LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ clanhf()

 real function clanhf ( character NORM, character TRANSR, character UPLO, integer N, complex, dimension( 0: * ) A, real, dimension( 0: * ) WORK )

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.

Purpose:
CLANHF  returns the value of the one norm,  or the Frobenius norm, or
the  infinity norm,  or the  element of  largest absolute value  of a
complex Hermitian matrix A in RFP format.
Returns
CLANHF
CLANHF = ( max(abs(A(i,j))), NORM = 'M' or 'm'
(
( norm1(A),         NORM = '1', 'O' or 'o'
(
( normI(A),         NORM = 'I' or 'i'
(
( normF(A),         NORM = 'F', 'f', 'E' or 'e'

where  norm1  denotes the  one norm of a matrix (maximum column sum),
normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
normF  denotes the  Frobenius norm of a matrix (square root of sum of
squares).  Note that  max(abs(A(i,j)))  is not a  matrix norm.
Parameters
 [in] NORM NORM is CHARACTER Specifies the value to be returned in CLANHF as described above. [in] TRANSR TRANSR is CHARACTER Specifies whether the RFP format of A is normal or conjugate-transposed format. = 'N': RFP format is Normal = 'C': RFP format is Conjugate-transposed [in] UPLO UPLO is CHARACTER On entry, UPLO specifies whether the RFP matrix A came from an upper or lower triangular matrix as follows: UPLO = 'U' or 'u' RFP A came from an upper triangular matrix UPLO = 'L' or 'l' RFP A came from a lower triangular matrix [in] N N is INTEGER The order of the matrix A. N >= 0. When N = 0, CLANHF is set to zero. [in] A A is COMPLEX array, dimension ( N*(N+1)/2 ); On entry, the matrix A in RFP Format. RFP Format is described by TRANSR, UPLO and N as follows: If TRANSR='N' then RFP A is (0:N,0:K-1) when N is even; K=N/2. RFP A is (0:N-1,0:K) when N is odd; K=N/2. If TRANSR = 'C' then RFP is the Conjugate-transpose of RFP A as defined when TRANSR = 'N'. The contents of RFP A are defined by UPLO as follows: If UPLO = 'U' the RFP A contains the ( N*(N+1)/2 ) elements of upper packed A either in normal or conjugate-transpose Format. If UPLO = 'L' the RFP A contains the ( N*(N+1) /2 ) elements of lower packed A either in normal or conjugate-transpose Format. The LDA of RFP A is (N+1)/2 when TRANSR = 'C'. When TRANSR is 'N' the LDA is N+1 when N is even and is N when is odd. See the Note below for more details. Unchanged on exit. [out] WORK WORK is REAL array, dimension (LWORK), where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, WORK is not referenced.
Further Details:
We first consider Standard Packed Format when N is even.
We give an example where N = 6.

AP is Upper             AP is Lower

00 01 02 03 04 05       00
11 12 13 14 15       10 11
22 23 24 25       20 21 22
33 34 35       30 31 32 33
44 45       40 41 42 43 44
55       50 51 52 53 54 55

Let TRANSR = 'N'. RFP holds AP as follows:
For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
three columns of AP upper. The lower triangle A(4:6,0:2) consists of
conjugate-transpose of the first three columns of AP upper.
For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
three columns of AP lower. The upper triangle A(0:2,0:2) consists of
conjugate-transpose of the last three columns of AP lower.
To denote conjugate we place -- above the element. This covers the
case N even and TRANSR = 'N'.

RFP A                   RFP A

-- -- --
03 04 05                33 43 53
-- --
13 14 15                00 44 54
--
23 24 25                10 11 55

33 34 35                20 21 22
--
00 44 45                30 31 32
-- --
01 11 55                40 41 42
-- -- --
02 12 22                50 51 52

Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
transpose of RFP A above. One therefore gets:

RFP A                   RFP A

-- -- -- --                -- -- -- -- -- --
03 13 23 33 00 01 02    33 00 10 20 30 40 50
-- -- -- -- --                -- -- -- -- --
04 14 24 34 44 11 12    43 44 11 21 31 41 51
-- -- -- -- -- --                -- -- -- --
05 15 25 35 45 55 22    53 54 55 22 32 42 52

We next  consider Standard Packed Format when N is odd.
We give an example where N = 5.

AP is Upper                 AP is Lower

00 01 02 03 04              00
11 12 13 14              10 11
22 23 24              20 21 22
33 34              30 31 32 33
44              40 41 42 43 44

Let TRANSR = 'N'. RFP holds AP as follows:
For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
three columns of AP upper. The lower triangle A(3:4,0:1) consists of
conjugate-transpose of the first two   columns of AP upper.
For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
three columns of AP lower. The upper triangle A(0:1,1:2) consists of
conjugate-transpose of the last two   columns of AP lower.
To denote conjugate we place -- above the element. This covers the
case N odd  and TRANSR = 'N'.

RFP A                   RFP A

-- --
02 03 04                00 33 43
--
12 13 14                10 11 44

22 23 24                20 21 22
--
00 33 34                30 31 32
-- --
01 11 44                40 41 42

Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
transpose of RFP A above. One therefore gets:

RFP A                   RFP A

-- -- --                   -- -- -- -- -- --
02 12 22 00 01             00 10 20 30 40 50
-- -- -- --                   -- -- -- -- --
03 13 23 33 11             33 11 21 31 41 51
-- -- -- -- --                   -- -- -- --
04 14 24 34 44             43 44 22 32 42 52

Definition at line 245 of file clanhf.f.

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  IF( ifm.EQ.1 ) THEN
686 * A is 'N'
687  k = n / 2
688  IF( noe.EQ.1 ) THEN
689 * n is odd & A is n by (n+1)/2
690  IF( ilu.EQ.0 ) 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  IF( i.EQ.k+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  IF( VALUE .LT. temp .OR. 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  IF( j.GT.0 ) 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  IF( VALUE .LT. temp .OR. 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  IF( ilu.EQ.0 ) 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  IF( VALUE .LT. temp .OR. 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  IF( VALUE .LT. temp .OR. sisnan( temp ) )
846  \$ VALUE = temp
847  END DO
848  END IF
849  END IF
850  ELSE
851 * ifm=0
852  k = n / 2
853  IF( noe.EQ.1 ) THEN
854 * n is odd & A is (n+1)/2 by n
855  IF( ilu.EQ.0 ) 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  IF( VALUE .LT. temp .OR. 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  IF( VALUE .LT. temp .OR. 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  IF( ilu.EQ.0 ) 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  IF( VALUE .LT. temp .OR. 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  IF( VALUE .LT. temp .OR. 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  IF( noe.EQ.1 ) THEN
1140 * n is odd
1141  IF( ifm.EQ.1 ) THEN
1142 * A is normal & A is n by k
1143  IF( ilu.EQ.0 ) 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  IF( aa.NE.zero ) THEN
1161  IF( scale.LT.aa ) 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  IF( aa.NE.zero ) THEN
1171  IF( scale.LT.aa ) 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  IF( aa.NE.zero ) THEN
1183  IF( scale.LT.aa ) 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  IF( aa.NE.zero ) THEN
1205  IF( scale.LT.aa ) 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  IF( aa.NE.zero ) THEN
1218  IF( scale.LT.aa ) 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  IF( aa.NE.zero ) THEN
1228  IF( scale.LT.aa ) 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  IF( ilu.EQ.0 ) 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  IF( aa.NE.zero ) THEN
1262  IF( scale.LT.aa ) 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  IF( aa.NE.zero ) THEN
1275  IF( scale.LT.aa ) 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  IF( aa.NE.zero ) THEN
1285  IF( scale.LT.aa ) 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  IF( aa.NE.zero ) THEN
1316  IF( scale.LT.aa ) 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  IF( aa.NE.zero ) THEN
1326  IF( scale.LT.aa ) 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  IF( aa.NE.zero ) THEN
1339  IF( scale.LT.aa ) 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  IF( ifm.EQ.1 ) THEN
1351 * A is normal
1352  IF( ilu.EQ.0 ) 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  IF( aa.NE.zero ) THEN
1370  IF( scale.LT.aa ) 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  IF( aa.NE.zero ) THEN
1380  IF( scale.LT.aa ) 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  IF( aa.NE.zero ) THEN
1407  IF( scale.LT.aa ) 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  IF( aa.NE.zero ) THEN
1417  IF( scale.LT.aa ) 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  IF( ilu.EQ.0 ) 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  IF( aa.NE.zero ) THEN
1451  IF( scale.LT.aa ) 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  IF( aa.NE.zero ) THEN
1464  IF( scale.LT.aa ) 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  IF( aa.NE.zero ) THEN
1474  IF( scale.LT.aa ) 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  IF( aa.NE.zero ) THEN
1488  IF( scale.LT.aa ) 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  IF( aa.NE.zero ) THEN
1516  IF( scale.LT.aa ) 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  IF( aa.NE.zero ) THEN
1529  IF( scale.LT.aa ) 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  IF( aa.NE.zero ) THEN
1539  IF( scale.LT.aa ) 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  IF( aa.NE.zero ) THEN
1552  IF( scale.LT.aa ) 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 *
subroutine classq(n, x, incx, scl, sumsq)
CLASSQ updates a sum of squares represented in scaled form.
Definition: classq.f90:137
logical function sisnan(SIN)
SISNAN tests input for NaN.
Definition: sisnan.f:59
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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
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