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

.in +1c
.ti -1c
.RI "subroutine \fBzebchvxx\fP (thresh, path)"
.br
.RI "\fBZEBCHVXX\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine zebchvxx (double precision thresh, character*3 path)"

.PP
\fBZEBCHVXX\fP \fBPurpose:\fP 
.PP
.nf
  ZEBCHVXX will run Z**SVXX on a series of Hilbert matrices and then
  compare the error bounds returned by Z**SVXX to see if the returned
  answer indeed falls within those bounds\&.

  Eight test ratios will be computed\&.  The tests will pass if they are \&.LT\&.
  THRESH\&.  There are two cases that are determined by 1 / (SQRT( N ) * EPS)\&.
  If that value is \&.LE\&. to the component wise reciprocal condition number,
  it uses the guaranteed case, other wise it uses the unguaranteed case\&.

  Test ratios:
     Let Xc be X_computed and Xt be X_truth\&.
     The norm used is the infinity norm\&.

     Let A be the guaranteed case and B be the unguaranteed case\&.

       1\&. Normwise guaranteed forward error bound\&.
       A: norm ( abs( Xc - Xt ) / norm ( Xt ) \&.LE\&. ERRBND( *, nwise_i, bnd_i ) and
          ERRBND( *, nwise_i, bnd_i ) \&.LE\&. MAX(SQRT(N),10) * EPS\&.
          If these conditions are met, the test ratio is set to be
          ERRBND( *, nwise_i, bnd_i ) / MAX(SQRT(N), 10)\&.  Otherwise it is 1/EPS\&.
       B: For this case, CGESVXX should just return 1\&.  If it is less than
          one, treat it the same as in 1A\&.  Otherwise it fails\&. (Set test
          ratio to ERRBND( *, nwise_i, bnd_i ) * THRESH?)

       2\&. Componentwise guaranteed forward error bound\&.
       A: norm ( abs( Xc(j) - Xt(j) ) ) / norm (Xt(j)) \&.LE\&. ERRBND( *, cwise_i, bnd_i )
          for all j \&.AND\&. ERRBND( *, cwise_i, bnd_i ) \&.LE\&. MAX(SQRT(N), 10) * EPS\&.
          If these conditions are met, the test ratio is set to be
          ERRBND( *, cwise_i, bnd_i ) / MAX(SQRT(N), 10)\&.  Otherwise it is 1/EPS\&.
       B: Same as normwise test ratio\&.

       3\&. Backwards error\&.
       A: The test ratio is set to BERR/EPS\&.
       B: Same test ratio\&.

       4\&. Reciprocal condition number\&.
       A: A condition number is computed with Xt and compared with the one
          returned from CGESVXX\&.  Let RCONDc be the RCOND returned by CGESVXX
          and RCONDt be the RCOND from the truth value\&.  Test ratio is set to
          MAX(RCONDc/RCONDt, RCONDt/RCONDc)\&.
       B: Test ratio is set to 1 / (EPS * RCONDc)\&.

       5\&. Reciprocal normwise condition number\&.
       A: The test ratio is set to
          MAX(ERRBND( *, nwise_i, cond_i ) / NCOND, NCOND / ERRBND( *, nwise_i, cond_i ))\&.
       B: Test ratio is set to 1 / (EPS * ERRBND( *, nwise_i, cond_i ))\&.

       6\&. Reciprocal componentwise condition number\&.
       A: Test ratio is set to
          MAX(ERRBND( *, cwise_i, cond_i ) / CCOND, CCOND / ERRBND( *, cwise_i, cond_i ))\&.
       B: Test ratio is set to 1 / (EPS * ERRBND( *, cwise_i, cond_i ))\&.

     \&.\&. Parameters \&.\&.
     NMAX is determined by the largest number in the inverse of the hilbert
     matrix\&.  Precision is exhausted when the largest entry in it is greater
     than 2 to the power of the number of bits in the fraction of the data
     type used plus one, which is 24 for single precision\&.
     NMAX should be 6 for single and 11 for double\&.
.fi
.PP
 
.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 \fB95\fP of file \fBzebchvxx\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.