TESTING/EIG/sget22.f(3)    Library Functions Manual    TESTING/EIG/sget22.f(3)

NAME
       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.

LAPACK                          Version 3.12.0         TESTING/EIG/sget22.f(3)