SCALAPACK 2.2.2
LAPACK: Linear Algebra PACKage
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pcheevr.f
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1 SUBROUTINE pcheevr( JOBZ, RANGE, UPLO, N, A, IA, JA,
2 $ DESCA, VL, VU, IL, IU, M, NZ, W, Z, IZ,
3 $ JZ, DESCZ,
4 $ WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK,
5 $ INFO )
6
7 IMPLICIT NONE
8*
9* -- ScaLAPACK routine (version 2.0.2) --
10* Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver
11* May 1 2012
12*
13* .. Scalar Arguments ..
14 CHARACTER JOBZ, RANGE, UPLO
15
16 INTEGER IA, IL, INFO, IU, IZ, JA, JZ, LIWORK, LRWORK,
17 $ LWORK, M, N, NZ
18 REAL VL, VU
19* ..
20* .. Array Arguments ..
21 INTEGER DESCA( * ), DESCZ( * ), IWORK( * )
22 REAL W( * ), RWORK( * )
23 COMPLEX A( * ), WORK( * ), Z( * )
24* ..
25*
26* Purpose
27* =======
28*
29* PCHEEVR computes selected eigenvalues and, optionally, eigenvectors
30* of a complex Hermitian matrix A distributed in 2D blockcyclic format
31* by calling the recommended sequence of ScaLAPACK routines.
32*
33* First, the matrix A is reduced to real symmetric tridiagonal form.
34* Then, the eigenproblem is solved using the parallel MRRR algorithm.
35* Last, if eigenvectors have been computed, a backtransformation is done.
36*
37* Upon successful completion, each processor stores a copy of all computed
38* eigenvalues in W. The eigenvector matrix Z is stored in
39* 2D blockcyclic format distributed over all processors.
40*
41* For constructive feedback and comments, please contact cvoemel@lbl.gov
42* C. Voemel
43*
44*
45* Arguments
46* =========
47*
48* JOBZ (global input) CHARACTER*1
49* Specifies whether or not to compute the eigenvectors:
50* = 'N': Compute eigenvalues only.
51* = 'V': Compute eigenvalues and eigenvectors.
52*
53* RANGE (global input) CHARACTER*1
54* = 'A': all eigenvalues will be found.
55* = 'V': all eigenvalues in the interval [VL,VU] will be found.
56* = 'I': the IL-th through IU-th eigenvalues will be found.
57*
58* UPLO (global input) CHARACTER*1
59* Specifies whether the upper or lower triangular part of the
60* symmetric matrix A is stored:
61* = 'U': Upper triangular
62* = 'L': Lower triangular
63*
64* N (global input) INTEGER
65* The number of rows and columns of the matrix A. N >= 0
66*
67* A (local input/workspace) 2D block cyclic COMPLEX array,
68* global dimension (N, N),
69* local dimension ( LLD_A, LOCc(JA+N-1) )
70* (see Notes below for more detailed explanation of 2d arrays)
71*
72* On entry, the symmetric matrix A. If UPLO = 'U', only the
73* upper triangular part of A is used to define the elements of
74* the symmetric matrix. If UPLO = 'L', only the lower
75* triangular part of A is used to define the elements of the
76* symmetric matrix.
77*
78* On exit, the lower triangle (if UPLO='L') or the upper
79* triangle (if UPLO='U') of A, including the diagonal, is
80* destroyed.
81*
82* IA (global input) INTEGER
83* A's global row index, which points to the beginning of the
84* submatrix which is to be operated on.
85* It should be set to 1 when operating on a full matrix.
86*
87* JA (global input) INTEGER
88* A's global column index, which points to the beginning of
89* the submatrix which is to be operated on.
90* It should be set to 1 when operating on a full matrix.
91*
92* DESCA (global and local input) INTEGER array of dimension DLEN_.
93* (The ScaLAPACK descriptor length is DLEN_ = 9.)
94* The array descriptor for the distributed matrix A.
95* The descriptor stores details about the 2D block-cyclic
96* storage, see the notes below.
97* If DESCA is incorrect, PCHEEVR cannot work correctly.
98* Also note the array alignment requirements specified below
99*
100* VL (global input) REAL
101* If RANGE='V', the lower bound of the interval to be searched
102* for eigenvalues. Not referenced if RANGE = 'A' or 'I'.
103*
104* VU (global input) REAL
105* If RANGE='V', the upper bound of the interval to be searched
106* for eigenvalues. Not referenced if RANGE = 'A' or 'I'.
107*
108* IL (global input) INTEGER
109* If RANGE='I', the index (from smallest to largest) of the
110* smallest eigenvalue to be returned. IL >= 1.
111* Not referenced if RANGE = 'A'.
112*
113* IU (global input) INTEGER
114* If RANGE='I', the index (from smallest to largest) of the
115* largest eigenvalue to be returned. min(IL,N) <= IU <= N.
116* Not referenced if RANGE = 'A'.
117*
118* M (global output) INTEGER
119* Total number of eigenvalues found. 0 <= M <= N.
120*
121* NZ (global output) INTEGER
122* Total number of eigenvectors computed. 0 <= NZ <= M.
123* The number of columns of Z that are filled.
124* If JOBZ .NE. 'V', NZ is not referenced.
125* If JOBZ .EQ. 'V', NZ = M
126*
127* W (global output) REAL array, dimension (N)
128* On normal exit, the first M entries contain the selected
129* eigenvalues in ascending order.
130*
131* Z (local output) COMPLEX array,
132* global dimension (N, N),
133* local dimension ( LLD_Z, LOCc(JZ+N-1) )
134* If JOBZ = 'V', then on normal exit the first M columns of Z
135* contain the orthonormal eigenvectors of the matrix
136* corresponding to the selected eigenvalues.
137* If JOBZ = 'N', then Z is not referenced.
138*
139* IZ (global input) INTEGER
140* Z's global row index, which points to the beginning of the
141* submatrix which is to be operated on.
142* It should be set to 1 when operating on a full matrix.
143*
144* JZ (global input) INTEGER
145* Z's global column index, which points to the beginning of
146* the submatrix which is to be operated on.
147* It should be set to 1 when operating on a full matrix.
148*
149* DESCZ (global and local input) INTEGER array of dimension DLEN_.
150* The array descriptor for the distributed matrix Z.
151* DESCZ( CTXT_ ) must equal DESCA( CTXT_ )
152*
153* WORK (local workspace/output) COMPLEX array,
154* dimension (LWORK)
155* WORK(1) returns workspace adequate workspace to allow
156* optimal performance.
157*
158* LWORK (local input) INTEGER
159* Size of WORK array, must be at least 3.
160* If only eigenvalues are requested:
161* LWORK >= N + MAX( NB * ( NP00 + 1 ), NB * 3 )
162* If eigenvectors are requested:
163* LWORK >= N + ( NP00 + MQ00 + NB ) * NB
164* For definitions of NP00 & MQ00, see LRWORK.
165*
166* For optimal performance, greater workspace is needed, i.e.
167* LWORK >= MAX( LWORK, NHETRD_LWORK )
168* Where LWORK is as defined above, and
169* NHETRD_LWORK = N + 2*( ANB+1 )*( 4*NPS+2 ) +
170* ( NPS + 1 ) * NPS
171*
172* ICTXT = DESCA( CTXT_ )
173* ANB = PJLAENV( ICTXT, 3, 'PCHETTRD', 'L', 0, 0, 0, 0 )
174* SQNPC = SQRT( REAL( NPROW * NPCOL ) )
175* NPS = MAX( NUMROC( N, 1, 0, 0, SQNPC ), 2*ANB )
176*
177* If LWORK = -1, then LWORK is global input and a workspace
178* query is assumed; the routine only calculates the
179* optimal size for all work arrays. Each of these
180* values is returned in the first entry of the corresponding
181* work array, and no error message is issued by PXERBLA.
182* NOTE THAT FOR OPTIMAL PERFORMANCE, LWOPT IS RETURNED
183* (THE OPTIMUM WORKSPACE) RATHER THAN THE MINIMUM NECESSARY
184* WORKSPACE LWMIN WHEN A WORKSPACE QUERY IS ISSUED.
185* FOR VERY SMALL MATRICES, LWOPT >> LWMIN.
186*
187* RWORK (local workspace/output) REAL array,
188* dimension (LRWORK)
189* On return, RWORK(1) contains the optimal amount of
190* workspace required for efficient execution.
191* if JOBZ='N' RWORK(1) = optimal amount of workspace
192* required to compute the eigenvalues.
193* if JOBZ='V' RWORK(1) = optimal amount of workspace
194* required to compute eigenvalues and eigenvectors.
195*
196* LRWORK (local input) INTEGER
197* Size of RWORK, must be at least 3.
198* See below for definitions of variables used to define LRWORK.
199* If no eigenvectors are requested (JOBZ = 'N') then
200* LRWORK >= 2 + 5 * N + MAX( 12 * N, NB * ( NP00 + 1 ) )
201* If eigenvectors are requested (JOBZ = 'V' ) then
202* the amount of workspace required is:
203* LRWORK >= 2 + 5 * N + MAX( 18*N, NP00 * MQ00 + 2 * NB * NB ) +
204* (2 + ICEIL( NEIG, NPROW*NPCOL))*N
205*
206* Variable definitions:
207* NEIG = number of eigenvectors requested
208* NB = DESCA( MB_ ) = DESCA( NB_ ) =
209* DESCZ( MB_ ) = DESCZ( NB_ )
210* NN = MAX( N, NB, 2 )
211* DESCA( RSRC_ ) = DESCA( NB_ ) = DESCZ( RSRC_ ) =
212* DESCZ( CSRC_ ) = 0
213* NP00 = NUMROC( NN, NB, 0, 0, NPROW )
214* MQ00 = NUMROC( MAX( NEIG, NB, 2 ), NB, 0, 0, NPCOL )
215* ICEIL( X, Y ) is a ScaLAPACK function returning
216* ceiling(X/Y)
217*
218* If LRWORK = -1, then LRWORK is global input and a workspace
219* query is assumed; the routine only calculates the size
220* required for optimal performance for all work arrays. Each of
221* these values is returned in the first entry of the
222* corresponding work arrays, and no error message is issued by
223* PXERBLA.
224*
225* IWORK (local workspace) INTEGER array
226* On return, IWORK(1) contains the amount of integer workspace
227* required.
228*
229* LIWORK (local input) INTEGER
230* size of IWORK
231*
232* Let NNP = MAX( N, NPROW*NPCOL + 1, 4 ). Then:
233* LIWORK >= 12*NNP + 2*N when the eigenvectors are desired
234* LIWORK >= 10*NNP + 2*N when only the eigenvalues have to be computed
235*
236* If LIWORK = -1, then LIWORK is global input and a workspace
237* query is assumed; the routine only calculates the minimum
238* and optimal size for all work arrays. Each of these
239* values is returned in the first entry of the corresponding
240* work array, and no error message is issued by PXERBLA.
241*
242* INFO (global output) INTEGER
243* = 0: successful exit
244* < 0: If the i-th argument is an array and the j-entry had
245* an illegal value, then INFO = -(i*100+j), if the i-th
246* argument is a scalar and had an illegal value, then
247* INFO = -i.
248*
249* Notes
250* =====
251*
252* Each global data object is described by an associated description
253* vector. This vector stores the information required to establish
254* the mapping between an object element and its corresponding process
255* and memory location.
256*
257* Let A be a generic term for any 2D block cyclicly distributed array.
258* Such a global array has an associated description vector DESCA.
259* In the following comments, the character _ should be read as
260* "of the global array".
261*
262* NOTATION STORED IN EXPLANATION
263* --------------- -------------- --------------------------------------
264* DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case,
265* DTYPE_A = 1.
266* CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
267* the BLACS process grid A is distribu-
268* ted over. The context itself is glo-
269* bal, but the handle (the integer
270* value) may vary.
271* M_A (global) DESCA( M_ ) The number of rows in the global
272* array A.
273* N_A (global) DESCA( N_ ) The number of columns in the global
274* array A.
275* MB_A (global) DESCA( MB_ ) The blocking factor used to distribute
276* the rows of the array.
277* NB_A (global) DESCA( NB_ ) The blocking factor used to distribute
278* the columns of the array.
279* RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
280* row of the array A is distributed.
281* CSRC_A (global) DESCA( CSRC_ ) The process column over which the
282* first column of the array A is
283* distributed.
284* LLD_A (local) DESCA( LLD_ ) The leading dimension of the local
285* array. LLD_A >= MAX(1,LOCr(M_A)).
286*
287* Let K be the number of rows or columns of a distributed matrix,
288* and assume that its process grid has dimension p x q.
289* LOCr( K ) denotes the number of elements of K that a process
290* would receive if K were distributed over the p processes of its
291* process column.
292* Similarly, LOCc( K ) denotes the number of elements of K that a
293* process would receive if K were distributed over the q processes of
294* its process row.
295* The values of LOCr() and LOCc() may be determined via a call to the
296* ScaLAPACK tool function, NUMROC:
297* LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
298* LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).
299* An upper bound for these quantities may be computed by:
300* LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
301* LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
302*
303* PCHEEVR assumes IEEE 754 standard compliant arithmetic.
304*
305* Alignment requirements
306* ======================
307*
308* The distributed submatrices A(IA:*, JA:*) and Z(IZ:IZ+M-1,JZ:JZ+N-1)
309* must satisfy the following alignment properties:
310*
311* 1.Identical (quadratic) dimension:
312* DESCA(M_) = DESCZ(M_) = DESCA(N_) = DESCZ(N_)
313* 2.Quadratic conformal blocking:
314* DESCA(MB_) = DESCA(NB_) = DESCZ(MB_) = DESCZ(NB_)
315* DESCA(RSRC_) = DESCZ(RSRC_)
316* 3.MOD( IA-1, MB_A ) = MOD( IZ-1, MB_Z ) = 0
317* 4.IAROW = IZROW
318*
319*
320* .. Parameters ..
321 INTEGER CTXT_, M_, N_,
322 $ MB_, NB_, RSRC_, CSRC_
323 PARAMETER ( CTXT_ = 2, m_ = 3, n_ = 4, mb_ = 5, nb_ = 6,
324 $ rsrc_ = 7, csrc_ = 8 )
325 REAL ZERO
326 PARAMETER ( ZERO = 0.0e0 )
327* ..
328* .. Local Scalars ..
329 LOGICAL ALLEIG, COLBRT, DOBCST, FINISH, FIRST, INDEIG,
330 $ lower, lquery, valeig, vstart, wantz
331 INTEGER ANB, DOL, DOU, DSTCOL, DSTROW, EIGCNT, FRSTCL,
332 $ I, IAROW, ICTXT, IIL, IINDERR, IINDWLC, IINFO,
333 $ iiu, im, indd, indd2, inde, inde2, inderr,
334 $ indilu, indrtau, indrw, indrwork, indtau,
335 $ indwlc, indwork, ipil, ipiu, iproc, izrow,
336 $ lastcl, lengthi, lengthi2, liwmin, llrwork,
337 $ llwork, lrwmin, lrwopt, lwmin, lwopt, maxcls,
338 $ mq00, mycol, myil, myiu, myproc, myrow, mz, nb,
339 $ ndepth, needil, neediu, nhetrd_lwopt, nnp,
340 $ np00, npcol, nprocs, nprow, nps, nsplit,
341 $ offset, parity, rlengthi, rlengthi2, rstarti,
342 $ size1, size2, sqnpc, srccol, srcrow, starti,
343 $ zoffset
344
345 REAL PIVMIN, SAFMIN, SCALE, VLL, VUU, WL,
346 $ WU
347*
348* .. Local Arrays ..
349 INTEGER IDUM1( 4 ), IDUM2( 4 )
350* ..
351* .. External Functions ..
352 LOGICAL LSAME
353 INTEGER ICEIL, INDXG2P, NUMROC, PJLAENV
354 REAL PSLAMCH
355 EXTERNAL ICEIL, INDXG2P, LSAME, NUMROC, PJLAENV,
356 $ pslamch
357* ..
358* .. External Subroutines ..
359 EXTERNAL blacs_gridinfo, chk1mat, igebr2d, igebs2d,
360 $ igerv2d, igesd2d, igsum2d, pcelget, pchentrd,
361 $ pchk1mat, pchk2mat, pclaevswp, pcunmtr,
362 $ pslared1d, pxerbla, scopy, sgebr2d, sgebs2d,
363 $ sgerv2d, sgesd2d, slarrc, slasrt2,
364 $ sstegr2a, sstegr2b, sstegr2
365* ..
366* .. Intrinsic Functions ..
367 INTRINSIC abs, cmplx, ichar, int, max, min, mod, real,
368 $ sqrt
369* ..
370* .. Executable Statements ..
371*
372
373 info = 0
374
375***********************************************************************
376*
377* Decode character arguments to find out what the code should do
378*
379***********************************************************************
380 wantz = lsame( jobz, 'V' )
381 lower = lsame( uplo, 'L' )
382 alleig = lsame( range, 'A' )
383 valeig = lsame( range, 'V' )
384 indeig = lsame( range, 'I' )
385 lquery = ( lwork.EQ.-1 .OR. lrwork.EQ.-1 .OR. liwork.EQ.-1 )
386
387***********************************************************************
388*
389* GET MACHINE PARAMETERS
390*
391***********************************************************************
392 ictxt = desca( ctxt_ )
393 safmin = pslamch( ictxt, 'Safe minimum' )
394
395***********************************************************************
396*
397* Set up pointers into the (complex) WORK array
398*
399***********************************************************************
400 indtau = 1
401 indwork = indtau + n
402 llwork = lwork - indwork + 1
403
404***********************************************************************
405*
406* Set up pointers into the RWORK array
407*
408***********************************************************************
409 indrtau = 1
410 indd = indrtau + n
411 inde = indd + n + 1
412 indd2 = inde + n + 1
413 inde2 = indd2 + n
414 indrwork = inde2 + n
415 llrwork = lrwork - indrwork + 1
416
417***********************************************************************
418*
419* BLACS PROCESSOR GRID SETUP
420*
421***********************************************************************
422 CALL blacs_gridinfo( ictxt, nprow, npcol, myrow, mycol )
423
424
425 nprocs = nprow * npcol
426 myproc = myrow * npcol + mycol
427 IF( nprow.EQ.-1 ) THEN
428 info = -( 800+ctxt_ )
429 ELSE IF( wantz ) THEN
430 IF( ictxt.NE.descz( ctxt_ ) ) THEN
431 info = -( 2100+ctxt_ )
432 END IF
433 END IF
434
435***********************************************************************
436*
437* COMPUTE REAL WORKSPACE
438*
439***********************************************************************
440 IF ( alleig ) THEN
441 mz = n
442 ELSE IF ( indeig ) THEN
443 mz = iu - il + 1
444 ELSE
445* Take upper bound for VALEIG case
446 mz = n
447 END IF
448*
449 nb = desca( nb_ )
450 np00 = numroc( n, nb, 0, 0, nprow )
451 mq00 = numroc( mz, nb, 0, 0, npcol )
452 IF ( wantz ) THEN
453 indrw = indrwork + max(18*n, np00*mq00 + 2*nb*nb)
454 lrwmin = indrw - 1 + (iceil(mz, nprocs) + 2)*n
455 lwmin = n + max((np00 + mq00 + nb) * nb, 3 * nb)
456 ELSE
457 indrw = indrwork + 12*n
458 lrwmin = indrw - 1
459 lwmin = n + max( nb*( np00 + 1 ), 3 * nb )
460 END IF
461
462* The code that validates the input requires 3 workspace entries
463 lrwmin = max(3, lrwmin)
464 lrwopt = lrwmin
465 lwmin = max(3, lwmin)
466 lwopt = lwmin
467*
468 anb = pjlaenv( ictxt, 3, 'PCHETTRD', 'L', 0, 0, 0, 0 )
469 sqnpc = int( sqrt( real( nprocs ) ) )
470 nps = max( numroc( n, 1, 0, 0, sqnpc ), 2*anb )
471 nhetrd_lwopt = 2*( anb+1 )*( 4*nps+2 ) + ( nps+4 )*nps
472 lwopt = max( lwopt, n+nhetrd_lwopt )
473*
474 size1 = indrw - indrwork
475
476***********************************************************************
477*
478* COMPUTE INTEGER WORKSPACE
479*
480***********************************************************************
481 nnp = max( n, nprocs+1, 4 )
482 IF ( wantz ) THEN
483 liwmin = 12*nnp + 2*n
484 ELSE
485 liwmin = 10*nnp + 2*n
486 END IF
487
488***********************************************************************
489*
490* Set up pointers into the IWORK array
491*
492***********************************************************************
493* Pointer to eigenpair distribution over processors
494 indilu = liwmin - 2*nprocs + 1
495 size2 = indilu - 2*n
496
497
498***********************************************************************
499*
500* Test the input arguments.
501*
502***********************************************************************
503 IF( info.EQ.0 ) THEN
504 CALL chk1mat( n, 4, n, 4, ia, ja, desca, 8, info )
505 IF( wantz )
506 $ CALL chk1mat( n, 4, n, 4, iz, jz, descz, 21, info )
507*
508 IF( info.EQ.0 ) THEN
509 IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
510 info = -1
511 ELSE IF( .NOT.( alleig .OR. valeig .OR. indeig ) ) THEN
512 info = -2
513 ELSE IF( .NOT.( lower .OR. lsame( uplo, 'U' ) ) ) THEN
514 info = -3
515 ELSE IF( mod( ia-1, desca( mb_ ) ).NE.0 ) THEN
516 info = -6
517 ELSE IF( valeig .AND. n.GT.0 .AND. vu.LE.vl ) THEN
518 info = -10
519 ELSE IF( indeig .AND. ( il.LT.1 .OR. il.GT.max( 1, n ) ) )
520 $ THEN
521 info = -11
522 ELSE IF( indeig .AND. ( iu.LT.min( n, il ) .OR. iu.GT.n ))
523 $ THEN
524 info = -12
525 ELSE IF( lwork.LT.lwmin .AND. .NOT.lquery ) THEN
526 info = -21
527 ELSE IF( lrwork.LT.lrwmin .AND. .NOT.lquery ) THEN
528 info = -23
529 ELSE IF( liwork.LT.liwmin .AND. .NOT.lquery ) THEN
530 info = -25
531 ELSE IF( desca( mb_ ).NE.desca( nb_ ) ) THEN
532 info = -( 800+nb_ )
533 END IF
534 IF( wantz ) THEN
535 iarow = indxg2p( 1, desca( nb_ ), myrow,
536 $ desca( rsrc_ ), nprow )
537 izrow = indxg2p( 1, desca( nb_ ), myrow,
538 $ descz( rsrc_ ), nprow )
539 IF( iarow.NE.izrow ) THEN
540 info = -19
541 ELSE IF( mod( ia-1, desca( mb_ ) ).NE.
542 $ mod( iz-1, descz( mb_ ) ) ) THEN
543 info = -19
544 ELSE IF( desca( m_ ).NE.descz( m_ ) ) THEN
545 info = -( 2100+m_ )
546 ELSE IF( desca( n_ ).NE.descz( n_ ) ) THEN
547 info = -( 2100+n_ )
548 ELSE IF( desca( mb_ ).NE.descz( mb_ ) ) THEN
549 info = -( 2100+mb_ )
550 ELSE IF( desca( nb_ ).NE.descz( nb_ ) ) THEN
551 info = -( 2100+nb_ )
552 ELSE IF( desca( rsrc_ ).NE.descz( rsrc_ ) ) THEN
553 info = -( 2100+rsrc_ )
554 ELSE IF( desca( csrc_ ).NE.descz( csrc_ ) ) THEN
555 info = -( 2100+csrc_ )
556 ELSE IF( ictxt.NE.descz( ctxt_ ) ) THEN
557 info = -( 2100+ctxt_ )
558 END IF
559 END IF
560 END IF
561 idum2( 1 ) = 1
562 IF( lower ) THEN
563 idum1( 2 ) = ichar( 'L' )
564 ELSE
565 idum1( 2 ) = ichar( 'U' )
566 END IF
567 idum2( 2 ) = 2
568 IF( alleig ) THEN
569 idum1( 3 ) = ichar( 'A' )
570 ELSE IF( indeig ) THEN
571 idum1( 3 ) = ichar( 'I' )
572 ELSE
573 idum1( 3 ) = ichar( 'V' )
574 END IF
575 idum2( 3 ) = 3
576 IF( lquery ) THEN
577 idum1( 4 ) = -1
578 ELSE
579 idum1( 4 ) = 1
580 END IF
581 idum2( 4 ) = 4
582 IF( wantz ) THEN
583 idum1( 1 ) = ichar( 'V' )
584 CALL pchk2mat( n, 4, n, 4, ia, ja, desca, 8, n, 4, n, 4,iz,
585 $ jz, descz, 21, 4, idum1, idum2, info )
586 ELSE
587 idum1( 1 ) = ichar( 'N' )
588 CALL pchk1mat( n, 4, n, 4, ia, ja, desca, 8, 4, idum1,
589 $ idum2, info )
590 END IF
591 work( 1 ) = cmplx( lwopt )
592 rwork( 1 ) = real( lrwopt )
593 iwork( 1 ) = liwmin
594 END IF
595*
596 IF( info.NE.0 ) THEN
597 CALL pxerbla( ictxt, 'PCHEEVR', -info )
598 RETURN
599 ELSE IF( lquery ) THEN
600 RETURN
601 END IF
602
603***********************************************************************
604*
605* Quick return if possible
606*
607***********************************************************************
608 IF( n.EQ.0 ) THEN
609 IF( wantz ) THEN
610 nz = 0
611 END IF
612 m = 0
613 work( 1 ) = cmplx( lwopt )
614 rwork( 1 ) = real( lrwopt )
615 iwork( 1 ) = liwmin
616 RETURN
617 END IF
618
619 IF( valeig ) THEN
620 vll = vl
621 vuu = vu
622 ELSE
623 vll = zero
624 vuu = zero
625 END IF
626*
627* No scaling done here, leave this to MRRR kernel.
628* Scale tridiagonal rather than full matrix.
629*
630***********************************************************************
631*
632* REDUCE MATRIX TO REAL SYMMETRIC TRIDIAGONAL FORM.
633*
634***********************************************************************
635
636
637 CALL pchentrd( uplo, n, a, ia, ja, desca, rwork( indd ),
638 $ rwork( inde ), work( indtau ), work( indwork ),
639 $ llwork, rwork( indrwork ), llrwork,iinfo )
640
641
642 IF (iinfo .NE. 0) THEN
643 CALL pxerbla( ictxt, 'PCHENTRD', -iinfo )
644 RETURN
645 END IF
646
647***********************************************************************
648*
649* DISTRIBUTE TRIDIAGONAL TO ALL PROCESSORS
650*
651***********************************************************************
652 offset = 0
653 IF( ia.EQ.1 .AND. ja.EQ.1 .AND.
654 $ desca( rsrc_ ).EQ.0 .AND. desca( csrc_ ).EQ.0 )
655 $ THEN
656 CALL pslared1d( n, ia, ja, desca, rwork( indd ),
657 $ rwork( indd2 ), rwork( indrwork ), llrwork )
658*
659 CALL pslared1d( n, ia, ja, desca, rwork( inde ),
660 $ rwork( inde2 ), rwork( indrwork ), llrwork )
661 IF( .NOT.lower )
662 $ offset = 1
663 ELSE
664 DO 10 i = 1, n
665 CALL pcelget( 'A', ' ', work( indwork ), a,
666 $ i+ia-1, i+ja-1, desca )
667 rwork( indd2+i-1 ) = real( work( indwork ) )
668 10 CONTINUE
669 IF( lsame( uplo, 'U' ) ) THEN
670 DO 20 i = 1, n - 1
671 CALL pcelget( 'A', ' ', work( indwork ), a,
672 $ i+ia-1, i+ja, desca )
673 rwork( inde2+i-1 ) = real( work( indwork ) )
674 20 CONTINUE
675 ELSE
676 DO 30 i = 1, n - 1
677 CALL pcelget( 'A', ' ', work( indwork ), a,
678 $ i+ia, i+ja-1, desca )
679 rwork( inde2+i-1 ) = real( work( indwork ) )
680 30 CONTINUE
681 END IF
682 END IF
683
684
685
686
687***********************************************************************
688*
689* SET IIL, IIU
690*
691***********************************************************************
692 IF ( alleig ) THEN
693 iil = 1
694 iiu = n
695 ELSE IF ( indeig ) THEN
696 iil = il
697 iiu = iu
698 ELSE IF ( valeig ) THEN
699 CALL slarrc('T', n, vll, vuu, rwork( indd2 ),
700 $ rwork( inde2 + offset ), safmin, eigcnt, iil, iiu, info)
701* Refine upper bound N that was taken
702 mz = eigcnt
703 iil = iil + 1
704 ENDIF
705
706 IF(mz.EQ.0) THEN
707 m = 0
708 IF( wantz ) THEN
709 nz = 0
710 END IF
711 work( 1 ) = real( lwopt )
712 iwork( 1 ) = liwmin
713 RETURN
714 END IF
715
716 myil = 0
717 myiu = 0
718 m = 0
719 im = 0
720
721***********************************************************************
722*
723* COMPUTE WORK ASSIGNMENTS
724*
725***********************************************************************
726
727*
728* Each processor computes the work assignments for all processors
729*
730 CALL pmpim2( iil, iiu, nprocs,
731 $ iwork(indilu), iwork(indilu+nprocs) )
732*
733* Find local work assignment
734*
735 myil = iwork(indilu+myproc)
736 myiu = iwork(indilu+nprocs+myproc)
737
738
739 zoffset = max(0, myil - iil - 1)
740 first = ( myil .EQ. iil )
741
742
743***********************************************************************
744*
745* CALLS TO MRRR KERNEL
746*
747***********************************************************************
748 IF(.NOT.wantz) THEN
749*
750* Compute eigenvalues only.
751*
752 iinfo = 0
753 IF ( myil.GT.0 ) THEN
754 dol = 1
755 dou = myiu - myil + 1
756 CALL sstegr2( jobz, 'I', n, rwork( indd2 ),
757 $ rwork( inde2+offset ), vll, vuu, myil, myiu,
758 $ im, w( 1 ), rwork( indrw ), n,
759 $ myiu - myil + 1,
760 $ iwork( 1 ), rwork( indrwork ), size1,
761 $ iwork( 2*n+1 ), size2,
762 $ dol, dou, zoffset, iinfo )
763* SSTEGR2 zeroes out the entire W array, so we can't just give
764* it the part of W we need. So here we copy the W entries into
765* their correct location
766 DO 49 i = 1, im
767 w( myil-iil+i ) = w( i )
768 49 CONTINUE
769* W( MYIL ) is at W( MYIL - IIL + 1 )
770* W( X ) is at W(X - IIL + 1 )
771 END IF
772 IF (iinfo .NE. 0) THEN
773 CALL pxerbla( ictxt, 'SSTEGR2', -iinfo )
774 RETURN
775 END IF
776 ELSEIF ( wantz .AND. nprocs.EQ.1 ) THEN
777*
778* Compute eigenvalues and -vectors, but only on one processor
779*
780 iinfo = 0
781 IF ( myil.GT.0 ) THEN
782 dol = myil - iil + 1
783 dou = myiu - iil + 1
784 CALL sstegr2( jobz, 'I', n, rwork( indd2 ),
785 $ rwork( inde2+offset ), vll, vuu, iil, iiu,
786 $ im, w( 1 ), rwork( indrw ), n,
787 $ n,
788 $ iwork( 1 ), rwork( indrwork ), size1,
789 $ iwork( 2*n+1 ), size2, dol, dou,
790 $ zoffset, iinfo )
791 ENDIF
792 IF (iinfo .NE. 0) THEN
793 CALL pxerbla( ictxt, 'SSTEGR2', -iinfo )
794 RETURN
795 END IF
796 ELSEIF ( wantz ) THEN
797* Compute representations in parallel.
798* Share eigenvalue computation for root between all processors
799* Then compute the eigenvectors.
800 iinfo = 0
801* Part 1. compute root representations and root eigenvalues
802 IF ( myil.GT.0 ) THEN
803 dol = myil - iil + 1
804 dou = myiu - iil + 1
805 CALL sstegr2a( jobz, 'I', n, rwork( indd2 ),
806 $ rwork( inde2+offset ), vll, vuu, iil, iiu,
807 $ im, w( 1 ), rwork( indrw ), n,
808 $ n, rwork( indrwork ), size1,
809 $ iwork( 2*n+1 ), size2, dol,
810 $ dou, needil, neediu,
811 $ inderr, nsplit, pivmin, scale, wl, wu,
812 $ iinfo )
813 ENDIF
814 IF (iinfo .NE. 0) THEN
815 CALL pxerbla( ictxt, 'SSTEGR2A', -iinfo )
816 RETURN
817 END IF
818*
819* The second part of parallel MRRR, the representation tree
820* construction begins. Upon successful completion, the
821* eigenvectors have been computed. This is indicated by
822* the flag FINISH.
823*
824 vstart = .true.
825 finish = (myil.LE.0)
826C Part 2. Share eigenvalues and uncertainties between all processors
827 iinderr = indrwork + inderr - 1
828
829*
830
831
832*
833* There are currently two ways to communicate eigenvalue information
834* using the BLACS.
835* 1.) BROADCAST
836* 2.) POINT2POINT between collaborators (those processors working
837* jointly on a cluster.
838* For efficiency, BROADCAST has been disabled.
839* At a later stage, other more efficient communication algorithms
840* might be implemented, e. g. group or tree-based communication.
841
842 dobcst = .false.
843 IF(dobcst) THEN
844* First gather everything on the first processor.
845* Then use BROADCAST-based communication
846 DO 45 i = 2, nprocs
847 IF (myproc .EQ. (i - 1)) THEN
848 dstrow = 0
849 dstcol = 0
850 starti = dol
851 iwork(1) = starti
852 IF(myil.GT.0) THEN
853 lengthi = myiu - myil + 1
854 ELSE
855 lengthi = 0
856 ENDIF
857 iwork(2) = lengthi
858 CALL igesd2d( ictxt, 2, 1, iwork, 2,
859 $ dstrow, dstcol )
860 IF (( starti.GE.1 ) .AND. ( lengthi.GE.1 )) THEN
861 lengthi2 = 2*lengthi
862* Copy eigenvalues into communication buffer
863 CALL scopy(lengthi,w( starti ),1,
864 $ rwork( indd ), 1)
865* Copy uncertainties into communication buffer
866 CALL scopy(lengthi,rwork(iinderr+starti-1),1,
867 $ rwork( indd+lengthi ), 1)
868* send buffer
869 CALL sgesd2d( ictxt, lengthi2,
870 $ 1, rwork( indd ), lengthi2,
871 $ dstrow, dstcol )
872 END IF
873 ELSE IF (myproc .EQ. 0) THEN
874 srcrow = (i-1) / npcol
875 srccol = mod(i-1, npcol)
876 CALL igerv2d( ictxt, 2, 1, iwork, 2,
877 $ srcrow, srccol )
878 starti = iwork(1)
879 lengthi = iwork(2)
880 IF (( starti.GE.1 ) .AND. ( lengthi.GE.1 )) THEN
881 lengthi2 = 2*lengthi
882* receive buffer
883 CALL sgerv2d( ictxt, lengthi2, 1,
884 $ rwork(indd), lengthi2, srcrow, srccol )
885* copy eigenvalues from communication buffer
886 CALL scopy( lengthi, rwork(indd), 1,
887 $ w( starti ), 1)
888* copy uncertainties (errors) from communication buffer
889 CALL scopy(lengthi,rwork(indd+lengthi),1,
890 $ rwork( iinderr+starti-1 ), 1)
891 END IF
892 END IF
893 45 CONTINUE
894 lengthi = iiu - iil + 1
895 lengthi2 = lengthi * 2
896 IF (myproc .EQ. 0) THEN
897* Broadcast eigenvalues and errors to all processors
898 CALL scopy(lengthi,w ,1, rwork( indd ), 1)
899 CALL scopy(lengthi,rwork( iinderr ),1,
900 $ rwork( indd+lengthi ), 1)
901 CALL sgebs2d( ictxt, 'A', ' ', lengthi2, 1,
902 $ rwork(indd), lengthi2 )
903 ELSE
904 srcrow = 0
905 srccol = 0
906 CALL sgebr2d( ictxt, 'A', ' ', lengthi2, 1,
907 $ rwork(indd), lengthi2, srcrow, srccol )
908 CALL scopy( lengthi, rwork(indd), 1, w, 1)
909 CALL scopy(lengthi,rwork(indd+lengthi),1,
910 $ rwork( iinderr ), 1)
911 END IF
912 ELSE
913* Enable point2point communication between collaborators
914
915* Find collaborators of MYPROC
916 IF( (nprocs.GT.1).AND.(myil.GT.0) ) THEN
917 CALL pmpcol( myproc, nprocs, iil, needil, neediu,
918 $ iwork(indilu), iwork(indilu+nprocs),
919 $ colbrt, frstcl, lastcl )
920 ELSE
921 colbrt = .false.
922 ENDIF
923
924 IF(colbrt) THEN
925* If the processor collaborates with others,
926* communicate information.
927 DO 47 iproc = frstcl, lastcl
928 IF (myproc .EQ. iproc) THEN
929 starti = dol
930 iwork(1) = starti
931 lengthi = myiu - myil + 1
932 iwork(2) = lengthi
933
934 IF ((starti.GE.1) .AND. (lengthi.GE.1)) THEN
935* Copy eigenvalues into communication buffer
936 CALL scopy(lengthi,w( starti ),1,
937 $ rwork(indd), 1)
938* Copy uncertainties into communication buffer
939 CALL scopy(lengthi,
940 $ rwork( iinderr+starti-1 ),1,
941 $ rwork(indd+lengthi), 1)
942 ENDIF
943
944 DO 46 i = frstcl, lastcl
945 IF(i.EQ.myproc) GOTO 46
946 dstrow = i/ npcol
947 dstcol = mod(i, npcol)
948 CALL igesd2d( ictxt, 2, 1, iwork, 2,
949 $ dstrow, dstcol )
950 IF ((starti.GE.1) .AND. (lengthi.GE.1)) THEN
951 lengthi2 = 2*lengthi
952* send buffer
953 CALL sgesd2d( ictxt, lengthi2,
954 $ 1, rwork(indd), lengthi2,
955 $ dstrow, dstcol )
956 END IF
957 46 CONTINUE
958 ELSE
959 srcrow = iproc / npcol
960 srccol = mod(iproc, npcol)
961 CALL igerv2d( ictxt, 2, 1, iwork, 2,
962 $ srcrow, srccol )
963 rstarti = iwork(1)
964 rlengthi = iwork(2)
965 IF ((rstarti.GE.1 ) .AND. (rlengthi.GE.1 )) THEN
966 rlengthi2 = 2*rlengthi
967 CALL sgerv2d( ictxt, rlengthi2, 1,
968 $ rwork(inde), rlengthi2,
969 $ srcrow, srccol )
970* copy eigenvalues from communication buffer
971 CALL scopy( rlengthi,rwork(inde), 1,
972 $ w( rstarti ), 1)
973* copy uncertainties (errors) from communication buffer
974 CALL scopy(rlengthi,rwork(inde+rlengthi),1,
975 $ rwork( iinderr+rstarti-1 ), 1)
976 END IF
977 END IF
978 47 CONTINUE
979 ENDIF
980 ENDIF
981
982* Part 3. Compute representation tree and eigenvectors.
983* What follows is a loop in which the tree
984* is constructed in parallel from top to bottom,
985* on level at a time, until all eigenvectors
986* have been computed.
987*
988 100 CONTINUE
989 IF ( myil.GT.0 ) THEN
990 CALL sstegr2b( jobz, n, rwork( indd2 ),
991 $ rwork( inde2+offset ),
992 $ im, w( 1 ), rwork( indrw ), n, n,
993 $ iwork( 1 ), rwork( indrwork ), size1,
994 $ iwork( 2*n+1 ), size2, dol,
995 $ dou, needil, neediu, indwlc,
996 $ pivmin, scale, wl, wu,
997 $ vstart, finish,
998 $ maxcls, ndepth, parity, zoffset, iinfo )
999 iindwlc = indrwork + indwlc - 1
1000 IF(.NOT.finish) THEN
1001 IF((needil.LT.dol).OR.(neediu.GT.dou)) THEN
1002 CALL pmpcol( myproc, nprocs, iil, needil, neediu,
1003 $ iwork(indilu), iwork(indilu+nprocs),
1004 $ colbrt, frstcl, lastcl )
1005 ELSE
1006 colbrt = .false.
1007 frstcl = myproc
1008 lastcl = myproc
1009 ENDIF
1010*
1011* Check if this processor collaborates, i.e.
1012* communication is needed.
1013*
1014 IF(colbrt) THEN
1015 DO 147 iproc = frstcl, lastcl
1016 IF (myproc .EQ. iproc) THEN
1017 starti = dol
1018 iwork(1) = starti
1019 IF(myil.GT.0) THEN
1020 lengthi = myiu - myil + 1
1021 ELSE
1022 lengthi = 0
1023 ENDIF
1024 iwork(2) = lengthi
1025 IF ((starti.GE.1).AND.(lengthi.GE.1)) THEN
1026* Copy eigenvalues into communication buffer
1027 CALL scopy(lengthi,
1028 $ rwork( iindwlc+starti-1 ),1,
1029 $ rwork(indd), 1)
1030* Copy uncertainties into communication buffer
1031 CALL scopy(lengthi,
1032 $ rwork( iinderr+starti-1 ),1,
1033 $ rwork(indd+lengthi), 1)
1034 ENDIF
1035
1036 DO 146 i = frstcl, lastcl
1037 IF(i.EQ.myproc) GOTO 146
1038 dstrow = i/ npcol
1039 dstcol = mod(i, npcol)
1040 CALL igesd2d( ictxt, 2, 1, iwork, 2,
1041 $ dstrow, dstcol )
1042 IF ((starti.GE.1).AND.(lengthi.GE.1)) THEN
1043 lengthi2 = 2*lengthi
1044* send buffer
1045 CALL sgesd2d( ictxt, lengthi2,
1046 $ 1, rwork(indd), lengthi2,
1047 $ dstrow, dstcol )
1048 END IF
1049 146 CONTINUE
1050 ELSE
1051 srcrow = iproc / npcol
1052 srccol = mod(iproc, npcol)
1053 CALL igerv2d( ictxt, 2, 1, iwork, 2,
1054 $ srcrow, srccol )
1055 rstarti = iwork(1)
1056 rlengthi = iwork(2)
1057 IF ((rstarti.GE.1).AND.(rlengthi.GE.1)) THEN
1058 rlengthi2 = 2*rlengthi
1059 CALL sgerv2d( ictxt,rlengthi2, 1,
1060 $ rwork(inde),rlengthi2,
1061 $ srcrow, srccol )
1062* copy eigenvalues from communication buffer
1063 CALL scopy(rlengthi,rwork(inde), 1,
1064 $ rwork( iindwlc+rstarti-1 ), 1)
1065* copy uncertainties (errors) from communication buffer
1066 CALL scopy(rlengthi,rwork(inde+rlengthi),
1067 $ 1,rwork( iinderr+rstarti-1 ), 1)
1068 END IF
1069 END IF
1070 147 CONTINUE
1071 ENDIF
1072 GOTO 100
1073 ENDIF
1074 ENDIF
1075 IF (iinfo .NE. 0) THEN
1076 CALL pxerbla( ictxt, 'SSTEGR2B', -iinfo )
1077 RETURN
1078 END IF
1079*
1080 ENDIF
1081
1082*
1083***********************************************************************
1084*
1085* MAIN PART ENDS HERE
1086*
1087***********************************************************************
1088*
1089
1090***********************************************************************
1091*
1092* ALLGATHER: EACH PROCESSOR SENDS ITS EIGENVALUES TO THE FIRST ONE,
1093* THEN THE FIRST PROCESSOR BROADCASTS ALL EIGENVALUES
1094*
1095***********************************************************************
1096
1097 DO 50 i = 2, nprocs
1098 IF (myproc .EQ. (i - 1)) THEN
1099 dstrow = 0
1100 dstcol = 0
1101 starti = myil - iil + 1
1102 iwork(1) = starti
1103 IF(myil.GT.0) THEN
1104 lengthi = myiu - myil + 1
1105 ELSE
1106 lengthi = 0
1107 ENDIF
1108 iwork(2) = lengthi
1109 CALL igesd2d( ictxt, 2, 1, iwork, 2,
1110 $ dstrow, dstcol )
1111 IF ((starti.GE.1).AND.(lengthi.GE.1)) THEN
1112 CALL sgesd2d( ictxt, lengthi,
1113 $ 1, w( starti ), lengthi,
1114 $ dstrow, dstcol )
1115 ENDIF
1116 ELSE IF (myproc .EQ. 0) THEN
1117 srcrow = (i-1) / npcol
1118 srccol = mod(i-1, npcol)
1119 CALL igerv2d( ictxt, 2, 1, iwork, 2,
1120 $ srcrow, srccol )
1121 starti = iwork(1)
1122 lengthi = iwork(2)
1123 IF ((starti.GE.1).AND.(lengthi.GE.1)) THEN
1124 CALL sgerv2d( ictxt, lengthi, 1,
1125 $ w( starti ), lengthi, srcrow, srccol )
1126 ENDIF
1127 ENDIF
1128 50 CONTINUE
1129
1130* Accumulate M from all processors
1131 m = im
1132 CALL igsum2d( ictxt, 'A', ' ', 1, 1, m, 1, -1, -1 )
1133
1134* Broadcast eigenvalues to all processors
1135 IF (myproc .EQ. 0) THEN
1136* Send eigenvalues
1137 CALL sgebs2d( ictxt, 'A', ' ', m, 1, w, m )
1138 ELSE
1139 srcrow = 0
1140 srccol = 0
1141 CALL sgebr2d( ictxt, 'A', ' ', m, 1,
1142 $ w, m, srcrow, srccol )
1143 END IF
1144*
1145* Sort the eigenvalues and keep permutation in IWORK to
1146* sort the eigenvectors accordingly
1147*
1148 DO 160 i = 1, m
1149 iwork( nprocs+1+i ) = i
1150 160 CONTINUE
1151 CALL slasrt2( 'I', m, w, iwork( nprocs+2 ), iinfo )
1152 IF (iinfo.NE.0) THEN
1153 CALL pxerbla( ictxt, 'SLASRT2', -iinfo )
1154 RETURN
1155 END IF
1156
1157***********************************************************************
1158*
1159* TRANSFORM Z FROM 1D WORKSPACE INTO 2D BLOCKCYCLIC STORAGE
1160*
1161***********************************************************************
1162 IF ( wantz ) THEN
1163 DO 170 i = 1, m
1164 iwork( m+nprocs+1+iwork( nprocs+1+i ) ) = i
1165 170 CONTINUE
1166* Store NVS in IWORK(1:NPROCS+1) for PCLAEVSWP
1167 iwork( 1 ) = 0
1168 DO 180 i = 1, nprocs
1169* Find IL and IU for processor i-1
1170* Has already been computed by PMPIM2 and stored
1171 ipil = iwork(indilu+i-1)
1172 ipiu = iwork(indilu+nprocs+i-1)
1173 IF (ipil .EQ. 0) THEN
1174 iwork( i + 1 ) = iwork( i )
1175 ELSE
1176 iwork( i + 1 ) = iwork( i ) + ipiu - ipil + 1
1177 ENDIF
1178 180 CONTINUE
1179
1180 IF ( first ) THEN
1181 CALL pclaevswp(n, rwork( indrw ), n, z, iz, jz,
1182 $ descz, iwork( 1 ), iwork( nprocs+m+2 ), rwork( indrwork ),
1183 $ size1 )
1184 ELSE
1185 CALL pclaevswp(n, rwork( indrw + n ), n, z, iz, jz,
1186 $ descz, iwork( 1 ), iwork( nprocs+m+2 ), rwork( indrwork ),
1187 $ size1 )
1188 END IF
1189*
1190 nz = m
1191*
1192
1193***********************************************************************
1194*
1195* Compute eigenvectors of A from eigenvectors of T
1196*
1197***********************************************************************
1198 IF( nz.GT.0 ) THEN
1199 CALL pcunmtr( 'L', uplo, 'N', n, nz, a, ia, ja, desca,
1200 $ work( indtau ), z, iz, jz, descz,
1201 $ work( indwork ), llwork, iinfo )
1202 END IF
1203 IF (iinfo.NE.0) THEN
1204 CALL pxerbla( ictxt, 'PCUNMTR', -iinfo )
1205 RETURN
1206 END IF
1207*
1208
1209 END IF
1210*
1211 work( 1 ) = cmplx( lwopt )
1212 rwork( 1 ) = real( lrwopt )
1213 iwork( 1 ) = liwmin
1214
1215 RETURN
1216*
1217* End of PCHEEVR
1218*
1219 END
cmplx
float cmplx[2]
Definition pblas.h:136
chk1mat
subroutine chk1mat(ma, mapos0, na, napos0, ia, ja, desca, descapos0, info)
Definition chk1mat.f:3
pcelget
subroutine pcelget(scope, top, alpha, a, ia, ja, desca)
Definition pcelget.f:2
max
#define max(A, B)
Definition pcgemr.c:180
min
#define min(A, B)
Definition pcgemr.c:181
pcheevr
subroutine pcheevr(jobz, range, uplo, n, a, ia, ja, desca, vl, vu, il, iu, m, nz, w, z, iz, jz, descz, work, lwork, rwork, lrwork, iwork, liwork, info)
Definition pcheevr.f:6
pchentrd
subroutine pchentrd(uplo, n, a, ia, ja, desca, d, e, tau, work, lwork, rwork, lrwork, info)
Definition pchentrd.f:3
pchk1mat
subroutine pchk1mat(ma, mapos0, na, napos0, ia, ja, desca, descapos0, nextra, ex, expos, info)
Definition pchkxmat.f:3
pchk2mat
subroutine pchk2mat(ma, mapos0, na, napos0, ia, ja, desca, descapos0, mb, mbpos0, nb, nbpos0, ib, jb, descb, descbpos0, nextra, ex, expos, info)
Definition pchkxmat.f:175
pclaevswp
subroutine pclaevswp(n, zin, ldzi, z, iz, jz, descz, nvs, key, rwork, lrwork)
Definition pclaevswp.f:5
pcunmtr
subroutine pcunmtr(side, uplo, trans, m, n, a, ia, ja, desca, tau, c, ic, jc, descc, work, lwork, info)
Definition pcunmtr.f:3
pmpcol
subroutine pmpcol(myproc, nprocs, iil, needil, neediu, pmyils, pmyius, colbrt, frstcl, lastcl)
Definition pmpcol.f:9
pmpim2
subroutine pmpim2(il, iu, nprocs, pmyils, pmyius)
Definition pmpim2.f:7
pslared1d
subroutine pslared1d(n, ia, ja, desc, bycol, byall, work, lwork)
Definition pslared1d.f:2
pxerbla
subroutine pxerbla(ictxt, srname, info)
Definition pxerbla.f:2
slasrt2
subroutine slasrt2(id, n, d, key, info)
Definition slasrt2.f:4
sstegr2
subroutine sstegr2(jobz, range, n, d, e, vl, vu, il, iu, m, w, z, ldz, nzc, isuppz, work, lwork, iwork, liwork, dol, dou, zoffset, info)
Definition sstegr2.f:4
sstegr2a
subroutine sstegr2a(jobz, range, n, d, e, vl, vu, il, iu, m, w, z, ldz, nzc, work, lwork, iwork, liwork, dol, dou, needil, neediu, inderr, nsplit, pivmin, scale, wl, wu, info)
Definition sstegr2a.f:6
sstegr2b
subroutine sstegr2b(jobz, n, d, e, m, w, z, ldz, nzc, isuppz, work, lwork, iwork, liwork, dol, dou, needil, neediu, indwlc, pivmin, scale, wl, wu, vstart, finish, maxcls, ndepth, parity, zoffset, info)
Definition sstegr2b.f:7