 LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ chegv_2stage()

 subroutine chegv_2stage ( integer ITYPE, character JOBZ, character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldb, * ) B, integer LDB, real, dimension( * ) W, complex, dimension( * ) WORK, integer LWORK, real, dimension( * ) RWORK, integer INFO )

CHEGV_2STAGE

Download CHEGV_2STAGE + dependencies [TGZ] [ZIP] [TXT]

Purpose:
``` CHEGV_2STAGE computes all the eigenvalues, and optionally, the eigenvectors
of a complex generalized Hermitian-definite eigenproblem, of the form
A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.
Here A and B are assumed to be Hermitian and B is also
positive definite.
This routine use the 2stage technique for the reduction to tridiagonal
which showed higher performance on recent architecture and for large
sizes N>2000.```
Parameters
 [in] ITYPE ``` ITYPE is INTEGER Specifies the problem type to be solved: = 1: A*x = (lambda)*B*x = 2: A*B*x = (lambda)*x = 3: B*A*x = (lambda)*x``` [in] JOBZ ``` JOBZ is CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors. Not available in this release.``` [in] UPLO ``` UPLO is CHARACTER*1 = 'U': Upper triangles of A and B are stored; = 'L': Lower triangles of A and B are stored.``` [in] N ``` N is INTEGER The order of the matrices A and B. N >= 0.``` [in,out] A ``` A is COMPLEX array, dimension (LDA, N) On entry, the Hermitian matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A. On exit, if JOBZ = 'V', then if INFO = 0, A contains the matrix Z of eigenvectors. The eigenvectors are normalized as follows: if ITYPE = 1 or 2, Z**H*B*Z = I; if ITYPE = 3, Z**H*inv(B)*Z = I. If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') or the lower triangle (if UPLO='L') of A, including the diagonal, is destroyed.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [in,out] B ``` B is COMPLEX array, dimension (LDB, N) On entry, the Hermitian positive definite matrix B. If UPLO = 'U', the leading N-by-N upper triangular part of B contains the upper triangular part of the matrix B. If UPLO = 'L', the leading N-by-N lower triangular part of B contains the lower triangular part of the matrix B. On exit, if INFO <= N, the part of B containing the matrix is overwritten by the triangular factor U or L from the Cholesky factorization B = U**H*U or B = L*L**H.``` [in] LDB ``` LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).``` [out] W ``` W is REAL array, dimension (N) If INFO = 0, the eigenvalues in ascending order.``` [out] WORK ``` WORK is COMPLEX array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.``` [in] LWORK ``` LWORK is INTEGER The length of the array WORK. LWORK >= 1, when N <= 1; otherwise If JOBZ = 'N' and N > 1, LWORK must be queried. LWORK = MAX(1, dimension) where dimension = max(stage1,stage2) + (KD+1)*N + N = N*KD + N*max(KD+1,FACTOPTNB) + max(2*KD*KD, KD*NTHREADS) + (KD+1)*N + N where KD is the blocking size of the reduction, FACTOPTNB is the blocking used by the QR or LQ algorithm, usually FACTOPTNB=128 is a good choice NTHREADS is the number of threads used when openMP compilation is enabled, otherwise =1. If JOBZ = 'V' and N > 1, LWORK must be queried. Not yet available If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.``` [out] RWORK ` RWORK is REAL array, dimension (max(1, 3*N-2))` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: CPOTRF or CHEEV returned an error code: <= N: if INFO = i, CHEEV failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero; > N: if INFO = N + i, for 1 <= i <= N, then the leading minor of order i of B is not positive definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed.```
Date
November 2017
Further Details:
```  All details about the 2stage techniques are available in:

Azzam Haidar, Hatem Ltaief, and Jack Dongarra.
Parallel reduction to condensed forms for symmetric eigenvalue problems
using aggregated fine-grained and memory-aware kernels. In Proceedings
of 2011 International Conference for High Performance Computing,
Networking, Storage and Analysis (SC '11), New York, NY, USA,
Article 8 , 11 pages.
http://doi.acm.org/10.1145/2063384.2063394

A. Haidar, J. Kurzak, P. Luszczek, 2013.
An improved parallel singular value algorithm and its implementation
for multicore hardware, In Proceedings of 2013 International Conference
for High Performance Computing, Networking, Storage and Analysis (SC '13).
Denver, Colorado, USA, 2013.
Article 90, 12 pages.
http://doi.acm.org/10.1145/2503210.2503292

A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra.
A novel hybrid CPU-GPU generalized eigensolver for electronic structure
calculations based on fine-grained memory aware tasks.
International Journal of High Performance Computing Applications.
Volume 28 Issue 2, Pages 196-209, May 2014.
http://hpc.sagepub.com/content/28/2/196 ```

Definition at line 234 of file chegv_2stage.f.

234 *
235  IMPLICIT NONE
236 *
237 * -- LAPACK driver routine (version 3.8.0) --
238 * -- LAPACK is a software package provided by Univ. of Tennessee, --
239 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
240 * November 2017
241 *
242 * .. Scalar Arguments ..
243  CHARACTER jobz, uplo
244  INTEGER info, itype, lda, ldb, lwork, n
245 * ..
246 * .. Array Arguments ..
247  REAL rwork( * ), w( * )
248  COMPLEX a( lda, * ), b( ldb, * ), work( * )
249 * ..
250 *
251 * =====================================================================
252 *
253 * .. Parameters ..
254  COMPLEX one
255  parameter( one = ( 1.0e+0, 0.0e+0 ) )
256 * ..
257 * .. Local Scalars ..
258  LOGICAL lquery, upper, wantz
259  CHARACTER trans
260  INTEGER neig, lwmin, lhtrd, lwtrd, kd, ib
261 * ..
262 * .. External Functions ..
263  LOGICAL lsame
264  INTEGER ilaenv2stage
265  EXTERNAL lsame, ilaenv2stage
266 * ..
267 * .. External Subroutines ..
268  EXTERNAL xerbla, chegst, cpotrf, ctrmm, ctrsm,
269  \$ cheev_2stage
270 * ..
271 * .. Intrinsic Functions ..
272  INTRINSIC max
273 * ..
274 * .. Executable Statements ..
275 *
276 * Test the input parameters.
277 *
278  wantz = lsame( jobz, 'V' )
279  upper = lsame( uplo, 'U' )
280  lquery = ( lwork.EQ.-1 )
281 *
282  info = 0
283  IF( itype.LT.1 .OR. itype.GT.3 ) THEN
284  info = -1
285  ELSE IF( .NOT.( lsame( jobz, 'N' ) ) ) THEN
286  info = -2
287  ELSE IF( .NOT.( upper .OR. lsame( uplo, 'L' ) ) ) THEN
288  info = -3
289  ELSE IF( n.LT.0 ) THEN
290  info = -4
291  ELSE IF( lda.LT.max( 1, n ) ) THEN
292  info = -6
293  ELSE IF( ldb.LT.max( 1, n ) ) THEN
294  info = -8
295  END IF
296 *
297  IF( info.EQ.0 ) THEN
298  kd = ilaenv2stage( 1, 'CHETRD_2STAGE', jobz, n, -1, -1, -1 )
299  ib = ilaenv2stage( 2, 'CHETRD_2STAGE', jobz, n, kd, -1, -1 )
300  lhtrd = ilaenv2stage( 3, 'CHETRD_2STAGE', jobz, n, kd, ib, -1 )
301  lwtrd = ilaenv2stage( 4, 'CHETRD_2STAGE', jobz, n, kd, ib, -1 )
302  lwmin = n + lhtrd + lwtrd
303  work( 1 ) = lwmin
304 *
305  IF( lwork.LT.lwmin .AND. .NOT.lquery ) THEN
306  info = -11
307  END IF
308  END IF
309 *
310  IF( info.NE.0 ) THEN
311  CALL xerbla( 'CHEGV_2STAGE ', -info )
312  RETURN
313  ELSE IF( lquery ) THEN
314  RETURN
315  END IF
316 *
317 * Quick return if possible
318 *
319  IF( n.EQ.0 )
320  \$ RETURN
321 *
322 * Form a Cholesky factorization of B.
323 *
324  CALL cpotrf( uplo, n, b, ldb, info )
325  IF( info.NE.0 ) THEN
326  info = n + info
327  RETURN
328  END IF
329 *
330 * Transform problem to standard eigenvalue problem and solve.
331 *
332  CALL chegst( itype, uplo, n, a, lda, b, ldb, info )
333  CALL cheev_2stage( jobz, uplo, n, a, lda, w,
334  \$ work, lwork, rwork, info )
335 *
336  IF( wantz ) THEN
337 *
338 * Backtransform eigenvectors to the original problem.
339 *
340  neig = n
341  IF( info.GT.0 )
342  \$ neig = info - 1
343  IF( itype.EQ.1 .OR. itype.EQ.2 ) THEN
344 *
345 * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
346 * backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y
347 *
348  IF( upper ) THEN
349  trans = 'N'
350  ELSE
351  trans = 'C'
352  END IF
353 *
354  CALL ctrsm( 'Left', uplo, trans, 'Non-unit', n, neig, one,
355  \$ b, ldb, a, lda )
356 *
357  ELSE IF( itype.EQ.3 ) THEN
358 *
359 * For B*A*x=(lambda)*x;
360 * backtransform eigenvectors: x = L*y or U**H *y
361 *
362  IF( upper ) THEN
363  trans = 'C'
364  ELSE
365  trans = 'N'
366  END IF
367 *
368  CALL ctrmm( 'Left', uplo, trans, 'Non-unit', n, neig, one,
369  \$ b, ldb, a, lda )
370  END IF
371  END IF
372 *
373  work( 1 ) = lwmin
374 *
375  RETURN
376 *
377 * End of CHEGV_2STAGE
378 *
subroutine ctrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
CTRSM
Definition: ctrsm.f:182
subroutine chegst(ITYPE, UPLO, N, A, LDA, B, LDB, INFO)
CHEGST
Definition: chegst.f:129
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine cpotrf(UPLO, N, A, LDA, INFO)
CPOTRF
Definition: cpotrf.f:109
subroutine cheev_2stage(JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, INFO)
CHEEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE mat...
Definition: cheev_2stage.f:191
subroutine ctrmm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
CTRMM
Definition: ctrmm.f:179
integer function ilaenv2stage(ISPEC, NAME, OPTS, N1, N2, N3, N4)
ILAENV2STAGE
Definition: ilaenv2stage.f:151
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