814 lines
31 KiB
FortranFixed
814 lines
31 KiB
FortranFixed
SUBROUTINE ZDRVGG( 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, ALPHA1, BETA1, ALPHA2, BETA2, VL, VR,
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$ WORK, LWORK, RWORK, RESULT, INFO )
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*
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* -- LAPACK test routine (version 3.1) --
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* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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* November 2006
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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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*
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* Purpose
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* =======
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*
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* ZDRVGG checks the nonsymmetric generalized eigenvalue driver
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* routines.
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* T T T
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* ZGEGS 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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* (upper triangular), and Q and Z are unitary. 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)=T(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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* ZGEGV 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 ZDRVGG 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 ZGEGS:
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*
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* H
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* (1) | A - Q S Z | / ( |A| n ulp )
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*
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* H
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* (2) | B - Q T Z | / ( |B| n ulp )
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*
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* H
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* (3) | I - QQ | / ( n ulp )
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*
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* H
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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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* |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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* Results from ZGEGV:
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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 unitary 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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*
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* Arguments
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* =========
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*
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* NSIZES (input) INTEGER
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* The number of sizes of matrices to use. If it is zero,
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* ZDRVGG does nothing. It must be at least zero.
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*
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* NN (input) 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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*
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* NTYPES (input) INTEGER
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* The number of elements in DOTYPE. If it is zero, ZDRVGG
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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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*
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* DOTYPE (input) 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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*
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* ISEED (input/output) 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 ZDRVGG to continue the same random number
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* sequence.
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*
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* THRESH (input) 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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*
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* THRSHN (input) 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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*
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* NOUNIT (input) 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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*
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* A (input/workspace) COMPLEX*16 array, dimension (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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*
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* LDA (input) 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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*
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* B (input/workspace) COMPLEX*16 array, dimension (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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*
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* S (workspace) COMPLEX*16 array, dimension (LDA, max(NN))
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* The upper triangular matrix computed from A by ZGEGS.
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*
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* T (workspace) COMPLEX*16 array, dimension (LDA, max(NN))
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* The upper triangular matrix computed from B by ZGEGS.
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*
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* S2 (workspace) COMPLEX*16 array, dimension (LDA, max(NN))
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* The matrix computed from A by ZGEGV. This will be the
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* Schur (upper triangular) form of some matrix related to A,
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* but will not, in general, be the same as S.
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*
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* T2 (workspace) COMPLEX*16 array, dimension (LDA, max(NN))
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* The matrix computed from B by ZGEGV. 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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*
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* Q (workspace) COMPLEX*16 array, dimension (LDQ, max(NN))
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* The (left) unitary matrix computed by ZGEGS.
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*
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* LDQ (input) 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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*
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* Z (workspace) COMPLEX*16 array, dimension (LDQ, max(NN))
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* The (right) unitary matrix computed by ZGEGS.
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*
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* ALPHA1 (workspace) COMPLEX*16 array, dimension (max(NN))
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* BETA1 (workspace) COMPLEX*16 array, dimension (max(NN))
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* The generalized eigenvalues of (A,B) computed by ZGEGS.
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* ALPHA1(k) / BETA1(k) is the k-th generalized eigenvalue of
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* the matrices in A and B.
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*
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* ALPHA2 (workspace) COMPLEX*16 array, dimension (max(NN))
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* BETA2 (workspace) COMPLEX*16 array, dimension (max(NN))
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* The generalized eigenvalues of (A,B) computed by ZGEGV.
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* ALPHA2(k) / BETA2(k) is the k-th generalized eigenvalue of
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* the matrices in A and B.
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*
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* VL (workspace) COMPLEX*16 array, dimension (LDQ, max(NN))
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* The (lower triangular) left eigenvector matrix for the
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* matrices in A and B.
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*
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* VR (workspace) COMPLEX*16 array, dimension (LDQ, max(NN))
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* The (upper triangular) right eigenvector matrix for the
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* matrices in A and B.
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*
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* WORK (workspace) COMPLEX*16 array, dimension (LWORK)
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*
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* LWORK (input) INTEGER
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* The number of entries in WORK. This must be at least
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* MAX( 2*N, N*(NB+1), (k+1)*(2*k+N+1) ), where "k" is the
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* sum of the blocksize and number-of-shifts for ZHGEQZ, and
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* NB is the greatest of the blocksizes for ZGEQRF, ZUNMQR,
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* and ZUNGQR. (The blocksizes and the number-of-shifts are
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* retrieved through calls to ILAENV.)
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*
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* RWORK (workspace) DOUBLE PRECISION array, dimension (8*N)
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*
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* RESULT (output) DOUBLE PRECISION array, dimension (7)
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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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*
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* INFO (output) 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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*
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* =====================================================================
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*
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LOGICAL DOTYPE( * )
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INTEGER ISEED( 4 ), NN( * )
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DOUBLE PRECISION RESULT( * ), RWORK( * )
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COMPLEX*16 A( LDA, * ), ALPHA1( * ), ALPHA2( * ),
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$ B( LDA, * ), BETA1( * ), BETA2( * ),
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$ Q( LDQ, * ), 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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* .. Parameters ..
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DOUBLE PRECISION ZERO, ONE
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PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
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COMPLEX*16 CZERO, CONE
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PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
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$ CONE = ( 1.0D+0, 0.0D+0 ) )
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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
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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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COMPLEX*16 CTEMP, X
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* ..
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* .. Local Arrays ..
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LOGICAL LASIGN( MAXTYP ), LBSIGN( MAXTYP )
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INTEGER 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
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COMPLEX*16 ZLARND
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EXTERNAL ILAENV, DLAMCH, ZLARND
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* ..
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* .. External Subroutines ..
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EXTERNAL ALASVM, DLABAD, XERBLA, ZGEGS, ZGEGV, ZGET51,
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$ ZGET52, ZLACPY, ZLARFG, ZLASET, ZLATM4, ZUNM2R
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, DBLE, DCONJG, DIMAG, MAX, MIN, SIGN
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* ..
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* .. Statement Functions ..
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DOUBLE PRECISION ABS1
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* ..
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* .. Statement Function definitions ..
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ABS1( X ) = ABS( DBLE( X ) ) + ABS( DIMAG( X ) )
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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 LASIGN / 6*.FALSE., .TRUE., .FALSE., 2*.TRUE.,
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$ 2*.FALSE., 3*.TRUE., .FALSE., .TRUE.,
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$ 3*.FALSE., 5*.TRUE., .FALSE. /
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DATA LBSIGN / 7*.FALSE., .TRUE., 2*.FALSE.,
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$ 2*.TRUE., 2*.FALSE., .TRUE., .FALSE., .TRUE.,
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$ 9*.FALSE. /
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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, 'ZGEQRF', ' ', NMAX, NMAX, -1, -1 ),
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$ ILAENV( 1, 'ZUNMQR', 'LC', NMAX, NMAX, NMAX, -1 ),
|
|
$ ILAENV( 1, 'ZUNGQR', ' ', NMAX, NMAX, NMAX, -1 ) )
|
|
NBZ = ILAENV( 1, 'ZHGEQZ', 'SII', NMAX, 1, NMAX, 0 )
|
|
NS = ILAENV( 4, 'ZHGEQZ', 'SII', NMAX, 1, NMAX, 0 )
|
|
I1 = NBZ + NS
|
|
LWKOPT = MAX( 2*NMAX, NMAX*( NB+1 ), ( 2*I1+NMAX+1 )*( I1+1 ) )
|
|
*
|
|
* Check for errors
|
|
*
|
|
IF( NSIZES.LT.0 ) THEN
|
|
INFO = -1
|
|
ELSE IF( BADNN ) THEN
|
|
INFO = -2
|
|
ELSE IF( NTYPES.LT.0 ) THEN
|
|
INFO = -3
|
|
ELSE IF( THRESH.LT.ZERO ) THEN
|
|
INFO = -6
|
|
ELSE IF( LDA.LE.1 .OR. LDA.LT.NMAX ) THEN
|
|
INFO = -10
|
|
ELSE IF( LDQ.LE.1 .OR. LDQ.LT.NMAX ) THEN
|
|
INFO = -19
|
|
ELSE IF( LWKOPT.GT.LWORK ) THEN
|
|
INFO = -30
|
|
END IF
|
|
*
|
|
IF( INFO.NE.0 ) THEN
|
|
CALL XERBLA( 'ZDRVGG', -INFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Quick return if possible
|
|
*
|
|
IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 )
|
|
$ RETURN
|
|
*
|
|
ULP = DLAMCH( 'Precision' )
|
|
SAFMIN = DLAMCH( 'Safe minimum' )
|
|
SAFMIN = SAFMIN / ULP
|
|
SAFMAX = ONE / SAFMIN
|
|
CALL DLABAD( SAFMIN, SAFMAX )
|
|
ULPINV = ONE / ULP
|
|
*
|
|
* The values RMAGN(2:3) depend on N, see below.
|
|
*
|
|
RMAGN( 0 ) = ZERO
|
|
RMAGN( 1 ) = ONE
|
|
*
|
|
* Loop over sizes, types
|
|
*
|
|
NTESTT = 0
|
|
NERRS = 0
|
|
NMATS = 0
|
|
*
|
|
DO 160 JSIZE = 1, NSIZES
|
|
N = NN( JSIZE )
|
|
N1 = MAX( 1, N )
|
|
RMAGN( 2 ) = SAFMAX*ULP / DBLE( N1 )
|
|
RMAGN( 3 ) = SAFMIN*ULPINV*N1
|
|
*
|
|
IF( NSIZES.NE.1 ) THEN
|
|
MTYPES = MIN( MAXTYP, NTYPES )
|
|
ELSE
|
|
MTYPES = MIN( MAXTYP+1, NTYPES )
|
|
END IF
|
|
*
|
|
DO 150 JTYPE = 1, MTYPES
|
|
IF( .NOT.DOTYPE( JTYPE ) )
|
|
$ GO TO 150
|
|
NMATS = NMATS + 1
|
|
NTEST = 0
|
|
*
|
|
* Save ISEED in case of an error.
|
|
*
|
|
DO 20 J = 1, 4
|
|
IOLDSD( J ) = ISEED( J )
|
|
20 CONTINUE
|
|
*
|
|
* Initialize RESULT
|
|
*
|
|
DO 30 J = 1, 7
|
|
RESULT( J ) = ZERO
|
|
30 CONTINUE
|
|
*
|
|
* Compute A and B
|
|
*
|
|
* Description of control parameters:
|
|
*
|
|
* KZLASS: =1 means w/o rotation, =2 means w/ rotation,
|
|
* =3 means random.
|
|
* KATYPE: the "type" to be passed to ZLATM4 for computing A.
|
|
* KAZERO: the pattern of zeros on the diagonal for A:
|
|
* =1: ( xxx ), =2: (0, xxx ) =3: ( 0, 0, xxx, 0 ),
|
|
* =4: ( 0, xxx, 0, 0 ), =5: ( 0, 0, 1, xxx, 0 ),
|
|
* =6: ( 0, 1, 0, xxx, 0 ). (xxx means a string of
|
|
* non-zero entries.)
|
|
* KAMAGN: the magnitude of the matrix: =0: zero, =1: O(1),
|
|
* =2: large, =3: small.
|
|
* LASIGN: .TRUE. if the diagonal elements of A are to be
|
|
* multiplied by a random magnitude 1 number.
|
|
* KBTYPE, KBZERO, KBMAGN, IBSIGN: the same, but for B.
|
|
* KTRIAN: =0: don't fill in the upper triangle, =1: do.
|
|
* KZ1, KZ2, KADD: used to implement KAZERO and KBZERO.
|
|
* RMAGN: used to implement KAMAGN and KBMAGN.
|
|
*
|
|
IF( MTYPES.GT.MAXTYP )
|
|
$ GO TO 110
|
|
IINFO = 0
|
|
IF( KCLASS( JTYPE ).LT.3 ) THEN
|
|
*
|
|
* Generate A (w/o rotation)
|
|
*
|
|
IF( ABS( KATYPE( JTYPE ) ).EQ.3 ) THEN
|
|
IN = 2*( ( N-1 ) / 2 ) + 1
|
|
IF( IN.NE.N )
|
|
$ CALL ZLASET( 'Full', N, N, CZERO, CZERO, A, LDA )
|
|
ELSE
|
|
IN = N
|
|
END IF
|
|
CALL ZLATM4( KATYPE( JTYPE ), IN, KZ1( KAZERO( JTYPE ) ),
|
|
$ KZ2( KAZERO( JTYPE ) ), LASIGN( JTYPE ),
|
|
$ RMAGN( KAMAGN( JTYPE ) ), ULP,
|
|
$ RMAGN( KTRIAN( JTYPE )*KAMAGN( JTYPE ) ), 2,
|
|
$ ISEED, A, LDA )
|
|
IADD = KADD( KAZERO( JTYPE ) )
|
|
IF( IADD.GT.0 .AND. IADD.LE.N )
|
|
$ A( IADD, IADD ) = RMAGN( KAMAGN( JTYPE ) )
|
|
*
|
|
* Generate B (w/o rotation)
|
|
*
|
|
IF( ABS( KBTYPE( JTYPE ) ).EQ.3 ) THEN
|
|
IN = 2*( ( N-1 ) / 2 ) + 1
|
|
IF( IN.NE.N )
|
|
$ CALL ZLASET( 'Full', N, N, CZERO, CZERO, B, LDA )
|
|
ELSE
|
|
IN = N
|
|
END IF
|
|
CALL ZLATM4( KBTYPE( JTYPE ), IN, KZ1( KBZERO( JTYPE ) ),
|
|
$ KZ2( KBZERO( JTYPE ) ), LBSIGN( JTYPE ),
|
|
$ RMAGN( KBMAGN( JTYPE ) ), ONE,
|
|
$ RMAGN( KTRIAN( JTYPE )*KBMAGN( JTYPE ) ), 2,
|
|
$ ISEED, B, LDA )
|
|
IADD = KADD( KBZERO( JTYPE ) )
|
|
IF( IADD.NE.0 .AND. IADD.LE.N )
|
|
$ B( IADD, IADD ) = RMAGN( KBMAGN( JTYPE ) )
|
|
*
|
|
IF( KCLASS( JTYPE ).EQ.2 .AND. N.GT.0 ) THEN
|
|
*
|
|
* Include rotations
|
|
*
|
|
* Generate Q, Z as Householder transformations times
|
|
* a diagonal matrix.
|
|
*
|
|
DO 50 JC = 1, N - 1
|
|
DO 40 JR = JC, N
|
|
Q( JR, JC ) = ZLARND( 3, ISEED )
|
|
Z( JR, JC ) = ZLARND( 3, ISEED )
|
|
40 CONTINUE
|
|
CALL ZLARFG( N+1-JC, Q( JC, JC ), Q( JC+1, JC ), 1,
|
|
$ WORK( JC ) )
|
|
WORK( 2*N+JC ) = SIGN( ONE, DBLE( Q( JC, JC ) ) )
|
|
Q( JC, JC ) = CONE
|
|
CALL ZLARFG( N+1-JC, Z( JC, JC ), Z( JC+1, JC ), 1,
|
|
$ WORK( N+JC ) )
|
|
WORK( 3*N+JC ) = SIGN( ONE, DBLE( Z( JC, JC ) ) )
|
|
Z( JC, JC ) = CONE
|
|
50 CONTINUE
|
|
CTEMP = ZLARND( 3, ISEED )
|
|
Q( N, N ) = CONE
|
|
WORK( N ) = CZERO
|
|
WORK( 3*N ) = CTEMP / ABS( CTEMP )
|
|
CTEMP = ZLARND( 3, ISEED )
|
|
Z( N, N ) = CONE
|
|
WORK( 2*N ) = CZERO
|
|
WORK( 4*N ) = CTEMP / ABS( CTEMP )
|
|
*
|
|
* Apply the diagonal matrices
|
|
*
|
|
DO 70 JC = 1, N
|
|
DO 60 JR = 1, N
|
|
A( JR, JC ) = WORK( 2*N+JR )*
|
|
$ DCONJG( WORK( 3*N+JC ) )*
|
|
$ A( JR, JC )
|
|
B( JR, JC ) = WORK( 2*N+JR )*
|
|
$ DCONJG( WORK( 3*N+JC ) )*
|
|
$ B( JR, JC )
|
|
60 CONTINUE
|
|
70 CONTINUE
|
|
CALL ZUNM2R( 'L', 'N', N, N, N-1, Q, LDQ, WORK, A,
|
|
$ LDA, WORK( 2*N+1 ), IINFO )
|
|
IF( IINFO.NE.0 )
|
|
$ GO TO 100
|
|
CALL ZUNM2R( 'R', 'C', N, N, N-1, Z, LDQ, WORK( N+1 ),
|
|
$ A, LDA, WORK( 2*N+1 ), IINFO )
|
|
IF( IINFO.NE.0 )
|
|
$ GO TO 100
|
|
CALL ZUNM2R( 'L', 'N', N, N, N-1, Q, LDQ, WORK, B,
|
|
$ LDA, WORK( 2*N+1 ), IINFO )
|
|
IF( IINFO.NE.0 )
|
|
$ GO TO 100
|
|
CALL ZUNM2R( 'R', 'C', N, N, N-1, Z, LDQ, WORK( N+1 ),
|
|
$ B, LDA, WORK( 2*N+1 ), IINFO )
|
|
IF( IINFO.NE.0 )
|
|
$ GO TO 100
|
|
END IF
|
|
ELSE
|
|
*
|
|
* Random matrices
|
|
*
|
|
DO 90 JC = 1, N
|
|
DO 80 JR = 1, N
|
|
A( JR, JC ) = RMAGN( KAMAGN( JTYPE ) )*
|
|
$ ZLARND( 4, ISEED )
|
|
B( JR, JC ) = RMAGN( KBMAGN( JTYPE ) )*
|
|
$ ZLARND( 4, ISEED )
|
|
80 CONTINUE
|
|
90 CONTINUE
|
|
END IF
|
|
*
|
|
100 CONTINUE
|
|
*
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUNIT, FMT = 9999 )'Generator', IINFO, N, JTYPE,
|
|
$ IOLDSD
|
|
INFO = ABS( IINFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
110 CONTINUE
|
|
*
|
|
* Call ZGEGS to compute H, T, Q, Z, alpha, and beta.
|
|
*
|
|
CALL ZLACPY( ' ', N, N, A, LDA, S, LDA )
|
|
CALL ZLACPY( ' ', N, N, B, LDA, T, LDA )
|
|
NTEST = 1
|
|
RESULT( 1 ) = ULPINV
|
|
*
|
|
CALL ZGEGS( 'V', 'V', N, S, LDA, T, LDA, ALPHA1, BETA1, Q,
|
|
$ LDQ, Z, LDQ, WORK, LWORK, RWORK, IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUNIT, FMT = 9999 )'ZGEGS', IINFO, N, JTYPE,
|
|
$ IOLDSD
|
|
INFO = ABS( IINFO )
|
|
GO TO 130
|
|
END IF
|
|
*
|
|
NTEST = 4
|
|
*
|
|
* Do tests 1--4
|
|
*
|
|
CALL ZGET51( 1, N, A, LDA, S, LDA, Q, LDQ, Z, LDQ, WORK,
|
|
$ RWORK, RESULT( 1 ) )
|
|
CALL ZGET51( 1, N, B, LDA, T, LDA, Q, LDQ, Z, LDQ, WORK,
|
|
$ RWORK, RESULT( 2 ) )
|
|
CALL ZGET51( 3, N, B, LDA, T, LDA, Q, LDQ, Q, LDQ, WORK,
|
|
$ RWORK, RESULT( 3 ) )
|
|
CALL ZGET51( 3, N, B, LDA, T, LDA, Z, LDQ, Z, LDQ, WORK,
|
|
$ RWORK, RESULT( 4 ) )
|
|
*
|
|
* Do test 5: compare eigenvalues with diagonals.
|
|
*
|
|
TEMP1 = ZERO
|
|
*
|
|
DO 120 J = 1, N
|
|
TEMP2 = ( ABS1( ALPHA1( J )-S( J, J ) ) /
|
|
$ MAX( SAFMIN, ABS1( ALPHA1( J ) ), ABS1( S( J,
|
|
$ J ) ) )+ABS1( BETA1( J )-T( J, J ) ) /
|
|
$ MAX( SAFMIN, ABS1( BETA1( J ) ), ABS1( T( J,
|
|
$ J ) ) ) ) / ULP
|
|
TEMP1 = MAX( TEMP1, TEMP2 )
|
|
120 CONTINUE
|
|
RESULT( 5 ) = TEMP1
|
|
*
|
|
* Call ZGEGV to compute S2, T2, VL, and VR, do tests.
|
|
*
|
|
* Eigenvalues and Eigenvectors
|
|
*
|
|
CALL ZLACPY( ' ', N, N, A, LDA, S2, LDA )
|
|
CALL ZLACPY( ' ', N, N, B, LDA, T2, LDA )
|
|
NTEST = 6
|
|
RESULT( 6 ) = ULPINV
|
|
*
|
|
CALL ZGEGV( 'V', 'V', N, S2, LDA, T2, LDA, ALPHA2, BETA2,
|
|
$ VL, LDQ, VR, LDQ, WORK, LWORK, RWORK, IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUNIT, FMT = 9999 )'ZGEGV', IINFO, N, JTYPE,
|
|
$ IOLDSD
|
|
INFO = ABS( IINFO )
|
|
GO TO 130
|
|
END IF
|
|
*
|
|
NTEST = 7
|
|
*
|
|
* Do Tests 6 and 7
|
|
*
|
|
CALL ZGET52( .TRUE., N, A, LDA, B, LDA, VL, LDQ, ALPHA2,
|
|
$ BETA2, WORK, RWORK, DUMMA( 1 ) )
|
|
RESULT( 6 ) = DUMMA( 1 )
|
|
IF( DUMMA( 2 ).GT.THRSHN ) THEN
|
|
WRITE( NOUNIT, FMT = 9998 )'Left', 'ZGEGV', DUMMA( 2 ),
|
|
$ N, JTYPE, IOLDSD
|
|
END IF
|
|
*
|
|
CALL ZGET52( .FALSE., N, A, LDA, B, LDA, VR, LDQ, ALPHA2,
|
|
$ BETA2, WORK, RWORK, DUMMA( 1 ) )
|
|
RESULT( 7 ) = DUMMA( 1 )
|
|
IF( DUMMA( 2 ).GT.THRESH ) THEN
|
|
WRITE( NOUNIT, FMT = 9998 )'Right', 'ZGEGV', DUMMA( 2 ),
|
|
$ N, JTYPE, IOLDSD
|
|
END IF
|
|
*
|
|
* End of Loop -- Check for RESULT(j) > THRESH
|
|
*
|
|
130 CONTINUE
|
|
*
|
|
NTESTT = NTESTT + NTEST
|
|
*
|
|
* Print out tests which fail.
|
|
*
|
|
DO 140 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 = 9997 )'ZGG'
|
|
*
|
|
* Matrix types
|
|
*
|
|
WRITE( NOUNIT, FMT = 9996 )
|
|
WRITE( NOUNIT, FMT = 9995 )
|
|
WRITE( NOUNIT, FMT = 9994 )'Unitary'
|
|
*
|
|
* Tests performed
|
|
*
|
|
WRITE( NOUNIT, FMT = 9993 )'unitary', '*',
|
|
$ 'conjugate transpose', ( '*', J = 1, 5 )
|
|
*
|
|
END IF
|
|
NERRS = NERRS + 1
|
|
IF( RESULT( JR ).LT.10000.0D0 ) THEN
|
|
WRITE( NOUNIT, FMT = 9992 )N, JTYPE, IOLDSD, JR,
|
|
$ RESULT( JR )
|
|
ELSE
|
|
WRITE( NOUNIT, FMT = 9991 )N, JTYPE, IOLDSD, JR,
|
|
$ RESULT( JR )
|
|
END IF
|
|
END IF
|
|
140 CONTINUE
|
|
*
|
|
150 CONTINUE
|
|
160 CONTINUE
|
|
*
|
|
* Summary
|
|
*
|
|
CALL ALASVM( 'ZGG', NOUNIT, NERRS, NTESTT, 0 )
|
|
RETURN
|
|
*
|
|
9999 FORMAT( ' ZDRVGG: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
|
|
$ I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
|
|
*
|
|
9998 FORMAT( ' ZDRVGG: ', A, ' Eigenvectors from ', A, ' incorrectly ',
|
|
$ 'normalized.', / ' Bits of error=', 0P, G10.3, ',', 9X,
|
|
$ 'N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5,
|
|
$ ')' )
|
|
*
|
|
9997 FORMAT( / 1X, A3,
|
|
$ ' -- Complex Generalized eigenvalue problem driver' )
|
|
*
|
|
9996 FORMAT( ' Matrix types (see ZDRVGG for details): ' )
|
|
*
|
|
9995 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)' )
|
|
9994 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.' )
|
|
*
|
|
9993 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 )
|
|
9992 FORMAT( ' Matrix order=', I5, ', type=', I2, ', seed=',
|
|
$ 4( I4, ',' ), ' result ', I3, ' is', 0P, F8.2 )
|
|
9991 FORMAT( ' Matrix order=', I5, ', type=', I2, ', seed=',
|
|
$ 4( I4, ',' ), ' result ', I3, ' is', 1P, D10.3 )
|
|
*
|
|
* End of ZDRVGG
|
|
*
|
|
END
|