Annotation of rpl/lapack/lapack/zhetrs_aa.f, revision 1.6
1.1 bertrand 1: *> \brief \b ZHETRS_AA
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZHETRS_AA + dependencies
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11: *> [TGZ]</a>
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13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhetrs_aa.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZHETRS_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: * COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
31: * ..
32: *
33: *
34: *
35: *> \par Purpose:
36: * =============
37: *>
38: *> \verbatim
39: *>
40: *> ZHETRS_AA solves a system of linear equations A*X = B with a complex
1.5 bertrand 41: *> hermitian matrix A using the factorization A = U**H*T*U or
42: *> A = L*T*L**H computed by ZHETRF_AA.
1.1 bertrand 43: *> \endverbatim
44: *
45: * Arguments:
46: * ==========
47: *
48: *> \param[in] UPLO
49: *> \verbatim
50: *> UPLO is CHARACTER*1
51: *> Specifies whether the details of the factorization are stored
52: *> as an upper or lower triangular matrix.
1.5 bertrand 53: *> = 'U': Upper triangular, form is A = U**H*T*U;
1.1 bertrand 54: *> = 'L': Lower triangular, form is A = L*T*L**H.
55: *> \endverbatim
56: *>
57: *> \param[in] N
58: *> \verbatim
59: *> N is INTEGER
60: *> The order of the matrix A. N >= 0.
61: *> \endverbatim
62: *>
63: *> \param[in] NRHS
64: *> \verbatim
65: *> NRHS is INTEGER
66: *> The number of right hand sides, i.e., the number of columns
67: *> of the matrix B. NRHS >= 0.
68: *> \endverbatim
69: *>
1.3 bertrand 70: *> \param[in] A
1.1 bertrand 71: *> \verbatim
72: *> A is COMPLEX*16 array, dimension (LDA,N)
73: *> Details of factors computed by ZHETRF_AA.
74: *> \endverbatim
75: *>
76: *> \param[in] LDA
77: *> \verbatim
78: *> LDA is INTEGER
79: *> The leading dimension of the array A. LDA >= max(1,N).
80: *> \endverbatim
81: *>
82: *> \param[in] IPIV
83: *> \verbatim
84: *> IPIV is INTEGER array, dimension (N)
85: *> Details of the interchanges as computed by ZHETRF_AA.
86: *> \endverbatim
87: *>
88: *> \param[in,out] B
89: *> \verbatim
90: *> B is COMPLEX*16 array, dimension (LDB,NRHS)
91: *> On entry, the right hand side matrix B.
92: *> On exit, the solution matrix X.
93: *> \endverbatim
94: *>
95: *> \param[in] LDB
96: *> \verbatim
97: *> LDB is INTEGER
98: *> The leading dimension of the array B. LDB >= max(1,N).
99: *> \endverbatim
100: *>
1.5 bertrand 101: *> \param[out] WORK
1.1 bertrand 102: *> \verbatim
1.5 bertrand 103: *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
1.1 bertrand 104: *> \endverbatim
105: *>
106: *> \param[in] LWORK
107: *> \verbatim
1.5 bertrand 108: *> LWORK is INTEGER
109: *> The dimension of the array WORK. LWORK >= max(1,3*N-2).
110: *> \endverbatim
1.1 bertrand 111: *>
112: *> \param[out] INFO
113: *> \verbatim
114: *> INFO is INTEGER
115: *> = 0: successful exit
116: *> < 0: if INFO = -i, the i-th argument had an illegal value
117: *> \endverbatim
118: *
119: * Authors:
120: * ========
121: *
122: *> \author Univ. of Tennessee
123: *> \author Univ. of California Berkeley
124: *> \author Univ. of Colorado Denver
125: *> \author NAG Ltd.
126: *
127: *> \ingroup complex16HEcomputational
128: *
129: * =====================================================================
130: SUBROUTINE ZHETRS_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
131: $ WORK, LWORK, INFO )
132: *
1.6 ! bertrand 133: * -- LAPACK computational routine --
1.1 bertrand 134: * -- LAPACK is a software package provided by Univ. of Tennessee, --
135: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
136: *
137: IMPLICIT NONE
138: *
139: * .. Scalar Arguments ..
140: CHARACTER UPLO
141: INTEGER N, NRHS, LDA, LDB, LWORK, INFO
142: * ..
143: * .. Array Arguments ..
144: INTEGER IPIV( * )
145: COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
146: * ..
147: *
148: * =====================================================================
149: *
150: COMPLEX*16 ONE
151: PARAMETER ( ONE = 1.0D+0 )
152: * ..
153: * .. Local Scalars ..
154: LOGICAL LQUERY, UPPER
155: INTEGER K, KP, LWKOPT
156: * ..
157: * .. External Functions ..
158: LOGICAL LSAME
159: EXTERNAL LSAME
160: * ..
161: * .. External Subroutines ..
1.3 bertrand 162: EXTERNAL ZGTSV, ZSWAP, ZTRSM, ZLACGV, ZLACPY, XERBLA
1.1 bertrand 163: * ..
164: * .. Intrinsic Functions ..
165: INTRINSIC MAX
166: * ..
167: * .. Executable Statements ..
168: *
169: INFO = 0
170: UPPER = LSAME( UPLO, 'U' )
171: LQUERY = ( LWORK.EQ.-1 )
172: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
173: INFO = -1
174: ELSE IF( N.LT.0 ) THEN
175: INFO = -2
176: ELSE IF( NRHS.LT.0 ) THEN
177: INFO = -3
178: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
179: INFO = -5
180: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
181: INFO = -8
182: ELSE IF( LWORK.LT.MAX( 1, 3*N-2 ) .AND. .NOT.LQUERY ) THEN
183: INFO = -10
184: END IF
185: IF( INFO.NE.0 ) THEN
186: CALL XERBLA( 'ZHETRS_AA', -INFO )
187: RETURN
188: ELSE IF( LQUERY ) THEN
189: LWKOPT = (3*N-2)
190: WORK( 1 ) = LWKOPT
191: RETURN
192: END IF
193: *
194: * Quick return if possible
195: *
196: IF( N.EQ.0 .OR. NRHS.EQ.0 )
197: $ RETURN
198: *
199: IF( UPPER ) THEN
200: *
1.5 bertrand 201: * Solve A*X = B, where A = U**H*T*U.
202: *
203: * 1) Forward substitution with U**H
204: *
205: IF( N.GT.1 ) THEN
206: *
207: * Pivot, P**T * B -> B
1.1 bertrand 208: *
1.5 bertrand 209: DO K = 1, N
210: KP = IPIV( K )
211: IF( KP.NE.K )
212: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
213: END DO
1.1 bertrand 214: *
1.5 bertrand 215: * Compute U**H \ B -> B [ (U**H \P**T * B) ]
1.1 bertrand 216: *
1.5 bertrand 217: CALL ZTRSM( 'L', 'U', 'C', 'U', N-1, NRHS, ONE, A( 1, 2 ),
218: $ LDA, B( 2, 1 ), LDB )
219: END IF
1.1 bertrand 220: *
1.5 bertrand 221: * 2) Solve with triangular matrix T
1.1 bertrand 222: *
1.5 bertrand 223: * Compute T \ B -> B [ T \ (U**H \P**T * B) ]
1.1 bertrand 224: *
1.5 bertrand 225: CALL ZLACPY( 'F', 1, N, A(1, 1), LDA+1, WORK(N), 1 )
1.1 bertrand 226: IF( N.GT.1 ) THEN
227: CALL ZLACPY( 'F', 1, N-1, A( 1, 2 ), LDA+1, WORK( 2*N ), 1)
1.5 bertrand 228: CALL ZLACPY( 'F', 1, N-1, A( 1, 2 ), LDA+1, WORK( 1 ), 1 )
1.1 bertrand 229: CALL ZLACGV( N-1, WORK( 1 ), 1 )
230: END IF
1.5 bertrand 231: CALL ZGTSV( N, NRHS, WORK(1), WORK(N), WORK(2*N), B, LDB,
232: $ INFO )
233: *
234: * 3) Backward substitution with U
235: *
236: IF( N.GT.1 ) THEN
1.1 bertrand 237: *
1.5 bertrand 238: * Compute U \ B -> B [ U \ (T \ (U**H \P**T * B) ) ]
1.1 bertrand 239: *
1.5 bertrand 240: CALL ZTRSM( 'L', 'U', 'N', 'U', N-1, NRHS, ONE, A( 1, 2 ),
241: $ LDA, B(2, 1), LDB)
1.1 bertrand 242: *
1.5 bertrand 243: * Pivot, P * B [ P * (U**H \ (T \ (U \P**T * B) )) ]
1.1 bertrand 244: *
1.5 bertrand 245: DO K = N, 1, -1
246: KP = IPIV( K )
247: IF( KP.NE.K )
248: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
249: END DO
250: END IF
1.1 bertrand 251: *
252: ELSE
253: *
1.5 bertrand 254: * Solve A*X = B, where A = L*T*L**H.
255: *
256: * 1) Forward substitution with L
1.1 bertrand 257: *
1.5 bertrand 258: IF( N.GT.1 ) THEN
259: *
260: * Pivot, P**T * B -> B
1.1 bertrand 261: *
1.5 bertrand 262: DO K = 1, N
263: KP = IPIV( K )
264: IF( KP.NE.K )
265: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
266: END DO
1.1 bertrand 267: *
1.5 bertrand 268: * Compute L \ B -> B [ (L \P**T * B) ]
1.1 bertrand 269: *
1.5 bertrand 270: CALL ZTRSM( 'L', 'L', 'N', 'U', N-1, NRHS, ONE, A( 2, 1 ),
271: $ LDA, B(2, 1), LDB)
272: END IF
273: *
274: * 2) Solve with triangular matrix T
1.1 bertrand 275: *
276: * Compute T \ B -> B [ T \ (L \P**T * B) ]
277: *
278: CALL ZLACPY( 'F', 1, N, A(1, 1), LDA+1, WORK(N), 1)
279: IF( N.GT.1 ) THEN
280: CALL ZLACPY( 'F', 1, N-1, A( 2, 1 ), LDA+1, WORK( 1 ), 1)
281: CALL ZLACPY( 'F', 1, N-1, A( 2, 1 ), LDA+1, WORK( 2*N ), 1)
282: CALL ZLACGV( N-1, WORK( 2*N ), 1 )
283: END IF
284: CALL ZGTSV(N, NRHS, WORK(1), WORK(N), WORK(2*N), B, LDB,
285: $ INFO)
286: *
1.5 bertrand 287: * 3) Backward substitution with L**H
288: *
289: IF( N.GT.1 ) THEN
1.1 bertrand 290: *
1.5 bertrand 291: * Compute L**H \ B -> B [ L**H \ (T \ (L \P**T * B) ) ]
1.1 bertrand 292: *
1.5 bertrand 293: CALL ZTRSM( 'L', 'L', 'C', 'U', N-1, NRHS, ONE, A( 2, 1 ),
294: $ LDA, B( 2, 1 ), LDB)
1.1 bertrand 295: *
1.5 bertrand 296: * Pivot, P * B [ P * (L**H \ (T \ (L \P**T * B) )) ]
297: *
298: DO K = N, 1, -1
299: KP = IPIV( K )
300: IF( KP.NE.K )
301: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
302: END DO
303: END IF
1.1 bertrand 304: *
305: END IF
306: *
307: RETURN
308: *
309: * End of ZHETRS_AA
310: *
311: END
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