1: *> \brief \b DSYTRS_AA
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DSYTRS_AA + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsytrs_aa.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsytrs_aa.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsytrs_aa.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DSYTRS_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
22: * WORK, 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: * DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * )
31: * ..
32: *
33: *
34: *> \par Purpose:
35: * =============
36: *>
37: *> \verbatim
38: *>
39: *> DSYTRS_AA solves a system of linear equations A*X = B with a real
40: *> symmetric matrix A using the factorization A = U**T*T*U or
41: *> A = L*T*L**T computed by DSYTRF_AA.
42: *> \endverbatim
43: *
44: * Arguments:
45: * ==========
46: *
47: *> \param[in] UPLO
48: *> \verbatim
49: *> UPLO is CHARACTER*1
50: *> Specifies whether the details of the factorization are stored
51: *> as an upper or lower triangular matrix.
52: *> = 'U': Upper triangular, form is A = U**T*T*U;
53: *> = 'L': Lower triangular, form is A = L*T*L**T.
54: *> \endverbatim
55: *>
56: *> \param[in] N
57: *> \verbatim
58: *> N is INTEGER
59: *> The order of the matrix A. N >= 0.
60: *> \endverbatim
61: *>
62: *> \param[in] NRHS
63: *> \verbatim
64: *> NRHS is INTEGER
65: *> The number of right hand sides, i.e., the number of columns
66: *> of the matrix B. NRHS >= 0.
67: *> \endverbatim
68: *>
69: *> \param[in] A
70: *> \verbatim
71: *> A is DOUBLE PRECISION array, dimension (LDA,N)
72: *> Details of factors computed by DSYTRF_AA.
73: *> \endverbatim
74: *>
75: *> \param[in] LDA
76: *> \verbatim
77: *> LDA is INTEGER
78: *> The leading dimension of the array A. LDA >= max(1,N).
79: *> \endverbatim
80: *>
81: *> \param[in] IPIV
82: *> \verbatim
83: *> IPIV is INTEGER array, dimension (N)
84: *> Details of the interchanges as computed by DSYTRF_AA.
85: *> \endverbatim
86: *>
87: *> \param[in,out] B
88: *> \verbatim
89: *> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
90: *> On entry, the right hand side matrix B.
91: *> On exit, the solution matrix X.
92: *> \endverbatim
93: *>
94: *> \param[in] LDB
95: *> \verbatim
96: *> LDB is INTEGER
97: *> The leading dimension of the array B. LDB >= max(1,N).
98: *> \endverbatim
99: *>
100: *> \param[out] WORK
101: *> \verbatim
102: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
103: *> \endverbatim
104: *>
105: *> \param[in] LWORK
106: *> \verbatim
107: *> LWORK is INTEGER
108: *> The dimension of the array WORK. LWORK >= max(1,3*N-2).
109: *> \endverbatim
110: *>
111: *> \param[out] INFO
112: *> \verbatim
113: *> INFO is INTEGER
114: *> = 0: successful exit
115: *> < 0: if INFO = -i, the i-th argument had an illegal value
116: *> \endverbatim
117: *
118: * Authors:
119: * ========
120: *
121: *> \author Univ. of Tennessee
122: *> \author Univ. of California Berkeley
123: *> \author Univ. of Colorado Denver
124: *> \author NAG Ltd.
125: *
126: *> \ingroup doubleSYcomputational
127: *
128: * =====================================================================
129: SUBROUTINE DSYTRS_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
130: $ WORK, LWORK, INFO )
131: *
132: * -- LAPACK computational routine --
133: * -- LAPACK is a software package provided by Univ. of Tennessee, --
134: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
135: *
136: IMPLICIT NONE
137: *
138: * .. Scalar Arguments ..
139: CHARACTER UPLO
140: INTEGER N, NRHS, LDA, LDB, LWORK, INFO
141: * ..
142: * .. Array Arguments ..
143: INTEGER IPIV( * )
144: DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * )
145: * ..
146: *
147: * =====================================================================
148: *
149: DOUBLE PRECISION ONE
150: PARAMETER ( ONE = 1.0D+0 )
151: * ..
152: * .. Local Scalars ..
153: LOGICAL LQUERY, UPPER
154: INTEGER K, KP, LWKOPT
155: * ..
156: * .. External Functions ..
157: LOGICAL LSAME
158: EXTERNAL LSAME
159: * ..
160: * .. External Subroutines ..
161: EXTERNAL DLACPY, DGTSV, DSWAP, DTRSM, XERBLA
162: * ..
163: * .. Intrinsic Functions ..
164: INTRINSIC MAX
165: * ..
166: * .. Executable Statements ..
167: *
168: INFO = 0
169: UPPER = LSAME( UPLO, 'U' )
170: LQUERY = ( LWORK.EQ.-1 )
171: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
172: INFO = -1
173: ELSE IF( N.LT.0 ) THEN
174: INFO = -2
175: ELSE IF( NRHS.LT.0 ) THEN
176: INFO = -3
177: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
178: INFO = -5
179: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
180: INFO = -8
181: ELSE IF( LWORK.LT.MAX( 1, 3*N-2 ) .AND. .NOT.LQUERY ) THEN
182: INFO = -10
183: END IF
184: IF( INFO.NE.0 ) THEN
185: CALL XERBLA( 'DSYTRS_AA', -INFO )
186: RETURN
187: ELSE IF( LQUERY ) THEN
188: LWKOPT = (3*N-2)
189: WORK( 1 ) = LWKOPT
190: RETURN
191: END IF
192: *
193: * Quick return if possible
194: *
195: IF( N.EQ.0 .OR. NRHS.EQ.0 )
196: $ RETURN
197: *
198: IF( UPPER ) THEN
199: *
200: * Solve A*X = B, where A = U**T*T*U.
201: *
202: * 1) Forward substitution with U**T
203: *
204: IF( N.GT.1 ) THEN
205: *
206: * Pivot, P**T * B -> B
207: *
208: DO K = 1, N
209: KP = IPIV( K )
210: IF( KP.NE.K )
211: $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
212: END DO
213: *
214: * Compute U**T \ B -> B [ (U**T \P**T * B) ]
215: *
216: CALL DTRSM('L', 'U', 'T', 'U', N-1, NRHS, ONE, A( 1, 2 ),
217: $ LDA, B( 2, 1 ), LDB)
218: END IF
219: *
220: * 2) Solve with triangular matrix T
221: *
222: * Compute T \ B -> B [ T \ (U**T \P**T * B) ]
223: *
224: CALL DLACPY( 'F', 1, N, A( 1, 1 ), LDA+1, WORK( N ), 1)
225: IF( N.GT.1 ) THEN
226: CALL DLACPY( 'F', 1, N-1, A( 1, 2 ), LDA+1, WORK( 1 ), 1 )
227: CALL DLACPY( 'F', 1, N-1, A( 1, 2 ), LDA+1, WORK( 2*N ), 1 )
228: END IF
229: CALL DGTSV( N, NRHS, WORK( 1 ), WORK( N ), WORK( 2*N ), B, LDB,
230: $ INFO )
231: *
232: * 3) Backward substitution with U
233: *
234: IF( N.GT.1 ) THEN
235: *
236: * Compute U \ B -> B [ U \ (T \ (U**T \P**T * B) ) ]
237: *
238: CALL DTRSM( 'L', 'U', 'N', 'U', N-1, NRHS, ONE, A( 1, 2 ),
239: $ LDA, B( 2, 1 ), LDB)
240: *
241: * Pivot, P * B -> B [ P * (U \ (T \ (U**T \P**T * B) )) ]
242: *
243: DO K = N, 1, -1
244: KP = IPIV( K )
245: IF( KP.NE.K )
246: $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
247: END DO
248: END IF
249: *
250: ELSE
251: *
252: * Solve A*X = B, where A = L*T*L**T.
253: *
254: * 1) Forward substitution with L
255: *
256: IF( N.GT.1 ) THEN
257: *
258: * Pivot, P**T * B -> B
259: *
260: DO K = 1, N
261: KP = IPIV( K )
262: IF( KP.NE.K )
263: $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
264: END DO
265: *
266: * Compute L \ B -> B [ (L \P**T * B) ]
267: *
268: CALL DTRSM( 'L', 'L', 'N', 'U', N-1, NRHS, ONE, A( 2, 1 ),
269: $ LDA, B( 2, 1 ), LDB)
270: END IF
271: *
272: * 2) Solve with triangular matrix T
273: *
274: * Compute T \ B -> B [ T \ (L \P**T * B) ]
275: *
276: CALL DLACPY( 'F', 1, N, A(1, 1), LDA+1, WORK(N), 1)
277: IF( N.GT.1 ) THEN
278: CALL DLACPY( 'F', 1, N-1, A( 2, 1 ), LDA+1, WORK( 1 ), 1 )
279: CALL DLACPY( 'F', 1, N-1, A( 2, 1 ), LDA+1, WORK( 2*N ), 1 )
280: END IF
281: CALL DGTSV( N, NRHS, WORK( 1 ), WORK(N), WORK( 2*N ), B, LDB,
282: $ INFO)
283: *
284: * 3) Backward substitution with L**T
285: *
286: IF( N.GT.1 ) THEN
287: *
288: * Compute (L**T \ B) -> B [ L**T \ (T \ (L \P**T * B) ) ]
289: *
290: CALL DTRSM( 'L', 'L', 'T', 'U', N-1, NRHS, ONE, A( 2, 1 ),
291: $ LDA, B( 2, 1 ), LDB)
292: *
293: * Pivot, P * B -> B [ P * (L**T \ (T \ (L \P**T * B) )) ]
294: *
295: DO K = N, 1, -1
296: KP = IPIV( K )
297: IF( KP.NE.K )
298: $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
299: END DO
300: END IF
301: *
302: END IF
303: *
304: RETURN
305: *
306: * End of DSYTRS_AA
307: *
308: END
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