<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
<meta http-equiv="X-UA-Compatible" content="IE=9"/>
<title>Lighthouse: lapack/dsprfs.f File Reference</title>
<link href="tabs.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="jquery.js"></script>
<script type="text/javascript" src="dynsections.js"></script>
<link href="tabs.css" rel="stylesheet" type="text/css" />
<link href="doxygen.css" rel="stylesheet" type="text/css"/>
</head>
<body>
<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
<!--<div id="titlearea">
</div>-->
<!-- end header part -->
<!-- Generated by Doxygen 1.8.9.1 -->
<div id="nav-path" class="navpath">
  <ul>
<li class="navelem"><a class="el" href="dir_42b7da8b2ebcfce3aea4b69198a0a9ad.html">lapack</a></li>  </ul>
</div>
</div><!-- top -->
<div class="header">
  <div class="summary">
<a href="#func-members">Functions/Subroutines</a>  </div>
  <div class="headertitle">
<div class="title">dsprfs.f File Reference</div>  </div>
</div><!--header-->
<div class="contents">
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
Functions/Subroutines</h2></td></tr>
<tr class="memitem:a494f27878d5670ad2570185062b96fc7"><td class="memItemLeft" align="right" valign="top">subroutine&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="dsprfs_8f.html#a494f27878d5670ad2570185062b96fc7">dsprfs</a> (UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO)</td></tr>
<tr class="memdesc:a494f27878d5670ad2570185062b96fc7"><td class="mdescLeft">&#160;</td><td class="mdescRight"><b>DSPRFS</b>  <a href="#a494f27878d5670ad2570185062b96fc7">More...</a><br /></td></tr>
<tr class="separator:a494f27878d5670ad2570185062b96fc7"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table>
<h2 class="groupheader">Function/Subroutine Documentation</h2>
<a class="anchor" id="a494f27878d5670ad2570185062b96fc7"></a>
<div class="memitem">
<div class="memproto">
      <table class="memname">
        <tr>
          <td class="memname">subroutine dsprfs </td>
          <td>(</td>
          <td class="paramtype">character&#160;</td>
          <td class="paramname"><em>UPLO</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">integer&#160;</td>
          <td class="paramname"><em>N</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">integer&#160;</td>
          <td class="paramname"><em>NRHS</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">double precision, dimension( * )&#160;</td>
          <td class="paramname"><em>AP</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">double precision, dimension( * )&#160;</td>
          <td class="paramname"><em>AFP</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">integer, dimension( * )&#160;</td>
          <td class="paramname"><em>IPIV</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">double precision, dimension( ldb, * )&#160;</td>
          <td class="paramname"><em>B</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">integer&#160;</td>
          <td class="paramname"><em>LDB</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">double precision, dimension( ldx, * )&#160;</td>
          <td class="paramname"><em>X</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">integer&#160;</td>
          <td class="paramname"><em>LDX</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">double precision, dimension( * )&#160;</td>
          <td class="paramname"><em>FERR</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">double precision, dimension( * )&#160;</td>
          <td class="paramname"><em>BERR</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">double precision, dimension( * )&#160;</td>
          <td class="paramname"><em>WORK</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">integer, dimension( * )&#160;</td>
          <td class="paramname"><em>IWORK</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">integer&#160;</td>
          <td class="paramname"><em>INFO</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p><b>DSPRFS</b> </p>
<p> 
 Download DSPRFS + dependencies 
 <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsprfs.f"> 
 [TGZ]</a> 
 <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsprfs.f"> 
 [ZIP]</a> 
 <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsprfs.f"> 
 [TXT]</a>
  </p><dl class="section user"><dt>Purpose: </dt><dd><pre class="fragment"> DSPRFS improves the computed solution to a system of linear
 equations when the coefficient matrix is symmetric indefinite
 and packed, and provides error bounds and backward error estimates
 for the solution.</pre> </dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramdir">[in]</td><td class="paramname">UPLO</td><td><pre class="fragment">          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored.</pre></td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">N</td><td><pre class="fragment">          N is INTEGER
          The order of the matrix A.  N &gt;= 0.</pre></td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">NRHS</td><td><pre class="fragment">          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices B and X.  NRHS &gt;= 0.</pre></td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">AP</td><td><pre class="fragment">          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
          The upper or lower triangle of the symmetric matrix A, packed
          columnwise in a linear array.  The j-th column of A is stored
          in the array AP as follows:
          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1&lt;=i&lt;=j;
          if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j&lt;=i&lt;=n.</pre></td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">AFP</td><td><pre class="fragment">          AFP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
          The factored form of the matrix A.  AFP contains the block
          diagonal matrix D and the multipliers used to obtain the
          factor U or L from the factorization A = U*D*U**T or
          A = L*D*L**T as computed by DSPTRF, stored as a packed
          triangular matrix.</pre></td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">IPIV</td><td><pre class="fragment">          IPIV is INTEGER array, dimension (N)
          Details of the interchanges and the block structure of D
          as determined by DSPTRF.</pre></td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">B</td><td><pre class="fragment">          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          The right hand side matrix B.</pre></td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">LDB</td><td><pre class="fragment">          LDB is INTEGER
          The leading dimension of the array B.  LDB &gt;= max(1,N).</pre></td></tr>
    <tr><td class="paramdir">[in,out]</td><td class="paramname">X</td><td><pre class="fragment">          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
          On entry, the solution matrix X, as computed by DSPTRS.
          On exit, the improved solution matrix X.</pre></td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">LDX</td><td><pre class="fragment">          LDX is INTEGER
          The leading dimension of the array X.  LDX &gt;= max(1,N).</pre></td></tr>
    <tr><td class="paramdir">[out]</td><td class="paramname">FERR</td><td><pre class="fragment">          FERR is DOUBLE PRECISION array, dimension (NRHS)
          The estimated forward error bound for each solution vector
          X(j) (the j-th column of the solution matrix X).
          If XTRUE is the true solution corresponding to X(j), FERR(j)
          is an estimated upper bound for the magnitude of the largest
          element in (X(j) - XTRUE) divided by the magnitude of the
          largest element in X(j).  The estimate is as reliable as
          the estimate for RCOND, and is almost always a slight
          overestimate of the true error.</pre></td></tr>
    <tr><td class="paramdir">[out]</td><td class="paramname">BERR</td><td><pre class="fragment">          BERR is DOUBLE PRECISION array, dimension (NRHS)
          The componentwise relative backward error of each solution
          vector X(j) (i.e., the smallest relative change in
          any element of A or B that makes X(j) an exact solution).</pre></td></tr>
    <tr><td class="paramdir">[out]</td><td class="paramname">WORK</td><td><pre class="fragment">          WORK is DOUBLE PRECISION array, dimension (3*N)</pre></td></tr>
    <tr><td class="paramdir">[out]</td><td class="paramname">IWORK</td><td><pre class="fragment">          IWORK is INTEGER array, dimension (N)</pre></td></tr>
    <tr><td class="paramdir">[out]</td><td class="paramname">INFO</td><td><pre class="fragment">          INFO is INTEGER
          = 0:  successful exit
          &lt; 0:  if INFO = -i, the i-th argument had an illegal value</pre> </td></tr>
  </table>
  </dd>
</dl>
<dl class="section user"><dt>Internal Parameters: </dt><dd><pre class="fragment">  ITMAX is the maximum number of steps of iterative refinement.</pre> </dd></dl>
<dl class="section author"><dt>Author</dt><dd>Univ. of Tennessee </dd>
<dd>
Univ. of California Berkeley </dd>
<dd>
Univ. of Colorado Denver </dd>
<dd>
NAG Ltd. </dd></dl>
<dl class="section date"><dt>Date</dt><dd>November 2011 </dd></dl>

</div>
</div>
</div><!-- contents -->
<!-- start footer part -->
<hr class="footer"/><address class="footer"><small>
Generated on Wed Apr 1 2015 16:27:43 for Lighthouse by &#160;<a href="http://www.doxygen.org/index.html">
<img class="footer" src="doxygen.png" alt="doxygen"/>
</a> 1.8.9.1
</small></address>
</body>
</html>
