LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ schksb()

 subroutine schksb ( integer NSIZES, integer, dimension( * ) NN, integer NWDTHS, integer, dimension( * ) KK, integer NTYPES, logical, dimension( * ) DOTYPE, integer, dimension( 4 ) ISEED, real THRESH, integer NOUNIT, real, dimension( lda, * ) A, integer LDA, real, dimension( * ) SD, real, dimension( * ) SE, real, dimension( ldu, * ) U, integer LDU, real, dimension( * ) WORK, integer LWORK, real, dimension( * ) RESULT, integer INFO )

SCHKSB

Purpose:
``` SCHKSB tests the reduction of a symmetric band matrix to tridiagonal
form, used with the symmetric eigenvalue problem.

SSBTRD factors a symmetric band matrix A as  U S U' , where ' means
transpose, S is symmetric tridiagonal, and U is orthogonal.
SSBTRD can use either just the lower or just the upper triangle
of A; SCHKSB checks both cases.

When SCHKSB is called, a number of matrix "sizes" ("n's"), a number
of bandwidths ("k's"), and a number of matrix "types" are
specified.  For each size ("n"), each bandwidth ("k") less than or
equal to "n", and each type of matrix, one matrix will be generated
and used to test the symmetric banded reduction routine.  For each
matrix, a number of tests will be performed:

(1)     | A - V S V' | / ( |A| n ulp )  computed by SSBTRD with
UPLO='U'

(2)     | I - UU' | / ( n ulp )

(3)     | A - V S V' | / ( |A| n ulp )  computed by SSBTRD with
UPLO='L'

(4)     | I - UU' | / ( n ulp )

The "sizes" are specified by an array NN(1:NSIZES); the value of
each element NN(j) specifies one size.
The "types" are specified by a logical array DOTYPE( 1:NTYPES );
if DOTYPE(j) is .TRUE., then matrix type "j" will be generated.
Currently, the list of possible types is:

(1)  The zero matrix.
(2)  The identity matrix.

(3)  A diagonal matrix with evenly spaced entries
1, ..., ULP  and random signs.
(ULP = (first number larger than 1) - 1 )
(4)  A diagonal matrix with geometrically spaced entries
1, ..., ULP  and random signs.
(5)  A diagonal matrix with "clustered" entries 1, ULP, ..., ULP
and random signs.

(6)  Same as (4), but multiplied by SQRT( overflow threshold )
(7)  Same as (4), but multiplied by SQRT( underflow threshold )

(8)  A matrix of the form  U' D U, where U is orthogonal and
D has evenly spaced entries 1, ..., ULP with random signs
on the diagonal.

(9)  A matrix of the form  U' D U, where U is orthogonal and
D has geometrically spaced entries 1, ..., ULP with random
signs on the diagonal.

(10) A matrix of the form  U' D U, where U is orthogonal and
D has "clustered" entries 1, ULP,..., ULP with random
signs on the diagonal.

(11) Same as (8), but multiplied by SQRT( overflow threshold )
(12) Same as (8), but multiplied by SQRT( underflow threshold )

(13) Symmetric matrix with random entries chosen from (-1,1).
(14) Same as (13), but multiplied by SQRT( overflow threshold )
(15) Same as (13), but multiplied by SQRT( underflow threshold )```
Parameters
 [in] NSIZES ``` NSIZES is INTEGER The number of sizes of matrices to use. If it is zero, SCHKSB does nothing. It must be at least zero.``` [in] NN ``` NN is INTEGER array, dimension (NSIZES) An array containing the sizes to be used for the matrices. Zero values will be skipped. The values must be at least zero.``` [in] NWDTHS ``` NWDTHS is INTEGER The number of bandwidths to use. If it is zero, SCHKSB does nothing. It must be at least zero.``` [in] KK ``` KK is INTEGER array, dimension (NWDTHS) An array containing the bandwidths to be used for the band matrices. The values must be at least zero.``` [in] NTYPES ``` NTYPES is INTEGER The number of elements in DOTYPE. If it is zero, SCHKSB does nothing. It must be at least zero. If it is MAXTYP+1 and NSIZES is 1, then an additional type, MAXTYP+1 is defined, which is to use whatever matrix is in A. This is only useful if DOTYPE(1:MAXTYP) is .FALSE. and DOTYPE(MAXTYP+1) is .TRUE. .``` [in] DOTYPE ``` DOTYPE is LOGICAL array, dimension (NTYPES) If DOTYPE(j) is .TRUE., then for each size in NN a matrix of that size and of type j will be generated. If NTYPES is smaller than the maximum number of types defined (PARAMETER MAXTYP), then types NTYPES+1 through MAXTYP will not be generated. If NTYPES is larger than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES) will be ignored.``` [in,out] ISEED ``` ISEED is INTEGER array, dimension (4) On entry ISEED specifies the seed of the random number generator. The array elements should be between 0 and 4095; if not they will be reduced mod 4096. Also, ISEED(4) must be odd. The random number generator uses a linear congruential sequence limited to small integers, and so should produce machine independent random numbers. The values of ISEED are changed on exit, and can be used in the next call to SCHKSB to continue the same random number sequence.``` [in] THRESH ``` THRESH is REAL A test will count as "failed" if the "error", computed as described above, exceeds THRESH. Note that the error is scaled to be O(1), so THRESH should be a reasonably small multiple of 1, e.g., 10 or 100. In particular, it should not depend on the precision (single vs. double) or the size of the matrix. It must be at least zero.``` [in] NOUNIT ``` NOUNIT is INTEGER The FORTRAN unit number for printing out error messages (e.g., if a routine returns IINFO not equal to 0.)``` [in,out] A ``` A is REAL array, dimension (LDA, max(NN)) Used to hold the matrix whose eigenvalues are to be computed.``` [in] LDA ``` LDA is INTEGER The leading dimension of A. It must be at least 2 (not 1!) and at least max( KK )+1.``` [out] SD ``` SD is REAL array, dimension (max(NN)) Used to hold the diagonal of the tridiagonal matrix computed by SSBTRD.``` [out] SE ``` SE is REAL array, dimension (max(NN)) Used to hold the off-diagonal of the tridiagonal matrix computed by SSBTRD.``` [out] U ``` U is REAL array, dimension (LDU, max(NN)) Used to hold the orthogonal matrix computed by SSBTRD.``` [in] LDU ``` LDU is INTEGER The leading dimension of U. It must be at least 1 and at least max( NN ).``` [out] WORK ` WORK is REAL array, dimension (LWORK)` [in] LWORK ``` LWORK is INTEGER The number of entries in WORK. This must be at least max( LDA+1, max(NN)+1 )*max(NN).``` [out] RESULT ``` RESULT is REAL array, dimension (4) The values computed by the tests described above. The values are currently limited to 1/ulp, to avoid overflow.``` [out] INFO ``` INFO is INTEGER If 0, then everything ran OK. ----------------------------------------------------------------------- Some Local Variables and Parameters: ---- ----- --------- --- ---------- ZERO, ONE Real 0 and 1. MAXTYP The number of types defined. NTEST The number of tests performed, or which can be performed so far, for the current matrix. NTESTT The total number of tests performed so far. NMAX Largest value in NN. NMATS The number of matrices generated so far. NERRS The number of tests which have exceeded THRESH so far. COND, IMODE Values to be passed to the matrix generators. ANORM Norm of A; passed to matrix generators. OVFL, UNFL Overflow and underflow thresholds. ULP, ULPINV Finest relative precision and its inverse. RTOVFL, RTUNFL Square roots of the previous 2 values. The following four arrays decode JTYPE: KTYPE(j) The general type (1-10) for type "j". KMODE(j) The MODE value to be passed to the matrix generator for type "j". KMAGN(j) The order of magnitude ( O(1), O(overflow^(1/2) ), O(underflow^(1/2) )```

Definition at line 290 of file schksb.f.

293*
294* -- LAPACK test routine --
295* -- LAPACK is a software package provided by Univ. of Tennessee, --
296* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
297*
298* .. Scalar Arguments ..
299 INTEGER INFO, LDA, LDU, LWORK, NOUNIT, NSIZES, NTYPES,
300 \$ NWDTHS
301 REAL THRESH
302* ..
303* .. Array Arguments ..
304 LOGICAL DOTYPE( * )
305 INTEGER ISEED( 4 ), KK( * ), NN( * )
306 REAL A( LDA, * ), RESULT( * ), SD( * ), SE( * ),
307 \$ U( LDU, * ), WORK( * )
308* ..
309*
310* =====================================================================
311*
312* .. Parameters ..
313 REAL ZERO, ONE, TWO, TEN
314 parameter( zero = 0.0e0, one = 1.0e0, two = 2.0e0,
315 \$ ten = 10.0e0 )
316 REAL HALF
317 parameter( half = one / two )
318 INTEGER MAXTYP
319 parameter( maxtyp = 15 )
320* ..
321* .. Local Scalars ..
323 INTEGER I, IINFO, IMODE, ITYPE, J, JC, JCOL, JR, JSIZE,
324 \$ JTYPE, JWIDTH, K, KMAX, MTYPES, N, NERRS,
325 \$ NMATS, NMAX, NTEST, NTESTT
326 REAL ANINV, ANORM, COND, OVFL, RTOVFL, RTUNFL,
327 \$ TEMP1, ULP, ULPINV, UNFL
328* ..
329* .. Local Arrays ..
330 INTEGER IDUMMA( 1 ), IOLDSD( 4 ), KMAGN( MAXTYP ),
331 \$ KMODE( MAXTYP ), KTYPE( MAXTYP )
332* ..
333* .. External Functions ..
334 REAL SLAMCH
335 EXTERNAL slamch
336* ..
337* .. External Subroutines ..
338 EXTERNAL slacpy, slasum, slatmr, slatms, slaset, ssbt21,
339 \$ ssbtrd, xerbla
340* ..
341* .. Intrinsic Functions ..
342 INTRINSIC abs, max, min, real, sqrt
343* ..
344* .. Data statements ..
345 DATA ktype / 1, 2, 5*4, 5*5, 3*8 /
346 DATA kmagn / 2*1, 1, 1, 1, 2, 3, 1, 1, 1, 2, 3, 1,
347 \$ 2, 3 /
348 DATA kmode / 2*0, 4, 3, 1, 4, 4, 4, 3, 1, 4, 4, 0,
349 \$ 0, 0 /
350* ..
351* .. Executable Statements ..
352*
353* Check for errors
354*
355 ntestt = 0
356 info = 0
357*
358* Important constants
359*
361 nmax = 1
362 DO 10 j = 1, nsizes
363 nmax = max( nmax, nn( j ) )
364 IF( nn( j ).LT.0 )
366 10 CONTINUE
367*
369 kmax = 0
370 DO 20 j = 1, nsizes
371 kmax = max( kmax, kk( j ) )
372 IF( kk( j ).LT.0 )
374 20 CONTINUE
375 kmax = min( nmax-1, kmax )
376*
377* Check for errors
378*
379 IF( nsizes.LT.0 ) THEN
380 info = -1
381 ELSE IF( badnn ) THEN
382 info = -2
383 ELSE IF( nwdths.LT.0 ) THEN
384 info = -3
385 ELSE IF( badnnb ) THEN
386 info = -4
387 ELSE IF( ntypes.LT.0 ) THEN
388 info = -5
389 ELSE IF( lda.LT.kmax+1 ) THEN
390 info = -11
391 ELSE IF( ldu.LT.nmax ) THEN
392 info = -15
393 ELSE IF( ( max( lda, nmax )+1 )*nmax.GT.lwork ) THEN
394 info = -17
395 END IF
396*
397 IF( info.NE.0 ) THEN
398 CALL xerbla( 'SCHKSB', -info )
399 RETURN
400 END IF
401*
402* Quick return if possible
403*
404 IF( nsizes.EQ.0 .OR. ntypes.EQ.0 .OR. nwdths.EQ.0 )
405 \$ RETURN
406*
407* More Important constants
408*
409 unfl = slamch( 'Safe minimum' )
410 ovfl = one / unfl
411 ulp = slamch( 'Epsilon' )*slamch( 'Base' )
412 ulpinv = one / ulp
413 rtunfl = sqrt( unfl )
414 rtovfl = sqrt( ovfl )
415*
416* Loop over sizes, types
417*
418 nerrs = 0
419 nmats = 0
420*
421 DO 190 jsize = 1, nsizes
422 n = nn( jsize )
423 aninv = one / real( max( 1, n ) )
424*
425 DO 180 jwidth = 1, nwdths
426 k = kk( jwidth )
427 IF( k.GT.n )
428 \$ GO TO 180
429 k = max( 0, min( n-1, k ) )
430*
431 IF( nsizes.NE.1 ) THEN
432 mtypes = min( maxtyp, ntypes )
433 ELSE
434 mtypes = min( maxtyp+1, ntypes )
435 END IF
436*
437 DO 170 jtype = 1, mtypes
438 IF( .NOT.dotype( jtype ) )
439 \$ GO TO 170
440 nmats = nmats + 1
441 ntest = 0
442*
443 DO 30 j = 1, 4
444 ioldsd( j ) = iseed( j )
445 30 CONTINUE
446*
447* Compute "A".
448* Store as "Upper"; later, we will copy to other format.
449*
450* Control parameters:
451*
452* KMAGN KMODE KTYPE
453* =1 O(1) clustered 1 zero
454* =2 large clustered 2 identity
455* =3 small exponential (none)
456* =4 arithmetic diagonal, (w/ eigenvalues)
457* =5 random log symmetric, w/ eigenvalues
458* =6 random (none)
459* =7 random diagonal
460* =8 random symmetric
461* =9 positive definite
462* =10 diagonally dominant tridiagonal
463*
464 IF( mtypes.GT.maxtyp )
465 \$ GO TO 100
466*
467 itype = ktype( jtype )
468 imode = kmode( jtype )
469*
470* Compute norm
471*
472 GO TO ( 40, 50, 60 )kmagn( jtype )
473*
474 40 CONTINUE
475 anorm = one
476 GO TO 70
477*
478 50 CONTINUE
479 anorm = ( rtovfl*ulp )*aninv
480 GO TO 70
481*
482 60 CONTINUE
483 anorm = rtunfl*n*ulpinv
484 GO TO 70
485*
486 70 CONTINUE
487*
488 CALL slaset( 'Full', lda, n, zero, zero, a, lda )
489 iinfo = 0
490 IF( jtype.LE.15 ) THEN
491 cond = ulpinv
492 ELSE
493 cond = ulpinv*aninv / ten
494 END IF
495*
496* Special Matrices -- Identity & Jordan block
497*
498* Zero
499*
500 IF( itype.EQ.1 ) THEN
501 iinfo = 0
502*
503 ELSE IF( itype.EQ.2 ) THEN
504*
505* Identity
506*
507 DO 80 jcol = 1, n
508 a( k+1, jcol ) = anorm
509 80 CONTINUE
510*
511 ELSE IF( itype.EQ.4 ) THEN
512*
513* Diagonal Matrix, [Eigen]values Specified
514*
515 CALL slatms( n, n, 'S', iseed, 'S', work, imode, cond,
516 \$ anorm, 0, 0, 'Q', a( k+1, 1 ), lda,
517 \$ work( n+1 ), iinfo )
518*
519 ELSE IF( itype.EQ.5 ) THEN
520*
521* Symmetric, eigenvalues specified
522*
523 CALL slatms( n, n, 'S', iseed, 'S', work, imode, cond,
524 \$ anorm, k, k, 'Q', a, lda, work( n+1 ),
525 \$ iinfo )
526*
527 ELSE IF( itype.EQ.7 ) THEN
528*
529* Diagonal, random eigenvalues
530*
531 CALL slatmr( n, n, 'S', iseed, 'S', work, 6, one, one,
532 \$ 'T', 'N', work( n+1 ), 1, one,
533 \$ work( 2*n+1 ), 1, one, 'N', idumma, 0, 0,
534 \$ zero, anorm, 'Q', a( k+1, 1 ), lda,
535 \$ idumma, iinfo )
536*
537 ELSE IF( itype.EQ.8 ) THEN
538*
539* Symmetric, random eigenvalues
540*
541 CALL slatmr( n, n, 'S', iseed, 'S', work, 6, one, one,
542 \$ 'T', 'N', work( n+1 ), 1, one,
543 \$ work( 2*n+1 ), 1, one, 'N', idumma, k, k,
544 \$ zero, anorm, 'Q', a, lda, idumma, iinfo )
545*
546 ELSE IF( itype.EQ.9 ) THEN
547*
548* Positive definite, eigenvalues specified.
549*
550 CALL slatms( n, n, 'S', iseed, 'P', work, imode, cond,
551 \$ anorm, k, k, 'Q', a, lda, work( n+1 ),
552 \$ iinfo )
553*
554 ELSE IF( itype.EQ.10 ) THEN
555*
556* Positive definite tridiagonal, eigenvalues specified.
557*
558 IF( n.GT.1 )
559 \$ k = max( 1, k )
560 CALL slatms( n, n, 'S', iseed, 'P', work, imode, cond,
561 \$ anorm, 1, 1, 'Q', a( k, 1 ), lda,
562 \$ work( n+1 ), iinfo )
563 DO 90 i = 2, n
564 temp1 = abs( a( k, i ) ) /
565 \$ sqrt( abs( a( k+1, i-1 )*a( k+1, i ) ) )
566 IF( temp1.GT.half ) THEN
567 a( k, i ) = half*sqrt( abs( a( k+1,
568 \$ i-1 )*a( k+1, i ) ) )
569 END IF
570 90 CONTINUE
571*
572 ELSE
573*
574 iinfo = 1
575 END IF
576*
577 IF( iinfo.NE.0 ) THEN
578 WRITE( nounit, fmt = 9999 )'Generator', iinfo, n,
579 \$ jtype, ioldsd
580 info = abs( iinfo )
581 RETURN
582 END IF
583*
584 100 CONTINUE
585*
586* Call SSBTRD to compute S and U from upper triangle.
587*
588 CALL slacpy( ' ', k+1, n, a, lda, work, lda )
589*
590 ntest = 1
591 CALL ssbtrd( 'V', 'U', n, k, work, lda, sd, se, u, ldu,
592 \$ work( lda*n+1 ), iinfo )
593*
594 IF( iinfo.NE.0 ) THEN
595 WRITE( nounit, fmt = 9999 )'SSBTRD(U)', iinfo, n,
596 \$ jtype, ioldsd
597 info = abs( iinfo )
598 IF( iinfo.LT.0 ) THEN
599 RETURN
600 ELSE
601 result( 1 ) = ulpinv
602 GO TO 150
603 END IF
604 END IF
605*
606* Do tests 1 and 2
607*
608 CALL ssbt21( 'Upper', n, k, 1, a, lda, sd, se, u, ldu,
609 \$ work, result( 1 ) )
610*
611* Convert A from Upper-Triangle-Only storage to
612* Lower-Triangle-Only storage.
613*
614 DO 120 jc = 1, n
615 DO 110 jr = 0, min( k, n-jc )
616 a( jr+1, jc ) = a( k+1-jr, jc+jr )
617 110 CONTINUE
618 120 CONTINUE
619 DO 140 jc = n + 1 - k, n
620 DO 130 jr = min( k, n-jc ) + 1, k
621 a( jr+1, jc ) = zero
622 130 CONTINUE
623 140 CONTINUE
624*
625* Call SSBTRD to compute S and U from lower triangle
626*
627 CALL slacpy( ' ', k+1, n, a, lda, work, lda )
628*
629 ntest = 3
630 CALL ssbtrd( 'V', 'L', n, k, work, lda, sd, se, u, ldu,
631 \$ work( lda*n+1 ), iinfo )
632*
633 IF( iinfo.NE.0 ) THEN
634 WRITE( nounit, fmt = 9999 )'SSBTRD(L)', iinfo, n,
635 \$ jtype, ioldsd
636 info = abs( iinfo )
637 IF( iinfo.LT.0 ) THEN
638 RETURN
639 ELSE
640 result( 3 ) = ulpinv
641 GO TO 150
642 END IF
643 END IF
644 ntest = 4
645*
646* Do tests 3 and 4
647*
648 CALL ssbt21( 'Lower', n, k, 1, a, lda, sd, se, u, ldu,
649 \$ work, result( 3 ) )
650*
651* End of Loop -- Check for RESULT(j) > THRESH
652*
653 150 CONTINUE
654 ntestt = ntestt + ntest
655*
656* Print out tests which fail.
657*
658 DO 160 jr = 1, ntest
659 IF( result( jr ).GE.thresh ) THEN
660*
661* If this is the first test to fail,
662* print a header to the data file.
663*
664 IF( nerrs.EQ.0 ) THEN
665 WRITE( nounit, fmt = 9998 )'SSB'
666 WRITE( nounit, fmt = 9997 )
667 WRITE( nounit, fmt = 9996 )
668 WRITE( nounit, fmt = 9995 )'Symmetric'
669 WRITE( nounit, fmt = 9994 )'orthogonal', '''',
670 \$ 'transpose', ( '''', j = 1, 4 )
671 END IF
672 nerrs = nerrs + 1
673 WRITE( nounit, fmt = 9993 )n, k, ioldsd, jtype,
674 \$ jr, result( jr )
675 END IF
676 160 CONTINUE
677*
678 170 CONTINUE
679 180 CONTINUE
680 190 CONTINUE
681*
682* Summary
683*
684 CALL slasum( 'SSB', nounit, nerrs, ntestt )
685 RETURN
686*
687 9999 FORMAT( ' SCHKSB: ', a, ' returned INFO=', i6, '.', / 9x, 'N=',
688 \$ i6, ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ), i5, ')' )
689*
690 9998 FORMAT( / 1x, a3,
691 \$ ' -- Real Symmetric Banded Tridiagonal Reduction Routines' )
692 9997 FORMAT( ' Matrix types (see SCHKSB for details): ' )
693*
694 9996 FORMAT( / ' Special Matrices:',
695 \$ / ' 1=Zero matrix. ',
696 \$ ' 5=Diagonal: clustered entries.',
697 \$ / ' 2=Identity matrix. ',
698 \$ ' 6=Diagonal: large, evenly spaced.',
699 \$ / ' 3=Diagonal: evenly spaced entries. ',
700 \$ ' 7=Diagonal: small, evenly spaced.',
701 \$ / ' 4=Diagonal: geometr. spaced entries.' )
702 9995 FORMAT( ' Dense ', a, ' Banded Matrices:',
703 \$ / ' 8=Evenly spaced eigenvals. ',
704 \$ ' 12=Small, evenly spaced eigenvals.',
705 \$ / ' 9=Geometrically spaced eigenvals. ',
706 \$ ' 13=Matrix with random O(1) entries.',
707 \$ / ' 10=Clustered eigenvalues. ',
708 \$ ' 14=Matrix with large random entries.',
709 \$ / ' 11=Large, evenly spaced eigenvals. ',
710 \$ ' 15=Matrix with small random entries.' )
711*
712 9994 FORMAT( / ' Tests performed: (S is Tridiag, U is ', a, ',',
713 \$ / 20x, a, ' means ', a, '.', / ' UPLO=''U'':',
714 \$ / ' 1= | A - U S U', a1, ' | / ( |A| n ulp ) ',
715 \$ ' 2= | I - U U', a1, ' | / ( n ulp )', / ' UPLO=''L'':',
716 \$ / ' 3= | A - U S U', a1, ' | / ( |A| n ulp ) ',
717 \$ ' 4= | I - U U', a1, ' | / ( n ulp )' )
718 9993 FORMAT( ' N=', i5, ', K=', i4, ', seed=', 4( i4, ',' ), ' type ',
719 \$ i2, ', test(', i2, ')=', g10.3 )
720*
721* End of SCHKSB
722*
subroutine slaset(UPLO, M, N, ALPHA, BETA, A, LDA)
SLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: slaset.f:110
subroutine slacpy(UPLO, M, N, A, LDA, B, LDB)
SLACPY copies all or part of one two-dimensional array to another.
Definition: slacpy.f:103
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine slatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
SLATMS
Definition: slatms.f:321
subroutine slatmr(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, RSIGN, GRADE, DL, MODEL, CONDL, DR, MODER, CONDR, PIVTNG, IPIVOT, KL, KU, SPARSE, ANORM, PACK, A, LDA, IWORK, INFO)
SLATMR
Definition: slatmr.f:471
subroutine ssbtrd(VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO)
SSBTRD
Definition: ssbtrd.f:163
subroutine ssbt21(UPLO, N, KA, KS, A, LDA, D, E, U, LDU, WORK, RESULT)
SSBT21
Definition: ssbt21.f:147
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
subroutine slasum(TYPE, IOUNIT, IE, NRUN)
SLASUM
Definition: slasum.f:41
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