1032 lines
37 KiB
Fortran
1032 lines
37 KiB
Fortran
*> \brief \b DDRVGG
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE DDRVGG( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
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* THRSHN, NOUNIT, A, LDA, B, S, T, S2, T2, Q,
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* LDQ, Z, ALPHR1, ALPHI1, BETA1, ALPHR2, ALPHI2,
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* BETA2, VL, VR, WORK, LWORK, RESULT, INFO )
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*
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* .. Scalar Arguments ..
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* INTEGER INFO, LDA, LDQ, LWORK, NOUNIT, NSIZES, NTYPES
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* DOUBLE PRECISION THRESH, THRSHN
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* ..
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* .. Array Arguments ..
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* LOGICAL DOTYPE( * )
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* INTEGER ISEED( 4 ), NN( * )
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* DOUBLE PRECISION A( LDA, * ), ALPHI1( * ), ALPHI2( * ),
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* $ ALPHR1( * ), ALPHR2( * ), B( LDA, * ),
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* $ BETA1( * ), BETA2( * ), Q( LDQ, * ),
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* $ RESULT( * ), S( LDA, * ), S2( LDA, * ),
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* $ T( LDA, * ), T2( LDA, * ), VL( LDQ, * ),
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* $ VR( LDQ, * ), WORK( * ), Z( LDQ, * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> DDRVGG checks the nonsymmetric generalized eigenvalue driver
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*> routines.
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*> T T T
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*> DGEGS factors A and B as Q S Z and Q T Z , where means
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*> transpose, T is upper triangular, S is in generalized Schur form
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*> (block upper triangular, with 1x1 and 2x2 blocks on the diagonal,
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*> the 2x2 blocks corresponding to complex conjugate pairs of
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*> generalized eigenvalues), and Q and Z are orthogonal. It also
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*> computes the generalized eigenvalues (alpha(1),beta(1)), ...,
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*> (alpha(n),beta(n)), where alpha(j)=S(j,j) and beta(j)=P(j,j) --
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*> thus, w(j) = alpha(j)/beta(j) is a root of the generalized
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*> eigenvalue problem
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*>
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*> det( A - w(j) B ) = 0
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*>
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*> and m(j) = beta(j)/alpha(j) is a root of the essentially equivalent
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*> problem
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*>
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*> det( m(j) A - B ) = 0
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*>
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*> DGEGV computes the generalized eigenvalues (alpha(1),beta(1)), ...,
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*> (alpha(n),beta(n)), the matrix L whose columns contain the
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*> generalized left eigenvectors l, and the matrix R whose columns
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*> contain the generalized right eigenvectors r for the pair (A,B).
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*>
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*> When DDRVGG is called, a number of matrix "sizes" ("n's") and a
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*> number of matrix "types" are specified. For each size ("n")
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*> and each type of matrix, one matrix will be generated and used
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*> to test the nonsymmetric eigenroutines. For each matrix, 7
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*> tests will be performed and compared with the threshhold THRESH:
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*>
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*> Results from DGEGS:
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*>
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*> T
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*> (1) | A - Q S Z | / ( |A| n ulp )
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*>
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*> T
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*> (2) | B - Q T Z | / ( |B| n ulp )
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*>
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*> T
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*> (3) | I - QQ | / ( n ulp )
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*>
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*> T
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*> (4) | I - ZZ | / ( n ulp )
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*>
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*> (5) maximum over j of D(j) where:
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*>
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*> if alpha(j) is real:
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*> |alpha(j) - S(j,j)| |beta(j) - T(j,j)|
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*> D(j) = ------------------------ + -----------------------
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*> max(|alpha(j)|,|S(j,j)|) max(|beta(j)|,|T(j,j)|)
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*>
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*> if alpha(j) is complex:
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*> | det( s S - w T ) |
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*> D(j) = ---------------------------------------------------
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*> ulp max( s norm(S), |w| norm(T) )*norm( s S - w T )
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*>
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*> and S and T are here the 2 x 2 diagonal blocks of S and T
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*> corresponding to the j-th eigenvalue.
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*>
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*> Results from DGEGV:
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*>
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*> (6) max over all left eigenvalue/-vector pairs (beta/alpha,l) of
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*>
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*> | l**H * (beta A - alpha B) | / ( ulp max( |beta A|, |alpha B| ) )
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*>
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*> where l**H is the conjugate tranpose of l.
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*>
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*> (7) max over all right eigenvalue/-vector pairs (beta/alpha,r) of
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*>
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*> | (beta A - alpha B) r | / ( ulp max( |beta A|, |alpha B| ) )
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*>
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*> Test Matrices
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*> ---- --------
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*>
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*> The sizes of the test matrices are specified by an array
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*> NN(1:NSIZES); the value of each element NN(j) specifies one size.
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*> The "types" are specified by a logical array DOTYPE( 1:NTYPES ); if
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*> DOTYPE(j) is .TRUE., then matrix type "j" will be generated.
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*> Currently, the list of possible types is:
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*>
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*> (1) ( 0, 0 ) (a pair of zero matrices)
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*>
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*> (2) ( I, 0 ) (an identity and a zero matrix)
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*>
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*> (3) ( 0, I ) (an identity and a zero matrix)
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*>
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*> (4) ( I, I ) (a pair of identity matrices)
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*>
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*> t t
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*> (5) ( J , J ) (a pair of transposed Jordan blocks)
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*>
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*> t ( I 0 )
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*> (6) ( X, Y ) where X = ( J 0 ) and Y = ( t )
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*> ( 0 I ) ( 0 J )
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*> and I is a k x k identity and J a (k+1)x(k+1)
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*> Jordan block; k=(N-1)/2
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*>
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*> (7) ( D, I ) where D is diag( 0, 1,..., N-1 ) (a diagonal
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*> matrix with those diagonal entries.)
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*> (8) ( I, D )
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*>
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*> (9) ( big*D, small*I ) where "big" is near overflow and small=1/big
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*>
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*> (10) ( small*D, big*I )
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*>
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*> (11) ( big*I, small*D )
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*>
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*> (12) ( small*I, big*D )
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*>
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*> (13) ( big*D, big*I )
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*>
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*> (14) ( small*D, small*I )
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*>
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*> (15) ( D1, D2 ) where D1 is diag( 0, 0, 1, ..., N-3, 0 ) and
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*> D2 is diag( 0, N-3, N-4,..., 1, 0, 0 )
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*> t t
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*> (16) Q ( J , J ) Z where Q and Z are random orthogonal matrices.
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*>
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*> (17) Q ( T1, T2 ) Z where T1 and T2 are upper triangular matrices
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*> with random O(1) entries above the diagonal
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*> and diagonal entries diag(T1) =
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*> ( 0, 0, 1, ..., N-3, 0 ) and diag(T2) =
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*> ( 0, N-3, N-4,..., 1, 0, 0 )
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*>
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*> (18) Q ( T1, T2 ) Z diag(T1) = ( 0, 0, 1, 1, s, ..., s, 0 )
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*> diag(T2) = ( 0, 1, 0, 1,..., 1, 0 )
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*> s = machine precision.
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*>
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*> (19) Q ( T1, T2 ) Z diag(T1)=( 0,0,1,1, 1-d, ..., 1-(N-5)*d=s, 0 )
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*> diag(T2) = ( 0, 1, 0, 1, ..., 1, 0 )
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*>
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*> N-5
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*> (20) Q ( T1, T2 ) Z diag(T1)=( 0, 0, 1, 1, a, ..., a =s, 0 )
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*> diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 )
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*>
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*> (21) Q ( T1, T2 ) Z diag(T1)=( 0, 0, 1, r1, r2, ..., r(N-4), 0 )
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*> diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 )
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*> where r1,..., r(N-4) are random.
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*>
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*> (22) Q ( big*T1, small*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
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*> diag(T2) = ( 0, 1, ..., 1, 0, 0 )
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*>
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*> (23) Q ( small*T1, big*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
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*> diag(T2) = ( 0, 1, ..., 1, 0, 0 )
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*>
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*> (24) Q ( small*T1, small*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
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*> diag(T2) = ( 0, 1, ..., 1, 0, 0 )
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*>
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*> (25) Q ( big*T1, big*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
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*> diag(T2) = ( 0, 1, ..., 1, 0, 0 )
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*>
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*> (26) Q ( T1, T2 ) Z where T1 and T2 are random upper-triangular
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*> matrices.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] NSIZES
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*> \verbatim
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*> NSIZES is INTEGER
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*> The number of sizes of matrices to use. If it is zero,
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*> DDRVGG does nothing. It must be at least zero.
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*> \endverbatim
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*>
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*> \param[in] NN
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*> \verbatim
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*> NN is INTEGER array, dimension (NSIZES)
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*> An array containing the sizes to be used for the matrices.
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*> Zero values will be skipped. The values must be at least
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*> zero.
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*> \endverbatim
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*>
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*> \param[in] NTYPES
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*> \verbatim
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*> NTYPES is INTEGER
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*> The number of elements in DOTYPE. If it is zero, DDRVGG
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*> does nothing. It must be at least zero. If it is MAXTYP+1
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*> and NSIZES is 1, then an additional type, MAXTYP+1 is
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*> defined, which is to use whatever matrix is in A. This
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*> is only useful if DOTYPE(1:MAXTYP) is .FALSE. and
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*> DOTYPE(MAXTYP+1) is .TRUE. .
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*> \endverbatim
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*>
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*> \param[in] DOTYPE
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*> \verbatim
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*> DOTYPE is LOGICAL array, dimension (NTYPES)
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*> If DOTYPE(j) is .TRUE., then for each size in NN a
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*> matrix of that size and of type j will be generated.
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*> If NTYPES is smaller than the maximum number of types
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*> defined (PARAMETER MAXTYP), then types NTYPES+1 through
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*> MAXTYP will not be generated. If NTYPES is larger
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*> than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
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*> will be ignored.
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*> \endverbatim
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*>
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*> \param[in,out] ISEED
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*> \verbatim
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*> ISEED is INTEGER array, dimension (4)
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*> On entry ISEED specifies the seed of the random number
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*> generator. The array elements should be between 0 and 4095;
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*> if not they will be reduced mod 4096. Also, ISEED(4) must
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*> be odd. The random number generator uses a linear
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*> congruential sequence limited to small integers, and so
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*> should produce machine independent random numbers. The
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*> values of ISEED are changed on exit, and can be used in the
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*> next call to DDRVGG to continue the same random number
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*> sequence.
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*> \endverbatim
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*>
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*> \param[in] THRESH
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*> \verbatim
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*> THRESH is DOUBLE PRECISION
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*> A test will count as "failed" if the "error", computed as
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*> described above, exceeds THRESH. Note that the error is
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*> scaled to be O(1), so THRESH should be a reasonably small
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*> multiple of 1, e.g., 10 or 100. In particular, it should
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*> not depend on the precision (single vs. double) or the size
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*> of the matrix. It must be at least zero.
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*> \endverbatim
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*>
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*> \param[in] THRSHN
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*> \verbatim
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*> THRSHN is DOUBLE PRECISION
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*> Threshhold for reporting eigenvector normalization error.
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*> If the normalization of any eigenvector differs from 1 by
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*> more than THRSHN*ulp, then a special error message will be
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*> printed. (This is handled separately from the other tests,
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*> since only a compiler or programming error should cause an
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*> error message, at least if THRSHN is at least 5--10.)
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*> \endverbatim
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*>
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*> \param[in] NOUNIT
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*> \verbatim
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*> NOUNIT is INTEGER
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*> The FORTRAN unit number for printing out error messages
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*> (e.g., if a routine returns IINFO not equal to 0.)
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*> \endverbatim
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*>
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*> \param[in,out] A
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*> \verbatim
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*> A is DOUBLE PRECISION array, dimension
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*> (LDA, max(NN))
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*> Used to hold the original A matrix. Used as input only
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*> if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and
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*> DOTYPE(MAXTYP+1)=.TRUE.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of A, B, S, T, S2, and T2.
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*> It must be at least 1 and at least max( NN ).
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*> \endverbatim
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*>
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*> \param[in,out] B
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*> \verbatim
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*> B is DOUBLE PRECISION array, dimension
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*> (LDA, max(NN))
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*> Used to hold the original B matrix. Used as input only
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*> if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and
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*> DOTYPE(MAXTYP+1)=.TRUE.
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*> \endverbatim
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*>
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*> \param[out] S
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*> \verbatim
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*> S is DOUBLE PRECISION array, dimension (LDA, max(NN))
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*> The Schur form matrix computed from A by DGEGS. On exit, S
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*> contains the Schur form matrix corresponding to the matrix
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*> in A.
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*> \endverbatim
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*>
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*> \param[out] T
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*> \verbatim
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*> T is DOUBLE PRECISION array, dimension (LDA, max(NN))
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*> The upper triangular matrix computed from B by DGEGS.
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*> \endverbatim
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*>
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*> \param[out] S2
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*> \verbatim
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*> S2 is DOUBLE PRECISION array, dimension (LDA, max(NN))
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*> The matrix computed from A by DGEGV. This will be the
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*> Schur form of some matrix related to A, but will not, in
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*> general, be the same as S.
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*> \endverbatim
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*>
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*> \param[out] T2
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*> \verbatim
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*> T2 is DOUBLE PRECISION array, dimension (LDA, max(NN))
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*> The matrix computed from B by DGEGV. This will be the
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*> Schur form of some matrix related to B, but will not, in
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*> general, be the same as T.
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*> \endverbatim
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*>
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*> \param[out] Q
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*> \verbatim
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*> Q is DOUBLE PRECISION array, dimension (LDQ, max(NN))
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*> The (left) orthogonal matrix computed by DGEGS.
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*> \endverbatim
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*>
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*> \param[in] LDQ
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*> \verbatim
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*> LDQ is INTEGER
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*> The leading dimension of Q, Z, VL, and VR. It must
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*> be at least 1 and at least max( NN ).
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*> \endverbatim
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*>
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*> \param[out] Z
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*> \verbatim
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*> Z is DOUBLE PRECISION array of
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*> dimension( LDQ, max(NN) )
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*> The (right) orthogonal matrix computed by DGEGS.
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*> \endverbatim
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*>
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*> \param[out] ALPHR1
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*> \verbatim
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*> ALPHR1 is DOUBLE PRECISION array, dimension (max(NN))
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*> \endverbatim
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*>
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*> \param[out] ALPHI1
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*> \verbatim
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*> ALPHI1 is DOUBLE PRECISION array, dimension (max(NN))
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*> \endverbatim
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*>
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*> \param[out] BETA1
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*> \verbatim
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*> BETA1 is DOUBLE PRECISION array, dimension (max(NN))
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*>
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*> The generalized eigenvalues of (A,B) computed by DGEGS.
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*> ( ALPHR1(k)+ALPHI1(k)*i ) / BETA1(k) is the k-th
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*> generalized eigenvalue of the matrices in A and B.
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*> \endverbatim
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*>
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*> \param[out] ALPHR2
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*> \verbatim
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*> ALPHR2 is DOUBLE PRECISION array, dimension (max(NN))
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*> \endverbatim
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*>
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*> \param[out] ALPHI2
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*> \verbatim
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*> ALPHI2 is DOUBLE PRECISION array, dimension (max(NN))
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*> \endverbatim
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*>
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*> \param[out] BETA2
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*> \verbatim
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*> BETA2 is DOUBLE PRECISION array, dimension (max(NN))
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*>
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*> The generalized eigenvalues of (A,B) computed by DGEGV.
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*> ( ALPHR2(k)+ALPHI2(k)*i ) / BETA2(k) is the k-th
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*> generalized eigenvalue of the matrices in A and B.
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*> \endverbatim
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*>
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*> \param[out] VL
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*> \verbatim
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*> VL is DOUBLE PRECISION array, dimension (LDQ, max(NN))
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*> The (block lower triangular) left eigenvector matrix for
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*> the matrices in A and B. (See DTGEVC for the format.)
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*> \endverbatim
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*>
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*> \param[out] VR
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*> \verbatim
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*> VR is DOUBLE PRECISION array, dimension (LDQ, max(NN))
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*> The (block upper triangular) right eigenvector matrix for
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*> the matrices in A and B. (See DTGEVC for the format.)
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is DOUBLE PRECISION array, dimension (LWORK)
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*> \endverbatim
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*>
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*> \param[in] LWORK
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*> \verbatim
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*> LWORK is INTEGER
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*> The number of entries in WORK. This must be at least
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*> 2*N + MAX( 6*N, N*(NB+1), (k+1)*(2*k+N+1) ), where
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*> "k" is the sum of the blocksize and number-of-shifts for
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*> DHGEQZ, and NB is the greatest of the blocksizes for
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*> DGEQRF, DORMQR, and DORGQR. (The blocksizes and the
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*> number-of-shifts are retrieved through calls to ILAENV.)
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*> \endverbatim
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*>
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*> \param[out] RESULT
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*> \verbatim
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*> RESULT is DOUBLE PRECISION array, dimension (15)
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*> The values computed by the tests described above.
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*> The values are currently limited to 1/ulp, to avoid
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*> overflow.
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> = 0: successful exit
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*> < 0: if INFO = -i, the i-th argument had an illegal value.
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*> > 0: A routine returned an error code. INFO is the
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*> absolute value of the INFO value returned.
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date November 2011
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*
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*> \ingroup double_eig
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*
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* =====================================================================
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SUBROUTINE DDRVGG( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
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$ THRSHN, NOUNIT, A, LDA, B, S, T, S2, T2, Q,
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$ LDQ, Z, ALPHR1, ALPHI1, BETA1, ALPHR2, ALPHI2,
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$ BETA2, VL, VR, WORK, LWORK, RESULT, INFO )
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*
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* -- LAPACK test routine (version 3.4.0) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* November 2011
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*
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* .. Scalar Arguments ..
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INTEGER INFO, LDA, LDQ, LWORK, NOUNIT, NSIZES, NTYPES
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DOUBLE PRECISION THRESH, THRSHN
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* ..
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* .. Array Arguments ..
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LOGICAL DOTYPE( * )
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INTEGER ISEED( 4 ), NN( * )
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DOUBLE PRECISION A( LDA, * ), ALPHI1( * ), ALPHI2( * ),
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$ ALPHR1( * ), ALPHR2( * ), B( LDA, * ),
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$ BETA1( * ), BETA2( * ), Q( LDQ, * ),
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$ RESULT( * ), S( LDA, * ), S2( LDA, * ),
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$ T( LDA, * ), T2( LDA, * ), VL( LDQ, * ),
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$ VR( LDQ, * ), WORK( * ), Z( LDQ, * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ZERO, ONE
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PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
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INTEGER MAXTYP
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PARAMETER ( MAXTYP = 26 )
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* ..
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* .. Local Scalars ..
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LOGICAL BADNN, ILABAD
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INTEGER I1, IADD, IINFO, IN, J, JC, JR, JSIZE, JTYPE,
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$ LWKOPT, MTYPES, N, N1, NB, NBZ, NERRS, NMATS,
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$ NMAX, NS, NTEST, NTESTT
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DOUBLE PRECISION SAFMAX, SAFMIN, TEMP1, TEMP2, ULP, ULPINV
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* ..
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* .. Local Arrays ..
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INTEGER IASIGN( MAXTYP ), IBSIGN( MAXTYP ),
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$ IOLDSD( 4 ), KADD( 6 ), KAMAGN( MAXTYP ),
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$ KATYPE( MAXTYP ), KAZERO( MAXTYP ),
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$ KBMAGN( MAXTYP ), KBTYPE( MAXTYP ),
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$ KBZERO( MAXTYP ), KCLASS( MAXTYP ),
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$ KTRIAN( MAXTYP ), KZ1( 6 ), KZ2( 6 )
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DOUBLE PRECISION DUMMA( 4 ), RMAGN( 0: 3 )
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* ..
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* .. External Functions ..
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INTEGER ILAENV
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DOUBLE PRECISION DLAMCH, DLARND
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EXTERNAL ILAENV, DLAMCH, DLARND
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* ..
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* .. External Subroutines ..
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EXTERNAL ALASVM, DGEGS, DGEGV, DGET51, DGET52, DGET53,
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$ DLABAD, DLACPY, DLARFG, DLASET, DLATM4, DORM2R,
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$ XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, DBLE, MAX, MIN, SIGN
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* ..
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* .. Data statements ..
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DATA KCLASS / 15*1, 10*2, 1*3 /
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DATA KZ1 / 0, 1, 2, 1, 3, 3 /
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DATA KZ2 / 0, 0, 1, 2, 1, 1 /
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DATA KADD / 0, 0, 0, 0, 3, 2 /
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DATA KATYPE / 0, 1, 0, 1, 2, 3, 4, 1, 4, 4, 1, 1, 4,
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$ 4, 4, 2, 4, 5, 8, 7, 9, 4*4, 0 /
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DATA KBTYPE / 0, 0, 1, 1, 2, -3, 1, 4, 1, 1, 4, 4,
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$ 1, 1, -4, 2, -4, 8*8, 0 /
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DATA KAZERO / 6*1, 2, 1, 2*2, 2*1, 2*2, 3, 1, 3,
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$ 4*5, 4*3, 1 /
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DATA KBZERO / 6*1, 1, 2, 2*1, 2*2, 2*1, 4, 1, 4,
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$ 4*6, 4*4, 1 /
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DATA KAMAGN / 8*1, 2, 3, 2, 3, 2, 3, 7*1, 2, 3, 3,
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$ 2, 1 /
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DATA KBMAGN / 8*1, 3, 2, 3, 2, 2, 3, 7*1, 3, 2, 3,
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$ 2, 1 /
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DATA KTRIAN / 16*0, 10*1 /
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DATA IASIGN / 6*0, 2, 0, 2*2, 2*0, 3*2, 0, 2, 3*0,
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$ 5*2, 0 /
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DATA IBSIGN / 7*0, 2, 2*0, 2*2, 2*0, 2, 0, 2, 9*0 /
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* ..
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* .. Executable Statements ..
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*
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* Check for errors
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*
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INFO = 0
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*
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BADNN = .FALSE.
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NMAX = 1
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DO 10 J = 1, NSIZES
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NMAX = MAX( NMAX, NN( J ) )
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IF( NN( J ).LT.0 )
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$ BADNN = .TRUE.
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10 CONTINUE
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*
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* Maximum blocksize and shift -- we assume that blocksize and number
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* of shifts are monotone increasing functions of N.
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*
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NB = MAX( 1, ILAENV( 1, 'DGEQRF', ' ', NMAX, NMAX, -1, -1 ),
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$ ILAENV( 1, 'DORMQR', 'LT', NMAX, NMAX, NMAX, -1 ),
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$ ILAENV( 1, 'DORGQR', ' ', NMAX, NMAX, NMAX, -1 ) )
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NBZ = ILAENV( 1, 'DHGEQZ', 'SII', NMAX, 1, NMAX, 0 )
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NS = ILAENV( 4, 'DHGEQZ', 'SII', NMAX, 1, NMAX, 0 )
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I1 = NBZ + NS
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LWKOPT = 2*NMAX + MAX( 6*NMAX, NMAX*( NB+1 ),
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$ ( 2*I1+NMAX+1 )*( I1+1 ) )
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*
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* Check for errors
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*
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IF( NSIZES.LT.0 ) THEN
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INFO = -1
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ELSE IF( BADNN ) THEN
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INFO = -2
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ELSE IF( NTYPES.LT.0 ) THEN
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INFO = -3
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ELSE IF( THRESH.LT.ZERO ) THEN
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INFO = -6
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ELSE IF( LDA.LE.1 .OR. LDA.LT.NMAX ) THEN
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INFO = -10
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ELSE IF( LDQ.LE.1 .OR. LDQ.LT.NMAX ) THEN
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INFO = -19
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ELSE IF( LWKOPT.GT.LWORK ) THEN
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INFO = -30
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END IF
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*
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'DDRVGG', -INFO )
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 )
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$ RETURN
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*
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SAFMIN = DLAMCH( 'Safe minimum' )
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ULP = DLAMCH( 'Epsilon' )*DLAMCH( 'Base' )
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SAFMIN = SAFMIN / ULP
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SAFMAX = ONE / SAFMIN
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CALL DLABAD( SAFMIN, SAFMAX )
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ULPINV = ONE / ULP
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*
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* The values RMAGN(2:3) depend on N, see below.
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*
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RMAGN( 0 ) = ZERO
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RMAGN( 1 ) = ONE
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*
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* Loop over sizes, types
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*
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NTESTT = 0
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NERRS = 0
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NMATS = 0
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*
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DO 170 JSIZE = 1, NSIZES
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N = NN( JSIZE )
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N1 = MAX( 1, N )
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RMAGN( 2 ) = SAFMAX*ULP / DBLE( N1 )
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RMAGN( 3 ) = SAFMIN*ULPINV*N1
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*
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IF( NSIZES.NE.1 ) THEN
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MTYPES = MIN( MAXTYP, NTYPES )
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ELSE
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MTYPES = MIN( MAXTYP+1, NTYPES )
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END IF
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*
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DO 160 JTYPE = 1, MTYPES
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IF( .NOT.DOTYPE( JTYPE ) )
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$ GO TO 160
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NMATS = NMATS + 1
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NTEST = 0
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*
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* Save ISEED in case of an error.
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*
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DO 20 J = 1, 4
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IOLDSD( J ) = ISEED( J )
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20 CONTINUE
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*
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* Initialize RESULT
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*
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DO 30 J = 1, 15
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RESULT( J ) = ZERO
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30 CONTINUE
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*
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* Compute A and B
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*
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* Description of control parameters:
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*
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* KZLASS: =1 means w/o rotation, =2 means w/ rotation,
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* =3 means random.
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* KATYPE: the "type" to be passed to DLATM4 for computing A.
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* KAZERO: the pattern of zeros on the diagonal for A:
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* =1: ( xxx ), =2: (0, xxx ) =3: ( 0, 0, xxx, 0 ),
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* =4: ( 0, xxx, 0, 0 ), =5: ( 0, 0, 1, xxx, 0 ),
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* =6: ( 0, 1, 0, xxx, 0 ). (xxx means a string of
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* non-zero entries.)
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* KAMAGN: the magnitude of the matrix: =0: zero, =1: O(1),
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* =2: large, =3: small.
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* IASIGN: 1 if the diagonal elements of A are to be
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* multiplied by a random magnitude 1 number, =2 if
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* randomly chosen diagonal blocks are to be rotated
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* to form 2x2 blocks.
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* KBTYPE, KBZERO, KBMAGN, IBSIGN: the same, but for B.
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* KTRIAN: =0: don't fill in the upper triangle, =1: do.
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* KZ1, KZ2, KADD: used to implement KAZERO and KBZERO.
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* RMAGN: used to implement KAMAGN and KBMAGN.
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*
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IF( MTYPES.GT.MAXTYP )
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$ GO TO 110
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IINFO = 0
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IF( KCLASS( JTYPE ).LT.3 ) THEN
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*
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* Generate A (w/o rotation)
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*
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IF( ABS( KATYPE( JTYPE ) ).EQ.3 ) THEN
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IN = 2*( ( N-1 ) / 2 ) + 1
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IF( IN.NE.N )
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$ CALL DLASET( 'Full', N, N, ZERO, ZERO, A, LDA )
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ELSE
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IN = N
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END IF
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CALL DLATM4( KATYPE( JTYPE ), IN, KZ1( KAZERO( JTYPE ) ),
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$ KZ2( KAZERO( JTYPE ) ), IASIGN( JTYPE ),
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$ RMAGN( KAMAGN( JTYPE ) ), ULP,
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$ RMAGN( KTRIAN( JTYPE )*KAMAGN( JTYPE ) ), 2,
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$ ISEED, A, LDA )
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IADD = KADD( KAZERO( JTYPE ) )
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IF( IADD.GT.0 .AND. IADD.LE.N )
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$ A( IADD, IADD ) = ONE
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*
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* Generate B (w/o rotation)
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*
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IF( ABS( KBTYPE( JTYPE ) ).EQ.3 ) THEN
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IN = 2*( ( N-1 ) / 2 ) + 1
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IF( IN.NE.N )
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$ CALL DLASET( 'Full', N, N, ZERO, ZERO, B, LDA )
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ELSE
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IN = N
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END IF
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CALL DLATM4( KBTYPE( JTYPE ), IN, KZ1( KBZERO( JTYPE ) ),
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$ KZ2( KBZERO( JTYPE ) ), IBSIGN( JTYPE ),
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$ RMAGN( KBMAGN( JTYPE ) ), ONE,
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$ RMAGN( KTRIAN( JTYPE )*KBMAGN( JTYPE ) ), 2,
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$ ISEED, B, LDA )
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IADD = KADD( KBZERO( JTYPE ) )
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IF( IADD.NE.0 .AND. IADD.LE.N )
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$ B( IADD, IADD ) = ONE
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*
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IF( KCLASS( JTYPE ).EQ.2 .AND. N.GT.0 ) THEN
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*
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* Include rotations
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*
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* Generate Q, Z as Householder transformations times
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* a diagonal matrix.
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*
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DO 50 JC = 1, N - 1
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DO 40 JR = JC, N
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Q( JR, JC ) = DLARND( 3, ISEED )
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Z( JR, JC ) = DLARND( 3, ISEED )
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40 CONTINUE
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CALL DLARFG( N+1-JC, Q( JC, JC ), Q( JC+1, JC ), 1,
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$ WORK( JC ) )
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WORK( 2*N+JC ) = SIGN( ONE, Q( JC, JC ) )
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Q( JC, JC ) = ONE
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CALL DLARFG( N+1-JC, Z( JC, JC ), Z( JC+1, JC ), 1,
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$ WORK( N+JC ) )
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WORK( 3*N+JC ) = SIGN( ONE, Z( JC, JC ) )
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Z( JC, JC ) = ONE
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50 CONTINUE
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Q( N, N ) = ONE
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WORK( N ) = ZERO
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WORK( 3*N ) = SIGN( ONE, DLARND( 2, ISEED ) )
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Z( N, N ) = ONE
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WORK( 2*N ) = ZERO
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WORK( 4*N ) = SIGN( ONE, DLARND( 2, ISEED ) )
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*
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* Apply the diagonal matrices
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*
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DO 70 JC = 1, N
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DO 60 JR = 1, N
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A( JR, JC ) = WORK( 2*N+JR )*WORK( 3*N+JC )*
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$ A( JR, JC )
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B( JR, JC ) = WORK( 2*N+JR )*WORK( 3*N+JC )*
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$ B( JR, JC )
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60 CONTINUE
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70 CONTINUE
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CALL DORM2R( 'L', 'N', N, N, N-1, Q, LDQ, WORK, A,
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$ LDA, WORK( 2*N+1 ), IINFO )
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IF( IINFO.NE.0 )
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$ GO TO 100
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CALL DORM2R( 'R', 'T', N, N, N-1, Z, LDQ, WORK( N+1 ),
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$ A, LDA, WORK( 2*N+1 ), IINFO )
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IF( IINFO.NE.0 )
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$ GO TO 100
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CALL DORM2R( 'L', 'N', N, N, N-1, Q, LDQ, WORK, B,
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$ LDA, WORK( 2*N+1 ), IINFO )
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IF( IINFO.NE.0 )
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$ GO TO 100
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CALL DORM2R( 'R', 'T', N, N, N-1, Z, LDQ, WORK( N+1 ),
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$ B, LDA, WORK( 2*N+1 ), IINFO )
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IF( IINFO.NE.0 )
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$ GO TO 100
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END IF
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ELSE
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*
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* Random matrices
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*
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DO 90 JC = 1, N
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DO 80 JR = 1, N
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A( JR, JC ) = RMAGN( KAMAGN( JTYPE ) )*
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$ DLARND( 2, ISEED )
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B( JR, JC ) = RMAGN( KBMAGN( JTYPE ) )*
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$ DLARND( 2, ISEED )
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80 CONTINUE
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90 CONTINUE
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END IF
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*
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100 CONTINUE
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*
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IF( IINFO.NE.0 ) THEN
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WRITE( NOUNIT, FMT = 9999 )'Generator', IINFO, N, JTYPE,
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$ IOLDSD
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INFO = ABS( IINFO )
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RETURN
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END IF
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*
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110 CONTINUE
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*
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* Call DGEGS to compute H, T, Q, Z, alpha, and beta.
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*
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CALL DLACPY( ' ', N, N, A, LDA, S, LDA )
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CALL DLACPY( ' ', N, N, B, LDA, T, LDA )
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NTEST = 1
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RESULT( 1 ) = ULPINV
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*
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CALL DGEGS( 'V', 'V', N, S, LDA, T, LDA, ALPHR1, ALPHI1,
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$ BETA1, Q, LDQ, Z, LDQ, WORK, LWORK, IINFO )
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IF( IINFO.NE.0 ) THEN
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WRITE( NOUNIT, FMT = 9999 )'DGEGS', IINFO, N, JTYPE,
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$ IOLDSD
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INFO = ABS( IINFO )
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GO TO 140
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END IF
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*
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NTEST = 4
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*
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* Do tests 1--4
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*
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CALL DGET51( 1, N, A, LDA, S, LDA, Q, LDQ, Z, LDQ, WORK,
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$ RESULT( 1 ) )
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CALL DGET51( 1, N, B, LDA, T, LDA, Q, LDQ, Z, LDQ, WORK,
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$ RESULT( 2 ) )
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CALL DGET51( 3, N, B, LDA, T, LDA, Q, LDQ, Q, LDQ, WORK,
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$ RESULT( 3 ) )
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CALL DGET51( 3, N, B, LDA, T, LDA, Z, LDQ, Z, LDQ, WORK,
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$ RESULT( 4 ) )
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*
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* Do test 5: compare eigenvalues with diagonals.
|
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* Also check Schur form of A.
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*
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TEMP1 = ZERO
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*
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DO 120 J = 1, N
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ILABAD = .FALSE.
|
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IF( ALPHI1( J ).EQ.ZERO ) THEN
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TEMP2 = ( ABS( ALPHR1( J )-S( J, J ) ) /
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$ MAX( SAFMIN, ABS( ALPHR1( J ) ), ABS( S( J,
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$ J ) ) )+ABS( BETA1( J )-T( J, J ) ) /
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$ MAX( SAFMIN, ABS( BETA1( J ) ), ABS( T( J,
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$ J ) ) ) ) / ULP
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IF( J.LT.N ) THEN
|
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IF( S( J+1, J ).NE.ZERO )
|
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$ ILABAD = .TRUE.
|
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END IF
|
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IF( J.GT.1 ) THEN
|
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IF( S( J, J-1 ).NE.ZERO )
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$ ILABAD = .TRUE.
|
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END IF
|
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ELSE
|
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IF( ALPHI1( J ).GT.ZERO ) THEN
|
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I1 = J
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ELSE
|
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I1 = J - 1
|
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END IF
|
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IF( I1.LE.0 .OR. I1.GE.N ) THEN
|
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ILABAD = .TRUE.
|
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ELSE IF( I1.LT.N-1 ) THEN
|
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IF( S( I1+2, I1+1 ).NE.ZERO )
|
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$ ILABAD = .TRUE.
|
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ELSE IF( I1.GT.1 ) THEN
|
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IF( S( I1, I1-1 ).NE.ZERO )
|
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$ ILABAD = .TRUE.
|
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END IF
|
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IF( .NOT.ILABAD ) THEN
|
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CALL DGET53( S( I1, I1 ), LDA, T( I1, I1 ), LDA,
|
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$ BETA1( J ), ALPHR1( J ), ALPHI1( J ),
|
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$ TEMP2, IINFO )
|
|
IF( IINFO.GE.3 ) THEN
|
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WRITE( NOUNIT, FMT = 9997 )IINFO, J, N, JTYPE,
|
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$ IOLDSD
|
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INFO = ABS( IINFO )
|
|
END IF
|
|
ELSE
|
|
TEMP2 = ULPINV
|
|
END IF
|
|
END IF
|
|
TEMP1 = MAX( TEMP1, TEMP2 )
|
|
IF( ILABAD ) THEN
|
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WRITE( NOUNIT, FMT = 9996 )J, N, JTYPE, IOLDSD
|
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END IF
|
|
120 CONTINUE
|
|
RESULT( 5 ) = TEMP1
|
|
*
|
|
* Call DGEGV to compute S2, T2, VL, and VR, do tests.
|
|
*
|
|
* Eigenvalues and Eigenvectors
|
|
*
|
|
CALL DLACPY( ' ', N, N, A, LDA, S2, LDA )
|
|
CALL DLACPY( ' ', N, N, B, LDA, T2, LDA )
|
|
NTEST = 6
|
|
RESULT( 6 ) = ULPINV
|
|
*
|
|
CALL DGEGV( 'V', 'V', N, S2, LDA, T2, LDA, ALPHR2, ALPHI2,
|
|
$ BETA2, VL, LDQ, VR, LDQ, WORK, LWORK, IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUNIT, FMT = 9999 )'DGEGV', IINFO, N, JTYPE,
|
|
$ IOLDSD
|
|
INFO = ABS( IINFO )
|
|
GO TO 140
|
|
END IF
|
|
*
|
|
NTEST = 7
|
|
*
|
|
* Do Tests 6 and 7
|
|
*
|
|
CALL DGET52( .TRUE., N, A, LDA, B, LDA, VL, LDQ, ALPHR2,
|
|
$ ALPHI2, BETA2, WORK, DUMMA( 1 ) )
|
|
RESULT( 6 ) = DUMMA( 1 )
|
|
IF( DUMMA( 2 ).GT.THRSHN ) THEN
|
|
WRITE( NOUNIT, FMT = 9998 )'Left', 'DGEGV', DUMMA( 2 ),
|
|
$ N, JTYPE, IOLDSD
|
|
END IF
|
|
*
|
|
CALL DGET52( .FALSE., N, A, LDA, B, LDA, VR, LDQ, ALPHR2,
|
|
$ ALPHI2, BETA2, WORK, DUMMA( 1 ) )
|
|
RESULT( 7 ) = DUMMA( 1 )
|
|
IF( DUMMA( 2 ).GT.THRESH ) THEN
|
|
WRITE( NOUNIT, FMT = 9998 )'Right', 'DGEGV', DUMMA( 2 ),
|
|
$ N, JTYPE, IOLDSD
|
|
END IF
|
|
*
|
|
* Check form of Complex eigenvalues.
|
|
*
|
|
DO 130 J = 1, N
|
|
ILABAD = .FALSE.
|
|
IF( ALPHI2( J ).GT.ZERO ) THEN
|
|
IF( J.EQ.N ) THEN
|
|
ILABAD = .TRUE.
|
|
ELSE IF( ALPHI2( J+1 ).GE.ZERO ) THEN
|
|
ILABAD = .TRUE.
|
|
END IF
|
|
ELSE IF( ALPHI2( J ).LT.ZERO ) THEN
|
|
IF( J.EQ.1 ) THEN
|
|
ILABAD = .TRUE.
|
|
ELSE IF( ALPHI2( J-1 ).LE.ZERO ) THEN
|
|
ILABAD = .TRUE.
|
|
END IF
|
|
END IF
|
|
IF( ILABAD ) THEN
|
|
WRITE( NOUNIT, FMT = 9996 )J, N, JTYPE, IOLDSD
|
|
END IF
|
|
130 CONTINUE
|
|
*
|
|
* End of Loop -- Check for RESULT(j) > THRESH
|
|
*
|
|
140 CONTINUE
|
|
*
|
|
NTESTT = NTESTT + NTEST
|
|
*
|
|
* Print out tests which fail.
|
|
*
|
|
DO 150 JR = 1, NTEST
|
|
IF( RESULT( JR ).GE.THRESH ) THEN
|
|
*
|
|
* If this is the first test to fail,
|
|
* print a header to the data file.
|
|
*
|
|
IF( NERRS.EQ.0 ) THEN
|
|
WRITE( NOUNIT, FMT = 9995 )'DGG'
|
|
*
|
|
* Matrix types
|
|
*
|
|
WRITE( NOUNIT, FMT = 9994 )
|
|
WRITE( NOUNIT, FMT = 9993 )
|
|
WRITE( NOUNIT, FMT = 9992 )'Orthogonal'
|
|
*
|
|
* Tests performed
|
|
*
|
|
WRITE( NOUNIT, FMT = 9991 )'orthogonal', '''',
|
|
$ 'transpose', ( '''', J = 1, 5 )
|
|
*
|
|
END IF
|
|
NERRS = NERRS + 1
|
|
IF( RESULT( JR ).LT.10000.0D0 ) THEN
|
|
WRITE( NOUNIT, FMT = 9990 )N, JTYPE, IOLDSD, JR,
|
|
$ RESULT( JR )
|
|
ELSE
|
|
WRITE( NOUNIT, FMT = 9989 )N, JTYPE, IOLDSD, JR,
|
|
$ RESULT( JR )
|
|
END IF
|
|
END IF
|
|
150 CONTINUE
|
|
*
|
|
160 CONTINUE
|
|
170 CONTINUE
|
|
*
|
|
* Summary
|
|
*
|
|
CALL ALASVM( 'DGG', NOUNIT, NERRS, NTESTT, 0 )
|
|
RETURN
|
|
*
|
|
9999 FORMAT( ' DDRVGG: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
|
|
$ I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
|
|
*
|
|
9998 FORMAT( ' DDRVGG: ', A, ' Eigenvectors from ', A, ' incorrectly ',
|
|
$ 'normalized.', / ' Bits of error=', 0P, G10.3, ',', 9X,
|
|
$ 'N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5,
|
|
$ ')' )
|
|
*
|
|
9997 FORMAT( ' DDRVGG: DGET53 returned INFO=', I1, ' for eigenvalue ',
|
|
$ I6, '.', / 9X, 'N=', I6, ', JTYPE=', I6, ', ISEED=(',
|
|
$ 3( I5, ',' ), I5, ')' )
|
|
*
|
|
9996 FORMAT( ' DDRVGG: S not in Schur form at eigenvalue ', I6, '.',
|
|
$ / 9X, 'N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ),
|
|
$ I5, ')' )
|
|
*
|
|
9995 FORMAT( / 1X, A3, ' -- Real Generalized eigenvalue problem driver'
|
|
$ )
|
|
*
|
|
9994 FORMAT( ' Matrix types (see DDRVGG for details): ' )
|
|
*
|
|
9993 FORMAT( ' Special Matrices:', 23X,
|
|
$ '(J''=transposed Jordan block)',
|
|
$ / ' 1=(0,0) 2=(I,0) 3=(0,I) 4=(I,I) 5=(J'',J'') ',
|
|
$ '6=(diag(J'',I), diag(I,J''))', / ' Diagonal Matrices: ( ',
|
|
$ 'D=diag(0,1,2,...) )', / ' 7=(D,I) 9=(large*D, small*I',
|
|
$ ') 11=(large*I, small*D) 13=(large*D, large*I)', /
|
|
$ ' 8=(I,D) 10=(small*D, large*I) 12=(small*I, large*D) ',
|
|
$ ' 14=(small*D, small*I)', / ' 15=(D, reversed D)' )
|
|
9992 FORMAT( ' Matrices Rotated by Random ', A, ' Matrices U, V:',
|
|
$ / ' 16=Transposed Jordan Blocks 19=geometric ',
|
|
$ 'alpha, beta=0,1', / ' 17=arithm. alpha&beta ',
|
|
$ ' 20=arithmetic alpha, beta=0,1', / ' 18=clustered ',
|
|
$ 'alpha, beta=0,1 21=random alpha, beta=0,1',
|
|
$ / ' Large & Small Matrices:', / ' 22=(large, small) ',
|
|
$ '23=(small,large) 24=(small,small) 25=(large,large)',
|
|
$ / ' 26=random O(1) matrices.' )
|
|
*
|
|
9991 FORMAT( / ' Tests performed: (S is Schur, T is triangular, ',
|
|
$ 'Q and Z are ', A, ',', / 20X,
|
|
$ 'l and r are the appropriate left and right', / 19X,
|
|
$ 'eigenvectors, resp., a is alpha, b is beta, and', / 19X, A,
|
|
$ ' means ', A, '.)', / ' 1 = | A - Q S Z', A,
|
|
$ ' | / ( |A| n ulp ) 2 = | B - Q T Z', A,
|
|
$ ' | / ( |B| n ulp )', / ' 3 = | I - QQ', A,
|
|
$ ' | / ( n ulp ) 4 = | I - ZZ', A,
|
|
$ ' | / ( n ulp )', /
|
|
$ ' 5 = difference between (alpha,beta) and diagonals of',
|
|
$ ' (S,T)', / ' 6 = max | ( b A - a B )', A,
|
|
$ ' l | / const. 7 = max | ( b A - a B ) r | / const.',
|
|
$ / 1X )
|
|
9990 FORMAT( ' Matrix order=', I5, ', type=', I2, ', seed=',
|
|
$ 4( I4, ',' ), ' result ', I3, ' is', 0P, F8.2 )
|
|
9989 FORMAT( ' Matrix order=', I5, ', type=', I2, ', seed=',
|
|
$ 4( I4, ',' ), ' result ', I3, ' is', 1P, D10.3 )
|
|
*
|
|
* End of DDRVGG
|
|
*
|
|
END
|