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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
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<h1 class="refname">slicot_mb02md</h1>
<hr/>
<h3>Solution of Total Least-Squares problem using a SVD approach.</h3>
<hr/>
<h3>Syntax</h3>
<hr/>
<table summary="syntax" style="width:50%">
<tr>
<td>[RANK_OUT, C_OUT, S, X, IWARN, INFO] = slicot_mb02md(JOB, M, N, L, RANK_IN, C_IN, TOL)</td>
</tr>
</table>
<h3>Input argument</h3>
<hr/>
<dl>
<dt><span class="term">JOB</span></dt>
<dd>
<p class="para">Determines whether the values of the parameters RANK and TOL are to be specified by the user or computed by the routine as follows: = 'R': Compute RANK only; = 'T': Compute TOL only; = 'B': Compute both RANK and TOL; = 'N': Compute neither RANK nor TOL.</p>
</dd>
<dt><span class="term">M</span></dt>
<dd>
<p class="para">The number of rows in the data matrix A and the observation matrix B.</p>
</dd>
<dt><span class="term">N</span></dt>
<dd>
<p class="para">The number of columns in the data matrix A.</p>
</dd>
<dt><span class="term">L</span></dt>
<dd>
<p class="para">The number of columns in the observation matrix B.</p>
</dd>
<dt><span class="term">RANK_IN</span></dt>
<dd>
<p class="para">if JOB = 'T' or JOB = 'N', then RANK must specify r, the rank of the TLS approximation [A + DA | B + DB].</p>
</dd>
<dt><span class="term">C_IN</span></dt>
<dd>
<p class="para">the leading M-by-(N+L) part of this array must contain the matrices A and B.</p>
</dd>
<dt><span class="term">TOL</span></dt>
<dd>
<p class="para">A tolerance used to determine the rank of the TLS approximation [A+DA|B+DB] and to check the multiplicity of the singular values of matrix C.</p>
</dd>
</dl>
<h3>Output argument</h3>
<hr/>
<dl>
<dt><span class="term">RANK_OUT</span></dt>
<dd>
<p class="para">if JOB = 'R' or JOB = 'B', and INFO = 0, then RANK contains the computed (effective) rank of the TLS approximation [A + DA | B + DB].</p>
</dd>
<dt><span class="term">C_OUT</span></dt>
<dd>
<p class="para">the leading (N+L)-by-(N+L) part of this array contains the (transformed) right singular vectors, including null space vectors, if any, of C = [A | B].</p>
</dd>
<dt><span class="term">S</span></dt>
<dd>
<p class="para">If INFO = 0, the singular values of matrix C</p>
</dd>
<dt><span class="term">X</span></dt>
<dd>
<p class="para">If INFO = 0, the leading N-by-L part of this array contains the solution X to the TLS problem specified by A and B.</p>
</dd>
<dt><span class="term">IWARN</span></dt>
<dd>
<p class="para">= 0: no warnings; = 1: if the rank of matrix C has been lowered because a singular value of multiplicity greater than 1 was found; = 2: if the rank of matrix C has been lowered because the upper triangular matrix F is (numerically) singular.</p>
</dd>
<dt><span class="term">INFO</span></dt>
<dd>
<p class="para">= 0: successful exit;</p>
</dd>
</dl>
<h3>Description</h3>
<hr/>
<p></p>
<p>To solve the Total Least Squares (TLS) problem using a Singular Value Decomposition (SVD) approach. The TLS problem assumes an overdetermined set of linear equations AX = B, where both the data matrix A as well as the observation matrix B are inaccurate. The routine also solves determined and underdetermined sets of equations by computing the minimum norm solution. It is assumed that all preprocessing measures (scaling, coordinate transformations, whitening, ... ) of the data have been performed in advance.</p>
<h3>Used function(s)</h3>
<hr/>
MB02MD
<h3>Bibliography</h3>
<hr/>
http://slicot.org/objects/software/shared/doc/MB02MD.html
<h3>Example</h3>
<hr/>
<pre>
<code class = "nelson">M = 6;
N = 3;
L = 1;
JOB = 'B';
TOL = 0.0;
RANK_IN = 1;
C_IN = [0.80010 0.39985 0.60005 0.89999;
0.29996 0.69990 0.39997 0.82997;
0.49994 0.60003 0.20012 0.79011;
0.90013 0.20016 0.79995 0.85002;
0.39998 0.80006 0.49985 0.99016;
0.20002 0.90007 0.70009 1.02994];
[RANK_OUT, C_OUT, S, X, IWARN, INFO] = slicot_mb02md(JOB, M, N, L, RANK_IN, C_IN, TOL)
</code>
</pre>
<h3>History</h3>
<hr/>
<table summary = "history" style="width:50%">
<tr>
<th>Version</th>
<th>Description</th>
</tr>
<tr>
<td>1.0.0</td>
<td>initial version</td>
</tr>
</table>
<h3>Author</h3>
<hr/>
<p>SLICOT Documentation</p>
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