.TH "TESTING/EIG/dget22.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
TESTING/EIG/dget22.f
.SH SYNOPSIS
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.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBdget22\fP (transa, transe, transw, n, a, lda, e, \fBlde\fP, wr, wi, work, result)"
.br
.RI "\fBDGET22\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine dget22 (character transa, character transe, character transw, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( \fBlde\fP, * ) e, integer lde, double precision, dimension( * ) wr, double precision, dimension( * ) wi, double precision, dimension( * ) work, double precision, dimension( 2 ) result)"

.PP
\fBDGET22\fP 
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\fBPurpose:\fP
.RS 4

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.nf
!>
!> 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\&.
!> 
.fi
.PP
 
.RE
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\fBParameters\fP
.RS 4
\fITRANSA\fP 
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!>          TRANSA is CHARACTER*1
!>          Specifies whether or not A is transposed\&.
!>          = 'N':  No transpose
!>          = 'T':  Transpose
!>          = 'C':  Conjugate transpose (= Transpose)
!> 
.fi
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.br
\fITRANSE\fP 
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.nf
!>          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)
!> 
.fi
.PP
.br
\fITRANSW\fP 
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.nf
!>          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)
!> 
.fi
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.br
\fIN\fP 
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!>          N is INTEGER
!>          The order of the matrix A\&.  N >= 0\&.
!> 
.fi
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\fIA\fP 
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!>          A is DOUBLE PRECISION array, dimension (LDA,N)
!>          The matrix whose eigenvectors are in E\&.
!> 
.fi
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\fILDA\fP 
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!>          LDA is INTEGER
!>          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
!> 
.fi
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\fIE\fP 
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!>          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\&.
!> 
.fi
.PP
.br
\fILDE\fP 
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!>          LDE is INTEGER
!>          The leading dimension of the array E\&.  LDE >= max(1,N)\&.
!> 
.fi
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\fIWR\fP 
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!>          WR is DOUBLE PRECISION array, dimension (N)
!> 
.fi
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\fIWI\fP 
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!>          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\&.
!> 
.fi
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\fIWORK\fP 
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!>          WORK is DOUBLE PRECISION array, dimension (N*(N+1))
!> 
.fi
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\fIRESULT\fP 
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!>          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
!> 
.fi
.PP
 
.RE
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\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

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Univ\&. of California Berkeley 

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Univ\&. of Colorado Denver 

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NAG Ltd\&. 
.RE
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Definition at line \fB166\fP of file \fBdget22\&.f\fP\&.
.SH "Author"
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Generated automatically by Doxygen for LAPACK from the source code\&.