Annotation of rpl/lapack/lapack/dsytrd_2stage.f, revision 1.3
1.1 bertrand 1: *> \brief \b DSYTRD_2STAGE
2: *
3: * @generated from zhetrd_2stage.f, fortran z -> d, Sun Nov 6 19:34:06 2016
4: *
5: * =========== DOCUMENTATION ===========
6: *
7: * Online html documentation available at
8: * http://www.netlib.org/lapack/explore-html/
9: *
10: *> \htmlonly
11: *> Download DSYTRD_2STAGE + dependencies
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsytrd_2stage.f">
13: *> [TGZ]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsytrd_2stage.f">
15: *> [ZIP]</a>
16: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsytrd_2stage.f">
17: *> [TXT]</a>
18: *> \endhtmlonly
19: *
20: * Definition:
21: * ===========
22: *
23: * SUBROUTINE DSYTRD_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: * DOUBLE PRECISION A( LDA, * ), TAU( * ),
35: * HOUS2( * ), WORK( * )
36: * ..
37: *
38: *
39: *> \par Purpose:
40: * =============
41: *>
42: *> \verbatim
43: *>
44: *> DSYTRD_2STAGE reduces a real symmetric matrix A to real symmetric
45: *> tridiagonal form T by a orthogonal similarity transformation:
46: *> Q1**T Q2**T* 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 DOUBLE PRECISION array, dimension (LDA,N)
80: *> On entry, the symmetric 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 orthogonal
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 orthogonal 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension LHOUS2, that
127: *> store 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. LHOUS2 = MAX(1, dimension)
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: *> LHOUS2 = MAX(1, dimension) where
141: *> dimension = 4*N if VECT='N'
142: *> not available now if VECT='H'
143: *> \endverbatim
144: *>
145: *> \param[out] WORK
146: *> \verbatim
1.3 ! bertrand 147: *> WORK is DOUBLE PRECISION array, dimension (LWORK)
1.1 bertrand 148: *> \endverbatim
149: *>
150: *> \param[in] LWORK
151: *> \verbatim
152: *> LWORK is INTEGER
153: *> The dimension of the array WORK. LWORK = MAX(1, dimension)
154: *> If LWORK = -1, or LHOUS2=-1,
155: *> then a workspace query is assumed; the routine
156: *> only calculates the optimal size of the WORK array, returns
157: *> this value as the first entry of the WORK array, and no error
158: *> message related to LWORK is issued by XERBLA.
159: *> LWORK = MAX(1, dimension) where
160: *> dimension = max(stage1,stage2) + (KD+1)*N
161: *> = N*KD + N*max(KD+1,FACTOPTNB)
162: *> + max(2*KD*KD, KD*NTHREADS)
163: *> + (KD+1)*N
164: *> where KD is the blocking size of the reduction,
165: *> FACTOPTNB is the blocking used by the QR or LQ
166: *> algorithm, usually FACTOPTNB=128 is a good choice
167: *> NTHREADS is the number of threads used when
168: *> openMP compilation is enabled, otherwise =1.
169: *> \endverbatim
170: *>
171: *> \param[out] INFO
172: *> \verbatim
173: *> INFO is INTEGER
174: *> = 0: successful exit
175: *> < 0: if INFO = -i, the i-th argument had an illegal value
176: *> \endverbatim
177: *
178: * Authors:
179: * ========
180: *
181: *> \author Univ. of Tennessee
182: *> \author Univ. of California Berkeley
183: *> \author Univ. of Colorado Denver
184: *> \author NAG Ltd.
185: *
1.3 ! bertrand 186: *> \date November 2017
1.1 bertrand 187: *
188: *> \ingroup doubleSYcomputational
189: *
190: *> \par Further Details:
191: * =====================
192: *>
193: *> \verbatim
194: *>
195: *> Implemented by Azzam Haidar.
196: *>
197: *> All details are available on technical report, SC11, SC13 papers.
198: *>
199: *> Azzam Haidar, Hatem Ltaief, and Jack Dongarra.
200: *> Parallel reduction to condensed forms for symmetric eigenvalue problems
201: *> using aggregated fine-grained and memory-aware kernels. In Proceedings
202: *> of 2011 International Conference for High Performance Computing,
203: *> Networking, Storage and Analysis (SC '11), New York, NY, USA,
204: *> Article 8 , 11 pages.
205: *> http://doi.acm.org/10.1145/2063384.2063394
206: *>
207: *> A. Haidar, J. Kurzak, P. Luszczek, 2013.
208: *> An improved parallel singular value algorithm and its implementation
209: *> for multicore hardware, In Proceedings of 2013 International Conference
210: *> for High Performance Computing, Networking, Storage and Analysis (SC '13).
211: *> Denver, Colorado, USA, 2013.
212: *> Article 90, 12 pages.
213: *> http://doi.acm.org/10.1145/2503210.2503292
214: *>
215: *> A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra.
216: *> A novel hybrid CPU-GPU generalized eigensolver for electronic structure
217: *> calculations based on fine-grained memory aware tasks.
218: *> International Journal of High Performance Computing Applications.
219: *> Volume 28 Issue 2, Pages 196-209, May 2014.
220: *> http://hpc.sagepub.com/content/28/2/196
221: *>
222: *> \endverbatim
223: *>
224: * =====================================================================
225: SUBROUTINE DSYTRD_2STAGE( VECT, UPLO, N, A, LDA, D, E, TAU,
226: $ HOUS2, LHOUS2, WORK, LWORK, INFO )
227: *
228: IMPLICIT NONE
229: *
1.3 ! bertrand 230: * -- LAPACK computational routine (version 3.8.0) --
1.1 bertrand 231: * -- LAPACK is a software package provided by Univ. of Tennessee, --
232: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.3 ! bertrand 233: * November 2017
1.1 bertrand 234: *
235: * .. Scalar Arguments ..
236: CHARACTER VECT, UPLO
237: INTEGER N, LDA, LWORK, LHOUS2, INFO
238: * ..
239: * .. Array Arguments ..
240: DOUBLE PRECISION D( * ), E( * )
241: DOUBLE PRECISION A( LDA, * ), TAU( * ),
242: $ HOUS2( * ), WORK( * )
243: * ..
244: *
245: * =====================================================================
246: * ..
247: * .. Local Scalars ..
248: LOGICAL LQUERY, UPPER, WANTQ
249: INTEGER KD, IB, LWMIN, LHMIN, LWRK, LDAB, WPOS, ABPOS
250: * ..
251: * .. External Subroutines ..
252: EXTERNAL XERBLA, DSYTRD_SY2SB, DSYTRD_SB2ST
253: * ..
254: * .. External Functions ..
255: LOGICAL LSAME
1.3 ! bertrand 256: INTEGER ILAENV2STAGE
! 257: EXTERNAL LSAME, ILAENV2STAGE
1.1 bertrand 258: * ..
259: * .. Executable Statements ..
260: *
261: * Test the input parameters
262: *
263: INFO = 0
264: WANTQ = LSAME( VECT, 'V' )
265: UPPER = LSAME( UPLO, 'U' )
266: LQUERY = ( LWORK.EQ.-1 ) .OR. ( LHOUS2.EQ.-1 )
267: *
268: * Determine the block size, the workspace size and the hous size.
269: *
1.3 ! bertrand 270: KD = ILAENV2STAGE( 1, 'DSYTRD_2STAGE', VECT, N, -1, -1, -1 )
! 271: IB = ILAENV2STAGE( 2, 'DSYTRD_2STAGE', VECT, N, KD, -1, -1 )
! 272: LHMIN = ILAENV2STAGE( 3, 'DSYTRD_2STAGE', VECT, N, KD, IB, -1 )
! 273: LWMIN = ILAENV2STAGE( 4, 'DSYTRD_2STAGE', VECT, N, KD, IB, -1 )
1.1 bertrand 274: * WRITE(*,*),'DSYTRD_2STAGE N KD UPLO LHMIN LWMIN ',N, KD, UPLO,
275: * $ LHMIN, LWMIN
276: *
277: IF( .NOT.LSAME( VECT, 'N' ) ) THEN
278: INFO = -1
279: ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
280: INFO = -2
281: ELSE IF( N.LT.0 ) THEN
282: INFO = -3
283: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
284: INFO = -5
285: ELSE IF( LHOUS2.LT.LHMIN .AND. .NOT.LQUERY ) THEN
286: INFO = -10
287: ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
288: INFO = -12
289: END IF
290: *
291: IF( INFO.EQ.0 ) THEN
292: HOUS2( 1 ) = LHMIN
293: WORK( 1 ) = LWMIN
294: END IF
295: *
296: IF( INFO.NE.0 ) THEN
297: CALL XERBLA( 'DSYTRD_2STAGE', -INFO )
298: RETURN
299: ELSE IF( LQUERY ) THEN
300: RETURN
301: END IF
302: *
303: * Quick return if possible
304: *
305: IF( N.EQ.0 ) THEN
306: WORK( 1 ) = 1
307: RETURN
308: END IF
309: *
310: * Determine pointer position
311: *
312: LDAB = KD+1
313: LWRK = LWORK-LDAB*N
314: ABPOS = 1
315: WPOS = ABPOS + LDAB*N
316: CALL DSYTRD_SY2SB( UPLO, N, KD, A, LDA, WORK( ABPOS ), LDAB,
317: $ TAU, WORK( WPOS ), LWRK, INFO )
318: IF( INFO.NE.0 ) THEN
319: CALL XERBLA( 'DSYTRD_SY2SB', -INFO )
320: RETURN
321: END IF
322: CALL DSYTRD_SB2ST( 'Y', VECT, UPLO, N, KD,
323: $ WORK( ABPOS ), LDAB, D, E,
324: $ HOUS2, LHOUS2, WORK( WPOS ), LWRK, INFO )
325: IF( INFO.NE.0 ) THEN
326: CALL XERBLA( 'DSYTRD_SB2ST', -INFO )
327: RETURN
328: END IF
329: *
330: *
331: HOUS2( 1 ) = LHMIN
332: WORK( 1 ) = LWMIN
333: RETURN
334: *
335: * End of DSYTRD_2STAGE
336: *
337: END
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