LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ sdrvvx()

 subroutine sdrvvx ( integer NSIZES, integer, dimension( * ) NN, integer NTYPES, logical, dimension( * ) DOTYPE, integer, dimension( 4 ) ISEED, real THRESH, integer NIUNIT, integer NOUNIT, real, dimension( lda, * ) A, integer LDA, real, dimension( lda, * ) H, real, dimension( * ) WR, real, dimension( * ) WI, real, dimension( * ) WR1, real, dimension( * ) WI1, real, dimension( ldvl, * ) VL, integer LDVL, real, dimension( ldvr, * ) VR, integer LDVR, real, dimension( ldlre, * ) LRE, integer LDLRE, real, dimension( * ) RCONDV, real, dimension( * ) RCNDV1, real, dimension( * ) RCDVIN, real, dimension( * ) RCONDE, real, dimension( * ) RCNDE1, real, dimension( * ) RCDEIN, real, dimension( * ) SCALE, real, dimension( * ) SCALE1, real, dimension( 11 ) RESULT, real, dimension( * ) WORK, integer NWORK, integer, dimension( * ) IWORK, integer INFO )

SDRVVX

Purpose:
```    SDRVVX  checks the nonsymmetric eigenvalue problem expert driver
SGEEVX.

SDRVVX uses both test matrices generated randomly depending on
data supplied in the calling sequence, as well as on data
read from an input file and including precomputed condition
numbers to which it compares the ones it computes.

When SDRVVX is called, a number of matrix "sizes" ("n's") and a
number of matrix "types" are specified in the calling sequence.
For each size ("n") and each type of matrix, one matrix will be
generated and used to test the nonsymmetric eigenroutines.  For
each matrix, 9 tests will be performed:

(1)     | A * VR - VR * W | / ( n |A| ulp )

Here VR is the matrix of unit right eigenvectors.
W is a block diagonal matrix, with a 1x1 block for each
real eigenvalue and a 2x2 block for each complex conjugate
pair.  If eigenvalues j and j+1 are a complex conjugate pair,
so WR(j) = WR(j+1) = wr and WI(j) = - WI(j+1) = wi, then the
2 x 2 block corresponding to the pair will be:

(  wr  wi  )
( -wi  wr  )

Such a block multiplying an n x 2 matrix  ( ur ui ) on the
right will be the same as multiplying  ur + i*ui  by  wr + i*wi.

(2)     | A**H * VL - VL * W**H | / ( n |A| ulp )

Here VL is the matrix of unit left eigenvectors, A**H is the
conjugate transpose of A, and W is as above.

(3)     | |VR(i)| - 1 | / ulp and largest component real

VR(i) denotes the i-th column of VR.

(4)     | |VL(i)| - 1 | / ulp and largest component real

VL(i) denotes the i-th column of VL.

(5)     W(full) = W(partial)

W(full) denotes the eigenvalues computed when VR, VL, RCONDV
and RCONDE are also computed, and W(partial) denotes the
eigenvalues computed when only some of VR, VL, RCONDV, and
RCONDE are computed.

(6)     VR(full) = VR(partial)

VR(full) denotes the right eigenvectors computed when VL, RCONDV
and RCONDE are computed, and VR(partial) denotes the result
when only some of VL and RCONDV are computed.

(7)     VL(full) = VL(partial)

VL(full) denotes the left eigenvectors computed when VR, RCONDV
and RCONDE are computed, and VL(partial) denotes the result
when only some of VR and RCONDV are computed.

(8)     0 if SCALE, ILO, IHI, ABNRM (full) =
SCALE, ILO, IHI, ABNRM (partial)
1/ulp otherwise

SCALE, ILO, IHI and ABNRM describe how the matrix is balanced.
(full) is when VR, VL, RCONDE and RCONDV are also computed, and
(partial) is when some are not computed.

(9)     RCONDV(full) = RCONDV(partial)

RCONDV(full) denotes the reciprocal condition numbers of the
right eigenvectors computed when VR, VL and RCONDE are also
computed. RCONDV(partial) denotes the reciprocal condition
numbers when only some of VR, VL and RCONDE are computed.

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 (transposed) Jordan block, with 1's on the diagonal.

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

(7)  Same as (4), but multiplied by a constant near
the overflow threshold
(8)  Same as (4), but multiplied by a constant near
the underflow threshold

(9)  A matrix of the form  U' T U, where U is orthogonal and
T has evenly spaced entries 1, ..., ULP with random signs
on the diagonal and random O(1) entries in the upper
triangle.

(10) A matrix of the form  U' T U, where U is orthogonal and
T has geometrically spaced entries 1, ..., ULP with random
signs on the diagonal and random O(1) entries in the upper
triangle.

(11) A matrix of the form  U' T U, where U is orthogonal and
T has "clustered" entries 1, ULP,..., ULP with random
signs on the diagonal and random O(1) entries in the upper
triangle.

(12) A matrix of the form  U' T U, where U is orthogonal and
T has real or complex conjugate paired eigenvalues randomly
chosen from ( ULP, 1 ) and random O(1) entries in the upper
triangle.

(13) A matrix of the form  X' T X, where X has condition
SQRT( ULP ) and T has evenly spaced entries 1, ..., ULP
with random signs on the diagonal and random O(1) entries
in the upper triangle.

(14) A matrix of the form  X' T X, where X has condition
SQRT( ULP ) and T has geometrically spaced entries
1, ..., ULP with random signs on the diagonal and random
O(1) entries in the upper triangle.

(15) A matrix of the form  X' T X, where X has condition
SQRT( ULP ) and T has "clustered" entries 1, ULP,..., ULP
with random signs on the diagonal and random O(1) entries
in the upper triangle.

(16) A matrix of the form  X' T X, where X has condition
SQRT( ULP ) and T has real or complex conjugate paired
eigenvalues randomly chosen from ( ULP, 1 ) and random
O(1) entries in the upper triangle.

(17) Same as (16), but multiplied by a constant
near the overflow threshold
(18) Same as (16), but multiplied by a constant
near the underflow threshold

(19) Nonsymmetric matrix with random entries chosen from (-1,1).
If N is at least 4, all entries in first two rows and last
row, and first column and last two columns are zero.
(20) Same as (19), but multiplied by a constant
near the overflow threshold
(21) Same as (19), but multiplied by a constant
near the underflow threshold

In addition, an input file will be read from logical unit number
NIUNIT. The file contains matrices along with precomputed
eigenvalues and reciprocal condition numbers for the eigenvalues
and right eigenvectors. For these matrices, in addition to tests
(1) to (9) we will compute the following two tests:

(10)  |RCONDV - RCDVIN| / cond(RCONDV)

RCONDV is the reciprocal right eigenvector condition number
computed by SGEEVX and RCDVIN (the precomputed true value)
is supplied as input. cond(RCONDV) is the condition number of
RCONDV, and takes errors in computing RCONDV into account, so
that the resulting quantity should be O(ULP). cond(RCONDV) is
essentially given by norm(A)/RCONDE.

(11)  |RCONDE - RCDEIN| / cond(RCONDE)

RCONDE is the reciprocal eigenvalue condition number
computed by SGEEVX and RCDEIN (the precomputed true value)
is supplied as input.  cond(RCONDE) is the condition number
of RCONDE, and takes errors in computing RCONDE into account,
so that the resulting quantity should be O(ULP). cond(RCONDE)
is essentially given by norm(A)/RCONDV.```
Parameters
 [in] NSIZES ``` NSIZES is INTEGER The number of sizes of matrices to use. NSIZES must be at least zero. If it is zero, no randomly generated matrices are tested, but any test matrices read from NIUNIT will be tested.``` [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] NTYPES ``` NTYPES is INTEGER The number of elements in DOTYPE. NTYPES must be at least zero. If it is zero, no randomly generated test matrices are tested, but and test matrices read from NIUNIT will be tested. 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 SDRVVX 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] NIUNIT ``` NIUNIT is INTEGER The FORTRAN unit number for reading in the data file of problems to solve.``` [in] NOUNIT ``` NOUNIT is INTEGER The FORTRAN unit number for printing out error messages (e.g., if a routine returns INFO not equal to 0.)``` [out] A ``` A is REAL array, dimension (LDA, max(NN,12)) Used to hold the matrix whose eigenvalues are to be computed. On exit, A contains the last matrix actually used.``` [in] LDA ``` LDA is INTEGER The leading dimension of the arrays A and H. LDA >= max(NN,12), since 12 is the dimension of the largest matrix in the precomputed input file.``` [out] H ``` H is REAL array, dimension (LDA, max(NN,12)) Another copy of the test matrix A, modified by SGEEVX.``` [out] WR ` WR is REAL array, dimension (max(NN))` [out] WI ``` WI is REAL array, dimension (max(NN)) The real and imaginary parts of the eigenvalues of A. On exit, WR + WI*i are the eigenvalues of the matrix in A.``` [out] WR1 ` WR1 is REAL array, dimension (max(NN,12))` [out] WI1 ``` WI1 is REAL array, dimension (max(NN,12)) Like WR, WI, these arrays contain the eigenvalues of A, but those computed when SGEEVX only computes a partial eigendecomposition, i.e. not the eigenvalues and left and right eigenvectors.``` [out] VL ``` VL is REAL array, dimension (LDVL, max(NN,12)) VL holds the computed left eigenvectors.``` [in] LDVL ``` LDVL is INTEGER Leading dimension of VL. Must be at least max(1,max(NN,12)).``` [out] VR ``` VR is REAL array, dimension (LDVR, max(NN,12)) VR holds the computed right eigenvectors.``` [in] LDVR ``` LDVR is INTEGER Leading dimension of VR. Must be at least max(1,max(NN,12)).``` [out] LRE ``` LRE is REAL array, dimension (LDLRE, max(NN,12)) LRE holds the computed right or left eigenvectors.``` [in] LDLRE ``` LDLRE is INTEGER Leading dimension of LRE. Must be at least max(1,max(NN,12))``` [out] RCONDV ``` RCONDV is REAL array, dimension (N) RCONDV holds the computed reciprocal condition numbers for eigenvectors.``` [out] RCNDV1 ``` RCNDV1 is REAL array, dimension (N) RCNDV1 holds more computed reciprocal condition numbers for eigenvectors.``` [out] RCDVIN ``` RCDVIN is REAL array, dimension (N) When COMP = .TRUE. RCDVIN holds the precomputed reciprocal condition numbers for eigenvectors to be compared with RCONDV.``` [out] RCONDE ``` RCONDE is REAL array, dimension (N) RCONDE holds the computed reciprocal condition numbers for eigenvalues.``` [out] RCNDE1 ``` RCNDE1 is REAL array, dimension (N) RCNDE1 holds more computed reciprocal condition numbers for eigenvalues.``` [out] RCDEIN ``` RCDEIN is REAL array, dimension (N) When COMP = .TRUE. RCDEIN holds the precomputed reciprocal condition numbers for eigenvalues to be compared with RCONDE.``` [out] SCALE ``` SCALE is REAL array, dimension (N) Holds information describing balancing of matrix.``` [out] SCALE1 ``` SCALE1 is REAL array, dimension (N) Holds information describing balancing of matrix.``` [out] RESULT ``` RESULT is REAL array, dimension (11) The values computed by the seven tests described above. The values are currently limited to 1/ulp, to avoid overflow.``` [out] WORK ` WORK is REAL array, dimension (NWORK)` [in] NWORK ``` NWORK is INTEGER The number of entries in WORK. This must be at least max(6*12+2*12**2,6*NN(j)+2*NN(j)**2) = max( 360 ,6*NN(j)+2*NN(j)**2) for all j.``` [out] IWORK ` IWORK is INTEGER array, dimension (2*max(NN,12))` [out] INFO ``` INFO is INTEGER If 0, then successful exit. If <0, then input parameter -INFO is incorrect. If >0, SLATMR, SLATMS, SLATME or SGET23 returned an error code, and INFO is its absolute value. ----------------------------------------------------------------------- Some Local Variables and Parameters: ---- ----- --------- --- ---------- ZERO, ONE Real 0 and 1. MAXTYP The number of types defined. NMAX Largest value in NN or 12. NERRS The number of tests which have exceeded THRESH COND, CONDS, 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. RTULP, RTULPI Square roots of the previous 4 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) ) KCONDS(j) Selectw whether CONDS is to be 1 or 1/sqrt(ulp). (0 means irrelevant.)```

Definition at line 515 of file sdrvvx.f.

520 *
521 * -- LAPACK test routine --
522 * -- LAPACK is a software package provided by Univ. of Tennessee, --
523 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
524 *
525 * .. Scalar Arguments ..
526  INTEGER INFO, LDA, LDLRE, LDVL, LDVR, NIUNIT, NOUNIT,
527  \$ NSIZES, NTYPES, NWORK
528  REAL THRESH
529 * ..
530 * .. Array Arguments ..
531  LOGICAL DOTYPE( * )
532  INTEGER ISEED( 4 ), IWORK( * ), NN( * )
533  REAL A( LDA, * ), H( LDA, * ), LRE( LDLRE, * ),
534  \$ RCDEIN( * ), RCDVIN( * ), RCNDE1( * ),
535  \$ RCNDV1( * ), RCONDE( * ), RCONDV( * ),
536  \$ RESULT( 11 ), SCALE( * ), SCALE1( * ),
537  \$ VL( LDVL, * ), VR( LDVR, * ), WI( * ),
538  \$ WI1( * ), WORK( * ), WR( * ), WR1( * )
539 * ..
540 *
541 * =====================================================================
542 *
543 * .. Parameters ..
544  REAL ZERO, ONE
545  parameter( zero = 0.0e0, one = 1.0e0 )
546  INTEGER MAXTYP
547  parameter( maxtyp = 21 )
548 * ..
549 * .. Local Scalars ..
551  CHARACTER BALANC
552  CHARACTER*3 PATH
553  INTEGER I, IBAL, IINFO, IMODE, ITYPE, IWK, J, JCOL,
554  \$ JSIZE, JTYPE, MTYPES, N, NERRS, NFAIL,
555  \$ NMAX, NNWORK, NTEST, NTESTF, NTESTT
556  REAL ANORM, COND, CONDS, OVFL, RTULP, RTULPI, ULP,
557  \$ ULPINV, UNFL
558 * ..
559 * .. Local Arrays ..
560  CHARACTER ADUMMA( 1 ), BAL( 4 )
561  INTEGER IDUMMA( 1 ), IOLDSD( 4 ), KCONDS( MAXTYP ),
562  \$ KMAGN( MAXTYP ), KMODE( MAXTYP ),
563  \$ KTYPE( MAXTYP )
564 * ..
565 * .. External Functions ..
566  REAL SLAMCH
567  EXTERNAL slamch
568 * ..
569 * .. External Subroutines ..
570  EXTERNAL sget23, slabad, slasum, slatme, slatmr, slatms,
571  \$ slaset, xerbla
572 * ..
573 * .. Intrinsic Functions ..
574  INTRINSIC abs, max, min, sqrt
575 * ..
576 * .. Data statements ..
577  DATA ktype / 1, 2, 3, 5*4, 4*6, 6*6, 3*9 /
578  DATA kmagn / 3*1, 1, 1, 1, 2, 3, 4*1, 1, 1, 1, 1, 2,
579  \$ 3, 1, 2, 3 /
580  DATA kmode / 3*0, 4, 3, 1, 4, 4, 4, 3, 1, 5, 4, 3,
581  \$ 1, 5, 5, 5, 4, 3, 1 /
582  DATA kconds / 3*0, 5*0, 4*1, 6*2, 3*0 /
583  DATA bal / 'N', 'P', 'S', 'B' /
584 * ..
585 * .. Executable Statements ..
586 *
587  path( 1: 1 ) = 'Single precision'
588  path( 2: 3 ) = 'VX'
589 *
590 * Check for errors
591 *
592  ntestt = 0
593  ntestf = 0
594  info = 0
595 *
596 * Important constants
597 *
599 *
600 * 12 is the largest dimension in the input file of precomputed
601 * problems
602 *
603  nmax = 12
604  DO 10 j = 1, nsizes
605  nmax = max( nmax, nn( j ) )
606  IF( nn( j ).LT.0 )
608  10 CONTINUE
609 *
610 * Check for errors
611 *
612  IF( nsizes.LT.0 ) THEN
613  info = -1
614  ELSE IF( badnn ) THEN
615  info = -2
616  ELSE IF( ntypes.LT.0 ) THEN
617  info = -3
618  ELSE IF( thresh.LT.zero ) THEN
619  info = -6
620  ELSE IF( lda.LT.1 .OR. lda.LT.nmax ) THEN
621  info = -10
622  ELSE IF( ldvl.LT.1 .OR. ldvl.LT.nmax ) THEN
623  info = -17
624  ELSE IF( ldvr.LT.1 .OR. ldvr.LT.nmax ) THEN
625  info = -19
626  ELSE IF( ldlre.LT.1 .OR. ldlre.LT.nmax ) THEN
627  info = -21
628  ELSE IF( 6*nmax+2*nmax**2.GT.nwork ) THEN
629  info = -32
630  END IF
631 *
632  IF( info.NE.0 ) THEN
633  CALL xerbla( 'SDRVVX', -info )
634  RETURN
635  END IF
636 *
637 * If nothing to do check on NIUNIT
638 *
639  IF( nsizes.EQ.0 .OR. ntypes.EQ.0 )
640  \$ GO TO 160
641 *
642 * More Important constants
643 *
644  unfl = slamch( 'Safe minimum' )
645  ovfl = one / unfl
646  CALL slabad( unfl, ovfl )
647  ulp = slamch( 'Precision' )
648  ulpinv = one / ulp
649  rtulp = sqrt( ulp )
650  rtulpi = one / rtulp
651 *
652 * Loop over sizes, types
653 *
654  nerrs = 0
655 *
656  DO 150 jsize = 1, nsizes
657  n = nn( jsize )
658  IF( nsizes.NE.1 ) THEN
659  mtypes = min( maxtyp, ntypes )
660  ELSE
661  mtypes = min( maxtyp+1, ntypes )
662  END IF
663 *
664  DO 140 jtype = 1, mtypes
665  IF( .NOT.dotype( jtype ) )
666  \$ GO TO 140
667 *
668 * Save ISEED in case of an error.
669 *
670  DO 20 j = 1, 4
671  ioldsd( j ) = iseed( j )
672  20 CONTINUE
673 *
674 * Compute "A"
675 *
676 * Control parameters:
677 *
678 * KMAGN KCONDS KMODE KTYPE
679 * =1 O(1) 1 clustered 1 zero
680 * =2 large large clustered 2 identity
681 * =3 small exponential Jordan
682 * =4 arithmetic diagonal, (w/ eigenvalues)
683 * =5 random log symmetric, w/ eigenvalues
684 * =6 random general, w/ eigenvalues
685 * =7 random diagonal
686 * =8 random symmetric
687 * =9 random general
688 * =10 random triangular
689 *
690  IF( mtypes.GT.maxtyp )
691  \$ GO TO 90
692 *
693  itype = ktype( jtype )
694  imode = kmode( jtype )
695 *
696 * Compute norm
697 *
698  GO TO ( 30, 40, 50 )kmagn( jtype )
699 *
700  30 CONTINUE
701  anorm = one
702  GO TO 60
703 *
704  40 CONTINUE
705  anorm = ovfl*ulp
706  GO TO 60
707 *
708  50 CONTINUE
709  anorm = unfl*ulpinv
710  GO TO 60
711 *
712  60 CONTINUE
713 *
714  CALL slaset( 'Full', lda, n, zero, zero, a, lda )
715  iinfo = 0
716  cond = ulpinv
717 *
718 * Special Matrices -- Identity & Jordan block
719 *
720 * Zero
721 *
722  IF( itype.EQ.1 ) THEN
723  iinfo = 0
724 *
725  ELSE IF( itype.EQ.2 ) THEN
726 *
727 * Identity
728 *
729  DO 70 jcol = 1, n
730  a( jcol, jcol ) = anorm
731  70 CONTINUE
732 *
733  ELSE IF( itype.EQ.3 ) THEN
734 *
735 * Jordan Block
736 *
737  DO 80 jcol = 1, n
738  a( jcol, jcol ) = anorm
739  IF( jcol.GT.1 )
740  \$ a( jcol, jcol-1 ) = one
741  80 CONTINUE
742 *
743  ELSE IF( itype.EQ.4 ) THEN
744 *
745 * Diagonal Matrix, [Eigen]values Specified
746 *
747  CALL slatms( n, n, 'S', iseed, 'S', work, imode, cond,
748  \$ anorm, 0, 0, 'N', a, lda, work( n+1 ),
749  \$ iinfo )
750 *
751  ELSE IF( itype.EQ.5 ) THEN
752 *
753 * Symmetric, eigenvalues specified
754 *
755  CALL slatms( n, n, 'S', iseed, 'S', work, imode, cond,
756  \$ anorm, n, n, 'N', a, lda, work( n+1 ),
757  \$ iinfo )
758 *
759  ELSE IF( itype.EQ.6 ) THEN
760 *
761 * General, eigenvalues specified
762 *
763  IF( kconds( jtype ).EQ.1 ) THEN
764  conds = one
765  ELSE IF( kconds( jtype ).EQ.2 ) THEN
766  conds = rtulpi
767  ELSE
768  conds = zero
769  END IF
770 *
771  adumma( 1 ) = ' '
772  CALL slatme( n, 'S', iseed, work, imode, cond, one,
773  \$ adumma, 'T', 'T', 'T', work( n+1 ), 4,
774  \$ conds, n, n, anorm, a, lda, work( 2*n+1 ),
775  \$ iinfo )
776 *
777  ELSE IF( itype.EQ.7 ) THEN
778 *
779 * Diagonal, random eigenvalues
780 *
781  CALL slatmr( n, n, 'S', iseed, 'S', work, 6, one, one,
782  \$ 'T', 'N', work( n+1 ), 1, one,
783  \$ work( 2*n+1 ), 1, one, 'N', idumma, 0, 0,
784  \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
785 *
786  ELSE IF( itype.EQ.8 ) THEN
787 *
788 * Symmetric, random eigenvalues
789 *
790  CALL slatmr( n, n, 'S', iseed, 'S', work, 6, one, one,
791  \$ 'T', 'N', work( n+1 ), 1, one,
792  \$ work( 2*n+1 ), 1, one, 'N', idumma, n, n,
793  \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
794 *
795  ELSE IF( itype.EQ.9 ) THEN
796 *
797 * General, random eigenvalues
798 *
799  CALL slatmr( n, n, 'S', iseed, 'N', work, 6, one, one,
800  \$ 'T', 'N', work( n+1 ), 1, one,
801  \$ work( 2*n+1 ), 1, one, 'N', idumma, n, n,
802  \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
803  IF( n.GE.4 ) THEN
804  CALL slaset( 'Full', 2, n, zero, zero, a, lda )
805  CALL slaset( 'Full', n-3, 1, zero, zero, a( 3, 1 ),
806  \$ lda )
807  CALL slaset( 'Full', n-3, 2, zero, zero, a( 3, n-1 ),
808  \$ lda )
809  CALL slaset( 'Full', 1, n, zero, zero, a( n, 1 ),
810  \$ lda )
811  END IF
812 *
813  ELSE IF( itype.EQ.10 ) THEN
814 *
815 * Triangular, random eigenvalues
816 *
817  CALL slatmr( n, n, 'S', iseed, 'N', work, 6, one, one,
818  \$ 'T', 'N', work( n+1 ), 1, one,
819  \$ work( 2*n+1 ), 1, one, 'N', idumma, n, 0,
820  \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
821 *
822  ELSE
823 *
824  iinfo = 1
825  END IF
826 *
827  IF( iinfo.NE.0 ) THEN
828  WRITE( nounit, fmt = 9992 )'Generator', iinfo, n, jtype,
829  \$ ioldsd
830  info = abs( iinfo )
831  RETURN
832  END IF
833 *
834  90 CONTINUE
835 *
836 * Test for minimal and generous workspace
837 *
838  DO 130 iwk = 1, 3
839  IF( iwk.EQ.1 ) THEN
840  nnwork = 3*n
841  ELSE IF( iwk.EQ.2 ) THEN
842  nnwork = 6*n + n**2
843  ELSE
844  nnwork = 6*n + 2*n**2
845  END IF
846  nnwork = max( nnwork, 1 )
847 *
848 * Test for all balancing options
849 *
850  DO 120 ibal = 1, 4
851  balanc = bal( ibal )
852 *
853 * Perform tests
854 *
855  CALL sget23( .false., balanc, jtype, thresh, ioldsd,
856  \$ nounit, n, a, lda, h, wr, wi, wr1, wi1,
857  \$ vl, ldvl, vr, ldvr, lre, ldlre, rcondv,
858  \$ rcndv1, rcdvin, rconde, rcnde1, rcdein,
859  \$ scale, scale1, result, work, nnwork,
860  \$ iwork, info )
861 *
862 * Check for RESULT(j) > THRESH
863 *
864  ntest = 0
865  nfail = 0
866  DO 100 j = 1, 9
867  IF( result( j ).GE.zero )
868  \$ ntest = ntest + 1
869  IF( result( j ).GE.thresh )
870  \$ nfail = nfail + 1
871  100 CONTINUE
872 *
873  IF( nfail.GT.0 )
874  \$ ntestf = ntestf + 1
875  IF( ntestf.EQ.1 ) THEN
876  WRITE( nounit, fmt = 9999 )path
877  WRITE( nounit, fmt = 9998 )
878  WRITE( nounit, fmt = 9997 )
879  WRITE( nounit, fmt = 9996 )
880  WRITE( nounit, fmt = 9995 )thresh
881  ntestf = 2
882  END IF
883 *
884  DO 110 j = 1, 9
885  IF( result( j ).GE.thresh ) THEN
886  WRITE( nounit, fmt = 9994 )balanc, n, iwk,
887  \$ ioldsd, jtype, j, result( j )
888  END IF
889  110 CONTINUE
890 *
891  nerrs = nerrs + nfail
892  ntestt = ntestt + ntest
893 *
894  120 CONTINUE
895  130 CONTINUE
896  140 CONTINUE
897  150 CONTINUE
898 *
899  160 CONTINUE
900 *
901 * Read in data from file to check accuracy of condition estimation.
902 * Assume input eigenvalues are sorted lexicographically (increasing
903 * by real part, then decreasing by imaginary part)
904 *
905  jtype = 0
906  170 CONTINUE
907  READ( niunit, fmt = *, END = 220 )n
908 *
909 * Read input data until N=0
910 *
911  IF( n.EQ.0 )
912  \$ GO TO 220
913  jtype = jtype + 1
914  iseed( 1 ) = jtype
915  DO 180 i = 1, n
916  READ( niunit, fmt = * )( a( i, j ), j = 1, n )
917  180 CONTINUE
918  DO 190 i = 1, n
919  READ( niunit, fmt = * )wr1( i ), wi1( i ), rcdein( i ),
920  \$ rcdvin( i )
921  190 CONTINUE
922  CALL sget23( .true., 'N', 22, thresh, iseed, nounit, n, a, lda, h,
923  \$ wr, wi, wr1, wi1, vl, ldvl, vr, ldvr, lre, ldlre,
924  \$ rcondv, rcndv1, rcdvin, rconde, rcnde1, rcdein,
925  \$ scale, scale1, result, work, 6*n+2*n**2, iwork,
926  \$ info )
927 *
928 * Check for RESULT(j) > THRESH
929 *
930  ntest = 0
931  nfail = 0
932  DO 200 j = 1, 11
933  IF( result( j ).GE.zero )
934  \$ ntest = ntest + 1
935  IF( result( j ).GE.thresh )
936  \$ nfail = nfail + 1
937  200 CONTINUE
938 *
939  IF( nfail.GT.0 )
940  \$ ntestf = ntestf + 1
941  IF( ntestf.EQ.1 ) THEN
942  WRITE( nounit, fmt = 9999 )path
943  WRITE( nounit, fmt = 9998 )
944  WRITE( nounit, fmt = 9997 )
945  WRITE( nounit, fmt = 9996 )
946  WRITE( nounit, fmt = 9995 )thresh
947  ntestf = 2
948  END IF
949 *
950  DO 210 j = 1, 11
951  IF( result( j ).GE.thresh ) THEN
952  WRITE( nounit, fmt = 9993 )n, jtype, j, result( j )
953  END IF
954  210 CONTINUE
955 *
956  nerrs = nerrs + nfail
957  ntestt = ntestt + ntest
958  GO TO 170
959  220 CONTINUE
960 *
961 * Summary
962 *
963  CALL slasum( path, nounit, nerrs, ntestt )
964 *
965  9999 FORMAT( / 1x, a3, ' -- Real Eigenvalue-Eigenvector Decomposition',
966  \$ ' Expert Driver', /
967  \$ ' Matrix types (see SDRVVX for details): ' )
968 *
969  9998 FORMAT( / ' Special Matrices:', / ' 1=Zero matrix. ',
970  \$ ' ', ' 5=Diagonal: geometr. spaced entries.',
971  \$ / ' 2=Identity matrix. ', ' 6=Diagona',
972  \$ 'l: clustered entries.', / ' 3=Transposed Jordan block. ',
973  \$ ' ', ' 7=Diagonal: large, evenly spaced.', / ' ',
974  \$ '4=Diagonal: evenly spaced entries. ', ' 8=Diagonal: s',
975  \$ 'mall, evenly spaced.' )
976  9997 FORMAT( ' Dense, Non-Symmetric Matrices:', / ' 9=Well-cond., ev',
977  \$ 'enly spaced eigenvals.', ' 14=Ill-cond., geomet. spaced e',
978  \$ 'igenals.', / ' 10=Well-cond., geom. spaced eigenvals. ',
979  \$ ' 15=Ill-conditioned, clustered e.vals.', / ' 11=Well-cond',
980  \$ 'itioned, clustered e.vals. ', ' 16=Ill-cond., random comp',
981  \$ 'lex ', / ' 12=Well-cond., random complex ', ' ',
982  \$ ' 17=Ill-cond., large rand. complx ', / ' 13=Ill-condi',
983  \$ 'tioned, evenly spaced. ', ' 18=Ill-cond., small rand.',
984  \$ ' complx ' )
985  9996 FORMAT( ' 19=Matrix with random O(1) entries. ', ' 21=Matrix ',
986  \$ 'with small random entries.', / ' 20=Matrix with large ran',
987  \$ 'dom entries. ', ' 22=Matrix read from input file', / )
988  9995 FORMAT( ' Tests performed with test threshold =', f8.2,
989  \$ / / ' 1 = | A VR - VR W | / ( n |A| ulp ) ',
990  \$ / ' 2 = | transpose(A) VL - VL W | / ( n |A| ulp ) ',
991  \$ / ' 3 = | |VR(i)| - 1 | / ulp ',
992  \$ / ' 4 = | |VL(i)| - 1 | / ulp ',
993  \$ / ' 5 = 0 if W same no matter if VR or VL computed,',
994  \$ ' 1/ulp otherwise', /
995  \$ ' 6 = 0 if VR same no matter what else computed,',
996  \$ ' 1/ulp otherwise', /
997  \$ ' 7 = 0 if VL same no matter what else computed,',
998  \$ ' 1/ulp otherwise', /
999  \$ ' 8 = 0 if RCONDV same no matter what else computed,',
1000  \$ ' 1/ulp otherwise', /
1001  \$ ' 9 = 0 if SCALE, ILO, IHI, ABNRM same no matter what else',
1002  \$ ' computed, 1/ulp otherwise',
1003  \$ / ' 10 = | RCONDV - RCONDV(precomputed) | / cond(RCONDV),',
1004  \$ / ' 11 = | RCONDE - RCONDE(precomputed) | / cond(RCONDE),' )
1005  9994 FORMAT( ' BALANC=''', a1, ''',N=', i4, ',IWK=', i1, ', seed=',
1006  \$ 4( i4, ',' ), ' type ', i2, ', test(', i2, ')=', g10.3 )
1007  9993 FORMAT( ' N=', i5, ', input example =', i3, ', test(', i2, ')=',
1008  \$ g10.3 )
1009  9992 FORMAT( ' SDRVVX: ', a, ' returned INFO=', i6, '.', / 9x, 'N=',
1010  \$ i6, ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ), i5, ')' )
1011 *
1012  RETURN
1013 *
1014 * End of SDRVVX
1015 *
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 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 slatme(N, DIST, ISEED, D, MODE, COND, DMAX, EI, RSIGN, UPPER, SIM, DS, MODES, CONDS, KL, KU, ANORM, A, LDA, WORK, INFO)
SLATME
Definition: slatme.f:332
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 sget23(COMP, BALANC, JTYPE, THRESH, ISEED, NOUNIT, N, A, LDA, H, WR, WI, WR1, WI1, VL, LDVL, VR, LDVR, LRE, LDLRE, RCONDV, RCNDV1, RCDVIN, RCONDE, RCNDE1, RCDEIN, SCALE, SCALE1, RESULT, WORK, LWORK, IWORK, INFO)
SGET23
Definition: sget23.f:378
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
subroutine slasum(TYPE, IOUNIT, IE, NRUN)
SLASUM
Definition: slasum.f:41
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