1: *> \brief \b ZHETRD_2STAGE
2: *
3: * @precisions fortran z -> s d c
4: *
5: * =========== DOCUMENTATION ===========
6: *
7: * Online html documentation available at
8: * http://www.netlib.org/lapack/explore-html/
9: *
10: *> \htmlonly
11: *> Download ZHETRD_2STAGE + dependencies
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhetrd_2stage.f">
13: *> [TGZ]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhetrd_2stage.f">
15: *> [ZIP]</a>
16: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhetrd_2stage.f">
17: *> [TXT]</a>
18: *> \endhtmlonly
19: *
20: * Definition:
21: * ===========
22: *
23: * SUBROUTINE ZHETRD_2STAGE( VECT, UPLO, N, A, LDA, D, E, TAU,
24: * HOUS2, LHOUS2, WORK, LWORK, INFO )
25: *
26: * IMPLICIT NONE
27: *
28: * .. Scalar Arguments ..
29: * CHARACTER VECT, UPLO
30: * INTEGER N, LDA, LWORK, LHOUS2, INFO
31: * ..
32: * .. Array Arguments ..
33: * DOUBLE PRECISION D( * ), E( * )
34: * COMPLEX*16 A( LDA, * ), TAU( * ),
35: * HOUS2( * ), WORK( * )
36: * ..
37: *
38: *
39: *> \par Purpose:
40: * =============
41: *>
42: *> \verbatim
43: *>
44: *> ZHETRD_2STAGE reduces a complex Hermitian matrix A to real symmetric
45: *> tridiagonal form T by a unitary similarity transformation:
46: *> Q1**H Q2**H* A * Q2 * Q1 = T.
47: *> \endverbatim
48: *
49: * Arguments:
50: * ==========
51: *
52: *> \param[in] VECT
53: *> \verbatim
54: *> VECT is CHARACTER*1
55: *> = 'N': No need for the Housholder representation,
56: *> in particular for the second stage (Band to
57: *> tridiagonal) and thus LHOUS2 is of size max(1, 4*N);
58: *> = 'V': the Householder representation is needed to
59: *> either generate Q1 Q2 or to apply Q1 Q2,
60: *> then LHOUS2 is to be queried and computed.
61: *> (NOT AVAILABLE IN THIS RELEASE).
62: *> \endverbatim
63: *>
64: *> \param[in] UPLO
65: *> \verbatim
66: *> UPLO is CHARACTER*1
67: *> = 'U': Upper triangle of A is stored;
68: *> = 'L': Lower triangle of A is stored.
69: *> \endverbatim
70: *>
71: *> \param[in] N
72: *> \verbatim
73: *> N is INTEGER
74: *> The order of the matrix A. N >= 0.
75: *> \endverbatim
76: *>
77: *> \param[in,out] A
78: *> \verbatim
79: *> A is COMPLEX*16 array, dimension (LDA,N)
80: *> On entry, the Hermitian matrix A. If UPLO = 'U', the leading
81: *> N-by-N upper triangular part of A contains the upper
82: *> triangular part of the matrix A, and the strictly lower
83: *> triangular part of A is not referenced. If UPLO = 'L', the
84: *> leading N-by-N lower triangular part of A contains the lower
85: *> triangular part of the matrix A, and the strictly upper
86: *> triangular part of A is not referenced.
87: *> On exit, if UPLO = 'U', the band superdiagonal
88: *> of A are overwritten by the corresponding elements of the
89: *> internal band-diagonal matrix AB, and the elements above
90: *> the KD superdiagonal, with the array TAU, represent the unitary
91: *> matrix Q1 as a product of elementary reflectors; if UPLO
92: *> = 'L', the diagonal and band subdiagonal of A are over-
93: *> written by the corresponding elements of the internal band-diagonal
94: *> matrix AB, and the elements below the KD subdiagonal, with
95: *> the array TAU, represent the unitary matrix Q1 as a product
96: *> of elementary reflectors. See Further Details.
97: *> \endverbatim
98: *>
99: *> \param[in] LDA
100: *> \verbatim
101: *> LDA is INTEGER
102: *> The leading dimension of the array A. LDA >= max(1,N).
103: *> \endverbatim
104: *>
105: *> \param[out] D
106: *> \verbatim
107: *> D is DOUBLE PRECISION array, dimension (N)
108: *> The diagonal elements of the tridiagonal matrix T.
109: *> \endverbatim
110: *>
111: *> \param[out] E
112: *> \verbatim
113: *> E is DOUBLE PRECISION array, dimension (N-1)
114: *> The off-diagonal elements of the tridiagonal matrix T.
115: *> \endverbatim
116: *>
117: *> \param[out] TAU
118: *> \verbatim
119: *> TAU is COMPLEX*16 array, dimension (N-KD)
120: *> The scalar factors of the elementary reflectors of
121: *> the first stage (see Further Details).
122: *> \endverbatim
123: *>
124: *> \param[out] HOUS2
125: *> \verbatim
126: *> HOUS2 is COMPLEX*16 array, dimension (LHOUS2)
127: *> Stores the Householder representation of the stage2
128: *> band to tridiagonal.
129: *> \endverbatim
130: *>
131: *> \param[in] LHOUS2
132: *> \verbatim
133: *> LHOUS2 is INTEGER
134: *> The dimension of the array HOUS2.
135: *> If LWORK = -1, or LHOUS2 = -1,
136: *> then a query is assumed; the routine
137: *> only calculates the optimal size of the HOUS2 array, returns
138: *> this value as the first entry of the HOUS2 array, and no error
139: *> message related to LHOUS2 is issued by XERBLA.
140: *> If VECT='N', LHOUS2 = max(1, 4*n);
141: *> if VECT='V', option not yet available.
142: *> \endverbatim
143: *>
144: *> \param[out] WORK
145: *> \verbatim
146: *> WORK is COMPLEX*16 array, dimension (LWORK)
147: *> \endverbatim
148: *>
149: *> \param[in] LWORK
150: *> \verbatim
151: *> LWORK is INTEGER
152: *> The dimension of the array WORK. LWORK = MAX(1, dimension)
153: *> If LWORK = -1, or LHOUS2=-1,
154: *> then a workspace query is assumed; the routine
155: *> only calculates the optimal size of the WORK array, returns
156: *> this value as the first entry of the WORK array, and no error
157: *> message related to LWORK is issued by XERBLA.
158: *> LWORK = MAX(1, dimension) where
159: *> dimension = max(stage1,stage2) + (KD+1)*N
160: *> = N*KD + N*max(KD+1,FACTOPTNB)
161: *> + max(2*KD*KD, KD*NTHREADS)
162: *> + (KD+1)*N
163: *> where KD is the blocking size of the reduction,
164: *> FACTOPTNB is the blocking used by the QR or LQ
165: *> algorithm, usually FACTOPTNB=128 is a good choice
166: *> NTHREADS is the number of threads used when
167: *> openMP compilation is enabled, otherwise =1.
168: *> \endverbatim
169: *>
170: *> \param[out] INFO
171: *> \verbatim
172: *> INFO is INTEGER
173: *> = 0: successful exit
174: *> < 0: if INFO = -i, the i-th argument had an illegal value
175: *> \endverbatim
176: *
177: * Authors:
178: * ========
179: *
180: *> \author Univ. of Tennessee
181: *> \author Univ. of California Berkeley
182: *> \author Univ. of Colorado Denver
183: *> \author NAG Ltd.
184: *
185: *> \ingroup complex16HEcomputational
186: *
187: *> \par Further Details:
188: * =====================
189: *>
190: *> \verbatim
191: *>
192: *> Implemented by Azzam Haidar.
193: *>
194: *> All details are available on technical report, SC11, SC13 papers.
195: *>
196: *> Azzam Haidar, Hatem Ltaief, and Jack Dongarra.
197: *> Parallel reduction to condensed forms for symmetric eigenvalue problems
198: *> using aggregated fine-grained and memory-aware kernels. In Proceedings
199: *> of 2011 International Conference for High Performance Computing,
200: *> Networking, Storage and Analysis (SC '11), New York, NY, USA,
201: *> Article 8 , 11 pages.
202: *> http://doi.acm.org/10.1145/2063384.2063394
203: *>
204: *> A. Haidar, J. Kurzak, P. Luszczek, 2013.
205: *> An improved parallel singular value algorithm and its implementation
206: *> for multicore hardware, In Proceedings of 2013 International Conference
207: *> for High Performance Computing, Networking, Storage and Analysis (SC '13).
208: *> Denver, Colorado, USA, 2013.
209: *> Article 90, 12 pages.
210: *> http://doi.acm.org/10.1145/2503210.2503292
211: *>
212: *> A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra.
213: *> A novel hybrid CPU-GPU generalized eigensolver for electronic structure
214: *> calculations based on fine-grained memory aware tasks.
215: *> International Journal of High Performance Computing Applications.
216: *> Volume 28 Issue 2, Pages 196-209, May 2014.
217: *> http://hpc.sagepub.com/content/28/2/196
218: *>
219: *> \endverbatim
220: *>
221: * =====================================================================
222: SUBROUTINE ZHETRD_2STAGE( VECT, UPLO, N, A, LDA, D, E, TAU,
223: $ HOUS2, LHOUS2, WORK, LWORK, INFO )
224: *
225: IMPLICIT NONE
226: *
227: * -- LAPACK computational routine --
228: * -- LAPACK is a software package provided by Univ. of Tennessee, --
229: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
230: *
231: * .. Scalar Arguments ..
232: CHARACTER VECT, UPLO
233: INTEGER N, LDA, LWORK, LHOUS2, INFO
234: * ..
235: * .. Array Arguments ..
236: DOUBLE PRECISION D( * ), E( * )
237: COMPLEX*16 A( LDA, * ), TAU( * ),
238: $ HOUS2( * ), WORK( * )
239: * ..
240: *
241: * =====================================================================
242: * ..
243: * .. Local Scalars ..
244: LOGICAL LQUERY, UPPER, WANTQ
245: INTEGER KD, IB, LWMIN, LHMIN, LWRK, LDAB, WPOS, ABPOS
246: * ..
247: * .. External Subroutines ..
248: EXTERNAL XERBLA, ZHETRD_HE2HB, ZHETRD_HB2ST
249: * ..
250: * .. External Functions ..
251: LOGICAL LSAME
252: INTEGER ILAENV2STAGE
253: EXTERNAL LSAME, ILAENV2STAGE
254: * ..
255: * .. Executable Statements ..
256: *
257: * Test the input parameters
258: *
259: INFO = 0
260: WANTQ = LSAME( VECT, 'V' )
261: UPPER = LSAME( UPLO, 'U' )
262: LQUERY = ( LWORK.EQ.-1 ) .OR. ( LHOUS2.EQ.-1 )
263: *
264: * Determine the block size, the workspace size and the hous size.
265: *
266: KD = ILAENV2STAGE( 1, 'ZHETRD_2STAGE', VECT, N, -1, -1, -1 )
267: IB = ILAENV2STAGE( 2, 'ZHETRD_2STAGE', VECT, N, KD, -1, -1 )
268: LHMIN = ILAENV2STAGE( 3, 'ZHETRD_2STAGE', VECT, N, KD, IB, -1 )
269: LWMIN = ILAENV2STAGE( 4, 'ZHETRD_2STAGE', VECT, N, KD, IB, -1 )
270: * WRITE(*,*),'ZHETRD_2STAGE N KD UPLO LHMIN LWMIN ',N, KD, UPLO,
271: * $ LHMIN, LWMIN
272: *
273: IF( .NOT.LSAME( VECT, 'N' ) ) THEN
274: INFO = -1
275: ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
276: INFO = -2
277: ELSE IF( N.LT.0 ) THEN
278: INFO = -3
279: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
280: INFO = -5
281: ELSE IF( LHOUS2.LT.LHMIN .AND. .NOT.LQUERY ) THEN
282: INFO = -10
283: ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
284: INFO = -12
285: END IF
286: *
287: IF( INFO.EQ.0 ) THEN
288: HOUS2( 1 ) = LHMIN
289: WORK( 1 ) = LWMIN
290: END IF
291: *
292: IF( INFO.NE.0 ) THEN
293: CALL XERBLA( 'ZHETRD_2STAGE', -INFO )
294: RETURN
295: ELSE IF( LQUERY ) THEN
296: RETURN
297: END IF
298: *
299: * Quick return if possible
300: *
301: IF( N.EQ.0 ) THEN
302: WORK( 1 ) = 1
303: RETURN
304: END IF
305: *
306: * Determine pointer position
307: *
308: LDAB = KD+1
309: LWRK = LWORK-LDAB*N
310: ABPOS = 1
311: WPOS = ABPOS + LDAB*N
312: CALL ZHETRD_HE2HB( UPLO, N, KD, A, LDA, WORK( ABPOS ), LDAB,
313: $ TAU, WORK( WPOS ), LWRK, INFO )
314: IF( INFO.NE.0 ) THEN
315: CALL XERBLA( 'ZHETRD_HE2HB', -INFO )
316: RETURN
317: END IF
318: CALL ZHETRD_HB2ST( 'Y', VECT, UPLO, N, KD,
319: $ WORK( ABPOS ), LDAB, D, E,
320: $ HOUS2, LHOUS2, WORK( WPOS ), LWRK, INFO )
321: IF( INFO.NE.0 ) THEN
322: CALL XERBLA( 'ZHETRD_HB2ST', -INFO )
323: RETURN
324: END IF
325: *
326: *
327: HOUS2( 1 ) = LHMIN
328: WORK( 1 ) = LWMIN
329: RETURN
330: *
331: * End of ZHETRD_2STAGE
332: *
333: END
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