uplo, n, nrhs, a, lda, ipiv, b, ldb, work,
218  \$ -1, info )
219  lwkopt_hetrs = int( work(1) )
220  lwkopt = max( lwkopt_hetrf, lwkopt_hetrs )
221  work( 1 ) = lwkopt
222  IF( lwork.LT.lwkopt .AND. .NOT.lquery ) THEN
223  info = -10
224  END IF
225  END IF
226 *
227  IF( info.NE.0 ) THEN
228  CALL xerbla( 'ZHESV_AA ', -info )
229  RETURN
230  ELSE IF( lquery ) THEN
231  RETURN
232  END IF
233 *
234 * Compute the factorization A = U*T*U**H or A = L*T*L**H.
235 *
236  CALL zhetrf_aa( uplo, n, a, lda, ipiv, work, lwork, info )
237  IF( info.EQ.0 ) THEN
238 *
239 * Solve the system A*X = B, overwriting B with X.
240 *
241  CALL zhetrs_aa( uplo, n, nrhs, a, lda, ipiv, b, ldb, work,
242  \$ lwork, info )
243 *
244  END IF
245 *
246  work( 1 ) = lwkopt
247 *
248  RETURN
249 *
250 * End of ZHESV_AA
251 *
252  END
subroutine zhesv_aa(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO)
ZHESV_AA computes the solution to system of linear equations A * X = B for HE matrices ...
Definition: zhesv_aa.f:164
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine zhetrf_aa(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
ZHETRF_AA
Definition: zhetrf_aa.f:134
subroutine zhetrs_aa(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO)
ZHETRS_AA
Definition: zhetrs_aa.f:132