.TH "TESTING/EIG/sget53.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
TESTING/EIG/sget53.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBsget53\fP (a, lda, b, ldb, scale, wr, wi, result, info)"
.br
.RI "\fBSGET53\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine sget53 (real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real scale, real wr, real wi, real result, integer info)"

.PP
\fBSGET53\fP 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 SGET53  checks the generalized eigenvalues computed by SLAG2\&.

 The basic test for an eigenvalue is:

                              | det( s A - w B ) |
     RESULT =  ---------------------------------------------------
               ulp max( s norm(A), |w| norm(B) )*norm( s A - w B )

 Two 'safety checks' are performed:

 (1)  ulp*max( s*norm(A), |w|*norm(B) )  must be at least
      safe_minimum\&.  This insures that the test performed is
      not essentially  det(0*A + 0*B)=0\&.

 (2)  s*norm(A) + |w|*norm(B) must be less than 1/safe_minimum\&.
      This insures that  s*A - w*B  will not overflow\&.

 If these tests are not passed, then  s  and  w  are scaled and
 tested anyway, if this is possible\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIA\fP 
.PP
.nf
          A is REAL array, dimension (LDA, 2)
          The 2x2 matrix A\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of A\&.  It must be at least 2\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is REAL array, dimension (LDB, N)
          The 2x2 upper-triangular matrix B\&.
.fi
.PP
.br
\fILDB\fP 
.PP
.nf
          LDB is INTEGER
          The leading dimension of B\&.  It must be at least 2\&.
.fi
.PP
.br
\fISCALE\fP 
.PP
.nf
          SCALE is REAL
          The 'scale factor' s in the formula  s A - w B \&.  It is
          assumed to be non-negative\&.
.fi
.PP
.br
\fIWR\fP 
.PP
.nf
          WR is REAL
          The real part of the eigenvalue  w  in the formula
          s A - w B \&.
.fi
.PP
.br
\fIWI\fP 
.PP
.nf
          WI is REAL
          The imaginary part of the eigenvalue  w  in the formula
          s A - w B \&.
.fi
.PP
.br
\fIRESULT\fP 
.PP
.nf
          RESULT is REAL
          If INFO is 2 or less, the value computed by the test
             described above\&.
          If INFO=3, this will just be 1/ulp\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          =0:  The input data pass the 'safety checks'\&.
          =1:  s*norm(A) + |w|*norm(B) > 1/safe_minimum\&.
          =2:  ulp*max( s*norm(A), |w|*norm(B) ) < safe_minimum
          =3:  same as INFO=2, but  s  and  w  could not be scaled so
               as to compute the test\&.
.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 \fB125\fP of file \fBsget53\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.