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clanhf.f
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1*> \brief \b CLANHF returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hermitian matrix in RFP format.
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download CLANHF + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clanhf.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clanhf.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clanhf.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* REAL FUNCTION CLANHF( NORM, TRANSR, UPLO, N, A, WORK )
22*
23* .. Scalar Arguments ..
24* CHARACTER NORM, TRANSR, UPLO
25* INTEGER N
26* ..
27* .. Array Arguments ..
28* REAL WORK( 0: * )
29* COMPLEX A( 0: * )
30* ..
31*
32*
33*> \par Purpose:
34* =============
35*>
36*> \verbatim
37*>
38*> CLANHF returns the value of the one norm, or the Frobenius norm, or
39*> the infinity norm, or the element of largest absolute value of a
40*> complex Hermitian matrix A in RFP format.
41*> \endverbatim
42*>
43*> \return CLANHF
44*> \verbatim
45*>
46*> CLANHF = ( max(abs(A(i,j))), NORM = 'M' or 'm'
47*> (
48*> ( norm1(A), NORM = '1', 'O' or 'o'
49*> (
50*> ( normI(A), NORM = 'I' or 'i'
51*> (
52*> ( normF(A), NORM = 'F', 'f', 'E' or 'e'
53*>
54*> where norm1 denotes the one norm of a matrix (maximum column sum),
55*> normI denotes the infinity norm of a matrix (maximum row sum) and
56*> normF denotes the Frobenius norm of a matrix (square root of sum of
57*> squares). Note that max(abs(A(i,j))) is not a matrix norm.
58*> \endverbatim
59*
60* Arguments:
61* ==========
62*
63*> \param[in] NORM
64*> \verbatim
65*> NORM is CHARACTER
66*> Specifies the value to be returned in CLANHF as described
67*> above.
68*> \endverbatim
69*>
70*> \param[in] TRANSR
71*> \verbatim
72*> TRANSR is CHARACTER
73*> Specifies whether the RFP format of A is normal or
74*> conjugate-transposed format.
75*> = 'N': RFP format is Normal
76*> = 'C': RFP format is Conjugate-transposed
77*> \endverbatim
78*>
79*> \param[in] UPLO
80*> \verbatim
81*> UPLO is CHARACTER
82*> On entry, UPLO specifies whether the RFP matrix A came from
83*> an upper or lower triangular matrix as follows:
84*>
85*> UPLO = 'U' or 'u' RFP A came from an upper triangular
86*> matrix
87*>
88*> UPLO = 'L' or 'l' RFP A came from a lower triangular
89*> matrix
90*> \endverbatim
91*>
92*> \param[in] N
93*> \verbatim
94*> N is INTEGER
95*> The order of the matrix A. N >= 0. When N = 0, CLANHF is
96*> set to zero.
97*> \endverbatim
98*>
99*> \param[in] A
100*> \verbatim
101*> A is COMPLEX array, dimension ( N*(N+1)/2 );
102*> On entry, the matrix A in RFP Format.
103*> RFP Format is described by TRANSR, UPLO and N as follows:
104*> If TRANSR='N' then RFP A is (0:N,0:K-1) when N is even;
105*> K=N/2. RFP A is (0:N-1,0:K) when N is odd; K=N/2. If
106*> TRANSR = 'C' then RFP is the Conjugate-transpose of RFP A
107*> as defined when TRANSR = 'N'. The contents of RFP A are
108*> defined by UPLO as follows: If UPLO = 'U' the RFP A
109*> contains the ( N*(N+1)/2 ) elements of upper packed A
110*> either in normal or conjugate-transpose Format. If
111*> UPLO = 'L' the RFP A contains the ( N*(N+1) /2 ) elements
112*> of lower packed A either in normal or conjugate-transpose
113*> Format. The LDA of RFP A is (N+1)/2 when TRANSR = 'C'. When
114*> TRANSR is 'N' the LDA is N+1 when N is even and is N when
115*> is odd. See the Note below for more details.
116*> Unchanged on exit.
117*> \endverbatim
118*>
119*> \param[out] WORK
120*> \verbatim
121*> WORK is REAL array, dimension (LWORK),
122*> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
123*> WORK is not referenced.
124*> \endverbatim
125*
126* Authors:
127* ========
128*
129*> \author Univ. of Tennessee
130*> \author Univ. of California Berkeley
131*> \author Univ. of Colorado Denver
132*> \author NAG Ltd.
133*
134*> \ingroup complexOTHERcomputational
135*
136*> \par Further Details:
137* =====================
138*>
139*> \verbatim
140*>
141*> We first consider Standard Packed Format when N is even.
142*> We give an example where N = 6.
143*>
144*> AP is Upper AP is Lower
145*>
146*> 00 01 02 03 04 05 00
147*> 11 12 13 14 15 10 11
148*> 22 23 24 25 20 21 22
149*> 33 34 35 30 31 32 33
150*> 44 45 40 41 42 43 44
151*> 55 50 51 52 53 54 55
152*>
153*>
154*> Let TRANSR = 'N'. RFP holds AP as follows:
155*> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
156*> three columns of AP upper. The lower triangle A(4:6,0:2) consists of
157*> conjugate-transpose of the first three columns of AP upper.
158*> For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
159*> three columns of AP lower. The upper triangle A(0:2,0:2) consists of
160*> conjugate-transpose of the last three columns of AP lower.
161*> To denote conjugate we place -- above the element. This covers the
162*> case N even and TRANSR = 'N'.
163*>
164*> RFP A RFP A
165*>
166*> -- -- --
167*> 03 04 05 33 43 53
168*> -- --
169*> 13 14 15 00 44 54
170*> --
171*> 23 24 25 10 11 55
172*>
173*> 33 34 35 20 21 22
174*> --
175*> 00 44 45 30 31 32
176*> -- --
177*> 01 11 55 40 41 42
178*> -- -- --
179*> 02 12 22 50 51 52
180*>
181*> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
182*> transpose of RFP A above. One therefore gets:
183*>
184*>
185*> RFP A RFP A
186*>
187*> -- -- -- -- -- -- -- -- -- --
188*> 03 13 23 33 00 01 02 33 00 10 20 30 40 50
189*> -- -- -- -- -- -- -- -- -- --
190*> 04 14 24 34 44 11 12 43 44 11 21 31 41 51
191*> -- -- -- -- -- -- -- -- -- --
192*> 05 15 25 35 45 55 22 53 54 55 22 32 42 52
193*>
194*>
195*> We next consider Standard Packed Format when N is odd.
196*> We give an example where N = 5.
197*>
198*> AP is Upper AP is Lower
199*>
200*> 00 01 02 03 04 00
201*> 11 12 13 14 10 11
202*> 22 23 24 20 21 22
203*> 33 34 30 31 32 33
204*> 44 40 41 42 43 44
205*>
206*>
207*> Let TRANSR = 'N'. RFP holds AP as follows:
208*> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
209*> three columns of AP upper. The lower triangle A(3:4,0:1) consists of
210*> conjugate-transpose of the first two columns of AP upper.
211*> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
212*> three columns of AP lower. The upper triangle A(0:1,1:2) consists of
213*> conjugate-transpose of the last two columns of AP lower.
214*> To denote conjugate we place -- above the element. This covers the
215*> case N odd and TRANSR = 'N'.
216*>
217*> RFP A RFP A
218*>
219*> -- --
220*> 02 03 04 00 33 43
221*> --
222*> 12 13 14 10 11 44
223*>
224*> 22 23 24 20 21 22
225*> --
226*> 00 33 34 30 31 32
227*> -- --
228*> 01 11 44 40 41 42
229*>
230*> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
231*> transpose of RFP A above. One therefore gets:
232*>
233*>
234*> RFP A RFP A
235*>
236*> -- -- -- -- -- -- -- -- --
237*> 02 12 22 00 01 00 10 20 30 40 50
238*> -- -- -- -- -- -- -- -- --
239*> 03 13 23 33 11 33 11 21 31 41 51
240*> -- -- -- -- -- -- -- -- --
241*> 04 14 24 34 44 43 44 22 32 42 52
242*> \endverbatim
243*>
244* =====================================================================
245 REAL function clanhf( norm, transr, uplo, n, a, work )
246*
247* -- LAPACK computational routine --
248* -- LAPACK is a software package provided by Univ. of Tennessee, --
249* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
250*
251* .. Scalar Arguments ..
252 CHARACTER norm, transr, uplo
253 INTEGER n
254* ..
255* .. Array Arguments ..
256 REAL work( 0: * )
257 COMPLEX a( 0: * )
258* ..
259*
260* =====================================================================
261*
262* .. Parameters ..
263 REAL one, zero
264 parameter( one = 1.0e+0, zero = 0.0e+0 )
265* ..
266* .. Local Scalars ..
267 INTEGER i, j, ifm, ilu, noe, n1, k, l, lda
268 REAL scale, s, VALUE, aa, temp
269* ..
270* .. External Functions ..
271 LOGICAL lsame, sisnan
272 EXTERNAL lsame, sisnan
273* ..
274* .. External Subroutines ..
275 EXTERNAL classq
276* ..
277* .. Intrinsic Functions ..
278 INTRINSIC abs, real, sqrt
279* ..
280* .. Executable Statements ..
281*
282 IF( n.EQ.0 ) THEN
283 clanhf = zero
284 RETURN
285 ELSE IF( n.EQ.1 ) THEN
286 clanhf = abs(real(a(0)))
287 RETURN
288 END IF
289*
290* set noe = 1 if n is odd. if n is even set noe=0
291*
292 noe = 1
293 IF( mod( n, 2 ).EQ.0 )
294 $ noe = 0
295*
296* set ifm = 0 when form='C' or 'c' and 1 otherwise
297*
298 ifm = 1
299 IF( lsame( transr, 'C' ) )
300 $ ifm = 0
301*
302* set ilu = 0 when uplo='U or 'u' and 1 otherwise
303*
304 ilu = 1
305 IF( lsame( uplo, 'U' ) )
306 $ ilu = 0
307*
308* set lda = (n+1)/2 when ifm = 0
309* set lda = n when ifm = 1 and noe = 1
310* set lda = n+1 when ifm = 1 and noe = 0
311*
312 IF( ifm.EQ.1 ) THEN
313 IF( noe.EQ.1 ) THEN
314 lda = n
315 ELSE
316* noe=0
317 lda = n + 1
318 END IF
319 ELSE
320* ifm=0
321 lda = ( n+1 ) / 2
322 END IF
323*
324 IF( lsame( norm, 'M' ) ) THEN
325*
326* Find max(abs(A(i,j))).
327*
328 k = ( n+1 ) / 2
329 VALUE = zero
330 IF( noe.EQ.1 ) THEN
331* n is odd & n = k + k - 1
332 IF( ifm.EQ.1 ) THEN
333* A is n by k
334 IF( ilu.EQ.1 ) THEN
335* uplo ='L'
336 j = 0
337* -> L(0,0)
338 temp = abs( real( a( j+j*lda ) ) )
339 IF( VALUE .LT. temp .OR. sisnan( temp ) )
340 $ VALUE = temp
341 DO i = 1, n - 1
342 temp = abs( a( i+j*lda ) )
343 IF( VALUE .LT. temp .OR. sisnan( temp ) )
344 $ VALUE = temp
345 END DO
346 DO j = 1, k - 1
347 DO i = 0, j - 2
348 temp = abs( a( i+j*lda ) )
349 IF( VALUE .LT. temp .OR. sisnan( temp ) )
350 $ VALUE = temp
351 END DO
352 i = j - 1
353* L(k+j,k+j)
354 temp = abs( real( a( i+j*lda ) ) )
355 IF( VALUE .LT. temp .OR. sisnan( temp ) )
356 $ VALUE = temp
357 i = j
358* -> L(j,j)
359 temp = abs( real( a( i+j*lda ) ) )
360 IF( VALUE .LT. temp .OR. sisnan( temp ) )
361 $ VALUE = temp
362 DO i = j + 1, n - 1
363 temp = abs( a( i+j*lda ) )
364 IF( VALUE .LT. temp .OR. sisnan( temp ) )
365 $ VALUE = temp
366 END DO
367 END DO
368 ELSE
369* uplo = 'U'
370 DO j = 0, k - 2
371 DO i = 0, k + j - 2
372 temp = abs( a( i+j*lda ) )
373 IF( VALUE .LT. temp .OR. sisnan( temp ) )
374 $ VALUE = temp
375 END DO
376 i = k + j - 1
377* -> U(i,i)
378 temp = abs( real( a( i+j*lda ) ) )
379 IF( VALUE .LT. temp .OR. sisnan( temp ) )
380 $ VALUE = temp
381 i = i + 1
382* =k+j; i -> U(j,j)
383 temp = abs( real( a( i+j*lda ) ) )
384 IF( VALUE .LT. temp .OR. sisnan( temp ) )
385 $ VALUE = temp
386 DO i = k + j + 1, n - 1
387 temp = abs( a( i+j*lda ) )
388 IF( VALUE .LT. temp .OR. sisnan( temp ) )
389 $ VALUE = temp
390 END DO
391 END DO
392 DO i = 0, n - 2
393 temp = abs( a( i+j*lda ) )
394 IF( VALUE .LT. temp .OR. sisnan( temp ) )
395 $ VALUE = temp
396* j=k-1
397 END DO
398* i=n-1 -> U(n-1,n-1)
399 temp = abs( real( a( i+j*lda ) ) )
400 IF( VALUE .LT. temp .OR. sisnan( temp ) )
401 $ VALUE = temp
402 END IF
403 ELSE
404* xpose case; A is k by n
405 IF( ilu.EQ.1 ) THEN
406* uplo ='L'
407 DO j = 0, k - 2
408 DO i = 0, j - 1
409 temp = abs( a( i+j*lda ) )
410 IF( VALUE .LT. temp .OR. sisnan( temp ) )
411 $ VALUE = temp
412 END DO
413 i = j
414* L(i,i)
415 temp = abs( real( a( i+j*lda ) ) )
416 IF( VALUE .LT. temp .OR. sisnan( temp ) )
417 $ VALUE = temp
418 i = j + 1
419* L(j+k,j+k)
420 temp = abs( real( a( i+j*lda ) ) )
421 IF( VALUE .LT. temp .OR. sisnan( temp ) )
422 $ VALUE = temp
423 DO i = j + 2, k - 1
424 temp = abs( a( i+j*lda ) )
425 IF( VALUE .LT. temp .OR. sisnan( temp ) )
426 $ VALUE = temp
427 END DO
428 END DO
429 j = k - 1
430 DO i = 0, k - 2
431 temp = abs( a( i+j*lda ) )
432 IF( VALUE .LT. temp .OR. sisnan( temp ) )
433 $ VALUE = temp
434 END DO
435 i = k - 1
436* -> L(i,i) is at A(i,j)
437 temp = abs( real( a( i+j*lda ) ) )
438 IF( VALUE .LT. temp .OR. sisnan( temp ) )
439 $ VALUE = temp
440 DO j = k, n - 1
441 DO i = 0, k - 1
442 temp = abs( a( i+j*lda ) )
443 IF( VALUE .LT. temp .OR. sisnan( temp ) )
444 $ VALUE = temp
445 END DO
446 END DO
447 ELSE
448* uplo = 'U'
449 DO j = 0, k - 2
450 DO i = 0, k - 1
451 temp = abs( a( i+j*lda ) )
452 IF( VALUE .LT. temp .OR. sisnan( temp ) )
453 $ VALUE = temp
454 END DO
455 END DO
456 j = k - 1
457* -> U(j,j) is at A(0,j)
458 temp = abs( real( a( 0+j*lda ) ) )
459 IF( VALUE .LT. temp .OR. sisnan( temp ) )
460 $ VALUE = temp
461 DO i = 1, k - 1
462 temp = abs( a( i+j*lda ) )
463 IF( VALUE .LT. temp .OR. sisnan( temp ) )
464 $ VALUE = temp
465 END DO
466 DO j = k, n - 1
467 DO i = 0, j - k - 1
468 temp = abs( a( i+j*lda ) )
469 IF( VALUE .LT. temp .OR. sisnan( temp ) )
470 $ VALUE = temp
471 END DO
472 i = j - k
473* -> U(i,i) at A(i,j)
474 temp = abs( real( a( i+j*lda ) ) )
475 IF( VALUE .LT. temp .OR. sisnan( temp ) )
476 $ VALUE = temp
477 i = j - k + 1
478* U(j,j)
479 temp = abs( real( a( i+j*lda ) ) )
480 IF( VALUE .LT. temp .OR. sisnan( temp ) )
481 $ VALUE = temp
482 DO i = j - k + 2, k - 1
483 temp = abs( a( i+j*lda ) )
484 IF( VALUE .LT. temp .OR. sisnan( temp ) )
485 $ VALUE = temp
486 END DO
487 END DO
488 END IF
489 END IF
490 ELSE
491* n is even & k = n/2
492 IF( ifm.EQ.1 ) THEN
493* A is n+1 by k
494 IF( ilu.EQ.1 ) THEN
495* uplo ='L'
496 j = 0
497* -> L(k,k) & j=1 -> L(0,0)
498 temp = abs( real( a( j+j*lda ) ) )
499 IF( VALUE .LT. temp .OR. sisnan( temp ) )
500 $ VALUE = temp
501 temp = abs( real( a( j+1+j*lda ) ) )
502 IF( VALUE .LT. temp .OR. sisnan( temp ) )
503 $ VALUE = temp
504 DO i = 2, n
505 temp = abs( a( i+j*lda ) )
506 IF( VALUE .LT. temp .OR. sisnan( temp ) )
507 $ VALUE = temp
508 END DO
509 DO j = 1, k - 1
510 DO i = 0, j - 1
511 temp = abs( a( i+j*lda ) )
512 IF( VALUE .LT. temp .OR. sisnan( temp ) )
513 $ VALUE = temp
514 END DO
515 i = j
516* L(k+j,k+j)
517 temp = abs( real( a( i+j*lda ) ) )
518 IF( VALUE .LT. temp .OR. sisnan( temp ) )
519 $ VALUE = temp
520 i = j + 1
521* -> L(j,j)
522 temp = abs( real( a( i+j*lda ) ) )
523 IF( VALUE .LT. temp .OR. sisnan( temp ) )
524 $ VALUE = temp
525 DO i = j + 2, n
526 temp = abs( a( i+j*lda ) )
527 IF( VALUE .LT. temp .OR. sisnan( temp ) )
528 $ VALUE = temp
529 END DO
530 END DO
531 ELSE
532* uplo = 'U'
533 DO j = 0, k - 2
534 DO i = 0, k + j - 1
535 temp = abs( a( i+j*lda ) )
536 IF( VALUE .LT. temp .OR. sisnan( temp ) )
537 $ VALUE = temp
538 END DO
539 i = k + j
540* -> U(i,i)
541 temp = abs( real( a( i+j*lda ) ) )
542 IF( VALUE .LT. temp .OR. sisnan( temp ) )
543 $ VALUE = temp
544 i = i + 1
545* =k+j+1; i -> U(j,j)
546 temp = abs( real( a( i+j*lda ) ) )
547 IF( VALUE .LT. temp .OR. sisnan( temp ) )
548 $ VALUE = temp
549 DO i = k + j + 2, n
550 temp = abs( a( i+j*lda ) )
551 IF( VALUE .LT. temp .OR. sisnan( temp ) )
552 $ VALUE = temp
553 END DO
554 END DO
555 DO i = 0, n - 2
556 temp = abs( a( i+j*lda ) )
557 IF( VALUE .LT. temp .OR. sisnan( temp ) )
558 $ VALUE = temp
559* j=k-1
560 END DO
561* i=n-1 -> U(n-1,n-1)
562 temp = abs( real( a( i+j*lda ) ) )
563 IF( VALUE .LT. temp .OR. sisnan( temp ) )
564 $ VALUE = temp
565 i = n
566* -> U(k-1,k-1)
567 temp = abs( real( a( i+j*lda ) ) )
568 IF( VALUE .LT. temp .OR. sisnan( temp ) )
569 $ VALUE = temp
570 END IF
571 ELSE
572* xpose case; A is k by n+1
573 IF( ilu.EQ.1 ) THEN
574* uplo ='L'
575 j = 0
576* -> L(k,k) at A(0,0)
577 temp = abs( real( a( j+j*lda ) ) )
578 IF( VALUE .LT. temp .OR. sisnan( temp ) )
579 $ VALUE = temp
580 DO i = 1, k - 1
581 temp = abs( a( i+j*lda ) )
582 IF( VALUE .LT. temp .OR. sisnan( temp ) )
583 $ VALUE = temp
584 END DO
585 DO j = 1, k - 1
586 DO i = 0, j - 2
587 temp = abs( a( i+j*lda ) )
588 IF( VALUE .LT. temp .OR. sisnan( temp ) )
589 $ VALUE = temp
590 END DO
591 i = j - 1
592* L(i,i)
593 temp = abs( real( a( i+j*lda ) ) )
594 IF( VALUE .LT. temp .OR. sisnan( temp ) )
595 $ VALUE = temp
596 i = j
597* L(j+k,j+k)
598 temp = abs( real( a( i+j*lda ) ) )
599 IF( VALUE .LT. temp .OR. sisnan( temp ) )
600 $ VALUE = temp
601 DO i = j + 1, k - 1
602 temp = abs( a( i+j*lda ) )
603 IF( VALUE .LT. temp .OR. sisnan( temp ) )
604 $ VALUE = temp
605 END DO
606 END DO
607 j = k
608 DO i = 0, k - 2
609 temp = abs( a( i+j*lda ) )
610 IF( VALUE .LT. temp .OR. sisnan( temp ) )
611 $ VALUE = temp
612 END DO
613 i = k - 1
614* -> L(i,i) is at A(i,j)
615 temp = abs( real( a( i+j*lda ) ) )
616 IF( VALUE .LT. temp .OR. sisnan( temp ) )
617 $ VALUE = temp
618 DO j = k + 1, n
619 DO i = 0, k - 1
620 temp = abs( a( i+j*lda ) )
621 IF( VALUE .LT. temp .OR. sisnan( temp ) )
622 $ VALUE = temp
623 END DO
624 END DO
625 ELSE
626* uplo = 'U'
627 DO j = 0, k - 1
628 DO i = 0, k - 1
629 temp = abs( a( i+j*lda ) )
630 IF( VALUE .LT. temp .OR. sisnan( temp ) )
631 $ VALUE = temp
632 END DO
633 END DO
634 j = k
635* -> U(j,j) is at A(0,j)
636 temp = abs( real( a( 0+j*lda ) ) )
637 IF( VALUE .LT. temp .OR. sisnan( temp ) )
638 $ VALUE = temp
639 DO i = 1, k - 1
640 temp = abs( a( i+j*lda ) )
641 IF( VALUE .LT. temp .OR. sisnan( temp ) )
642 $ VALUE = temp
643 END DO
644 DO j = k + 1, n - 1
645 DO i = 0, j - k - 2
646 temp = abs( a( i+j*lda ) )
647 IF( VALUE .LT. temp .OR. sisnan( temp ) )
648 $ VALUE = temp
649 END DO
650 i = j - k - 1
651* -> U(i,i) at A(i,j)
652 temp = abs( real( a( i+j*lda ) ) )
653 IF( VALUE .LT. temp .OR. sisnan( temp ) )
654 $ VALUE = temp
655 i = j - k
656* U(j,j)
657 temp = abs( real( a( i+j*lda ) ) )
658 IF( VALUE .LT. temp .OR. sisnan( temp ) )
659 $ VALUE = temp
660 DO i = j - k + 1, k - 1
661 temp = abs( a( i+j*lda ) )
662 IF( VALUE .LT. temp .OR. sisnan( temp ) )
663 $ VALUE = temp
664 END DO
665 END DO
666 j = n
667 DO i = 0, k - 2
668 temp = abs( a( i+j*lda ) )
669 IF( VALUE .LT. temp .OR. sisnan( temp ) )
670 $ VALUE = temp
671 END DO
672 i = k - 1
673* U(k,k) at A(i,j)
674 temp = abs( real( a( i+j*lda ) ) )
675 IF( VALUE .LT. temp .OR. sisnan( temp ) )
676 $ VALUE = temp
677 END IF
678 END IF
679 END IF
680 ELSE IF( ( lsame( norm, 'I' ) ) .OR. ( lsame( norm, 'O' ) ) .OR.
681 $ ( norm.EQ.'1' ) ) THEN
682*
683* Find normI(A) ( = norm1(A), since A is Hermitian).
684*
685.EQ. IF( IFM1 ) THEN
686* A is 'N'
687 K = N / 2
688.EQ. IF( NOE1 ) THEN
689* n is odd & A is n by (n+1)/2
690.EQ. IF( ILU0 ) THEN
691* uplo = 'U'
692 DO I = 0, K - 1
693 WORK( I ) = ZERO
694 END DO
695 DO J = 0, K
696 S = ZERO
697 DO I = 0, K + J - 1
698 AA = ABS( A( I+J*LDA ) )
699* -> A(i,j+k)
700 S = S + AA
701 WORK( I ) = WORK( I ) + AA
702 END DO
703 AA = ABS( REAL( A( I+J*LDA ) ) )
704* -> A(j+k,j+k)
705 WORK( J+K ) = S + AA
706.EQ. IF( IK+K )
707 $ GO TO 10
708 I = I + 1
709 AA = ABS( REAL( A( I+J*LDA ) ) )
710* -> A(j,j)
711 WORK( J ) = WORK( J ) + AA
712 S = ZERO
713 DO L = J + 1, K - 1
714 I = I + 1
715 AA = ABS( A( I+J*LDA ) )
716* -> A(l,j)
717 S = S + AA
718 WORK( L ) = WORK( L ) + AA
719 END DO
720 WORK( J ) = WORK( J ) + S
721 END DO
722 10 CONTINUE
723 VALUE = WORK( 0 )
724 DO I = 1, N-1
725 TEMP = WORK( I )
726.LT..OR. IF( VALUE TEMP SISNAN( TEMP ) )
727 $ VALUE = TEMP
728 END DO
729 ELSE
730* ilu = 1 & uplo = 'L'
731 K = K + 1
732* k=(n+1)/2 for n odd and ilu=1
733 DO I = K, N - 1
734 WORK( I ) = ZERO
735 END DO
736 DO J = K - 1, 0, -1
737 S = ZERO
738 DO I = 0, J - 2
739 AA = ABS( A( I+J*LDA ) )
740* -> A(j+k,i+k)
741 S = S + AA
742 WORK( I+K ) = WORK( I+K ) + AA
743 END DO
744.GT. IF( J0 ) THEN
745 AA = ABS( REAL( A( I+J*LDA ) ) )
746* -> A(j+k,j+k)
747 S = S + AA
748 WORK( I+K ) = WORK( I+K ) + S
749* i=j
750 I = I + 1
751 END IF
752 AA = ABS( REAL( A( I+J*LDA ) ) )
753* -> A(j,j)
754 WORK( J ) = AA
755 S = ZERO
756 DO L = J + 1, N - 1
757 I = I + 1
758 AA = ABS( A( I+J*LDA ) )
759* -> A(l,j)
760 S = S + AA
761 WORK( L ) = WORK( L ) + AA
762 END DO
763 WORK( J ) = WORK( J ) + S
764 END DO
765 VALUE = WORK( 0 )
766 DO I = 1, N-1
767 TEMP = WORK( I )
768.LT..OR. IF( VALUE TEMP SISNAN( TEMP ) )
769 $ VALUE = TEMP
770 END DO
771 END IF
772 ELSE
773* n is even & A is n+1 by k = n/2
774.EQ. IF( ILU0 ) THEN
775* uplo = 'U'
776 DO I = 0, K - 1
777 WORK( I ) = ZERO
778 END DO
779 DO J = 0, K - 1
780 S = ZERO
781 DO I = 0, K + J - 1
782 AA = ABS( A( I+J*LDA ) )
783* -> A(i,j+k)
784 S = S + AA
785 WORK( I ) = WORK( I ) + AA
786 END DO
787 AA = ABS( REAL( A( I+J*LDA ) ) )
788* -> A(j+k,j+k)
789 WORK( J+K ) = S + AA
790 I = I + 1
791 AA = ABS( REAL( A( I+J*LDA ) ) )
792* -> A(j,j)
793 WORK( J ) = WORK( J ) + AA
794 S = ZERO
795 DO L = J + 1, K - 1
796 I = I + 1
797 AA = ABS( A( I+J*LDA ) )
798* -> A(l,j)
799 S = S + AA
800 WORK( L ) = WORK( L ) + AA
801 END DO
802 WORK( J ) = WORK( J ) + S
803 END DO
804 VALUE = WORK( 0 )
805 DO I = 1, N-1
806 TEMP = WORK( I )
807.LT..OR. IF( VALUE TEMP SISNAN( TEMP ) )
808 $ VALUE = TEMP
809 END DO
810 ELSE
811* ilu = 1 & uplo = 'L'
812 DO I = K, N - 1
813 WORK( I ) = ZERO
814 END DO
815 DO J = K - 1, 0, -1
816 S = ZERO
817 DO I = 0, J - 1
818 AA = ABS( A( I+J*LDA ) )
819* -> A(j+k,i+k)
820 S = S + AA
821 WORK( I+K ) = WORK( I+K ) + AA
822 END DO
823 AA = ABS( REAL( A( I+J*LDA ) ) )
824* -> A(j+k,j+k)
825 S = S + AA
826 WORK( I+K ) = WORK( I+K ) + S
827* i=j
828 I = I + 1
829 AA = ABS( REAL( A( I+J*LDA ) ) )
830* -> A(j,j)
831 WORK( J ) = AA
832 S = ZERO
833 DO L = J + 1, N - 1
834 I = I + 1
835 AA = ABS( A( I+J*LDA ) )
836* -> A(l,j)
837 S = S + AA
838 WORK( L ) = WORK( L ) + AA
839 END DO
840 WORK( J ) = WORK( J ) + S
841 END DO
842 VALUE = WORK( 0 )
843 DO I = 1, N-1
844 TEMP = WORK( I )
845.LT..OR. IF( VALUE TEMP SISNAN( TEMP ) )
846 $ VALUE = TEMP
847 END DO
848 END IF
849 END IF
850 ELSE
851* ifm=0
852 K = N / 2
853.EQ. IF( NOE1 ) THEN
854* n is odd & A is (n+1)/2 by n
855.EQ. IF( ILU0 ) THEN
856* uplo = 'U'
857 N1 = K
858* n/2
859 K = K + 1
860* k is the row size and lda
861 DO I = N1, N - 1
862 WORK( I ) = ZERO
863 END DO
864 DO J = 0, N1 - 1
865 S = ZERO
866 DO I = 0, K - 1
867 AA = ABS( A( I+J*LDA ) )
868* A(j,n1+i)
869 WORK( I+N1 ) = WORK( I+N1 ) + AA
870 S = S + AA
871 END DO
872 WORK( J ) = S
873 END DO
874* j=n1=k-1 is special
875 S = ABS( REAL( A( 0+J*LDA ) ) )
876* A(k-1,k-1)
877 DO I = 1, K - 1
878 AA = ABS( A( I+J*LDA ) )
879* A(k-1,i+n1)
880 WORK( I+N1 ) = WORK( I+N1 ) + AA
881 S = S + AA
882 END DO
883 WORK( J ) = WORK( J ) + S
884 DO J = K, N - 1
885 S = ZERO
886 DO I = 0, J - K - 1
887 AA = ABS( A( I+J*LDA ) )
888* A(i,j-k)
889 WORK( I ) = WORK( I ) + AA
890 S = S + AA
891 END DO
892* i=j-k
893 AA = ABS( REAL( A( I+J*LDA ) ) )
894* A(j-k,j-k)
895 S = S + AA
896 WORK( J-K ) = WORK( J-K ) + S
897 I = I + 1
898 S = ABS( REAL( A( I+J*LDA ) ) )
899* A(j,j)
900 DO L = J + 1, N - 1
901 I = I + 1
902 AA = ABS( A( I+J*LDA ) )
903* A(j,l)
904 WORK( L ) = WORK( L ) + AA
905 S = S + AA
906 END DO
907 WORK( J ) = WORK( J ) + S
908 END DO
909 VALUE = WORK( 0 )
910 DO I = 1, N-1
911 TEMP = WORK( I )
912.LT..OR. IF( VALUE TEMP SISNAN( TEMP ) )
913 $ VALUE = TEMP
914 END DO
915 ELSE
916* ilu=1 & uplo = 'L'
917 K = K + 1
918* k=(n+1)/2 for n odd and ilu=1
919 DO I = K, N - 1
920 WORK( I ) = ZERO
921 END DO
922 DO J = 0, K - 2
923* process
924 S = ZERO
925 DO I = 0, J - 1
926 AA = ABS( A( I+J*LDA ) )
927* A(j,i)
928 WORK( I ) = WORK( I ) + AA
929 S = S + AA
930 END DO
931 AA = ABS( REAL( A( I+J*LDA ) ) )
932* i=j so process of A(j,j)
933 S = S + AA
934 WORK( J ) = S
935* is initialised here
936 I = I + 1
937* i=j process A(j+k,j+k)
938 AA = ABS( REAL( A( I+J*LDA ) ) )
939 S = AA
940 DO L = K + J + 1, N - 1
941 I = I + 1
942 AA = ABS( A( I+J*LDA ) )
943* A(l,k+j)
944 S = S + AA
945 WORK( L ) = WORK( L ) + AA
946 END DO
947 WORK( K+J ) = WORK( K+J ) + S
948 END DO
949* j=k-1 is special :process col A(k-1,0:k-1)
950 S = ZERO
951 DO I = 0, K - 2
952 AA = ABS( A( I+J*LDA ) )
953* A(k,i)
954 WORK( I ) = WORK( I ) + AA
955 S = S + AA
956 END DO
957* i=k-1
958 AA = ABS( REAL( A( I+J*LDA ) ) )
959* A(k-1,k-1)
960 S = S + AA
961 WORK( I ) = S
962* done with col j=k+1
963 DO J = K, N - 1
964* process col j of A = A(j,0:k-1)
965 S = ZERO
966 DO I = 0, K - 1
967 AA = ABS( A( I+J*LDA ) )
968* A(j,i)
969 WORK( I ) = WORK( I ) + AA
970 S = S + AA
971 END DO
972 WORK( J ) = WORK( J ) + S
973 END DO
974 VALUE = WORK( 0 )
975 DO I = 1, N-1
976 TEMP = WORK( I )
977.LT..OR. IF( VALUE TEMP SISNAN( TEMP ) )
978 $ VALUE = TEMP
979 END DO
980 END IF
981 ELSE
982* n is even & A is k=n/2 by n+1
983.EQ. IF( ILU0 ) THEN
984* uplo = 'U'
985 DO I = K, N - 1
986 WORK( I ) = ZERO
987 END DO
988 DO J = 0, K - 1
989 S = ZERO
990 DO I = 0, K - 1
991 AA = ABS( A( I+J*LDA ) )
992* A(j,i+k)
993 WORK( I+K ) = WORK( I+K ) + AA
994 S = S + AA
995 END DO
996 WORK( J ) = S
997 END DO
998* j=k
999 AA = ABS( REAL( A( 0+J*LDA ) ) )
1000* A(k,k)
1001 S = AA
1002 DO I = 1, K - 1
1003 AA = ABS( A( I+J*LDA ) )
1004* A(k,k+i)
1005 WORK( I+K ) = WORK( I+K ) + AA
1006 S = S + AA
1007 END DO
1008 WORK( J ) = WORK( J ) + S
1009 DO J = K + 1, N - 1
1010 S = ZERO
1011 DO I = 0, J - 2 - K
1012 AA = ABS( A( I+J*LDA ) )
1013* A(i,j-k-1)
1014 WORK( I ) = WORK( I ) + AA
1015 S = S + AA
1016 END DO
1017* i=j-1-k
1018 AA = ABS( REAL( A( I+J*LDA ) ) )
1019* A(j-k-1,j-k-1)
1020 S = S + AA
1021 WORK( J-K-1 ) = WORK( J-K-1 ) + S
1022 I = I + 1
1023 AA = ABS( REAL( A( I+J*LDA ) ) )
1024* A(j,j)
1025 S = AA
1026 DO L = J + 1, N - 1
1027 I = I + 1
1028 AA = ABS( A( I+J*LDA ) )
1029* A(j,l)
1030 WORK( L ) = WORK( L ) + AA
1031 S = S + AA
1032 END DO
1033 WORK( J ) = WORK( J ) + S
1034 END DO
1035* j=n
1036 S = ZERO
1037 DO I = 0, K - 2
1038 AA = ABS( A( I+J*LDA ) )
1039* A(i,k-1)
1040 WORK( I ) = WORK( I ) + AA
1041 S = S + AA
1042 END DO
1043* i=k-1
1044 AA = ABS( REAL( A( I+J*LDA ) ) )
1045* A(k-1,k-1)
1046 S = S + AA
1047 WORK( I ) = WORK( I ) + S
1048 VALUE = WORK( 0 )
1049 DO I = 1, N-1
1050 TEMP = WORK( I )
1051.LT..OR. IF( VALUE TEMP SISNAN( TEMP ) )
1052 $ VALUE = TEMP
1053 END DO
1054 ELSE
1055* ilu=1 & uplo = 'L'
1056 DO I = K, N - 1
1057 WORK( I ) = ZERO
1058 END DO
1059* j=0 is special :process col A(k:n-1,k)
1060 S = ABS( REAL( A( 0 ) ) )
1061* A(k,k)
1062 DO I = 1, K - 1
1063 AA = ABS( A( I ) )
1064* A(k+i,k)
1065 WORK( I+K ) = WORK( I+K ) + AA
1066 S = S + AA
1067 END DO
1068 WORK( K ) = WORK( K ) + S
1069 DO J = 1, K - 1
1070* process
1071 S = ZERO
1072 DO I = 0, J - 2
1073 AA = ABS( A( I+J*LDA ) )
1074* A(j-1,i)
1075 WORK( I ) = WORK( I ) + AA
1076 S = S + AA
1077 END DO
1078 AA = ABS( REAL( A( I+J*LDA ) ) )
1079* i=j-1 so process of A(j-1,j-1)
1080 S = S + AA
1081 WORK( J-1 ) = S
1082* is initialised here
1083 I = I + 1
1084* i=j process A(j+k,j+k)
1085 AA = ABS( REAL( A( I+J*LDA ) ) )
1086 S = AA
1087 DO L = K + J + 1, N - 1
1088 I = I + 1
1089 AA = ABS( A( I+J*LDA ) )
1090* A(l,k+j)
1091 S = S + AA
1092 WORK( L ) = WORK( L ) + AA
1093 END DO
1094 WORK( K+J ) = WORK( K+J ) + S
1095 END DO
1096* j=k is special :process col A(k,0:k-1)
1097 S = ZERO
1098 DO I = 0, K - 2
1099 AA = ABS( A( I+J*LDA ) )
1100* A(k,i)
1101 WORK( I ) = WORK( I ) + AA
1102 S = S + AA
1103 END DO
1104*
1105* i=k-1
1106 AA = ABS( REAL( A( I+J*LDA ) ) )
1107* A(k-1,k-1)
1108 S = S + AA
1109 WORK( I ) = S
1110* done with col j=k+1
1111 DO J = K + 1, N
1112*
1113* process col j-1 of A = A(j-1,0:k-1)
1114 S = ZERO
1115 DO I = 0, K - 1
1116 AA = ABS( A( I+J*LDA ) )
1117* A(j-1,i)
1118 WORK( I ) = WORK( I ) + AA
1119 S = S + AA
1120 END DO
1121 WORK( J-1 ) = WORK( J-1 ) + S
1122 END DO
1123 VALUE = WORK( 0 )
1124 DO I = 1, N-1
1125 TEMP = WORK( I )
1126.LT..OR. IF( VALUE TEMP SISNAN( TEMP ) )
1127 $ VALUE = TEMP
1128 END DO
1129 END IF
1130 END IF
1131 END IF
1132 ELSE IF( ( LSAME( NORM, 'f.OR.' ) ) ( LSAME( NORM, 'e' ) ) ) THEN
1133*
1134* Find normF(A).
1135*
1136 K = ( N+1 ) / 2
1137 SCALE = ZERO
1138 S = ONE
1139.EQ. IF( NOE1 ) THEN
1140* n is odd
1141.EQ. IF( IFM1 ) THEN
1142* A is normal & A is n by k
1143.EQ. IF( ILU0 ) THEN
1144* A is upper
1145 DO J = 0, K - 3
1146 CALL CLASSQ( K-J-2, A( K+J+1+J*LDA ), 1, SCALE, S )
1147* L at A(k,0)
1148 END DO
1149 DO J = 0, K - 1
1150 CALL CLASSQ( K+J-1, A( 0+J*LDA ), 1, SCALE, S )
1151* trap U at A(0,0)
1152 END DO
1153 S = S + S
1154* double s for the off diagonal elements
1155 L = K - 1
1156* -> U(k,k) at A(k-1,0)
1157 DO I = 0, K - 2
1158 AA = REAL( A( L ) )
1159* U(k+i,k+i)
1160.NE. IF( AAZERO ) THEN
1161.LT. IF( SCALEAA ) THEN
1162 S = ONE + S*( SCALE / AA )**2
1163 SCALE = AA
1164 ELSE
1165 S = S + ( AA / SCALE )**2
1166 END IF
1167 END IF
1168 AA = REAL( A( L+1 ) )
1169* U(i,i)
1170.NE. IF( AAZERO ) THEN
1171.LT. IF( SCALEAA ) THEN
1172 S = ONE + S*( SCALE / AA )**2
1173 SCALE = AA
1174 ELSE
1175 S = S + ( AA / SCALE )**2
1176 END IF
1177 END IF
1178 L = L + LDA + 1
1179 END DO
1180 AA = REAL( A( L ) )
1181* U(n-1,n-1)
1182.NE. IF( AAZERO ) THEN
1183.LT. IF( SCALEAA ) THEN
1184 S = ONE + S*( SCALE / AA )**2
1185 SCALE = AA
1186 ELSE
1187 S = S + ( AA / SCALE )**2
1188 END IF
1189 END IF
1190 ELSE
1191* ilu=1 & A is lower
1192 DO J = 0, K - 1
1193 CALL CLASSQ( N-J-1, A( J+1+J*LDA ), 1, SCALE, S )
1194* trap L at A(0,0)
1195 END DO
1196 DO J = 1, K - 2
1197 CALL CLASSQ( J, A( 0+( 1+J )*LDA ), 1, SCALE, S )
1198* U at A(0,1)
1199 END DO
1200 S = S + S
1201* double s for the off diagonal elements
1202 AA = REAL( A( 0 ) )
1203* L(0,0) at A(0,0)
1204.NE. IF( AAZERO ) THEN
1205.LT. IF( SCALEAA ) THEN
1206 S = ONE + S*( SCALE / AA )**2
1207 SCALE = AA
1208 ELSE
1209 S = S + ( AA / SCALE )**2
1210 END IF
1211 END IF
1212 L = LDA
1213* -> L(k,k) at A(0,1)
1214 DO I = 1, K - 1
1215 AA = REAL( A( L ) )
1216* L(k-1+i,k-1+i)
1217.NE. IF( AAZERO ) THEN
1218.LT. IF( SCALEAA ) THEN
1219 S = ONE + S*( SCALE / AA )**2
1220 SCALE = AA
1221 ELSE
1222 S = S + ( AA / SCALE )**2
1223 END IF
1224 END IF
1225 AA = REAL( A( L+1 ) )
1226* L(i,i)
1227.NE. IF( AAZERO ) THEN
1228.LT. IF( SCALEAA ) THEN
1229 S = ONE + S*( SCALE / AA )**2
1230 SCALE = AA
1231 ELSE
1232 S = S + ( AA / SCALE )**2
1233 END IF
1234 END IF
1235 L = L + LDA + 1
1236 END DO
1237 END IF
1238 ELSE
1239* A is xpose & A is k by n
1240.EQ. IF( ILU0 ) THEN
1241* A**H is upper
1242 DO J = 1, K - 2
1243 CALL CLASSQ( J, A( 0+( K+J )*LDA ), 1, SCALE, S )
1244* U at A(0,k)
1245 END DO
1246 DO J = 0, K - 2
1247 CALL CLASSQ( K, A( 0+J*LDA ), 1, SCALE, S )
1248* k by k-1 rect. at A(0,0)
1249 END DO
1250 DO J = 0, K - 2
1251 CALL CLASSQ( K-J-1, A( J+1+( J+K-1 )*LDA ), 1,
1252 $ SCALE, S )
1253* L at A(0,k-1)
1254 END DO
1255 S = S + S
1256* double s for the off diagonal elements
1257 L = 0 + K*LDA - LDA
1258* -> U(k-1,k-1) at A(0,k-1)
1259 AA = REAL( A( L ) )
1260* U(k-1,k-1)
1261.NE. IF( AAZERO ) THEN
1262.LT. IF( SCALEAA ) THEN
1263 S = ONE + S*( SCALE / AA )**2
1264 SCALE = AA
1265 ELSE
1266 S = S + ( AA / SCALE )**2
1267 END IF
1268 END IF
1269 L = L + LDA
1270* -> U(0,0) at A(0,k)
1271 DO J = K, N - 1
1272 AA = REAL( A( L ) )
1273* -> U(j-k,j-k)
1274.NE. IF( AAZERO ) THEN
1275.LT. IF( SCALEAA ) THEN
1276 S = ONE + S*( SCALE / AA )**2
1277 SCALE = AA
1278 ELSE
1279 S = S + ( AA / SCALE )**2
1280 END IF
1281 END IF
1282 AA = REAL( A( L+1 ) )
1283* -> U(j,j)
1284.NE. IF( AAZERO ) THEN
1285.LT. IF( SCALEAA ) THEN
1286 S = ONE + S*( SCALE / AA )**2
1287 SCALE = AA
1288 ELSE
1289 S = S + ( AA / SCALE )**2
1290 END IF
1291 END IF
1292 L = L + LDA + 1
1293 END DO
1294 ELSE
1295* A**H is lower
1296 DO J = 1, K - 1
1297 CALL CLASSQ( J, A( 0+J*LDA ), 1, SCALE, S )
1298* U at A(0,0)
1299 END DO
1300 DO J = K, N - 1
1301 CALL CLASSQ( K, A( 0+J*LDA ), 1, SCALE, S )
1302* k by k-1 rect. at A(0,k)
1303 END DO
1304 DO J = 0, K - 3
1305 CALL CLASSQ( K-J-2, A( J+2+J*LDA ), 1, SCALE, S )
1306* L at A(1,0)
1307 END DO
1308 S = S + S
1309* double s for the off diagonal elements
1310 L = 0
1311* -> L(0,0) at A(0,0)
1312 DO I = 0, K - 2
1313 AA = REAL( A( L ) )
1314* L(i,i)
1315.NE. IF( AAZERO ) THEN
1316.LT. IF( SCALEAA ) THEN
1317 S = ONE + S*( SCALE / AA )**2
1318 SCALE = AA
1319 ELSE
1320 S = S + ( AA / SCALE )**2
1321 END IF
1322 END IF
1323 AA = REAL( A( L+1 ) )
1324* L(k+i,k+i)
1325.NE. IF( AAZERO ) THEN
1326.LT. IF( SCALEAA ) THEN
1327 S = ONE + S*( SCALE / AA )**2
1328 SCALE = AA
1329 ELSE
1330 S = S + ( AA / SCALE )**2
1331 END IF
1332 END IF
1333 L = L + LDA + 1
1334 END DO
1335* L-> k-1 + (k-1)*lda or L(k-1,k-1) at A(k-1,k-1)
1336 AA = REAL( A( L ) )
1337* L(k-1,k-1) at A(k-1,k-1)
1338.NE. IF( AAZERO ) THEN
1339.LT. IF( SCALEAA ) THEN
1340 S = ONE + S*( SCALE / AA )**2
1341 SCALE = AA
1342 ELSE
1343 S = S + ( AA / SCALE )**2
1344 END IF
1345 END IF
1346 END IF
1347 END IF
1348 ELSE
1349* n is even
1350.EQ. IF( IFM1 ) THEN
1351* A is normal
1352.EQ. IF( ILU0 ) THEN
1353* A is upper
1354 DO J = 0, K - 2
1355 CALL CLASSQ( K-J-1, A( K+J+2+J*LDA ), 1, SCALE, S )
1356* L at A(k+1,0)
1357 END DO
1358 DO J = 0, K - 1
1359 CALL CLASSQ( K+J, A( 0+J*LDA ), 1, SCALE, S )
1360* trap U at A(0,0)
1361 END DO
1362 S = S + S
1363* double s for the off diagonal elements
1364 L = K
1365* -> U(k,k) at A(k,0)
1366 DO I = 0, K - 1
1367 AA = REAL( A( L ) )
1368* U(k+i,k+i)
1369.NE. IF( AAZERO ) THEN
1370.LT. IF( SCALEAA ) THEN
1371 S = ONE + S*( SCALE / AA )**2
1372 SCALE = AA
1373 ELSE
1374 S = S + ( AA / SCALE )**2
1375 END IF
1376 END IF
1377 AA = REAL( A( L+1 ) )
1378* U(i,i)
1379.NE. IF( AAZERO ) THEN
1380.LT. IF( SCALEAA ) THEN
1381 S = ONE + S*( SCALE / AA )**2
1382 SCALE = AA
1383 ELSE
1384 S = S + ( AA / SCALE )**2
1385 END IF
1386 END IF
1387 L = L + LDA + 1
1388 END DO
1389 ELSE
1390* ilu=1 & A is lower
1391 DO J = 0, K - 1
1392 CALL CLASSQ( N-J-1, A( J+2+J*LDA ), 1, SCALE, S )
1393* trap L at A(1,0)
1394 END DO
1395 DO J = 1, K - 1
1396 CALL CLASSQ( J, A( 0+J*LDA ), 1, SCALE, S )
1397* U at A(0,0)
1398 END DO
1399 S = S + S
1400* double s for the off diagonal elements
1401 L = 0
1402* -> L(k,k) at A(0,0)
1403 DO I = 0, K - 1
1404 AA = REAL( A( L ) )
1405* L(k-1+i,k-1+i)
1406.NE. IF( AAZERO ) THEN
1407.LT. IF( SCALEAA ) THEN
1408 S = ONE + S*( SCALE / AA )**2
1409 SCALE = AA
1410 ELSE
1411 S = S + ( AA / SCALE )**2
1412 END IF
1413 END IF
1414 AA = REAL( A( L+1 ) )
1415* L(i,i)
1416.NE. IF( AAZERO ) THEN
1417.LT. IF( SCALEAA ) THEN
1418 S = ONE + S*( SCALE / AA )**2
1419 SCALE = AA
1420 ELSE
1421 S = S + ( AA / SCALE )**2
1422 END IF
1423 END IF
1424 L = L + LDA + 1
1425 END DO
1426 END IF
1427 ELSE
1428* A is xpose
1429.EQ. IF( ILU0 ) THEN
1430* A**H is upper
1431 DO J = 1, K - 1
1432 CALL CLASSQ( J, A( 0+( K+1+J )*LDA ), 1, SCALE, S )
1433* U at A(0,k+1)
1434 END DO
1435 DO J = 0, K - 1
1436 CALL CLASSQ( K, A( 0+J*LDA ), 1, SCALE, S )
1437* k by k rect. at A(0,0)
1438 END DO
1439 DO J = 0, K - 2
1440 CALL CLASSQ( K-J-1, A( J+1+( J+K )*LDA ), 1, SCALE,
1441 $ S )
1442* L at A(0,k)
1443 END DO
1444 S = S + S
1445* double s for the off diagonal elements
1446 L = 0 + K*LDA
1447* -> U(k,k) at A(0,k)
1448 AA = REAL( A( L ) )
1449* U(k,k)
1450.NE. IF( AAZERO ) THEN
1451.LT. IF( SCALEAA ) THEN
1452 S = ONE + S*( SCALE / AA )**2
1453 SCALE = AA
1454 ELSE
1455 S = S + ( AA / SCALE )**2
1456 END IF
1457 END IF
1458 L = L + LDA
1459* -> U(0,0) at A(0,k+1)
1460 DO J = K + 1, N - 1
1461 AA = REAL( A( L ) )
1462* -> U(j-k-1,j-k-1)
1463.NE. IF( AAZERO ) THEN
1464.LT. IF( SCALEAA ) THEN
1465 S = ONE + S*( SCALE / AA )**2
1466 SCALE = AA
1467 ELSE
1468 S = S + ( AA / SCALE )**2
1469 END IF
1470 END IF
1471 AA = REAL( A( L+1 ) )
1472* -> U(j,j)
1473.NE. IF( AAZERO ) THEN
1474.LT. IF( SCALEAA ) THEN
1475 S = ONE + S*( SCALE / AA )**2
1476 SCALE = AA
1477 ELSE
1478 S = S + ( AA / SCALE )**2
1479 END IF
1480 END IF
1481 L = L + LDA + 1
1482 END DO
1483* L=k-1+n*lda
1484* -> U(k-1,k-1) at A(k-1,n)
1485 AA = REAL( A( L ) )
1486* U(k,k)
1487.NE. IF( AAZERO ) THEN
1488.LT. IF( SCALEAA ) THEN
1489 S = ONE + S*( SCALE / AA )**2
1490 SCALE = AA
1491 ELSE
1492 S = S + ( AA / SCALE )**2
1493 END IF
1494 END IF
1495 ELSE
1496* A**H is lower
1497 DO J = 1, K - 1
1498 CALL CLASSQ( J, A( 0+( J+1 )*LDA ), 1, SCALE, S )
1499* U at A(0,1)
1500 END DO
1501 DO J = K + 1, N
1502 CALL CLASSQ( K, A( 0+J*LDA ), 1, SCALE, S )
1503* k by k rect. at A(0,k+1)
1504 END DO
1505 DO J = 0, K - 2
1506 CALL CLASSQ( K-J-1, A( J+1+J*LDA ), 1, SCALE, S )
1507* L at A(0,0)
1508 END DO
1509 S = S + S
1510* double s for the off diagonal elements
1511 L = 0
1512* -> L(k,k) at A(0,0)
1513 AA = REAL( A( L ) )
1514* L(k,k) at A(0,0)
1515.NE. IF( AAZERO ) THEN
1516.LT. IF( SCALEAA ) THEN
1517 S = ONE + S*( SCALE / AA )**2
1518 SCALE = AA
1519 ELSE
1520 S = S + ( AA / SCALE )**2
1521 END IF
1522 END IF
1523 L = LDA
1524* -> L(0,0) at A(0,1)
1525 DO I = 0, K - 2
1526 AA = REAL( A( L ) )
1527* L(i,i)
1528.NE. IF( AAZERO ) THEN
1529.LT. IF( SCALEAA ) THEN
1530 S = ONE + S*( SCALE / AA )**2
1531 SCALE = AA
1532 ELSE
1533 S = S + ( AA / SCALE )**2
1534 END IF
1535 END IF
1536 AA = REAL( A( L+1 ) )
1537* L(k+i+1,k+i+1)
1538.NE. IF( AAZERO ) THEN
1539.LT. IF( SCALEAA ) THEN
1540 S = ONE + S*( SCALE / AA )**2
1541 SCALE = AA
1542 ELSE
1543 S = S + ( AA / SCALE )**2
1544 END IF
1545 END IF
1546 L = L + LDA + 1
1547 END DO
1548* L-> k - 1 + k*lda or L(k-1,k-1) at A(k-1,k)
1549 AA = REAL( A( L ) )
1550* L(k-1,k-1) at A(k-1,k)
1551.NE. IF( AAZERO ) THEN
1552.LT. IF( SCALEAA ) THEN
1553 S = ONE + S*( SCALE / AA )**2
1554 SCALE = AA
1555 ELSE
1556 S = S + ( AA / SCALE )**2
1557 END IF
1558 END IF
1559 END IF
1560 END IF
1561 END IF
1562 VALUE = SCALE*SQRT( S )
1563 END IF
1564*
1565 CLANHF = VALUE
1566 RETURN
1567*
1568* End of CLANHF
1569*
1570 END
norm
norm(diag(diag(diag(inv(mat))) -id.SOL), 2) % destroy mumps instance id.JOB
sisnan
logical function sisnan(sin)
SISNAN tests input for NaN.
Definition sisnan.f:59
classq
subroutine classq(n, x, incx, scl, sumsq)
CLASSQ updates a sum of squares represented in scaled form.
Definition classq.f90:137
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:53
clanhf
real function clanhf(norm, transr, uplo, n, a, work)
CLANHF returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition clanhf.f:246