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

 subroutine ddrvev ( integer NSIZES, integer, dimension( * ) NN, integer NTYPES, logical, dimension( * ) DOTYPE, integer, dimension( 4 ) ISEED, double precision THRESH, 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( 7 ) RESULT, double precision, dimension( * ) WORK, integer NWORK, integer, dimension( * ) IWORK, integer INFO )

DDRVEV

Purpose:
```    DDRVEV  checks the nonsymmetric eigenvalue problem driver DGEEV.

When DDRVEV is called, a number of matrix "sizes" ("n's") and a
number of matrix "types" are specified.  For each size ("n")
and each type of matrix, one matrix will be generated and used
to test the nonsymmetric eigenroutines.  For each matrix, 7
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 whether largest component real

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

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

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

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

W(full) denotes the eigenvalues computed when both VR and VL
are also computed, and W(partial) denotes the eigenvalues
computed when only W, only W and VR, or only W and VL are
computed.

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

VR(full) denotes the right eigenvectors computed when both VR
and VL are computed, and VR(partial) denotes the result
when only VR is computed.

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

VL(full) denotes the left eigenvectors computed when both VR
and VL are also computed, and VL(partial) denotes the result
when only VL is 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```
Parameters
 [in] NSIZES ``` NSIZES is INTEGER The number of sizes of matrices to use. If it is zero, DDRVEV 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] NTYPES ``` NTYPES is INTEGER The number of elements in DOTYPE. If it is zero, DDRVEV 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 DDRVEV 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 INFO not equal to 0.)``` [out] A ``` A is DOUBLE PRECISION array, dimension (LDA, max(NN)) 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 A, and H. LDA must be at least 1 and at least max(NN).``` [out] H ``` H is DOUBLE PRECISION array, dimension (LDA, max(NN)) Another copy of the test matrix A, modified by DGEEV.``` [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))` [out] WI1 ``` WI1 is DOUBLE PRECISION array, dimension (max(NN)) Like WR, WI, these arrays contain the eigenvalues of A, but those computed when DGEEV 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)) VL holds the computed left eigenvectors.``` [in] LDVL ``` LDVL is INTEGER Leading dimension of VL. Must be at least max(1,max(NN)).``` [out] VR ``` VR is DOUBLE PRECISION array, dimension (LDVR, max(NN)) VR holds the computed right eigenvectors.``` [in] LDVR ``` LDVR is INTEGER Leading dimension of VR. Must be at least max(1,max(NN)).``` [out] LRE ``` LRE is DOUBLE PRECISION array, dimension (LDLRE,max(NN)) 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)).``` [out] RESULT ``` RESULT is DOUBLE PRECISION array, dimension (7) 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 5*NN(j)+2*NN(j)**2 for all j.``` [out] IWORK ` IWORK is INTEGER array, dimension (max(NN))` [out] INFO ``` INFO is INTEGER If 0, then everything ran OK. -1: NSIZES < 0 -2: Some NN(j) < 0 -3: NTYPES < 0 -6: THRESH < 0 -9: LDA < 1 or LDA < NMAX, where NMAX is max( NN(j) ). -16: LDVL < 1 or LDVL < NMAX, where NMAX is max( NN(j) ). -18: LDVR < 1 or LDVR < NMAX, where NMAX is max( NN(j) ). -20: LDLRE < 1 or LDLRE < NMAX, where NMAX is max( NN(j) ). -23: NWORK too small. If DLATMR, SLATMS, SLATME or DGEEV returns an error code, the absolute value of it is returned. ----------------------------------------------------------------------- Some Local Variables and Parameters: ---- ----- --------- --- ---------- ZERO, ONE Real 0 and 1. MAXTYP The number of types defined. NMAX Largest value in NN. 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 402 of file ddrvev.f.

406*
407* -- LAPACK test routine --
408* -- LAPACK is a software package provided by Univ. of Tennessee, --
409* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
410*
411* .. Scalar Arguments ..
412 INTEGER INFO, LDA, LDLRE, LDVL, LDVR, NOUNIT, NSIZES,
413 \$ NTYPES, NWORK
414 DOUBLE PRECISION THRESH
415* ..
416* .. Array Arguments ..
417 LOGICAL DOTYPE( * )
418 INTEGER ISEED( 4 ), IWORK( * ), NN( * )
419 DOUBLE PRECISION A( LDA, * ), H( LDA, * ), LRE( LDLRE, * ),
420 \$ RESULT( 7 ), VL( LDVL, * ), VR( LDVR, * ),
421 \$ WI( * ), WI1( * ), WORK( * ), WR( * ), WR1( * )
422* ..
423*
424* =====================================================================
425*
426* .. Parameters ..
427 DOUBLE PRECISION ZERO, ONE
428 parameter( zero = 0.0d0, one = 1.0d0 )
429 DOUBLE PRECISION TWO
430 parameter( two = 2.0d0 )
431 INTEGER MAXTYP
432 parameter( maxtyp = 21 )
433* ..
434* .. Local Scalars ..
436 CHARACTER*3 PATH
437 INTEGER IINFO, IMODE, ITYPE, IWK, J, JCOL, JJ, JSIZE,
438 \$ JTYPE, MTYPES, N, NERRS, NFAIL, NMAX, NNWORK,
439 \$ NTEST, NTESTF, NTESTT
440 DOUBLE PRECISION ANORM, COND, CONDS, OVFL, RTULP, RTULPI, TNRM,
441 \$ ULP, ULPINV, UNFL, VMX, VRMX, VTST
442* ..
443* .. Local Arrays ..
445 INTEGER IDUMMA( 1 ), IOLDSD( 4 ), KCONDS( MAXTYP ),
446 \$ KMAGN( MAXTYP ), KMODE( MAXTYP ),
447 \$ KTYPE( MAXTYP )
448 DOUBLE PRECISION DUM( 1 ), RES( 2 )
449* ..
450* .. External Functions ..
451 DOUBLE PRECISION DLAMCH, DLAPY2, DNRM2
452 EXTERNAL dlamch, dlapy2, dnrm2
453* ..
454* .. External Subroutines ..
455 EXTERNAL dgeev, dget22, dlabad, dlacpy, dlaset, dlasum,
457* ..
458* .. Intrinsic Functions ..
459 INTRINSIC abs, max, min, sqrt
460* ..
461* .. Data statements ..
462 DATA ktype / 1, 2, 3, 5*4, 4*6, 6*6, 3*9 /
463 DATA kmagn / 3*1, 1, 1, 1, 2, 3, 4*1, 1, 1, 1, 1, 2,
464 \$ 3, 1, 2, 3 /
465 DATA kmode / 3*0, 4, 3, 1, 4, 4, 4, 3, 1, 5, 4, 3,
466 \$ 1, 5, 5, 5, 4, 3, 1 /
467 DATA kconds / 3*0, 5*0, 4*1, 6*2, 3*0 /
468* ..
469* .. Executable Statements ..
470*
471 path( 1: 1 ) = 'Double precision'
472 path( 2: 3 ) = 'EV'
473*
474* Check for errors
475*
476 ntestt = 0
477 ntestf = 0
478 info = 0
479*
480* Important constants
481*
483 nmax = 0
484 DO 10 j = 1, nsizes
485 nmax = max( nmax, nn( j ) )
486 IF( nn( j ).LT.0 )
488 10 CONTINUE
489*
490* Check for errors
491*
492 IF( nsizes.LT.0 ) THEN
493 info = -1
494 ELSE IF( badnn ) THEN
495 info = -2
496 ELSE IF( ntypes.LT.0 ) THEN
497 info = -3
498 ELSE IF( thresh.LT.zero ) THEN
499 info = -6
500 ELSE IF( nounit.LE.0 ) THEN
501 info = -7
502 ELSE IF( lda.LT.1 .OR. lda.LT.nmax ) THEN
503 info = -9
504 ELSE IF( ldvl.LT.1 .OR. ldvl.LT.nmax ) THEN
505 info = -16
506 ELSE IF( ldvr.LT.1 .OR. ldvr.LT.nmax ) THEN
507 info = -18
508 ELSE IF( ldlre.LT.1 .OR. ldlre.LT.nmax ) THEN
509 info = -20
510 ELSE IF( 5*nmax+2*nmax**2.GT.nwork ) THEN
511 info = -23
512 END IF
513*
514 IF( info.NE.0 ) THEN
515 CALL xerbla( 'DDRVEV', -info )
516 RETURN
517 END IF
518*
519* Quick return if nothing to do
520*
521 IF( nsizes.EQ.0 .OR. ntypes.EQ.0 )
522 \$ RETURN
523*
524* More Important constants
525*
526 unfl = dlamch( 'Safe minimum' )
527 ovfl = one / unfl
528 CALL dlabad( unfl, ovfl )
529 ulp = dlamch( 'Precision' )
530 ulpinv = one / ulp
531 rtulp = sqrt( ulp )
532 rtulpi = one / rtulp
533*
534* Loop over sizes, types
535*
536 nerrs = 0
537*
538 DO 270 jsize = 1, nsizes
539 n = nn( jsize )
540 IF( nsizes.NE.1 ) THEN
541 mtypes = min( maxtyp, ntypes )
542 ELSE
543 mtypes = min( maxtyp+1, ntypes )
544 END IF
545*
546 DO 260 jtype = 1, mtypes
547 IF( .NOT.dotype( jtype ) )
548 \$ GO TO 260
549*
550* Save ISEED in case of an error.
551*
552 DO 20 j = 1, 4
553 ioldsd( j ) = iseed( j )
554 20 CONTINUE
555*
556* Compute "A"
557*
558* Control parameters:
559*
560* KMAGN KCONDS KMODE KTYPE
561* =1 O(1) 1 clustered 1 zero
562* =2 large large clustered 2 identity
563* =3 small exponential Jordan
564* =4 arithmetic diagonal, (w/ eigenvalues)
565* =5 random log symmetric, w/ eigenvalues
566* =6 random general, w/ eigenvalues
567* =7 random diagonal
568* =8 random symmetric
569* =9 random general
570* =10 random triangular
571*
572 IF( mtypes.GT.maxtyp )
573 \$ GO TO 90
574*
575 itype = ktype( jtype )
576 imode = kmode( jtype )
577*
578* Compute norm
579*
580 GO TO ( 30, 40, 50 )kmagn( jtype )
581*
582 30 CONTINUE
583 anorm = one
584 GO TO 60
585*
586 40 CONTINUE
587 anorm = ovfl*ulp
588 GO TO 60
589*
590 50 CONTINUE
591 anorm = unfl*ulpinv
592 GO TO 60
593*
594 60 CONTINUE
595*
596 CALL dlaset( 'Full', lda, n, zero, zero, a, lda )
597 iinfo = 0
598 cond = ulpinv
599*
600* Special Matrices -- Identity & Jordan block
601*
602* Zero
603*
604 IF( itype.EQ.1 ) THEN
605 iinfo = 0
606*
607 ELSE IF( itype.EQ.2 ) THEN
608*
609* Identity
610*
611 DO 70 jcol = 1, n
612 a( jcol, jcol ) = anorm
613 70 CONTINUE
614*
615 ELSE IF( itype.EQ.3 ) THEN
616*
617* Jordan Block
618*
619 DO 80 jcol = 1, n
620 a( jcol, jcol ) = anorm
621 IF( jcol.GT.1 )
622 \$ a( jcol, jcol-1 ) = one
623 80 CONTINUE
624*
625 ELSE IF( itype.EQ.4 ) THEN
626*
627* Diagonal Matrix, [Eigen]values Specified
628*
629 CALL dlatms( n, n, 'S', iseed, 'S', work, imode, cond,
630 \$ anorm, 0, 0, 'N', a, lda, work( n+1 ),
631 \$ iinfo )
632*
633 ELSE IF( itype.EQ.5 ) THEN
634*
635* Symmetric, eigenvalues specified
636*
637 CALL dlatms( n, n, 'S', iseed, 'S', work, imode, cond,
638 \$ anorm, n, n, 'N', a, lda, work( n+1 ),
639 \$ iinfo )
640*
641 ELSE IF( itype.EQ.6 ) THEN
642*
643* General, eigenvalues specified
644*
645 IF( kconds( jtype ).EQ.1 ) THEN
646 conds = one
647 ELSE IF( kconds( jtype ).EQ.2 ) THEN
648 conds = rtulpi
649 ELSE
650 conds = zero
651 END IF
652*
653 adumma( 1 ) = ' '
654 CALL dlatme( n, 'S', iseed, work, imode, cond, one,
655 \$ adumma, 'T', 'T', 'T', work( n+1 ), 4,
656 \$ conds, n, n, anorm, a, lda, work( 2*n+1 ),
657 \$ iinfo )
658*
659 ELSE IF( itype.EQ.7 ) THEN
660*
661* Diagonal, random eigenvalues
662*
663 CALL dlatmr( n, n, 'S', iseed, 'S', work, 6, one, one,
664 \$ 'T', 'N', work( n+1 ), 1, one,
665 \$ work( 2*n+1 ), 1, one, 'N', idumma, 0, 0,
666 \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
667*
668 ELSE IF( itype.EQ.8 ) THEN
669*
670* Symmetric, random eigenvalues
671*
672 CALL dlatmr( n, n, 'S', iseed, 'S', work, 6, one, one,
673 \$ 'T', 'N', work( n+1 ), 1, one,
674 \$ work( 2*n+1 ), 1, one, 'N', idumma, n, n,
675 \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
676*
677 ELSE IF( itype.EQ.9 ) THEN
678*
679* General, random eigenvalues
680*
681 CALL dlatmr( n, n, 'S', iseed, 'N', work, 6, one, one,
682 \$ 'T', 'N', work( n+1 ), 1, one,
683 \$ work( 2*n+1 ), 1, one, 'N', idumma, n, n,
684 \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
685 IF( n.GE.4 ) THEN
686 CALL dlaset( 'Full', 2, n, zero, zero, a, lda )
687 CALL dlaset( 'Full', n-3, 1, zero, zero, a( 3, 1 ),
688 \$ lda )
689 CALL dlaset( 'Full', n-3, 2, zero, zero, a( 3, n-1 ),
690 \$ lda )
691 CALL dlaset( 'Full', 1, n, zero, zero, a( n, 1 ),
692 \$ lda )
693 END IF
694*
695 ELSE IF( itype.EQ.10 ) THEN
696*
697* Triangular, random eigenvalues
698*
699 CALL dlatmr( n, n, 'S', iseed, 'N', work, 6, one, one,
700 \$ 'T', 'N', work( n+1 ), 1, one,
701 \$ work( 2*n+1 ), 1, one, 'N', idumma, n, 0,
702 \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
703*
704 ELSE
705*
706 iinfo = 1
707 END IF
708*
709 IF( iinfo.NE.0 ) THEN
710 WRITE( nounit, fmt = 9993 )'Generator', iinfo, n, jtype,
711 \$ ioldsd
712 info = abs( iinfo )
713 RETURN
714 END IF
715*
716 90 CONTINUE
717*
718* Test for minimal and generous workspace
719*
720 DO 250 iwk = 1, 2
721 IF( iwk.EQ.1 ) THEN
722 nnwork = 4*n
723 ELSE
724 nnwork = 5*n + 2*n**2
725 END IF
726 nnwork = max( nnwork, 1 )
727*
728* Initialize RESULT
729*
730 DO 100 j = 1, 7
731 result( j ) = -one
732 100 CONTINUE
733*
734* Compute eigenvalues and eigenvectors, and test them
735*
736 CALL dlacpy( 'F', n, n, a, lda, h, lda )
737 CALL dgeev( 'V', 'V', n, h, lda, wr, wi, vl, ldvl, vr,
738 \$ ldvr, work, nnwork, iinfo )
739 IF( iinfo.NE.0 ) THEN
740 result( 1 ) = ulpinv
741 WRITE( nounit, fmt = 9993 )'DGEEV1', iinfo, n, jtype,
742 \$ ioldsd
743 info = abs( iinfo )
744 GO TO 220
745 END IF
746*
747* Do Test (1)
748*
749 CALL dget22( 'N', 'N', 'N', n, a, lda, vr, ldvr, wr, wi,
750 \$ work, res )
751 result( 1 ) = res( 1 )
752*
753* Do Test (2)
754*
755 CALL dget22( 'T', 'N', 'T', n, a, lda, vl, ldvl, wr, wi,
756 \$ work, res )
757 result( 2 ) = res( 1 )
758*
759* Do Test (3)
760*
761 DO 120 j = 1, n
762 tnrm = one
763 IF( wi( j ).EQ.zero ) THEN
764 tnrm = dnrm2( n, vr( 1, j ), 1 )
765 ELSE IF( wi( j ).GT.zero ) THEN
766 tnrm = dlapy2( dnrm2( n, vr( 1, j ), 1 ),
767 \$ dnrm2( n, vr( 1, j+1 ), 1 ) )
768 END IF
769 result( 3 ) = max( result( 3 ),
770 \$ min( ulpinv, abs( tnrm-one ) / ulp ) )
771 IF( wi( j ).GT.zero ) THEN
772 vmx = zero
773 vrmx = zero
774 DO 110 jj = 1, n
775 vtst = dlapy2( vr( jj, j ), vr( jj, j+1 ) )
776 IF( vtst.GT.vmx )
777 \$ vmx = vtst
778 IF( vr( jj, j+1 ).EQ.zero .AND.
779 \$ abs( vr( jj, j ) ).GT.vrmx )
780 \$ vrmx = abs( vr( jj, j ) )
781 110 CONTINUE
782 IF( vrmx / vmx.LT.one-two*ulp )
783 \$ result( 3 ) = ulpinv
784 END IF
785 120 CONTINUE
786*
787* Do Test (4)
788*
789 DO 140 j = 1, n
790 tnrm = one
791 IF( wi( j ).EQ.zero ) THEN
792 tnrm = dnrm2( n, vl( 1, j ), 1 )
793 ELSE IF( wi( j ).GT.zero ) THEN
794 tnrm = dlapy2( dnrm2( n, vl( 1, j ), 1 ),
795 \$ dnrm2( n, vl( 1, j+1 ), 1 ) )
796 END IF
797 result( 4 ) = max( result( 4 ),
798 \$ min( ulpinv, abs( tnrm-one ) / ulp ) )
799 IF( wi( j ).GT.zero ) THEN
800 vmx = zero
801 vrmx = zero
802 DO 130 jj = 1, n
803 vtst = dlapy2( vl( jj, j ), vl( jj, j+1 ) )
804 IF( vtst.GT.vmx )
805 \$ vmx = vtst
806 IF( vl( jj, j+1 ).EQ.zero .AND.
807 \$ abs( vl( jj, j ) ).GT.vrmx )
808 \$ vrmx = abs( vl( jj, j ) )
809 130 CONTINUE
810 IF( vrmx / vmx.LT.one-two*ulp )
811 \$ result( 4 ) = ulpinv
812 END IF
813 140 CONTINUE
814*
815* Compute eigenvalues only, and test them
816*
817 CALL dlacpy( 'F', n, n, a, lda, h, lda )
818 CALL dgeev( 'N', 'N', n, h, lda, wr1, wi1, dum, 1, dum,
819 \$ 1, work, nnwork, iinfo )
820 IF( iinfo.NE.0 ) THEN
821 result( 1 ) = ulpinv
822 WRITE( nounit, fmt = 9993 )'DGEEV2', iinfo, n, jtype,
823 \$ ioldsd
824 info = abs( iinfo )
825 GO TO 220
826 END IF
827*
828* Do Test (5)
829*
830 DO 150 j = 1, n
831 IF( wr( j ).NE.wr1( j ) .OR. wi( j ).NE.wi1( j ) )
832 \$ result( 5 ) = ulpinv
833 150 CONTINUE
834*
835* Compute eigenvalues and right eigenvectors, and test them
836*
837 CALL dlacpy( 'F', n, n, a, lda, h, lda )
838 CALL dgeev( 'N', 'V', n, h, lda, wr1, wi1, dum, 1, lre,
839 \$ ldlre, work, nnwork, iinfo )
840 IF( iinfo.NE.0 ) THEN
841 result( 1 ) = ulpinv
842 WRITE( nounit, fmt = 9993 )'DGEEV3', iinfo, n, jtype,
843 \$ ioldsd
844 info = abs( iinfo )
845 GO TO 220
846 END IF
847*
848* Do Test (5) again
849*
850 DO 160 j = 1, n
851 IF( wr( j ).NE.wr1( j ) .OR. wi( j ).NE.wi1( j ) )
852 \$ result( 5 ) = ulpinv
853 160 CONTINUE
854*
855* Do Test (6)
856*
857 DO 180 j = 1, n
858 DO 170 jj = 1, n
859 IF( vr( j, jj ).NE.lre( j, jj ) )
860 \$ result( 6 ) = ulpinv
861 170 CONTINUE
862 180 CONTINUE
863*
864* Compute eigenvalues and left eigenvectors, and test them
865*
866 CALL dlacpy( 'F', n, n, a, lda, h, lda )
867 CALL dgeev( 'V', 'N', n, h, lda, wr1, wi1, lre, ldlre,
868 \$ dum, 1, work, nnwork, iinfo )
869 IF( iinfo.NE.0 ) THEN
870 result( 1 ) = ulpinv
871 WRITE( nounit, fmt = 9993 )'DGEEV4', iinfo, n, jtype,
872 \$ ioldsd
873 info = abs( iinfo )
874 GO TO 220
875 END IF
876*
877* Do Test (5) again
878*
879 DO 190 j = 1, n
880 IF( wr( j ).NE.wr1( j ) .OR. wi( j ).NE.wi1( j ) )
881 \$ result( 5 ) = ulpinv
882 190 CONTINUE
883*
884* Do Test (7)
885*
886 DO 210 j = 1, n
887 DO 200 jj = 1, n
888 IF( vl( j, jj ).NE.lre( j, jj ) )
889 \$ result( 7 ) = ulpinv
890 200 CONTINUE
891 210 CONTINUE
892*
893* End of Loop -- Check for RESULT(j) > THRESH
894*
895 220 CONTINUE
896*
897 ntest = 0
898 nfail = 0
899 DO 230 j = 1, 7
900 IF( result( j ).GE.zero )
901 \$ ntest = ntest + 1
902 IF( result( j ).GE.thresh )
903 \$ nfail = nfail + 1
904 230 CONTINUE
905*
906 IF( nfail.GT.0 )
907 \$ ntestf = ntestf + 1
908 IF( ntestf.EQ.1 ) THEN
909 WRITE( nounit, fmt = 9999 )path
910 WRITE( nounit, fmt = 9998 )
911 WRITE( nounit, fmt = 9997 )
912 WRITE( nounit, fmt = 9996 )
913 WRITE( nounit, fmt = 9995 )thresh
914 ntestf = 2
915 END IF
916*
917 DO 240 j = 1, 7
918 IF( result( j ).GE.thresh ) THEN
919 WRITE( nounit, fmt = 9994 )n, iwk, ioldsd, jtype,
920 \$ j, result( j )
921 END IF
922 240 CONTINUE
923*
924 nerrs = nerrs + nfail
925 ntestt = ntestt + ntest
926*
927 250 CONTINUE
928 260 CONTINUE
929 270 CONTINUE
930*
931* Summary
932*
933 CALL dlasum( path, nounit, nerrs, ntestt )
934*
935 9999 FORMAT( / 1x, a3, ' -- Real Eigenvalue-Eigenvector Decomposition',
936 \$ ' Driver', / ' Matrix types (see DDRVEV for details): ' )
937*
938 9998 FORMAT( / ' Special Matrices:', / ' 1=Zero matrix. ',
939 \$ ' ', ' 5=Diagonal: geometr. spaced entries.',
940 \$ / ' 2=Identity matrix. ', ' 6=Diagona',
941 \$ 'l: clustered entries.', / ' 3=Transposed Jordan block. ',
942 \$ ' ', ' 7=Diagonal: large, evenly spaced.', / ' ',
943 \$ '4=Diagonal: evenly spaced entries. ', ' 8=Diagonal: s',
944 \$ 'mall, evenly spaced.' )
945 9997 FORMAT( ' Dense, Non-Symmetric Matrices:', / ' 9=Well-cond., ev',
946 \$ 'enly spaced eigenvals.', ' 14=Ill-cond., geomet. spaced e',
947 \$ 'igenals.', / ' 10=Well-cond., geom. spaced eigenvals. ',
948 \$ ' 15=Ill-conditioned, clustered e.vals.', / ' 11=Well-cond',
949 \$ 'itioned, clustered e.vals. ', ' 16=Ill-cond., random comp',
950 \$ 'lex ', / ' 12=Well-cond., random complex ', 6x, ' ',
951 \$ ' 17=Ill-cond., large rand. complx ', / ' 13=Ill-condi',
952 \$ 'tioned, evenly spaced. ', ' 18=Ill-cond., small rand.',
953 \$ ' complx ' )
954 9996 FORMAT( ' 19=Matrix with random O(1) entries. ', ' 21=Matrix ',
955 \$ 'with small random entries.', / ' 20=Matrix with large ran',
956 \$ 'dom entries. ', / )
957 9995 FORMAT( ' Tests performed with test threshold =', f8.2,
958 \$ / / ' 1 = | A VR - VR W | / ( n |A| ulp ) ',
959 \$ / ' 2 = | transpose(A) VL - VL W | / ( n |A| ulp ) ',
960 \$ / ' 3 = | |VR(i)| - 1 | / ulp ',
961 \$ / ' 4 = | |VL(i)| - 1 | / ulp ',
962 \$ / ' 5 = 0 if W same no matter if VR or VL computed,',
963 \$ ' 1/ulp otherwise', /
964 \$ ' 6 = 0 if VR same no matter if VL computed,',
965 \$ ' 1/ulp otherwise', /
966 \$ ' 7 = 0 if VL same no matter if VR computed,',
967 \$ ' 1/ulp otherwise', / )
968 9994 FORMAT( ' N=', i5, ', IWK=', i2, ', seed=', 4( i4, ',' ),
969 \$ ' type ', i2, ', test(', i2, ')=', g10.3 )
970 9993 FORMAT( ' DDRVEV: ', a, ' returned INFO=', i6, '.', / 9x, 'N=',
971 \$ i6, ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ), i5, ')' )
972*
973 RETURN
974*
975* End of DDRVEV
976*
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
double precision function dlapy2(X, Y)
DLAPY2 returns sqrt(x2+y2).
Definition: dlapy2.f:63
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine dlasum(TYPE, IOUNIT, IE, NRUN)
DLASUM
Definition: dlasum.f:43
subroutine dget22(TRANSA, TRANSE, TRANSW, N, A, LDA, E, LDE, WR, WI, WORK, RESULT)
DGET22
Definition: dget22.f:168
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
subroutine dgeev(JOBVL, JOBVR, N, A, LDA, WR, WI, VL, LDVL, VR, LDVR, WORK, LWORK, INFO)
DGEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices
Definition: dgeev.f:192
real(wp) function dnrm2(n, x, incx)
DNRM2
Definition: dnrm2.f90:89
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