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pzhegst.f
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1*
2*
3 SUBROUTINE pzhegst( IBTYPE, UPLO, N, A, IA, JA, DESCA, B, IB, JB,
4 $ DESCB, SCALE, INFO )
5*
6* -- ScaLAPACK routine (version 1.7) --
7* University of Tennessee, Knoxville, Oak Ridge National Laboratory,
8* and University of California, Berkeley.
9* May 1, 1997
10*
11* .. Scalar Arguments ..
12 CHARACTER UPLO
13 INTEGER IA, IB, IBTYPE, INFO, JA, JB, N
14 DOUBLE PRECISION SCALE
15* ..
16* .. Array Arguments ..
17 INTEGER DESCA( * ), DESCB( * )
18 COMPLEX*16 A( * ), B( * )
19* ..
20*
21* Purpose
22* =======
23*
24* PZHEGST reduces a complex Hermitian-definite generalized eigenproblem
25* to standard form.
26*
27* In the following sub( A ) denotes A( IA:IA+N-1, JA:JA+N-1 ) and
28* sub( B ) denotes B( IB:IB+N-1, JB:JB+N-1 ).
29*
30* If IBTYPE = 1, the problem is sub( A )*x = lambda*sub( B )*x,
31* and sub( A ) is overwritten by inv(U**H)*sub( A )*inv(U) or
32* inv(L)*sub( A )*inv(L**H)
33*
34* If IBTYPE = 2 or 3, the problem is sub( A )*sub( B )*x = lambda*x or
35* sub( B )*sub( A )*x = lambda*x, and sub( A ) is overwritten by
36* U*sub( A )*U**H or L**H*sub( A )*L.
37*
38* sub( B ) must have been previously factorized as U**H*U or L*L**H by
39* PZPOTRF.
40*
41* Notes
42* =====
43*
44* Each global data object is described by an associated description
45* vector. This vector stores the information required to establish
46* the mapping between an object element and its corresponding process
47* and memory location.
48*
49* Let A be a generic term for any 2D block cyclicly distributed array.
50* Such a global array has an associated description vector DESCA.
51* In the following comments, the character _ should be read as
52* "of the global array".
53*
54* NOTATION STORED IN EXPLANATION
55* --------------- -------------- --------------------------------------
56* DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case,
57* DTYPE_A = 1.
58* CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
59* the BLACS process grid A is distribu-
60* ted over. The context itself is glo-
61* bal, but the handle (the integer
62* value) may vary.
63* M_A (global) DESCA( M_ ) The number of rows in the global
64* array A.
65* N_A (global) DESCA( N_ ) The number of columns in the global
66* array A.
67* MB_A (global) DESCA( MB_ ) The blocking factor used to distribute
68* the rows of the array.
69* NB_A (global) DESCA( NB_ ) The blocking factor used to distribute
70* the columns of the array.
71* RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
72* row of the array A is distributed.
73* CSRC_A (global) DESCA( CSRC_ ) The process column over which the
74* first column of the array A is
75* distributed.
76* LLD_A (local) DESCA( LLD_ ) The leading dimension of the local
77* array. LLD_A >= MAX(1,LOCr(M_A)).
78*
79* Let K be the number of rows or columns of a distributed matrix,
80* and assume that its process grid has dimension p x q.
81* LOCr( K ) denotes the number of elements of K that a process
82* would receive if K were distributed over the p processes of its
83* process column.
84* Similarly, LOCc( K ) denotes the number of elements of K that a
85* process would receive if K were distributed over the q processes of
86* its process row.
87* The values of LOCr() and LOCc() may be determined via a call to the
88* ScaLAPACK tool function, NUMROC:
89* LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
90* LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).
91* An upper bound for these quantities may be computed by:
92* LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
93* LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
94*
95* Arguments
96* =========
97*
98* IBTYPE (global input) INTEGER
99* = 1: compute inv(U**H)*sub( A )*inv(U) or
100* inv(L)*sub( A )*inv(L**H);
101* = 2 or 3: compute U*sub( A )*U**H or L**H*sub( A )*L.
102*
103* UPLO (global input) CHARACTER
104* = 'U': Upper triangle of sub( A ) is stored and sub( B ) is
105* factored as U**H*U;
106* = 'L': Lower triangle of sub( A ) is stored and sub( B ) is
107* factored as L*L**H.
108*
109* N (global input) INTEGER
110* The order of the matrices sub( A ) and sub( B ). N >= 0.
111*
112* A (local input/local output) COMPLEX*16 pointer into the
113* local memory to an array of dimension (LLD_A, LOCc(JA+N-1)).
114* On entry, this array contains the local pieces of the
115* N-by-N Hermitian distributed matrix sub( A ). If UPLO = 'U',
116* the leading N-by-N upper triangular part of sub( A ) contains
117* the upper triangular part of the matrix, and its strictly
118* lower triangular part is not referenced. If UPLO = 'L', the
119* leading N-by-N lower triangular part of sub( A ) contains
120* the lower triangular part of the matrix, and its strictly
121* upper triangular part is not referenced.
122*
123* On exit, if INFO = 0, the transformed matrix, stored in the
124* same format as sub( A ).
125*
126* IA (global input) INTEGER
127* A's global row index, which points to the beginning of the
128* submatrix which is to be operated on.
129*
130* JA (global input) INTEGER
131* A's global column index, which points to the beginning of
132* the submatrix which is to be operated on.
133*
134* DESCA (global and local input) INTEGER array of dimension DLEN_.
135* The array descriptor for the distributed matrix A.
136*
137* B (local input) COMPLEX*16 pointer into the local memory
138* to an array of dimension (LLD_B, LOCc(JB+N-1)). On entry,
139* this array contains the local pieces of the triangular factor
140* from the Cholesky factorization of sub( B ), as returned by
141* PZPOTRF.
142*
143* IB (global input) INTEGER
144* B's global row index, which points to the beginning of the
145* submatrix which is to be operated on.
146*
147* JB (global input) INTEGER
148* B's global column index, which points to the beginning of
149* the submatrix which is to be operated on.
150*
151* DESCB (global and local input) INTEGER array of dimension DLEN_.
152* The array descriptor for the distributed matrix B.
153*
154* SCALE (global output) DOUBLE PRECISION
155* Amount by which the eigenvalues should be scaled to
156* compensate for the scaling performed in this routine.
157* At present, SCALE is always returned as 1.0, it is
158* returned here to allow for future enhancement.
159*
160* INFO (global output) INTEGER
161* = 0: successful exit
162* < 0: If the i-th argument is an array and the j-entry had
163* an illegal value, then INFO = -(i*100+j), if the i-th
164* argument is a scalar and had an illegal value, then
165* INFO = -i.
166*
167* =====================================================================
168*
169* .. Parameters ..
170 INTEGER BLOCK_CYCLIC_2D, DLEN_, DTYPE_, CTXT_, M_, N_,
171 $ mb_, nb_, rsrc_, csrc_, lld_
172 parameter( block_cyclic_2d = 1, dlen_ = 9, dtype_ = 1,
173 $ ctxt_ = 2, m_ = 3, n_ = 4, mb_ = 5, nb_ = 6,
174 $ rsrc_ = 7, csrc_ = 8, lld_ = 9 )
175 DOUBLE PRECISION ONE
176 parameter( one = 1.0d+0 )
177 COMPLEX*16 CONE, HALF
178 parameter( cone = ( 1.0d+0, 0.0d+0 ),
179 $ half = ( 0.5d+0, 0.0d+0 ) )
180* ..
181* .. Local Scalars ..
182 LOGICAL UPPER
183 INTEGER IACOL, IAROW, IBCOL, IBROW, ICOFFA, ICOFFB,
184 $ ictxt, iroffa, iroffb, k, kb, mycol, myrow, nb,
185 $ npcol, nprow
186* ..
187* .. Local Arrays ..
188 INTEGER IDUM1( 2 ), IDUM2( 2 )
189* ..
190* .. External Subroutines ..
191 EXTERNAL blacs_gridinfo, chk1mat, pchk2mat, pxerbla,
192 $ pzhegs2, pzhemm, pzher2k, pztrmm, pztrsm
193* ..
194* .. Intrinsic Functions ..
195 INTRINSIC ichar, min, mod
196* ..
197* .. External Functions ..
198 LOGICAL LSAME
199 INTEGER ICEIL, INDXG2P
200 EXTERNAL lsame, iceil, indxg2p
201* ..
202* .. Executable Statements ..
203* This is just to keep ftnchek happy
204 IF( block_cyclic_2d*csrc_*ctxt_*dlen_*dtype_*lld_*mb_*m_*nb_*n_*
205 $ rsrc_.LT.0 )RETURN
206*
207* Get grid parameters
208*
209 scale = one
210*
211 ictxt = desca( ctxt_ )
212 CALL blacs_gridinfo( ictxt, nprow, npcol, myrow, mycol )
213*
214* Test the input parameters
215*
216 info = 0
217 IF( nprow.EQ.-1 ) THEN
218 info = -( 700+ctxt_ )
219 ELSE
220 upper = lsame( uplo, 'u' )
221 CALL CHK1MAT( N, 3, N, 3, IA, JA, DESCA, 7, INFO )
222 CALL CHK1MAT( N, 3, N, 3, IB, JB, DESCB, 11, INFO )
223.EQ. IF( INFO0 ) THEN
224 IAROW = INDXG2P( IA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ),
225 $ NPROW )
226 IBROW = INDXG2P( IB, DESCB( MB_ ), MYROW, DESCB( RSRC_ ),
227 $ NPROW )
228 IACOL = INDXG2P( JA, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ),
229 $ NPCOL )
230 IBCOL = INDXG2P( JB, DESCB( NB_ ), MYCOL, DESCB( CSRC_ ),
231 $ NPCOL )
232 IROFFA = MOD( IA-1, DESCA( MB_ ) )
233 ICOFFA = MOD( JA-1, DESCA( NB_ ) )
234 IROFFB = MOD( IB-1, DESCB( MB_ ) )
235 ICOFFB = MOD( JB-1, DESCB( NB_ ) )
236.LT..OR..GT. IF( IBTYPE1 IBTYPE3 ) THEN
237 INFO = -1
238.NOT..AND..NOT. ELSE IF( UPPER LSAME( UPLO, 'l' ) ) THEN
239 INFO = -2
240.LT. ELSE IF( N0 ) THEN
241 INFO = -3
242.NE. ELSE IF( IROFFA0 ) THEN
243 INFO = -5
244.NE. ELSE IF( ICOFFA0 ) THEN
245 INFO = -6
246.NE. ELSE IF( DESCA( MB_ )DESCA( NB_ ) ) THEN
247 INFO = -( 700+NB_ )
248.NE..OR..NE. ELSE IF( IROFFB0 IBROWIAROW ) THEN
249 INFO = -9
250.NE..OR..NE. ELSE IF( ICOFFB0 IBCOLIACOL ) THEN
251 INFO = -10
252.NE. ELSE IF( DESCB( MB_ )DESCA( MB_ ) ) THEN
253 INFO = -( 1100+MB_ )
254.NE. ELSE IF( DESCB( NB_ )DESCA( NB_ ) ) THEN
255 INFO = -( 1100+NB_ )
256.NE. ELSE IF( ICTXTDESCB( CTXT_ ) ) THEN
257 INFO = -( 1100+CTXT_ )
258 END IF
259 END IF
260 IDUM1( 1 ) = IBTYPE
261 IDUM2( 1 ) = 1
262 IF( UPPER ) THEN
263 IDUM1( 2 ) = ICHAR( 'u' )
264 ELSE
265 IDUM1( 2 ) = ICHAR( 'l' )
266 END IF
267 IDUM2( 2 ) = 2
268 CALL PCHK2MAT( N, 3, N, 3, IA, JA, DESCA, 7, N, 3, N, 3, IB,
269 $ JB, DESCB, 11, 2, IDUM1, IDUM2, INFO )
270 END IF
271*
272.NE. IF( INFO0 ) THEN
273 CALL PXERBLA( ICTXT, 'pzhegst', -INFO )
274 RETURN
275 END IF
276*
277* Quick return if possible
278*
279.EQ. IF( N0 )
280 $ RETURN
281*
282.EQ. IF( IBTYPE1 ) THEN
283 IF( UPPER ) THEN
284*
285* Compute inv(U')*sub( A )*inv(U)
286*
287 K = 1
288 NB = DESCA( NB_ )
289 KB = MIN( ICEIL( JA, NB )*NB, JA+N-1 ) - JA + 1
290*
291 10 CONTINUE
292*
293* Update the upper triangle of A(ia+k-1:ia+n-1,ja+k-1:ja+n-1)
294*
295 CALL PZHEGS2( IBTYPE, UPLO, KB, A, IA+K-1, JA+K-1, DESCA, B,
296 $ IB+K-1, IB+K-1, DESCB, INFO )
297.LE. IF( K+KBN ) THEN
298 CALL PZTRSM( 'left', UPLO, 'conjugate transpose',
299 $ 'non-unit', KB, N-K-KB+1, CONE, B, IB+K-1,
300 $ JB+K-1, DESCB, A, IA+K-1, JA+K+KB-1, DESCA )
301 CALL PZHEMM( 'left', UPLO, KB, N-K-KB+1, -HALF, A,
302 $ IA+K-1, JA+K-1, DESCA, B, IB+K-1, JB+K+KB-1,
303 $ DESCB, CONE, A, IA+K-1, JA+K+KB-1, DESCA )
304 CALL PZHER2K( UPLO, 'conjugate transpose', N-K-KB+1, KB,
305 $ -CONE, A, IA+K-1, JA+K+KB-1, DESCA, B,
306 $ IB+K-1, JB+K+KB-1, DESCB, ONE, A,
307 $ IA+K+KB-1, JA+K+KB-1, DESCA )
308 CALL PZHEMM( 'left', UPLO, KB, N-K-KB+1, -HALF, A,
309 $ IA+K-1, JA+K-1, DESCA, B, IB+K-1, JB+K+KB-1,
310 $ DESCB, CONE, A, IA+K-1, JA+K+KB-1, DESCA )
311 CALL PZTRSM( 'right', UPLO, 'no transpose', 'non-unit',
312 $ KB, N-K-KB+1, CONE, B, IB+K+KB-1, JB+K+KB-1,
313 $ DESCB, A, IA+K-1, JA+K+KB-1, DESCA )
314 END IF
315 K = K + KB
316 KB = MIN( N-K+1, NB )
317*
318.LE. IF( KN )
319 $ GO TO 10
320*
321 ELSE
322*
323* Compute inv(L)*sub( A )*inv(L')
324*
325 K = 1
326 NB = DESCA( MB_ )
327 KB = MIN( ICEIL( IA, NB )*NB, IA+N-1 ) - IA + 1
328*
329 20 CONTINUE
330*
331* Update the lower triangle of A(ia+k-1:ia+n-1,ja+k-1:ja+n-1)
332*
333 CALL PZHEGS2( IBTYPE, UPLO, KB, A, IA+K-1, JA+K-1, DESCA, B,
334 $ IB+K-1, JB+K-1, DESCB, INFO )
335.LE. IF( K+KBN ) THEN
336 CALL PZTRSM( 'right', UPLO, 'conjugate transpose',
337 $ 'non-unit', N-K-KB+1, KB, CONE, B, IB+K-1,
338 $ JB+K-1, DESCB, A, IA+K+KB-1, JA+K-1, DESCA )
339 CALL PZHEMM( 'right', UPLO, N-K-KB+1, KB, -HALF, A,
340 $ IA+K-1, JA+K-1, DESCA, B, IB+K+KB-1, JB+K-1,
341 $ DESCB, CONE, A, IA+K+KB-1, JA+K-1, DESCA )
342 CALL PZHER2K( UPLO, 'no transpose', N-K-KB+1, KB, -CONE,
343 $ A, IA+K+KB-1, JA+K-1, DESCA, B, IB+K+KB-1,
344 $ JB+K-1, DESCB, ONE, A, IA+K+KB-1,
345 $ JA+K+KB-1, DESCA )
346 CALL PZHEMM( 'right', UPLO, N-K-KB+1, KB, -HALF, A,
347 $ IA+K-1, JA+K-1, DESCA, B, IB+K+KB-1, JB+K-1,
348 $ DESCB, CONE, A, IA+K+KB-1, JA+K-1, DESCA )
349 CALL PZTRSM( 'left', UPLO, 'no transpose', 'non-unit',
350 $ N-K-KB+1, KB, CONE, B, IB+K+KB-1, JB+K+KB-1,
351 $ DESCB, A, IA+K+KB-1, JA+K-1, DESCA )
352 END IF
353 K = K + KB
354 KB = MIN( N-K+1, NB )
355*
356.LE. IF( KN )
357 $ GO TO 20
358*
359 END IF
360*
361 ELSE
362*
363 IF( UPPER ) THEN
364*
365* Compute U*sub( A )*U'
366*
367 K = 1
368 NB = DESCA( NB_ )
369 KB = MIN( ICEIL( JA, NB )*NB, JA+N-1 ) - JA + 1
370*
371 30 CONTINUE
372*
373* Update the upper triangle of A(ia:ia+k+kb-2,ja:ja+k+kb-2)
374*
375 CALL PZTRMM( 'left', UPLO, 'no transpose', 'non-unit', K-1,
376 $ KB, CONE, B, IB, JB, DESCB, A, IA, JA+K-1,
377 $ DESCA )
378 CALL PZHEMM( 'right', UPLO, K-1, KB, HALF, A, IA+K-1,
379 $ JA+K-1, DESCA, B, IB, JB+K-1, DESCB, CONE, A,
380 $ IA, JA+K-1, DESCA )
381 CALL PZHER2K( UPLO, 'no transpose', K-1, KB, CONE, A, IA,
382 $ JA+K-1, DESCA, B, IB, JB+K-1, DESCB, ONE, A,
383 $ IA, JA, DESCA )
384 CALL PZHEMM( 'right', UPLO, K-1, KB, HALF, A, IA+K-1,
385 $ JA+K-1, DESCA, B, IB, JB+K-1, DESCB, CONE, A,
386 $ IA, JA+K-1, DESCA )
387 CALL PZTRMM( 'right', UPLO, 'conjugate transpose',
388 $ 'non-unit', K-1, KB, CONE, B, IB+K-1, JB+K-1,
389 $ DESCB, A, IA, JA+K-1, DESCA )
390 CALL PZHEGS2( IBTYPE, UPLO, KB, A, IA+K-1, JA+K-1, DESCA, B,
391 $ IB+K-1, JB+K-1, DESCB, INFO )
392*
393 K = K + KB
394 KB = MIN( N-K+1, NB )
395*
396.LE. IF( KN )
397 $ GO TO 30
398*
399 ELSE
400*
401* Compute L'*sub( A )*L
402*
403 K = 1
404 NB = DESCA( MB_ )
405 KB = MIN( ICEIL( IA, NB )*NB, IA+N-1 ) - IA + 1
406*
407 40 CONTINUE
408*
409* Update the lower triangle of A(ia:ia+k+kb-2,ja:ja+k+kb-2)
410*
411 CALL PZTRMM( 'right', UPLO, 'no transpose', 'non-unit', KB,
412 $ K-1, CONE, B, IB, JB, DESCB, A, IA+K-1, JA,
413 $ DESCA )
414 CALL PZHEMM( 'left', UPLO, KB, K-1, HALF, A, IA+K-1, JA+K-1,
415 $ DESCA, B, IB+K-1, JB, DESCB, CONE, A, IA+K-1,
416 $ JA, DESCA )
417 CALL PZHER2K( UPLO, 'conjugate transpose', k-1, kb, cone, a,
418 $ ia+k-1, ja, desca, b, ib+k-1, jb, descb, one,
419 $ a, ia, ja, desca )
420 CALL pzhemm( 'Left', uplo, kb, k-1, half, a, ia+k-1, ja+k-1,
421 $ desca, b, ib+k-1, jb, descb, cone, a, ia+k-1,
422 $ ja, desca )
423 CALL pztrmm( 'Left', uplo, 'Conjugate transpose',
424 $ 'Non-unit', kb, k-1, cone, b, ib+k-1, jb+k-1,
425 $ descb, a, ia+k-1, ja, desca )
426 CALL pzhegs2( ibtype, uplo, kb, a, ia+k-1, ja+k-1, desca, b,
427 $ ib+k-1, jb+k-1, descb, info )
428*
429 k = k + kb
430 kb = min( n-k+1, nb )
431*
432 IF( k.LE.n )
433 $ GO TO 40
434*
435 END IF
436*
437 END IF
438*
439 RETURN
440*
441* End of PZHEGST
442*
443 END
min
#define min(a, b)
Definition macros.h:20
chk1mat
subroutine chk1mat(ma, mapos0, na, napos0, ia, ja, desca, descapos0, info)
Definition mpi.f:1577
pxerbla
subroutine pxerbla(contxt, srname, info)
Definition mpi.f:1600
pztrsm
subroutine pztrsm(side, uplo, transa, diag, m, n, alpha, a, ia, ja, desca, b, ib, jb, descb)
Definition mpi.f:1483
pchk2mat
subroutine pchk2mat(ma, mapos0, na, napos0, ia, ja, desca, descapos0, mb, mbpos0, nb, nbpos0, ib, jb, descb, descbpos0, nextra, ex, expos, info)
Definition mpi.f:1588
blacs_gridinfo
subroutine blacs_gridinfo(cntxt, nprow, npcol, myrow, mycol)
Definition mpi.f:754
pzhegs2
subroutine pzhegs2(ibtype, uplo, n, a, ia, ja, desca, b, ib, jb, descb, info)
Definition pzhegs2.f:5
pzhegst
subroutine pzhegst(ibtype, uplo, n, a, ia, ja, desca, b, ib, jb, descb, scale, info)
Definition pzhegst.f:5