 LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine zchkbb ( integer NSIZES, integer, dimension( * ) MVAL, integer, dimension( * ) NVAL, integer NWDTHS, integer, dimension( * ) KK, integer NTYPES, logical, dimension( * ) DOTYPE, integer NRHS, integer, dimension( 4 ) ISEED, double precision THRESH, integer NOUNIT, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( ldab, * ) AB, integer LDAB, double precision, dimension( * ) BD, double precision, dimension( * ) BE, complex*16, dimension( ldq, * ) Q, integer LDQ, complex*16, dimension( ldp, * ) P, integer LDP, complex*16, dimension( ldc, * ) C, integer LDC, complex*16, dimension( ldc, * ) CC, complex*16, dimension( * ) WORK, integer LWORK, double precision, dimension( * ) RWORK, double precision, dimension( * ) RESULT, integer INFO )

ZCHKBB

Purpose:
``` ZCHKBB tests the reduction of a general complex rectangular band
matrix to real bidiagonal form.

ZGBBRD factors a general band matrix A as  Q B P* , where * means
conjugate transpose, B is upper bidiagonal, and Q and P are unitary;
ZGBBRD can also overwrite a given matrix C with Q* C .

For each pair of matrix dimensions (M,N) and each selected matrix
type, an M by N matrix A and an M by NRHS matrix C are generated.
The problem dimensions are as follows
A:          M x N
Q:          M x M
P:          N x N
B:          min(M,N) x min(M,N)
C:          M x NRHS

For each generated matrix, 4 tests are performed:

(1)   | A - Q B PT | / ( |A| max(M,N) ulp ), PT = P'

(2)   | I - Q' Q | / ( M ulp )

(3)   | I - PT PT' | / ( N ulp )

(4)   | Y - Q' C | / ( |Y| max(M,NRHS) ulp ), where Y = Q' C.

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:

The possible matrix types are

(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 (3), but multiplied by SQRT( overflow threshold )
(7)  Same as (3), but multiplied by SQRT( underflow threshold )

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

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

(10) A matrix of the form  U D V, where U and V are 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) Rectangular 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 values of M and N contained in the vectors MVAL and NVAL. The matrix sizes are used in pairs (M,N). If NSIZES is zero, ZCHKBB does nothing. NSIZES must be at least zero.``` [in] MVAL ``` MVAL is INTEGER array, dimension (NSIZES) The values of the matrix row dimension M.``` [in] NVAL ``` NVAL is INTEGER array, dimension (NSIZES) The values of the matrix column dimension N.``` [in] NWDTHS ``` NWDTHS is INTEGER The number of bandwidths to use. If it is zero, ZCHKBB 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, ZCHKBB 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] NRHS ``` NRHS is INTEGER The number of columns in the "right-hand side" matrix C. If NRHS = 0, then the operations on the right-hand side will not be tested. NRHS must be at least 0.``` [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 ZCHKBB 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 A.``` [in] LDA ``` LDA is INTEGER The leading dimension of A. It must be at least 1 and at least max( NN ).``` [out] AB ``` AB is DOUBLE PRECISION array, dimension (LDAB, max(NN)) Used to hold A in band storage format.``` [in] LDAB ``` LDAB is INTEGER The leading dimension of AB. It must be at least 2 (not 1!) and at least max( KK )+1.``` [out] BD ``` BD is DOUBLE PRECISION array, dimension (max(NN)) Used to hold the diagonal of the bidiagonal matrix computed by ZGBBRD.``` [out] BE ``` BE is DOUBLE PRECISION array, dimension (max(NN)) Used to hold the off-diagonal of the bidiagonal matrix computed by ZGBBRD.``` [out] Q ``` Q is COMPLEX*16 array, dimension (LDQ, max(NN)) Used to hold the unitary matrix Q computed by ZGBBRD.``` [in] LDQ ``` LDQ is INTEGER The leading dimension of Q. It must be at least 1 and at least max( NN ).``` [out] P ``` P is COMPLEX*16 array, dimension (LDP, max(NN)) Used to hold the unitary matrix P computed by ZGBBRD.``` [in] LDP ``` LDP is INTEGER The leading dimension of P. It must be at least 1 and at least max( NN ).``` [out] C ``` C is COMPLEX*16 array, dimension (LDC, max(NN)) Used to hold the matrix C updated by ZGBBRD.``` [in] LDC ``` LDC is INTEGER The leading dimension of U. It must be at least 1 and at least max( NN ).``` [out] CC ``` CC is COMPLEX*16 array, dimension (LDC, max(NN)) Used to hold a copy of the matrix C.``` [out] WORK ` WORK is COMPLEX*16 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] RWORK ` RWORK is DOUBLE PRECISION array, dimension (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) )```
Date
November 2011

Definition at line 363 of file zchkbb.f.

363 *
364 * -- LAPACK test routine (input) --
365 * -- LAPACK is a software package provided by Univ. of Tennessee, --
366 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
367 * November 2011
368 *
369 * .. Scalar Arguments ..
370  INTEGER info, lda, ldab, ldc, ldp, ldq, lwork, nounit,
371  \$ nrhs, nsizes, ntypes, nwdths
372  DOUBLE PRECISION thresh
373 * ..
374 * .. Array Arguments ..
375  LOGICAL dotype( * )
376  INTEGER iseed( 4 ), kk( * ), mval( * ), nval( * )
377  DOUBLE PRECISION bd( * ), be( * ), result( * ), rwork( * )
378  COMPLEX*16 a( lda, * ), ab( ldab, * ), c( ldc, * ),
379  \$ cc( ldc, * ), p( ldp, * ), q( ldq, * ),
380  \$ work( * )
381 * ..
382 *
383 * =====================================================================
384 *
385 * .. Parameters ..
386  COMPLEX*16 czero, cone
387  parameter ( czero = ( 0.0d+0, 0.0d+0 ),
388  \$ cone = ( 1.0d+0, 0.0d+0 ) )
389  DOUBLE PRECISION zero, one
390  parameter ( zero = 0.0d+0, one = 1.0d+0 )
391  INTEGER maxtyp
392  parameter ( maxtyp = 15 )
393 * ..
394 * .. Local Scalars ..
396  INTEGER i, iinfo, imode, itype, j, jcol, jr, jsize,
397  \$ jtype, jwidth, k, kl, kmax, ku, m, mmax, mnmax,
398  \$ mnmin, mtypes, n, nerrs, nmats, nmax, ntest,
399  \$ ntestt
400  DOUBLE PRECISION amninv, anorm, cond, ovfl, rtovfl, rtunfl, ulp,
401  \$ ulpinv, unfl
402 * ..
403 * .. Local Arrays ..
404  INTEGER idumma( 1 ), ioldsd( 4 ), kmagn( maxtyp ),
405  \$ kmode( maxtyp ), ktype( maxtyp )
406 * ..
407 * .. External Functions ..
408  DOUBLE PRECISION dlamch
409  EXTERNAL dlamch
410 * ..
411 * .. External Subroutines ..
412  EXTERNAL dlahd2, dlasum, xerbla, zbdt01, zbdt02, zgbbrd,
414 * ..
415 * .. Intrinsic Functions ..
416  INTRINSIC abs, dble, max, min, sqrt
417 * ..
418 * .. Data statements ..
419  DATA ktype / 1, 2, 5*4, 5*6, 3*9 /
420  DATA kmagn / 2*1, 3*1, 2, 3, 3*1, 2, 3, 1, 2, 3 /
421  DATA kmode / 2*0, 4, 3, 1, 4, 4, 4, 3, 1, 4, 4, 0,
422  \$ 0, 0 /
423 * ..
424 * .. Executable Statements ..
425 *
426 * Check for errors
427 *
428  ntestt = 0
429  info = 0
430 *
431 * Important constants
432 *
435  mmax = 1
436  nmax = 1
437  mnmax = 1
438  DO 10 j = 1, nsizes
439  mmax = max( mmax, mval( j ) )
440  IF( mval( j ).LT.0 )
442  nmax = max( nmax, nval( j ) )
443  IF( nval( j ).LT.0 )
445  mnmax = max( mnmax, min( mval( j ), nval( j ) ) )
446  10 CONTINUE
447 *
449  kmax = 0
450  DO 20 j = 1, nwdths
451  kmax = max( kmax, kk( j ) )
452  IF( kk( j ).LT.0 )
454  20 CONTINUE
455 *
456 * Check for errors
457 *
458  IF( nsizes.LT.0 ) THEN
459  info = -1
460  ELSE IF( badmm ) THEN
461  info = -2
462  ELSE IF( badnn ) THEN
463  info = -3
464  ELSE IF( nwdths.LT.0 ) THEN
465  info = -4
466  ELSE IF( badnnb ) THEN
467  info = -5
468  ELSE IF( ntypes.LT.0 ) THEN
469  info = -6
470  ELSE IF( nrhs.LT.0 ) THEN
471  info = -8
472  ELSE IF( lda.LT.nmax ) THEN
473  info = -13
474  ELSE IF( ldab.LT.2*kmax+1 ) THEN
475  info = -15
476  ELSE IF( ldq.LT.nmax ) THEN
477  info = -19
478  ELSE IF( ldp.LT.nmax ) THEN
479  info = -21
480  ELSE IF( ldc.LT.nmax ) THEN
481  info = -23
482  ELSE IF( ( max( lda, nmax )+1 )*nmax.GT.lwork ) THEN
483  info = -26
484  END IF
485 *
486  IF( info.NE.0 ) THEN
487  CALL xerbla( 'ZCHKBB', -info )
488  RETURN
489  END IF
490 *
491 * Quick return if possible
492 *
493  IF( nsizes.EQ.0 .OR. ntypes.EQ.0 .OR. nwdths.EQ.0 )
494  \$ RETURN
495 *
496 * More Important constants
497 *
498  unfl = dlamch( 'Safe minimum' )
499  ovfl = one / unfl
500  ulp = dlamch( 'Epsilon' )*dlamch( 'Base' )
501  ulpinv = one / ulp
502  rtunfl = sqrt( unfl )
503  rtovfl = sqrt( ovfl )
504 *
505 * Loop over sizes, widths, types
506 *
507  nerrs = 0
508  nmats = 0
509 *
510  DO 160 jsize = 1, nsizes
511  m = mval( jsize )
512  n = nval( jsize )
513  mnmin = min( m, n )
514  amninv = one / dble( max( 1, m, n ) )
515 *
516  DO 150 jwidth = 1, nwdths
517  k = kk( jwidth )
518  IF( k.GE.m .AND. k.GE.n )
519  \$ GO TO 150
520  kl = max( 0, min( m-1, k ) )
521  ku = max( 0, min( n-1, k ) )
522 *
523  IF( nsizes.NE.1 ) THEN
524  mtypes = min( maxtyp, ntypes )
525  ELSE
526  mtypes = min( maxtyp+1, ntypes )
527  END IF
528 *
529  DO 140 jtype = 1, mtypes
530  IF( .NOT.dotype( jtype ) )
531  \$ GO TO 140
532  nmats = nmats + 1
533  ntest = 0
534 *
535  DO 30 j = 1, 4
536  ioldsd( j ) = iseed( j )
537  30 CONTINUE
538 *
539 * Compute "A".
540 *
541 * Control parameters:
542 *
543 * KMAGN KMODE KTYPE
544 * =1 O(1) clustered 1 zero
545 * =2 large clustered 2 identity
546 * =3 small exponential (none)
547 * =4 arithmetic diagonal, (w/ singular values)
548 * =5 random log (none)
549 * =6 random nonhermitian, w/ singular values
550 * =7 (none)
551 * =8 (none)
552 * =9 random nonhermitian
553 *
554  IF( mtypes.GT.maxtyp )
555  \$ GO TO 90
556 *
557  itype = ktype( jtype )
558  imode = kmode( jtype )
559 *
560 * Compute norm
561 *
562  GO TO ( 40, 50, 60 )kmagn( jtype )
563 *
564  40 CONTINUE
565  anorm = one
566  GO TO 70
567 *
568  50 CONTINUE
569  anorm = ( rtovfl*ulp )*amninv
570  GO TO 70
571 *
572  60 CONTINUE
573  anorm = rtunfl*max( m, n )*ulpinv
574  GO TO 70
575 *
576  70 CONTINUE
577 *
578  CALL zlaset( 'Full', lda, n, czero, czero, a, lda )
579  CALL zlaset( 'Full', ldab, n, czero, czero, ab, ldab )
580  iinfo = 0
581  cond = ulpinv
582 *
583 * Special Matrices -- Identity & Jordan block
584 *
585 * Zero
586 *
587  IF( itype.EQ.1 ) THEN
588  iinfo = 0
589 *
590  ELSE IF( itype.EQ.2 ) THEN
591 *
592 * Identity
593 *
594  DO 80 jcol = 1, n
595  a( jcol, jcol ) = anorm
596  80 CONTINUE
597 *
598  ELSE IF( itype.EQ.4 ) THEN
599 *
600 * Diagonal Matrix, singular values specified
601 *
602  CALL zlatms( m, n, 'S', iseed, 'N', rwork, imode,
603  \$ cond, anorm, 0, 0, 'N', a, lda, work,
604  \$ iinfo )
605 *
606  ELSE IF( itype.EQ.6 ) THEN
607 *
608 * Nonhermitian, singular values specified
609 *
610  CALL zlatms( m, n, 'S', iseed, 'N', rwork, imode,
611  \$ cond, anorm, kl, ku, 'N', a, lda, work,
612  \$ iinfo )
613 *
614  ELSE IF( itype.EQ.9 ) THEN
615 *
616 * Nonhermitian, random entries
617 *
618  CALL zlatmr( m, n, 'S', iseed, 'N', work, 6, one,
619  \$ cone, 'T', 'N', work( n+1 ), 1, one,
620  \$ work( 2*n+1 ), 1, one, 'N', idumma, kl,
621  \$ ku, zero, anorm, 'N', a, lda, idumma,
622  \$ iinfo )
623 *
624  ELSE
625 *
626  iinfo = 1
627  END IF
628 *
629 * Generate Right-Hand Side
630 *
631  CALL zlatmr( m, nrhs, 'S', iseed, 'N', work, 6, one,
632  \$ cone, 'T', 'N', work( m+1 ), 1, one,
633  \$ work( 2*m+1 ), 1, one, 'N', idumma, m, nrhs,
634  \$ zero, one, 'NO', c, ldc, idumma, iinfo )
635 *
636  IF( iinfo.NE.0 ) THEN
637  WRITE( nounit, fmt = 9999 )'Generator', iinfo, n,
638  \$ jtype, ioldsd
639  info = abs( iinfo )
640  RETURN
641  END IF
642 *
643  90 CONTINUE
644 *
645 * Copy A to band storage.
646 *
647  DO 110 j = 1, n
648  DO 100 i = max( 1, j-ku ), min( m, j+kl )
649  ab( ku+1+i-j, j ) = a( i, j )
650  100 CONTINUE
651  110 CONTINUE
652 *
653 * Copy C
654 *
655  CALL zlacpy( 'Full', m, nrhs, c, ldc, cc, ldc )
656 *
657 * Call ZGBBRD to compute B, Q and P, and to update C.
658 *
659  CALL zgbbrd( 'B', m, n, nrhs, kl, ku, ab, ldab, bd, be,
660  \$ q, ldq, p, ldp, cc, ldc, work, rwork,
661  \$ iinfo )
662 *
663  IF( iinfo.NE.0 ) THEN
664  WRITE( nounit, fmt = 9999 )'ZGBBRD', iinfo, n, jtype,
665  \$ ioldsd
666  info = abs( iinfo )
667  IF( iinfo.LT.0 ) THEN
668  RETURN
669  ELSE
670  result( 1 ) = ulpinv
671  GO TO 120
672  END IF
673  END IF
674 *
675 * Test 1: Check the decomposition A := Q * B * P'
676 * 2: Check the orthogonality of Q
677 * 3: Check the orthogonality of P
678 * 4: Check the computation of Q' * C
679 *
680  CALL zbdt01( m, n, -1, a, lda, q, ldq, bd, be, p, ldp,
681  \$ work, rwork, result( 1 ) )
682  CALL zunt01( 'Columns', m, m, q, ldq, work, lwork, rwork,
683  \$ result( 2 ) )
684  CALL zunt01( 'Rows', n, n, p, ldp, work, lwork, rwork,
685  \$ result( 3 ) )
686  CALL zbdt02( m, nrhs, c, ldc, cc, ldc, q, ldq, work,
687  \$ rwork, result( 4 ) )
688 *
689 * End of Loop -- Check for RESULT(j) > THRESH
690 *
691  ntest = 4
692  120 CONTINUE
693  ntestt = ntestt + ntest
694 *
695 * Print out tests which fail.
696 *
697  DO 130 jr = 1, ntest
698  IF( result( jr ).GE.thresh ) THEN
699  IF( nerrs.EQ.0 )
700  \$ CALL dlahd2( nounit, 'ZBB' )
701  nerrs = nerrs + 1
702  WRITE( nounit, fmt = 9998 )m, n, k, ioldsd, jtype,
703  \$ jr, result( jr )
704  END IF
705  130 CONTINUE
706 *
707  140 CONTINUE
708  150 CONTINUE
709  160 CONTINUE
710 *
711 * Summary
712 *
713  CALL dlasum( 'ZBB', nounit, nerrs, ntestt )
714  RETURN
715 *
716  9999 FORMAT( ' ZCHKBB: ', a, ' returned INFO=', i5, '.', / 9x, 'M=',
717  \$ i5, ' N=', i5, ' K=', i5, ', JTYPE=', i5, ', ISEED=(',
718  \$ 3( i5, ',' ), i5, ')' )
719  9998 FORMAT( ' M =', i4, ' N=', i4, ', K=', i3, ', seed=',
720  \$ 4( i4, ',' ), ' type ', i2, ', test(', i2, ')=', g10.3 )
721 *
722 * End of ZCHKBB
723 *
subroutine zlacpy(UPLO, M, N, A, LDA, B, LDB)
ZLACPY copies all or part of one two-dimensional array to another.
Definition: zlacpy.f:105
subroutine zlatmr(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)
ZLATMR
Definition: zlatmr.f:492
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
subroutine zlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
ZLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values...
Definition: zlaset.f:108
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine zunt01(ROWCOL, M, N, U, LDU, WORK, LWORK, RWORK, RESID)
ZUNT01
Definition: zunt01.f:128
subroutine zbdt01(M, N, KD, A, LDA, Q, LDQ, D, E, PT, LDPT, WORK, RWORK, RESID)
ZBDT01
Definition: zbdt01.f:148
subroutine zbdt02(M, N, B, LDB, C, LDC, U, LDU, WORK, RWORK, RESID)
ZBDT02
Definition: zbdt02.f:121
subroutine dlasum(TYPE, IOUNIT, IE, NRUN)
DLASUM
Definition: dlasum.f:45
subroutine dlahd2(IOUNIT, PATH)
DLAHD2
Definition: dlahd2.f:67
subroutine zlatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
ZLATMS
Definition: zlatms.f:334
subroutine zgbbrd(VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q, LDQ, PT, LDPT, C, LDC, WORK, RWORK, INFO)
ZGBBRD
Definition: zgbbrd.f:195

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