LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ sdrgev3()

subroutine sdrgev3 ( integer  NSIZES,
integer, dimension( * )  NN,
integer  NTYPES,
logical, dimension( * )  DOTYPE,
integer, dimension( 4 )  ISEED,
real  THRESH,
integer  NOUNIT,
real, dimension( lda, * )  A,
integer  LDA,
real, dimension( lda, * )  B,
real, dimension( lda, * )  S,
real, dimension( lda, * )  T,
real, dimension( ldq, * )  Q,
integer  LDQ,
real, dimension( ldq, * )  Z,
real, dimension( ldqe, * )  QE,
integer  LDQE,
real, dimension( * )  ALPHAR,
real, dimension( * )  ALPHAI,
real, dimension( * )  BETA,
real, dimension( * )  ALPHR1,
real, dimension( * )  ALPHI1,
real, dimension( * )  BETA1,
real, dimension( * )  WORK,
integer  LWORK,
real, dimension( * )  RESULT,
integer  INFO 
)

SDRGEV3

Purpose:
 SDRGEV3 checks the nonsymmetric generalized eigenvalue problem driver
 routine SGGEV3.

 SGGEV3 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 SDRGEV3 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 SGGEV3:

 (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,
          SDRGEV3 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, SDRGEV3
          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 SDRGEV3 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 REAL 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 REAL 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 REAL array,
                                 dimension (LDA, max(NN))
          The Schur form matrix computed from A by SGGEV3.  On exit, S
          contains the Schur form matrix corresponding to the matrix
          in A.
[out]T
          T is REAL array,
                                 dimension (LDA, max(NN))
          The upper triangular matrix computed from B by SGGEV3.
[out]Q
          Q is REAL array,
                                 dimension (LDQ, max(NN))
          The (left) eigenvectors matrix computed by SGGEV3.
[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 REAL array, dimension( LDQ, max(NN) )
          The (right) orthogonal matrix computed by SGGEV3.
[out]QE
          QE is REAL 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 REAL array, dimension (max(NN))
[out]ALPHAI
          ALPHAI is REAL array, dimension (max(NN))
[out]BETA
          BETA is REAL array, dimension (max(NN))
 \verbatim
          The generalized eigenvalues of (A,B) computed by SGGEV3.
          ( ALPHAR(k)+ALPHAI(k)*i ) / BETA(k) is the k-th
          generalized eigenvalue of A and B.
[out]ALPHR1
          ALPHR1 is REAL array, dimension (max(NN))
[out]ALPHI1
          ALPHI1 is REAL array, dimension (max(NN))
[out]BETA1
          BETA1 is REAL array, dimension (max(NN))

          Like ALPHAR, ALPHAI, BETA, these arrays contain the
          eigenvalues of A and B, but those computed when SGGEV3 only
          computes a partial eigendecomposition, i.e. not the
          eigenvalues and left and right eigenvectors.
[out]WORK
          WORK is REAL 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 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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 404 of file sdrgev3.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  REAL THRESH
417 * ..
418 * .. Array Arguments ..
419  LOGICAL DOTYPE( * )
420  INTEGER ISEED( 4 ), NN( * )
421  REAL A( LDA, * ), ALPHAI( * ), ALPHI1( * ),
422  $ ALPHAR( * ), 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  REAL ZERO, ONE
432  parameter( zero = 0.0e+0, one = 1.0e+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  REAL 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  REAL RMAGN( 0: 3 )
451 * ..
452 * .. External Functions ..
453  INTEGER ILAENV
454  REAL SLAMCH, SLARND
455  EXTERNAL ilaenv, slamch, slarnd
456 * ..
457 * .. External Subroutines ..
458  EXTERNAL alasvm, sget52, sggev3, slabad, slacpy, slarfg,
460 * ..
461 * .. Intrinsic Functions ..
462  INTRINSIC abs, max, min, real, 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, 'SGEQRF', ' ', 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( 'SDRGEV3', -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 = slamch( 'Safe minimum' )
546  ulp = slamch( 'Epsilon' )*slamch( 'Base' )
547  safmin = safmin / ulp
548  safmax = one / safmin
549  CALL slabad( safmin, safmax )
550  ulpinv = one / ulp
551 *
552 * The values RMAGN(2:3) depend on N, see below.
553 *
554  rmagn( 0 ) = zero
555  rmagn( 1 ) = one
556 *
557 * Loop over sizes, types
558 *
559  ntestt = 0
560  nerrs = 0
561  nmats = 0
562 *
563  DO 220 jsize = 1, nsizes
564  n = nn( jsize )
565  n1 = max( 1, n )
566  rmagn( 2 ) = safmax*ulp / real( n1 )
567  rmagn( 3 ) = safmin*ulpinv*n1
568 *
569  IF( nsizes.NE.1 ) THEN
570  mtypes = min( maxtyp, ntypes )
571  ELSE
572  mtypes = min( maxtyp+1, ntypes )
573  END IF
574 *
575  DO 210 jtype = 1, mtypes
576  IF( .NOT.dotype( jtype ) )
577  $ GO TO 210
578  nmats = nmats + 1
579 *
580 * Save ISEED in case of an error.
581 *
582  DO 20 j = 1, 4
583  ioldsd( j ) = iseed( j )
584  20 CONTINUE
585 *
586 * Generate test matrices A and B
587 *
588 * Description of control parameters:
589 *
590 * KCLASS: =1 means w/o rotation, =2 means w/ rotation,
591 * =3 means random.
592 * KATYPE: the "type" to be passed to SLATM4 for computing A.
593 * KAZERO: the pattern of zeros on the diagonal for A:
594 * =1: ( xxx ), =2: (0, xxx ) =3: ( 0, 0, xxx, 0 ),
595 * =4: ( 0, xxx, 0, 0 ), =5: ( 0, 0, 1, xxx, 0 ),
596 * =6: ( 0, 1, 0, xxx, 0 ). (xxx means a string of
597 * non-zero entries.)
598 * KAMAGN: the magnitude of the matrix: =0: zero, =1: O(1),
599 * =2: large, =3: small.
600 * IASIGN: 1 if the diagonal elements of A are to be
601 * multiplied by a random magnitude 1 number, =2 if
602 * randomly chosen diagonal blocks are to be rotated
603 * to form 2x2 blocks.
604 * KBTYPE, KBZERO, KBMAGN, IBSIGN: the same, but for B.
605 * KTRIAN: =0: don't fill in the upper triangle, =1: do.
606 * KZ1, KZ2, KADD: used to implement KAZERO and KBZERO.
607 * RMAGN: used to implement KAMAGN and KBMAGN.
608 *
609  IF( mtypes.GT.maxtyp )
610  $ GO TO 100
611  ierr = 0
612  IF( kclass( jtype ).LT.3 ) THEN
613 *
614 * Generate A (w/o rotation)
615 *
616  IF( abs( katype( jtype ) ).EQ.3 ) THEN
617  in = 2*( ( n-1 ) / 2 ) + 1
618  IF( in.NE.n )
619  $ CALL slaset( 'Full', n, n, zero, zero, a, lda )
620  ELSE
621  in = n
622  END IF
623  CALL slatm4( katype( jtype ), in, kz1( kazero( jtype ) ),
624  $ kz2( kazero( jtype ) ), iasign( jtype ),
625  $ rmagn( kamagn( jtype ) ), ulp,
626  $ rmagn( ktrian( jtype )*kamagn( jtype ) ), 2,
627  $ iseed, a, lda )
628  iadd = kadd( kazero( jtype ) )
629  IF( iadd.GT.0 .AND. iadd.LE.n )
630  $ a( iadd, iadd ) = one
631 *
632 * Generate B (w/o rotation)
633 *
634  IF( abs( kbtype( jtype ) ).EQ.3 ) THEN
635  in = 2*( ( n-1 ) / 2 ) + 1
636  IF( in.NE.n )
637  $ CALL slaset( 'Full', n, n, zero, zero, b, lda )
638  ELSE
639  in = n
640  END IF
641  CALL slatm4( kbtype( jtype ), in, kz1( kbzero( jtype ) ),
642  $ kz2( kbzero( jtype ) ), ibsign( jtype ),
643  $ rmagn( kbmagn( jtype ) ), one,
644  $ rmagn( ktrian( jtype )*kbmagn( jtype ) ), 2,
645  $ iseed, b, lda )
646  iadd = kadd( kbzero( jtype ) )
647  IF( iadd.NE.0 .AND. iadd.LE.n )
648  $ b( iadd, iadd ) = one
649 *
650  IF( kclass( jtype ).EQ.2 .AND. n.GT.0 ) THEN
651 *
652 * Include rotations
653 *
654 * Generate Q, Z as Householder transformations times
655 * a diagonal matrix.
656 *
657  DO 40 jc = 1, n - 1
658  DO 30 jr = jc, n
659  q( jr, jc ) = slarnd( 3, iseed )
660  z( jr, jc ) = slarnd( 3, iseed )
661  30 CONTINUE
662  CALL slarfg( n+1-jc, q( jc, jc ), q( jc+1, jc ), 1,
663  $ work( jc ) )
664  work( 2*n+jc ) = sign( one, q( jc, jc ) )
665  q( jc, jc ) = one
666  CALL slarfg( n+1-jc, z( jc, jc ), z( jc+1, jc ), 1,
667  $ work( n+jc ) )
668  work( 3*n+jc ) = sign( one, z( jc, jc ) )
669  z( jc, jc ) = one
670  40 CONTINUE
671  q( n, n ) = one
672  work( n ) = zero
673  work( 3*n ) = sign( one, slarnd( 2, iseed ) )
674  z( n, n ) = one
675  work( 2*n ) = zero
676  work( 4*n ) = sign( one, slarnd( 2, iseed ) )
677 *
678 * Apply the diagonal matrices
679 *
680  DO 60 jc = 1, n
681  DO 50 jr = 1, n
682  a( jr, jc ) = work( 2*n+jr )*work( 3*n+jc )*
683  $ a( jr, jc )
684  b( jr, jc ) = work( 2*n+jr )*work( 3*n+jc )*
685  $ b( jr, jc )
686  50 CONTINUE
687  60 CONTINUE
688  CALL sorm2r( 'L', 'N', n, n, n-1, q, ldq, work, a,
689  $ lda, work( 2*n+1 ), ierr )
690  IF( ierr.NE.0 )
691  $ GO TO 90
692  CALL sorm2r( 'R', 'T', n, n, n-1, z, ldq, work( n+1 ),
693  $ a, lda, work( 2*n+1 ), ierr )
694  IF( ierr.NE.0 )
695  $ GO TO 90
696  CALL sorm2r( 'L', 'N', n, n, n-1, q, ldq, work, b,
697  $ lda, work( 2*n+1 ), ierr )
698  IF( ierr.NE.0 )
699  $ GO TO 90
700  CALL sorm2r( 'R', 'T', n, n, n-1, z, ldq, work( n+1 ),
701  $ b, lda, work( 2*n+1 ), ierr )
702  IF( ierr.NE.0 )
703  $ GO TO 90
704  END IF
705  ELSE
706 *
707 * Random matrices
708 *
709  DO 80 jc = 1, n
710  DO 70 jr = 1, n
711  a( jr, jc ) = rmagn( kamagn( jtype ) )*
712  $ slarnd( 2, iseed )
713  b( jr, jc ) = rmagn( kbmagn( jtype ) )*
714  $ slarnd( 2, iseed )
715  70 CONTINUE
716  80 CONTINUE
717  END IF
718 *
719  90 CONTINUE
720 *
721  IF( ierr.NE.0 ) THEN
722  WRITE( nounit, fmt = 9999 )'Generator', ierr, n, jtype,
723  $ ioldsd
724  info = abs( ierr )
725  RETURN
726  END IF
727 *
728  100 CONTINUE
729 *
730  DO 110 i = 1, 7
731  result( i ) = -one
732  110 CONTINUE
733 *
734 * Call XLAENV to set the parameters used in SLAQZ0
735 *
736  CALL xlaenv( 12, 10 )
737  CALL xlaenv( 13, 12 )
738  CALL xlaenv( 14, 13 )
739  CALL xlaenv( 15, 2 )
740  CALL xlaenv( 17, 10 )
741 *
742 * Call SGGEV3 to compute eigenvalues and eigenvectors.
743 *
744  CALL slacpy( ' ', n, n, a, lda, s, lda )
745  CALL slacpy( ' ', n, n, b, lda, t, lda )
746  CALL sggev3( 'V', 'V', n, s, lda, t, lda, alphar, alphai,
747  $ beta, q, ldq, z, ldq, work, lwork, ierr )
748  IF( ierr.NE.0 .AND. ierr.NE.n+1 ) THEN
749  result( 1 ) = ulpinv
750  WRITE( nounit, fmt = 9999 )'SGGEV31', ierr, n, jtype,
751  $ ioldsd
752  info = abs( ierr )
753  GO TO 190
754  END IF
755 *
756 * Do the tests (1) and (2)
757 *
758  CALL sget52( .true., n, a, lda, b, lda, q, ldq, alphar,
759  $ alphai, beta, work, result( 1 ) )
760  IF( result( 2 ).GT.thresh ) THEN
761  WRITE( nounit, fmt = 9998 )'Left', 'SGGEV31',
762  $ result( 2 ), n, jtype, ioldsd
763  END IF
764 *
765 * Do the tests (3) and (4)
766 *
767  CALL sget52( .false., n, a, lda, b, lda, z, ldq, alphar,
768  $ alphai, beta, work, result( 3 ) )
769  IF( result( 4 ).GT.thresh ) THEN
770  WRITE( nounit, fmt = 9998 )'Right', 'SGGEV31',
771  $ result( 4 ), n, jtype, ioldsd
772  END IF
773 *
774 * Do the test (5)
775 *
776  CALL slacpy( ' ', n, n, a, lda, s, lda )
777  CALL slacpy( ' ', n, n, b, lda, t, lda )
778  CALL sggev3( 'N', 'N', n, s, lda, t, lda, alphr1, alphi1,
779  $ beta1, q, ldq, z, ldq, work, lwork, ierr )
780  IF( ierr.NE.0 .AND. ierr.NE.n+1 ) THEN
781  result( 1 ) = ulpinv
782  WRITE( nounit, fmt = 9999 )'SGGEV32', ierr, n, jtype,
783  $ ioldsd
784  info = abs( ierr )
785  GO TO 190
786  END IF
787 *
788  DO 120 j = 1, n
789  IF( alphar( j ).NE.alphr1( j ) .OR.
790  $ beta( j ).NE. beta1( j ) ) THEN
791  result( 5 ) = ulpinv
792  END IF
793  120 CONTINUE
794 *
795 * Do the test (6): Compute eigenvalues and left eigenvectors,
796 * and test them
797 *
798  CALL slacpy( ' ', n, n, a, lda, s, lda )
799  CALL slacpy( ' ', n, n, b, lda, t, lda )
800  CALL sggev3( 'V', 'N', n, s, lda, t, lda, alphr1, alphi1,
801  $ beta1, qe, ldqe, z, ldq, work, lwork, ierr )
802  IF( ierr.NE.0 .AND. ierr.NE.n+1 ) THEN
803  result( 1 ) = ulpinv
804  WRITE( nounit, fmt = 9999 )'SGGEV33', ierr, n, jtype,
805  $ ioldsd
806  info = abs( ierr )
807  GO TO 190
808  END IF
809 *
810  DO 130 j = 1, n
811  IF( alphar( j ).NE.alphr1( j ) .OR. alphai( j ).NE.
812  $ alphi1( j ) .OR. beta( j ).NE.beta1( j ) )
813  $ result( 6 ) = ulpinv
814  130 CONTINUE
815 *
816  DO 150 j = 1, n
817  DO 140 jc = 1, n
818  IF( q( j, jc ).NE.qe( j, jc ) )
819  $ result( 6 ) = ulpinv
820  140 CONTINUE
821  150 CONTINUE
822 *
823 * DO the test (7): Compute eigenvalues and right eigenvectors,
824 * and test them
825 *
826  CALL slacpy( ' ', n, n, a, lda, s, lda )
827  CALL slacpy( ' ', n, n, b, lda, t, lda )
828  CALL sggev3( 'N', 'V', n, s, lda, t, lda, alphr1, alphi1,
829  $ beta1, q, ldq, qe, ldqe, work, lwork, ierr )
830  IF( ierr.NE.0 .AND. ierr.NE.n+1 ) THEN
831  result( 1 ) = ulpinv
832  WRITE( nounit, fmt = 9999 )'SGGEV34', ierr, n, jtype,
833  $ ioldsd
834  info = abs( ierr )
835  GO TO 190
836  END IF
837 *
838  DO 160 j = 1, n
839  IF( alphar( j ).NE.alphr1( j ) .OR. alphai( j ).NE.
840  $ alphi1( j ) .OR. beta( j ).NE.beta1( j ) )
841  $ result( 7 ) = ulpinv
842  160 CONTINUE
843 *
844  DO 180 j = 1, n
845  DO 170 jc = 1, n
846  IF( z( j, jc ).NE.qe( j, jc ) )
847  $ result( 7 ) = ulpinv
848  170 CONTINUE
849  180 CONTINUE
850 *
851 * End of Loop -- Check for RESULT(j) > THRESH
852 *
853  190 CONTINUE
854 *
855  ntestt = ntestt + 7
856 *
857 * Print out tests which fail.
858 *
859  DO 200 jr = 1, 7
860  IF( result( jr ).GE.thresh ) THEN
861 *
862 * If this is the first test to fail,
863 * print a header to the data file.
864 *
865  IF( nerrs.EQ.0 ) THEN
866  WRITE( nounit, fmt = 9997 )'SGV'
867 *
868 * Matrix types
869 *
870  WRITE( nounit, fmt = 9996 )
871  WRITE( nounit, fmt = 9995 )
872  WRITE( nounit, fmt = 9994 )'Orthogonal'
873 *
874 * Tests performed
875 *
876  WRITE( nounit, fmt = 9993 )
877 *
878  END IF
879  nerrs = nerrs + 1
880  IF( result( jr ).LT.10000.0 ) THEN
881  WRITE( nounit, fmt = 9992 )n, jtype, ioldsd, jr,
882  $ result( jr )
883  ELSE
884  WRITE( nounit, fmt = 9991 )n, jtype, ioldsd, jr,
885  $ result( jr )
886  END IF
887  END IF
888  200 CONTINUE
889 *
890  210 CONTINUE
891  220 CONTINUE
892 *
893 * Summary
894 *
895  CALL alasvm( 'SGV', nounit, nerrs, ntestt, 0 )
896 *
897  work( 1 ) = maxwrk
898 *
899  RETURN
900 *
901  9999 FORMAT( ' SDRGEV3: ', a, ' returned INFO=', i6, '.', / 3x, 'N=',
902  $ i6, ', JTYPE=', i6, ', ISEED=(', 4( i4, ',' ), i5, ')' )
903 *
904  9998 FORMAT( ' SDRGEV3: ', a, ' Eigenvectors from ', a,
905  $ ' incorrectly normalized.', / ' Bits of error=', 0p, g10.3,
906  $ ',', 3x, 'N=', i4, ', JTYPE=', i3, ', ISEED=(',
907  $ 4( i4, ',' ), i5, ')' )
908 *
909  9997 FORMAT( / 1x, a3, ' -- Real Generalized eigenvalue problem driver'
910  $ )
911 *
912  9996 FORMAT( ' Matrix types (see SDRGEV3 for details): ' )
913 *
914  9995 FORMAT( ' Special Matrices:', 23x,
915  $ '(J''=transposed Jordan block)',
916  $ / ' 1=(0,0) 2=(I,0) 3=(0,I) 4=(I,I) 5=(J'',J'') ',
917  $ '6=(diag(J'',I), diag(I,J''))', / ' Diagonal Matrices: ( ',
918  $ 'D=diag(0,1,2,...) )', / ' 7=(D,I) 9=(large*D, small*I',
919  $ ') 11=(large*I, small*D) 13=(large*D, large*I)', /
920  $ ' 8=(I,D) 10=(small*D, large*I) 12=(small*I, large*D) ',
921  $ ' 14=(small*D, small*I)', / ' 15=(D, reversed D)' )
922  9994 FORMAT( ' Matrices Rotated by Random ', a, ' Matrices U, V:',
923  $ / ' 16=Transposed Jordan Blocks 19=geometric ',
924  $ 'alpha, beta=0,1', / ' 17=arithm. alpha&beta ',
925  $ ' 20=arithmetic alpha, beta=0,1', / ' 18=clustered ',
926  $ 'alpha, beta=0,1 21=random alpha, beta=0,1',
927  $ / ' Large & Small Matrices:', / ' 22=(large, small) ',
928  $ '23=(small,large) 24=(small,small) 25=(large,large)',
929  $ / ' 26=random O(1) matrices.' )
930 *
931  9993 FORMAT( / ' Tests performed: ',
932  $ / ' 1 = max | ( b A - a B )''*l | / const.,',
933  $ / ' 2 = | |VR(i)| - 1 | / ulp,',
934  $ / ' 3 = max | ( b A - a B )*r | / const.',
935  $ / ' 4 = | |VL(i)| - 1 | / ulp,',
936  $ / ' 5 = 0 if W same no matter if r or l computed,',
937  $ / ' 6 = 0 if l same no matter if l computed,',
938  $ / ' 7 = 0 if r same no matter if r computed,', / 1x )
939  9992 FORMAT( ' Matrix order=', i5, ', type=', i2, ', seed=',
940  $ 4( i4, ',' ), ' result ', i2, ' is', 0p, f8.2 )
941  9991 FORMAT( ' Matrix order=', i5, ', type=', i2, ', seed=',
942  $ 4( i4, ',' ), ' result ', i2, ' is', 1p, e10.3 )
943 *
944 * End of SDRGEV3
945 *
subroutine slabad(SMALL, LARGE)
SLABAD
Definition: slabad.f:74
subroutine slaset(UPLO, M, N, ALPHA, BETA, A, LDA)
SLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: slaset.f:110
subroutine slacpy(UPLO, M, N, A, LDA, B, LDB)
SLACPY copies all or part of one two-dimensional array to another.
Definition: slacpy.f:103
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
ILAENV
Definition: ilaenv.f:162
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine alasvm(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASVM
Definition: alasvm.f:73
subroutine xlaenv(ISPEC, NVALUE)
XLAENV
Definition: xlaenv.f:81
real function slarnd(IDIST, ISEED)
SLARND
Definition: slarnd.f:73
subroutine sggev3(JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, VL, LDVL, VR, LDVR, WORK, LWORK, INFO)
SGGEV3 computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices (...
Definition: sggev3.f:226
subroutine slarfg(N, ALPHA, X, INCX, TAU)
SLARFG generates an elementary reflector (Householder matrix).
Definition: slarfg.f:106
subroutine sorm2r(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, INFO)
SORM2R multiplies a general matrix by the orthogonal matrix from a QR factorization determined by sge...
Definition: sorm2r.f:159
subroutine sget52(LEFT, N, A, LDA, B, LDB, E, LDE, ALPHAR, ALPHAI, BETA, WORK, RESULT)
SGET52
Definition: sget52.f:199
subroutine slatm4(ITYPE, N, NZ1, NZ2, ISIGN, AMAGN, RCOND, TRIANG, IDIST, ISEED, A, LDA)
SLATM4
Definition: slatm4.f:175
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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