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zdrvgg.f File Reference

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Functions/Subroutines

subroutine zdrvgg (NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH, THRSHN, NOUNIT, A, LDA, B, S, T, S2, T2, Q, LDQ, Z, ALPHA1, BETA1, ALPHA2, BETA2, VL, VR, WORK, LWORK, RWORK, RESULT, INFO)
 ZDRVGG More...
 

Function/Subroutine Documentation

subroutine zdrvgg ( integer  NSIZES,
integer, dimension( * )  NN,
integer  NTYPES,
logical, dimension( * )  DOTYPE,
integer, dimension( 4 )  ISEED,
double precision  THRESH,
double precision  THRSHN,
integer  NOUNIT,
complex*16, dimension( lda, * )  A,
integer  LDA,
complex*16, dimension( lda, * )  B,
complex*16, dimension( lda, * )  S,
complex*16, dimension( lda, * )  T,
complex*16, dimension( lda, * )  S2,
complex*16, dimension( lda, * )  T2,
complex*16, dimension( ldq, * )  Q,
integer  LDQ,
complex*16, dimension( ldq, * )  Z,
complex*16, dimension( * )  ALPHA1,
complex*16, dimension( * )  BETA1,
complex*16, dimension( * )  ALPHA2,
complex*16, dimension( * )  BETA2,
complex*16, dimension( ldq, * )  VL,
complex*16, dimension( ldq, * )  VR,
complex*16, dimension( * )  WORK,
integer  LWORK,
double precision, dimension( * )  RWORK,
double precision, dimension( * )  RESULT,
integer  INFO 
)

ZDRVGG

Purpose:
 ZDRVGG  checks the nonsymmetric generalized eigenvalue driver
 routines.
                               T          T        T
 ZGEGS factors A and B as Q S Z  and Q T Z , where   means
 transpose, T is upper triangular, S is in generalized Schur form
 (upper triangular), and Q and Z are unitary.  It also
 computes the generalized eigenvalues (alpha(1),beta(1)), ...,
 (alpha(n),beta(n)), where alpha(j)=S(j,j) and beta(j)=T(j,j) --
 thus, w(j) = alpha(j)/beta(j) is a root of the generalized
 eigenvalue problem

     det( A - w(j) B ) = 0

 and m(j) = beta(j)/alpha(j) is a root of the essentially equivalent
 problem

     det( m(j) A - B ) = 0

 ZGEGV computes the generalized eigenvalues (alpha(1),beta(1)), ...,
 (alpha(n),beta(n)), the matrix L whose columns contain the
 generalized left eigenvectors l, and the matrix R whose columns
 contain the generalized right eigenvectors r for the pair (A,B).

 When ZDRVGG 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 and compared with the threshhold THRESH:

 Results from ZGEGS:

                  H
 (1)   | A - Q S Z  | / ( |A| n ulp )

                  H
 (2)   | B - Q T Z  | / ( |B| n ulp )

               H
 (3)   | I - QQ  | / ( n ulp )

               H
 (4)   | I - ZZ  | / ( n ulp )

 (5)   maximum over j of D(j)  where:

                     |alpha(j) - S(j,j)|        |beta(j) - T(j,j)|
           D(j) = ------------------------ + -----------------------
                  max(|alpha(j)|,|S(j,j)|)   max(|beta(j)|,|T(j,j)|)

 Results from ZGEGV:

 (6)   max over all left eigenvalue/-vector pairs (beta/alpha,l) of

    | l**H * (beta A - alpha B) | / ( ulp max( |beta A|, |alpha B| ) )

       where l**H is the conjugate tranpose of l.

 (7)   max over all right eigenvalue/-vector pairs (beta/alpha,r) of

       | (beta A - alpha B) r | / ( ulp max( |beta A|, |alpha B| ) )

 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 unitary 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,
          ZDRVGG 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, ZDRVGG
          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 ZDRVGG 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]THRSHN
          THRSHN is DOUBLE PRECISION
          Threshhold for reporting eigenvector normalization error.
          If the normalization of any eigenvector differs from 1 by
          more than THRSHN*ulp, then a special error message will be
          printed.  (This is handled separately from the other tests,
          since only a compiler or programming error should cause an
          error message, at least if THRSHN is at least 5--10.)
[in]NOUNIT
          NOUNIT is INTEGER
          The FORTRAN unit number for printing out error messages
          (e.g., if a routine returns IINFO not equal to 0.)
[in,out]A
          A is COMPLEX*16 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, T, S2, and T2.
          It must be at least 1 and at least max( NN ).
[in,out]B
          B is COMPLEX*16 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*16 array, dimension (LDA, max(NN))
          The upper triangular matrix computed from A by ZGEGS.
[out]T
          T is COMPLEX*16 array, dimension (LDA, max(NN))
          The upper triangular matrix computed from B by ZGEGS.
[out]S2
          S2 is COMPLEX*16 array, dimension (LDA, max(NN))
          The matrix computed from A by ZGEGV.  This will be the
          Schur (upper triangular) form of some matrix related to A,
          but will not, in general, be the same as S.
[out]T2
          T2 is COMPLEX*16 array, dimension (LDA, max(NN))
          The matrix computed from B by ZGEGV.  This will be the
          Schur form of some matrix related to B, but will not, in
          general, be the same as T.
[out]Q
          Q is COMPLEX*16 array, dimension (LDQ, max(NN))
          The (left) unitary matrix computed by ZGEGS.
[in]LDQ
          LDQ is INTEGER
          The leading dimension of Q, Z, VL, and VR.  It must
          be at least 1 and at least max( NN ).
[out]Z
          Z is COMPLEX*16 array, dimension (LDQ, max(NN))
          The (right) unitary matrix computed by ZGEGS.
[out]ALPHA1
          ALPHA1 is COMPLEX*16 array, dimension (max(NN))
[out]BETA1
          BETA1 is COMPLEX*16 array, dimension (max(NN))

          The generalized eigenvalues of (A,B) computed by ZGEGS.
          ALPHA1(k) / BETA1(k)  is the k-th generalized eigenvalue of
          the matrices in A and B.
[out]ALPHA2
          ALPHA2 is COMPLEX*16 array, dimension (max(NN))
[out]BETA2
          BETA2 is COMPLEX*16 array, dimension (max(NN))

          The generalized eigenvalues of (A,B) computed by ZGEGV.
          ALPHA2(k) / BETA2(k)  is the k-th generalized eigenvalue of
          the matrices in A and B.
[out]VL
          VL is COMPLEX*16 array, dimension (LDQ, max(NN))
          The (lower triangular) left eigenvector matrix for the
          matrices in A and B.
[out]VR
          VR is COMPLEX*16 array, dimension (LDQ, max(NN))
          The (upper triangular) right eigenvector matrix for the
          matrices in A and B.
[out]WORK
          WORK is COMPLEX*16 array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          The number of entries in WORK.  This must be at least
          MAX( 2*N, N*(NB+1), (k+1)*(2*k+N+1) ), where "k" is the
          sum of the blocksize and number-of-shifts for ZHGEQZ, and
          NB is the greatest of the blocksizes for ZGEQRF, ZUNMQR,
          and ZUNGQR.  (The blocksizes and the number-of-shifts are
          retrieved through calls to ILAENV.)
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (8*N)
[out]RESULT
          RESULT is DOUBLE PRECISION array, dimension (7)
          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.
Date
November 2011

Definition at line 420 of file zdrvgg.f.

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