1: *> \brief <b> DSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices</b>
2: *
3: * @generated from SRC/chesv_aa_2stage.f, fortran c -> d, Tue Oct 31 11:22:31 2017
4: *
5: * =========== DOCUMENTATION ===========
6: *
7: * Online html documentation available at
8: * http://www.netlib.org/lapack/explore-html/
9: *
10: *> \htmlonly
11: *> Download DSYSV_AA_2STAGE + dependencies
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13: *> [TGZ]</a>
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15: *> [ZIP]</a>
16: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsysv_aa_2stage.f">
17: *> [TXT]</a>
18: *> \endhtmlonly
19: *
20: * Definition:
21: * ===========
22: *
23: * SUBROUTINE DSYSV_AA_2STAGE( UPLO, N, NRHS, A, LDA, TB, LTB,
24: * IPIV, IPIV2, B, LDB, WORK, LWORK,
25: * INFO )
26: *
27: * .. Scalar Arguments ..
28: * CHARACTER UPLO
29: * INTEGER N, NRHS, LDA, LTB, LDB, LWORK, INFO
30: * ..
31: * .. Array Arguments ..
32: * INTEGER IPIV( * ), IPIV2( * )
33: * DOUBLE PRECISION A( LDA, * ), TB( * ), B( LDB, *), WORK( * )
34: * ..
35: *
36: *> \par Purpose:
37: * =============
38: *>
39: *> \verbatim
40: *>
41: *> DSYSV_AA_2STAGE computes the solution to a real system of
42: *> linear equations
43: *> A * X = B,
44: *> where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
45: *> matrices.
46: *>
47: *> Aasen's 2-stage algorithm is used to factor A as
48: *> A = U * T * U**T, if UPLO = 'U', or
49: *> A = L * T * L**T, if UPLO = 'L',
50: *> where U (or L) is a product of permutation and unit upper (lower)
51: *> triangular matrices, and T is symmetric and band. The matrix T is
52: *> then LU-factored with partial pivoting. The factored form of A
53: *> is then used to solve the system of equations A * X = B.
54: *>
55: *> This is the blocked version of the algorithm, calling Level 3 BLAS.
56: *> \endverbatim
57: *
58: * Arguments:
59: * ==========
60: *
61: *> \param[in] UPLO
62: *> \verbatim
63: *> UPLO is CHARACTER*1
64: *> = 'U': Upper triangle of A is stored;
65: *> = 'L': Lower triangle of A is stored.
66: *> \endverbatim
67: *>
68: *> \param[in] N
69: *> \verbatim
70: *> N is INTEGER
71: *> The order of the matrix A. N >= 0.
72: *> \endverbatim
73: *>
74: *> \param[in] NRHS
75: *> \verbatim
76: *> NRHS is INTEGER
77: *> The number of right hand sides, i.e., the number of columns
78: *> of the matrix B. NRHS >= 0.
79: *> \endverbatim
80: *>
81: *> \param[in,out] A
82: *> \verbatim
83: *> A is DOUBLE PRECISION array, dimension (LDA,N)
84: *> On entry, the symmetric matrix A. If UPLO = 'U', the leading
85: *> N-by-N upper triangular part of A contains the upper
86: *> triangular part of the matrix A, and the strictly lower
87: *> triangular part of A is not referenced. If UPLO = 'L', the
88: *> leading N-by-N lower triangular part of A contains the lower
89: *> triangular part of the matrix A, and the strictly upper
90: *> triangular part of A is not referenced.
91: *>
92: *> On exit, L is stored below (or above) the subdiaonal blocks,
93: *> when UPLO is 'L' (or 'U').
94: *> \endverbatim
95: *>
96: *> \param[in] LDA
97: *> \verbatim
98: *> LDA is INTEGER
99: *> The leading dimension of the array A. LDA >= max(1,N).
100: *> \endverbatim
101: *>
102: *> \param[out] TB
103: *> \verbatim
104: *> TB is DOUBLE PRECISION array, dimension (LTB)
105: *> On exit, details of the LU factorization of the band matrix.
106: *> \endverbatim
107: *>
108: *> \param[in] LTB
109: *> \verbatim
110: *> The size of the array TB. LTB >= 4*N, internally
111: *> used to select NB such that LTB >= (3*NB+1)*N.
112: *>
113: *> If LTB = -1, then a workspace query is assumed; the
114: *> routine only calculates the optimal size of LTB,
115: *> returns this value as the first entry of TB, and
116: *> no error message related to LTB is issued by XERBLA.
117: *> \endverbatim
118: *>
119: *> \param[out] IPIV
120: *> \verbatim
121: *> IPIV is INTEGER array, dimension (N)
122: *> On exit, it contains the details of the interchanges, i.e.,
123: *> the row and column k of A were interchanged with the
124: *> row and column IPIV(k).
125: *> \endverbatim
126: *>
127: *> \param[out] IPIV2
128: *> \verbatim
129: *> IPIV is INTEGER array, dimension (N)
130: *> On exit, it contains the details of the interchanges, i.e.,
131: *> the row and column k of T were interchanged with the
132: *> row and column IPIV(k).
133: *> \endverbatim
134: *>
135: *> \param[in,out] B
136: *> \verbatim
137: *> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
138: *> On entry, the right hand side matrix B.
139: *> On exit, the solution matrix X.
140: *> \endverbatim
141: *>
142: *> \param[in] LDB
143: *> \verbatim
144: *> LDB is INTEGER
145: *> The leading dimension of the array B. LDB >= max(1,N).
146: *> \endverbatim
147: *>
148: *> \param[out] WORK
149: *> \verbatim
150: *> WORK is DOUBLE PRECISION workspace of size LWORK
151: *> \endverbatim
152: *>
153: *> \param[in] LWORK
154: *> \verbatim
155: *> The size of WORK. LWORK >= N, internally used to select NB
156: *> such that LWORK >= N*NB.
157: *>
158: *> If LWORK = -1, then a workspace query is assumed; the
159: *> routine only calculates the optimal size of the WORK array,
160: *> returns this value as the first entry of the WORK array, and
161: *> no error message related to LWORK is issued by XERBLA.
162: *> \endverbatim
163: *>
164: *> \param[out] INFO
165: *> \verbatim
166: *> INFO is INTEGER
167: *> = 0: successful exit
168: *> < 0: if INFO = -i, the i-th argument had an illegal value.
169: *> > 0: if INFO = i, band LU factorization failed on i-th column
170: *> \endverbatim
171: *
172: * Authors:
173: * ========
174: *
175: *> \author Univ. of Tennessee
176: *> \author Univ. of California Berkeley
177: *> \author Univ. of Colorado Denver
178: *> \author NAG Ltd.
179: *
180: *> \date November 2017
181: *
182: *> \ingroup doubleSYsolve
183: *
184: * =====================================================================
185: SUBROUTINE DSYSV_AA_2STAGE( UPLO, N, NRHS, A, LDA, TB, LTB,
186: $ IPIV, IPIV2, B, LDB, WORK, LWORK,
187: $ INFO )
188: *
189: * -- LAPACK computational routine (version 3.8.0) --
190: * -- LAPACK is a software package provided by Univ. of Tennessee, --
191: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
192: * November 2017
193: *
194: IMPLICIT NONE
195: *
196: * .. Scalar Arguments ..
197: CHARACTER UPLO
198: INTEGER N, NRHS, LDA, LDB, LTB, LWORK, INFO
199: * ..
200: * .. Array Arguments ..
201: INTEGER IPIV( * ), IPIV2( * )
202: DOUBLE PRECISION A( LDA, * ), B( LDB, * ), TB( * ), WORK( * )
203: * ..
204: *
205: * =====================================================================
206: *
207: * .. Local Scalars ..
208: LOGICAL UPPER, TQUERY, WQUERY
209: INTEGER LWKOPT
210: * ..
211: * .. External Functions ..
212: LOGICAL LSAME
213: EXTERNAL LSAME
214: * ..
215: * .. External Subroutines ..
216: EXTERNAL DSYTRF_AA_2STAGE, DSYTRS_AA_2STAGE,
217: $ XERBLA
218: * ..
219: * .. Intrinsic Functions ..
220: INTRINSIC MAX
221: * ..
222: * .. Executable Statements ..
223: *
224: * Test the input parameters.
225: *
226: INFO = 0
227: UPPER = LSAME( UPLO, 'U' )
228: WQUERY = ( LWORK.EQ.-1 )
229: TQUERY = ( LTB.EQ.-1 )
230: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
231: INFO = -1
232: ELSE IF( N.LT.0 ) THEN
233: INFO = -2
234: ELSE IF( NRHS.LT.0 ) THEN
235: INFO = -3
236: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
237: INFO = -5
238: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
239: INFO = -11
240: END IF
241: *
242: IF( INFO.EQ.0 ) THEN
243: CALL DSYTRF_AA_2STAGE( UPLO, N, A, LDA, TB, -1, IPIV,
244: $ IPIV2, WORK, -1, INFO )
245: LWKOPT = INT( WORK(1) )
246: IF( LTB.LT.INT( TB(1) ) .AND. .NOT.TQUERY ) THEN
247: INFO = -7
248: ELSE IF( LWORK.LT.LWKOPT .AND. .NOT.WQUERY ) THEN
249: INFO = -13
250: END IF
251: END IF
252: *
253: IF( INFO.NE.0 ) THEN
254: CALL XERBLA( 'DSYSV_AA_2STAGE', -INFO )
255: RETURN
256: ELSE IF( WQUERY .OR. TQUERY ) THEN
257: RETURN
258: END IF
259: *
260: *
261: * Compute the factorization A = U*T*U**T or A = L*T*L**T.
262: *
263: CALL DSYTRF_AA_2STAGE( UPLO, N, A, LDA, TB, LTB, IPIV, IPIV2,
264: $ WORK, LWORK, INFO )
265: IF( INFO.EQ.0 ) THEN
266: *
267: * Solve the system A*X = B, overwriting B with X.
268: *
269: CALL DSYTRS_AA_2STAGE( UPLO, N, NRHS, A, LDA, TB, LTB, IPIV,
270: $ IPIV2, B, LDB, INFO )
271: *
272: END IF
273: *
274: WORK( 1 ) = LWKOPT
275: *
276: RETURN
277: *
278: * End of DSYSV_AA_2STAGE
279: *
280: END
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