Annotation of rpl/lapack/lapack/zsysv_aa_2stage.f, revision 1.3
1.1 bertrand 1: *> \brief <b> ZSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices</b>
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZSYSV_AA_2STAGE + dependencies
1.3 ! bertrand 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zsysv_aa_2stage.f">
1.1 bertrand 11: *> [TGZ]</a>
1.3 ! bertrand 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zsysv_aa_2stage.f">
1.1 bertrand 13: *> [ZIP]</a>
1.3 ! bertrand 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsysv_aa_2stage.f">
1.1 bertrand 15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZSYSV_AA_2STAGE( UPLO, N, NRHS, A, LDA, TB, LTB,
22: * IPIV, IPIV2, B, LDB, WORK, LWORK,
23: * INFO )
24: *
25: * .. Scalar Arguments ..
26: * CHARACTER UPLO
27: * INTEGER N, NRHS, LDA, LTB, LDB, LWORK, INFO
28: * ..
29: * .. Array Arguments ..
30: * INTEGER IPIV( * ), IPIV2( * )
31: * COMPLEX*16 A( LDA, * ), TB( * ), B( LDB, *), WORK( * )
32: * ..
33: *
34: *> \par Purpose:
35: * =============
36: *>
37: *> \verbatim
38: *>
39: *> ZSYSV_AA_2STAGE computes the solution to a complex system of
40: *> linear equations
41: *> A * X = B,
42: *> where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
43: *> matrices.
44: *>
45: *> Aasen's 2-stage algorithm is used to factor A as
1.2 bertrand 46: *> A = U**T * T * U, if UPLO = 'U', or
47: *> A = L * T * L**T, if UPLO = 'L',
1.1 bertrand 48: *> where U (or L) is a product of permutation and unit upper (lower)
49: *> triangular matrices, and T is symmetric and band. The matrix T is
50: *> then LU-factored with partial pivoting. The factored form of A
51: *> is then used to solve the system of equations A * X = B.
52: *>
53: *> This is the blocked version of the algorithm, calling Level 3 BLAS.
54: *> \endverbatim
55: *
56: * Arguments:
57: * ==========
58: *
59: *> \param[in] UPLO
60: *> \verbatim
61: *> UPLO is CHARACTER*1
62: *> = 'U': Upper triangle of A is stored;
63: *> = 'L': Lower triangle of A is stored.
64: *> \endverbatim
65: *>
66: *> \param[in] N
67: *> \verbatim
68: *> N is INTEGER
69: *> The order of the matrix A. N >= 0.
70: *> \endverbatim
71: *>
72: *> \param[in] NRHS
73: *> \verbatim
74: *> NRHS is INTEGER
75: *> The number of right hand sides, i.e., the number of columns
76: *> of the matrix B. NRHS >= 0.
77: *> \endverbatim
78: *>
79: *> \param[in,out] A
80: *> \verbatim
81: *> A is COMPLEX*16 array, dimension (LDA,N)
82: *> On entry, the symmetric matrix A. If UPLO = 'U', the leading
83: *> N-by-N upper triangular part of A contains the upper
84: *> triangular part of the matrix A, and the strictly lower
85: *> triangular part of A is not referenced. If UPLO = 'L', the
86: *> leading N-by-N lower triangular part of A contains the lower
87: *> triangular part of the matrix A, and the strictly upper
88: *> triangular part of A is not referenced.
89: *>
90: *> On exit, L is stored below (or above) the subdiaonal blocks,
91: *> when UPLO is 'L' (or 'U').
92: *> \endverbatim
93: *>
94: *> \param[in] LDA
95: *> \verbatim
96: *> LDA is INTEGER
97: *> The leading dimension of the array A. LDA >= max(1,N).
98: *> \endverbatim
99: *>
100: *> \param[out] TB
101: *> \verbatim
102: *> TB is COMPLEX*16 array, dimension (LTB)
103: *> On exit, details of the LU factorization of the band matrix.
104: *> \endverbatim
105: *>
106: *> \param[in] LTB
107: *> \verbatim
1.2 bertrand 108: *> LTB is INTEGER
1.1 bertrand 109: *> The size of the array TB. LTB >= 4*N, internally
110: *> used to select NB such that LTB >= (3*NB+1)*N.
111: *>
112: *> If LTB = -1, then a workspace query is assumed; the
113: *> routine only calculates the optimal size of LTB,
114: *> returns this value as the first entry of TB, and
115: *> no error message related to LTB is issued by XERBLA.
116: *> \endverbatim
117: *>
118: *> \param[out] IPIV
119: *> \verbatim
120: *> IPIV is INTEGER array, dimension (N)
121: *> On exit, it contains the details of the interchanges, i.e.,
122: *> the row and column k of A were interchanged with the
123: *> row and column IPIV(k).
124: *> \endverbatim
125: *>
126: *> \param[out] IPIV2
127: *> \verbatim
1.2 bertrand 128: *> IPIV2 is INTEGER array, dimension (N)
1.1 bertrand 129: *> On exit, it contains the details of the interchanges, i.e.,
130: *> the row and column k of T were interchanged with the
131: *> row and column IPIV(k).
132: *> \endverbatim
133: *>
134: *> \param[in,out] B
135: *> \verbatim
136: *> B is COMPLEX*16 array, dimension (LDB,NRHS)
137: *> On entry, the right hand side matrix B.
138: *> On exit, the solution matrix X.
139: *> \endverbatim
140: *>
141: *> \param[in] LDB
142: *> \verbatim
143: *> LDB is INTEGER
144: *> The leading dimension of the array B. LDB >= max(1,N).
145: *> \endverbatim
146: *>
147: *> \param[out] WORK
148: *> \verbatim
149: *> WORK is COMPLEX*16 workspace of size LWORK
150: *> \endverbatim
151: *>
152: *> \param[in] LWORK
153: *> \verbatim
1.2 bertrand 154: *> LWORK is INTEGER
1.1 bertrand 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: *> \ingroup complex16SYcomputational
181: *
182: * =====================================================================
183: SUBROUTINE ZSYSV_AA_2STAGE( UPLO, N, NRHS, A, LDA, TB, LTB,
184: $ IPIV, IPIV2, B, LDB, WORK, LWORK,
185: $ INFO )
186: *
1.3 ! bertrand 187: * -- LAPACK computational routine --
1.1 bertrand 188: * -- LAPACK is a software package provided by Univ. of Tennessee, --
189: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
190: *
191: IMPLICIT NONE
192: *
193: * .. Scalar Arguments ..
194: CHARACTER UPLO
195: INTEGER N, NRHS, LDA, LDB, LTB, LWORK, INFO
196: * ..
197: * .. Array Arguments ..
198: INTEGER IPIV( * ), IPIV2( * )
199: COMPLEX*16 A( LDA, * ), B( LDB, * ), TB( * ), WORK( * )
200: * ..
201: *
202: * =====================================================================
203: *
204: * .. Local Scalars ..
205: LOGICAL UPPER, TQUERY, WQUERY
206: INTEGER LWKOPT
207: * ..
208: * .. External Functions ..
209: LOGICAL LSAME
210: EXTERNAL LSAME
211: * ..
212: * .. External Subroutines ..
213: EXTERNAL XERBLA, ZSYTRF_AA_2STAGE,
214: $ ZSYTRS_AA_2STAGE
215: * ..
216: * .. Intrinsic Functions ..
217: INTRINSIC MAX
218: * ..
219: * .. Executable Statements ..
220: *
221: * Test the input parameters.
222: *
223: INFO = 0
224: UPPER = LSAME( UPLO, 'U' )
225: WQUERY = ( LWORK.EQ.-1 )
226: TQUERY = ( LTB.EQ.-1 )
227: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
228: INFO = -1
229: ELSE IF( N.LT.0 ) THEN
230: INFO = -2
231: ELSE IF( NRHS.LT.0 ) THEN
232: INFO = -3
233: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
234: INFO = -5
1.2 bertrand 235: ELSE IF( LTB.LT.( 4*N ) .AND. .NOT.TQUERY ) THEN
236: INFO = -7
1.1 bertrand 237: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
238: INFO = -11
1.2 bertrand 239: ELSE IF( LWORK.LT.N .AND. .NOT.WQUERY ) THEN
240: INFO = -13
1.1 bertrand 241: END IF
242: *
243: IF( INFO.EQ.0 ) THEN
244: CALL ZSYTRF_AA_2STAGE( UPLO, N, A, LDA, TB, -1, IPIV,
245: $ IPIV2, WORK, -1, INFO )
246: LWKOPT = INT( WORK(1) )
247: END IF
248: *
249: IF( INFO.NE.0 ) THEN
250: CALL XERBLA( 'ZSYSV_AA_2STAGE', -INFO )
251: RETURN
252: ELSE IF( WQUERY .OR. TQUERY ) THEN
253: RETURN
254: END IF
255: *
256: *
1.2 bertrand 257: * Compute the factorization A = U**T*T*U or A = L*T*L**T.
1.1 bertrand 258: *
259: CALL ZSYTRF_AA_2STAGE( UPLO, N, A, LDA, TB, LTB, IPIV, IPIV2,
260: $ WORK, LWORK, INFO )
261: IF( INFO.EQ.0 ) THEN
262: *
263: * Solve the system A*X = B, overwriting B with X.
264: *
265: CALL ZSYTRS_AA_2STAGE( UPLO, N, NRHS, A, LDA, TB, LTB, IPIV,
266: $ IPIV2, B, LDB, INFO )
267: *
268: END IF
269: *
270: WORK( 1 ) = LWKOPT
271: *
272: * End of ZSYSV_AA_2STAGE
273: *
274: END
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