.TH "TESTING/EIG/zget52.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
TESTING/EIG/zget52.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBzget52\fP (left, n, a, lda, b, ldb, e, \fBlde\fP, alpha, beta, work, rwork, result)"
.br
.RI "\fBZGET52\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine zget52 (logical left, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( \fBlde\fP, * ) e, integer lde, complex*16, dimension( * ) alpha, complex*16, dimension( * ) beta, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, double precision, dimension( 2 ) result)"

.PP
\fBZGET52\fP 
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\fBPurpose:\fP
.RS 4

.PP
.nf
 ZGET52  does an eigenvector check for the generalized eigenvalue
 problem\&.

 The basic test for right eigenvectors is:

                           | b(i) A E(i) -  a(i) B E(i) |
         RESULT(1) = max   -------------------------------
                      i    n ulp max( |b(i) A|, |a(i) B| )

 using the 1-norm\&.  Here, a(i)/b(i) = w is the i-th generalized
 eigenvalue of A - w B, or, equivalently, b(i)/a(i) = m is the i-th
 generalized eigenvalue of m A - B\&.

                         H   H  _      _
 For left eigenvectors, A , B , a, and b  are used\&.

 ZGET52 also tests the normalization of E\&.  Each eigenvector is
 supposed to be normalized so that the maximum 'absolute value'
 of its elements is 1, where in this case, 'absolute value'
 of a complex value x is  |Re(x)| + |Im(x)| ; let us call this
 maximum 'absolute value' norm of a vector v  M(v)\&.
 If a(i)=b(i)=0, then the eigenvector is set to be the jth coordinate
 vector\&. The normalization test is:

         RESULT(2) =      max       | M(v(i)) - 1 | / ( n ulp )
                    eigenvectors v(i)
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fILEFT\fP 
.PP
.nf
          LEFT is LOGICAL
          =\&.TRUE\&.:  The eigenvectors in the columns of E are assumed
                    to be *left* eigenvectors\&.
          =\&.FALSE\&.: The eigenvectors in the columns of E are assumed
                    to be *right* eigenvectors\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The size of the matrices\&.  If it is zero, ZGET52 does
          nothing\&.  It must be at least zero\&.
.fi
.PP
.br
\fIA\fP 
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.nf
          A is COMPLEX*16 array, dimension (LDA, N)
          The matrix A\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of A\&.  It must be at least 1
          and at least N\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is COMPLEX*16 array, dimension (LDB, N)
          The matrix B\&.
.fi
.PP
.br
\fILDB\fP 
.PP
.nf
          LDB is INTEGER
          The leading dimension of B\&.  It must be at least 1
          and at least N\&.
.fi
.PP
.br
\fIE\fP 
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.nf
          E is COMPLEX*16 array, dimension (LDE, N)
          The matrix of eigenvectors\&.  It must be O( 1 )\&.
.fi
.PP
.br
\fILDE\fP 
.PP
.nf
          LDE is INTEGER
          The leading dimension of E\&.  It must be at least 1 and at
          least N\&.
.fi
.PP
.br
\fIALPHA\fP 
.PP
.nf
          ALPHA is COMPLEX*16 array, dimension (N)
          The values a(i) as described above, which, along with b(i),
          define the generalized eigenvalues\&.
.fi
.PP
.br
\fIBETA\fP 
.PP
.nf
          BETA is COMPLEX*16 array, dimension (N)
          The values b(i) as described above, which, along with a(i),
          define the generalized eigenvalues\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is COMPLEX*16 array, dimension (N**2)
.fi
.PP
.br
\fIRWORK\fP 
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.nf
          RWORK is DOUBLE PRECISION array, dimension (N)
.fi
.PP
.br
\fIRESULT\fP 
.PP
.nf
          RESULT is DOUBLE PRECISION array, dimension (2)
          The values computed by the test described above\&.  If A E or
          B E is likely to overflow, then RESULT(1:2) is set to
          10 / ulp\&.
.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 \fB160\fP of file \fBzget52\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.