 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ ddrvvx()

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

DDRVVX

Purpose:
```    DDRVVX  checks the nonsymmetric eigenvalue problem expert driver
DGEEVX.

DDRVVX 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 DDRVVX 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 DGEEVX 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 DGEEVX 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 DDRVVX 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] 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDA, max(NN,12)) Another copy of the test matrix A, modified by DGEEVX.``` [out] WR ` WR is DOUBLE PRECISION array, dimension (max(NN))` [out] WI ``` WI is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (max(NN,12))` [out] WI1 ``` WI1 is DOUBLE PRECISION array, dimension (max(NN,12)) Like WR, WI, these arrays contain the eigenvalues of A, but those computed when DGEEVX only computes a partial eigendecomposition, i.e. not the eigenvalues and left and right eigenvectors.``` [out] VL ``` VL is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (N) RCONDV holds the computed reciprocal condition numbers for eigenvectors.``` [out] RCNDV1 ``` RCNDV1 is DOUBLE PRECISION array, dimension (N) RCNDV1 holds more computed reciprocal condition numbers for eigenvectors.``` [out] RCDVIN ``` RCDVIN is DOUBLE PRECISION array, dimension (N) When COMP = .TRUE. RCDVIN holds the precomputed reciprocal condition numbers for eigenvectors to be compared with RCONDV.``` [out] RCONDE ``` RCONDE is DOUBLE PRECISION array, dimension (N) RCONDE holds the computed reciprocal condition numbers for eigenvalues.``` [out] RCNDE1 ``` RCNDE1 is DOUBLE PRECISION array, dimension (N) RCNDE1 holds more computed reciprocal condition numbers for eigenvalues.``` [out] RCDEIN ``` RCDEIN is DOUBLE PRECISION array, dimension (N) When COMP = .TRUE. RCDEIN holds the precomputed reciprocal condition numbers for eigenvalues to be compared with RCONDE.``` [out] SCALE ``` SCALE is DOUBLE PRECISION array, dimension (N) Holds information describing balancing of matrix.``` [out] SCALE1 ``` SCALE1 is DOUBLE PRECISION array, dimension (N) Holds information describing balancing of matrix.``` [out] RESULT ``` RESULT is DOUBLE PRECISION 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 DOUBLE PRECISION 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, DLATMR, SLATMS, SLATME or DGET23 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 516 of file ddrvvx.f.

521 *
522 * -- LAPACK test routine --
523 * -- LAPACK is a software package provided by Univ. of Tennessee, --
524 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
525 *
526 * .. Scalar Arguments ..
527  INTEGER INFO, LDA, LDLRE, LDVL, LDVR, NIUNIT, NOUNIT,
528  \$ NSIZES, NTYPES, NWORK
529  DOUBLE PRECISION THRESH
530 * ..
531 * .. Array Arguments ..
532  LOGICAL DOTYPE( * )
533  INTEGER ISEED( 4 ), IWORK( * ), NN( * )
534  DOUBLE PRECISION A( LDA, * ), H( LDA, * ), LRE( LDLRE, * ),
535  \$ RCDEIN( * ), RCDVIN( * ), RCNDE1( * ),
536  \$ RCNDV1( * ), RCONDE( * ), RCONDV( * ),
537  \$ RESULT( 11 ), SCALE( * ), SCALE1( * ),
538  \$ VL( LDVL, * ), VR( LDVR, * ), WI( * ),
539  \$ WI1( * ), WORK( * ), WR( * ), WR1( * )
540 * ..
541 *
542 * =====================================================================
543 *
544 * .. Parameters ..
545  DOUBLE PRECISION ZERO, ONE
546  parameter( zero = 0.0d0, one = 1.0d0 )
547  INTEGER MAXTYP
548  parameter( maxtyp = 21 )
549 * ..
550 * .. Local Scalars ..
552  CHARACTER BALANC
553  CHARACTER*3 PATH
554  INTEGER I, IBAL, IINFO, IMODE, ITYPE, IWK, J, JCOL,
555  \$ JSIZE, JTYPE, MTYPES, N, NERRS, NFAIL, NMAX,
556  \$ NNWORK, NTEST, NTESTF, NTESTT
557  DOUBLE PRECISION ANORM, COND, CONDS, OVFL, RTULP, RTULPI, ULP,
558  \$ ULPINV, UNFL
559 * ..
560 * .. Local Arrays ..
561  CHARACTER ADUMMA( 1 ), BAL( 4 )
562  INTEGER IDUMMA( 1 ), IOLDSD( 4 ), KCONDS( MAXTYP ),
563  \$ KMAGN( MAXTYP ), KMODE( MAXTYP ),
564  \$ KTYPE( MAXTYP )
565 * ..
566 * .. External Functions ..
567  DOUBLE PRECISION DLAMCH
568  EXTERNAL dlamch
569 * ..
570 * .. External Subroutines ..
571  EXTERNAL dget23, dlabad, dlaset, dlasum, dlatme, dlatmr,
572  \$ dlatms, xerbla
573 * ..
574 * .. Intrinsic Functions ..
575  INTRINSIC abs, max, min, sqrt
576 * ..
577 * .. Data statements ..
578  DATA ktype / 1, 2, 3, 5*4, 4*6, 6*6, 3*9 /
579  DATA kmagn / 3*1, 1, 1, 1, 2, 3, 4*1, 1, 1, 1, 1, 2,
580  \$ 3, 1, 2, 3 /
581  DATA kmode / 3*0, 4, 3, 1, 4, 4, 4, 3, 1, 5, 4, 3,
582  \$ 1, 5, 5, 5, 4, 3, 1 /
583  DATA kconds / 3*0, 5*0, 4*1, 6*2, 3*0 /
584  DATA bal / 'N', 'P', 'S', 'B' /
585 * ..
586 * .. Executable Statements ..
587 *
588  path( 1: 1 ) = 'Double precision'
589  path( 2: 3 ) = 'VX'
590 *
591 * Check for errors
592 *
593  ntestt = 0
594  ntestf = 0
595  info = 0
596 *
597 * Important constants
598 *
600 *
601 * 12 is the largest dimension in the input file of precomputed
602 * problems
603 *
604  nmax = 12
605  DO 10 j = 1, nsizes
606  nmax = max( nmax, nn( j ) )
607  IF( nn( j ).LT.0 )
609  10 CONTINUE
610 *
611 * Check for errors
612 *
613  IF( nsizes.LT.0 ) THEN
614  info = -1
615  ELSE IF( badnn ) THEN
616  info = -2
617  ELSE IF( ntypes.LT.0 ) THEN
618  info = -3
619  ELSE IF( thresh.LT.zero ) THEN
620  info = -6
621  ELSE IF( lda.LT.1 .OR. lda.LT.nmax ) THEN
622  info = -10
623  ELSE IF( ldvl.LT.1 .OR. ldvl.LT.nmax ) THEN
624  info = -17
625  ELSE IF( ldvr.LT.1 .OR. ldvr.LT.nmax ) THEN
626  info = -19
627  ELSE IF( ldlre.LT.1 .OR. ldlre.LT.nmax ) THEN
628  info = -21
629  ELSE IF( 6*nmax+2*nmax**2.GT.nwork ) THEN
630  info = -32
631  END IF
632 *
633  IF( info.NE.0 ) THEN
634  CALL xerbla( 'DDRVVX', -info )
635  RETURN
636  END IF
637 *
638 * If nothing to do check on NIUNIT
639 *
640  IF( nsizes.EQ.0 .OR. ntypes.EQ.0 )
641  \$ GO TO 160
642 *
643 * More Important constants
644 *
645  unfl = dlamch( 'Safe minimum' )
646  ovfl = one / unfl
647  CALL dlabad( unfl, ovfl )
648  ulp = dlamch( 'Precision' )
649  ulpinv = one / ulp
650  rtulp = sqrt( ulp )
651  rtulpi = one / rtulp
652 *
653 * Loop over sizes, types
654 *
655  nerrs = 0
656 *
657  DO 150 jsize = 1, nsizes
658  n = nn( jsize )
659  IF( nsizes.NE.1 ) THEN
660  mtypes = min( maxtyp, ntypes )
661  ELSE
662  mtypes = min( maxtyp+1, ntypes )
663  END IF
664 *
665  DO 140 jtype = 1, mtypes
666  IF( .NOT.dotype( jtype ) )
667  \$ GO TO 140
668 *
669 * Save ISEED in case of an error.
670 *
671  DO 20 j = 1, 4
672  ioldsd( j ) = iseed( j )
673  20 CONTINUE
674 *
675 * Compute "A"
676 *
677 * Control parameters:
678 *
679 * KMAGN KCONDS KMODE KTYPE
680 * =1 O(1) 1 clustered 1 zero
681 * =2 large large clustered 2 identity
682 * =3 small exponential Jordan
683 * =4 arithmetic diagonal, (w/ eigenvalues)
684 * =5 random log symmetric, w/ eigenvalues
685 * =6 random general, w/ eigenvalues
686 * =7 random diagonal
687 * =8 random symmetric
688 * =9 random general
689 * =10 random triangular
690 *
691  IF( mtypes.GT.maxtyp )
692  \$ GO TO 90
693 *
694  itype = ktype( jtype )
695  imode = kmode( jtype )
696 *
697 * Compute norm
698 *
699  GO TO ( 30, 40, 50 )kmagn( jtype )
700 *
701  30 CONTINUE
702  anorm = one
703  GO TO 60
704 *
705  40 CONTINUE
706  anorm = ovfl*ulp
707  GO TO 60
708 *
709  50 CONTINUE
710  anorm = unfl*ulpinv
711  GO TO 60
712 *
713  60 CONTINUE
714 *
715  CALL dlaset( 'Full', lda, n, zero, zero, a, lda )
716  iinfo = 0
717  cond = ulpinv
718 *
719 * Special Matrices -- Identity & Jordan block
720 *
721 * Zero
722 *
723  IF( itype.EQ.1 ) THEN
724  iinfo = 0
725 *
726  ELSE IF( itype.EQ.2 ) THEN
727 *
728 * Identity
729 *
730  DO 70 jcol = 1, n
731  a( jcol, jcol ) = anorm
732  70 CONTINUE
733 *
734  ELSE IF( itype.EQ.3 ) THEN
735 *
736 * Jordan Block
737 *
738  DO 80 jcol = 1, n
739  a( jcol, jcol ) = anorm
740  IF( jcol.GT.1 )
741  \$ a( jcol, jcol-1 ) = one
742  80 CONTINUE
743 *
744  ELSE IF( itype.EQ.4 ) THEN
745 *
746 * Diagonal Matrix, [Eigen]values Specified
747 *
748  CALL dlatms( n, n, 'S', iseed, 'S', work, imode, cond,
749  \$ anorm, 0, 0, 'N', a, lda, work( n+1 ),
750  \$ iinfo )
751 *
752  ELSE IF( itype.EQ.5 ) THEN
753 *
754 * Symmetric, eigenvalues specified
755 *
756  CALL dlatms( n, n, 'S', iseed, 'S', work, imode, cond,
757  \$ anorm, n, n, 'N', a, lda, work( n+1 ),
758  \$ iinfo )
759 *
760  ELSE IF( itype.EQ.6 ) THEN
761 *
762 * General, eigenvalues specified
763 *
764  IF( kconds( jtype ).EQ.1 ) THEN
765  conds = one
766  ELSE IF( kconds( jtype ).EQ.2 ) THEN
767  conds = rtulpi
768  ELSE
769  conds = zero
770  END IF
771 *
772  adumma( 1 ) = ' '
773  CALL dlatme( n, 'S', iseed, work, imode, cond, one,
774  \$ adumma, 'T', 'T', 'T', work( n+1 ), 4,
775  \$ conds, n, n, anorm, a, lda, work( 2*n+1 ),
776  \$ iinfo )
777 *
778  ELSE IF( itype.EQ.7 ) THEN
779 *
780 * Diagonal, random eigenvalues
781 *
782  CALL dlatmr( n, n, 'S', iseed, 'S', work, 6, one, one,
783  \$ 'T', 'N', work( n+1 ), 1, one,
784  \$ work( 2*n+1 ), 1, one, 'N', idumma, 0, 0,
785  \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
786 *
787  ELSE IF( itype.EQ.8 ) THEN
788 *
789 * Symmetric, random eigenvalues
790 *
791  CALL dlatmr( n, n, 'S', iseed, 'S', work, 6, one, one,
792  \$ 'T', 'N', work( n+1 ), 1, one,
793  \$ work( 2*n+1 ), 1, one, 'N', idumma, n, n,
794  \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
795 *
796  ELSE IF( itype.EQ.9 ) THEN
797 *
798 * General, random eigenvalues
799 *
800  CALL dlatmr( n, n, 'S', iseed, 'N', work, 6, one, one,
801  \$ 'T', 'N', work( n+1 ), 1, one,
802  \$ work( 2*n+1 ), 1, one, 'N', idumma, n, n,
803  \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
804  IF( n.GE.4 ) THEN
805  CALL dlaset( 'Full', 2, n, zero, zero, a, lda )
806  CALL dlaset( 'Full', n-3, 1, zero, zero, a( 3, 1 ),
807  \$ lda )
808  CALL dlaset( 'Full', n-3, 2, zero, zero, a( 3, n-1 ),
809  \$ lda )
810  CALL dlaset( 'Full', 1, n, zero, zero, a( n, 1 ),
811  \$ lda )
812  END IF
813 *
814  ELSE IF( itype.EQ.10 ) THEN
815 *
816 * Triangular, random eigenvalues
817 *
818  CALL dlatmr( n, n, 'S', iseed, 'N', work, 6, one, one,
819  \$ 'T', 'N', work( n+1 ), 1, one,
820  \$ work( 2*n+1 ), 1, one, 'N', idumma, n, 0,
821  \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
822 *
823  ELSE
824 *
825  iinfo = 1
826  END IF
827 *
828  IF( iinfo.NE.0 ) THEN
829  WRITE( nounit, fmt = 9992 )'Generator', iinfo, n, jtype,
830  \$ ioldsd
831  info = abs( iinfo )
832  RETURN
833  END IF
834 *
835  90 CONTINUE
836 *
837 * Test for minimal and generous workspace
838 *
839  DO 130 iwk = 1, 3
840  IF( iwk.EQ.1 ) THEN
841  nnwork = 3*n
842  ELSE IF( iwk.EQ.2 ) THEN
843  nnwork = 6*n + n**2
844  ELSE
845  nnwork = 6*n + 2*n**2
846  END IF
847  nnwork = max( nnwork, 1 )
848 *
849 * Test for all balancing options
850 *
851  DO 120 ibal = 1, 4
852  balanc = bal( ibal )
853 *
854 * Perform tests
855 *
856  CALL dget23( .false., balanc, jtype, thresh, ioldsd,
857  \$ nounit, n, a, lda, h, wr, wi, wr1, wi1,
858  \$ vl, ldvl, vr, ldvr, lre, ldlre, rcondv,
859  \$ rcndv1, rcdvin, rconde, rcnde1, rcdein,
860  \$ scale, scale1, result, work, nnwork,
861  \$ iwork, info )
862 *
863 * Check for RESULT(j) > THRESH
864 *
865  ntest = 0
866  nfail = 0
867  DO 100 j = 1, 9
868  IF( result( j ).GE.zero )
869  \$ ntest = ntest + 1
870  IF( result( j ).GE.thresh )
871  \$ nfail = nfail + 1
872  100 CONTINUE
873 *
874  IF( nfail.GT.0 )
875  \$ ntestf = ntestf + 1
876  IF( ntestf.EQ.1 ) THEN
877  WRITE( nounit, fmt = 9999 )path
878  WRITE( nounit, fmt = 9998 )
879  WRITE( nounit, fmt = 9997 )
880  WRITE( nounit, fmt = 9996 )
881  WRITE( nounit, fmt = 9995 )thresh
882  ntestf = 2
883  END IF
884 *
885  DO 110 j = 1, 9
886  IF( result( j ).GE.thresh ) THEN
887  WRITE( nounit, fmt = 9994 )balanc, n, iwk,
888  \$ ioldsd, jtype, j, result( j )
889  END IF
890  110 CONTINUE
891 *
892  nerrs = nerrs + nfail
893  ntestt = ntestt + ntest
894 *
895  120 CONTINUE
896  130 CONTINUE
897  140 CONTINUE
898  150 CONTINUE
899 *
900  160 CONTINUE
901 *
902 * Read in data from file to check accuracy of condition estimation.
903 * Assume input eigenvalues are sorted lexicographically (increasing
904 * by real part, then decreasing by imaginary part)
905 *
906  jtype = 0
907  170 CONTINUE
908  READ( niunit, fmt = *, END = 220 )n
909 *
910 * Read input data until N=0
911 *
912  IF( n.EQ.0 )
913  \$ GO TO 220
914  jtype = jtype + 1
915  iseed( 1 ) = jtype
916  DO 180 i = 1, n
917  READ( niunit, fmt = * )( a( i, j ), j = 1, n )
918  180 CONTINUE
919  DO 190 i = 1, n
920  READ( niunit, fmt = * )wr1( i ), wi1( i ), rcdein( i ),
921  \$ rcdvin( i )
922  190 CONTINUE
923  CALL dget23( .true., 'N', 22, thresh, iseed, nounit, n, a, lda, h,
924  \$ wr, wi, wr1, wi1, vl, ldvl, vr, ldvr, lre, ldlre,
925  \$ rcondv, rcndv1, rcdvin, rconde, rcnde1, rcdein,
926  \$ scale, scale1, result, work, 6*n+2*n**2, iwork,
927  \$ info )
928 *
929 * Check for RESULT(j) > THRESH
930 *
931  ntest = 0
932  nfail = 0
933  DO 200 j = 1, 11
934  IF( result( j ).GE.zero )
935  \$ ntest = ntest + 1
936  IF( result( j ).GE.thresh )
937  \$ nfail = nfail + 1
938  200 CONTINUE
939 *
940  IF( nfail.GT.0 )
941  \$ ntestf = ntestf + 1
942  IF( ntestf.EQ.1 ) THEN
943  WRITE( nounit, fmt = 9999 )path
944  WRITE( nounit, fmt = 9998 )
945  WRITE( nounit, fmt = 9997 )
946  WRITE( nounit, fmt = 9996 )
947  WRITE( nounit, fmt = 9995 )thresh
948  ntestf = 2
949  END IF
950 *
951  DO 210 j = 1, 11
952  IF( result( j ).GE.thresh ) THEN
953  WRITE( nounit, fmt = 9993 )n, jtype, j, result( j )
954  END IF
955  210 CONTINUE
956 *
957  nerrs = nerrs + nfail
958  ntestt = ntestt + ntest
959  GO TO 170
960  220 CONTINUE
961 *
962 * Summary
963 *
964  CALL dlasum( path, nounit, nerrs, ntestt )
965 *
966  9999 FORMAT( / 1x, a3, ' -- Real Eigenvalue-Eigenvector Decomposition',
967  \$ ' Expert Driver', /
968  \$ ' Matrix types (see DDRVVX for details): ' )
969 *
970  9998 FORMAT( / ' Special Matrices:', / ' 1=Zero matrix. ',
971  \$ ' ', ' 5=Diagonal: geometr. spaced entries.',
972  \$ / ' 2=Identity matrix. ', ' 6=Diagona',
973  \$ 'l: clustered entries.', / ' 3=Transposed Jordan block. ',
974  \$ ' ', ' 7=Diagonal: large, evenly spaced.', / ' ',
975  \$ '4=Diagonal: evenly spaced entries. ', ' 8=Diagonal: s',
976  \$ 'mall, evenly spaced.' )
977  9997 FORMAT( ' Dense, Non-Symmetric Matrices:', / ' 9=Well-cond., ev',
978  \$ 'enly spaced eigenvals.', ' 14=Ill-cond., geomet. spaced e',
979  \$ 'igenals.', / ' 10=Well-cond., geom. spaced eigenvals. ',
980  \$ ' 15=Ill-conditioned, clustered e.vals.', / ' 11=Well-cond',
981  \$ 'itioned, clustered e.vals. ', ' 16=Ill-cond., random comp',
982  \$ 'lex ', / ' 12=Well-cond., random complex ', ' ',
983  \$ ' 17=Ill-cond., large rand. complx ', / ' 13=Ill-condi',
984  \$ 'tioned, evenly spaced. ', ' 18=Ill-cond., small rand.',
985  \$ ' complx ' )
986  9996 FORMAT( ' 19=Matrix with random O(1) entries. ', ' 21=Matrix ',
987  \$ 'with small random entries.', / ' 20=Matrix with large ran',
988  \$ 'dom entries. ', ' 22=Matrix read from input file', / )
989  9995 FORMAT( ' Tests performed with test threshold =', f8.2,
990  \$ / / ' 1 = | A VR - VR W | / ( n |A| ulp ) ',
991  \$ / ' 2 = | transpose(A) VL - VL W | / ( n |A| ulp ) ',
992  \$ / ' 3 = | |VR(i)| - 1 | / ulp ',
993  \$ / ' 4 = | |VL(i)| - 1 | / ulp ',
994  \$ / ' 5 = 0 if W same no matter if VR or VL computed,',
995  \$ ' 1/ulp otherwise', /
996  \$ ' 6 = 0 if VR same no matter what else computed,',
997  \$ ' 1/ulp otherwise', /
998  \$ ' 7 = 0 if VL same no matter what else computed,',
999  \$ ' 1/ulp otherwise', /
1000  \$ ' 8 = 0 if RCONDV same no matter what else computed,',
1001  \$ ' 1/ulp otherwise', /
1002  \$ ' 9 = 0 if SCALE, ILO, IHI, ABNRM same no matter what else',
1003  \$ ' computed, 1/ulp otherwise',
1004  \$ / ' 10 = | RCONDV - RCONDV(precomputed) | / cond(RCONDV),',
1005  \$ / ' 11 = | RCONDE - RCONDE(precomputed) | / cond(RCONDE),' )
1006  9994 FORMAT( ' BALANC=''', a1, ''',N=', i4, ',IWK=', i1, ', seed=',
1007  \$ 4( i4, ',' ), ' type ', i2, ', test(', i2, ')=', g10.3 )
1008  9993 FORMAT( ' N=', i5, ', input example =', i3, ', test(', i2, ')=',
1009  \$ g10.3 )
1010  9992 FORMAT( ' DDRVVX: ', a, ' returned INFO=', i6, '.', / 9x, 'N=',
1011  \$ i6, ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ), i5, ')' )
1012 *
1013  RETURN
1014 *
1015 * End of DDRVVX
1016 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
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 dlasum(TYPE, IOUNIT, IE, NRUN)
DLASUM
Definition: dlasum.f:43
subroutine dget23(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)
DGET23
Definition: dget23.f:378
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 dlatme(N, DIST, ISEED, D, MODE, COND, DMAX, EI, RSIGN, UPPER, SIM, DS, MODES, CONDS, KL, KU, ANORM, A, LDA, WORK, INFO)
DLATME
Definition: dlatme.f:332
subroutine dlatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
DLATMS
Definition: dlatms.f:321
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