LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine cdrgev ( integer NSIZES, integer, dimension( * ) NN, integer NTYPES, logical, dimension( * ) DOTYPE, integer, dimension( 4 ) ISEED, real THRESH, integer NOUNIT, complex, dimension( lda, * ) A, integer LDA, complex, dimension( lda, * ) B, complex, dimension( lda, * ) S, complex, dimension( lda, * ) T, complex, dimension( ldq, * ) Q, integer LDQ, complex, dimension( ldq, * ) Z, complex, dimension( ldqe, * ) QE, integer LDQE, complex, dimension( * ) ALPHA, complex, dimension( * ) BETA, complex, dimension( * ) ALPHA1, complex, dimension( * ) BETA1, complex, dimension( * ) WORK, integer LWORK, real, dimension( * ) RWORK, real, dimension( * ) RESULT, integer INFO )

CDRGEV

Purpose:
``` CDRGEV checks the nonsymmetric generalized eigenvalue problem driver
routine CGGEV.

CGGEV 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 CDRGEV 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, 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 CGGEV:

(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 "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)  ( 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 "big" 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, CDRGES 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, CDRGEV 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 CDRGES 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] 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 COMPLEX 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 COMPLEX 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 COMPLEX array, dimension (LDA, max(NN)) The Schur form matrix computed from A by CGGEV. On exit, S contains the Schur form matrix corresponding to the matrix in A.``` [out] T ``` T is COMPLEX array, dimension (LDA, max(NN)) The upper triangular matrix computed from B by CGGEV.``` [out] Q ``` Q is COMPLEX array, dimension (LDQ, max(NN)) The (left) eigenvectors matrix computed by CGGEV.``` [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 COMPLEX array, dimension( LDQ, max(NN) ) The (right) orthogonal matrix computed by CGGEV.``` [out] QE ``` QE is COMPLEX 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] ALPHA ` ALPHA is COMPLEX array, dimension (max(NN))` [out] BETA ``` BETA is COMPLEX array, dimension (max(NN)) The generalized eigenvalues of (A,B) computed by CGGEV. ( ALPHAR(k)+ALPHAI(k)*i ) / BETA(k) is the k-th generalized eigenvalue of A and B.``` [out] ALPHA1 ` ALPHA1 is COMPLEX array, dimension (max(NN))` [out] BETA1 ``` BETA1 is COMPLEX array, dimension (max(NN)) Like ALPHAR, ALPHAI, BETA, these arrays contain the eigenvalues of A and B, but those computed when CGGEV only computes a partial eigendecomposition, i.e. not the eigenvalues and left and right eigenvectors.``` [out] WORK ` WORK is COMPLEX array, dimension (LWORK)` [in] LWORK ``` LWORK is INTEGER The number of entries in WORK. LWORK >= N*(N+1)``` [out] RWORK ``` RWORK is REAL array, dimension (8*N) Real workspace.``` [out] RESULT ``` RESULT is REAL 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.```
Date
June 2016

Definition at line 401 of file cdrgev.f.

401 *
402 * -- LAPACK test routine (version 3.6.1) --
403 * -- LAPACK is a software package provided by Univ. of Tennessee, --
404 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
405 * June 2016
406 *
407 * .. Scalar Arguments ..
408  INTEGER info, lda, ldq, ldqe, lwork, nounit, nsizes,
409  \$ ntypes
410  REAL thresh
411 * ..
412 * .. Array Arguments ..
413  LOGICAL dotype( * )
414  INTEGER iseed( 4 ), nn( * )
415  REAL result( * ), rwork( * )
416  COMPLEX a( lda, * ), alpha( * ), alpha1( * ),
417  \$ b( lda, * ), beta( * ), beta1( * ),
418  \$ q( ldq, * ), qe( ldqe, * ), s( lda, * ),
419  \$ t( lda, * ), work( * ), z( ldq, * )
420 * ..
421 *
422 * =====================================================================
423 *
424 * .. Parameters ..
425  REAL zero, one
426  parameter ( zero = 0.0e+0, one = 1.0e+0 )
427  COMPLEX czero, cone
428  parameter ( czero = ( 0.0e+0, 0.0e+0 ),
429  \$ cone = ( 1.0e+0, 0.0e+0 ) )
430  INTEGER maxtyp
431  parameter ( maxtyp = 26 )
432 * ..
433 * .. Local Scalars ..
435  INTEGER i, iadd, ierr, in, j, jc, jr, jsize, jtype,
436  \$ maxwrk, minwrk, mtypes, n, n1, nb, nerrs,
437  \$ nmats, nmax, ntestt
438  REAL safmax, safmin, ulp, ulpinv
439  COMPLEX ctemp
440 * ..
441 * .. Local Arrays ..
442  LOGICAL lasign( maxtyp ), lbsign( maxtyp )
443  INTEGER ioldsd( 4 ), kadd( 6 ), kamagn( maxtyp ),
444  \$ katype( maxtyp ), kazero( maxtyp ),
445  \$ kbmagn( maxtyp ), kbtype( maxtyp ),
446  \$ kbzero( maxtyp ), kclass( maxtyp ),
447  \$ ktrian( maxtyp ), kz1( 6 ), kz2( 6 )
448  REAL rmagn( 0: 3 )
449 * ..
450 * .. External Functions ..
451  INTEGER ilaenv
452  REAL slamch
453  COMPLEX clarnd
454  EXTERNAL ilaenv, slamch, clarnd
455 * ..
456 * .. External Subroutines ..
457  EXTERNAL alasvm, cget52, cggev, clacpy, clarfg, claset,
459 * ..
460 * .. Intrinsic Functions ..
461  INTRINSIC abs, conjg, max, min, REAL, sign
462 * ..
463 * .. Data statements ..
464  DATA kclass / 15*1, 10*2, 1*3 /
465  DATA kz1 / 0, 1, 2, 1, 3, 3 /
466  DATA kz2 / 0, 0, 1, 2, 1, 1 /
467  DATA kadd / 0, 0, 0, 0, 3, 2 /
468  DATA katype / 0, 1, 0, 1, 2, 3, 4, 1, 4, 4, 1, 1, 4,
469  \$ 4, 4, 2, 4, 5, 8, 7, 9, 4*4, 0 /
470  DATA kbtype / 0, 0, 1, 1, 2, -3, 1, 4, 1, 1, 4, 4,
471  \$ 1, 1, -4, 2, -4, 8*8, 0 /
472  DATA kazero / 6*1, 2, 1, 2*2, 2*1, 2*2, 3, 1, 3,
473  \$ 4*5, 4*3, 1 /
474  DATA kbzero / 6*1, 1, 2, 2*1, 2*2, 2*1, 4, 1, 4,
475  \$ 4*6, 4*4, 1 /
476  DATA kamagn / 8*1, 2, 3, 2, 3, 2, 3, 7*1, 2, 3, 3,
477  \$ 2, 1 /
478  DATA kbmagn / 8*1, 3, 2, 3, 2, 2, 3, 7*1, 3, 2, 3,
479  \$ 2, 1 /
480  DATA ktrian / 16*0, 10*1 /
481  DATA lasign / 6*.false., .true., .false., 2*.true.,
482  \$ 2*.false., 3*.true., .false., .true.,
483  \$ 3*.false., 5*.true., .false. /
484  DATA lbsign / 7*.false., .true., 2*.false.,
485  \$ 2*.true., 2*.false., .true., .false., .true.,
486  \$ 9*.false. /
487 * ..
488 * .. Executable Statements ..
489 *
490 * Check for errors
491 *
492  info = 0
493 *
495  nmax = 1
496  DO 10 j = 1, nsizes
497  nmax = max( nmax, nn( j ) )
498  IF( nn( j ).LT.0 )
500  10 CONTINUE
501 *
502  IF( nsizes.LT.0 ) THEN
503  info = -1
504  ELSE IF( badnn ) THEN
505  info = -2
506  ELSE IF( ntypes.LT.0 ) THEN
507  info = -3
508  ELSE IF( thresh.LT.zero ) THEN
509  info = -6
510  ELSE IF( lda.LE.1 .OR. lda.LT.nmax ) THEN
511  info = -9
512  ELSE IF( ldq.LE.1 .OR. ldq.LT.nmax ) THEN
513  info = -14
514  ELSE IF( ldqe.LE.1 .OR. ldqe.LT.nmax ) THEN
515  info = -17
516  END IF
517 *
518 * Compute workspace
519 * (Note: Comments in the code beginning "Workspace:" describe the
520 * minimal amount of workspace needed at that point in the code,
521 * as well as the preferred amount for good performance.
522 * NB refers to the optimal block size for the immediately
523 * following subroutine, as returned by ILAENV.
524 *
525  minwrk = 1
526  IF( info.EQ.0 .AND. lwork.GE.1 ) THEN
527  minwrk = nmax*( nmax+1 )
528  nb = max( 1, ilaenv( 1, 'CGEQRF', ' ', nmax, nmax, -1, -1 ),
529  \$ ilaenv( 1, 'CUNMQR', 'LC', nmax, nmax, nmax, -1 ),
530  \$ ilaenv( 1, 'CUNGQR', ' ', nmax, nmax, nmax, -1 ) )
531  maxwrk = max( 2*nmax, nmax*( nb+1 ), nmax*( nmax+1 ) )
532  work( 1 ) = maxwrk
533  END IF
534 *
535  IF( lwork.LT.minwrk )
536  \$ info = -23
537 *
538  IF( info.NE.0 ) THEN
539  CALL xerbla( 'CDRGEV', -info )
540  RETURN
541  END IF
542 *
543 * Quick return if possible
544 *
545  IF( nsizes.EQ.0 .OR. ntypes.EQ.0 )
546  \$ RETURN
547 *
548  ulp = slamch( 'Precision' )
549  safmin = slamch( 'Safe minimum' )
550  safmin = safmin / ulp
551  safmax = one / safmin
552  CALL slabad( safmin, safmax )
553  ulpinv = one / ulp
554 *
555 * The values RMAGN(2:3) depend on N, see below.
556 *
557  rmagn( 0 ) = zero
558  rmagn( 1 ) = one
559 *
560 * Loop over sizes, types
561 *
562  ntestt = 0
563  nerrs = 0
564  nmats = 0
565 *
566  DO 220 jsize = 1, nsizes
567  n = nn( jsize )
568  n1 = max( 1, n )
569  rmagn( 2 ) = safmax*ulp / REAL( n1 )
570  rmagn( 3 ) = safmin*ulpinv*n1
571 *
572  IF( nsizes.NE.1 ) THEN
573  mtypes = min( maxtyp, ntypes )
574  ELSE
575  mtypes = min( maxtyp+1, ntypes )
576  END IF
577 *
578  DO 210 jtype = 1, mtypes
579  IF( .NOT.dotype( jtype ) )
580  \$ GO TO 210
581  nmats = nmats + 1
582 *
583 * Save ISEED in case of an error.
584 *
585  DO 20 j = 1, 4
586  ioldsd( j ) = iseed( j )
587  20 CONTINUE
588 *
589 * Generate test matrices A and B
590 *
591 * Description of control parameters:
592 *
593 * KCLASS: =1 means w/o rotation, =2 means w/ rotation,
594 * =3 means random.
595 * KATYPE: the "type" to be passed to CLATM4 for computing A.
596 * KAZERO: the pattern of zeros on the diagonal for A:
597 * =1: ( xxx ), =2: (0, xxx ) =3: ( 0, 0, xxx, 0 ),
598 * =4: ( 0, xxx, 0, 0 ), =5: ( 0, 0, 1, xxx, 0 ),
599 * =6: ( 0, 1, 0, xxx, 0 ). (xxx means a string of
600 * non-zero entries.)
601 * KAMAGN: the magnitude of the matrix: =0: zero, =1: O(1),
602 * =2: large, =3: small.
603 * LASIGN: .TRUE. if the diagonal elements of A are to be
604 * multiplied by a random magnitude 1 number.
605 * KBTYPE, KBZERO, KBMAGN, LBSIGN: the same, but for B.
606 * KTRIAN: =0: don't fill in the upper triangle, =1: do.
607 * KZ1, KZ2, KADD: used to implement KAZERO and KBZERO.
608 * RMAGN: used to implement KAMAGN and KBMAGN.
609 *
610  IF( mtypes.GT.maxtyp )
611  \$ GO TO 100
612  ierr = 0
613  IF( kclass( jtype ).LT.3 ) THEN
614 *
615 * Generate A (w/o rotation)
616 *
617  IF( abs( katype( jtype ) ).EQ.3 ) THEN
618  in = 2*( ( n-1 ) / 2 ) + 1
619  IF( in.NE.n )
620  \$ CALL claset( 'Full', n, n, czero, czero, a, lda )
621  ELSE
622  in = n
623  END IF
624  CALL clatm4( katype( jtype ), in, kz1( kazero( jtype ) ),
625  \$ kz2( kazero( jtype ) ), lasign( jtype ),
626  \$ rmagn( kamagn( jtype ) ), ulp,
627  \$ rmagn( ktrian( jtype )*kamagn( jtype ) ), 2,
628  \$ iseed, a, lda )
631  \$ a( iadd, iadd ) = rmagn( kamagn( jtype ) )
632 *
633 * Generate B (w/o rotation)
634 *
635  IF( abs( kbtype( jtype ) ).EQ.3 ) THEN
636  in = 2*( ( n-1 ) / 2 ) + 1
637  IF( in.NE.n )
638  \$ CALL claset( 'Full', n, n, czero, czero, b, lda )
639  ELSE
640  in = n
641  END IF
642  CALL clatm4( kbtype( jtype ), in, kz1( kbzero( jtype ) ),
643  \$ kz2( kbzero( jtype ) ), lbsign( jtype ),
644  \$ rmagn( kbmagn( jtype ) ), one,
645  \$ rmagn( ktrian( jtype )*kbmagn( jtype ) ), 2,
646  \$ iseed, b, lda )
649  \$ b( iadd, iadd ) = rmagn( kbmagn( jtype ) )
650 *
651  IF( kclass( jtype ).EQ.2 .AND. n.GT.0 ) THEN
652 *
653 * Include rotations
654 *
655 * Generate Q, Z as Householder transformations times
656 * a diagonal matrix.
657 *
658  DO 40 jc = 1, n - 1
659  DO 30 jr = jc, n
660  q( jr, jc ) = clarnd( 3, iseed )
661  z( jr, jc ) = clarnd( 3, iseed )
662  30 CONTINUE
663  CALL clarfg( n+1-jc, q( jc, jc ), q( jc+1, jc ), 1,
664  \$ work( jc ) )
665  work( 2*n+jc ) = sign( one, REAL( Q( JC, JC ) ) )
666  q( jc, jc ) = cone
667  CALL clarfg( n+1-jc, z( jc, jc ), z( jc+1, jc ), 1,
668  \$ work( n+jc ) )
669  work( 3*n+jc ) = sign( one, REAL( Z( JC, JC ) ) )
670  z( jc, jc ) = cone
671  40 CONTINUE
672  ctemp = clarnd( 3, iseed )
673  q( n, n ) = cone
674  work( n ) = czero
675  work( 3*n ) = ctemp / abs( ctemp )
676  ctemp = clarnd( 3, iseed )
677  z( n, n ) = cone
678  work( 2*n ) = czero
679  work( 4*n ) = ctemp / abs( ctemp )
680 *
681 * Apply the diagonal matrices
682 *
683  DO 60 jc = 1, n
684  DO 50 jr = 1, n
685  a( jr, jc ) = work( 2*n+jr )*
686  \$ conjg( work( 3*n+jc ) )*
687  \$ a( jr, jc )
688  b( jr, jc ) = work( 2*n+jr )*
689  \$ conjg( work( 3*n+jc ) )*
690  \$ b( jr, jc )
691  50 CONTINUE
692  60 CONTINUE
693  CALL cunm2r( 'L', 'N', n, n, n-1, q, ldq, work, a,
694  \$ lda, work( 2*n+1 ), ierr )
695  IF( ierr.NE.0 )
696  \$ GO TO 90
697  CALL cunm2r( 'R', 'C', n, n, n-1, z, ldq, work( n+1 ),
698  \$ a, lda, work( 2*n+1 ), ierr )
699  IF( ierr.NE.0 )
700  \$ GO TO 90
701  CALL cunm2r( 'L', 'N', n, n, n-1, q, ldq, work, b,
702  \$ lda, work( 2*n+1 ), ierr )
703  IF( ierr.NE.0 )
704  \$ GO TO 90
705  CALL cunm2r( 'R', 'C', n, n, n-1, z, ldq, work( n+1 ),
706  \$ b, lda, work( 2*n+1 ), ierr )
707  IF( ierr.NE.0 )
708  \$ GO TO 90
709  END IF
710  ELSE
711 *
712 * Random matrices
713 *
714  DO 80 jc = 1, n
715  DO 70 jr = 1, n
716  a( jr, jc ) = rmagn( kamagn( jtype ) )*
717  \$ clarnd( 4, iseed )
718  b( jr, jc ) = rmagn( kbmagn( jtype ) )*
719  \$ clarnd( 4, iseed )
720  70 CONTINUE
721  80 CONTINUE
722  END IF
723 *
724  90 CONTINUE
725 *
726  IF( ierr.NE.0 ) THEN
727  WRITE( nounit, fmt = 9999 )'Generator', ierr, n, jtype,
728  \$ ioldsd
729  info = abs( ierr )
730  RETURN
731  END IF
732 *
733  100 CONTINUE
734 *
735  DO 110 i = 1, 7
736  result( i ) = -one
737  110 CONTINUE
738 *
739 * Call CGGEV to compute eigenvalues and eigenvectors.
740 *
741  CALL clacpy( ' ', n, n, a, lda, s, lda )
742  CALL clacpy( ' ', n, n, b, lda, t, lda )
743  CALL cggev( 'V', 'V', n, s, lda, t, lda, alpha, beta, q,
744  \$ ldq, z, ldq, work, lwork, rwork, ierr )
745  IF( ierr.NE.0 .AND. ierr.NE.n+1 ) THEN
746  result( 1 ) = ulpinv
747  WRITE( nounit, fmt = 9999 )'CGGEV1', ierr, n, jtype,
748  \$ ioldsd
749  info = abs( ierr )
750  GO TO 190
751  END IF
752 *
753 * Do the tests (1) and (2)
754 *
755  CALL cget52( .true., n, a, lda, b, lda, q, ldq, alpha, beta,
756  \$ work, rwork, result( 1 ) )
757  IF( result( 2 ).GT.thresh ) THEN
758  WRITE( nounit, fmt = 9998 )'Left', 'CGGEV1',
759  \$ result( 2 ), n, jtype, ioldsd
760  END IF
761 *
762 * Do the tests (3) and (4)
763 *
764  CALL cget52( .false., n, a, lda, b, lda, z, ldq, alpha,
765  \$ beta, work, rwork, result( 3 ) )
766  IF( result( 4 ).GT.thresh ) THEN
767  WRITE( nounit, fmt = 9998 )'Right', 'CGGEV1',
768  \$ result( 4 ), n, jtype, ioldsd
769  END IF
770 *
771 * Do test (5)
772 *
773  CALL clacpy( ' ', n, n, a, lda, s, lda )
774  CALL clacpy( ' ', n, n, b, lda, t, lda )
775  CALL cggev( 'N', 'N', n, s, lda, t, lda, alpha1, beta1, q,
776  \$ ldq, z, ldq, work, lwork, rwork, ierr )
777  IF( ierr.NE.0 .AND. ierr.NE.n+1 ) THEN
778  result( 1 ) = ulpinv
779  WRITE( nounit, fmt = 9999 )'CGGEV2', ierr, n, jtype,
780  \$ ioldsd
781  info = abs( ierr )
782  GO TO 190
783  END IF
784 *
785  DO 120 j = 1, n
786  IF( alpha( j ).NE.alpha1( j ) .OR. beta( j ).NE.
787  \$ beta1( j ) )result( 5 ) = ulpinv
788  120 CONTINUE
789 *
790 * Do test (6): Compute eigenvalues and left eigenvectors,
791 * and test them
792 *
793  CALL clacpy( ' ', n, n, a, lda, s, lda )
794  CALL clacpy( ' ', n, n, b, lda, t, lda )
795  CALL cggev( 'V', 'N', n, s, lda, t, lda, alpha1, beta1, qe,
796  \$ ldqe, z, ldq, work, lwork, rwork, ierr )
797  IF( ierr.NE.0 .AND. ierr.NE.n+1 ) THEN
798  result( 1 ) = ulpinv
799  WRITE( nounit, fmt = 9999 )'CGGEV3', ierr, n, jtype,
800  \$ ioldsd
801  info = abs( ierr )
802  GO TO 190
803  END IF
804 *
805  DO 130 j = 1, n
806  IF( alpha( j ).NE.alpha1( j ) .OR. beta( j ).NE.
807  \$ beta1( j ) )result( 6 ) = ulpinv
808  130 CONTINUE
809 *
810  DO 150 j = 1, n
811  DO 140 jc = 1, n
812  IF( q( j, jc ).NE.qe( j, jc ) )
813  \$ result( 6 ) = ulpinv
814  140 CONTINUE
815  150 CONTINUE
816 *
817 * Do test (7): Compute eigenvalues and right eigenvectors,
818 * and test them
819 *
820  CALL clacpy( ' ', n, n, a, lda, s, lda )
821  CALL clacpy( ' ', n, n, b, lda, t, lda )
822  CALL cggev( 'N', 'V', n, s, lda, t, lda, alpha1, beta1, q,
823  \$ ldq, qe, ldqe, work, lwork, rwork, ierr )
824  IF( ierr.NE.0 .AND. ierr.NE.n+1 ) THEN
825  result( 1 ) = ulpinv
826  WRITE( nounit, fmt = 9999 )'CGGEV4', ierr, n, jtype,
827  \$ ioldsd
828  info = abs( ierr )
829  GO TO 190
830  END IF
831 *
832  DO 160 j = 1, n
833  IF( alpha( j ).NE.alpha1( j ) .OR. beta( j ).NE.
834  \$ beta1( j ) )result( 7 ) = ulpinv
835  160 CONTINUE
836 *
837  DO 180 j = 1, n
838  DO 170 jc = 1, n
839  IF( z( j, jc ).NE.qe( j, jc ) )
840  \$ result( 7 ) = ulpinv
841  170 CONTINUE
842  180 CONTINUE
843 *
844 * End of Loop -- Check for RESULT(j) > THRESH
845 *
846  190 CONTINUE
847 *
848  ntestt = ntestt + 7
849 *
850 * Print out tests which fail.
851 *
852  DO 200 jr = 1, 7
853  IF( result( jr ).GE.thresh ) THEN
854 *
855 * If this is the first test to fail,
856 * print a header to the data file.
857 *
858  IF( nerrs.EQ.0 ) THEN
859  WRITE( nounit, fmt = 9997 )'CGV'
860 *
861 * Matrix types
862 *
863  WRITE( nounit, fmt = 9996 )
864  WRITE( nounit, fmt = 9995 )
865  WRITE( nounit, fmt = 9994 )'Orthogonal'
866 *
867 * Tests performed
868 *
869  WRITE( nounit, fmt = 9993 )
870 *
871  END IF
872  nerrs = nerrs + 1
873  IF( result( jr ).LT.10000.0 ) THEN
874  WRITE( nounit, fmt = 9992 )n, jtype, ioldsd, jr,
875  \$ result( jr )
876  ELSE
877  WRITE( nounit, fmt = 9991 )n, jtype, ioldsd, jr,
878  \$ result( jr )
879  END IF
880  END IF
881  200 CONTINUE
882 *
883  210 CONTINUE
884  220 CONTINUE
885 *
886 * Summary
887 *
888  CALL alasvm( 'CGV', nounit, nerrs, ntestt, 0 )
889 *
890  work( 1 ) = maxwrk
891 *
892  RETURN
893 *
894  9999 FORMAT( ' CDRGEV: ', a, ' returned INFO=', i6, '.', / 3x, 'N=',
895  \$ i6, ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ), i5, ')' )
896 *
897  9998 FORMAT( ' CDRGEV: ', a, ' Eigenvectors from ', a, ' incorrectly ',
898  \$ 'normalized.', / ' Bits of error=', 0p, g10.3, ',', 3x,
899  \$ 'N=', i4, ', JTYPE=', i3, ', ISEED=(', 3( i4, ',' ), i5,
900  \$ ')' )
901 *
902  9997 FORMAT( / 1x, a3, ' -- Complex Generalized eigenvalue problem ',
903  \$ 'driver' )
904 *
905  9996 FORMAT( ' Matrix types (see CDRGEV for details): ' )
906 *
907  9995 FORMAT( ' Special Matrices:', 23x,
908  \$ '(J''=transposed Jordan block)',
909  \$ / ' 1=(0,0) 2=(I,0) 3=(0,I) 4=(I,I) 5=(J'',J'') ',
910  \$ '6=(diag(J'',I), diag(I,J''))', / ' Diagonal Matrices: ( ',
911  \$ 'D=diag(0,1,2,...) )', / ' 7=(D,I) 9=(large*D, small*I',
912  \$ ') 11=(large*I, small*D) 13=(large*D, large*I)', /
913  \$ ' 8=(I,D) 10=(small*D, large*I) 12=(small*I, large*D) ',
914  \$ ' 14=(small*D, small*I)', / ' 15=(D, reversed D)' )
915  9994 FORMAT( ' Matrices Rotated by Random ', a, ' Matrices U, V:',
916  \$ / ' 16=Transposed Jordan Blocks 19=geometric ',
917  \$ 'alpha, beta=0,1', / ' 17=arithm. alpha&beta ',
918  \$ ' 20=arithmetic alpha, beta=0,1', / ' 18=clustered ',
919  \$ 'alpha, beta=0,1 21=random alpha, beta=0,1',
920  \$ / ' Large & Small Matrices:', / ' 22=(large, small) ',
921  \$ '23=(small,large) 24=(small,small) 25=(large,large)',
922  \$ / ' 26=random O(1) matrices.' )
923 *
924  9993 FORMAT( / ' Tests performed: ',
925  \$ / ' 1 = max | ( b A - a B )''*l | / const.,',
926  \$ / ' 2 = | |VR(i)| - 1 | / ulp,',
927  \$ / ' 3 = max | ( b A - a B )*r | / const.',
928  \$ / ' 4 = | |VL(i)| - 1 | / ulp,',
929  \$ / ' 5 = 0 if W same no matter if r or l computed,',
930  \$ / ' 6 = 0 if l same no matter if l computed,',
931  \$ / ' 7 = 0 if r same no matter if r computed,', / 1x )
932  9992 FORMAT( ' Matrix order=', i5, ', type=', i2, ', seed=',
933  \$ 4( i4, ',' ), ' result ', i2, ' is', 0p, f8.2 )
934  9991 FORMAT( ' Matrix order=', i5, ', type=', i2, ', seed=',
935  \$ 4( i4, ',' ), ' result ', i2, ' is', 1p, e10.3 )
936 *
937 * End of CDRGEV
938 *
subroutine alasvm(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASVM
Definition: alasvm.f:75
subroutine cunm2r(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, INFO)
CUNM2R multiplies a general matrix by the unitary matrix from a QR factorization determined by cgeqrf...
Definition: cunm2r.f:161
complex function clarnd(IDIST, ISEED)
CLARND
Definition: clarnd.f:77
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine claset(UPLO, M, N, ALPHA, BETA, A, LDA)
CLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values...
Definition: claset.f:108
subroutine cget52(LEFT, N, A, LDA, B, LDB, E, LDE, ALPHA, BETA, WORK, RWORK, RESULT)
CGET52
Definition: cget52.f:163
subroutine clatm4(ITYPE, N, NZ1, NZ2, RSIGN, AMAGN, RCOND, TRIANG, IDIST, ISEED, A, LDA)
CLATM4
Definition: clatm4.f:173
subroutine clacpy(UPLO, M, N, A, LDA, B, LDB)
CLACPY copies all or part of one two-dimensional array to another.
Definition: clacpy.f:105
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
Definition: tstiee.f:83
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
subroutine cggev(JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA, VL, LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO)
CGGEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices ...
Definition: cggev.f:219
subroutine clarfg(N, ALPHA, X, INCX, TAU)
CLARFG generates an elementary reflector (Householder matrix).
Definition: clarfg.f:108

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