LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ dlansf()

 double precision function dlansf ( character NORM, character TRANSR, character UPLO, integer N, double precision, dimension( 0: * ) A, double precision, dimension( 0: * ) WORK )

DLANSF returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric matrix in RFP format.

Purpose:
``` DLANSF returns the value of the one norm, or the Frobenius norm, or
the infinity norm, or the element of largest absolute value of a
real symmetric matrix A in RFP format.```
Returns
DLANSF
```    DLANSF = ( 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*1 Specifies the value to be returned in DLANSF as described above.``` [in] TRANSR ``` TRANSR is CHARACTER*1 Specifies whether the RFP format of A is normal or transposed format. = 'N': RFP format is Normal; = 'T': RFP format is Transpose.``` [in] UPLO ``` UPLO is CHARACTER*1 On entry, UPLO specifies whether the RFP matrix A came from an upper or lower triangular matrix as follows: = 'U': RFP A came from an upper triangular matrix; = '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, DLANSF is set to zero.``` [in] A ``` A is DOUBLE PRECISION array, dimension ( N*(N+1)/2 ); On entry, the upper (if UPLO = 'U') or lower (if UPLO = 'L') part of the symmetric matrix A stored in RFP format. See the "Notes" below for more details. Unchanged on exit.``` [out] WORK ``` WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, WORK is not referenced.```
Date
December 2016
Further Details:
```  We first consider Rectangular Full Packed (RFP) 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
the 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
the transpose of the last three columns of AP lower.
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 = 'T'. RFP A in both UPLO cases is just the
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 then consider Rectangular Full Packed (RFP) 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
the 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
the transpose of the last two columns of AP lower.
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 = 'T'. RFP A in both UPLO cases is just the
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 211 of file dlansf.f.

211 *
212 * -- LAPACK computational routine (version 3.7.0) --
213 * -- LAPACK is a software package provided by Univ. of Tennessee, --
214 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
215 * December 2016
216 *
217 * .. Scalar Arguments ..
218  CHARACTER norm, transr, uplo
219  INTEGER n
220 * ..
221 * .. Array Arguments ..
222  DOUBLE PRECISION a( 0: * ), work( 0: * )
223 * ..
224 *
225 * =====================================================================
226 *
227 * .. Parameters ..
228  DOUBLE PRECISION one, zero
229  parameter( one = 1.0d+0, zero = 0.0d+0 )
230 * ..
231 * .. Local Scalars ..
232  INTEGER i, j, ifm, ilu, noe, n1, k, l, lda
233  DOUBLE PRECISION scale, s, VALUE, aa, temp
234 * ..
235 * .. External Functions ..
236  LOGICAL lsame, disnan
237  EXTERNAL lsame, disnan
238 * ..
239 * .. External Subroutines ..
240  EXTERNAL dlassq
241 * ..
242 * .. Intrinsic Functions ..
243  INTRINSIC abs, max, sqrt
244 * ..
245 * .. Executable Statements ..
246 *
247  IF( n.EQ.0 ) THEN
248  dlansf = zero
249  RETURN
250  ELSE IF( n.EQ.1 ) THEN
251  dlansf = abs( a(0) )
252  RETURN
253  END IF
254 *
255 * set noe = 1 if n is odd. if n is even set noe=0
256 *
257  noe = 1
258  IF( mod( n, 2 ).EQ.0 )
259  \$ noe = 0
260 *
261 * set ifm = 0 when form='T or 't' and 1 otherwise
262 *
263  ifm = 1
264  IF( lsame( transr, 'T' ) )
265  \$ ifm = 0
266 *
267 * set ilu = 0 when uplo='U or 'u' and 1 otherwise
268 *
269  ilu = 1
270  IF( lsame( uplo, 'U' ) )
271  \$ ilu = 0
272 *
273 * set lda = (n+1)/2 when ifm = 0
274 * set lda = n when ifm = 1 and noe = 1
275 * set lda = n+1 when ifm = 1 and noe = 0
276 *
277  IF( ifm.EQ.1 ) THEN
278  IF( noe.EQ.1 ) THEN
279  lda = n
280  ELSE
281 * noe=0
282  lda = n + 1
283  END IF
284  ELSE
285 * ifm=0
286  lda = ( n+1 ) / 2
287  END IF
288 *
289  IF( lsame( norm, 'M' ) ) THEN
290 *
291 * Find max(abs(A(i,j))).
292 *
293  k = ( n+1 ) / 2
294  VALUE = zero
295  IF( noe.EQ.1 ) THEN
296 * n is odd
297  IF( ifm.EQ.1 ) THEN
298 * A is n by k
299  DO j = 0, k - 1
300  DO i = 0, n - 1
301  temp = abs( a( i+j*lda ) )
302  IF( VALUE .LT. temp .OR. disnan( temp ) )
303  \$ VALUE = temp
304  END DO
305  END DO
306  ELSE
307 * xpose case; A is k by n
308  DO j = 0, n - 1
309  DO i = 0, k - 1
310  temp = abs( a( i+j*lda ) )
311  IF( VALUE .LT. temp .OR. disnan( temp ) )
312  \$ VALUE = temp
313  END DO
314  END DO
315  END IF
316  ELSE
317 * n is even
318  IF( ifm.EQ.1 ) THEN
319 * A is n+1 by k
320  DO j = 0, k - 1
321  DO i = 0, n
322  temp = abs( a( i+j*lda ) )
323  IF( VALUE .LT. temp .OR. disnan( temp ) )
324  \$ VALUE = temp
325  END DO
326  END DO
327  ELSE
328 * xpose case; A is k by n+1
329  DO j = 0, n
330  DO i = 0, k - 1
331  temp = abs( a( i+j*lda ) )
332  IF( VALUE .LT. temp .OR. disnan( temp ) )
333  \$ VALUE = temp
334  END DO
335  END DO
336  END IF
337  END IF
338  ELSE IF( ( lsame( norm, 'I' ) ) .OR. ( lsame( norm, 'O' ) ) .OR.
339  \$ ( norm.EQ.'1' ) ) THEN
340 *
341 * Find normI(A) ( = norm1(A), since A is symmetric).
342 *
343  IF( ifm.EQ.1 ) THEN
344  k = n / 2
345  IF( noe.EQ.1 ) THEN
346 * n is odd
347  IF( ilu.EQ.0 ) THEN
348  DO i = 0, k - 1
349  work( i ) = zero
350  END DO
351  DO j = 0, k
352  s = zero
353  DO i = 0, k + j - 1
354  aa = abs( a( i+j*lda ) )
355 * -> A(i,j+k)
356  s = s + aa
357  work( i ) = work( i ) + aa
358  END DO
359  aa = abs( a( i+j*lda ) )
360 * -> A(j+k,j+k)
361  work( j+k ) = s + aa
362  IF( i.EQ.k+k )
363  \$ GO TO 10
364  i = i + 1
365  aa = abs( a( i+j*lda ) )
366 * -> A(j,j)
367  work( j ) = work( j ) + aa
368  s = zero
369  DO l = j + 1, k - 1
370  i = i + 1
371  aa = abs( a( i+j*lda ) )
372 * -> A(l,j)
373  s = s + aa
374  work( l ) = work( l ) + aa
375  END DO
376  work( j ) = work( j ) + s
377  END DO
378  10 CONTINUE
379  VALUE = work( 0 )
380  DO i = 1, n-1
381  temp = work( i )
382  IF( VALUE .LT. temp .OR. disnan( temp ) )
383  \$ VALUE = temp
384  END DO
385  ELSE
386 * ilu = 1
387  k = k + 1
388 * k=(n+1)/2 for n odd and ilu=1
389  DO i = k, n - 1
390  work( i ) = zero
391  END DO
392  DO j = k - 1, 0, -1
393  s = zero
394  DO i = 0, j - 2
395  aa = abs( a( i+j*lda ) )
396 * -> A(j+k,i+k)
397  s = s + aa
398  work( i+k ) = work( i+k ) + aa
399  END DO
400  IF( j.GT.0 ) THEN
401  aa = abs( a( i+j*lda ) )
402 * -> A(j+k,j+k)
403  s = s + aa
404  work( i+k ) = work( i+k ) + s
405 * i=j
406  i = i + 1
407  END IF
408  aa = abs( a( i+j*lda ) )
409 * -> A(j,j)
410  work( j ) = aa
411  s = zero
412  DO l = j + 1, n - 1
413  i = i + 1
414  aa = abs( a( i+j*lda ) )
415 * -> A(l,j)
416  s = s + aa
417  work( l ) = work( l ) + aa
418  END DO
419  work( j ) = work( j ) + s
420  END DO
421  VALUE = work( 0 )
422  DO i = 1, n-1
423  temp = work( i )
424  IF( VALUE .LT. temp .OR. disnan( temp ) )
425  \$ VALUE = temp
426  END DO
427  END IF
428  ELSE
429 * n is even
430  IF( ilu.EQ.0 ) THEN
431  DO i = 0, k - 1
432  work( i ) = zero
433  END DO
434  DO j = 0, k - 1
435  s = zero
436  DO i = 0, k + j - 1
437  aa = abs( a( i+j*lda ) )
438 * -> A(i,j+k)
439  s = s + aa
440  work( i ) = work( i ) + aa
441  END DO
442  aa = abs( a( i+j*lda ) )
443 * -> A(j+k,j+k)
444  work( j+k ) = s + aa
445  i = i + 1
446  aa = abs( a( i+j*lda ) )
447 * -> A(j,j)
448  work( j ) = work( j ) + aa
449  s = zero
450  DO l = j + 1, k - 1
451  i = i + 1
452  aa = abs( a( i+j*lda ) )
453 * -> A(l,j)
454  s = s + aa
455  work( l ) = work( l ) + aa
456  END DO
457  work( j ) = work( j ) + s
458  END DO
459  VALUE = work( 0 )
460  DO i = 1, n-1
461  temp = work( i )
462  IF( VALUE .LT. temp .OR. disnan( temp ) )
463  \$ VALUE = temp
464  END DO
465  ELSE
466 * ilu = 1
467  DO i = k, n - 1
468  work( i ) = zero
469  END DO
470  DO j = k - 1, 0, -1
471  s = zero
472  DO i = 0, j - 1
473  aa = abs( a( i+j*lda ) )
474 * -> A(j+k,i+k)
475  s = s + aa
476  work( i+k ) = work( i+k ) + aa
477  END DO
478  aa = abs( a( i+j*lda ) )
479 * -> A(j+k,j+k)
480  s = s + aa
481  work( i+k ) = work( i+k ) + s
482 * i=j
483  i = i + 1
484  aa = abs( a( i+j*lda ) )
485 * -> A(j,j)
486  work( j ) = aa
487  s = zero
488  DO l = j + 1, n - 1
489  i = i + 1
490  aa = abs( a( i+j*lda ) )
491 * -> A(l,j)
492  s = s + aa
493  work( l ) = work( l ) + aa
494  END DO
495  work( j ) = work( j ) + s
496  END DO
497  VALUE = work( 0 )
498  DO i = 1, n-1
499  temp = work( i )
500  IF( VALUE .LT. temp .OR. disnan( temp ) )
501  \$ VALUE = temp
502  END DO
503  END IF
504  END IF
505  ELSE
506 * ifm=0
507  k = n / 2
508  IF( noe.EQ.1 ) THEN
509 * n is odd
510  IF( ilu.EQ.0 ) THEN
511  n1 = k
512 * n/2
513  k = k + 1
514 * k is the row size and lda
515  DO i = n1, n - 1
516  work( i ) = zero
517  END DO
518  DO j = 0, n1 - 1
519  s = zero
520  DO i = 0, k - 1
521  aa = abs( a( i+j*lda ) )
522 * A(j,n1+i)
523  work( i+n1 ) = work( i+n1 ) + aa
524  s = s + aa
525  END DO
526  work( j ) = s
527  END DO
528 * j=n1=k-1 is special
529  s = abs( a( 0+j*lda ) )
530 * A(k-1,k-1)
531  DO i = 1, k - 1
532  aa = abs( a( i+j*lda ) )
533 * A(k-1,i+n1)
534  work( i+n1 ) = work( i+n1 ) + aa
535  s = s + aa
536  END DO
537  work( j ) = work( j ) + s
538  DO j = k, n - 1
539  s = zero
540  DO i = 0, j - k - 1
541  aa = abs( a( i+j*lda ) )
542 * A(i,j-k)
543  work( i ) = work( i ) + aa
544  s = s + aa
545  END DO
546 * i=j-k
547  aa = abs( a( i+j*lda ) )
548 * A(j-k,j-k)
549  s = s + aa
550  work( j-k ) = work( j-k ) + s
551  i = i + 1
552  s = abs( a( i+j*lda ) )
553 * A(j,j)
554  DO l = j + 1, n - 1
555  i = i + 1
556  aa = abs( a( i+j*lda ) )
557 * A(j,l)
558  work( l ) = work( l ) + aa
559  s = s + aa
560  END DO
561  work( j ) = work( j ) + s
562  END DO
563  VALUE = work( 0 )
564  DO i = 1, n-1
565  temp = work( i )
566  IF( VALUE .LT. temp .OR. disnan( temp ) )
567  \$ VALUE = temp
568  END DO
569  ELSE
570 * ilu=1
571  k = k + 1
572 * k=(n+1)/2 for n odd and ilu=1
573  DO i = k, n - 1
574  work( i ) = zero
575  END DO
576  DO j = 0, k - 2
577 * process
578  s = zero
579  DO i = 0, j - 1
580  aa = abs( a( i+j*lda ) )
581 * A(j,i)
582  work( i ) = work( i ) + aa
583  s = s + aa
584  END DO
585  aa = abs( a( i+j*lda ) )
586 * i=j so process of A(j,j)
587  s = s + aa
588  work( j ) = s
589 * is initialised here
590  i = i + 1
591 * i=j process A(j+k,j+k)
592  aa = abs( a( i+j*lda ) )
593  s = aa
594  DO l = k + j + 1, n - 1
595  i = i + 1
596  aa = abs( a( i+j*lda ) )
597 * A(l,k+j)
598  s = s + aa
599  work( l ) = work( l ) + aa
600  END DO
601  work( k+j ) = work( k+j ) + s
602  END DO
603 * j=k-1 is special :process col A(k-1,0:k-1)
604  s = zero
605  DO i = 0, k - 2
606  aa = abs( a( i+j*lda ) )
607 * A(k,i)
608  work( i ) = work( i ) + aa
609  s = s + aa
610  END DO
611 * i=k-1
612  aa = abs( a( i+j*lda ) )
613 * A(k-1,k-1)
614  s = s + aa
615  work( i ) = s
616 * done with col j=k+1
617  DO j = k, n - 1
618 * process col j of A = A(j,0:k-1)
619  s = zero
620  DO i = 0, k - 1
621  aa = abs( a( i+j*lda ) )
622 * A(j,i)
623  work( i ) = work( i ) + aa
624  s = s + aa
625  END DO
626  work( j ) = work( j ) + s
627  END DO
628  VALUE = work( 0 )
629  DO i = 1, n-1
630  temp = work( i )
631  IF( VALUE .LT. temp .OR. disnan( temp ) )
632  \$ VALUE = temp
633  END DO
634  END IF
635  ELSE
636 * n is even
637  IF( ilu.EQ.0 ) THEN
638  DO i = k, n - 1
639  work( i ) = zero
640  END DO
641  DO j = 0, k - 1
642  s = zero
643  DO i = 0, k - 1
644  aa = abs( a( i+j*lda ) )
645 * A(j,i+k)
646  work( i+k ) = work( i+k ) + aa
647  s = s + aa
648  END DO
649  work( j ) = s
650  END DO
651 * j=k
652  aa = abs( a( 0+j*lda ) )
653 * A(k,k)
654  s = aa
655  DO i = 1, k - 1
656  aa = abs( a( i+j*lda ) )
657 * A(k,k+i)
658  work( i+k ) = work( i+k ) + aa
659  s = s + aa
660  END DO
661  work( j ) = work( j ) + s
662  DO j = k + 1, n - 1
663  s = zero
664  DO i = 0, j - 2 - k
665  aa = abs( a( i+j*lda ) )
666 * A(i,j-k-1)
667  work( i ) = work( i ) + aa
668  s = s + aa
669  END DO
670 * i=j-1-k
671  aa = abs( a( i+j*lda ) )
672 * A(j-k-1,j-k-1)
673  s = s + aa
674  work( j-k-1 ) = work( j-k-1 ) + s
675  i = i + 1
676  aa = abs( a( i+j*lda ) )
677 * A(j,j)
678  s = aa
679  DO l = j + 1, n - 1
680  i = i + 1
681  aa = abs( a( i+j*lda ) )
682 * A(j,l)
683  work( l ) = work( l ) + aa
684  s = s + aa
685  END DO
686  work( j ) = work( j ) + s
687  END DO
688 * j=n
689  s = zero
690  DO i = 0, k - 2
691  aa = abs( a( i+j*lda ) )
692 * A(i,k-1)
693  work( i ) = work( i ) + aa
694  s = s + aa
695  END DO
696 * i=k-1
697  aa = abs( a( i+j*lda ) )
698 * A(k-1,k-1)
699  s = s + aa
700  work( i ) = work( i ) + s
701  VALUE = work( 0 )
702  DO i = 1, n-1
703  temp = work( i )
704  IF( VALUE .LT. temp .OR. disnan( temp ) )
705  \$ VALUE = temp
706  END DO
707  ELSE
708 * ilu=1
709  DO i = k, n - 1
710  work( i ) = zero
711  END DO
712 * j=0 is special :process col A(k:n-1,k)
713  s = abs( a( 0 ) )
714 * A(k,k)
715  DO i = 1, k - 1
716  aa = abs( a( i ) )
717 * A(k+i,k)
718  work( i+k ) = work( i+k ) + aa
719  s = s + aa
720  END DO
721  work( k ) = work( k ) + s
722  DO j = 1, k - 1
723 * process
724  s = zero
725  DO i = 0, j - 2
726  aa = abs( a( i+j*lda ) )
727 * A(j-1,i)
728  work( i ) = work( i ) + aa
729  s = s + aa
730  END DO
731  aa = abs( a( i+j*lda ) )
732 * i=j-1 so process of A(j-1,j-1)
733  s = s + aa
734  work( j-1 ) = s
735 * is initialised here
736  i = i + 1
737 * i=j process A(j+k,j+k)
738  aa = abs( a( i+j*lda ) )
739  s = aa
740  DO l = k + j + 1, n - 1
741  i = i + 1
742  aa = abs( a( i+j*lda ) )
743 * A(l,k+j)
744  s = s + aa
745  work( l ) = work( l ) + aa
746  END DO
747  work( k+j ) = work( k+j ) + s
748  END DO
749 * j=k is special :process col A(k,0:k-1)
750  s = zero
751  DO i = 0, k - 2
752  aa = abs( a( i+j*lda ) )
753 * A(k,i)
754  work( i ) = work( i ) + aa
755  s = s + aa
756  END DO
757 * i=k-1
758  aa = abs( a( i+j*lda ) )
759 * A(k-1,k-1)
760  s = s + aa
761  work( i ) = s
762 * done with col j=k+1
763  DO j = k + 1, n
764 * process col j-1 of A = A(j-1,0:k-1)
765  s = zero
766  DO i = 0, k - 1
767  aa = abs( a( i+j*lda ) )
768 * A(j-1,i)
769  work( i ) = work( i ) + aa
770  s = s + aa
771  END DO
772  work( j-1 ) = work( j-1 ) + s
773  END DO
774  VALUE = work( 0 )
775  DO i = 1, n-1
776  temp = work( i )
777  IF( VALUE .LT. temp .OR. disnan( temp ) )
778  \$ VALUE = temp
779  END DO
780  END IF
781  END IF
782  END IF
783  ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
784 *
785 * Find normF(A).
786 *
787  k = ( n+1 ) / 2
788  scale = zero
789  s = one
790  IF( noe.EQ.1 ) THEN
791 * n is odd
792  IF( ifm.EQ.1 ) THEN
793 * A is normal
794  IF( ilu.EQ.0 ) THEN
795 * A is upper
796  DO j = 0, k - 3
797  CALL dlassq( k-j-2, a( k+j+1+j*lda ), 1, scale, s )
798 * L at A(k,0)
799  END DO
800  DO j = 0, k - 1
801  CALL dlassq( k+j-1, a( 0+j*lda ), 1, scale, s )
802 * trap U at A(0,0)
803  END DO
804  s = s + s
805 * double s for the off diagonal elements
806  CALL dlassq( k-1, a( k ), lda+1, scale, s )
807 * tri L at A(k,0)
808  CALL dlassq( k, a( k-1 ), lda+1, scale, s )
809 * tri U at A(k-1,0)
810  ELSE
811 * ilu=1 & A is lower
812  DO j = 0, k - 1
813  CALL dlassq( n-j-1, a( j+1+j*lda ), 1, scale, s )
814 * trap L at A(0,0)
815  END DO
816  DO j = 0, k - 2
817  CALL dlassq( j, a( 0+( 1+j )*lda ), 1, scale, s )
818 * U at A(0,1)
819  END DO
820  s = s + s
821 * double s for the off diagonal elements
822  CALL dlassq( k, a( 0 ), lda+1, scale, s )
823 * tri L at A(0,0)
824  CALL dlassq( k-1, a( 0+lda ), lda+1, scale, s )
825 * tri U at A(0,1)
826  END IF
827  ELSE
828 * A is xpose
829  IF( ilu.EQ.0 ) THEN
830 * A**T is upper
831  DO j = 1, k - 2
832  CALL dlassq( j, a( 0+( k+j )*lda ), 1, scale, s )
833 * U at A(0,k)
834  END DO
835  DO j = 0, k - 2
836  CALL dlassq( k, a( 0+j*lda ), 1, scale, s )
837 * k by k-1 rect. at A(0,0)
838  END DO
839  DO j = 0, k - 2
840  CALL dlassq( k-j-1, a( j+1+( j+k-1 )*lda ), 1,
841  \$ scale, s )
842 * L at A(0,k-1)
843  END DO
844  s = s + s
845 * double s for the off diagonal elements
846  CALL dlassq( k-1, a( 0+k*lda ), lda+1, scale, s )
847 * tri U at A(0,k)
848  CALL dlassq( k, a( 0+( k-1 )*lda ), lda+1, scale, s )
849 * tri L at A(0,k-1)
850  ELSE
851 * A**T is lower
852  DO j = 1, k - 1
853  CALL dlassq( j, a( 0+j*lda ), 1, scale, s )
854 * U at A(0,0)
855  END DO
856  DO j = k, n - 1
857  CALL dlassq( k, a( 0+j*lda ), 1, scale, s )
858 * k by k-1 rect. at A(0,k)
859  END DO
860  DO j = 0, k - 3
861  CALL dlassq( k-j-2, a( j+2+j*lda ), 1, scale, s )
862 * L at A(1,0)
863  END DO
864  s = s + s
865 * double s for the off diagonal elements
866  CALL dlassq( k, a( 0 ), lda+1, scale, s )
867 * tri U at A(0,0)
868  CALL dlassq( k-1, a( 1 ), lda+1, scale, s )
869 * tri L at A(1,0)
870  END IF
871  END IF
872  ELSE
873 * n is even
874  IF( ifm.EQ.1 ) THEN
875 * A is normal
876  IF( ilu.EQ.0 ) THEN
877 * A is upper
878  DO j = 0, k - 2
879  CALL dlassq( k-j-1, a( k+j+2+j*lda ), 1, scale, s )
880 * L at A(k+1,0)
881  END DO
882  DO j = 0, k - 1
883  CALL dlassq( k+j, a( 0+j*lda ), 1, scale, s )
884 * trap U at A(0,0)
885  END DO
886  s = s + s
887 * double s for the off diagonal elements
888  CALL dlassq( k, a( k+1 ), lda+1, scale, s )
889 * tri L at A(k+1,0)
890  CALL dlassq( k, a( k ), lda+1, scale, s )
891 * tri U at A(k,0)
892  ELSE
893 * ilu=1 & A is lower
894  DO j = 0, k - 1
895  CALL dlassq( n-j-1, a( j+2+j*lda ), 1, scale, s )
896 * trap L at A(1,0)
897  END DO
898  DO j = 1, k - 1
899  CALL dlassq( j, a( 0+j*lda ), 1, scale, s )
900 * U at A(0,0)
901  END DO
902  s = s + s
903 * double s for the off diagonal elements
904  CALL dlassq( k, a( 1 ), lda+1, scale, s )
905 * tri L at A(1,0)
906  CALL dlassq( k, a( 0 ), lda+1, scale, s )
907 * tri U at A(0,0)
908  END IF
909  ELSE
910 * A is xpose
911  IF( ilu.EQ.0 ) THEN
912 * A**T is upper
913  DO j = 1, k - 1
914  CALL dlassq( j, a( 0+( k+1+j )*lda ), 1, scale, s )
915 * U at A(0,k+1)
916  END DO
917  DO j = 0, k - 1
918  CALL dlassq( k, a( 0+j*lda ), 1, scale, s )
919 * k by k rect. at A(0,0)
920  END DO
921  DO j = 0, k - 2
922  CALL dlassq( k-j-1, a( j+1+( j+k )*lda ), 1, scale,
923  \$ s )
924 * L at A(0,k)
925  END DO
926  s = s + s
927 * double s for the off diagonal elements
928  CALL dlassq( k, a( 0+( k+1 )*lda ), lda+1, scale, s )
929 * tri U at A(0,k+1)
930  CALL dlassq( k, a( 0+k*lda ), lda+1, scale, s )
931 * tri L at A(0,k)
932  ELSE
933 * A**T is lower
934  DO j = 1, k - 1
935  CALL dlassq( j, a( 0+( j+1 )*lda ), 1, scale, s )
936 * U at A(0,1)
937  END DO
938  DO j = k + 1, n
939  CALL dlassq( k, a( 0+j*lda ), 1, scale, s )
940 * k by k rect. at A(0,k+1)
941  END DO
942  DO j = 0, k - 2
943  CALL dlassq( k-j-1, a( j+1+j*lda ), 1, scale, s )
944 * L at A(0,0)
945  END DO
946  s = s + s
947 * double s for the off diagonal elements
948  CALL dlassq( k, a( lda ), lda+1, scale, s )
949 * tri L at A(0,1)
950  CALL dlassq( k, a( 0 ), lda+1, scale, s )
951 * tri U at A(0,0)
952  END IF
953  END IF
954  END IF
955  VALUE = scale*sqrt( s )
956  END IF
957 *
958  dlansf = VALUE
959  RETURN
960 *
961 * End of DLANSF
962 *
subroutine dlassq(N, X, INCX, SCALE, SUMSQ)
DLASSQ updates a sum of squares represented in scaled form.
Definition: dlassq.f:105
double precision function dlansf(NORM, TRANSR, UPLO, N, A, WORK)
DLANSF returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric matrix in RFP format.
Definition: dlansf.f:211
logical function disnan(DIN)
DISNAN tests input for NaN.
Definition: disnan.f:61
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
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