Annotation of rpl/lapack/lapack/dsbevd_2stage.f, revision 1.5
1.1 bertrand 1: *> \brief <b> DSBEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices</b>
2: *
3: * @precisions fortran d -> s
4: *
5: * =========== DOCUMENTATION ===========
6: *
7: * Online html documentation available at
8: * http://www.netlib.org/lapack/explore-html/
9: *
10: *> \htmlonly
11: *> Download DSBEVD_2STAGE + dependencies
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsbevd_2stage.f">
13: *> [TGZ]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsbevd_2stage.f">
15: *> [ZIP]</a>
16: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsbevd_2stage.f">
17: *> [TXT]</a>
18: *> \endhtmlonly
19: *
20: * Definition:
21: * ===========
22: *
23: * SUBROUTINE DSBEVD_2STAGE( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ,
24: * WORK, LWORK, IWORK, LIWORK, INFO )
25: *
26: * IMPLICIT NONE
27: *
28: * .. Scalar Arguments ..
29: * CHARACTER JOBZ, UPLO
30: * INTEGER INFO, KD, LDAB, LDZ, LIWORK, LWORK, N
31: * ..
32: * .. Array Arguments ..
33: * INTEGER IWORK( * )
34: * DOUBLE PRECISION AB( LDAB, * ), W( * ), WORK( * ), Z( LDZ, * )
35: * ..
36: *
37: *
38: *> \par Purpose:
39: * =============
40: *>
41: *> \verbatim
42: *>
43: *> DSBEVD_2STAGE computes all the eigenvalues and, optionally, eigenvectors of
44: *> a real symmetric band matrix A using the 2stage technique for
45: *> the reduction to tridiagonal. If eigenvectors are desired, it uses
46: *> a divide and conquer algorithm.
47: *>
48: *> The divide and conquer algorithm makes very mild assumptions about
49: *> floating point arithmetic. It will work on machines with a guard
50: *> digit in add/subtract, or on those binary machines without guard
51: *> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
52: *> Cray-2. It could conceivably fail on hexadecimal or decimal machines
53: *> without guard digits, but we know of none.
54: *> \endverbatim
55: *
56: * Arguments:
57: * ==========
58: *
59: *> \param[in] JOBZ
60: *> \verbatim
61: *> JOBZ is CHARACTER*1
62: *> = 'N': Compute eigenvalues only;
63: *> = 'V': Compute eigenvalues and eigenvectors.
64: *> Not available in this release.
65: *> \endverbatim
66: *>
67: *> \param[in] UPLO
68: *> \verbatim
69: *> UPLO is CHARACTER*1
70: *> = 'U': Upper triangle of A is stored;
71: *> = 'L': Lower triangle of A is stored.
72: *> \endverbatim
73: *>
74: *> \param[in] N
75: *> \verbatim
76: *> N is INTEGER
77: *> The order of the matrix A. N >= 0.
78: *> \endverbatim
79: *>
80: *> \param[in] KD
81: *> \verbatim
82: *> KD is INTEGER
83: *> The number of superdiagonals of the matrix A if UPLO = 'U',
84: *> or the number of subdiagonals if UPLO = 'L'. KD >= 0.
85: *> \endverbatim
86: *>
87: *> \param[in,out] AB
88: *> \verbatim
89: *> AB is DOUBLE PRECISION array, dimension (LDAB, N)
90: *> On entry, the upper or lower triangle of the symmetric band
91: *> matrix A, stored in the first KD+1 rows of the array. The
92: *> j-th column of A is stored in the j-th column of the array AB
93: *> as follows:
94: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
95: *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
96: *>
97: *> On exit, AB is overwritten by values generated during the
98: *> reduction to tridiagonal form. If UPLO = 'U', the first
99: *> superdiagonal and the diagonal of the tridiagonal matrix T
100: *> are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
101: *> the diagonal and first subdiagonal of T are returned in the
102: *> first two rows of AB.
103: *> \endverbatim
104: *>
105: *> \param[in] LDAB
106: *> \verbatim
107: *> LDAB is INTEGER
108: *> The leading dimension of the array AB. LDAB >= KD + 1.
109: *> \endverbatim
110: *>
111: *> \param[out] W
112: *> \verbatim
113: *> W is DOUBLE PRECISION array, dimension (N)
114: *> If INFO = 0, the eigenvalues in ascending order.
115: *> \endverbatim
116: *>
117: *> \param[out] Z
118: *> \verbatim
119: *> Z is DOUBLE PRECISION array, dimension (LDZ, N)
120: *> If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
121: *> eigenvectors of the matrix A, with the i-th column of Z
122: *> holding the eigenvector associated with W(i).
123: *> If JOBZ = 'N', then Z is not referenced.
124: *> \endverbatim
125: *>
126: *> \param[in] LDZ
127: *> \verbatim
128: *> LDZ is INTEGER
129: *> The leading dimension of the array Z. LDZ >= 1, and if
130: *> JOBZ = 'V', LDZ >= max(1,N).
131: *> \endverbatim
132: *>
133: *> \param[out] WORK
134: *> \verbatim
135: *> WORK is DOUBLE PRECISION array, dimension LWORK
136: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
137: *> \endverbatim
138: *>
139: *> \param[in] LWORK
140: *> \verbatim
141: *> LWORK is INTEGER
142: *> The length of the array WORK. LWORK >= 1, when N <= 1;
143: *> otherwise
144: *> If JOBZ = 'N' and N > 1, LWORK must be queried.
145: *> LWORK = MAX(1, dimension) where
146: *> dimension = (2KD+1)*N + KD*NTHREADS + N
147: *> where KD is the size of the band.
148: *> NTHREADS is the number of threads used when
149: *> openMP compilation is enabled, otherwise =1.
150: *> If JOBZ = 'V' and N > 1, LWORK must be queried. Not yet available.
151: *>
152: *> If LWORK = -1, then a workspace query is assumed; the routine
153: *> only calculates the optimal sizes of the WORK and IWORK
154: *> arrays, returns these values as the first entries of the WORK
155: *> and IWORK arrays, and no error message related to LWORK or
156: *> LIWORK is issued by XERBLA.
157: *> \endverbatim
158: *>
159: *> \param[out] IWORK
160: *> \verbatim
161: *> IWORK is INTEGER array, dimension (MAX(1,LIWORK))
162: *> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
163: *> \endverbatim
164: *>
165: *> \param[in] LIWORK
166: *> \verbatim
167: *> LIWORK is INTEGER
168: *> The dimension of the array IWORK.
169: *> If JOBZ = 'N' or N <= 1, LIWORK must be at least 1.
170: *> If JOBZ = 'V' and N > 2, LIWORK must be at least 3 + 5*N.
171: *>
172: *> If LIWORK = -1, then a workspace query is assumed; the
173: *> routine only calculates the optimal sizes of the WORK and
174: *> IWORK arrays, returns these values as the first entries of
175: *> the WORK and IWORK arrays, and no error message related to
176: *> LWORK or LIWORK is issued by XERBLA.
177: *> \endverbatim
178: *>
179: *> \param[out] INFO
180: *> \verbatim
181: *> INFO is INTEGER
182: *> = 0: successful exit
183: *> < 0: if INFO = -i, the i-th argument had an illegal value
184: *> > 0: if INFO = i, the algorithm failed to converge; i
185: *> off-diagonal elements of an intermediate tridiagonal
186: *> form did not converge to zero.
187: *> \endverbatim
188: *
189: * Authors:
190: * ========
191: *
192: *> \author Univ. of Tennessee
193: *> \author Univ. of California Berkeley
194: *> \author Univ. of Colorado Denver
195: *> \author NAG Ltd.
196: *
197: *> \ingroup doubleOTHEReigen
198: *
199: *> \par Further Details:
200: * =====================
201: *>
202: *> \verbatim
203: *>
204: *> All details about the 2stage techniques are available in:
205: *>
206: *> Azzam Haidar, Hatem Ltaief, and Jack Dongarra.
207: *> Parallel reduction to condensed forms for symmetric eigenvalue problems
208: *> using aggregated fine-grained and memory-aware kernels. In Proceedings
209: *> of 2011 International Conference for High Performance Computing,
210: *> Networking, Storage and Analysis (SC '11), New York, NY, USA,
211: *> Article 8 , 11 pages.
212: *> http://doi.acm.org/10.1145/2063384.2063394
213: *>
214: *> A. Haidar, J. Kurzak, P. Luszczek, 2013.
215: *> An improved parallel singular value algorithm and its implementation
216: *> for multicore hardware, In Proceedings of 2013 International Conference
217: *> for High Performance Computing, Networking, Storage and Analysis (SC '13).
218: *> Denver, Colorado, USA, 2013.
219: *> Article 90, 12 pages.
220: *> http://doi.acm.org/10.1145/2503210.2503292
221: *>
222: *> A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra.
223: *> A novel hybrid CPU-GPU generalized eigensolver for electronic structure
224: *> calculations based on fine-grained memory aware tasks.
225: *> International Journal of High Performance Computing Applications.
226: *> Volume 28 Issue 2, Pages 196-209, May 2014.
227: *> http://hpc.sagepub.com/content/28/2/196
228: *>
229: *> \endverbatim
230: *
231: * =====================================================================
232: SUBROUTINE DSBEVD_2STAGE( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ,
233: $ WORK, LWORK, IWORK, LIWORK, INFO )
234: *
235: IMPLICIT NONE
236: *
1.5 ! bertrand 237: * -- LAPACK driver routine --
1.1 bertrand 238: * -- LAPACK is a software package provided by Univ. of Tennessee, --
239: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
240: *
241: * .. Scalar Arguments ..
242: CHARACTER JOBZ, UPLO
243: INTEGER INFO, KD, LDAB, LDZ, LIWORK, LWORK, N
244: * ..
245: * .. Array Arguments ..
246: INTEGER IWORK( * )
247: DOUBLE PRECISION AB( LDAB, * ), W( * ), WORK( * ), Z( LDZ, * )
248: * ..
249: *
250: * =====================================================================
251: *
252: * .. Parameters ..
253: DOUBLE PRECISION ZERO, ONE
254: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
255: * ..
256: * .. Local Scalars ..
257: LOGICAL LOWER, LQUERY, WANTZ
258: INTEGER IINFO, INDE, INDWK2, INDWRK, ISCALE, LIWMIN,
259: $ LLWORK, LWMIN, LHTRD, LWTRD, IB, INDHOUS,
260: $ LLWRK2
261: DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
262: $ SMLNUM
263: * ..
264: * .. External Functions ..
265: LOGICAL LSAME
1.3 bertrand 266: INTEGER ILAENV2STAGE
1.1 bertrand 267: DOUBLE PRECISION DLAMCH, DLANSB
1.3 bertrand 268: EXTERNAL LSAME, DLAMCH, DLANSB, ILAENV2STAGE
1.1 bertrand 269: * ..
270: * .. External Subroutines ..
271: EXTERNAL DGEMM, DLACPY, DLASCL, DSCAL, DSTEDC,
272: $ DSTERF, XERBLA, DSYTRD_SB2ST
273: * ..
274: * .. Intrinsic Functions ..
275: INTRINSIC SQRT
276: * ..
277: * .. Executable Statements ..
278: *
279: * Test the input parameters.
280: *
281: WANTZ = LSAME( JOBZ, 'V' )
282: LOWER = LSAME( UPLO, 'L' )
283: LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
284: *
285: INFO = 0
286: IF( N.LE.1 ) THEN
287: LIWMIN = 1
288: LWMIN = 1
289: ELSE
1.3 bertrand 290: IB = ILAENV2STAGE( 2, 'DSYTRD_SB2ST', JOBZ, N, KD, -1, -1 )
291: LHTRD = ILAENV2STAGE( 3, 'DSYTRD_SB2ST', JOBZ, N, KD, IB, -1 )
292: LWTRD = ILAENV2STAGE( 4, 'DSYTRD_SB2ST', JOBZ, N, KD, IB, -1 )
1.1 bertrand 293: IF( WANTZ ) THEN
294: LIWMIN = 3 + 5*N
295: LWMIN = 1 + 5*N + 2*N**2
296: ELSE
297: LIWMIN = 1
298: LWMIN = MAX( 2*N, N+LHTRD+LWTRD )
299: END IF
300: END IF
301: IF( .NOT.( LSAME( JOBZ, 'N' ) ) ) THEN
302: INFO = -1
303: ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
304: INFO = -2
305: ELSE IF( N.LT.0 ) THEN
306: INFO = -3
307: ELSE IF( KD.LT.0 ) THEN
308: INFO = -4
309: ELSE IF( LDAB.LT.KD+1 ) THEN
310: INFO = -6
311: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
312: INFO = -9
313: END IF
314: *
315: IF( INFO.EQ.0 ) THEN
316: WORK( 1 ) = LWMIN
317: IWORK( 1 ) = LIWMIN
318: *
319: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
320: INFO = -11
321: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
322: INFO = -13
323: END IF
324: END IF
325: *
326: IF( INFO.NE.0 ) THEN
327: CALL XERBLA( 'DSBEVD_2STAGE', -INFO )
328: RETURN
329: ELSE IF( LQUERY ) THEN
330: RETURN
331: END IF
332: *
333: * Quick return if possible
334: *
335: IF( N.EQ.0 )
336: $ RETURN
337: *
338: IF( N.EQ.1 ) THEN
339: W( 1 ) = AB( 1, 1 )
340: IF( WANTZ )
341: $ Z( 1, 1 ) = ONE
342: RETURN
343: END IF
344: *
345: * Get machine constants.
346: *
347: SAFMIN = DLAMCH( 'Safe minimum' )
348: EPS = DLAMCH( 'Precision' )
349: SMLNUM = SAFMIN / EPS
350: BIGNUM = ONE / SMLNUM
351: RMIN = SQRT( SMLNUM )
352: RMAX = SQRT( BIGNUM )
353: *
354: * Scale matrix to allowable range, if necessary.
355: *
356: ANRM = DLANSB( 'M', UPLO, N, KD, AB, LDAB, WORK )
357: ISCALE = 0
358: IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
359: ISCALE = 1
360: SIGMA = RMIN / ANRM
361: ELSE IF( ANRM.GT.RMAX ) THEN
362: ISCALE = 1
363: SIGMA = RMAX / ANRM
364: END IF
365: IF( ISCALE.EQ.1 ) THEN
366: IF( LOWER ) THEN
367: CALL DLASCL( 'B', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
368: ELSE
369: CALL DLASCL( 'Q', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
370: END IF
371: END IF
372: *
373: * Call DSYTRD_SB2ST to reduce band symmetric matrix to tridiagonal form.
374: *
375: INDE = 1
376: INDHOUS = INDE + N
377: INDWRK = INDHOUS + LHTRD
378: LLWORK = LWORK - INDWRK + 1
379: INDWK2 = INDWRK + N*N
380: LLWRK2 = LWORK - INDWK2 + 1
381: *
382: CALL DSYTRD_SB2ST( "N", JOBZ, UPLO, N, KD, AB, LDAB, W,
383: $ WORK( INDE ), WORK( INDHOUS ), LHTRD,
384: $ WORK( INDWRK ), LLWORK, IINFO )
385: *
386: * For eigenvalues only, call DSTERF. For eigenvectors, call SSTEDC.
387: *
388: IF( .NOT.WANTZ ) THEN
389: CALL DSTERF( N, W, WORK( INDE ), INFO )
390: ELSE
391: CALL DSTEDC( 'I', N, W, WORK( INDE ), WORK( INDWRK ), N,
392: $ WORK( INDWK2 ), LLWRK2, IWORK, LIWORK, INFO )
393: CALL DGEMM( 'N', 'N', N, N, N, ONE, Z, LDZ, WORK( INDWRK ), N,
394: $ ZERO, WORK( INDWK2 ), N )
395: CALL DLACPY( 'A', N, N, WORK( INDWK2 ), N, Z, LDZ )
396: END IF
397: *
398: * If matrix was scaled, then rescale eigenvalues appropriately.
399: *
400: IF( ISCALE.EQ.1 )
401: $ CALL DSCAL( N, ONE / SIGMA, W, 1 )
402: *
403: WORK( 1 ) = LWMIN
404: IWORK( 1 ) = LIWMIN
405: RETURN
406: *
407: * End of DSBEVD_2STAGE
408: *
409: END
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