# cget22.f - Man Page

TESTING/EIG/cget22.f

## Synopsis

### Functions/Subroutines

subroutine cget22 (transa, transe, transw, n, a, lda, e, lde, w, work, rwork, result)
CGET22

## Function/Subroutine Documentation

### subroutine cget22 (character transa, character transe, character transw, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( lde, * ) e, integer lde, complex, dimension( * ) w, complex, dimension( * ) work, real, dimension( * ) rwork, real, dimension( 2 ) result)

CGET22

Purpose:

``` CGET22 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.  The max-norm of a complex n-vector x in this case is the
maximum of |re(x(i)| + |im(x(i)| over i = 1, ..., n.```
Parameters

TRANSA

```          TRANSA is CHARACTER*1
Specifies whether or not A is transposed.
= 'N':  No transpose
= 'T':  Transpose
= 'C':  Conjugate 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, eigenvectors are in rows of E```

TRANSW

```          TRANSW is CHARACTER*1
Specifies whether or not W is transposed.
= 'N':  No transpose
= 'T':  Transpose, same as TRANSW = 'N'
= '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 COMPLEX 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 COMPLEX 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).```

W

```          W is COMPLEX array, dimension (N)
The eigenvalues of A.```

WORK

`          WORK is COMPLEX array, dimension (N*N)`

RWORK

`          RWORK is REAL array, dimension (N)`

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

NAG Ltd.

Definition at line 142 of file cget22.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page cget22(3) is an alias of cget22.f(3).

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