.TH "TESTING/EIG/sget22.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
TESTING/EIG/sget22.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBsget22\fP (transa, transe, transw, n, a, lda, e, \fBlde\fP, wr, wi, work, result)"
.br
.RI "\fBSGET22\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine sget22 (character transa, character transe, character transw, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( \fBlde\fP, * ) e, integer lde, real, dimension( * ) wr, real, dimension( * ) wi, real, dimension( * ) work, real, dimension( 2 ) result)"

.PP
\fBSGET22\fP 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 SGET22 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
.PP
\fBParameters\fP
.RS 4
\fITRANSA\fP 
.PP
.nf
          TRANSA is CHARACTER*1
          Specifies whether or not A is transposed\&.
          = 'N':  No transpose
          = 'T':  Transpose
          = 'C':  Conjugate transpose (= Transpose)
.fi
.PP
.br
\fITRANSE\fP 
.PP
.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 
.PP
.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
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is REAL array, dimension (LDA,N)
          The matrix whose eigenvectors are in E\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
.fi
.PP
.br
\fIE\fP 
.PP
.nf
          E is REAL 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 
.PP
.nf
          LDE is INTEGER
          The leading dimension of the array E\&.  LDE >= max(1,N)\&.
.fi
.PP
.br
\fIWR\fP 
.PP
.nf
          WR is REAL array, dimension (N)
.fi
.PP
.br
\fIWI\fP 
.PP
.nf
          WI is REAL 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
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is REAL array, dimension (N*(N+1))
.fi
.PP
.br
\fIRESULT\fP 
.PP
.nf
          RESULT is REAL 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
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB166\fP of file \fBsget22\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.