zget22.f - Man Page

TESTING/EIG/zget22.f

Synopsis

Functions/Subroutines

subroutine zget22 (transa, transe, transw, n, a, lda, e, lde, w, work, rwork, result)
ZGET22

Function/Subroutine Documentation

subroutine zget22 (character transa, character transe, character transw, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( lde, * ) e, integer lde, complex*16, dimension( * ) w, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, double precision, dimension( 2 ) result)

ZGET22

Purpose:

 ZGET22 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*16 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*16 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*16 array, dimension (N)
          The eigenvalues of A.

WORK

          WORK is COMPLEX*16 array, dimension (N*N)

RWORK

          RWORK is DOUBLE PRECISION array, dimension (N)

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
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 142 of file zget22.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

The man page zget22(3) is an alias of zget22.f(3).

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