LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ dchksb()

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

DCHKSB

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

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

When DCHKSB 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 DSBTRD with
UPLO='U'

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

(3)     | A - V S V' | / ( |A| n ulp )  computed by DSBTRD 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, DCHKSB 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, DCHKSB 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, DCHKSB 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 DCHKSB to continue the same random number sequence.``` [in] THRESH ``` THRESH is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (max(NN)) Used to hold the diagonal of the tridiagonal matrix computed by DSBTRD.``` [out] SE ``` SE is DOUBLE PRECISION array, dimension (max(NN)) Used to hold the off-diagonal of the tridiagonal matrix computed by DSBTRD.``` [out] U ``` U is DOUBLE PRECISION array, dimension (LDU, max(NN)) Used to hold the orthogonal matrix computed by DSBTRD.``` [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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 dchksb.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  DOUBLE PRECISION THRESH
302 * ..
303 * .. Array Arguments ..
304  LOGICAL DOTYPE( * )
305  INTEGER ISEED( 4 ), KK( * ), NN( * )
306  DOUBLE PRECISION A( LDA, * ), RESULT( * ), SD( * ), SE( * ),
307  \$ U( LDU, * ), WORK( * )
308 * ..
309 *
310 * =====================================================================
311 *
312 * .. Parameters ..
313  DOUBLE PRECISION ZERO, ONE, TWO, TEN
314  parameter( zero = 0.0d0, one = 1.0d0, two = 2.0d0,
315  \$ ten = 10.0d0 )
316  DOUBLE PRECISION 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  DOUBLE PRECISION 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  DOUBLE PRECISION DLAMCH
335  EXTERNAL dlamch
336 * ..
337 * .. External Subroutines ..
338  EXTERNAL dlacpy, dlaset, dlasum, dlatmr, dlatms, dsbt21,
339  \$ dsbtrd, xerbla
340 * ..
341 * .. Intrinsic Functions ..
342  INTRINSIC abs, dble, max, min, 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( 'DCHKSB', -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 = dlamch( 'Safe minimum' )
410  ovfl = one / unfl
411  ulp = dlamch( 'Epsilon' )*dlamch( '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 / dble( 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 dlaset( '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 dlatms( 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 dlatms( 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 dlatmr( 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 dlatmr( 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 dlatms( 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 dlatms( 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 DSBTRD to compute S and U from upper triangle.
587 *
588  CALL dlacpy( ' ', k+1, n, a, lda, work, lda )
589 *
590  ntest = 1
591  CALL dsbtrd( '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 )'DSBTRD(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 dsbt21( '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 DSBTRD to compute S and U from lower triangle
626 *
627  CALL dlacpy( ' ', k+1, n, a, lda, work, lda )
628 *
629  ntest = 3
630  CALL dsbtrd( '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 )'DSBTRD(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 dsbt21( '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 )'DSB'
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 dlasum( 'DSB', nounit, nerrs, ntestt )
685  RETURN
686 *
687  9999 FORMAT( ' DCHKSB: ', 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 DCHKSB 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 DCHKSB
722 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine dlacpy(UPLO, M, N, A, LDA, B, LDB)
DLACPY copies all or part of one two-dimensional array to another.
Definition: dlacpy.f:103
subroutine dlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
DLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: dlaset.f:110
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine dsbt21(UPLO, N, KA, KS, A, LDA, D, E, U, LDU, WORK, RESULT)
DSBT21
Definition: dsbt21.f:147
subroutine dlasum(TYPE, IOUNIT, IE, NRUN)
DLASUM
Definition: dlasum.f:43
subroutine dlatmr(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)
DLATMR
Definition: dlatmr.f:471
subroutine dlatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
DLATMS
Definition: dlatms.f:321
subroutine dsbtrd(VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO)
DSBTRD
Definition: dsbtrd.f:163
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