SCALAPACK 2.2.2
LAPACK: Linear Algebra PACKage
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pzlanhe.f
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1 DOUBLE PRECISION FUNCTION pzlanhe( NORM, UPLO, N, A, IA, JA,
2 $ DESCA, WORK )
3*
4* -- ScaLAPACK auxiliary routine (version 1.7) --
5* University of Tennessee, Knoxville, Oak Ridge National Laboratory,
6* and University of California, Berkeley.
7* May 1, 1997
8*
9* .. Scalar Arguments ..
10 CHARACTER norm, uplo
11 INTEGER ia, ja, n
12* ..
13* .. Array Arguments ..
14 INTEGER desca( * )
15 DOUBLE PRECISION work( * )
16 COMPLEX*16 a( * )
17* ..
18*
19* Purpose
20* =======
21*
22* PZLANHE returns the value of the one norm, or the Frobenius norm,
23* or the infinity norm, or the element of largest absolute value of a
24* complex hermitian distributed matrix sub(A) = A(IA:IA+N-1,JA:JA+N-1).
25*
26* PZLANHE returns the value
27*
28* ( max(abs(A(i,j))), NORM = 'M' or 'm' with IA <= i <= IA+N-1,
29* ( and JA <= j <= JA+N-1,
30* (
31* ( norm1( sub( A ) ), NORM = '1', 'O' or 'o'
32* (
33* ( normI( sub( A ) ), NORM = 'I' or 'i'
34* (
35* ( normF( sub( A ) ), NORM = 'F', 'f', 'E' or 'e'
36*
37* where norm1 denotes the one norm of a matrix (maximum column sum),
38* normI denotes the infinity norm of a matrix (maximum row sum) and
39* normF denotes the Frobenius norm of a matrix (square root of sum of
40* squares). Note that max(abs(A(i,j))) is not a matrix norm.
41*
42* Notes
43* =====
44*
45* Each global data object is described by an associated description
46* vector. This vector stores the information required to establish
47* the mapping between an object element and its corresponding process
48* and memory location.
49*
50* Let A be a generic term for any 2D block cyclicly distributed array.
51* Such a global array has an associated description vector DESCA.
52* In the following comments, the character _ should be read as
53* "of the global array".
54*
55* NOTATION STORED IN EXPLANATION
56* --------------- -------------- --------------------------------------
57* DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case,
58* DTYPE_A = 1.
59* CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
60* the BLACS process grid A is distribu-
61* ted over. The context itself is glo-
62* bal, but the handle (the integer
63* value) may vary.
64* M_A (global) DESCA( M_ ) The number of rows in the global
65* array A.
66* N_A (global) DESCA( N_ ) The number of columns in the global
67* array A.
68* MB_A (global) DESCA( MB_ ) The blocking factor used to distribute
69* the rows of the array.
70* NB_A (global) DESCA( NB_ ) The blocking factor used to distribute
71* the columns of the array.
72* RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
73* row of the array A is distributed.
74* CSRC_A (global) DESCA( CSRC_ ) The process column over which the
75* first column of the array A is
76* distributed.
77* LLD_A (local) DESCA( LLD_ ) The leading dimension of the local
78* array. LLD_A >= MAX(1,LOCr(M_A)).
79*
80* Let K be the number of rows or columns of a distributed matrix,
81* and assume that its process grid has dimension p x q.
82* LOCr( K ) denotes the number of elements of K that a process
83* would receive if K were distributed over the p processes of its
84* process column.
85* Similarly, LOCc( K ) denotes the number of elements of K that a
86* process would receive if K were distributed over the q processes of
87* its process row.
88* The values of LOCr() and LOCc() may be determined via a call to the
89* ScaLAPACK tool function, NUMROC:
90* LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
91* LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).
92* An upper bound for these quantities may be computed by:
93* LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
94* LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
95*
96* Arguments
97* =========
98*
99* NORM (global input) CHARACTER
100* Specifies the value to be returned in PZLANHE as described
101* above.
102*
103* UPLO (global input) CHARACTER
104* Specifies whether the upper or lower triangular part of the
105* hermitian matrix sub( A ) is to be referenced.
106* = 'U': Upper triangular part of sub( A ) is referenced,
107* = 'L': Lower triangular part of sub( A ) is referenced.
108*
109* N (global input) INTEGER
110* The number of rows and columns to be operated on i.e the
111* number of rows and columns of the distributed submatrix
112* sub( A ). When N = 0, PZLANHE is set to zero. N >= 0.
113*
114* A (local input) COMPLEX*16 pointer into the local memory
115* to an array of dimension (LLD_A, LOCc(JA+N-1)) containing the
116* local pieces of the hermitian distributed matrix sub( A ).
117* If UPLO = 'U', the leading N-by-N upper triangular part of
118* sub( A ) contains the upper triangular matrix which norm is
119* to be computed, and the strictly lower triangular part of
120* this matrix is not referenced. If UPLO = 'L', the leading
121* N-by-N lower triangular part of sub( A ) contains the lower
122* triangular matrix which norm is to be computed, and the
123* strictly upper triangular part of sub( A ) is not referenced.
124*
125* IA (global input) INTEGER
126* The row index in the global array A indicating the first
127* row of sub( A ).
128*
129* JA (global input) INTEGER
130* The column index in the global array A indicating the
131* first column of sub( A ).
132*
133* DESCA (global and local input) INTEGER array of dimension DLEN_.
134* The array descriptor for the distributed matrix A.
135*
136* WORK (local workspace) DOUBLE PRECISION array dimension (LWORK)
137* LWORK >= 0 if NORM = 'M' or 'm' (not referenced),
138* 2*Nq0+Np0+LDW if NORM = '1', 'O', 'o', 'I' or 'i',
139* where LDW is given by:
140* IF( NPROW.NE.NPCOL ) THEN
141* LDW = MB_A*CEIL(CEIL(Np0/MB_A)/(LCM/NPROW))
142* ELSE
143* LDW = 0
144* END IF
145* 0 if NORM = 'F', 'f', 'E' or 'e' (not referenced),
146*
147* where LCM is the least common multiple of NPROW and NPCOL
148* LCM = ILCM( NPROW, NPCOL ) and CEIL denotes the ceiling
149* operation (ICEIL).
150*
151* IROFFA = MOD( IA-1, MB_A ), ICOFFA = MOD( JA-1, NB_A ),
152* IAROW = INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW ),
153* IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ),
154* Np0 = NUMROC( N+IROFFA, MB_A, MYROW, IAROW, NPROW ),
155* Nq0 = NUMROC( N+ICOFFA, NB_A, MYCOL, IACOL, NPCOL ),
156*
157* ICEIL, ILCM, INDXG2P and NUMROC are ScaLAPACK tool functions;
158* MYROW, MYCOL, NPROW and NPCOL can be determined by calling
159* the subroutine BLACS_GRIDINFO.
160*
161* =====================================================================
162*
163* .. Parameters ..
164 INTEGER block_cyclic_2d, csrc_, ctxt_, dlen_, dtype_,
165 $ lld_, mb_, m_, nb_, n_, rsrc_
166 parameter( block_cyclic_2d = 1, dlen_ = 9, dtype_ = 1,
167 $ ctxt_ = 2, m_ = 3, n_ = 4, mb_ = 5, nb_ = 6,
168 $ rsrc_ = 7, csrc_ = 8, lld_ = 9 )
169 DOUBLE PRECISION one, zero
170 parameter( one = 1.0d+0, zero = 0.0d+0 )
171* ..
172* .. Local Scalars ..
173 INTEGER i, iarow, iacol, ib, icoff, ictxt, icurcol,
174 $ icurrow, ii, iia, in, iroff, icsr, icsr0,
175 $ ioffa, irsc, irsc0, irsr, irsr0, jj, jja, k,
176 $ lda, ll, mycol, myrow, np, npcol, nprow, nq
177 DOUBLE PRECISION absa, scale, sum, value
178* ..
179* .. Local Arrays ..
180 DOUBLE PRECISION rwork( 2 )
181* ..
182* .. External Subroutines ..
183 EXTERNAL blacs_gridinfo, daxpy, dcombssq,
184 $ dgamx2d, dgsum2d, dgebr2d,
185 $ dgebs2d, pdcol2row, pdtreecomb,
186 $ zlassq
187* ..
188* .. External Functions ..
189 LOGICAL lsame
190 INTEGER iceil, idamax, numroc
191 EXTERNAL iceil, idamax, lsame, numroc
192* ..
193* .. Intrinsic Functions ..
194 INTRINSIC abs, dble, max, min, mod, sqrt
195* ..
196* .. Executable Statements ..
197*
198* Get grid parameters and local indexes.
199*
200 ictxt = desca( ctxt_ )
201 CALL blacs_gridinfo( ictxt, nprow, npcol, myrow, mycol )
202 CALL infog2l( ia, ja, desca, nprow, npcol, myrow, mycol,
203 $ iia, jja, iarow, iacol )
204*
205 iroff = mod( ia-1, desca( mb_ ) )
206 icoff = mod( ja-1, desca( nb_ ) )
207 np = numroc( n+iroff, desca( mb_ ), myrow, iarow, nprow )
208 nq = numroc( n+icoff, desca( nb_ ), mycol, iacol, npcol )
209 icsr = 1
210 irsr = icsr + nq
211 irsc = irsr + nq
212 IF( myrow.EQ.iarow ) THEN
213 irsc0 = irsc + iroff
214 np = np - iroff
215 ELSE
216 irsc0 = irsc
217 END IF
218 IF( mycol.EQ.iacol ) THEN
219 icsr0 = icsr + icoff
220 irsr0 = irsr + icoff
221 nq = nq - icoff
222 ELSE
223 icsr0 = icsr
224 irsr0 = irsr
225 END IF
226 in = min( iceil( ia, desca( mb_ ) ) * desca( mb_ ), ia+n-1 )
227 lda = desca( lld_ )
228*
229* If the matrix is Hermitian, we address only a triangular portion
230* of the matrix. A sum of row (column) i of the complete matrix
231* can be obtained by adding along row i and column i of the the
232* triangular matrix, stopping/starting at the diagonal, which is
233* the point of reflection. The pictures below demonstrate this.
234* In the following code, the row sums created by --- rows below are
235* refered to as ROWSUMS, and the column sums shown by | are refered
236* to as COLSUMS. Infinity-norm = 1-norm = ROWSUMS+COLSUMS.
237*
238* UPLO = 'U' UPLO = 'L'
239* ____i______ ___________
240* |\ | | |\ |
241* | \ | | | \ |
242* | \ | | | \ |
243* | \|------| i i|---\ |
244* | \ | | |\ |
245* | \ | | | \ |
246* | \ | | | \ |
247* | \ | | | \ |
248* | \ | | | \ |
249* | \ | | | \ |
250* |__________\| |___|______\|
251* i
252*
253* II, JJ : local indices into array A
254* ICURROW : process row containing diagonal block
255* ICURCOL : process column containing diagonal block
256* IRSC0 : pointer to part of work used to store the ROWSUMS while
257* they are stored along a process column
258* IRSR0 : pointer to part of work used to store the ROWSUMS after
259* they have been transposed to be along a process row
260*
261 ii = iia
262 jj = jja
263*
264 IF( n.EQ.0 ) THEN
265*
266 VALUE = zero
267*
268 ELSE IF( lsame( norm, 'M' ) ) THEN
269*
270* Find max(abs(A(i,j))).
271*
272 VALUE = zero
273*
274 IF( lsame( uplo, 'U' ) ) THEN
275*
276* Handle first block separately
277*
278 ib = in-ia+1
279*
280* Find COLMAXS
281*
282 IF( mycol.EQ.iacol ) THEN
283 DO 20 k = (jj-1)*lda, (jj+ib-2)*lda, lda
284 IF( ii.GT.iia ) THEN
285 DO 10 ll = iia, ii-1
286 VALUE = max( VALUE, abs( a( ll+k ) ) )
287 10 CONTINUE
288 END IF
289 IF( myrow.EQ.iarow )
290 $ ii = ii + 1
291 20 CONTINUE
292*
293* Reset local indices so we can find ROWMAXS
294*
295 IF( myrow.EQ.iarow )
296 $ ii = ii - ib
297*
298 END IF
299*
300* Find ROWMAXS
301*
302 IF( myrow.EQ.iarow ) THEN
303 DO 40 k = ii, ii+ib-1
304 IF( mycol.EQ.iacol ) THEN
305 IF( jj.LE.jja+nq-1 ) THEN
306 VALUE = max( VALUE,
307 $ abs( dble( a( k+(jj-1)*lda ) ) ) )
308 DO 30 ll = jj*lda, (jja+nq-2)*lda, lda
309 VALUE = max( VALUE, abs( a( k+ll ) ) )
310 30 CONTINUE
311 END IF
312 ELSE
313 IF( jj.LE.jja+nq-1 ) THEN
314 DO 35 ll = (jj-1)*lda, (jja+nq-2)*lda, lda
315 VALUE = max( VALUE, abs( a( k+ll ) ) )
316 35 CONTINUE
317 END IF
318 END IF
319 IF( mycol.EQ.iacol )
320 $ jj = jj + 1
321 40 CONTINUE
322 ii = ii + ib
323 ELSE IF( mycol.EQ.iacol ) THEN
324 jj = jj + ib
325 END IF
326*
327 icurrow = mod( iarow+1, nprow )
328 icurcol = mod( iacol+1, npcol )
329*
330* Loop over the remaining rows/columns of the matrix.
331*
332 DO 90 i = in+1, ia+n-1, desca( mb_ )
333 ib = min( desca( mb_ ), ia+n-i )
334*
335* Find COLMAXS
336*
337 IF( mycol.EQ.icurcol ) THEN
338 DO 60 k = (jj-1)*lda, (jj+ib-2)*lda, lda
339 IF( ii.GT.iia ) THEN
340 DO 50 ll = iia, ii-1
341 VALUE = max( VALUE, abs( a( ll+k ) ) )
342 50 CONTINUE
343 END IF
344 IF( myrow.EQ.icurrow )
345 $ ii = ii + 1
346 60 CONTINUE
347*
348* Reset local indices so we can find ROWMAXS
349*
350 IF( myrow.EQ.icurrow )
351 $ ii = ii - ib
352 END IF
353*
354* Find ROWMAXS
355*
356 IF( myrow.EQ.icurrow ) THEN
357 DO 80 k = ii, ii+ib-1
358 IF( mycol.EQ.icurcol ) THEN
359 IF( jj.LE.jja+nq-1 ) THEN
360 VALUE = max( VALUE,
361 $ abs( dble( a( k+(jj-1)*lda ) ) ) )
362 DO 70 ll = jj*lda, (jja+nq-2)*lda, lda
363 VALUE = max( VALUE, abs( a( k+ll ) ) )
364 70 CONTINUE
365 END IF
366 ELSE
367 IF( jj.LE.jja+nq-1 ) THEN
368 DO 75 ll = (jj-1)*lda, (jja+nq-2)*lda, lda
369 VALUE = max( VALUE, abs( a( k+ll ) ) )
370 75 CONTINUE
371 END IF
372 END IF
373 IF( mycol.EQ.icurcol )
374 $ jj = jj + 1
375 80 CONTINUE
376 ii = ii + ib
377 ELSE IF( mycol.EQ.icurcol ) THEN
378 jj = jj + ib
379 END IF
380 icurrow = mod( icurrow+1, nprow )
381 icurcol = mod( icurcol+1, npcol )
382 90 CONTINUE
383*
384 ELSE
385*
386* Handle first block separately
387*
388 ib = in-ia+1
389*
390* Find COLMAXS
391*
392 IF( mycol.EQ.iacol ) THEN
393 DO 110 k = (jj-1)*lda, (jj+ib-2)*lda, lda
394 IF( myrow.EQ.iarow ) THEN
395 IF( ii.LE.iia+np-1 ) THEN
396 VALUE = max( VALUE, abs( dble( a( ii+k ) ) ) )
397 DO 100 ll = ii+1, iia+np-1
398 VALUE = max( VALUE, abs( a( ll+k ) ) )
399 100 CONTINUE
400 END IF
401 ELSE
402 IF( ii.LE.iia+np-1 ) THEN
403 DO 105 ll = ii, iia+np-1
404 VALUE = max( VALUE, abs( a( ll+k ) ) )
405 105 CONTINUE
406 END IF
407 END IF
408 IF( myrow.EQ.iarow )
409 $ ii = ii + 1
410 110 CONTINUE
411*
412* Reset local indices so we can find ROWMAXS
413*
414 IF( myrow.EQ.iarow )
415 $ ii = ii - ib
416 END IF
417*
418* Find ROWMAXS
419*
420 IF( myrow.EQ.iarow ) THEN
421 DO 130 k = 0, ib-1
422 IF( jj.GT.jja ) THEN
423 DO 120 ll = (jja-1)*lda, (jj-2)*lda, lda
424 VALUE = max( VALUE, abs( a( ii+ll ) ) )
425 120 CONTINUE
426 END IF
427 ii = ii + 1
428 IF( mycol.EQ.iacol )
429 $ jj = jj + 1
430 130 CONTINUE
431 ELSE IF( mycol.EQ.iacol ) THEN
432 jj = jj + ib
433 END IF
434*
435 icurrow = mod( iarow+1, nprow )
436 icurcol = mod( iacol+1, npcol )
437*
438* Loop over rows/columns of global matrix.
439*
440 DO 180 i = in+1, ia+n-1, desca( mb_ )
441 ib = min( desca( mb_ ), ia+n-i )
442*
443* Find COLMAXS
444*
445 IF( mycol.EQ.icurcol ) THEN
446 DO 150 k = (jj-1)*lda, (jj+ib-2)*lda, lda
447 IF( myrow.EQ.icurrow ) THEN
448 IF( ii.LE.iia+np-1 ) THEN
449 VALUE = max( VALUE,
450 $ abs( dble( a( ii+k ) ) ) )
451 DO 140 ll = ii+1, iia+np-1
452 VALUE = max( VALUE, abs( a( ll+k ) ) )
453 140 CONTINUE
454 END IF
455 ELSE
456 IF( ii.LE.iia+np-1 ) THEN
457 DO 145 ll = ii, iia+np-1
458 VALUE = max( VALUE, abs( a( ll+k ) ) )
459 145 CONTINUE
460 END IF
461 END IF
462 IF( myrow.EQ.icurrow )
463 $ ii = ii + 1
464 150 CONTINUE
465*
466* Reset local indices so we can find ROWMAXS
467*
468 IF( myrow.EQ.icurrow )
469 $ ii = ii - ib
470 END IF
471*
472* Find ROWMAXS
473*
474 IF( myrow.EQ.icurrow ) THEN
475 DO 170 k = 0, ib-1
476 IF( jj.GT.jja ) THEN
477 DO 160 ll = (jja-1)*lda, (jj-2)*lda, lda
478 VALUE = max( VALUE, abs( a( ii+ll ) ) )
479 160 CONTINUE
480 END IF
481 ii = ii + 1
482 IF( mycol.EQ.icurcol )
483 $ jj = jj + 1
484 170 CONTINUE
485 ELSE IF( mycol.EQ.icurcol ) THEN
486 jj = jj + ib
487 END IF
488 icurrow = mod( icurrow+1, nprow )
489 icurcol = mod( icurcol+1, npcol )
490*
491 180 CONTINUE
492*
493 END IF
494*
495* Gather the result on process (IAROW,IACOL).
496*
497 CALL dgamx2d( ictxt, 'All', ' ', 1, 1, VALUE, 1, i, k, -1,
498 $ iarow, iacol )
499*
500 ELSE IF( lsame( norm, 'I' ) .OR. lsame( norm, 'O' ) .OR.
501 $ norm.EQ.'1' ) THEN
502*
503* Find normI( sub( A ) ) ( = norm1( sub( A ) ), since sub( A ) is
504* hermitian).
505*
506 IF( lsame( uplo, 'U' ) ) THEN
507*
508* Handle first block separately
509*
510 ib = in-ia+1
511*
512* Find COLSUMS
513*
514 IF( mycol.EQ.iacol ) THEN
515 ioffa = ( jj - 1 ) * lda
516 DO 200 k = 0, ib-1
517 sum = zero
518 IF( ii.GT.iia ) THEN
519 DO 190 ll = iia, ii-1
520 sum = sum + abs( a( ll+ioffa ) )
521 190 CONTINUE
522 END IF
523 ioffa = ioffa + lda
524 work( jj+k-jja+icsr0 ) = sum
525 IF( myrow.EQ.iarow )
526 $ ii = ii + 1
527 200 CONTINUE
528*
529* Reset local indices so we can find ROWSUMS
530*
531 IF( myrow.EQ.iarow )
532 $ ii = ii - ib
533*
534 END IF
535*
536* Find ROWSUMS
537*
538 IF( myrow.EQ.iarow ) THEN
539 DO 220 k = ii, ii+ib-1
540 sum = zero
541 IF( mycol.EQ.iacol ) THEN
542 IF( jja+nq.GT.jj ) THEN
543 sum = abs( dble( a( k+(jj-1)*lda ) ) )
544 DO 210 ll = jj*lda, (jja+nq-2)*lda, lda
545 sum = sum + abs( a( k+ll ) )
546 210 CONTINUE
547 END IF
548 ELSE
549 IF( jja+nq.GT.jj ) THEN
550 DO 215 ll = (jj-1)*lda, (jja+nq-2)*lda, lda
551 sum = sum + abs( a( k+ll ) )
552 215 CONTINUE
553 END IF
554 END IF
555 work( k-iia+irsc0 ) = sum
556 IF( mycol.EQ.iacol )
557 $ jj = jj + 1
558 220 CONTINUE
559 ii = ii + ib
560 ELSE IF( mycol.EQ.iacol ) THEN
561 jj = jj + ib
562 END IF
563*
564 icurrow = mod( iarow+1, nprow )
565 icurcol = mod( iacol+1, npcol )
566*
567* Loop over remaining rows/columns of global matrix.
568*
569 DO 270 i = in+1, ia+n-1, desca( mb_ )
570 ib = min( desca( mb_ ), ia+n-i )
571*
572* Find COLSUMS
573*
574 IF( mycol.EQ.icurcol ) THEN
575 ioffa = ( jj - 1 ) * lda
576 DO 240 k = 0, ib-1
577 sum = zero
578 IF( ii.GT.iia ) THEN
579 DO 230 ll = iia, ii-1
580 sum = sum + abs( a( ioffa+ll ) )
581 230 CONTINUE
582 END IF
583 ioffa = ioffa + lda
584 work( jj+k-jja+icsr0 ) = sum
585 IF( myrow.EQ.icurrow )
586 $ ii = ii + 1
587 240 CONTINUE
588*
589* Reset local indices so we can find ROWSUMS
590*
591 IF( myrow.EQ.icurrow )
592 $ ii = ii - ib
593*
594 END IF
595*
596* Find ROWSUMS
597*
598 IF( myrow.EQ.icurrow ) THEN
599 DO 260 k = ii, ii+ib-1
600 sum = zero
601 IF( mycol.EQ.icurcol ) THEN
602 IF( jja+nq.GT.jj ) THEN
603 sum = abs( dble( a( k+(jj-1)*lda ) ) )
604 DO 250 ll = jj*lda, (jja+nq-2)*lda, lda
605 sum = sum + abs( a( k+ll ) )
606 250 CONTINUE
607 END IF
608 ELSE
609 IF( jja+nq.GT.jj ) THEN
610 DO 255 ll = (jj-1)*lda, (jja+nq-2)*lda, lda
611 sum = sum + abs( a( k+ll ) )
612 255 CONTINUE
613 END IF
614 END IF
615 work( k-iia+irsc0 ) = sum
616 IF( mycol.EQ.icurcol )
617 $ jj = jj + 1
618 260 CONTINUE
619 ii = ii + ib
620 ELSE IF( mycol.EQ.icurcol ) THEN
621 jj = jj + ib
622 END IF
623*
624 icurrow = mod( icurrow+1, nprow )
625 icurcol = mod( icurcol+1, npcol )
626*
627 270 CONTINUE
628*
629 ELSE
630*
631* Handle first block separately
632*
633 ib = in-ia+1
634*
635* Find COLSUMS
636*
637 IF( mycol.EQ.iacol ) THEN
638 ioffa = (jj-1)*lda
639 DO 290 k = 0, ib-1
640 sum = zero
641 IF( myrow.EQ.iarow ) THEN
642 IF( iia+np.GT.ii ) THEN
643 sum = abs( dble( a( ioffa+ii ) ) )
644 DO 280 ll = ii+1, iia+np-1
645 sum = sum + abs( a( ioffa+ll ) )
646 280 CONTINUE
647 END IF
648 ELSE
649 DO 285 ll = ii, iia+np-1
650 sum = sum + abs( a( ioffa+ll ) )
651 285 CONTINUE
652 END IF
653 ioffa = ioffa + lda
654 work( jj+k-jja+icsr0 ) = sum
655 IF( myrow.EQ.iarow )
656 $ ii = ii + 1
657 290 CONTINUE
658*
659* Reset local indices so we can find ROWSUMS
660*
661 IF( myrow.EQ.iarow )
662 $ ii = ii - ib
663*
664 END IF
665*
666* Find ROWSUMS
667*
668 IF( myrow.EQ.iarow ) THEN
669 DO 310 k = ii, ii+ib-1
670 sum = zero
671 IF( jj.GT.jja ) THEN
672 DO 300 ll = (jja-1)*lda, (jj-2)*lda, lda
673 sum = sum + abs( a( k+ll ) )
674 300 CONTINUE
675 END IF
676 work( k-iia+irsc0 ) = sum
677 IF( mycol.EQ.iacol )
678 $ jj = jj + 1
679 310 CONTINUE
680 ii = ii + ib
681 ELSE IF( mycol.EQ.iacol ) THEN
682 jj = jj + ib
683 END IF
684*
685 icurrow = mod( iarow+1, nprow )
686 icurcol = mod( iacol+1, npcol )
687*
688* Loop over rows/columns of global matrix.
689*
690 DO 360 i = in+1, ia+n-1, desca( mb_ )
691 ib = min( desca( mb_ ), ia+n-i )
692*
693* Find COLSUMS
694*
695 IF( mycol.EQ.icurcol ) THEN
696 ioffa = ( jj - 1 ) * lda
697 DO 330 k = 0, ib-1
698 sum = zero
699 IF( myrow.EQ.icurrow ) THEN
700 IF( iia+np.GT.ii ) THEN
701 sum = abs( dble( a( ii+ioffa ) ) )
702 DO 320 ll = ii+1, iia+np-1
703 sum = sum + abs( a( ll+ioffa ) )
704 320 CONTINUE
705 ELSE IF( ii.EQ.iia+np-1 ) THEN
706 sum = abs( dble( a( ii+ioffa ) ) )
707 END IF
708 ELSE
709 DO 325 ll = ii, iia+np-1
710 sum = sum + abs( a( ll+ioffa ) )
711 325 CONTINUE
712 END IF
713 ioffa = ioffa + lda
714 work( jj+k-jja+icsr0 ) = sum
715 IF( myrow.EQ.icurrow )
716 $ ii = ii + 1
717 330 CONTINUE
718*
719* Reset local indices so we can find ROWSUMS
720*
721 IF( myrow.EQ.icurrow )
722 $ ii = ii - ib
723*
724 END IF
725*
726* Find ROWSUMS
727*
728 IF( myrow.EQ.icurrow ) THEN
729 DO 350 k = ii, ii+ib-1
730 sum = zero
731 IF( jj.GT.jja ) THEN
732 DO 340 ll = (jja-1)*lda, (jj-2)*lda, lda
733 sum = sum + abs( a( k+ll ) )
734 340 CONTINUE
735 END IF
736 work(k-iia+irsc0) = sum
737 IF( mycol.EQ.icurcol )
738 $ jj = jj + 1
739 350 CONTINUE
740 ii = ii + ib
741 ELSE IF( mycol.EQ.icurcol ) THEN
742 jj = jj + ib
743 END IF
744*
745 icurrow = mod( icurrow+1, nprow )
746 icurcol = mod( icurcol+1, npcol )
747*
748 360 CONTINUE
749 END IF
750*
751* After calls to DGSUM2D, process row 0 will have global
752* COLSUMS and process column 0 will have global ROWSUMS.
753* Transpose ROWSUMS and add to COLSUMS to get global row/column
754* sum, the max of which is the infinity or 1 norm.
755*
756 IF( mycol.EQ.iacol )
757 $ nq = nq + icoff
758 CALL dgsum2d( ictxt, 'Columnwise', ' ', 1, nq, work( icsr ), 1,
759 $ iarow, mycol )
760 IF( myrow.EQ.iarow )
761 $ np = np + iroff
762 CALL dgsum2d( ictxt, 'Rowwise', ' ', np, 1, work( irsc ),
763 $ max( 1, np ), myrow, iacol )
764*
765 CALL pdcol2row( ictxt, n, 1, desca( mb_ ), work( irsc ),
766 $ max( 1, np ), work( irsr ), max( 1, nq ),
767 $ iarow, iacol, iarow, iacol, work( irsc+np ) )
768*
769 IF( myrow.EQ.iarow ) THEN
770 IF( mycol.EQ.iacol )
771 $ nq = nq - icoff
772 CALL daxpy( nq, one, work( irsr0 ), 1, work( icsr0 ), 1 )
773 IF( nq.LT.1 ) THEN
774 VALUE = zero
775 ELSE
776 VALUE = work( idamax( nq, work( icsr0 ), 1 ) )
777 END IF
778 CALL dgamx2d( ictxt, 'Rowwise', ' ', 1, 1, VALUE, 1, i, k,
779 $ -1, iarow, iacol )
780 END IF
781*
782 ELSE IF( lsame( norm, 'F' ) .OR. lsame( norm, 'E' ) ) THEN
783*
784* Find normF( sub( A ) ).
785*
786 scale = zero
787 sum = one
788*
789* Add off-diagonal entries, first
790*
791 IF( lsame( uplo, 'U' ) ) THEN
792*
793* Handle first block separately
794*
795 ib = in-ia+1
796*
797 IF( mycol.EQ.iacol ) THEN
798 DO 370 k = (jj-1)*lda, (jj+ib-2)*lda, lda
799 CALL zlassq( ii-iia, a( iia+k ), 1, scale, sum )
800 CALL zlassq( ii-iia, a( iia+k ), 1, scale, sum )
801 IF( myrow.EQ.iarow ) THEN
802 IF( dble( a( ii+k ) ).NE.zero ) THEN
803 absa = abs( dble( a( ii+k ) ) )
804 IF( scale.LT.absa ) THEN
805 sum = one + sum * ( scale / absa )**2
806 scale = absa
807 ELSE
808 sum = sum + ( absa / scale )**2
809 END IF
810 END IF
811 ii = ii + 1
812 END IF
813 370 CONTINUE
814*
815 jj = jj + ib
816 ELSE IF( myrow.EQ.iarow ) THEN
817 ii = ii + ib
818 END IF
819*
820 icurrow = mod( iarow+1, nprow )
821 icurcol = mod( iacol+1, npcol )
822*
823* Loop over rows/columns of global matrix.
824*
825 DO 390 i = in+1, ia+n-1, desca( mb_ )
826 ib = min( desca( mb_ ), ia+n-i )
827*
828 IF( mycol.EQ.icurcol ) THEN
829 DO 380 k = (jj-1)*lda, (jj+ib-2)*lda, lda
830 CALL zlassq( ii-iia, a( iia+k ), 1, scale, sum )
831 CALL zlassq( ii-iia, a( iia+k ), 1, scale, sum )
832 IF( myrow.EQ.icurrow ) THEN
833 IF( dble( a( ii+k ) ).NE.zero ) THEN
834 absa = abs( dble( a( ii+k ) ) )
835 IF( scale.LT.absa ) THEN
836 sum = one + sum * ( scale / absa )**2
837 scale = absa
838 ELSE
839 sum = sum + ( absa / scale )**2
840 END IF
841 END IF
842 ii = ii + 1
843 END IF
844 380 CONTINUE
845*
846 jj = jj + ib
847 ELSE IF( myrow.EQ.icurrow ) THEN
848 ii = ii + ib
849 END IF
850*
851 icurrow = mod( icurrow+1, nprow )
852 icurcol = mod( icurcol+1, npcol )
853*
854 390 CONTINUE
855*
856 ELSE
857*
858* Handle first block separately
859*
860 ib = in-ia+1
861*
862 IF( mycol.EQ.iacol ) THEN
863 DO 400 k = (jj-1)*lda, (jj+ib-2)*lda, lda
864 IF( myrow.EQ.iarow ) THEN
865 IF( dble( a( ii+k ) ).NE.zero ) THEN
866 absa = abs( dble( a( ii+k ) ) )
867 IF( scale.LT.absa ) THEN
868 sum = one + sum * ( scale / absa )**2
869 scale = absa
870 ELSE
871 sum = sum + ( absa / scale )**2
872 END IF
873 END IF
874 ii = ii + 1
875 END IF
876 CALL zlassq( iia+np-ii, a( ii+k ), 1, scale, sum )
877 CALL zlassq( iia+np-ii, a( ii+k ), 1, scale, sum )
878 400 CONTINUE
879*
880 jj = jj + ib
881 ELSE IF( myrow.EQ.iarow ) THEN
882 ii = ii + ib
883 END IF
884*
885 icurrow = mod( iarow+1, nprow )
886 icurcol = mod( iacol+1, npcol )
887*
888* Loop over rows/columns of global matrix.
889*
890 DO 420 i = in+1, ia+n-1, desca( mb_ )
891 ib = min( desca( mb_ ), ia+n-i )
892*
893 IF( mycol.EQ.icurcol ) THEN
894 DO 410 k = (jj-1)*lda, (jj+ib-2)*lda, lda
895 IF( myrow.EQ.icurrow ) THEN
896 IF( dble( a( ii+k ) ).NE.zero ) THEN
897 absa = abs( dble( a( ii+k ) ) )
898 IF( scale.LT.absa ) THEN
899 sum = one + sum * ( scale / absa )**2
900 scale = absa
901 ELSE
902 sum = sum + ( absa / scale )**2
903 END IF
904 END IF
905 ii = ii + 1
906 END IF
907 CALL zlassq( iia+np-ii, a( ii+k ), 1, scale, sum )
908 CALL zlassq( iia+np-ii, a( ii+k ), 1, scale, sum )
909 410 CONTINUE
910*
911 jj = jj + ib
912 ELSE IF( myrow.EQ.icurrow ) THEN
913 ii = ii + ib
914 END IF
915*
916 icurrow = mod( icurrow+1, nprow )
917 icurcol = mod( icurcol+1, npcol )
918*
919 420 CONTINUE
920*
921 END IF
922*
923* Perform the global scaled sum
924*
925 rwork( 1 ) = scale
926 rwork( 2 ) = sum
927*
928 CALL pdtreecomb( ictxt, 'All', 2, rwork, iarow, iacol,
929 $ dcombssq )
930 VALUE = rwork( 1 ) * sqrt( rwork( 2 ) )
931*
932 END IF
933*
934* Broadcast the result to the other processes
935*
936 IF( myrow.EQ.iarow .AND. mycol.EQ.iacol ) THEN
937 CALL dgebs2d( ictxt, 'All', ' ', 1, 1, VALUE, 1 )
938 ELSE
939 CALL dgebr2d( ictxt, 'All', ' ', 1, 1, VALUE, 1, iarow,
940 $ iacol )
941 END IF
942*
943 pzlanhe = VALUE
944*
945 RETURN
946*
947* End of PZLANHE
948*
949 END
iceil
integer function iceil(inum, idenom)
Definition iceil.f:2
infog2l
subroutine infog2l(grindx, gcindx, desc, nprow, npcol, myrow, mycol, lrindx, lcindx, rsrc, csrc)
Definition infog2l.f:3
numroc
integer function numroc(n, nb, iproc, isrcproc, nprocs)
Definition numroc.f:2
max
#define max(A, B)
Definition pcgemr.c:180
min
#define min(A, B)
Definition pcgemr.c:181
pdcol2row
subroutine pdcol2row(ictxt, m, n, nb, vs, ldvs, vd, ldvd, rsrc, csrc, rdest, cdest, work)
Definition pdcol2row.f:3
dcombssq
subroutine dcombssq(v1, v2)
Definition pdtreecomb.f:259
pdtreecomb
subroutine pdtreecomb(ictxt, scope, n, mine, rdest0, cdest0, subptr)
Definition pdtreecomb.f:3
pzlanhe
double precision function pzlanhe(norm, uplo, n, a, ia, ja, desca, work)
Definition pzlanhe.f:3
lsame
logical function lsame(ca, cb)
Definition tools.f:1724