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initial docs for balance()

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conrad
2025-04-09 16:57:20 +10:00
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@@ -8630,20 +8630,67 @@ See also:
<div class="pagebreak"></div><div class="noprint"><hr class="greyline"><br></div>
<a name="balance"></a>
<b>TODO: balance</b>
<b>B = balance( A )</b>
<br><b>B = balance( A, opt )</b>
<br>
<br><b>balance( B, A )</b>
<br><b>balance( B, A, opt )</b>
<br>
<br><b>balance( D, P, B, A )</b>
<br><b>balance( D, P, B, A, opt )</b>
<ul>
<li>
...
Create a transformed version of square-sized matrix <i>A</i> so that its row and column norms are roughly the same
</li>
<br>
<li>
...
The scaling details are optionally provided in vector <i>D</i>
</li>
<br>
<li>
The permutation details are optionally provided in vector <i>P</i>, which must have the type <a href="#Col">uvec</a>
</li>
<br>
<li>The <i>opt</i> argument is optional and specifies the transformation; it is one of:
<ul>
<table>
<tbody>
<tr><td style="text-align: right;"><code>"scale"</code></td><td>&nbsp;=&nbsp;</td><td>apply only scaling</td></tr>
<tr><td style="text-align: right;"><code>"permute"</code></td><td>&nbsp;=&nbsp;</td><td>apply only permutation</td></tr>
<tr><td style="text-align: right;"><code>"both"</code></td><td>&nbsp;=&nbsp;</td><td>apply both scaling and permutation (default setting)</td></tr>
</tbody>
</table>
</ul>
</li>
<br>
<li>
If matrix <i>A</i> is not square sized, a <i>std::logic_error</i> exception is thrown
</li>
<br>
<li>If the decomposition fails:
<ul>
<li><i>B = balance(A)</i> resets <i>B</i> and throws a <i>std::runtime_error</i> exception</li>
<li><i>balance(B,A)</i> resets <i>B</i> and returns a bool set to <i>false</i> (exception is not thrown)</li>
<li><i>balance(D,P,B,A)</i> resets <i>D</i>, <i>P</i>, <i>B</i>, and returns a bool set to <i>false</i> (exception is not thrown)</li>
</ul>
</li>
<br>
<li>
Examples:
<ul>
<pre>
mat A = { { 1 0.01 0.0001 },
{ 100 1 0.01 },
{ 10000 100 1 } };
mat B = balance(A);
vec D;
uvec P;
mat BB;
balance(D, P, BB, A);
</pre>
</ul>
</li>
@@ -8651,8 +8698,8 @@ Examples:
<li>
See also:
<ul>
<li><a href="#norm">norm()</a></li>
<li><a href="#vecnorm">vecnorm()</a></li>
<li><a href="#normalise">normalise()</a></li>
<li><a href="#eig_gen">eig_gen()</a></li>
</ul>
</li>
@@ -10719,6 +10766,7 @@ See also:
<ul>
<li><a href="#norm">norm()</a></li>
<li><a href="#vecnorm">vecnorm()</a></li>
<li><a href="#balance">balance()</a></li>
<li><a href="#dot">norm_dot()</a></li>
<li><a href="https://mathworld.wolfram.com/NormalizedVector.html">Normalised vector in MathWorld</a>
<li><a href="https://en.wikipedia.org/wiki/Unit_vector">Unit vector in Wikipedia</a>
@@ -12186,6 +12234,7 @@ See also:
<ul>
<li><a href="#norm">norm()</a></li>
<li><a href="#normalise">normalise()</a></li>
<li><a href="#balance">balance()</a></li>
<li><a href="https://en.wikipedia.org/wiki/Norm_(mathematics)">vector norm in Wikipedia</a></li>
<li><a href="https://mathworld.wolfram.com/VectorNorm.html">vector norm in MathWorld</a></li>
</ul>
@@ -20160,6 +20209,7 @@ List of additions and changes for each version:
<li>Version 14.6:
<ul>
<li>(under development)</li>
<li>added <a href="#balance">balance()</a> for producing balanced matrices where column and row norms are roughly the same</li>
<li>...</li>
</ul>
</li>