LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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◆ slaqtr()

subroutine slaqtr ( logical  LTRAN,
logical  LREAL,
integer  N,
real, dimension( ldt, * )  T,
integer  LDT,
real, dimension( * )  B,
real  W,
real  SCALE,
real, dimension( * )  X,
real, dimension( * )  WORK,
integer  INFO 
)

SLAQTR solves a real quasi-triangular system of equations, or a complex quasi-triangular system of special form, in real arithmetic.

Download SLAQTR + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 SLAQTR solves the real quasi-triangular system

              op(T)*p = scale*c,               if LREAL = .TRUE.

 or the complex quasi-triangular systems

            op(T + iB)*(p+iq) = scale*(c+id),  if LREAL = .FALSE.

 in real arithmetic, where T is upper quasi-triangular.
 If LREAL = .FALSE., then the first diagonal block of T must be
 1 by 1, B is the specially structured matrix

                B = [ b(1) b(2) ... b(n) ]
                    [       w            ]
                    [           w        ]
                    [              .     ]
                    [                 w  ]

 op(A) = A or A**T, A**T denotes the transpose of
 matrix A.

 On input, X = [ c ].  On output, X = [ p ].
               [ d ]                  [ q ]

 This subroutine is designed for the condition number estimation
 in routine STRSNA.
Parameters
[in]LTRAN
          LTRAN is LOGICAL
          On entry, LTRAN specifies the option of conjugate transpose:
             = .FALSE.,    op(T+i*B) = T+i*B,
             = .TRUE.,     op(T+i*B) = (T+i*B)**T.
[in]LREAL
          LREAL is LOGICAL
          On entry, LREAL specifies the input matrix structure:
             = .FALSE.,    the input is complex
             = .TRUE.,     the input is real
[in]N
          N is INTEGER
          On entry, N specifies the order of T+i*B. N >= 0.
[in]T
          T is REAL array, dimension (LDT,N)
          On entry, T contains a matrix in Schur canonical form.
          If LREAL = .FALSE., then the first diagonal block of T must
          be 1 by 1.
[in]LDT
          LDT is INTEGER
          The leading dimension of the matrix T. LDT >= max(1,N).
[in]B
          B is REAL array, dimension (N)
          On entry, B contains the elements to form the matrix
          B as described above.
          If LREAL = .TRUE., B is not referenced.
[in]W
          W is REAL
          On entry, W is the diagonal element of the matrix B.
          If LREAL = .TRUE., W is not referenced.
[out]SCALE
          SCALE is REAL
          On exit, SCALE is the scale factor.
[in,out]X
          X is REAL array, dimension (2*N)
          On entry, X contains the right hand side of the system.
          On exit, X is overwritten by the solution.
[out]WORK
          WORK is REAL array, dimension (N)
[out]INFO
          INFO is INTEGER
          On exit, INFO is set to
             0: successful exit.
               1: the some diagonal 1 by 1 block has been perturbed by
                  a small number SMIN to keep nonsingularity.
               2: the some diagonal 2 by 2 block has been perturbed by
                  a small number in SLALN2 to keep nonsingularity.
          NOTE: In the interests of speed, this routine does not
                check the inputs for errors.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 163 of file slaqtr.f.

165*
166* -- LAPACK auxiliary routine --
167* -- LAPACK is a software package provided by Univ. of Tennessee, --
168* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
169*
170* .. Scalar Arguments ..
171 LOGICAL LREAL, LTRAN
172 INTEGER INFO, LDT, N
173 REAL SCALE, W
174* ..
175* .. Array Arguments ..
176 REAL B( * ), T( LDT, * ), WORK( * ), X( * )
177* ..
178*
179* =====================================================================
180*
181* .. Parameters ..
182 REAL ZERO, ONE
183 parameter( zero = 0.0e+0, one = 1.0e+0 )
184* ..
185* .. Local Scalars ..
186 LOGICAL NOTRAN
187 INTEGER I, IERR, J, J1, J2, JNEXT, K, N1, N2
188 REAL BIGNUM, EPS, REC, SCALOC, SI, SMIN, SMINW,
189 $ SMLNUM, SR, TJJ, TMP, XJ, XMAX, XNORM, Z
190* ..
191* .. Local Arrays ..
192 REAL D( 2, 2 ), V( 2, 2 )
193* ..
194* .. External Functions ..
195 INTEGER ISAMAX
196 REAL SASUM, SDOT, SLAMCH, SLANGE
197 EXTERNAL isamax, sasum, sdot, slamch, slange
198* ..
199* .. External Subroutines ..
200 EXTERNAL saxpy, sladiv, slaln2, sscal
201* ..
202* .. Intrinsic Functions ..
203 INTRINSIC abs, max
204* ..
205* .. Executable Statements ..
206*
207* Do not test the input parameters for errors
208*
209 notran = .NOT.ltran
210 info = 0
211*
212* Quick return if possible
213*
214 IF( n.EQ.0 )
215 $ RETURN
216*
217* Set constants to control overflow
218*
219 eps = slamch( 'P' )
220 smlnum = slamch( 'S' ) / eps
221 bignum = one / smlnum
222*
223 xnorm = slange( 'M', n, n, t, ldt, d )
224 IF( .NOT.lreal )
225 $ xnorm = max( xnorm, abs( w ), slange( 'M', n, 1, b, n, d ) )
226 smin = max( smlnum, eps*xnorm )
227*
228* Compute 1-norm of each column of strictly upper triangular
229* part of T to control overflow in triangular solver.
230*
231 work( 1 ) = zero
232 DO 10 j = 2, n
233 work( j ) = sasum( j-1, t( 1, j ), 1 )
234 10 CONTINUE
235*
236 IF( .NOT.lreal ) THEN
237 DO 20 i = 2, n
238 work( i ) = work( i ) + abs( b( i ) )
239 20 CONTINUE
240 END IF
241*
242 n2 = 2*n
243 n1 = n
244 IF( .NOT.lreal )
245 $ n1 = n2
246 k = isamax( n1, x, 1 )
247 xmax = abs( x( k ) )
248 scale = one
249*
250 IF( xmax.GT.bignum ) THEN
251 scale = bignum / xmax
252 CALL sscal( n1, scale, x, 1 )
253 xmax = bignum
254 END IF
255*
256 IF( lreal ) THEN
257*
258 IF( notran ) THEN
259*
260* Solve T*p = scale*c
261*
262 jnext = n
263 DO 30 j = n, 1, -1
264 IF( j.GT.jnext )
265 $ GO TO 30
266 j1 = j
267 j2 = j
268 jnext = j - 1
269 IF( j.GT.1 ) THEN
270 IF( t( j, j-1 ).NE.zero ) THEN
271 j1 = j - 1
272 jnext = j - 2
273 END IF
274 END IF
275*
276 IF( j1.EQ.j2 ) THEN
277*
278* Meet 1 by 1 diagonal block
279*
280* Scale to avoid overflow when computing
281* x(j) = b(j)/T(j,j)
282*
283 xj = abs( x( j1 ) )
284 tjj = abs( t( j1, j1 ) )
285 tmp = t( j1, j1 )
286 IF( tjj.LT.smin ) THEN
287 tmp = smin
288 tjj = smin
289 info = 1
290 END IF
291*
292 IF( xj.EQ.zero )
293 $ GO TO 30
294*
295 IF( tjj.LT.one ) THEN
296 IF( xj.GT.bignum*tjj ) THEN
297 rec = one / xj
298 CALL sscal( n, rec, x, 1 )
299 scale = scale*rec
300 xmax = xmax*rec
301 END IF
302 END IF
303 x( j1 ) = x( j1 ) / tmp
304 xj = abs( x( j1 ) )
305*
306* Scale x if necessary to avoid overflow when adding a
307* multiple of column j1 of T.
308*
309 IF( xj.GT.one ) THEN
310 rec = one / xj
311 IF( work( j1 ).GT.( bignum-xmax )*rec ) THEN
312 CALL sscal( n, rec, x, 1 )
313 scale = scale*rec
314 END IF
315 END IF
316 IF( j1.GT.1 ) THEN
317 CALL saxpy( j1-1, -x( j1 ), t( 1, j1 ), 1, x, 1 )
318 k = isamax( j1-1, x, 1 )
319 xmax = abs( x( k ) )
320 END IF
321*
322 ELSE
323*
324* Meet 2 by 2 diagonal block
325*
326* Call 2 by 2 linear system solve, to take
327* care of possible overflow by scaling factor.
328*
329 d( 1, 1 ) = x( j1 )
330 d( 2, 1 ) = x( j2 )
331 CALL slaln2( .false., 2, 1, smin, one, t( j1, j1 ),
332 $ ldt, one, one, d, 2, zero, zero, v, 2,
333 $ scaloc, xnorm, ierr )
334 IF( ierr.NE.0 )
335 $ info = 2
336*
337 IF( scaloc.NE.one ) THEN
338 CALL sscal( n, scaloc, x, 1 )
339 scale = scale*scaloc
340 END IF
341 x( j1 ) = v( 1, 1 )
342 x( j2 ) = v( 2, 1 )
343*
344* Scale V(1,1) (= X(J1)) and/or V(2,1) (=X(J2))
345* to avoid overflow in updating right-hand side.
346*
347 xj = max( abs( v( 1, 1 ) ), abs( v( 2, 1 ) ) )
348 IF( xj.GT.one ) THEN
349 rec = one / xj
350 IF( max( work( j1 ), work( j2 ) ).GT.
351 $ ( bignum-xmax )*rec ) THEN
352 CALL sscal( n, rec, x, 1 )
353 scale = scale*rec
354 END IF
355 END IF
356*
357* Update right-hand side
358*
359 IF( j1.GT.1 ) THEN
360 CALL saxpy( j1-1, -x( j1 ), t( 1, j1 ), 1, x, 1 )
361 CALL saxpy( j1-1, -x( j2 ), t( 1, j2 ), 1, x, 1 )
362 k = isamax( j1-1, x, 1 )
363 xmax = abs( x( k ) )
364 END IF
365*
366 END IF
367*
368 30 CONTINUE
369*
370 ELSE
371*
372* Solve T**T*p = scale*c
373*
374 jnext = 1
375 DO 40 j = 1, n
376 IF( j.LT.jnext )
377 $ GO TO 40
378 j1 = j
379 j2 = j
380 jnext = j + 1
381 IF( j.LT.n ) THEN
382 IF( t( j+1, j ).NE.zero ) THEN
383 j2 = j + 1
384 jnext = j + 2
385 END IF
386 END IF
387*
388 IF( j1.EQ.j2 ) THEN
389*
390* 1 by 1 diagonal block
391*
392* Scale if necessary to avoid overflow in forming the
393* right-hand side element by inner product.
394*
395 xj = abs( x( j1 ) )
396 IF( xmax.GT.one ) THEN
397 rec = one / xmax
398 IF( work( j1 ).GT.( bignum-xj )*rec ) THEN
399 CALL sscal( n, rec, x, 1 )
400 scale = scale*rec
401 xmax = xmax*rec
402 END IF
403 END IF
404*
405 x( j1 ) = x( j1 ) - sdot( j1-1, t( 1, j1 ), 1, x, 1 )
406*
407 xj = abs( x( j1 ) )
408 tjj = abs( t( j1, j1 ) )
409 tmp = t( j1, j1 )
410 IF( tjj.LT.smin ) THEN
411 tmp = smin
412 tjj = smin
413 info = 1
414 END IF
415*
416 IF( tjj.LT.one ) THEN
417 IF( xj.GT.bignum*tjj ) THEN
418 rec = one / xj
419 CALL sscal( n, rec, x, 1 )
420 scale = scale*rec
421 xmax = xmax*rec
422 END IF
423 END IF
424 x( j1 ) = x( j1 ) / tmp
425 xmax = max( xmax, abs( x( j1 ) ) )
426*
427 ELSE
428*
429* 2 by 2 diagonal block
430*
431* Scale if necessary to avoid overflow in forming the
432* right-hand side elements by inner product.
433*
434 xj = max( abs( x( j1 ) ), abs( x( j2 ) ) )
435 IF( xmax.GT.one ) THEN
436 rec = one / xmax
437 IF( max( work( j2 ), work( j1 ) ).GT.( bignum-xj )*
438 $ rec ) THEN
439 CALL sscal( n, rec, x, 1 )
440 scale = scale*rec
441 xmax = xmax*rec
442 END IF
443 END IF
444*
445 d( 1, 1 ) = x( j1 ) - sdot( j1-1, t( 1, j1 ), 1, x,
446 $ 1 )
447 d( 2, 1 ) = x( j2 ) - sdot( j1-1, t( 1, j2 ), 1, x,
448 $ 1 )
449*
450 CALL slaln2( .true., 2, 1, smin, one, t( j1, j1 ),
451 $ ldt, one, one, d, 2, zero, zero, v, 2,
452 $ scaloc, xnorm, ierr )
453 IF( ierr.NE.0 )
454 $ info = 2
455*
456 IF( scaloc.NE.one ) THEN
457 CALL sscal( n, scaloc, x, 1 )
458 scale = scale*scaloc
459 END IF
460 x( j1 ) = v( 1, 1 )
461 x( j2 ) = v( 2, 1 )
462 xmax = max( abs( x( j1 ) ), abs( x( j2 ) ), xmax )
463*
464 END IF
465 40 CONTINUE
466 END IF
467*
468 ELSE
469*
470 sminw = max( eps*abs( w ), smin )
471 IF( notran ) THEN
472*
473* Solve (T + iB)*(p+iq) = c+id
474*
475 jnext = n
476 DO 70 j = n, 1, -1
477 IF( j.GT.jnext )
478 $ GO TO 70
479 j1 = j
480 j2 = j
481 jnext = j - 1
482 IF( j.GT.1 ) THEN
483 IF( t( j, j-1 ).NE.zero ) THEN
484 j1 = j - 1
485 jnext = j - 2
486 END IF
487 END IF
488*
489 IF( j1.EQ.j2 ) THEN
490*
491* 1 by 1 diagonal block
492*
493* Scale if necessary to avoid overflow in division
494*
495 z = w
496 IF( j1.EQ.1 )
497 $ z = b( 1 )
498 xj = abs( x( j1 ) ) + abs( x( n+j1 ) )
499 tjj = abs( t( j1, j1 ) ) + abs( z )
500 tmp = t( j1, j1 )
501 IF( tjj.LT.sminw ) THEN
502 tmp = sminw
503 tjj = sminw
504 info = 1
505 END IF
506*
507 IF( xj.EQ.zero )
508 $ GO TO 70
509*
510 IF( tjj.LT.one ) THEN
511 IF( xj.GT.bignum*tjj ) THEN
512 rec = one / xj
513 CALL sscal( n2, rec, x, 1 )
514 scale = scale*rec
515 xmax = xmax*rec
516 END IF
517 END IF
518 CALL sladiv( x( j1 ), x( n+j1 ), tmp, z, sr, si )
519 x( j1 ) = sr
520 x( n+j1 ) = si
521 xj = abs( x( j1 ) ) + abs( x( n+j1 ) )
522*
523* Scale x if necessary to avoid overflow when adding a
524* multiple of column j1 of T.
525*
526 IF( xj.GT.one ) THEN
527 rec = one / xj
528 IF( work( j1 ).GT.( bignum-xmax )*rec ) THEN
529 CALL sscal( n2, rec, x, 1 )
530 scale = scale*rec
531 END IF
532 END IF
533*
534 IF( j1.GT.1 ) THEN
535 CALL saxpy( j1-1, -x( j1 ), t( 1, j1 ), 1, x, 1 )
536 CALL saxpy( j1-1, -x( n+j1 ), t( 1, j1 ), 1,
537 $ x( n+1 ), 1 )
538*
539 x( 1 ) = x( 1 ) + b( j1 )*x( n+j1 )
540 x( n+1 ) = x( n+1 ) - b( j1 )*x( j1 )
541*
542 xmax = zero
543 DO 50 k = 1, j1 - 1
544 xmax = max( xmax, abs( x( k ) )+
545 $ abs( x( k+n ) ) )
546 50 CONTINUE
547 END IF
548*
549 ELSE
550*
551* Meet 2 by 2 diagonal block
552*
553 d( 1, 1 ) = x( j1 )
554 d( 2, 1 ) = x( j2 )
555 d( 1, 2 ) = x( n+j1 )
556 d( 2, 2 ) = x( n+j2 )
557 CALL slaln2( .false., 2, 2, sminw, one, t( j1, j1 ),
558 $ ldt, one, one, d, 2, zero, -w, v, 2,
559 $ scaloc, xnorm, ierr )
560 IF( ierr.NE.0 )
561 $ info = 2
562*
563 IF( scaloc.NE.one ) THEN
564 CALL sscal( 2*n, scaloc, x, 1 )
565 scale = scaloc*scale
566 END IF
567 x( j1 ) = v( 1, 1 )
568 x( j2 ) = v( 2, 1 )
569 x( n+j1 ) = v( 1, 2 )
570 x( n+j2 ) = v( 2, 2 )
571*
572* Scale X(J1), .... to avoid overflow in
573* updating right hand side.
574*
575 xj = max( abs( v( 1, 1 ) )+abs( v( 1, 2 ) ),
576 $ abs( v( 2, 1 ) )+abs( v( 2, 2 ) ) )
577 IF( xj.GT.one ) THEN
578 rec = one / xj
579 IF( max( work( j1 ), work( j2 ) ).GT.
580 $ ( bignum-xmax )*rec ) THEN
581 CALL sscal( n2, rec, x, 1 )
582 scale = scale*rec
583 END IF
584 END IF
585*
586* Update the right-hand side.
587*
588 IF( j1.GT.1 ) THEN
589 CALL saxpy( j1-1, -x( j1 ), t( 1, j1 ), 1, x, 1 )
590 CALL saxpy( j1-1, -x( j2 ), t( 1, j2 ), 1, x, 1 )
591*
592 CALL saxpy( j1-1, -x( n+j1 ), t( 1, j1 ), 1,
593 $ x( n+1 ), 1 )
594 CALL saxpy( j1-1, -x( n+j2 ), t( 1, j2 ), 1,
595 $ x( n+1 ), 1 )
596*
597 x( 1 ) = x( 1 ) + b( j1 )*x( n+j1 ) +
598 $ b( j2 )*x( n+j2 )
599 x( n+1 ) = x( n+1 ) - b( j1 )*x( j1 ) -
600 $ b( j2 )*x( j2 )
601*
602 xmax = zero
603 DO 60 k = 1, j1 - 1
604 xmax = max( abs( x( k ) )+abs( x( k+n ) ),
605 $ xmax )
606 60 CONTINUE
607 END IF
608*
609 END IF
610 70 CONTINUE
611*
612 ELSE
613*
614* Solve (T + iB)**T*(p+iq) = c+id
615*
616 jnext = 1
617 DO 80 j = 1, n
618 IF( j.LT.jnext )
619 $ GO TO 80
620 j1 = j
621 j2 = j
622 jnext = j + 1
623 IF( j.LT.n ) THEN
624 IF( t( j+1, j ).NE.zero ) THEN
625 j2 = j + 1
626 jnext = j + 2
627 END IF
628 END IF
629*
630 IF( j1.EQ.j2 ) THEN
631*
632* 1 by 1 diagonal block
633*
634* Scale if necessary to avoid overflow in forming the
635* right-hand side element by inner product.
636*
637 xj = abs( x( j1 ) ) + abs( x( j1+n ) )
638 IF( xmax.GT.one ) THEN
639 rec = one / xmax
640 IF( work( j1 ).GT.( bignum-xj )*rec ) THEN
641 CALL sscal( n2, rec, x, 1 )
642 scale = scale*rec
643 xmax = xmax*rec
644 END IF
645 END IF
646*
647 x( j1 ) = x( j1 ) - sdot( j1-1, t( 1, j1 ), 1, x, 1 )
648 x( n+j1 ) = x( n+j1 ) - sdot( j1-1, t( 1, j1 ), 1,
649 $ x( n+1 ), 1 )
650 IF( j1.GT.1 ) THEN
651 x( j1 ) = x( j1 ) - b( j1 )*x( n+1 )
652 x( n+j1 ) = x( n+j1 ) + b( j1 )*x( 1 )
653 END IF
654 xj = abs( x( j1 ) ) + abs( x( j1+n ) )
655*
656 z = w
657 IF( j1.EQ.1 )
658 $ z = b( 1 )
659*
660* Scale if necessary to avoid overflow in
661* complex division
662*
663 tjj = abs( t( j1, j1 ) ) + abs( z )
664 tmp = t( j1, j1 )
665 IF( tjj.LT.sminw ) THEN
666 tmp = sminw
667 tjj = sminw
668 info = 1
669 END IF
670*
671 IF( tjj.LT.one ) THEN
672 IF( xj.GT.bignum*tjj ) THEN
673 rec = one / xj
674 CALL sscal( n2, rec, x, 1 )
675 scale = scale*rec
676 xmax = xmax*rec
677 END IF
678 END IF
679 CALL sladiv( x( j1 ), x( n+j1 ), tmp, -z, sr, si )
680 x( j1 ) = sr
681 x( j1+n ) = si
682 xmax = max( abs( x( j1 ) )+abs( x( j1+n ) ), xmax )
683*
684 ELSE
685*
686* 2 by 2 diagonal block
687*
688* Scale if necessary to avoid overflow in forming the
689* right-hand side element by inner product.
690*
691 xj = max( abs( x( j1 ) )+abs( x( n+j1 ) ),
692 $ abs( x( j2 ) )+abs( x( n+j2 ) ) )
693 IF( xmax.GT.one ) THEN
694 rec = one / xmax
695 IF( max( work( j1 ), work( j2 ) ).GT.
696 $ ( bignum-xj ) / xmax ) THEN
697 CALL sscal( n2, rec, x, 1 )
698 scale = scale*rec
699 xmax = xmax*rec
700 END IF
701 END IF
702*
703 d( 1, 1 ) = x( j1 ) - sdot( j1-1, t( 1, j1 ), 1, x,
704 $ 1 )
705 d( 2, 1 ) = x( j2 ) - sdot( j1-1, t( 1, j2 ), 1, x,
706 $ 1 )
707 d( 1, 2 ) = x( n+j1 ) - sdot( j1-1, t( 1, j1 ), 1,
708 $ x( n+1 ), 1 )
709 d( 2, 2 ) = x( n+j2 ) - sdot( j1-1, t( 1, j2 ), 1,
710 $ x( n+1 ), 1 )
711 d( 1, 1 ) = d( 1, 1 ) - b( j1 )*x( n+1 )
712 d( 2, 1 ) = d( 2, 1 ) - b( j2 )*x( n+1 )
713 d( 1, 2 ) = d( 1, 2 ) + b( j1 )*x( 1 )
714 d( 2, 2 ) = d( 2, 2 ) + b( j2 )*x( 1 )
715*
716 CALL slaln2( .true., 2, 2, sminw, one, t( j1, j1 ),
717 $ ldt, one, one, d, 2, zero, w, v, 2,
718 $ scaloc, xnorm, ierr )
719 IF( ierr.NE.0 )
720 $ info = 2
721*
722 IF( scaloc.NE.one ) THEN
723 CALL sscal( n2, scaloc, x, 1 )
724 scale = scaloc*scale
725 END IF
726 x( j1 ) = v( 1, 1 )
727 x( j2 ) = v( 2, 1 )
728 x( n+j1 ) = v( 1, 2 )
729 x( n+j2 ) = v( 2, 2 )
730 xmax = max( abs( x( j1 ) )+abs( x( n+j1 ) ),
731 $ abs( x( j2 ) )+abs( x( n+j2 ) ), xmax )
732*
733 END IF
734*
735 80 CONTINUE
736*
737 END IF
738*
739 END IF
740*
741 RETURN
742*
743* End of SLAQTR
744*
integer function isamax(N, SX, INCX)
ISAMAX
Definition: isamax.f:71
real function slange(NORM, M, N, A, LDA, WORK)
SLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: slange.f:114
subroutine slaln2(LTRANS, NA, NW, SMIN, CA, A, LDA, D1, D2, B, LDB, WR, WI, X, LDX, SCALE, XNORM, INFO)
SLALN2 solves a 1-by-1 or 2-by-2 linear system of equations of the specified form.
Definition: slaln2.f:218
subroutine sladiv(A, B, C, D, P, Q)
SLADIV performs complex division in real arithmetic, avoiding unnecessary overflow.
Definition: sladiv.f:91
subroutine sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:79
real function sdot(N, SX, INCX, SY, INCY)
SDOT
Definition: sdot.f:82
subroutine saxpy(N, SA, SX, INCX, SY, INCY)
SAXPY
Definition: saxpy.f:89
real function sasum(N, SX, INCX)
SASUM
Definition: sasum.f:72
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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