LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ ddrgev()

subroutine ddrgev ( 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, * ) b,
double precision, dimension( lda, * ) s,
double precision, dimension( lda, * ) t,
double precision, dimension( ldq, * ) q,
integer ldq,
double precision, dimension( ldq, * ) z,
double precision, dimension( ldqe, * ) qe,
integer ldqe,
double precision, dimension( * ) alphar,
double precision, dimension( * ) alphai,
double precision, dimension( * ) beta,
double precision, dimension( * ) alphr1,
double precision, dimension( * ) alphi1,
double precision, dimension( * ) beta1,
double precision, dimension( * ) work,
integer lwork,
double precision, dimension( * ) result,
integer info )

DDRGEV

Purpose:
!>
!> DDRGEV checks the nonsymmetric generalized eigenvalue problem driver
!> routine DGGEV.
!>
!> DGGEV computes for a pair of n-by-n nonsymmetric matrices (A,B) the
!> generalized eigenvalues and, optionally, the left and right
!> eigenvectors.
!>
!> A generalized eigenvalue for a pair of matrices (A,B) is a scalar w
!> or a ratio  alpha/beta = w, such that A - w*B is singular.  It is
!> usually represented as the pair (alpha,beta), as there is reasonable
!> interpretation for beta=0, and even for both being zero.
!>
!> A right generalized eigenvector corresponding to a generalized
!> eigenvalue  w  for a pair of matrices (A,B) is a vector r  such that
!> (A - wB) * r = 0.  A left generalized eigenvector is a vector l such
!> that l**H * (A - wB) = 0, where l**H is the conjugate-transpose of l.
!>
!> When DDRGEV is called, a number of matrix  () and a
!> number of matrix  are specified.  For each size ()
!> and each type of matrix, a pair of matrices (A, B) will be generated
!> and used for testing.  For each matrix pair, the following tests
!> will be performed and compared with the threshold THRESH.
!>
!> Results from DGGEV:
!>
!> (1)  max over all left eigenvalue/-vector pairs (alpha/beta,l) of
!>
!>      | VL**H * (beta A - alpha B) |/( ulp max(|beta A|, |alpha B|) )
!>
!>      where VL**H is the conjugate-transpose of VL.
!>
!> (2)  | |VL(i)| - 1 | / ulp and whether largest component real
!>
!>      VL(i) denotes the i-th column of VL.
!>
!> (3)  max over all left eigenvalue/-vector pairs (alpha/beta,r) of
!>
!>      | (beta A - alpha B) * VR | / ( ulp max(|beta A|, |alpha B|) )
!>
!> (4)  | |VR(i)| - 1 | / ulp and whether largest component real
!>
!>      VR(i) denotes the i-th column of VR.
!>
!> (5)  W(full) = W(partial)
!>      W(full) denotes the eigenvalues computed when both l and r
!>      are also computed, and W(partial) denotes the eigenvalues
!>      computed when only W, only W and r, or only W and l are
!>      computed.
!>
!> (6)  VL(full) = VL(partial)
!>      VL(full) denotes the left eigenvectors computed when both l
!>      and r are computed, and VL(partial) denotes the result
!>      when only l is computed.
!>
!> (7)  VR(full) = VR(partial)
!>      VR(full) denotes the right eigenvectors computed when both l
!>      and r are also computed, and VR(partial) denotes the result
!>      when only l is computed.
!>
!>
!> Test Matrices
!> ---- --------
!>
!> The sizes of the test matrices are specified by an array
!> NN(1:NSIZES); the value of each element NN(j) specifies one size.
!> The  are specified by a logical array DOTYPE( 1:NTYPES ); if
!> DOTYPE(j) is .TRUE., then matrix type  will be generated.
!> Currently, the list of possible types is:
!>
!> (1)  ( 0, 0 )         (a pair of zero matrices)
!>
!> (2)  ( I, 0 )         (an identity and a zero matrix)
!>
!> (3)  ( 0, I )         (an identity and a zero matrix)
!>
!> (4)  ( I, I )         (a pair of identity matrices)
!>
!>         t   t
!> (5)  ( J , J  )       (a pair of transposed Jordan blocks)
!>
!>                                     t                ( I   0  )
!> (6)  ( X, Y )         where  X = ( J   0  )  and Y = (      t )
!>                                  ( 0   I  )          ( 0   J  )
!>                       and I is a k x k identity and J a (k+1)x(k+1)
!>                       Jordan block; k=(N-1)/2
!>
!> (7)  ( D, I )         where D is diag( 0, 1,..., N-1 ) (a diagonal
!>                       matrix with those diagonal entries.)
!> (8)  ( I, D )
!>
!> (9)  ( big*D, small*I ) where  is near overflow and small=1/big
!>
!> (10) ( small*D, big*I )
!>
!> (11) ( big*I, small*D )
!>
!> (12) ( small*I, big*D )
!>
!> (13) ( big*D, big*I )
!>
!> (14) ( small*D, small*I )
!>
!> (15) ( D1, D2 )        where D1 is diag( 0, 0, 1, ..., N-3, 0 ) and
!>                        D2 is diag( 0, N-3, N-4,..., 1, 0, 0 )
!>           t   t
!> (16) Q ( J , J ) Z     where Q and Z are random orthogonal matrices.
!>
!> (17) Q ( T1, T2 ) Z    where T1 and T2 are upper triangular matrices
!>                        with random O(1) entries above the diagonal
!>                        and diagonal entries diag(T1) =
!>                        ( 0, 0, 1, ..., N-3, 0 ) and diag(T2) =
!>                        ( 0, N-3, N-4,..., 1, 0, 0 )
!>
!> (18) Q ( T1, T2 ) Z    diag(T1) = ( 0, 0, 1, 1, s, ..., s, 0 )
!>                        diag(T2) = ( 0, 1, 0, 1,..., 1, 0 )
!>                        s = machine precision.
!>
!> (19) Q ( T1, T2 ) Z    diag(T1)=( 0,0,1,1, 1-d, ..., 1-(N-5)*d=s, 0 )
!>                        diag(T2) = ( 0, 1, 0, 1, ..., 1, 0 )
!>
!>                                                        N-5
!> (20) Q ( T1, T2 ) Z    diag(T1)=( 0, 0, 1, 1, a, ..., a   =s, 0 )
!>                        diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 )
!>
!> (21) Q ( T1, T2 ) Z    diag(T1)=( 0, 0, 1, r1, r2, ..., r(N-4), 0 )
!>                        diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 )
!>                        where r1,..., r(N-4) are random.
!>
!> (22) Q ( big*T1, small*T2 ) Z    diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
!>                                  diag(T2) = ( 0, 1, ..., 1, 0, 0 )
!>
!> (23) Q ( small*T1, big*T2 ) Z    diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
!>                                  diag(T2) = ( 0, 1, ..., 1, 0, 0 )
!>
!> (24) Q ( small*T1, small*T2 ) Z  diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
!>                                  diag(T2) = ( 0, 1, ..., 1, 0, 0 )
!>
!> (25) Q ( big*T1, big*T2 ) Z      diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
!>                                  diag(T2) = ( 0, 1, ..., 1, 0, 0 )
!>
!> (26) Q ( T1, T2 ) Z     where T1 and T2 are random upper-triangular
!>                         matrices.
!>
!>
Parameters
[in]NSIZES
!>          NSIZES is INTEGER
!>          The number of sizes of matrices to use.  If it is zero,
!>          DDRGES does nothing.  NSIZES >= 0.
!>
[in]NN
!>          NN is INTEGER array, dimension (NSIZES)
!>          An array containing the sizes to be used for the matrices.
!>          Zero values will be skipped.  NN >= 0.
!>
[in]NTYPES
!>          NTYPES is INTEGER
!>          The number of elements in DOTYPE.   If it is zero, DDRGES
!>          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 DDRGES to continue the same random number
!>          sequence.
!>
[in]THRESH
!>          THRESH is DOUBLE PRECISION
!>          A test will count as  if the , 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 IERR not equal to 0.)
!>
[in,out]A
!>          A is DOUBLE PRECISION array,
!>                                       dimension(LDA, max(NN))
!>          Used to hold the original A matrix.  Used as input only
!>          if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and
!>          DOTYPE(MAXTYP+1)=.TRUE.
!>
[in]LDA
!>          LDA is INTEGER
!>          The leading dimension of A, B, S, and T.
!>          It must be at least 1 and at least max( NN ).
!>
[in,out]B
!>          B is DOUBLE PRECISION array,
!>                                       dimension(LDA, max(NN))
!>          Used to hold the original B matrix.  Used as input only
!>          if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and
!>          DOTYPE(MAXTYP+1)=.TRUE.
!>
[out]S
!>          S is DOUBLE PRECISION array,
!>                                 dimension (LDA, max(NN))
!>          The Schur form matrix computed from A by DGGES.  On exit, S
!>          contains the Schur form matrix corresponding to the matrix
!>          in A.
!>
[out]T
!>          T is DOUBLE PRECISION array,
!>                                 dimension (LDA, max(NN))
!>          The upper triangular matrix computed from B by DGGES.
!>
[out]Q
!>          Q is DOUBLE PRECISION array,
!>                                 dimension (LDQ, max(NN))
!>          The (left) eigenvectors matrix computed by DGGEV.
!>
[in]LDQ
!>          LDQ is INTEGER
!>          The leading dimension of Q and Z. It must
!>          be at least 1 and at least max( NN ).
!>
[out]Z
!>          Z is DOUBLE PRECISION array, dimension( LDQ, max(NN) )
!>          The (right) orthogonal matrix computed by DGGES.
!>
[out]QE
!>          QE is DOUBLE PRECISION array, dimension( LDQ, max(NN) )
!>          QE holds the computed right or left eigenvectors.
!>
[in]LDQE
!>          LDQE is INTEGER
!>          The leading dimension of QE. LDQE >= max(1,max(NN)).
!>
[out]ALPHAR
!>          ALPHAR is DOUBLE PRECISION array, dimension (max(NN))
!>
[out]ALPHAI
!>          ALPHAI is DOUBLE PRECISION array, dimension (max(NN))
!>
[out]BETA
!>          BETA is DOUBLE PRECISION array, dimension (max(NN))
!>
!>          The generalized eigenvalues of (A,B) computed by DGGEV.
!>          ( ALPHAR(k)+ALPHAI(k)*i ) / BETA(k) is the k-th
!>          generalized eigenvalue of A and B.
!>
[out]ALPHR1
!>          ALPHR1 is DOUBLE PRECISION array, dimension (max(NN))
!>
[out]ALPHI1
!>          ALPHI1 is DOUBLE PRECISION array, dimension (max(NN))
!>
[out]BETA1
!>          BETA1 is DOUBLE PRECISION array, dimension (max(NN))
!>
!>          Like ALPHAR, ALPHAI, BETA, these arrays contain the
!>          eigenvalues of A and B, but those computed when DGGEV only
!>          computes a partial eigendecomposition, i.e. not the
!>          eigenvalues and left and right eigenvectors.
!>
[out]WORK
!>          WORK is DOUBLE PRECISION array, dimension (LWORK)
!>
[in]LWORK
!>          LWORK is INTEGER
!>          The number of entries in WORK.  LWORK >= MAX( 8*N, N*(N+1) ).
!>
[out]RESULT
!>          RESULT is DOUBLE PRECISION array, dimension (2)
!>          The values computed by the tests described above.
!>          The values are currently limited to 1/ulp, to avoid overflow.
!>
[out]INFO
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value.
!>          > 0:  A routine returned an error code.  INFO is the
!>                absolute value of the INFO value returned.
!>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 404 of file ddrgev.f.

408*
409* -- LAPACK test routine --
410* -- LAPACK is a software package provided by Univ. of Tennessee, --
411* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
412*
413* .. Scalar Arguments ..
414 INTEGER INFO, LDA, LDQ, LDQE, LWORK, NOUNIT, NSIZES,
415 $ NTYPES
416 DOUBLE PRECISION THRESH
417* ..
418* .. Array Arguments ..
419 LOGICAL DOTYPE( * )
420 INTEGER ISEED( 4 ), NN( * )
421 DOUBLE PRECISION A( LDA, * ), ALPHAI( * ), ALPHAR( * ),
422 $ ALPHI1( * ), ALPHR1( * ), B( LDA, * ),
423 $ BETA( * ), BETA1( * ), Q( LDQ, * ),
424 $ QE( LDQE, * ), RESULT( * ), S( LDA, * ),
425 $ T( LDA, * ), WORK( * ), Z( LDQ, * )
426* ..
427*
428* =====================================================================
429*
430* .. Parameters ..
431 DOUBLE PRECISION ZERO, ONE
432 parameter( zero = 0.0d+0, one = 1.0d+0 )
433 INTEGER MAXTYP
434 parameter( maxtyp = 26 )
435* ..
436* .. Local Scalars ..
437 LOGICAL BADNN
438 INTEGER I, IADD, IERR, IN, J, JC, JR, JSIZE, JTYPE,
439 $ MAXWRK, MINWRK, MTYPES, N, N1, NERRS, NMATS,
440 $ NMAX, NTESTT
441 DOUBLE PRECISION SAFMAX, SAFMIN, ULP, ULPINV
442* ..
443* .. Local Arrays ..
444 INTEGER IASIGN( MAXTYP ), IBSIGN( MAXTYP ),
445 $ IOLDSD( 4 ), KADD( 6 ), KAMAGN( MAXTYP ),
446 $ KATYPE( MAXTYP ), KAZERO( MAXTYP ),
447 $ KBMAGN( MAXTYP ), KBTYPE( MAXTYP ),
448 $ KBZERO( MAXTYP ), KCLASS( MAXTYP ),
449 $ KTRIAN( MAXTYP ), KZ1( 6 ), KZ2( 6 )
450 DOUBLE PRECISION RMAGN( 0: 3 )
451* ..
452* .. External Functions ..
453 INTEGER ILAENV
454 DOUBLE PRECISION DLAMCH, DLARND
455 EXTERNAL ilaenv, dlamch, dlarnd
456* ..
457* .. External Subroutines ..
458 EXTERNAL alasvm, dget52, dggev, dlacpy, dlarfg,
459 $ dlaset, dlatm4, dorm2r, xerbla
460* ..
461* .. Intrinsic Functions ..
462 INTRINSIC abs, dble, max, min, sign
463* ..
464* .. Data statements ..
465 DATA kclass / 15*1, 10*2, 1*3 /
466 DATA kz1 / 0, 1, 2, 1, 3, 3 /
467 DATA kz2 / 0, 0, 1, 2, 1, 1 /
468 DATA kadd / 0, 0, 0, 0, 3, 2 /
469 DATA katype / 0, 1, 0, 1, 2, 3, 4, 1, 4, 4, 1, 1, 4,
470 $ 4, 4, 2, 4, 5, 8, 7, 9, 4*4, 0 /
471 DATA kbtype / 0, 0, 1, 1, 2, -3, 1, 4, 1, 1, 4, 4,
472 $ 1, 1, -4, 2, -4, 8*8, 0 /
473 DATA kazero / 6*1, 2, 1, 2*2, 2*1, 2*2, 3, 1, 3,
474 $ 4*5, 4*3, 1 /
475 DATA kbzero / 6*1, 1, 2, 2*1, 2*2, 2*1, 4, 1, 4,
476 $ 4*6, 4*4, 1 /
477 DATA kamagn / 8*1, 2, 3, 2, 3, 2, 3, 7*1, 2, 3, 3,
478 $ 2, 1 /
479 DATA kbmagn / 8*1, 3, 2, 3, 2, 2, 3, 7*1, 3, 2, 3,
480 $ 2, 1 /
481 DATA ktrian / 16*0, 10*1 /
482 DATA iasign / 6*0, 2, 0, 2*2, 2*0, 3*2, 0, 2, 3*0,
483 $ 5*2, 0 /
484 DATA ibsign / 7*0, 2, 2*0, 2*2, 2*0, 2, 0, 2, 9*0 /
485* ..
486* .. Executable Statements ..
487*
488* Check for errors
489*
490 info = 0
491*
492 badnn = .false.
493 nmax = 1
494 DO 10 j = 1, nsizes
495 nmax = max( nmax, nn( j ) )
496 IF( nn( j ).LT.0 )
497 $ badnn = .true.
498 10 CONTINUE
499*
500 IF( nsizes.LT.0 ) THEN
501 info = -1
502 ELSE IF( badnn ) THEN
503 info = -2
504 ELSE IF( ntypes.LT.0 ) THEN
505 info = -3
506 ELSE IF( thresh.LT.zero ) THEN
507 info = -6
508 ELSE IF( lda.LE.1 .OR. lda.LT.nmax ) THEN
509 info = -9
510 ELSE IF( ldq.LE.1 .OR. ldq.LT.nmax ) THEN
511 info = -14
512 ELSE IF( ldqe.LE.1 .OR. ldqe.LT.nmax ) THEN
513 info = -17
514 END IF
515*
516* Compute workspace
517* (Note: Comments in the code beginning "Workspace:" describe the
518* minimal amount of workspace needed at that point in the code,
519* as well as the preferred amount for good performance.
520* NB refers to the optimal block size for the immediately
521* following subroutine, as returned by ILAENV.
522*
523 minwrk = 1
524 IF( info.EQ.0 .AND. lwork.GE.1 ) THEN
525 minwrk = max( 1, 8*nmax, nmax*( nmax+1 ) )
526 maxwrk = 7*nmax + nmax*ilaenv( 1, 'DGEQRF', ' ', nmax, 1, nmax,
527 $ 0 )
528 maxwrk = max( maxwrk, nmax*( nmax+1 ) )
529 work( 1 ) = maxwrk
530 END IF
531*
532 IF( lwork.LT.minwrk )
533 $ info = -25
534*
535 IF( info.NE.0 ) THEN
536 CALL xerbla( 'DDRGEV', -info )
537 RETURN
538 END IF
539*
540* Quick return if possible
541*
542 IF( nsizes.EQ.0 .OR. ntypes.EQ.0 )
543 $ RETURN
544*
545 safmin = dlamch( 'Safe minimum' )
546 ulp = dlamch( 'Epsilon' )*dlamch( 'Base' )
547 safmin = safmin / ulp
548 safmax = one / safmin
549 ulpinv = one / ulp
550*
551* The values RMAGN(2:3) depend on N, see below.
552*
553 rmagn( 0 ) = zero
554 rmagn( 1 ) = one
555*
556* Loop over sizes, types
557*
558 ntestt = 0
559 nerrs = 0
560 nmats = 0
561*
562 DO 220 jsize = 1, nsizes
563 n = nn( jsize )
564 n1 = max( 1, n )
565 rmagn( 2 ) = safmax*ulp / dble( n1 )
566 rmagn( 3 ) = safmin*ulpinv*n1
567*
568 IF( nsizes.NE.1 ) THEN
569 mtypes = min( maxtyp, ntypes )
570 ELSE
571 mtypes = min( maxtyp+1, ntypes )
572 END IF
573*
574 DO 210 jtype = 1, mtypes
575 IF( .NOT.dotype( jtype ) )
576 $ GO TO 210
577 nmats = nmats + 1
578*
579* Save ISEED in case of an error.
580*
581 DO 20 j = 1, 4
582 ioldsd( j ) = iseed( j )
583 20 CONTINUE
584*
585* Generate test matrices A and B
586*
587* Description of control parameters:
588*
589* KZLASS: =1 means w/o rotation, =2 means w/ rotation,
590* =3 means random.
591* KATYPE: the "type" to be passed to DLATM4 for computing A.
592* KAZERO: the pattern of zeros on the diagonal for A:
593* =1: ( xxx ), =2: (0, xxx ) =3: ( 0, 0, xxx, 0 ),
594* =4: ( 0, xxx, 0, 0 ), =5: ( 0, 0, 1, xxx, 0 ),
595* =6: ( 0, 1, 0, xxx, 0 ). (xxx means a string of
596* non-zero entries.)
597* KAMAGN: the magnitude of the matrix: =0: zero, =1: O(1),
598* =2: large, =3: small.
599* IASIGN: 1 if the diagonal elements of A are to be
600* multiplied by a random magnitude 1 number, =2 if
601* randomly chosen diagonal blocks are to be rotated
602* to form 2x2 blocks.
603* KBTYPE, KBZERO, KBMAGN, IBSIGN: the same, but for B.
604* KTRIAN: =0: don't fill in the upper triangle, =1: do.
605* KZ1, KZ2, KADD: used to implement KAZERO and KBZERO.
606* RMAGN: used to implement KAMAGN and KBMAGN.
607*
608 IF( mtypes.GT.maxtyp )
609 $ GO TO 100
610 ierr = 0
611 IF( kclass( jtype ).LT.3 ) THEN
612*
613* Generate A (w/o rotation)
614*
615 IF( abs( katype( jtype ) ).EQ.3 ) THEN
616 in = 2*( ( n-1 ) / 2 ) + 1
617 IF( in.NE.n )
618 $ CALL dlaset( 'Full', n, n, zero, zero, a, lda )
619 ELSE
620 in = n
621 END IF
622 CALL dlatm4( katype( jtype ), in, kz1( kazero( jtype ) ),
623 $ kz2( kazero( jtype ) ), iasign( jtype ),
624 $ rmagn( kamagn( jtype ) ), ulp,
625 $ rmagn( ktrian( jtype )*kamagn( jtype ) ), 2,
626 $ iseed, a, lda )
627 iadd = kadd( kazero( jtype ) )
628 IF( iadd.GT.0 .AND. iadd.LE.n )
629 $ a( iadd, iadd ) = one
630*
631* Generate B (w/o rotation)
632*
633 IF( abs( kbtype( jtype ) ).EQ.3 ) THEN
634 in = 2*( ( n-1 ) / 2 ) + 1
635 IF( in.NE.n )
636 $ CALL dlaset( 'Full', n, n, zero, zero, b, lda )
637 ELSE
638 in = n
639 END IF
640 CALL dlatm4( kbtype( jtype ), in, kz1( kbzero( jtype ) ),
641 $ kz2( kbzero( jtype ) ), ibsign( jtype ),
642 $ rmagn( kbmagn( jtype ) ), one,
643 $ rmagn( ktrian( jtype )*kbmagn( jtype ) ), 2,
644 $ iseed, b, lda )
645 iadd = kadd( kbzero( jtype ) )
646 IF( iadd.NE.0 .AND. iadd.LE.n )
647 $ b( iadd, iadd ) = one
648*
649 IF( kclass( jtype ).EQ.2 .AND. n.GT.0 ) THEN
650*
651* Include rotations
652*
653* Generate Q, Z as Householder transformations times
654* a diagonal matrix.
655*
656 DO 40 jc = 1, n - 1
657 DO 30 jr = jc, n
658 q( jr, jc ) = dlarnd( 3, iseed )
659 z( jr, jc ) = dlarnd( 3, iseed )
660 30 CONTINUE
661 CALL dlarfg( n+1-jc, q( jc, jc ), q( jc+1, jc ), 1,
662 $ work( jc ) )
663 work( 2*n+jc ) = sign( one, q( jc, jc ) )
664 q( jc, jc ) = one
665 CALL dlarfg( n+1-jc, z( jc, jc ), z( jc+1, jc ), 1,
666 $ work( n+jc ) )
667 work( 3*n+jc ) = sign( one, z( jc, jc ) )
668 z( jc, jc ) = one
669 40 CONTINUE
670 q( n, n ) = one
671 work( n ) = zero
672 work( 3*n ) = sign( one, dlarnd( 2, iseed ) )
673 z( n, n ) = one
674 work( 2*n ) = zero
675 work( 4*n ) = sign( one, dlarnd( 2, iseed ) )
676*
677* Apply the diagonal matrices
678*
679 DO 60 jc = 1, n
680 DO 50 jr = 1, n
681 a( jr, jc ) = work( 2*n+jr )*work( 3*n+jc )*
682 $ a( jr, jc )
683 b( jr, jc ) = work( 2*n+jr )*work( 3*n+jc )*
684 $ b( jr, jc )
685 50 CONTINUE
686 60 CONTINUE
687 CALL dorm2r( 'L', 'N', n, n, n-1, q, ldq, work, a,
688 $ lda, work( 2*n+1 ), ierr )
689 IF( ierr.NE.0 )
690 $ GO TO 90
691 CALL dorm2r( 'R', 'T', n, n, n-1, z, ldq, work( n+1 ),
692 $ a, lda, work( 2*n+1 ), ierr )
693 IF( ierr.NE.0 )
694 $ GO TO 90
695 CALL dorm2r( 'L', 'N', n, n, n-1, q, ldq, work, b,
696 $ lda, work( 2*n+1 ), ierr )
697 IF( ierr.NE.0 )
698 $ GO TO 90
699 CALL dorm2r( 'R', 'T', n, n, n-1, z, ldq, work( n+1 ),
700 $ b, lda, work( 2*n+1 ), ierr )
701 IF( ierr.NE.0 )
702 $ GO TO 90
703 END IF
704 ELSE
705*
706* Random matrices
707*
708 DO 80 jc = 1, n
709 DO 70 jr = 1, n
710 a( jr, jc ) = rmagn( kamagn( jtype ) )*
711 $ dlarnd( 2, iseed )
712 b( jr, jc ) = rmagn( kbmagn( jtype ) )*
713 $ dlarnd( 2, iseed )
714 70 CONTINUE
715 80 CONTINUE
716 END IF
717*
718 90 CONTINUE
719*
720 IF( ierr.NE.0 ) THEN
721 WRITE( nounit, fmt = 9999 )'Generator', ierr, n, jtype,
722 $ ioldsd
723 info = abs( ierr )
724 RETURN
725 END IF
726*
727 100 CONTINUE
728*
729 DO 110 i = 1, 7
730 result( i ) = -one
731 110 CONTINUE
732*
733* Call DGGEV to compute eigenvalues and eigenvectors.
734*
735 CALL dlacpy( ' ', n, n, a, lda, s, lda )
736 CALL dlacpy( ' ', n, n, b, lda, t, lda )
737 CALL dggev( 'V', 'V', n, s, lda, t, lda, alphar, alphai,
738 $ beta, q, ldq, z, ldq, work, lwork, ierr )
739 IF( ierr.NE.0 .AND. ierr.NE.n+1 ) THEN
740 result( 1 ) = ulpinv
741 WRITE( nounit, fmt = 9999 )'DGGEV1', ierr, n, jtype,
742 $ ioldsd
743 info = abs( ierr )
744 GO TO 190
745 END IF
746*
747* Do the tests (1) and (2)
748*
749 CALL dget52( .true., n, a, lda, b, lda, q, ldq, alphar,
750 $ alphai, beta, work, result( 1 ) )
751 IF( result( 2 ).GT.thresh ) THEN
752 WRITE( nounit, fmt = 9998 )'Left', 'DGGEV1',
753 $ result( 2 ), n, jtype, ioldsd
754 END IF
755*
756* Do the tests (3) and (4)
757*
758 CALL dget52( .false., n, a, lda, b, lda, z, ldq, alphar,
759 $ alphai, beta, work, result( 3 ) )
760 IF( result( 4 ).GT.thresh ) THEN
761 WRITE( nounit, fmt = 9998 )'Right', 'DGGEV1',
762 $ result( 4 ), n, jtype, ioldsd
763 END IF
764*
765* Do the test (5)
766*
767 CALL dlacpy( ' ', n, n, a, lda, s, lda )
768 CALL dlacpy( ' ', n, n, b, lda, t, lda )
769 CALL dggev( 'N', 'N', n, s, lda, t, lda, alphr1, alphi1,
770 $ beta1, q, ldq, z, ldq, work, lwork, ierr )
771 IF( ierr.NE.0 .AND. ierr.NE.n+1 ) THEN
772 result( 1 ) = ulpinv
773 WRITE( nounit, fmt = 9999 )'DGGEV2', ierr, n, jtype,
774 $ ioldsd
775 info = abs( ierr )
776 GO TO 190
777 END IF
778*
779 DO 120 j = 1, n
780 IF( alphar( j ).NE.alphr1( j ) .OR. alphai( j ).NE.
781 $ alphi1( j ) .OR. beta( j ).NE.beta1( j ) )result( 5 )
782 $ = ulpinv
783 120 CONTINUE
784*
785* Do the test (6): Compute eigenvalues and left eigenvectors,
786* and test them
787*
788 CALL dlacpy( ' ', n, n, a, lda, s, lda )
789 CALL dlacpy( ' ', n, n, b, lda, t, lda )
790 CALL dggev( 'V', 'N', n, s, lda, t, lda, alphr1, alphi1,
791 $ beta1, qe, ldqe, z, ldq, work, lwork, ierr )
792 IF( ierr.NE.0 .AND. ierr.NE.n+1 ) THEN
793 result( 1 ) = ulpinv
794 WRITE( nounit, fmt = 9999 )'DGGEV3', ierr, n, jtype,
795 $ ioldsd
796 info = abs( ierr )
797 GO TO 190
798 END IF
799*
800 DO 130 j = 1, n
801 IF( alphar( j ).NE.alphr1( j ) .OR. alphai( j ).NE.
802 $ alphi1( j ) .OR. beta( j ).NE.beta1( j ) )result( 6 )
803 $ = ulpinv
804 130 CONTINUE
805*
806 DO 150 j = 1, n
807 DO 140 jc = 1, n
808 IF( q( j, jc ).NE.qe( j, jc ) )
809 $ result( 6 ) = ulpinv
810 140 CONTINUE
811 150 CONTINUE
812*
813* DO the test (7): Compute eigenvalues and right eigenvectors,
814* and test them
815*
816 CALL dlacpy( ' ', n, n, a, lda, s, lda )
817 CALL dlacpy( ' ', n, n, b, lda, t, lda )
818 CALL dggev( 'N', 'V', n, s, lda, t, lda, alphr1, alphi1,
819 $ beta1, q, ldq, qe, ldqe, work, lwork, ierr )
820 IF( ierr.NE.0 .AND. ierr.NE.n+1 ) THEN
821 result( 1 ) = ulpinv
822 WRITE( nounit, fmt = 9999 )'DGGEV4', ierr, n, jtype,
823 $ ioldsd
824 info = abs( ierr )
825 GO TO 190
826 END IF
827*
828 DO 160 j = 1, n
829 IF( alphar( j ).NE.alphr1( j ) .OR. alphai( j ).NE.
830 $ alphi1( j ) .OR. beta( j ).NE.beta1( j ) )result( 7 )
831 $ = ulpinv
832 160 CONTINUE
833*
834 DO 180 j = 1, n
835 DO 170 jc = 1, n
836 IF( z( j, jc ).NE.qe( j, jc ) )
837 $ result( 7 ) = ulpinv
838 170 CONTINUE
839 180 CONTINUE
840*
841* End of Loop -- Check for RESULT(j) > THRESH
842*
843 190 CONTINUE
844*
845 ntestt = ntestt + 7
846*
847* Print out tests which fail.
848*
849 DO 200 jr = 1, 7
850 IF( result( jr ).GE.thresh ) THEN
851*
852* If this is the first test to fail,
853* print a header to the data file.
854*
855 IF( nerrs.EQ.0 ) THEN
856 WRITE( nounit, fmt = 9997 )'DGV'
857*
858* Matrix types
859*
860 WRITE( nounit, fmt = 9996 )
861 WRITE( nounit, fmt = 9995 )
862 WRITE( nounit, fmt = 9994 )'Orthogonal'
863*
864* Tests performed
865*
866 WRITE( nounit, fmt = 9993 )
867*
868 END IF
869 nerrs = nerrs + 1
870 IF( result( jr ).LT.10000.0d0 ) THEN
871 WRITE( nounit, fmt = 9992 )n, jtype, ioldsd, jr,
872 $ result( jr )
873 ELSE
874 WRITE( nounit, fmt = 9991 )n, jtype, ioldsd, jr,
875 $ result( jr )
876 END IF
877 END IF
878 200 CONTINUE
879*
880 210 CONTINUE
881 220 CONTINUE
882*
883* Summary
884*
885 CALL alasvm( 'DGV', nounit, nerrs, ntestt, 0 )
886*
887 work( 1 ) = maxwrk
888*
889 RETURN
890*
891 9999 FORMAT( ' DDRGEV: ', a, ' returned INFO=', i6, '.', / 3x, 'N=',
892 $ i6, ', JTYPE=', i6, ', ISEED=(', 4( i4, ',' ), i5, ')' )
893*
894 9998 FORMAT( ' DDRGEV: ', a, ' Eigenvectors from ', a, ' incorrectly ',
895 $ 'normalized.', / ' Bits of error=', 0p, g10.3, ',', 3x,
896 $ 'N=', i4, ', JTYPE=', i3, ', ISEED=(', 4( i4, ',' ), i5,
897 $ ')' )
898*
899 9997 FORMAT( / 1x, a3, ' -- Real Generalized eigenvalue problem driver'
900 $ )
901*
902 9996 FORMAT( ' Matrix types (see DDRGEV for details): ' )
903*
904 9995 FORMAT( ' Special Matrices:', 23x,
905 $ '(J''=transposed Jordan block)',
906 $ / ' 1=(0,0) 2=(I,0) 3=(0,I) 4=(I,I) 5=(J'',J'') ',
907 $ '6=(diag(J'',I), diag(I,J''))', / ' Diagonal Matrices: ( ',
908 $ 'D=diag(0,1,2,...) )', / ' 7=(D,I) 9=(large*D, small*I',
909 $ ') 11=(large*I, small*D) 13=(large*D, large*I)', /
910 $ ' 8=(I,D) 10=(small*D, large*I) 12=(small*I, large*D) ',
911 $ ' 14=(small*D, small*I)', / ' 15=(D, reversed D)' )
912 9994 FORMAT( ' Matrices Rotated by Random ', a, ' Matrices U, V:',
913 $ / ' 16=Transposed Jordan Blocks 19=geometric ',
914 $ 'alpha, beta=0,1', / ' 17=arithm. alpha&beta ',
915 $ ' 20=arithmetic alpha, beta=0,1', / ' 18=clustered ',
916 $ 'alpha, beta=0,1 21=random alpha, beta=0,1',
917 $ / ' Large & Small Matrices:', / ' 22=(large, small) ',
918 $ '23=(small,large) 24=(small,small) 25=(large,large)',
919 $ / ' 26=random O(1) matrices.' )
920*
921 9993 FORMAT( / ' Tests performed: ',
922 $ / ' 1 = max | ( b A - a B )''*l | / const.,',
923 $ / ' 2 = | |VR(i)| - 1 | / ulp,',
924 $ / ' 3 = max | ( b A - a B )*r | / const.',
925 $ / ' 4 = | |VL(i)| - 1 | / ulp,',
926 $ / ' 5 = 0 if W same no matter if r or l computed,',
927 $ / ' 6 = 0 if l same no matter if l computed,',
928 $ / ' 7 = 0 if r same no matter if r computed,', / 1x )
929 9992 FORMAT( ' Matrix order=', i5, ', type=', i2, ', seed=',
930 $ 4( i4, ',' ), ' result ', i2, ' is', 0p, f8.2 )
931 9991 FORMAT( ' Matrix order=', i5, ', type=', i2, ', seed=',
932 $ 4( i4, ',' ), ' result ', i2, ' is', 1p, d10.3 )
933*
934* End of DDRGEV
935*
alasvm
subroutine alasvm(type, nout, nfail, nrun, nerrs)
ALASVM
Definition alasvm.f:73
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
dget52
subroutine dget52(left, n, a, lda, b, ldb, e, lde, alphar, alphai, beta, work, result)
DGET52
Definition dget52.f:199
dlarnd
double precision function dlarnd(idist, iseed)
DLARND
Definition dlarnd.f:73
dlatm4
subroutine dlatm4(itype, n, nz1, nz2, isign, amagn, rcond, triang, idist, iseed, a, lda)
DLATM4
Definition dlatm4.f:175
dggev
subroutine dggev(jobvl, jobvr, n, a, lda, b, ldb, alphar, alphai, beta, vl, ldvl, vr, ldvr, work, lwork, info)
DGGEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices
Definition dggev.f:225
ilaenv
integer function ilaenv(ispec, name, opts, n1, n2, n3, n4)
ILAENV
Definition ilaenv.f:160
dlacpy
subroutine dlacpy(uplo, m, n, a, lda, b, ldb)
DLACPY copies all or part of one two-dimensional array to another.
Definition dlacpy.f:101
dlamch
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
dlarfg
subroutine dlarfg(n, alpha, x, incx, tau)
DLARFG generates an elementary reflector (Householder matrix).
Definition dlarfg.f:104
dlaset
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:108
dorm2r
subroutine dorm2r(side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
DORM2R multiplies a general matrix by the orthogonal matrix from a QR factorization determined by sge...
Definition dorm2r.f:156
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