dget22.f3

!>
!> DGET22 does an eigenvector check.
!>
!> The basic test is:
!>
!>    RESULT(1) = | A E  -  E W | / ( |A| |E| ulp )
!>
!> using the 1-norm.  It also tests the normalization of E:
!>
!>    RESULT(2) = max | m-norm(E(j)) - 1 | / ( n ulp )
!>                 j
!>
!> where E(j) is the j-th eigenvector, and m-norm is the max-norm of a
!> vector.  If an eigenvector is complex, as determined from WI(j)
!> nonzero, then the max-norm of the vector ( er + i*ei ) is the maximum
!> of
!>    |er(1)| + |ei(1)|, ... , |er(n)| + |ei(n)|
!>
!> W is a block diagonal matrix, with a 1 by 1 block for each real
!> eigenvalue and a 2 by 2 block for each complex conjugate pair.
!> If eigenvalues j and j+1 are a complex conjugate pair, so that
!> WR(j) = WR(j+1) = wr and WI(j) = - WI(j+1) = wi, then the 2 by 2
!> block corresponding to the pair will be:
!>
!>    (  wr  wi  )
!>    ( -wi  wr  )
!>
!> Such a block multiplying an n by 2 matrix ( ur ui ) on the right
!> will be the same as multiplying  ur + i*ui  by  wr + i*wi.
!>
!> To handle various schemes for storage of left eigenvectors, there are
!> options to use A-transpose instead of A, E-transpose instead of E,
!> and/or W-transpose instead of W.
!> 

TRANSA

!>          TRANSA is CHARACTER*1
!>          Specifies whether or not A is transposed.
!>          = 'N':  No transpose
!>          = 'T':  Transpose
!>          = 'C':  Conjugate transpose (= Transpose)
!> 

TRANSE

!>          TRANSE is CHARACTER*1
!>          Specifies whether or not E is transposed.
!>          = 'N':  No transpose, eigenvectors are in columns of E
!>          = 'T':  Transpose, eigenvectors are in rows of E
!>          = 'C':  Conjugate transpose (= Transpose)
!> 

TRANSW

!>          TRANSW is CHARACTER*1
!>          Specifies whether or not W is transposed.
!>          = 'N':  No transpose
!>          = 'T':  Transpose, use -WI(j) instead of WI(j)
!>          = 'C':  Conjugate transpose, use -WI(j) instead of WI(j)
!> 

N

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!> 

A

!>          A is DOUBLE PRECISION array, dimension (LDA,N)
!>          The matrix whose eigenvectors are in E.
!> 

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!> 

E

!>          E is DOUBLE PRECISION array, dimension (LDE,N)
!>          The matrix of eigenvectors. If TRANSE = 'N', the eigenvectors
!>          are stored in the columns of E, if TRANSE = 'T' or 'C', the
!>          eigenvectors are stored in the rows of E.
!> 

LDE

!>          LDE is INTEGER
!>          The leading dimension of the array E.  LDE >= max(1,N).
!> 

WR

!>          WR is DOUBLE PRECISION array, dimension (N)
!> 

WI

!>          WI is DOUBLE PRECISION array, dimension (N)
!>
!>          The real and imaginary parts of the eigenvalues of A.
!>          Purely real eigenvalues are indicated by WI(j) = 0.
!>          Complex conjugate pairs are indicated by WR(j)=WR(j+1) and
!>          WI(j) = - WI(j+1) non-zero; the real part is assumed to be
!>          stored in the j-th row/column and the imaginary part in
!>          the (j+1)-th row/column.
!> 

WORK

!>          WORK is DOUBLE PRECISION array, dimension (N*(N+1))
!> 

RESULT

!>          RESULT is DOUBLE PRECISION array, dimension (2)
!>          RESULT(1) = | A E  -  E W | / ( |A| |E| ulp )
!>          RESULT(2) = max | m-norm(E(j)) - 1 | / ( n ulp )
!>                       j
!> 

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