# sget22.f - Man Page

TESTING/EIG/sget22.f

## Synopsis

### Functions/Subroutines

subroutine sget22 (transa, transe, transw, n, a, lda, e, lde, wr, wi, work, result)
SGET22

## Function/Subroutine Documentation

### subroutine sget22 (character transa, character transe, character transw, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( lde, * ) e, integer lde, real, dimension( * ) wr, real, dimension( * ) wi, real, dimension( * ) work, real, dimension( 2 ) result)

SGET22

Purpose:

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.
Parameters

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 REAL 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 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.

LDE

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

WR

WR is REAL array, dimension (N)

WI

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.

WORK

WORK is REAL array, dimension (N*(N+1))

RESULT

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
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 166 of file sget22.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page sget22(3) is an alias of sget22.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK