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Math.NET Numerics: 5.0.0-alpha01 docs update

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Christoph Ruegg 5 years ago
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c33e6c39f5
14 changed files with 358 additions and 191 deletions
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  1. 10
      Build.html
  2. 72
      DescriptiveStatistics.html
  3. 19
      Generate.html
  4. 111
      IFsharpNotebook.html
  5. 18
      LinearEquations.html
  6. 15
      MKL.html
  7. 66
      Matrix.html
  8. 130
      Probability.html
  9. 67
      Random.html
  10. 4
      Regression.html
  11. 2
      ReleaseNotes-MKL.html
  12. 2
      ReleaseNotes-OpenBLAS.html
  13. 22
      ReleaseNotes.html
  14. 11
      index.html

10
Build.html
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@ -104,14 +104,14 @@ is <em>not</em> required when using Visual Studio or the .NET Core SDK directly.
<span class="l">13: </span>
<span class="l">14: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="o">.</span><span class="o">/</span><span class="i">build</span><span class="o">.</span><span class="i">sh</span> # <span class="i">normal</span> <span class="i">build</span> <span class="k">and</span> <span class="i">unit</span> <span class="i">tests</span>, <span class="k">when</span> <span class="i">using</span> <span class="i">bash</span> <span class="i">shell</span> <span class="i">on</span> <span class="i">Windows</span> <span class="k">or</span> <span class="i">Linux</span><span class="o">.</span>
<span class="i">build</span><span class="o">.</span><span class="i">cmd</span> # <span class="i">normal</span> <span class="i">build</span> <span class="k">and</span> <span class="i">unit</span> <span class="i">tests</span>, <span class="k">when</span> <span class="i">using</span> <span class="i">Windows</span> <span class="i">CMD</span> <span class="i">shell</span><span class="o">.</span>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="o">.</span><span class="o">/</span><span class="i">build</span><span class="o">.</span><span class="i">sh</span> # <span class="i">normal</span> <span class="i">build</span> <span class="k">and</span> <span onmouseout="hideTip(event, 'fs1', 1)" onmouseover="showTip(event, 'fs1', 1)" class="i">unit</span> <span class="i">tests</span>, <span class="k">when</span> <span onmouseout="hideTip(event, 'fs2', 2)" onmouseover="showTip(event, 'fs2', 2)" class="i">using</span> <span class="i">bash</span> <span class="i">shell</span> <span class="i">on</span> <span class="i">Windows</span> <span class="k">or</span> <span class="i">Linux</span><span class="o">.</span>
<span class="i">build</span><span class="o">.</span><span class="i">cmd</span> # <span class="i">normal</span> <span class="i">build</span> <span class="k">and</span> <span onmouseout="hideTip(event, 'fs1', 3)" onmouseover="showTip(event, 'fs1', 3)" class="i">unit</span> <span class="i">tests</span>, <span class="k">when</span> <span onmouseout="hideTip(event, 'fs2', 4)" onmouseover="showTip(event, 'fs2', 4)" class="i">using</span> <span class="i">Windows</span> <span class="i">CMD</span> <span class="i">shell</span><span class="o">.</span>
<span class="o">.</span><span class="o">/</span><span class="i">build</span><span class="o">.</span><span class="i">sh</span> <span class="i">build</span> # <span class="i">normal</span> <span class="i">build</span>
<span class="o">.</span><span class="o">/</span><span class="i">build</span><span class="o">.</span><span class="i">sh</span> <span class="i">build</span> <span class="i">strongname</span> # <span class="i">normal</span> <span class="i">build</span> <span class="k">and</span> <span class="i">also</span> <span class="i">build</span> <span class="i">strong</span><span class="o">-</span><span class="i">named</span> <span class="i">variant</span>
<span class="o">.</span><span class="o">/</span><span class="i">build</span><span class="o">.</span><span class="i">sh</span> <span class="i">test</span> # <span class="i">normal</span> <span class="i">build</span>, <span class="i">run</span> <span class="i">unit</span> <span class="i">tests</span>
<span class="o">.</span><span class="o">/</span><span class="i">build</span><span class="o">.</span><span class="i">sh</span> <span class="i">test</span> <span class="i">quick</span> # <span class="i">normal</span> <span class="i">build</span>, <span class="i">run</span> <span class="i">unit</span> <span class="i">tests</span> <span class="i">except</span> <span class="i">long</span> <span class="i">running</span> <span class="i">ones</span>
<span class="o">.</span><span class="o">/</span><span class="i">build</span><span class="o">.</span><span class="i">sh</span> <span class="i">test</span> # <span class="i">normal</span> <span class="i">build</span>, <span class="i">run</span> <span onmouseout="hideTip(event, 'fs1', 5)" onmouseover="showTip(event, 'fs1', 5)" class="i">unit</span> <span class="i">tests</span>
<span class="o">.</span><span class="o">/</span><span class="i">build</span><span class="o">.</span><span class="i">sh</span> <span class="i">test</span> <span class="i">quick</span> # <span class="i">normal</span> <span class="i">build</span>, <span class="i">run</span> <span onmouseout="hideTip(event, 'fs1', 6)" onmouseover="showTip(event, 'fs1', 6)" class="i">unit</span> <span class="i">tests</span> <span class="i">except</span> <span class="i">long</span> <span class="i">running</span> <span class="i">ones</span>
<span class="o">.</span><span class="o">/</span><span class="i">build</span><span class="o">.</span><span class="i">sh</span> <span class="i">clean</span> # <span class="i">cleanup</span> <span class="i">build</span> <span class="i">artifacts</span>
<span class="o">.</span><span class="o">/</span><span class="i">build</span><span class="o">.</span><span class="i">sh</span> <span class="i">docs</span> # <span class="i">generate</span> <span class="i">documentation</span>
@ -273,6 +273,8 @@ this is also what the unit tests do when you run the <code>MklTest</code> build
</li>
</ul>
<div class="tip" id="fs1">type unit = Unit<br /><br />Full name: Microsoft.FSharp.Core.unit</div>
<div class="tip" id="fs2">val using : resource:&#39;T -&gt; action:(&#39;T -&gt; &#39;U) -&gt; &#39;U (requires &#39;T :&gt; System.IDisposable)<br /><br />Full name: Microsoft.FSharp.Core.Operators.using</div>
</div>
<div class="span3">

72
DescriptiveStatistics.html
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@ -148,13 +148,13 @@ The mean is affected by outliers, so if you need a more robust estimate consider
<span class="l">7: </span>
<span class="l">8: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="k">let</span> <span class="i">whiteNoise</span> <span class="o">=</span> <span class="i">Generate</span><span class="o">.</span><span class="i">Normal</span>(<span class="n">1000</span>, <span class="i">mean</span><span class="o">=</span><span class="n">10.0</span>, <span class="i">standardDeviation</span><span class="o">=</span><span class="n">2.0</span>)
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="k">let</span> <span onmouseout="hideTip(event, 'fs1', 1)" onmouseover="showTip(event, 'fs1', 1)" class="i">whiteNoise</span> <span class="o">=</span> <span class="i">Generate</span><span class="o">.</span><span class="i">Normal</span>(<span class="n">1000</span>, <span class="i">mean</span><span class="o">=</span><span class="n">10.0</span>, <span class="i">standardDeviation</span><span class="o">=</span><span class="n">2.0</span>)
<span class="fsi">val samples : float [] = [|12.90021939; 9.631515037; 7.810008046; 14.13301053; ...|] </span>
<span class="i">Statistics</span><span class="o">.</span><span class="i">Mean</span> <span class="i">whiteNoise</span>
<span class="i">Statistics</span><span class="o">.</span><span class="i">Mean</span> <span onmouseout="hideTip(event, 'fs1', 2)" onmouseover="showTip(event, 'fs1', 2)" class="i">whiteNoise</span>
<span class="fsi">val it : float = 10.02162347</span>
<span class="k">let</span> <span class="i">wave</span> <span class="o">=</span> <span class="i">Generate</span><span class="o">.</span><span class="i">Sinusoidal</span>(<span class="n">1000</span>, <span class="i">samplingRate</span><span class="o">=</span><span class="n">100.</span>, <span class="i">frequency</span><span class="o">=</span><span class="n">5.</span>, <span class="i">amplitude</span><span class="o">=</span><span class="n">0.5</span>)
<span class="i">Statistics</span><span class="o">.</span><span class="i">Mean</span> <span class="i">wave</span>
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs2', 3)" onmouseover="showTip(event, 'fs2', 3)" class="i">wave</span> <span class="o">=</span> <span class="i">Generate</span><span class="o">.</span><span class="i">Sinusoidal</span>(<span class="n">1000</span>, <span class="i">samplingRate</span><span class="o">=</span><span class="n">100.</span>, <span class="i">frequency</span><span class="o">=</span><span class="n">5.</span>, <span class="i">amplitude</span><span class="o">=</span><span class="n">0.5</span>)
<span class="i">Statistics</span><span class="o">.</span><span class="i">Mean</span> <span onmouseout="hideTip(event, 'fs2', 4)" onmouseover="showTip(event, 'fs2', 4)" class="i">wave</span>
<span class="fsi">val it : float = -4.133520783e-17</span>
</code></pre></td>
</tr>
@ -180,12 +180,12 @@ Bessel's correction with an <span class="math">\(N-1\)</span> normalizer to a sa
<span class="l">6: </span>
<span class="l">7: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="i">Statistics</span><span class="o">.</span><span class="i">Variance</span> <span class="i">whiteNoise</span>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="i">Statistics</span><span class="o">.</span><span class="i">Variance</span> <span onmouseout="hideTip(event, 'fs1', 5)" onmouseover="showTip(event, 'fs1', 5)" class="i">whiteNoise</span>
<span class="fsi">val it : float = 3.819436094</span>
<span class="i">Statistics</span><span class="o">.</span><span class="i">StandardDeviation</span> <span class="i">whiteNoise</span>
<span class="i">Statistics</span><span class="o">.</span><span class="i">StandardDeviation</span> <span onmouseout="hideTip(event, 'fs1', 6)" onmouseover="showTip(event, 'fs1', 6)" class="i">whiteNoise</span>
<span class="fsi">val it : float = 1.954337764</span>
<span class="i">Statistics</span><span class="o">.</span><span class="i">Variance</span> <span class="i">wave</span>
<span class="i">Statistics</span><span class="o">.</span><span class="i">Variance</span> <span onmouseout="hideTip(event, 'fs2', 7)" onmouseover="showTip(event, 'fs2', 7)" class="i">wave</span>
<span class="fsi">val it : float = 0.1251251251</span>
</code></pre></td>
</tr>
@ -199,7 +199,7 @@ that evaluate both in a single pass:</p>
<table class="pre"><tr><td class="lines"><pre class="fssnip"><span class="l">1: </span>
<span class="l">2: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="i">Statistics</span><span class="o">.</span><span class="i">MeanVariance</span> <span class="i">whiteNoise</span>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="i">Statistics</span><span class="o">.</span><span class="i">MeanVariance</span> <span onmouseout="hideTip(event, 'fs1', 8)" onmouseover="showTip(event, 'fs1', 8)" class="i">whiteNoise</span>
<span class="fsi">val it : float * float = (10.02162347, 3.819436094)</span>
</code></pre></td>
</tr>
@ -217,9 +217,9 @@ apply Bessel's correction to bias in case of sample data.</p>
<span class="l">3: </span>
<span class="l">4: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="i">Statistics</span><span class="o">.</span><span class="i">Covariance</span>(<span class="i">whiteNoise</span>, <span class="i">whiteNoise</span>)
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="i">Statistics</span><span class="o">.</span><span class="i">Covariance</span>(<span onmouseout="hideTip(event, 'fs1', 9)" onmouseover="showTip(event, 'fs1', 9)" class="i">whiteNoise</span>, <span onmouseout="hideTip(event, 'fs1', 10)" onmouseover="showTip(event, 'fs1', 10)" class="i">whiteNoise</span>)
<span class="fsi">val it : float = 3.819436094</span>
<span class="i">Statistics</span><span class="o">.</span><span class="i">Covariance</span>(<span class="i">whiteNoise</span>, <span class="i">wave</span>)
<span class="i">Statistics</span><span class="o">.</span><span class="i">Covariance</span>(<span onmouseout="hideTip(event, 'fs1', 11)" onmouseover="showTip(event, 'fs1', 11)" class="i">whiteNoise</span>, <span onmouseout="hideTip(event, 'fs2', 12)" onmouseover="showTip(event, 'fs2', 12)" class="i">wave</span>)
<span class="fsi">val it : float = 0.04397985084</span>
</code></pre></td>
</tr>
@ -257,17 +257,17 @@ and also the rest of the library.</p>
<span class="l">11: </span>
<span class="l">12: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="i">Statistics</span><span class="o">.</span><span class="i">OrderStatistic</span>(<span class="i">whiteNoise</span>, <span class="n">1</span>)
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="i">Statistics</span><span class="o">.</span><span class="i">OrderStatistic</span>(<span onmouseout="hideTip(event, 'fs1', 13)" onmouseover="showTip(event, 'fs1', 13)" class="i">whiteNoise</span>, <span class="n">1</span>)
<span class="fsi">val it : float = 3.633070184</span>
<span class="i">Statistics</span><span class="o">.</span><span class="i">OrderStatistic</span>(<span class="i">whiteNoise</span>, <span class="n">1000</span>)
<span class="i">Statistics</span><span class="o">.</span><span class="i">OrderStatistic</span>(<span onmouseout="hideTip(event, 'fs1', 14)" onmouseover="showTip(event, 'fs1', 14)" class="i">whiteNoise</span>, <span class="n">1000</span>)
<span class="fsi">val it : float = 16.65183566</span>
<span class="k">let</span> <span class="i">os</span> <span class="o">=</span> <span class="i">Statistics</span><span class="o">.</span><span class="i">orderStatisticFunc</span> <span class="i">whiteNoise</span>
<span class="i">os</span> <span class="n">250</span>
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs3', 15)" onmouseover="showTip(event, 'fs3', 15)" class="f">os</span> <span class="o">=</span> <span class="i">Statistics</span><span class="o">.</span><span class="i">orderStatisticFunc</span> <span onmouseout="hideTip(event, 'fs1', 16)" onmouseover="showTip(event, 'fs1', 16)" class="i">whiteNoise</span>
<span onmouseout="hideTip(event, 'fs3', 17)" onmouseover="showTip(event, 'fs3', 17)" class="f">os</span> <span class="n">250</span>
<span class="fsi">val it : float = 8.645491746</span>
<span class="i">os</span> <span class="n">500</span>
<span onmouseout="hideTip(event, 'fs3', 18)" onmouseover="showTip(event, 'fs3', 18)" class="f">os</span> <span class="n">500</span>
<span class="fsi">val it : float = 10.11872428</span>
<span class="i">os</span> <span class="n">750</span>
<span onmouseout="hideTip(event, 'fs3', 19)" onmouseover="showTip(event, 'fs3', 19)" class="f">os</span> <span class="n">750</span>
<span class="fsi">val it : float = 11.33170746</span>
</code></pre></td>
</tr>
@ -288,9 +288,9 @@ median-unbiased regardless of the sample distribution. If you need another conve
<span class="l">3: </span>
<span class="l">4: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="i">Statistics</span><span class="o">.</span><span class="i">Median</span> <span class="i">whiteNoise</span>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="i">Statistics</span><span class="o">.</span><span class="i">Median</span> <span onmouseout="hideTip(event, 'fs1', 20)" onmouseover="showTip(event, 'fs1', 20)" class="i">whiteNoise</span>
<span class="fsi">val it : float = 10.11872428</span>
<span class="i">Statistics</span><span class="o">.</span><span class="i">Median</span> <span class="i">wave</span>
<span class="i">Statistics</span><span class="o">.</span><span class="i">Median</span> <span onmouseout="hideTip(event, 'fs2', 21)" onmouseover="showTip(event, 'fs2', 21)" class="i">wave</span>
<span class="fsi">val it : float = -2.452600839e-16</span>
</code></pre></td>
</tr>
@ -312,9 +312,9 @@ estimates the median as discussed above.</p>
<span class="l">3: </span>
<span class="l">4: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="i">Statistics</span><span class="o">.</span><span class="i">LowerQuartile</span> <span class="i">whiteNoise</span>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="i">Statistics</span><span class="o">.</span><span class="i">LowerQuartile</span> <span onmouseout="hideTip(event, 'fs1', 22)" onmouseover="showTip(event, 'fs1', 22)" class="i">whiteNoise</span>
<span class="fsi">val it : float = 8.645491746</span>
<span class="i">Statistics</span><span class="o">.</span><span class="i">UpperQuartile</span> <span class="i">whiteNoise</span>
<span class="i">Statistics</span><span class="o">.</span><span class="i">UpperQuartile</span> <span onmouseout="hideTip(event, 'fs1', 23)" onmouseover="showTip(event, 'fs1', 23)" class="i">whiteNoise</span>
<span class="fsi">val it : float = 11.33213732</span>
</code></pre></td>
</tr>
@ -330,9 +330,9 @@ the maximum value. All these values can be visualized in the popular box plot di
<span class="l">3: </span>
<span class="l">4: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="i">Statistics</span><span class="o">.</span><span class="i">FiveNumberSummary</span> <span class="i">whiteNoise</span>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="i">Statistics</span><span class="o">.</span><span class="i">FiveNumberSummary</span> <span onmouseout="hideTip(event, 'fs1', 24)" onmouseover="showTip(event, 'fs1', 24)" class="i">whiteNoise</span>
<span class="fsi">val it : float [] = [|3.633070184; 8.645937823; 10.12165054; 11.33213732; 16.65183566|] </span>
<span class="i">Statistics</span><span class="o">.</span><span class="i">FiveNumberSummary</span> <span class="i">wave</span>
<span class="i">Statistics</span><span class="o">.</span><span class="i">FiveNumberSummary</span> <span onmouseout="hideTip(event, 'fs2', 25)" onmouseover="showTip(event, 'fs2', 25)" class="i">wave</span>
<span class="fsi">val it : float [] = [|-0.5; -0.3584185509; -2.452600839e-16; 0.3584185509; 0.5|] </span>
</code></pre></td>
</tr>
@ -346,7 +346,7 @@ and is a robust indicator of spread. In box plots the IQR is the total height of
<table class="pre"><tr><td class="lines"><pre class="fssnip"><span class="l">1: </span>
<span class="l">2: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="i">Statistics</span><span class="o">.</span><span class="i">InterquartileRange</span> <span class="i">whiteNoise</span>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="i">Statistics</span><span class="o">.</span><span class="i">InterquartileRange</span> <span onmouseout="hideTip(event, 'fs1', 26)" onmouseover="showTip(event, 'fs1', 26)" class="i">whiteNoise</span>
<span class="fsi">val it : float = 2.686199498</span>
</code></pre></td>
</tr>
@ -366,9 +366,9 @@ The 0-percentile represents the minimum value, 25 the first quartile, 50 the med
<span class="l">3: </span>
<span class="l">4: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="i">Statistics</span><span class="o">.</span><span class="i">Percentile</span>(<span class="i">whiteNoise</span>, <span class="n">5</span>)
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="i">Statistics</span><span class="o">.</span><span class="i">Percentile</span>(<span onmouseout="hideTip(event, 'fs1', 27)" onmouseover="showTip(event, 'fs1', 27)" class="i">whiteNoise</span>, <span class="n">5</span>)
<span class="fsi">val it : float = 6.693373507</span>
<span class="i">Statistics</span><span class="o">.</span><span class="i">Percentile</span>(<span class="i">whiteNoise</span>, <span class="n">98</span>)
<span class="i">Statistics</span><span class="o">.</span><span class="i">Percentile</span>(<span onmouseout="hideTip(event, 'fs1', 28)" onmouseover="showTip(event, 'fs1', 28)" class="i">whiteNoise</span>, <span class="n">98</span>)
<span class="fsi">val it : float = 13.97580653</span>
</code></pre></td>
</tr>
@ -385,7 +385,7 @@ the inverse cumulative distribution function of the sample distribution.</p>
<table class="pre"><tr><td class="lines"><pre class="fssnip"><span class="l">1: </span>
<span class="l">2: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="i">Statistics</span><span class="o">.</span><span class="i">Quantile</span>(<span class="i">whiteNoise</span>, <span class="n">0.98</span>)
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="i">Statistics</span><span class="o">.</span><span class="i">Quantile</span>(<span onmouseout="hideTip(event, 'fs1', 29)" onmouseover="showTip(event, 'fs1', 29)" class="i">whiteNoise</span>, <span class="n">0.98</span>)
<span class="fsi">val it : float = 13.97580653</span>
</code></pre></td>
</tr>
@ -447,7 +447,7 @@ Similar to <code>QuantileDefinition</code>, the <code>RankDefinition</code> enum
<span class="l">5: </span>
<span class="l">6: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="i">Statistics</span><span class="o">.</span><span class="i">Ranks</span>(<span class="i">whiteNoise</span>)
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="i">Statistics</span><span class="o">.</span><span class="i">Ranks</span>(<span onmouseout="hideTip(event, 'fs1', 30)" onmouseover="showTip(event, 'fs1', 30)" class="i">whiteNoise</span>)
<span class="fsi">val it : float [] = [|634.0; 736.0; 405.0; 395.0; 197.0; 167.0; 722.0; 44.0; ...|] </span>
<span class="i">Statistics</span><span class="o">.</span><span class="i">Ranks</span>([| <span class="n">13.0</span>; <span class="n">14.0</span>; <span class="n">11.0</span>; <span class="n">12.0</span>; <span class="n">13.0</span> |], <span class="i">RankDefinition</span><span class="o">.</span><span class="i">Average</span>)
<span class="fsi">val it : float [] = [|3.5; 5.0; 1.0; 2.0; 3.5|] </span>
@ -468,9 +468,9 @@ function crosses <span class="math">\(\tau\)</span>.</p>
<span class="l">3: </span>
<span class="l">4: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="i">Statistics</span><span class="o">.</span><span class="i">QuantileRank</span>(<span class="i">whiteNoise</span>, <span class="n">13.0</span>)
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="i">Statistics</span><span class="o">.</span><span class="i">QuantileRank</span>(<span onmouseout="hideTip(event, 'fs1', 31)" onmouseover="showTip(event, 'fs1', 31)" class="i">whiteNoise</span>, <span class="n">13.0</span>)
<span class="fsi">val it : float = 0.9370045563</span>
<span class="i">Statistics</span><span class="o">.</span><span class="i">QuantileRank</span>(<span class="i">whiteNoise</span>, <span class="n">6.7</span>, <span class="i">RankDefinition</span><span class="o">.</span><span class="i">Average</span>)
<span class="i">Statistics</span><span class="o">.</span><span class="i">QuantileRank</span>(<span onmouseout="hideTip(event, 'fs1', 32)" onmouseover="showTip(event, 'fs1', 32)" class="i">whiteNoise</span>, <span class="n">6.7</span>, <span class="i">RankDefinition</span><span class="o">.</span><span class="i">Average</span>)
<span class="fsi">val it : float = 0.04960610389</span>
</code></pre></td>
</tr>
@ -495,14 +495,14 @@ function crosses <span class="math">\(\tau\)</span>.</p>
<span class="l">12: </span>
<span class="l">13: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="k">let</span> <span class="i">ecdf</span> <span class="o">=</span> <span class="i">Statistics</span><span class="o">.</span><span class="i">EmpiricalCDFFunc</span> <span class="i">whiteNoise</span>
<span class="i">Generate</span><span class="o">.</span><span class="i">LinearSpacedMap</span>(<span class="n">20</span>, <span class="i">start</span><span class="o">=</span><span class="n">3.0</span>, <span class="i">stop</span><span class="o">=</span><span class="n">17.0</span>, <span class="i">map</span><span class="o">=</span><span class="i">ecdf</span>)
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="k">let</span> <span onmouseout="hideTip(event, 'fs4', 33)" onmouseover="showTip(event, 'fs4', 33)" class="i">ecdf</span> <span class="o">=</span> <span class="i">Statistics</span><span class="o">.</span><span class="i">EmpiricalCDFFunc</span> <span onmouseout="hideTip(event, 'fs1', 34)" onmouseover="showTip(event, 'fs1', 34)" class="i">whiteNoise</span>
<span class="i">Generate</span><span class="o">.</span><span class="i">LinearSpacedMap</span>(<span class="n">20</span>, <span class="i">start</span><span class="o">=</span><span class="n">3.0</span>, <span class="i">stop</span><span class="o">=</span><span class="n">17.0</span>, <span class="i">map</span><span class="o">=</span><span onmouseout="hideTip(event, 'fs4', 35)" onmouseover="showTip(event, 'fs4', 35)" class="i">ecdf</span>)
<span class="fsi">val it : float [] =</span>
<span class="fsi"> [|0.0; 0.001; 0.002; 0.005; 0.022; 0.05; 0.094; 0.172; 0.278; 0.423; 0.555; </span>
<span class="fsi"> 0.705; 0.843; 0.921; 0.944; 0.983; 0.992; 0.997; 0.999; 1.0|] </span>
<span class="k">let</span> <span class="i">eicdf</span> <span class="o">=</span> <span class="i">Statistics</span><span class="o">.</span><span class="i">empiricalInvCDFFunc</span> <span class="i">whiteNoise</span>
[ <span class="k">for</span> <span class="i">tau</span> <span class="k">in</span> <span class="n">0.0</span><span class="o">..</span><span class="n">0.05</span><span class="o">..</span><span class="n">1.0</span> <span class="k">-&gt;</span> <span class="i">eicdf</span> <span class="i">tau</span> ]
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs5', 36)" onmouseover="showTip(event, 'fs5', 36)" class="f">eicdf</span> <span class="o">=</span> <span class="i">Statistics</span><span class="o">.</span><span class="i">empiricalInvCDFFunc</span> <span onmouseout="hideTip(event, 'fs1', 37)" onmouseover="showTip(event, 'fs1', 37)" class="i">whiteNoise</span>
[ <span class="k">for</span> <span onmouseout="hideTip(event, 'fs6', 38)" onmouseover="showTip(event, 'fs6', 38)" class="i">tau</span> <span class="k">in</span> <span class="n">0.0</span><span class="o">..</span><span class="n">0.05</span><span class="o">..</span><span class="n">1.0</span> <span class="k">-&gt;</span> <span onmouseout="hideTip(event, 'fs5', 39)" onmouseover="showTip(event, 'fs5', 39)" class="f">eicdf</span> <span onmouseout="hideTip(event, 'fs6', 40)" onmouseover="showTip(event, 'fs6', 40)" class="i">tau</span> ]
<span class="fsi">val it : float [] =</span>
<span class="fsi"> [3.633070184; 6.682142043; 7.520000817; 8.040513497; 8.347587493; </span>
<span class="fsi"> 8.645491746; 9.02681611; 9.298987151; 9.522627142; 9.819352699; 10.11872428; </span>
@ -534,6 +534,12 @@ correlation coefficient, as well as their correlation matrix for a set of vector
<span class="k">double</span> correlation <span class="o">=</span> Correlation.Pearson(dataF, dataG);
</code></pre></td></tr></table>
<div class="tip" id="fs1">val whiteNoise : obj<br /><br />Full name: DescriptiveStatistics.whiteNoise</div>
<div class="tip" id="fs2">val wave : obj<br /><br />Full name: DescriptiveStatistics.wave</div>
<div class="tip" id="fs3">val os : (int -&gt; obj)<br /><br />Full name: DescriptiveStatistics.os</div>
<div class="tip" id="fs4">val ecdf : obj<br /><br />Full name: DescriptiveStatistics.ecdf</div>
<div class="tip" id="fs5">val eicdf : (float -&gt; obj)<br /><br />Full name: DescriptiveStatistics.eicdf</div>
<div class="tip" id="fs6">val tau : float</div>
</div>
<div class="span3">

19
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@ -77,7 +77,7 @@ single colon <code>:</code> and double colon <code>::</code> operators in MATLAB
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp">[ <span class="n">10.0</span> <span class="o">..</span> <span class="n">2.0</span> <span class="o">..</span> <span class="n">15.0</span> ]
<span class="fsi">val it : float list = [10.0; 12.0; 14.0] </span>
[ <span class="k">for</span> <span class="i">x</span> <span class="k">in</span> <span class="n">10.0</span> <span class="o">..</span> <span class="n">2.0</span> <span class="o">..</span> <span class="n">15.0</span> <span class="k">-&gt;</span> <span class="i">sin</span> <span class="i">x</span> ]
[ <span class="k">for</span> <span onmouseout="hideTip(event, 'fs1', 1)" onmouseover="showTip(event, 'fs1', 1)" class="i">x</span> <span class="k">in</span> <span class="n">10.0</span> <span class="o">..</span> <span class="n">2.0</span> <span class="o">..</span> <span class="n">15.0</span> <span class="k">-&gt;</span> <span onmouseout="hideTip(event, 'fs2', 2)" onmouseover="showTip(event, 'fs2', 2)" class="f">sin</span> <span onmouseout="hideTip(event, 'fs1', 3)" onmouseover="showTip(event, 'fs1', 3)" class="i">x</span> ]
<span class="fsi">val it : float list = [-0.5440211109; -0.536572918; 0.9906073557] </span>
</code></pre></td>
</tr>
@ -111,7 +111,7 @@ Generate.LinearSpacedMap(<span class="n">15</span>, <span class="n">0.0</span>,
<span class="l">4: </span>
<span class="l">5: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="i">Generate</span><span class="o">.</span><span class="i">linearSpacedMap</span> <span class="n">15</span> <span class="n">0.0</span> <span class="i">Math</span><span class="o">.</span><span class="i">PI</span> <span class="i">sin</span>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="i">Generate</span><span class="o">.</span><span class="i">linearSpacedMap</span> <span class="n">15</span> <span class="n">0.0</span> <span class="i">Math</span><span class="o">.</span><span class="i">PI</span> <span onmouseout="hideTip(event, 'fs2', 4)" onmouseover="showTip(event, 'fs2', 4)" class="i">sin</span>
<span class="fsi">val it : float [] = </span>
<span class="fsi"> [|0.0; 0.222520934; 0.4338837391; 0.6234898019; 0.7818314825; 0.9009688679; </span>
<span class="fsi"> 0.9749279122; 1.0; 0.9749279122; 0.9009688679; 0.7818314825; 0.6234898019; </span>
@ -245,7 +245,7 @@ Generate.Map(a, x <span class="o">=</span><span class="o">&gt;</span> x <span cl
<table class="pre"><tr><td class="lines"><pre class="fssnip"><span class="l">1: </span>
<span class="l">2: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="i">Array</span><span class="o">.</span><span class="i">map</span> ((<span class="o">+</span>) <span class="n">1.0</span>) <span class="i">a</span>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span onmouseout="hideTip(event, 'fs3', 5)" onmouseover="showTip(event, 'fs3', 5)" class="t">Array</span><span class="o">.</span><span onmouseout="hideTip(event, 'fs4', 6)" onmouseover="showTip(event, 'fs4', 6)" class="f">map</span> ((<span class="o">+</span>) <span class="n">1.0</span>) <span onmouseout="hideTip(event, 'fs5', 7)" onmouseover="showTip(event, 'fs5', 7)" class="i">a</span>
<span class="fsi">val it : float [] = [|3.0; 5.0; 4.0; 7.0|] </span>
</code></pre></td>
</tr>
@ -261,8 +261,8 @@ You can use LINQ, but that operates on sequences instead of arrays:</p>
<span class="l">2: </span>
<span class="l">3: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="k">let</span> <span class="i">b</span> <span class="o">=</span> [| <span class="n">1.0</span>; <span class="o">-</span><span class="n">1.0</span>; <span class="n">2.0</span>; <span class="o">-</span><span class="n">2.0</span> |]
<span class="i">Generate</span><span class="o">.</span><span class="i">Map2</span>(<span class="i">a</span>, <span class="i">b</span>, <span class="k">fun</span> <span class="i">x</span> <span class="i">y</span> <span class="k">-&gt;</span> <span class="i">x</span> <span class="o">+</span> <span class="i">y</span>)
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="k">let</span> <span onmouseout="hideTip(event, 'fs6', 8)" onmouseover="showTip(event, 'fs6', 8)" class="i">b</span> <span class="o">=</span> [| <span class="n">1.0</span>; <span class="o">-</span><span class="n">1.0</span>; <span class="n">2.0</span>; <span class="o">-</span><span class="n">2.0</span> |]
<span class="i">Generate</span><span class="o">.</span><span class="i">Map2</span>(<span onmouseout="hideTip(event, 'fs5', 9)" onmouseover="showTip(event, 'fs5', 9)" class="i">a</span>, <span onmouseout="hideTip(event, 'fs6', 10)" onmouseover="showTip(event, 'fs6', 10)" class="i">b</span>, <span class="k">fun</span> <span class="i">x</span> <span class="i">y</span> <span class="k">-&gt;</span> <span class="i">x</span> <span class="o">+</span> <span class="i">y</span>)
<span class="fsi">val it : float [] = [|3.0; 3.0; 5.0; 4.0|] </span>
</code></pre></td>
</tr>
@ -271,7 +271,7 @@ You can use LINQ, but that operates on sequences instead of arrays:</p>
<table class="pre"><tr><td class="lines"><pre class="fssnip"><span class="l">1: </span>
<span class="l">2: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="i">Array</span><span class="o">.</span><span class="i">map2</span> (<span class="o">+</span>) <span class="i">a</span> <span class="i">b</span>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span onmouseout="hideTip(event, 'fs3', 11)" onmouseover="showTip(event, 'fs3', 11)" class="t">Array</span><span class="o">.</span><span onmouseout="hideTip(event, 'fs7', 12)" onmouseover="showTip(event, 'fs7', 12)" class="f">map2</span> (<span class="o">+</span>) <span onmouseout="hideTip(event, 'fs5', 13)" onmouseover="showTip(event, 'fs5', 13)" class="i">a</span> <span onmouseout="hideTip(event, 'fs6', 14)" onmouseover="showTip(event, 'fs6', 14)" class="i">b</span>
<span class="fsi">val it : float [] = [|3.0; 3.0; 5.0; 4.0|] </span>
</code></pre></td>
</tr>
@ -282,6 +282,13 @@ You can use LINQ, but that operates on sequences instead of arrays:</p>
<td class="snippet"><pre class="fssnip highlighted"><code lang="csharp">a.Zip(b, (x, y) <span class="o">=</span><span class="o">&gt;</span> x <span class="o">+</span> y).ToArray();
</code></pre></td></tr></table>
<div class="tip" id="fs1">val x : float</div>
<div class="tip" id="fs2">val sin : value:&#39;T -&gt; &#39;T (requires member Sin)<br /><br />Full name: Microsoft.FSharp.Core.Operators.sin</div>
<div class="tip" id="fs3">module Array<br /><br />from Microsoft.FSharp.Collections</div>
<div class="tip" id="fs4">val map : mapping:(&#39;T -&gt; &#39;U) -&gt; array:&#39;T [] -&gt; &#39;U []<br /><br />Full name: Microsoft.FSharp.Collections.Array.map</div>
<div class="tip" id="fs5">val a : float []<br /><br />Full name: Generate.a</div>
<div class="tip" id="fs6">val b : float []<br /><br />Full name: Generate.b</div>
<div class="tip" id="fs7">val map2 : mapping:(&#39;T1 -&gt; &#39;T2 -&gt; &#39;U) -&gt; array1:&#39;T1 [] -&gt; array2:&#39;T2 [] -&gt; &#39;U []<br /><br />Full name: Microsoft.FSharp.Collections.Array.map2</div>
</div>
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@ -129,54 +129,85 @@ Unfortunately loading this script requires the exact version in the path - if yo
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="k">open</span> <span class="i">MathNet</span><span class="o">.</span><span class="i">Numerics</span><span class="o">.</span><span class="i">LinearAlgebra</span>
<span class="k">let</span> <span class="k">inline</span> (|<span class="i">Float</span>|_|) (<span class="i">v</span><span class="o">:</span><span class="i">obj</span>) <span class="o">=</span>
<span class="k">if</span> <span class="i">v</span> <span class="o">:?</span> <span class="i">float</span> <span class="k">then</span> <span class="i">Some</span>(<span class="i">v</span> <span class="o">:?&gt;</span> <span class="i">float</span>) <span class="k">else</span> <span class="i">None</span>
<span class="k">let</span> <span class="k">inline</span> (|<span class="i">Float32</span>|_|) (<span class="i">v</span><span class="o">:</span><span class="i">obj</span>) <span class="o">=</span>
<span class="k">if</span> <span class="i">v</span> <span class="o">:?</span> <span class="i">float32</span> <span class="k">then</span> <span class="i">Some</span>(<span class="i">v</span> <span class="o">:?&gt;</span> <span class="i">float32</span>) <span class="k">else</span> <span class="i">None</span>
<span class="k">let</span> <span class="k">inline</span> (|<span class="i">PositiveInfinity</span>|_|) (<span class="i">v</span><span class="o">:</span> <span class="o">^</span><span class="i">T</span>) <span class="o">=</span>
<span class="k">if</span> (<span class="o">^</span><span class="i">T</span> <span class="o">:</span> (<span class="k">static</span> <span class="k">member</span> <span class="i">IsPositiveInfinity</span><span class="o">:</span> <span class="o">&#39;</span><span class="i">T</span> <span class="k">-&gt;</span> <span class="i">bool</span>) (<span class="i">v</span>))
<span class="k">then</span> <span class="i">Some</span> <span class="i">PositiveInfinity</span> <span class="k">else</span> <span class="i">None</span>
<span class="k">let</span> <span class="k">inline</span> (|<span class="i">NegativeInfinity</span>|_|) (<span class="i">v</span><span class="o">:</span> <span class="o">^</span><span class="i">T</span>) <span class="o">=</span>
<span class="k">if</span> (<span class="o">^</span><span class="i">T</span> <span class="o">:</span> (<span class="k">static</span> <span class="k">member</span> <span class="i">IsNegativeInfinity</span><span class="o">:</span> <span class="o">&#39;</span><span class="i">T</span> <span class="k">-&gt;</span> <span class="i">bool</span>) (<span class="i">v</span>))
<span class="k">then</span> <span class="i">Some</span> <span class="i">NegativeInfinity</span> <span class="k">else</span> <span class="i">None</span>
<span class="k">let</span> <span class="k">inline</span> (|<span class="i">NaN</span>|_|) (<span class="i">v</span><span class="o">:</span> <span class="o">^</span><span class="i">T</span>) <span class="o">=</span>
<span class="k">if</span> (<span class="o">^</span><span class="i">T</span> <span class="o">:</span> (<span class="k">static</span> <span class="k">member</span> <span class="i">IsNaN</span><span class="o">:</span> <span class="o">&#39;</span><span class="i">T</span> <span class="k">-&gt;</span> <span class="i">bool</span>) (<span class="i">v</span>))
<span class="k">then</span> <span class="i">Some</span> <span class="i">NaN</span> <span class="k">else</span> <span class="i">None</span>
<span class="k">let</span> <span class="k">inline</span> (|<span class="p">Float</span>|_|) (<span onmouseout="hideTip(event, 'fs1', 1)" onmouseover="showTip(event, 'fs1', 1)" class="i">v</span><span class="o">:</span><span onmouseout="hideTip(event, 'fs2', 2)" onmouseover="showTip(event, 'fs2', 2)" class="t">obj</span>) <span class="o">=</span>
<span class="k">if</span> <span onmouseout="hideTip(event, 'fs1', 3)" onmouseover="showTip(event, 'fs1', 3)" class="i">v</span> <span class="o">:?</span> <span onmouseout="hideTip(event, 'fs3', 4)" onmouseover="showTip(event, 'fs3', 4)" class="t">float</span> <span class="k">then</span> <span onmouseout="hideTip(event, 'fs4', 5)" onmouseover="showTip(event, 'fs4', 5)" class="p">Some</span>(<span onmouseout="hideTip(event, 'fs1', 6)" onmouseover="showTip(event, 'fs1', 6)" class="i">v</span> <span class="o">:?&gt;</span> <span onmouseout="hideTip(event, 'fs3', 7)" onmouseover="showTip(event, 'fs3', 7)" class="t">float</span>) <span class="k">else</span> <span onmouseout="hideTip(event, 'fs5', 8)" onmouseover="showTip(event, 'fs5', 8)" class="p">None</span>
<span class="k">let</span> <span class="k">inline</span> (|<span class="p">Float32</span>|_|) (<span onmouseout="hideTip(event, 'fs1', 9)" onmouseover="showTip(event, 'fs1', 9)" class="i">v</span><span class="o">:</span><span onmouseout="hideTip(event, 'fs2', 10)" onmouseover="showTip(event, 'fs2', 10)" class="t">obj</span>) <span class="o">=</span>
<span class="k">if</span> <span onmouseout="hideTip(event, 'fs1', 11)" onmouseover="showTip(event, 'fs1', 11)" class="i">v</span> <span class="o">:?</span> <span onmouseout="hideTip(event, 'fs6', 12)" onmouseover="showTip(event, 'fs6', 12)" class="t">float32</span> <span class="k">then</span> <span onmouseout="hideTip(event, 'fs4', 13)" onmouseover="showTip(event, 'fs4', 13)" class="p">Some</span>(<span onmouseout="hideTip(event, 'fs1', 14)" onmouseover="showTip(event, 'fs1', 14)" class="i">v</span> <span class="o">:?&gt;</span> <span onmouseout="hideTip(event, 'fs6', 15)" onmouseover="showTip(event, 'fs6', 15)" class="t">float32</span>) <span class="k">else</span> <span onmouseout="hideTip(event, 'fs5', 16)" onmouseover="showTip(event, 'fs5', 16)" class="p">None</span>
<span class="k">let</span> <span class="k">inline</span> (|<span class="p">PositiveInfinity</span>|_|) (<span onmouseout="hideTip(event, 'fs7', 17)" onmouseover="showTip(event, 'fs7', 17)" class="i">v</span><span class="o">:</span> <span class="o">^</span><span class="i">T</span>) <span class="o">=</span>
<span class="k">if</span> (<span class="o">^</span><span class="i">T</span> <span class="o">:</span> (<span class="k">static</span> <span class="k">member</span> <span class="i">IsPositiveInfinity</span><span class="o">:</span> <span class="o">&#39;</span><span class="i">T</span> <span class="k">-&gt;</span> <span onmouseout="hideTip(event, 'fs8', 18)" onmouseover="showTip(event, 'fs8', 18)" class="t">bool</span>) (<span onmouseout="hideTip(event, 'fs7', 19)" onmouseover="showTip(event, 'fs7', 19)" class="i">v</span>))
<span class="k">then</span> <span onmouseout="hideTip(event, 'fs4', 20)" onmouseover="showTip(event, 'fs4', 20)" class="p">Some</span> <span class="p">PositiveInfinity</span> <span class="k">else</span> <span onmouseout="hideTip(event, 'fs5', 21)" onmouseover="showTip(event, 'fs5', 21)" class="p">None</span>
<span class="k">let</span> <span class="k">inline</span> (|<span class="p">NegativeInfinity</span>|_|) (<span onmouseout="hideTip(event, 'fs9', 22)" onmouseover="showTip(event, 'fs9', 22)" class="i">v</span><span class="o">:</span> <span class="o">^</span><span class="i">T</span>) <span class="o">=</span>
<span class="k">if</span> (<span class="o">^</span><span class="i">T</span> <span class="o">:</span> (<span class="k">static</span> <span class="k">member</span> <span class="i">IsNegativeInfinity</span><span class="o">:</span> <span class="o">&#39;</span><span class="i">T</span> <span class="k">-&gt;</span> <span onmouseout="hideTip(event, 'fs8', 23)" onmouseover="showTip(event, 'fs8', 23)" class="t">bool</span>) (<span onmouseout="hideTip(event, 'fs9', 24)" onmouseover="showTip(event, 'fs9', 24)" class="i">v</span>))
<span class="k">then</span> <span onmouseout="hideTip(event, 'fs4', 25)" onmouseover="showTip(event, 'fs4', 25)" class="p">Some</span> <span class="p">NegativeInfinity</span> <span class="k">else</span> <span onmouseout="hideTip(event, 'fs5', 26)" onmouseover="showTip(event, 'fs5', 26)" class="p">None</span>
<span class="k">let</span> <span class="k">inline</span> (|<span class="p">NaN</span>|_|) (<span onmouseout="hideTip(event, 'fs10', 27)" onmouseover="showTip(event, 'fs10', 27)" class="i">v</span><span class="o">:</span> <span class="o">^</span><span class="i">T</span>) <span class="o">=</span>
<span class="k">if</span> (<span class="o">^</span><span class="i">T</span> <span class="o">:</span> (<span class="k">static</span> <span class="k">member</span> <span class="i">IsNaN</span><span class="o">:</span> <span class="o">&#39;</span><span class="i">T</span> <span class="k">-&gt;</span> <span onmouseout="hideTip(event, 'fs8', 28)" onmouseover="showTip(event, 'fs8', 28)" class="t">bool</span>) (<span onmouseout="hideTip(event, 'fs10', 29)" onmouseover="showTip(event, 'fs10', 29)" class="i">v</span>))
<span class="k">then</span> <span onmouseout="hideTip(event, 'fs4', 30)" onmouseover="showTip(event, 'fs4', 30)" class="p">Some</span> <span class="p">NaN</span> <span class="k">else</span> <span onmouseout="hideTip(event, 'fs5', 31)" onmouseover="showTip(event, 'fs5', 31)" class="p">None</span>
<span class="k">let</span> <span class="k">inline</span> <span class="i">formatMathValue</span> (<span class="i">floatFormat</span><span class="o">:</span><span class="i">string</span>) <span class="o">=</span> <span class="k">function</span>
| <span class="i">PositiveInfinity</span> <span class="k">-&gt;</span> <span class="s">&quot;\\infty&quot;</span>
| <span class="i">NegativeInfinity</span> <span class="k">-&gt;</span> <span class="s">&quot;-\\infty&quot;</span>
| <span class="i">NaN</span> <span class="k">-&gt;</span> <span class="s">&quot;\\times&quot;</span>
| <span class="i">Float</span> <span class="i">v</span> <span class="k">-&gt;</span> <span class="i">v</span><span class="o">.</span><span class="i">ToString</span>(<span class="i">floatFormat</span>)
| <span class="i">Float32</span> <span class="i">v</span> <span class="k">-&gt;</span> <span class="i">v</span><span class="o">.</span><span class="i">ToString</span>(<span class="i">floatFormat</span>)
| <span class="i">v</span> <span class="k">-&gt;</span> <span class="i">v</span><span class="o">.</span><span class="i">ToString</span>()
<span class="k">let</span> <span class="k">inline</span> <span onmouseout="hideTip(event, 'fs11', 32)" onmouseover="showTip(event, 'fs11', 32)" class="f">formatMathValue</span> (<span onmouseout="hideTip(event, 'fs12', 33)" onmouseover="showTip(event, 'fs12', 33)" class="i">floatFormat</span><span class="o">:</span><span onmouseout="hideTip(event, 'fs13', 34)" onmouseover="showTip(event, 'fs13', 34)" class="t">string</span>) <span class="o">=</span> <span class="k">function</span>
| <span onmouseout="hideTip(event, 'fs14', 35)" onmouseover="showTip(event, 'fs14', 35)" class="p">PositiveInfinity</span> <span class="k">-&gt;</span> <span class="s">&quot;</span><span class="e">\\</span><span class="s">infty&quot;</span>
| <span onmouseout="hideTip(event, 'fs15', 36)" onmouseover="showTip(event, 'fs15', 36)" class="p">NegativeInfinity</span> <span class="k">-&gt;</span> <span class="s">&quot;-</span><span class="e">\\</span><span class="s">infty&quot;</span>
| <span onmouseout="hideTip(event, 'fs16', 37)" onmouseover="showTip(event, 'fs16', 37)" class="p">NaN</span> <span class="k">-&gt;</span> <span class="s">&quot;</span><span class="e">\\</span><span class="s">times&quot;</span>
| <span onmouseout="hideTip(event, 'fs17', 38)" onmouseover="showTip(event, 'fs17', 38)" class="p">Float</span> <span onmouseout="hideTip(event, 'fs18', 39)" onmouseover="showTip(event, 'fs18', 39)" class="i">v</span> <span class="k">-&gt;</span> <span onmouseout="hideTip(event, 'fs18', 40)" onmouseover="showTip(event, 'fs18', 40)" class="i">v</span><span class="o">.</span><span onmouseout="hideTip(event, 'fs19', 41)" onmouseover="showTip(event, 'fs19', 41)" class="f">ToString</span>(<span onmouseout="hideTip(event, 'fs12', 42)" onmouseover="showTip(event, 'fs12', 42)" class="i">floatFormat</span>)
| <span onmouseout="hideTip(event, 'fs20', 43)" onmouseover="showTip(event, 'fs20', 43)" class="p">Float32</span> <span onmouseout="hideTip(event, 'fs21', 44)" onmouseover="showTip(event, 'fs21', 44)" class="i">v</span> <span class="k">-&gt;</span> <span onmouseout="hideTip(event, 'fs21', 45)" onmouseover="showTip(event, 'fs21', 45)" class="i">v</span><span class="o">.</span><span onmouseout="hideTip(event, 'fs22', 46)" onmouseover="showTip(event, 'fs22', 46)" class="f">ToString</span>(<span onmouseout="hideTip(event, 'fs12', 47)" onmouseover="showTip(event, 'fs12', 47)" class="i">floatFormat</span>)
| <span onmouseout="hideTip(event, 'fs23', 48)" onmouseover="showTip(event, 'fs23', 48)" class="i">v</span> <span class="k">-&gt;</span> <span onmouseout="hideTip(event, 'fs23', 49)" onmouseover="showTip(event, 'fs23', 49)" class="i">v</span><span class="o">.</span><span onmouseout="hideTip(event, 'fs24', 50)" onmouseover="showTip(event, 'fs24', 50)" class="f">ToString</span>()
<span class="k">let</span> <span class="k">inline</span> <span class="i">formatMatrix</span> (<span class="i">matrix</span><span class="o">:</span> <span class="i">Matrix</span><span class="o">&lt;</span><span class="o">&#39;</span><span class="i">T</span><span class="o">&gt;</span>) <span class="o">=</span>
<span class="i">String</span><span class="o">.</span><span class="i">concat</span> <span class="i">Environment</span><span class="o">.</span><span class="i">NewLine</span>
[ <span class="s">&quot;\\begin{bmatrix}&quot;</span>
<span class="i">matrix</span><span class="o">.</span><span class="i">ToMatrixString</span>(<span class="n">10</span>,<span class="n">4</span>,<span class="n">7</span>,<span class="n">2</span>,<span class="s">&quot;\\cdots&quot;</span>,<span class="s">&quot;\\vdots&quot;</span>,<span class="s">&quot;\\ddots&quot;</span>,
<span class="s">&quot; &amp; &quot;</span>, <span class="s">&quot;\\\\ &quot;</span> <span class="o">+</span> <span class="i">Environment</span><span class="o">.</span><span class="i">NewLine</span>, (<span class="k">fun</span> <span class="i">x</span> <span class="k">-&gt;</span> <span class="i">formatMathValue</span> <span class="s">&quot;G4&quot;</span> <span class="i">x</span>))
<span class="s">&quot;\\end{bmatrix}&quot;</span> ]
<span class="k">let</span> <span class="k">inline</span> <span onmouseout="hideTip(event, 'fs25', 51)" onmouseover="showTip(event, 'fs25', 51)" class="f">formatMatrix</span> (<span onmouseout="hideTip(event, 'fs26', 52)" onmouseover="showTip(event, 'fs26', 52)" class="i">matrix</span><span class="o">:</span> <span class="i">Matrix</span><span class="o">&lt;</span><span class="o">&#39;</span><span class="i">T</span><span class="o">&gt;</span>) <span class="o">=</span>
<span onmouseout="hideTip(event, 'fs27', 53)" onmouseover="showTip(event, 'fs27', 53)" class="t">String</span><span class="o">.</span><span onmouseout="hideTip(event, 'fs28', 54)" onmouseover="showTip(event, 'fs28', 54)" class="f">concat</span> <span class="i">Environment</span><span class="o">.</span><span class="i">NewLine</span>
[ <span class="s">&quot;</span><span class="e">\\</span><span class="s">begin{bmatrix}&quot;</span>
<span onmouseout="hideTip(event, 'fs26', 55)" onmouseover="showTip(event, 'fs26', 55)" class="i">matrix</span><span class="o">.</span><span class="i">ToMatrixString</span>(<span class="n">10</span>,<span class="n">4</span>,<span class="n">7</span>,<span class="n">2</span>,<span class="s">&quot;</span><span class="e">\\</span><span class="s">cdots&quot;</span>,<span class="s">&quot;</span><span class="e">\\</span><span class="s">vdots&quot;</span>,<span class="s">&quot;</span><span class="e">\\</span><span class="s">ddots&quot;</span>,
<span class="s">&quot; &amp; &quot;</span>, <span class="s">&quot;</span><span class="e">\\</span><span class="s"></span><span class="e">\\</span><span class="s"> &quot;</span> <span class="o">+</span> <span class="i">Environment</span><span class="o">.</span><span class="i">NewLine</span>, (<span class="k">fun</span> <span class="i">x</span> <span class="k">-&gt;</span> <span onmouseout="hideTip(event, 'fs11', 56)" onmouseover="showTip(event, 'fs11', 56)" class="i">formatMathValue</span> <span class="s">&quot;G4&quot;</span> <span class="i">x</span>))
<span class="s">&quot;</span><span class="e">\\</span><span class="s">end{bmatrix}&quot;</span> ]
<span class="k">let</span> <span class="k">inline</span> <span class="i">formatVector</span> (<span class="i">vector</span><span class="o">:</span> <span class="i">Vector</span><span class="o">&lt;</span><span class="o">&#39;</span><span class="i">T</span><span class="o">&gt;</span>) <span class="o">=</span>
<span class="i">String</span><span class="o">.</span><span class="i">concat</span> <span class="i">Environment</span><span class="o">.</span><span class="i">NewLine</span>
[ <span class="s">&quot;\\begin{bmatrix}&quot;</span>
<span class="i">vector</span><span class="o">.</span><span class="i">ToVectorString</span>(<span class="n">12</span>, <span class="n">80</span>, <span class="s">&quot;\\vdots&quot;</span>, <span class="s">&quot; &amp; &quot;</span>, <span class="s">&quot;\\\\ &quot;</span> <span class="o">+</span> <span class="i">Environment</span><span class="o">.</span><span class="i">NewLine</span>,
(<span class="k">fun</span> <span class="i">x</span> <span class="k">-&gt;</span> <span class="i">formatMathValue</span> <span class="s">&quot;G4&quot;</span> <span class="i">x</span>))
<span class="s">&quot;\\end{bmatrix}&quot;</span> ]
<span class="k">let</span> <span class="k">inline</span> <span onmouseout="hideTip(event, 'fs29', 57)" onmouseover="showTip(event, 'fs29', 57)" class="f">formatVector</span> (<span onmouseout="hideTip(event, 'fs30', 58)" onmouseover="showTip(event, 'fs30', 58)" class="i">vector</span><span class="o">:</span> <span class="i">Vector</span><span class="o">&lt;</span><span class="o">&#39;</span><span class="i">T</span><span class="o">&gt;</span>) <span class="o">=</span>
<span onmouseout="hideTip(event, 'fs27', 59)" onmouseover="showTip(event, 'fs27', 59)" class="t">String</span><span class="o">.</span><span onmouseout="hideTip(event, 'fs28', 60)" onmouseover="showTip(event, 'fs28', 60)" class="f">concat</span> <span class="i">Environment</span><span class="o">.</span><span class="i">NewLine</span>
[ <span class="s">&quot;</span><span class="e">\\</span><span class="s">begin{bmatrix}&quot;</span>
<span onmouseout="hideTip(event, 'fs30', 61)" onmouseover="showTip(event, 'fs30', 61)" class="i">vector</span><span class="o">.</span><span class="i">ToVectorString</span>(<span class="n">12</span>, <span class="n">80</span>, <span class="s">&quot;</span><span class="e">\\</span><span class="s">vdots&quot;</span>, <span class="s">&quot; &amp; &quot;</span>, <span class="s">&quot;</span><span class="e">\\</span><span class="s"></span><span class="e">\\</span><span class="s"> &quot;</span> <span class="o">+</span> <span class="i">Environment</span><span class="o">.</span><span class="i">NewLine</span>,
(<span class="k">fun</span> <span class="i">x</span> <span class="k">-&gt;</span> <span onmouseout="hideTip(event, 'fs11', 62)" onmouseover="showTip(event, 'fs11', 62)" class="i">formatMathValue</span> <span class="s">&quot;G4&quot;</span> <span class="i">x</span>))
<span class="s">&quot;</span><span class="e">\\</span><span class="s">end{bmatrix}&quot;</span> ]
<span class="i">App</span><span class="o">.</span><span class="i">AddDisplayPrinter</span> (<span class="k">fun</span> (<span class="i">x</span><span class="o">:</span><span class="i">Matrix</span><span class="o">&lt;</span><span class="i">float</span><span class="o">&gt;</span>) <span class="k">-&gt;</span>
{ <span class="i">ContentType</span> <span class="o">=</span> <span class="s">&quot;text/latex&quot;</span>; <span class="i">Data</span> <span class="o">=</span> <span class="i">formatMatrix</span> <span class="i">x</span> })
<span class="i">App</span><span class="o">.</span><span class="i">AddDisplayPrinter</span> (<span class="k">fun</span> (<span class="i">x</span><span class="o">:</span><span class="i">Matrix</span><span class="o">&lt;</span><span class="i">float32</span><span class="o">&gt;</span>) <span class="k">-&gt;</span>
{ <span class="i">ContentType</span> <span class="o">=</span> <span class="s">&quot;text/latex&quot;</span>; <span class="i">Data</span> <span class="o">=</span> <span class="i">formatMatrix</span> <span class="i">x</span> })
<span class="i">App</span><span class="o">.</span><span class="i">AddDisplayPrinter</span> (<span class="k">fun</span> (<span class="i">x</span><span class="o">:</span><span class="i">Vector</span><span class="o">&lt;</span><span class="i">float</span><span class="o">&gt;</span>) <span class="k">-&gt;</span>
{ <span class="i">ContentType</span> <span class="o">=</span> <span class="s">&quot;text/latex&quot;</span>; <span class="i">Data</span> <span class="o">=</span> <span class="i">formatVector</span> <span class="i">x</span> })
<span class="i">App</span><span class="o">.</span><span class="i">AddDisplayPrinter</span> (<span class="k">fun</span> (<span class="i">x</span><span class="o">:</span><span class="i">Vector</span><span class="o">&lt;</span><span class="i">float32</span><span class="o">&gt;</span>) <span class="k">-&gt;</span>
{ <span class="i">ContentType</span> <span class="o">=</span> <span class="s">&quot;text/latex&quot;</span>; <span class="i">Data</span> <span class="o">=</span> <span class="i">formatVector</span> <span class="i">x</span> })
<span class="i">App</span><span class="o">.</span><span class="i">AddDisplayPrinter</span> (<span class="k">fun</span> (<span class="i">x</span><span class="o">:</span><span class="i">Matrix</span><span class="o">&lt;</span><span onmouseout="hideTip(event, 'fs3', 63)" onmouseover="showTip(event, 'fs3', 63)" class="i">float</span><span class="o">&gt;</span>) <span class="k">-&gt;</span>
{ <span class="i">ContentType</span> <span class="o">=</span> <span class="s">&quot;text/latex&quot;</span>; <span onmouseout="hideTip(event, 'fs31', 64)" onmouseover="showTip(event, 'fs31', 64)" class="i">Data</span> <span class="o">=</span> <span onmouseout="hideTip(event, 'fs25', 65)" onmouseover="showTip(event, 'fs25', 65)" class="i">formatMatrix</span> <span class="i">x</span> })
<span class="i">App</span><span class="o">.</span><span class="i">AddDisplayPrinter</span> (<span class="k">fun</span> (<span class="i">x</span><span class="o">:</span><span class="i">Matrix</span><span class="o">&lt;</span><span onmouseout="hideTip(event, 'fs6', 66)" onmouseover="showTip(event, 'fs6', 66)" class="i">float32</span><span class="o">&gt;</span>) <span class="k">-&gt;</span>
{ <span class="i">ContentType</span> <span class="o">=</span> <span class="s">&quot;text/latex&quot;</span>; <span onmouseout="hideTip(event, 'fs31', 67)" onmouseover="showTip(event, 'fs31', 67)" class="i">Data</span> <span class="o">=</span> <span onmouseout="hideTip(event, 'fs25', 68)" onmouseover="showTip(event, 'fs25', 68)" class="i">formatMatrix</span> <span class="i">x</span> })
<span class="i">App</span><span class="o">.</span><span class="i">AddDisplayPrinter</span> (<span class="k">fun</span> (<span class="i">x</span><span class="o">:</span><span class="i">Vector</span><span class="o">&lt;</span><span onmouseout="hideTip(event, 'fs3', 69)" onmouseover="showTip(event, 'fs3', 69)" class="i">float</span><span class="o">&gt;</span>) <span class="k">-&gt;</span>
{ <span class="i">ContentType</span> <span class="o">=</span> <span class="s">&quot;text/latex&quot;</span>; <span onmouseout="hideTip(event, 'fs31', 70)" onmouseover="showTip(event, 'fs31', 70)" class="i">Data</span> <span class="o">=</span> <span onmouseout="hideTip(event, 'fs29', 71)" onmouseover="showTip(event, 'fs29', 71)" class="i">formatVector</span> <span class="i">x</span> })
<span class="i">App</span><span class="o">.</span><span class="i">AddDisplayPrinter</span> (<span class="k">fun</span> (<span class="i">x</span><span class="o">:</span><span class="i">Vector</span><span class="o">&lt;</span><span onmouseout="hideTip(event, 'fs6', 72)" onmouseover="showTip(event, 'fs6', 72)" class="i">float32</span><span class="o">&gt;</span>) <span class="k">-&gt;</span>
{ <span class="i">ContentType</span> <span class="o">=</span> <span class="s">&quot;text/latex&quot;</span>; <span onmouseout="hideTip(event, 'fs31', 73)" onmouseover="showTip(event, 'fs31', 73)" class="i">Data</span> <span class="o">=</span> <span onmouseout="hideTip(event, 'fs29', 74)" onmouseover="showTip(event, 'fs29', 74)" class="i">formatVector</span> <span class="i">x</span> })
</code></pre></td>
</tr>
</table>
<div class="tip" id="fs1">val v : obj</div>
<div class="tip" id="fs2">type obj = System.Object<br /><br />Full name: Microsoft.FSharp.Core.obj</div>
<div class="tip" id="fs3">Multiple items<br />val float : value:&#39;T -&gt; float (requires member op_Explicit)<br /><br />Full name: Microsoft.FSharp.Core.Operators.float<br /><br />--------------------<br />type float = System.Double<br /><br />Full name: Microsoft.FSharp.Core.float<br /><br />--------------------<br />type float&lt;&#39;Measure&gt; = float<br /><br />Full name: Microsoft.FSharp.Core.float&lt;_&gt;</div>
<div class="tip" id="fs4">union case Option.Some: Value: &#39;T -&gt; Option&lt;&#39;T&gt;</div>
<div class="tip" id="fs5">union case Option.None: Option&lt;&#39;T&gt;</div>
<div class="tip" id="fs6">Multiple items<br />val float32 : value:&#39;T -&gt; float32 (requires member op_Explicit)<br /><br />Full name: Microsoft.FSharp.Core.Operators.float32<br /><br />--------------------<br />type float32 = System.Single<br /><br />Full name: Microsoft.FSharp.Core.float32<br /><br />--------------------<br />type float32&lt;&#39;Measure&gt; = float32<br /><br />Full name: Microsoft.FSharp.Core.float32&lt;_&gt;</div>
<div class="tip" id="fs7">val v : &#39;T (requires member IsPositiveInfinity)</div>
<div class="tip" id="fs8">type bool = System.Boolean<br /><br />Full name: Microsoft.FSharp.Core.bool</div>
<div class="tip" id="fs9">val v : &#39;T (requires member IsNegativeInfinity)</div>
<div class="tip" id="fs10">val v : &#39;T (requires member IsNaN)</div>
<div class="tip" id="fs11">val formatMathValue : floatFormat:string -&gt; _arg1:&#39;a -&gt; string (requires member IsNaN and member IsPositiveInfinity and member IsNegativeInfinity)<br /><br />Full name: IFsharpNotebook.formatMathValue</div>
<div class="tip" id="fs12">val floatFormat : string</div>
<div class="tip" id="fs13">Multiple items<br />val string : value:&#39;T -&gt; string<br /><br />Full name: Microsoft.FSharp.Core.Operators.string<br /><br />--------------------<br />type string = System.String<br /><br />Full name: Microsoft.FSharp.Core.string</div>
<div class="tip" id="fs14">active recognizer PositiveInfinity: &#39;T -&gt; unit option<br /><br />Full name: IFsharpNotebook.( |PositiveInfinity|_| )</div>
<div class="tip" id="fs15">active recognizer NegativeInfinity: &#39;T -&gt; unit option<br /><br />Full name: IFsharpNotebook.( |NegativeInfinity|_| )</div>
<div class="tip" id="fs16">active recognizer NaN: &#39;T -&gt; unit option<br /><br />Full name: IFsharpNotebook.( |NaN|_| )</div>
<div class="tip" id="fs17">active recognizer Float: obj -&gt; float option<br /><br />Full name: IFsharpNotebook.( |Float|_| )</div>
<div class="tip" id="fs18">val v : float</div>
<div class="tip" id="fs19">System.Double.ToString() : string<br />System.Double.ToString(provider: System.IFormatProvider) : string<br />System.Double.ToString(format: string) : string<br />System.Double.ToString(format: string, provider: System.IFormatProvider) : string</div>
<div class="tip" id="fs20">active recognizer Float32: obj -&gt; float32 option<br /><br />Full name: IFsharpNotebook.( |Float32|_| )</div>
<div class="tip" id="fs21">val v : float32</div>
<div class="tip" id="fs22">System.Single.ToString() : string<br />System.Single.ToString(format: string) : string<br />System.Single.ToString(provider: System.IFormatProvider) : string<br />System.Single.ToString(format: string, provider: System.IFormatProvider) : string</div>
<div class="tip" id="fs23">val v : &#39;a (requires member IsNaN and member IsPositiveInfinity and member IsNegativeInfinity)</div>
<div class="tip" id="fs24">System.Object.ToString() : string</div>
<div class="tip" id="fs25">val formatMatrix : matrix:&#39;a -&gt; string<br /><br />Full name: IFsharpNotebook.formatMatrix</div>
<div class="tip" id="fs26">val matrix : &#39;a</div>
<div class="tip" id="fs27">module String<br /><br />from Microsoft.FSharp.Core</div>
<div class="tip" id="fs28">val concat : sep:string -&gt; strings:seq&lt;string&gt; -&gt; string<br /><br />Full name: Microsoft.FSharp.Core.String.concat</div>
<div class="tip" id="fs29">val formatVector : vector:&#39;a -&gt; string<br /><br />Full name: IFsharpNotebook.formatVector</div>
<div class="tip" id="fs30">val vector : &#39;a</div>
<div class="tip" id="fs31">namespace Microsoft.FSharp.Data</div>
</div>
<div class="span3">

18
LinearEquations.html
View File

@ -117,11 +117,11 @@ a_{m1} &amp; a_{m2} &amp; \cdots &amp; a_{mn}
<span class="l">4: </span>
<span class="l">5: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="k">let</span> <span class="i">A</span> <span class="o">=</span> <span class="i">matrix</span> [[ <span class="n">3.0</span>; <span class="n">2.0</span>; <span class="o">-</span><span class="n">1.0</span> ]
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="k">let</span> <span onmouseout="hideTip(event, 'fs1', 1)" onmouseover="showTip(event, 'fs1', 1)" class="i">A</span> <span class="o">=</span> <span class="i">matrix</span> [[ <span class="n">3.0</span>; <span class="n">2.0</span>; <span class="o">-</span><span class="n">1.0</span> ]
[ <span class="n">2.0</span>; <span class="o">-</span><span class="n">2.0</span>; <span class="n">4.0</span> ]
[ <span class="o">-</span><span class="n">1.0</span>; <span class="n">0.5</span>; <span class="o">-</span><span class="n">1.0</span> ]]
<span class="k">let</span> <span class="i">b</span> <span class="o">=</span> <span class="i">vector</span> [ <span class="n">1.0</span>; <span class="o">-</span><span class="n">2.0</span>; <span class="n">0.0</span> ]
<span class="k">let</span> <span class="i">x</span> <span class="o">=</span> <span class="i">A</span><span class="o">.</span><span class="i">Solve</span>(<span class="i">b</span>) <span class="c">// 1;-2;-2</span>
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs2', 2)" onmouseover="showTip(event, 'fs2', 2)" class="i">b</span> <span class="o">=</span> <span class="i">vector</span> [ <span class="n">1.0</span>; <span class="o">-</span><span class="n">2.0</span>; <span class="n">0.0</span> ]
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs3', 3)" onmouseover="showTip(event, 'fs3', 3)" class="i">x</span> <span class="o">=</span> <span onmouseout="hideTip(event, 'fs1', 4)" onmouseover="showTip(event, 'fs1', 4)" class="i">A</span><span class="o">.</span><span class="i">Solve</span>(<span onmouseout="hideTip(event, 'fs2', 5)" onmouseover="showTip(event, 'fs2', 5)" class="i">b</span>) <span class="c">// 1;-2;-2</span>
</code></pre></td>
</tr>
</table>
@ -158,16 +158,22 @@ become zero on the right side), by introducing a new column each. First we subtr
<span class="l">5: </span>
<span class="l">6: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="k">let</span> <span class="i">A&#39;</span> <span class="o">=</span> <span class="i">matrix</span> [[ <span class="n">3.0</span>; <span class="n">4.0</span>; <span class="o">-</span><span class="n">1.0</span>; <span class="n">0.0</span> ]
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="k">let</span> <span onmouseout="hideTip(event, 'fs4', 6)" onmouseover="showTip(event, 'fs4', 6)" class="i">A&#39;</span> <span class="o">=</span> <span class="i">matrix</span> [[ <span class="n">3.0</span>; <span class="n">4.0</span>; <span class="o">-</span><span class="n">1.0</span>; <span class="n">0.0</span> ]
[ <span class="n">4.0</span>; <span class="n">5.0</span>; <span class="n">0.0</span>; <span class="o">-</span><span class="n">1.0</span> ]
[ <span class="n">5.0</span>; <span class="n">6.0</span>; <span class="n">0.0</span>; <span class="n">0.0</span>; ]
[ <span class="n">6.0</span>; <span class="n">7.0</span>; <span class="n">0.0</span>; <span class="n">0.0</span> ]]
<span class="k">let</span> <span class="i">b&#39;</span> <span class="o">=</span> <span class="i">vector</span> [ <span class="n">0.0</span>; <span class="n">0.0</span>; <span class="n">20.0</span>; <span class="n">0.0</span> ]
<span class="k">let</span> <span class="i">x&#39;</span> <span class="o">=</span> <span class="i">A&#39;</span><span class="o">.</span><span class="i">Solve</span>(<span class="i">b&#39;</span>) <span class="c">// -140; 120; 60; 40</span>
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs5', 7)" onmouseover="showTip(event, 'fs5', 7)" class="i">b&#39;</span> <span class="o">=</span> <span class="i">vector</span> [ <span class="n">0.0</span>; <span class="n">0.0</span>; <span class="n">20.0</span>; <span class="n">0.0</span> ]
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs6', 8)" onmouseover="showTip(event, 'fs6', 8)" class="i">x&#39;</span> <span class="o">=</span> <span onmouseout="hideTip(event, 'fs4', 9)" onmouseover="showTip(event, 'fs4', 9)" class="i">A&#39;</span><span class="o">.</span><span class="i">Solve</span>(<span onmouseout="hideTip(event, 'fs5', 10)" onmouseover="showTip(event, 'fs5', 10)" class="i">b&#39;</span>) <span class="c">// -140; 120; 60; 40</span>
</code></pre></td>
</tr>
</table>
<div class="tip" id="fs1">val A : obj<br /><br />Full name: LinearEquations.A</div>
<div class="tip" id="fs2">val b : obj<br /><br />Full name: LinearEquations.b</div>
<div class="tip" id="fs3">val x : obj<br /><br />Full name: LinearEquations.x</div>
<div class="tip" id="fs4">val A&#39; : obj<br /><br />Full name: LinearEquations.A&#39;</div>
<div class="tip" id="fs5">val b&#39; : obj<br /><br />Full name: LinearEquations.b&#39;</div>
<div class="tip" id="fs6">val x&#39; : obj<br /><br />Full name: LinearEquations.x&#39;</div>
</div>
<div class="span3">

15
MKL.html
View File

@ -174,8 +174,8 @@ directory somewhere and use them directly from there:</p>
<table class="pre"><tr><td class="lines"><pre class="fssnip"><span class="l">1: </span>
<span class="l">2: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="i">Control</span><span class="o">.</span><span class="i">NativeProviderPath</span> <span class="o">&lt;-</span> <span class="s">@&quot;C:\MKL&quot;</span>
<span class="i">Control</span><span class="o">.</span><span class="i">UseNativeMKL</span>()
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span onmouseout="hideTip(event, 'fs1', 1)" onmouseover="showTip(event, 'fs1', 1)" class="i">Control</span><span class="o">.</span><span class="i">NativeProviderPath</span> <span class="o">&lt;-</span> <span class="s">@&quot;C:\MKL&quot;</span>
<span onmouseout="hideTip(event, 'fs1', 2)" onmouseover="showTip(event, 'fs1', 2)" class="i">Control</span><span class="o">.</span><span class="i">UseNativeMKL</span>()
</code></pre></td>
</tr>
</table>
@ -189,11 +189,11 @@ MKL provider automatically.</p>
<span class="l">4: </span>
<span class="l">5: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="k">open</span> <span class="i">System</span><span class="o">.</span><span class="i">IO</span>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="k">open</span> <span onmouseout="hideTip(event, 'fs2', 3)" onmouseover="showTip(event, 'fs2', 3)" class="i">System</span><span class="o">.</span><span onmouseout="hideTip(event, 'fs3', 4)" onmouseover="showTip(event, 'fs3', 4)" class="i">IO</span>
<span class="k">open</span> <span class="i">MathNet</span><span class="o">.</span><span class="i">Numerics</span>
<span class="i">Control</span><span class="o">.</span><span class="i">NativeProviderPath</span> <span class="o">&lt;-</span> <span class="i">Path</span><span class="o">.</span><span class="i">Combine</span>(<span class="k">__SOURCE_DIRECTORY__</span>,<span class="s">&quot;../&quot;</span>)
<span class="i">Control</span><span class="o">.</span><span class="i">UseNativeMKL</span>()
<span onmouseout="hideTip(event, 'fs1', 5)" onmouseover="showTip(event, 'fs1', 5)" class="i">Control</span><span class="o">.</span><span class="i">NativeProviderPath</span> <span class="o">&lt;-</span> <span onmouseout="hideTip(event, 'fs4', 6)" onmouseover="showTip(event, 'fs4', 6)" class="i">Path</span><span class="o">.</span><span onmouseout="hideTip(event, 'fs5', 7)" onmouseover="showTip(event, 'fs5', 7)" class="i">Combine</span>(<span class="k">__SOURCE_DIRECTORY__</span>,<span class="s">&quot;../&quot;</span>)
<span onmouseout="hideTip(event, 'fs1', 8)" onmouseover="showTip(event, 'fs1', 8)" class="i">Control</span><span class="o">.</span><span class="i">UseNativeMKL</span>()
</code></pre></td>
</tr>
</table>
@ -320,6 +320,11 @@ Numerics MKL native provider for free for your own use. However, it does <em>not
redistribute it again yourself to customers of your own product. <strong>If you need to redistribute,
buy a license from Intel. If unsure, contact the Intel sales team to clarify.</strong></p>
<div class="tip" id="fs1">namespace Microsoft.FSharp.Control</div>
<div class="tip" id="fs2">namespace System</div>
<div class="tip" id="fs3">namespace System.IO</div>
<div class="tip" id="fs4">type Path =<br />&#160;&#160;static val DirectorySeparatorChar : char<br />&#160;&#160;static val AltDirectorySeparatorChar : char<br />&#160;&#160;static val VolumeSeparatorChar : char<br />&#160;&#160;static val InvalidPathChars : char[]<br />&#160;&#160;static val PathSeparator : char<br />&#160;&#160;static member ChangeExtension : path:string * extension:string -&gt; string<br />&#160;&#160;static member Combine : [&lt;ParamArray&gt;] paths:string[] -&gt; string + 3 overloads<br />&#160;&#160;static member GetDirectoryName : path:string -&gt; string<br />&#160;&#160;static member GetExtension : path:string -&gt; string<br />&#160;&#160;static member GetFileName : path:string -&gt; string<br />&#160;&#160;...<br /><br />Full name: System.IO.Path</div>
<div class="tip" id="fs5">Path.Combine([&lt;System.ParamArray&gt;] paths: string []) : string<br />Path.Combine(path1: string, path2: string) : string<br />Path.Combine(path1: string, path2: string, path3: string) : string<br />Path.Combine(path1: string, path2: string, path3: string, path4: string) : string</div>
</div>
<div class="span3">

66
Matrix.html
View File

@ -325,31 +325,31 @@ V.Dense(x);
<span class="l">24: </span>
<span class="l">25: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="k">let</span> <span class="i">m1</span> <span class="o">=</span> <span class="i">matrix</span> [[ <span class="n">2.0</span>; <span class="n">3.0</span> ]
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="k">let</span> <span onmouseout="hideTip(event, 'fs1', 1)" onmouseover="showTip(event, 'fs1', 1)" class="i">m1</span> <span class="o">=</span> <span class="i">matrix</span> [[ <span class="n">2.0</span>; <span class="n">3.0</span> ]
[ <span class="n">4.0</span>; <span class="n">5.0</span> ]]
<span class="k">let</span> <span class="i">v1</span> <span class="o">=</span> <span class="i">vector</span> [ <span class="n">1.0</span>; <span class="n">2.0</span>; <span class="n">3.0</span> ]
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs2', 2)" onmouseover="showTip(event, 'fs2', 2)" class="i">v1</span> <span class="o">=</span> <span class="i">vector</span> [ <span class="n">1.0</span>; <span class="n">2.0</span>; <span class="n">3.0</span> ]
<span class="c">// dense 3x4 matrix filled with zeros.</span>
<span class="c">// (usually the type is inferred, but not for zero matrices)</span>
<span class="k">let</span> <span class="i">m2</span> <span class="o">=</span> <span class="i">DenseMatrix</span><span class="o">.</span><span class="i">zero</span><span class="o">&lt;</span><span class="i">float</span><span class="o">&gt;</span> <span class="n">3</span> <span class="n">4</span>
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs3', 3)" onmouseover="showTip(event, 'fs3', 3)" class="i">m2</span> <span class="o">=</span> <span class="i">DenseMatrix</span><span class="o">.</span><span class="i">zero</span><span class="o">&lt;</span><span onmouseout="hideTip(event, 'fs4', 4)" onmouseover="showTip(event, 'fs4', 4)" class="i">float</span><span class="o">&gt;</span> <span class="n">3</span> <span class="n">4</span>
<span class="c">// dense 3x4 matrix initialized by a function</span>
<span class="k">let</span> <span class="i">m3</span> <span class="o">=</span> <span class="i">DenseMatrix</span><span class="o">.</span><span class="i">init</span> <span class="n">3</span> <span class="n">4</span> (<span class="k">fun</span> <span class="i">i</span> <span class="i">j</span> <span class="k">-&gt;</span> <span class="i">float</span> (<span class="i">i</span><span class="o">+</span><span class="i">j</span>))
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs5', 5)" onmouseover="showTip(event, 'fs5', 5)" class="i">m3</span> <span class="o">=</span> <span class="i">DenseMatrix</span><span class="o">.</span><span class="i">init</span> <span class="n">3</span> <span class="n">4</span> (<span class="k">fun</span> <span class="i">i</span> <span class="i">j</span> <span class="k">-&gt;</span> <span onmouseout="hideTip(event, 'fs4', 6)" onmouseover="showTip(event, 'fs4', 6)" class="i">float</span> (<span class="i">i</span><span class="o">+</span><span class="i">j</span>))
<span class="c">// diagonal 4x4 identity matrix of single precision</span>
<span class="k">let</span> <span class="i">m4</span> <span class="o">=</span> <span class="i">DiagonalMatrix</span><span class="o">.</span><span class="i">identity</span><span class="o">&lt;</span><span class="i">float32</span><span class="o">&gt;</span> <span class="n">4</span>
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs6', 7)" onmouseover="showTip(event, 'fs6', 7)" class="i">m4</span> <span class="o">=</span> <span class="i">DiagonalMatrix</span><span class="o">.</span><span class="i">identity</span><span class="o">&lt;</span><span onmouseout="hideTip(event, 'fs7', 8)" onmouseover="showTip(event, 'fs7', 8)" class="i">float32</span><span class="o">&gt;</span> <span class="n">4</span>
<span class="c">// dense 3x4 matrix created from a sequence of sequence-columns</span>
<span class="k">let</span> <span class="i">x</span> <span class="o">=</span> <span class="i">Seq</span><span class="o">.</span><span class="i">init</span> <span class="n">4</span> (<span class="k">fun</span> <span class="i">c</span> <span class="k">-&gt;</span> <span class="i">Seq</span><span class="o">.</span><span class="i">init</span> <span class="n">3</span> (<span class="k">fun</span> <span class="i">r</span> <span class="k">-&gt;</span> <span class="i">float</span> (<span class="n">100</span><span class="o">*</span><span class="i">r</span> <span class="o">+</span> <span class="i">c</span>)))
<span class="k">let</span> <span class="i">m5</span> <span class="o">=</span> <span class="i">DenseMatrix</span><span class="o">.</span><span class="i">ofColumnSeq</span> <span class="i">x</span>
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs8', 9)" onmouseover="showTip(event, 'fs8', 9)" class="i">x</span> <span class="o">=</span> <span onmouseout="hideTip(event, 'fs9', 10)" onmouseover="showTip(event, 'fs9', 10)" class="t">Seq</span><span class="o">.</span><span onmouseout="hideTip(event, 'fs10', 11)" onmouseover="showTip(event, 'fs10', 11)" class="f">init</span> <span class="n">4</span> (<span class="k">fun</span> <span onmouseout="hideTip(event, 'fs11', 12)" onmouseover="showTip(event, 'fs11', 12)" class="i">c</span> <span class="k">-&gt;</span> <span onmouseout="hideTip(event, 'fs9', 13)" onmouseover="showTip(event, 'fs9', 13)" class="t">Seq</span><span class="o">.</span><span onmouseout="hideTip(event, 'fs10', 14)" onmouseover="showTip(event, 'fs10', 14)" class="f">init</span> <span class="n">3</span> (<span class="k">fun</span> <span onmouseout="hideTip(event, 'fs12', 15)" onmouseover="showTip(event, 'fs12', 15)" class="i">r</span> <span class="k">-&gt;</span> <span onmouseout="hideTip(event, 'fs4', 16)" onmouseover="showTip(event, 'fs4', 16)" class="f">float</span> (<span class="n">100</span><span class="o">*</span><span onmouseout="hideTip(event, 'fs12', 17)" onmouseover="showTip(event, 'fs12', 17)" class="i">r</span> <span class="o">+</span> <span onmouseout="hideTip(event, 'fs11', 18)" onmouseover="showTip(event, 'fs11', 18)" class="i">c</span>)))
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs13', 19)" onmouseover="showTip(event, 'fs13', 19)" class="i">m5</span> <span class="o">=</span> <span class="i">DenseMatrix</span><span class="o">.</span><span class="i">ofColumnSeq</span> <span onmouseout="hideTip(event, 'fs8', 20)" onmouseover="showTip(event, 'fs8', 20)" class="i">x</span>
<span class="c">// random matrix with standard distribution:</span>
<span class="k">let</span> <span class="i">m6</span> <span class="o">=</span> <span class="i">DenseMatrix</span><span class="o">.</span><span class="i">randomStandard</span><span class="o">&lt;</span><span class="i">float</span><span class="o">&gt;</span> <span class="n">3</span> <span class="n">4</span>
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs14', 21)" onmouseover="showTip(event, 'fs14', 21)" class="i">m6</span> <span class="o">=</span> <span class="i">DenseMatrix</span><span class="o">.</span><span class="i">randomStandard</span><span class="o">&lt;</span><span onmouseout="hideTip(event, 'fs4', 22)" onmouseover="showTip(event, 'fs4', 22)" class="i">float</span><span class="o">&gt;</span> <span class="n">3</span> <span class="n">4</span>
<span class="c">// random matrix with a uniform and one with a Gamma distribution:</span>
<span class="k">let</span> <span class="i">m7a</span> <span class="o">=</span> <span class="i">DenseMatrix</span><span class="o">.</span><span class="i">random</span><span class="o">&lt;</span><span class="i">float</span><span class="o">&gt;</span> <span class="n">3</span> <span class="n">4</span> (<span class="i">ContinuousUniform</span>(<span class="o">-</span><span class="n">2.0</span>, <span class="n">4.0</span>))
<span class="k">let</span> <span class="i">m7b</span> <span class="o">=</span> <span class="i">DenseMatrix</span><span class="o">.</span><span class="i">random</span><span class="o">&lt;</span><span class="i">float</span><span class="o">&gt;</span> <span class="n">3</span> <span class="n">4</span> (<span class="i">Gamma</span>(<span class="n">1.0</span>, <span class="n">2.0</span>))
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs15', 23)" onmouseover="showTip(event, 'fs15', 23)" class="i">m7a</span> <span class="o">=</span> <span class="i">DenseMatrix</span><span class="o">.</span><span class="i">random</span><span class="o">&lt;</span><span onmouseout="hideTip(event, 'fs4', 24)" onmouseover="showTip(event, 'fs4', 24)" class="i">float</span><span class="o">&gt;</span> <span class="n">3</span> <span class="n">4</span> (<span class="i">ContinuousUniform</span>(<span class="o">-</span><span class="n">2.0</span>, <span class="n">4.0</span>))
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs16', 25)" onmouseover="showTip(event, 'fs16', 25)" class="i">m7b</span> <span class="o">=</span> <span class="i">DenseMatrix</span><span class="o">.</span><span class="i">random</span><span class="o">&lt;</span><span onmouseout="hideTip(event, 'fs4', 26)" onmouseover="showTip(event, 'fs4', 26)" class="i">float</span><span class="o">&gt;</span> <span class="n">3</span> <span class="n">4</span> (<span class="i">Gamma</span>(<span class="n">1.0</span>, <span class="n">2.0</span>))
</code></pre></td>
</tr>
</table>
@ -367,14 +367,14 @@ operators <code>.*</code>, <code>./</code> and <code>.%</code> available for con
<span class="l">7: </span>
<span class="l">8: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="k">let</span> <span class="i">m</span> <span class="o">=</span> <span class="i">matrix</span> [[ <span class="n">1.0</span>; <span class="n">4.0</span>; <span class="n">7.0</span> ]
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="k">let</span> <span onmouseout="hideTip(event, 'fs17', 27)" onmouseover="showTip(event, 'fs17', 27)" class="i">m</span> <span class="o">=</span> <span class="i">matrix</span> [[ <span class="n">1.0</span>; <span class="n">4.0</span>; <span class="n">7.0</span> ]
[ <span class="n">2.0</span>; <span class="n">5.0</span>; <span class="n">8.0</span> ]
[ <span class="n">3.0</span>; <span class="n">6.0</span>; <span class="n">9.0</span> ]]
<span class="k">let</span> <span class="i">v</span> <span class="o">=</span> <span class="i">vector</span> [ <span class="n">10.0</span>; <span class="n">20.0</span>; <span class="n">30.0</span> ]
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs18', 28)" onmouseover="showTip(event, 'fs18', 28)" class="i">v</span> <span class="o">=</span> <span class="i">vector</span> [ <span class="n">10.0</span>; <span class="n">20.0</span>; <span class="n">30.0</span> ]
<span class="k">let</span> <span class="i">v&#39;</span> <span class="o">=</span> <span class="i">m</span> <span class="o">*</span> <span class="i">v</span>
<span class="k">let</span> <span class="i">m&#39;</span> <span class="o">=</span> <span class="i">m</span> <span class="o">+</span> <span class="n">2.0</span><span class="o">*</span><span class="i">m</span>
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs19', 29)" onmouseover="showTip(event, 'fs19', 29)" class="i">v&#39;</span> <span class="o">=</span> <span onmouseout="hideTip(event, 'fs17', 30)" onmouseover="showTip(event, 'fs17', 30)" class="i">m</span> <span class="o">*</span> <span onmouseout="hideTip(event, 'fs18', 31)" onmouseover="showTip(event, 'fs18', 31)" class="i">v</span>
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs20', 32)" onmouseover="showTip(event, 'fs20', 32)" class="i">m&#39;</span> <span class="o">=</span> <span onmouseout="hideTip(event, 'fs17', 33)" onmouseover="showTip(event, 'fs17', 33)" class="i">m</span> <span class="o">+</span> <span class="n">2.0</span><span class="o">*</span><span onmouseout="hideTip(event, 'fs17', 34)" onmouseover="showTip(event, 'fs17', 34)" class="i">m</span>
</code></pre></td>
</tr>
</table>
@ -571,7 +571,7 @@ m[<span class="n">0</span>,<span class="n">2</span>]; <span class="c">// -1</spa
<p>In F#:</p>
<table class="pre"><tr><td class="lines"><pre class="fssnip"><span class="l">1: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="i">m</span><span class="o">.</span>[<span class="n">2</span>,<span class="n">0</span>] <span class="c">// 20</span>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span onmouseout="hideTip(event, 'fs17', 35)" onmouseover="showTip(event, 'fs17', 35)" class="i">m</span><span class="o">.</span>[<span class="n">2</span>,<span class="n">0</span>] <span class="c">// 20</span>
</code></pre></td>
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</table>
@ -599,11 +599,11 @@ to overwrite those elements with the provided data.</p>
<span class="l">4: </span>
<span class="l">5: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="k">let</span> <span class="i">m</span> <span class="o">=</span> <span class="i">DenseMatrix</span><span class="o">.</span><span class="i">init</span> <span class="n">6</span> <span class="n">4</span> (<span class="k">fun</span> <span class="i">i</span> <span class="i">j</span> <span class="k">-&gt;</span> <span class="i">float</span> (<span class="n">10</span><span class="o">*</span><span class="i">i</span> <span class="o">+</span> <span class="i">j</span>))
<span class="i">m</span><span class="o">.</span>[<span class="n">0</span>,<span class="n">0..</span><span class="n">3</span>] <span class="c">// vector [0,1,2,3]</span>
<span class="i">m</span><span class="o">.</span>[<span class="n">1..</span><span class="n">2</span>,<span class="n">0..</span><span class="n">3</span>] <span class="c">// matrix [10,11,12,13; 20,21,22,23]</span>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="k">let</span> <span onmouseout="hideTip(event, 'fs21', 36)" onmouseover="showTip(event, 'fs21', 36)" class="i">m</span> <span class="o">=</span> <span class="i">DenseMatrix</span><span class="o">.</span><span class="i">init</span> <span class="n">6</span> <span class="n">4</span> (<span class="k">fun</span> <span class="i">i</span> <span class="i">j</span> <span class="k">-&gt;</span> <span onmouseout="hideTip(event, 'fs4', 37)" onmouseover="showTip(event, 'fs4', 37)" class="i">float</span> (<span class="n">10</span><span class="o">*</span><span class="i">i</span> <span class="o">+</span> <span class="i">j</span>))
<span onmouseout="hideTip(event, 'fs21', 38)" onmouseover="showTip(event, 'fs21', 38)" class="i">m</span><span class="o">.</span>[<span class="n">0</span>,<span class="n">0..</span><span class="n">3</span>] <span class="c">// vector [0,1,2,3]</span>
<span onmouseout="hideTip(event, 'fs21', 39)" onmouseover="showTip(event, 'fs21', 39)" class="i">m</span><span class="o">.</span>[<span class="n">1..</span><span class="n">2</span>,<span class="n">0..</span><span class="n">3</span>] <span class="c">// matrix [10,11,12,13; 20,21,22,23]</span>
<span class="c">// overwrite a sub-matrix with the content of another matrix:</span>
<span class="i">m</span><span class="o">.</span>[<span class="n">0..</span><span class="n">1</span>,<span class="n">1..</span><span class="n">2</span>] <span class="o">&lt;-</span> <span class="i">matrix</span> [[ <span class="n">3.0</span>; <span class="n">4.0</span> ]; [ <span class="n">5.0</span>; <span class="n">6.0</span> ]]
<span onmouseout="hideTip(event, 'fs21', 40)" onmouseover="showTip(event, 'fs21', 40)" class="i">m</span><span class="o">.</span>[<span class="n">0..</span><span class="n">1</span>,<span class="n">1..</span><span class="n">2</span>] <span class="o">&lt;-</span> <span class="i">matrix</span> [[ <span class="n">3.0</span>; <span class="n">4.0</span> ]; [ <span class="n">5.0</span>; <span class="n">6.0</span> ]]
</code></pre></td>
</tr>
</table>
@ -689,8 +689,8 @@ Vector&lt;Double&gt; v <span class="o">=</span> u.Map(c <span class="o">=</span>
<table class="pre"><tr><td class="lines"><pre class="fssnip"><span class="l">1: </span>
<span class="l">2: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="k">let</span> <span class="i">u</span> <span class="o">=</span> <span class="i">DenseVector</span><span class="o">.</span><span class="i">randomStandard</span><span class="o">&lt;</span><span class="i">Complex</span><span class="o">&gt;</span> <span class="n">10</span>
<span class="k">let</span> <span class="i">v</span> <span class="o">=</span> <span class="i">u</span> <span class="o">|&gt;</span> <span class="i">Vector</span><span class="o">.</span><span class="i">map</span> (<span class="k">fun</span> <span class="i">c</span> <span class="k">-&gt;</span> <span class="i">c</span><span class="o">.</span><span class="i">Real</span>)
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="k">let</span> <span onmouseout="hideTip(event, 'fs22', 41)" onmouseover="showTip(event, 'fs22', 41)" class="i">u</span> <span class="o">=</span> <span class="i">DenseVector</span><span class="o">.</span><span class="i">randomStandard</span><span class="o">&lt;</span><span onmouseout="hideTip(event, 'fs23', 42)" onmouseover="showTip(event, 'fs23', 42)" class="i">Complex</span><span class="o">&gt;</span> <span class="n">10</span>
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs24', 43)" onmouseover="showTip(event, 'fs24', 43)" class="i">v</span> <span class="o">=</span> <span onmouseout="hideTip(event, 'fs22', 44)" onmouseover="showTip(event, 'fs22', 44)" class="i">u</span> <span class="o">|&gt;</span> <span class="i">Vector</span><span class="o">.</span><span class="i">map</span> (<span class="k">fun</span> <span class="i">c</span> <span class="k">-&gt;</span> <span class="i">c</span><span class="o">.</span><span class="i">Real</span>)
</code></pre></td>
</tr>
</table>
@ -917,6 +917,30 @@ DenseMatrix 5x100-Double
to load the MathNet.Numerics.fsx script of the F# package. Besides loading
the assemblies it also adds proper FSI printers for both matrices and vectors.</p>
<div class="tip" id="fs1">val m1 : obj<br /><br />Full name: Matrix.m1</div>
<div class="tip" id="fs2">val v1 : obj<br /><br />Full name: Matrix.v1</div>
<div class="tip" id="fs3">val m2 : obj<br /><br />Full name: Matrix.m2</div>
<div class="tip" id="fs4">Multiple items<br />val float : value:&#39;T -&gt; float (requires member op_Explicit)<br /><br />Full name: Microsoft.FSharp.Core.Operators.float<br /><br />--------------------<br />type float = System.Double<br /><br />Full name: Microsoft.FSharp.Core.float<br /><br />--------------------<br />type float&lt;&#39;Measure&gt; = float<br /><br />Full name: Microsoft.FSharp.Core.float&lt;_&gt;</div>
<div class="tip" id="fs5">val m3 : obj<br /><br />Full name: Matrix.m3</div>
<div class="tip" id="fs6">val m4 : obj<br /><br />Full name: Matrix.m4</div>
<div class="tip" id="fs7">Multiple items<br />val float32 : value:&#39;T -&gt; float32 (requires member op_Explicit)<br /><br />Full name: Microsoft.FSharp.Core.Operators.float32<br /><br />--------------------<br />type float32 = System.Single<br /><br />Full name: Microsoft.FSharp.Core.float32<br /><br />--------------------<br />type float32&lt;&#39;Measure&gt; = float32<br /><br />Full name: Microsoft.FSharp.Core.float32&lt;_&gt;</div>
<div class="tip" id="fs8">val x : seq&lt;seq&lt;float&gt;&gt;<br /><br />Full name: Matrix.x</div>
<div class="tip" id="fs9">module Seq<br /><br />from Microsoft.FSharp.Collections</div>
<div class="tip" id="fs10">val init : count:int -&gt; initializer:(int -&gt; &#39;T) -&gt; seq&lt;&#39;T&gt;<br /><br />Full name: Microsoft.FSharp.Collections.Seq.init</div>
<div class="tip" id="fs11">val c : int</div>
<div class="tip" id="fs12">val r : int</div>
<div class="tip" id="fs13">val m5 : obj<br /><br />Full name: Matrix.m5</div>
<div class="tip" id="fs14">val m6 : obj<br /><br />Full name: Matrix.m6</div>
<div class="tip" id="fs15">val m7a : obj<br /><br />Full name: Matrix.m7a</div>
<div class="tip" id="fs16">val m7b : obj<br /><br />Full name: Matrix.m7b</div>
<div class="tip" id="fs17">val m : float<br /><br />Full name: Matrix.m</div>
<div class="tip" id="fs18">val v : float<br /><br />Full name: Matrix.v</div>
<div class="tip" id="fs19">val v&#39; : float<br /><br />Full name: Matrix.v&#39;</div>
<div class="tip" id="fs20">val m&#39; : float<br /><br />Full name: Matrix.m&#39;</div>
<div class="tip" id="fs21">val m : obj<br /><br />Full name: Matrix.m</div>
<div class="tip" id="fs22">val u : obj<br /><br />Full name: Matrix.u</div>
<div class="tip" id="fs23">Multiple items<br />type Complex =<br />&#160;&#160;struct<br />&#160;&#160;&#160;&#160;new : real:float * imaginary:float -&gt; Complex<br />&#160;&#160;&#160;&#160;member Equals : obj:obj -&gt; bool + 1 overload<br />&#160;&#160;&#160;&#160;member GetHashCode : unit -&gt; int<br />&#160;&#160;&#160;&#160;member Imaginary : float<br />&#160;&#160;&#160;&#160;member Magnitude : float<br />&#160;&#160;&#160;&#160;member Phase : float<br />&#160;&#160;&#160;&#160;member Real : float<br />&#160;&#160;&#160;&#160;member ToString : unit -&gt; string + 3 overloads<br />&#160;&#160;&#160;&#160;static val Zero : Complex<br />&#160;&#160;&#160;&#160;static val One : Complex<br />&#160;&#160;&#160;&#160;...<br />&#160;&#160;end<br /><br />Full name: System.Numerics.Complex<br /><br />--------------------<br />Complex()<br />Complex(real: float, imaginary: float) : unit</div>
<div class="tip" id="fs24">val v : obj<br /><br />Full name: Matrix.v</div>
</div>
<div class="span3">

130
Probability.html
View File

@ -198,12 +198,12 @@ gamma<span class="n">2</span>.RandomSource <span class="o">=</span> <span class=
<span class="l">7: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="c">// some probability distributions</span>
<span class="k">let</span> <span class="i">normal</span> <span class="o">=</span> <span class="i">Normal</span><span class="o">.</span><span class="i">WithMeanVariance</span>(<span class="n">3.0</span>, <span class="n">1.5</span>, <span class="i">a</span>)
<span class="k">let</span> <span class="i">exponential</span> <span class="o">=</span> <span class="i">Exponential</span>(<span class="n">2.4</span>)
<span class="k">let</span> <span class="i">gamma</span> <span class="o">=</span> <span class="i">Gamma</span>(<span class="n">2.0</span>, <span class="n">1.5</span>, <span class="i">Random</span><span class="o">.</span><span class="i">crypto</span>())
<span class="k">let</span> <span class="i">cauchy</span> <span class="o">=</span> <span class="i">Cauchy</span>(<span class="n">0.0</span>, <span class="n">1.0</span>, <span class="i">Random</span><span class="o">.</span><span class="i">mrg32k3aWith</span> <span class="n">10</span> <span class="k">false</span>)
<span class="k">let</span> <span class="i">poisson</span> <span class="o">=</span> <span class="i">Poisson</span>(<span class="n">3.0</span>)
<span class="k">let</span> <span class="i">geometric</span> <span class="o">=</span> <span class="i">Geometric</span>(<span class="n">0.8</span>, <span class="i">Random</span><span class="o">.</span><span class="i">system</span>())
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs1', 1)" onmouseover="showTip(event, 'fs1', 1)" class="i">normal</span> <span class="o">=</span> <span class="i">Normal</span><span class="o">.</span><span class="i">WithMeanVariance</span>(<span class="n">3.0</span>, <span class="n">1.5</span>, <span class="i">a</span>)
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs2', 2)" onmouseover="showTip(event, 'fs2', 2)" class="i">exponential</span> <span class="o">=</span> <span class="i">Exponential</span>(<span class="n">2.4</span>)
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs3', 3)" onmouseover="showTip(event, 'fs3', 3)" class="i">gamma</span> <span class="o">=</span> <span class="i">Gamma</span>(<span class="n">2.0</span>, <span class="n">1.5</span>, <span class="i">Random</span><span class="o">.</span><span class="i">crypto</span>())
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs4', 4)" onmouseover="showTip(event, 'fs4', 4)" class="i">cauchy</span> <span class="o">=</span> <span class="i">Cauchy</span>(<span class="n">0.0</span>, <span class="n">1.0</span>, <span class="i">Random</span><span class="o">.</span><span class="i">mrg32k3aWith</span> <span class="n">10</span> <span class="k">false</span>)
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs5', 5)" onmouseover="showTip(event, 'fs5', 5)" class="i">poisson</span> <span class="o">=</span> <span class="i">Poisson</span>(<span class="n">3.0</span>)
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs6', 6)" onmouseover="showTip(event, 'fs6', 6)" class="i">geometric</span> <span class="o">=</span> <span class="i">Geometric</span>(<span class="n">0.8</span>, <span class="i">Random</span><span class="o">.</span><span class="i">system</span>())
</code></pre></td>
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</table>
@ -213,9 +213,9 @@ estimation from a set of samples:</p>
<span class="l">2: </span>
<span class="l">3: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="k">let</span> <span class="i">estimation</span> <span class="o">=</span> <span class="i">LogNormal</span><span class="o">.</span><span class="i">Estimate</span>([| <span class="n">2.0</span>; <span class="n">1.5</span>; <span class="n">2.1</span>; <span class="n">1.2</span>; <span class="n">3.0</span>; <span class="n">2.4</span>; <span class="n">1.8</span> |])
<span class="k">let</span> <span class="i">mean</span>, <span class="i">variance</span> <span class="o">=</span> <span class="i">estimation</span><span class="o">.</span><span class="i">Mean</span>, <span class="i">estimation</span><span class="o">.</span><span class="i">Variance</span>
<span class="k">let</span> <span class="i">moreSamples</span> <span class="o">=</span> <span class="i">estimation</span><span class="o">.</span><span class="i">Samples</span>() <span class="o">|&gt;</span> <span class="i">Seq</span><span class="o">.</span><span class="i">take</span> <span class="n">10</span> <span class="o">|&gt;</span> <span class="i">Seq</span><span class="o">.</span><span class="i">toArray</span>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="k">let</span> <span onmouseout="hideTip(event, 'fs7', 7)" onmouseover="showTip(event, 'fs7', 7)" class="i">estimation</span> <span class="o">=</span> <span class="i">LogNormal</span><span class="o">.</span><span class="i">Estimate</span>([| <span class="n">2.0</span>; <span class="n">1.5</span>; <span class="n">2.1</span>; <span class="n">1.2</span>; <span class="n">3.0</span>; <span class="n">2.4</span>; <span class="n">1.8</span> |])
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs8', 8)" onmouseover="showTip(event, 'fs8', 8)" class="i">mean</span>, <span onmouseout="hideTip(event, 'fs9', 9)" onmouseover="showTip(event, 'fs9', 9)" class="i">variance</span> <span class="o">=</span> <span onmouseout="hideTip(event, 'fs7', 10)" onmouseover="showTip(event, 'fs7', 10)" class="i">estimation</span><span class="o">.</span><span class="i">Mean</span>, <span onmouseout="hideTip(event, 'fs7', 11)" onmouseover="showTip(event, 'fs7', 11)" class="i">estimation</span><span class="o">.</span><span class="i">Variance</span>
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs10', 12)" onmouseover="showTip(event, 'fs10', 12)" class="i">moreSamples</span> <span class="o">=</span> <span onmouseout="hideTip(event, 'fs7', 13)" onmouseover="showTip(event, 'fs7', 13)" class="i">estimation</span><span class="o">.</span><span class="i">Samples</span>() <span class="o">|&gt;</span> <span onmouseout="hideTip(event, 'fs11', 14)" onmouseover="showTip(event, 'fs11', 14)" class="t">Seq</span><span class="o">.</span><span onmouseout="hideTip(event, 'fs12', 15)" onmouseover="showTip(event, 'fs12', 15)" class="f">take</span> <span class="n">10</span> <span class="o">|&gt;</span> <span onmouseout="hideTip(event, 'fs11', 16)" onmouseover="showTip(event, 'fs11', 16)" class="t">Seq</span><span class="o">.</span><span onmouseout="hideTip(event, 'fs13', 17)" onmouseover="showTip(event, 'fs13', 17)" class="f">toArray</span>
</code></pre></td>
</tr>
</table>
@ -249,16 +249,16 @@ but one can easily replace this with more sophisticated random number generators
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="c">// sample some random numbers from these distributions</span>
<span class="c">// continuous distributions sample to floating-point numbers:</span>
<span class="k">let</span> <span class="i">continuous</span> <span class="o">=</span>
[ <span class="k">yield</span> <span class="i">normal</span><span class="o">.</span><span class="i">Sample</span>()
<span class="k">yield</span> <span class="i">exponential</span><span class="o">.</span><span class="i">Sample</span>()
<span class="k">yield!</span> <span class="i">gamma</span><span class="o">.</span><span class="i">Samples</span>() <span class="o">|&gt;</span> <span class="i">Seq</span><span class="o">.</span><span class="i">take</span> <span class="n">10</span> ]
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs14', 18)" onmouseover="showTip(event, 'fs14', 18)" class="i">continuous</span> <span class="o">=</span>
[ <span class="k">yield</span> <span onmouseout="hideTip(event, 'fs1', 19)" onmouseover="showTip(event, 'fs1', 19)" class="i">normal</span><span class="o">.</span><span class="i">Sample</span>()
<span class="k">yield</span> <span onmouseout="hideTip(event, 'fs2', 20)" onmouseover="showTip(event, 'fs2', 20)" class="i">exponential</span><span class="o">.</span><span class="i">Sample</span>()
<span class="k">yield!</span> <span onmouseout="hideTip(event, 'fs3', 21)" onmouseover="showTip(event, 'fs3', 21)" class="i">gamma</span><span class="o">.</span><span class="i">Samples</span>() <span class="o">|&gt;</span> <span onmouseout="hideTip(event, 'fs11', 22)" onmouseover="showTip(event, 'fs11', 22)" class="t">Seq</span><span class="o">.</span><span onmouseout="hideTip(event, 'fs12', 23)" onmouseover="showTip(event, 'fs12', 23)" class="f">take</span> <span class="n">10</span> ]
<span class="c">// discrete distributions on the other hand sample to integers:</span>
<span class="k">let</span> <span class="i">discrete</span> <span class="o">=</span>
[ <span class="i">poisson</span><span class="o">.</span><span class="i">Sample</span>()
<span class="i">poisson</span><span class="o">.</span><span class="i">Sample</span>()
<span class="i">geometric</span><span class="o">.</span><span class="i">Sample</span>() ]
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs15', 24)" onmouseover="showTip(event, 'fs15', 24)" class="i">discrete</span> <span class="o">=</span>
[ <span onmouseout="hideTip(event, 'fs5', 25)" onmouseover="showTip(event, 'fs5', 25)" class="i">poisson</span><span class="o">.</span><span class="i">Sample</span>()
<span onmouseout="hideTip(event, 'fs5', 26)" onmouseover="showTip(event, 'fs5', 26)" class="i">poisson</span><span class="o">.</span><span class="i">Sample</span>()
<span onmouseout="hideTip(event, 'fs6', 27)" onmouseover="showTip(event, 'fs6', 27)" class="i">geometric</span><span class="o">.</span><span class="i">Sample</span>() ]
</code></pre></td>
</tr>
</table>
@ -273,12 +273,12 @@ Note that no intermediate value caching is possible this way and parameters must
<span class="l">7: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="c">// using the default number generator (SystemRandomSource.Default)</span>
<span class="k">let</span> <span class="i">w</span> <span class="o">=</span> <span class="i">Rayleigh</span><span class="o">.</span><span class="i">Sample</span>(<span class="n">1.5</span>)
<span class="k">let</span> <span class="i">x</span> <span class="o">=</span> <span class="i">Hypergeometric</span><span class="o">.</span><span class="i">Sample</span>(<span class="n">100</span>, <span class="n">20</span>, <span class="n">5</span>)
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs16', 28)" onmouseover="showTip(event, 'fs16', 28)" class="i">w</span> <span class="o">=</span> <span class="i">Rayleigh</span><span class="o">.</span><span class="i">Sample</span>(<span class="n">1.5</span>)
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs17', 29)" onmouseover="showTip(event, 'fs17', 29)" class="i">x</span> <span class="o">=</span> <span class="i">Hypergeometric</span><span class="o">.</span><span class="i">Sample</span>(<span class="n">100</span>, <span class="n">20</span>, <span class="n">5</span>)
<span class="c">// or by manually providing the uniform random number generator</span>
<span class="k">let</span> <span class="i">u</span> <span class="o">=</span> <span class="i">Normal</span><span class="o">.</span><span class="i">Sample</span>(<span class="i">Random</span><span class="o">.</span><span class="i">system</span>(), <span class="n">2.0</span>, <span class="n">4.0</span>)
<span class="k">let</span> <span class="i">v</span> <span class="o">=</span> <span class="i">Laplace</span><span class="o">.</span><span class="i">Samples</span>(<span class="i">Random</span><span class="o">.</span><span class="i">mersenneTwister</span>(), <span class="n">1.0</span>, <span class="n">3.0</span>) <span class="o">|&gt;</span> <span class="i">Seq</span><span class="o">.</span><span class="i">take</span> <span class="n">100</span> <span class="o">|&gt;</span> <span class="i">List</span><span class="o">.</span><span class="i">ofSeq</span>
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs18', 30)" onmouseover="showTip(event, 'fs18', 30)" class="i">u</span> <span class="o">=</span> <span class="i">Normal</span><span class="o">.</span><span class="i">Sample</span>(<span class="i">Random</span><span class="o">.</span><span class="i">system</span>(), <span class="n">2.0</span>, <span class="n">4.0</span>)
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs19', 31)" onmouseover="showTip(event, 'fs19', 31)" class="i">v</span> <span class="o">=</span> <span class="i">Laplace</span><span class="o">.</span><span class="i">Samples</span>(<span class="i">Random</span><span class="o">.</span><span class="i">mersenneTwister</span>(), <span class="n">1.0</span>, <span class="n">3.0</span>) <span class="o">|&gt;</span> <span onmouseout="hideTip(event, 'fs11', 32)" onmouseover="showTip(event, 'fs11', 32)" class="t">Seq</span><span class="o">.</span><span onmouseout="hideTip(event, 'fs12', 33)" onmouseover="showTip(event, 'fs12', 33)" class="f">take</span> <span class="n">100</span> <span class="o">|&gt;</span> <span onmouseout="hideTip(event, 'fs20', 34)" onmouseover="showTip(event, 'fs20', 34)" class="t">List</span><span class="o">.</span><span onmouseout="hideTip(event, 'fs21', 35)" onmouseover="showTip(event, 'fs21', 35)" class="f">ofSeq</span>
</code></pre></td>
</tr>
</table>
@ -297,8 +297,8 @@ Laplace.Samples(samples, <span class="n">1.0</span>, <span class="n">2.0</span>)
<table class="pre"><tr><td class="lines"><pre class="fssnip"><span class="l">1: </span>
<span class="l">2: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="i">Seq</span><span class="o">.</span><span class="i">scan</span> (<span class="o">+</span>) <span class="n">0.0</span> (<span class="i">Normal</span><span class="o">.</span><span class="i">Samples</span>(<span class="n">0.0</span>, <span class="n">1.0</span>)) <span class="o">|&gt;</span> <span class="i">Seq</span><span class="o">.</span><span class="i">take</span> <span class="n">10</span> <span class="o">|&gt;</span> <span class="i">Seq</span><span class="o">.</span><span class="i">toArray</span>
<span class="i">Seq</span><span class="o">.</span><span class="i">scan</span> (<span class="o">+</span>) <span class="n">0.0</span> (<span class="i">Cauchy</span><span class="o">.</span><span class="i">Samples</span>(<span class="n">0.0</span>, <span class="n">1.0</span>)) <span class="o">|&gt;</span> <span class="i">Seq</span><span class="o">.</span><span class="i">take</span> <span class="n">10</span> <span class="o">|&gt;</span> <span class="i">Seq</span><span class="o">.</span><span class="i">toArray</span>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span onmouseout="hideTip(event, 'fs11', 36)" onmouseover="showTip(event, 'fs11', 36)" class="t">Seq</span><span class="o">.</span><span onmouseout="hideTip(event, 'fs22', 37)" onmouseover="showTip(event, 'fs22', 37)" class="f">scan</span> (<span class="o">+</span>) <span class="n">0.0</span> (<span class="i">Normal</span><span class="o">.</span><span class="i">Samples</span>(<span class="n">0.0</span>, <span class="n">1.0</span>)) <span class="o">|&gt;</span> <span onmouseout="hideTip(event, 'fs11', 38)" onmouseover="showTip(event, 'fs11', 38)" class="t">Seq</span><span class="o">.</span><span onmouseout="hideTip(event, 'fs12', 39)" onmouseover="showTip(event, 'fs12', 39)" class="f">take</span> <span class="n">10</span> <span class="o">|&gt;</span> <span onmouseout="hideTip(event, 'fs11', 40)" onmouseover="showTip(event, 'fs11', 40)" class="t">Seq</span><span class="o">.</span><span onmouseout="hideTip(event, 'fs13', 41)" onmouseover="showTip(event, 'fs13', 41)" class="f">toArray</span>
<span onmouseout="hideTip(event, 'fs11', 42)" onmouseover="showTip(event, 'fs11', 42)" class="t">Seq</span><span class="o">.</span><span onmouseout="hideTip(event, 'fs22', 43)" onmouseover="showTip(event, 'fs22', 43)" class="f">scan</span> (<span class="o">+</span>) <span class="n">0.0</span> (<span class="i">Cauchy</span><span class="o">.</span><span class="i">Samples</span>(<span class="n">0.0</span>, <span class="n">1.0</span>)) <span class="o">|&gt;</span> <span onmouseout="hideTip(event, 'fs11', 44)" onmouseover="showTip(event, 'fs11', 44)" class="t">Seq</span><span class="o">.</span><span onmouseout="hideTip(event, 'fs12', 45)" onmouseover="showTip(event, 'fs12', 45)" class="f">take</span> <span class="n">10</span> <span class="o">|&gt;</span> <span onmouseout="hideTip(event, 'fs11', 46)" onmouseover="showTip(event, 'fs11', 46)" class="t">Seq</span><span class="o">.</span><span onmouseout="hideTip(event, 'fs13', 47)" onmouseover="showTip(event, 'fs13', 47)" class="f">toArray</span>
</code></pre></td>
</tr>
</table>
@ -331,26 +331,26 @@ some of them are also available with the <code>Ln</code>-suffix.</p>
<span class="l">21: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="c">// distribution properties of the gamma we&#39;ve configured above</span>
<span class="k">let</span> <span class="i">gammaStats</span> <span class="o">=</span>
( <span class="i">gamma</span><span class="o">.</span><span class="i">Mean</span>,
<span class="i">gamma</span><span class="o">.</span><span class="i">Variance</span>,
<span class="i">gamma</span><span class="o">.</span><span class="i">StdDev</span>,
<span class="i">gamma</span><span class="o">.</span><span class="i">Entropy</span>,
<span class="i">gamma</span><span class="o">.</span><span class="i">Skewness</span>,
<span class="i">gamma</span><span class="o">.</span><span class="i">Mode</span> )
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs23', 48)" onmouseover="showTip(event, 'fs23', 48)" class="i">gammaStats</span> <span class="o">=</span>
( <span onmouseout="hideTip(event, 'fs3', 49)" onmouseover="showTip(event, 'fs3', 49)" class="i">gamma</span><span class="o">.</span><span class="i">Mean</span>,
<span onmouseout="hideTip(event, 'fs3', 50)" onmouseover="showTip(event, 'fs3', 50)" class="i">gamma</span><span class="o">.</span><span class="i">Variance</span>,
<span onmouseout="hideTip(event, 'fs3', 51)" onmouseover="showTip(event, 'fs3', 51)" class="i">gamma</span><span class="o">.</span><span class="i">StdDev</span>,
<span onmouseout="hideTip(event, 'fs3', 52)" onmouseover="showTip(event, 'fs3', 52)" class="i">gamma</span><span class="o">.</span><span class="i">Entropy</span>,
<span onmouseout="hideTip(event, 'fs3', 53)" onmouseover="showTip(event, 'fs3', 53)" class="i">gamma</span><span class="o">.</span><span class="i">Skewness</span>,
<span onmouseout="hideTip(event, 'fs3', 54)" onmouseover="showTip(event, 'fs3', 54)" class="i">gamma</span><span class="o">.</span><span class="i">Mode</span> )
<span class="c">// probability distribution functions of the normal we&#39;ve configured above.</span>
<span class="k">let</span> <span class="i">nd</span> <span class="o">=</span> <span class="i">normal</span><span class="o">.</span><span class="i">Density</span>(<span class="n">4.0</span>) <span class="c">(* PDF *)</span>
<span class="k">let</span> <span class="i">ndLn</span> <span class="o">=</span> <span class="i">normal</span><span class="o">.</span><span class="i">DensityLn</span>(<span class="n">4.0</span>) <span class="c">(* ln(PDF) *)</span>
<span class="k">let</span> <span class="i">nc</span> <span class="o">=</span> <span class="i">normal</span><span class="o">.</span><span class="i">CumulativeDistribution</span>(<span class="n">4.0</span>) <span class="c">(* CDF *)</span>
<span class="k">let</span> <span class="i">nic</span> <span class="o">=</span> <span class="i">normal</span><span class="o">.</span><span class="i">InverseCumulativeDistribution</span>(<span class="n">0.7</span>) <span class="c">(* CDF^(-1) *)</span>
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs24', 55)" onmouseover="showTip(event, 'fs24', 55)" class="i">nd</span> <span class="o">=</span> <span onmouseout="hideTip(event, 'fs1', 56)" onmouseover="showTip(event, 'fs1', 56)" class="i">normal</span><span class="o">.</span><span class="i">Density</span>(<span class="n">4.0</span>) <span class="c">(* PDF *)</span>
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs25', 57)" onmouseover="showTip(event, 'fs25', 57)" class="i">ndLn</span> <span class="o">=</span> <span onmouseout="hideTip(event, 'fs1', 58)" onmouseover="showTip(event, 'fs1', 58)" class="i">normal</span><span class="o">.</span><span class="i">DensityLn</span>(<span class="n">4.0</span>) <span class="c">(* ln(PDF) *)</span>
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs26', 59)" onmouseover="showTip(event, 'fs26', 59)" class="i">nc</span> <span class="o">=</span> <span onmouseout="hideTip(event, 'fs1', 60)" onmouseover="showTip(event, 'fs1', 60)" class="i">normal</span><span class="o">.</span><span class="i">CumulativeDistribution</span>(<span class="n">4.0</span>) <span class="c">(* CDF *)</span>
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs27', 61)" onmouseover="showTip(event, 'fs27', 61)" class="i">nic</span> <span class="o">=</span> <span onmouseout="hideTip(event, 'fs1', 62)" onmouseover="showTip(event, 'fs1', 62)" class="i">normal</span><span class="o">.</span><span class="i">InverseCumulativeDistribution</span>(<span class="n">0.7</span>) <span class="c">(* CDF^(-1) *)</span>
<span class="c">// Distribution functions can also be evaluated without creating an object,</span>
<span class="c">// but then you have to pass in the distribution parameters as first arguments:</span>
<span class="k">let</span> <span class="i">nd2</span> <span class="o">=</span> <span class="i">Normal</span><span class="o">.</span><span class="i">PDF</span>(<span class="n">3.0</span>, <span class="i">sqrt</span> <span class="n">1.5</span>, <span class="n">4.0</span>)
<span class="k">let</span> <span class="i">ndLn2</span> <span class="o">=</span> <span class="i">Normal</span><span class="o">.</span><span class="i">PDFLn</span>(<span class="n">3.0</span>, <span class="i">sqrt</span> <span class="n">1.5</span>, <span class="n">4.0</span>)
<span class="k">let</span> <span class="i">nc2</span> <span class="o">=</span> <span class="i">Normal</span><span class="o">.</span><span class="i">CDF</span>(<span class="n">3.0</span>, <span class="i">sqrt</span> <span class="n">1.5</span>, <span class="n">4.0</span>)
<span class="k">let</span> <span class="i">nic2</span> <span class="o">=</span> <span class="i">Normal</span><span class="o">.</span><span class="i">InvCDF</span>(<span class="n">3.0</span>, <span class="i">sqrt</span> <span class="n">1.5</span>, <span class="n">0.7</span>)
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs28', 63)" onmouseover="showTip(event, 'fs28', 63)" class="i">nd2</span> <span class="o">=</span> <span class="i">Normal</span><span class="o">.</span><span class="i">PDF</span>(<span class="n">3.0</span>, <span onmouseout="hideTip(event, 'fs29', 64)" onmouseover="showTip(event, 'fs29', 64)" class="i">sqrt</span> <span class="n">1.5</span>, <span class="n">4.0</span>)
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs30', 65)" onmouseover="showTip(event, 'fs30', 65)" class="i">ndLn2</span> <span class="o">=</span> <span class="i">Normal</span><span class="o">.</span><span class="i">PDFLn</span>(<span class="n">3.0</span>, <span onmouseout="hideTip(event, 'fs29', 66)" onmouseover="showTip(event, 'fs29', 66)" class="i">sqrt</span> <span class="n">1.5</span>, <span class="n">4.0</span>)
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs31', 67)" onmouseover="showTip(event, 'fs31', 67)" class="i">nc2</span> <span class="o">=</span> <span class="i">Normal</span><span class="o">.</span><span class="i">CDF</span>(<span class="n">3.0</span>, <span onmouseout="hideTip(event, 'fs29', 68)" onmouseover="showTip(event, 'fs29', 68)" class="i">sqrt</span> <span class="n">1.5</span>, <span class="n">4.0</span>)
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs32', 69)" onmouseover="showTip(event, 'fs32', 69)" class="i">nic2</span> <span class="o">=</span> <span class="i">Normal</span><span class="o">.</span><span class="i">InvCDF</span>(<span class="n">3.0</span>, <span onmouseout="hideTip(event, 'fs29', 70)" onmouseover="showTip(event, 'fs29', 70)" class="i">sqrt</span> <span class="n">1.5</span>, <span class="n">0.7</span>)
</code></pre></td>
</tr>
</table>
@ -376,25 +376,65 @@ This way they can be composed and transformed arbitrarily if curried:</p>
<span class="l">16: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="c">/// Transform a sample from a distribution</span>
<span class="k">let</span> <span class="i">s1</span> <span class="i">rng</span> <span class="o">=</span> <span class="i">tanh</span> (<span class="i">Sample</span><span class="o">.</span><span class="i">normal</span> <span class="n">2.0</span> <span class="n">0.5</span> <span class="i">rng</span>)
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs33', 71)" onmouseover="showTip(event, 'fs33', 71)" class="f">s1</span> <span onmouseout="hideTip(event, 'fs34', 72)" onmouseover="showTip(event, 'fs34', 72)" class="i">rng</span> <span class="o">=</span> <span onmouseout="hideTip(event, 'fs35', 73)" onmouseover="showTip(event, 'fs35', 73)" class="f">tanh</span> (<span class="i">Sample</span><span class="o">.</span><span onmouseout="hideTip(event, 'fs1', 74)" onmouseover="showTip(event, 'fs1', 74)" class="i">normal</span> <span class="n">2.0</span> <span class="n">0.5</span> <span onmouseout="hideTip(event, 'fs34', 75)" onmouseover="showTip(event, 'fs34', 75)" class="i">rng</span>)
<span class="c">/// But we really want to transform the function, not the resulting sample:</span>
<span class="k">let</span> <span class="i">s1f</span> <span class="i">rng</span> <span class="o">=</span> <span class="i">Sample</span><span class="o">.</span><span class="i">map</span> <span class="i">tanh</span> (<span class="i">Sample</span><span class="o">.</span><span class="i">normal</span> <span class="n">2.0</span> <span class="n">0.5</span>) <span class="i">rng</span>
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs36', 76)" onmouseover="showTip(event, 'fs36', 76)" class="f">s1f</span> <span onmouseout="hideTip(event, 'fs34', 77)" onmouseover="showTip(event, 'fs34', 77)" class="i">rng</span> <span class="o">=</span> <span class="i">Sample</span><span class="o">.</span><span class="i">map</span> <span onmouseout="hideTip(event, 'fs35', 78)" onmouseover="showTip(event, 'fs35', 78)" class="i">tanh</span> (<span class="i">Sample</span><span class="o">.</span><span onmouseout="hideTip(event, 'fs1', 79)" onmouseover="showTip(event, 'fs1', 79)" class="i">normal</span> <span class="n">2.0</span> <span class="n">0.5</span>) <span onmouseout="hideTip(event, 'fs34', 80)" onmouseover="showTip(event, 'fs34', 80)" class="i">rng</span>
<span class="c">/// Exactly the same also works with functions generating full sequences</span>
<span class="k">let</span> <span class="i">s1s</span> <span class="i">rng</span> <span class="o">=</span> <span class="i">Sample</span><span class="o">.</span><span class="i">mapSeq</span> <span class="i">tanh</span> (<span class="i">Sample</span><span class="o">.</span><span class="i">normalSeq</span> <span class="n">2.0</span> <span class="n">0.5</span>) <span class="i">rng</span>
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs37', 81)" onmouseover="showTip(event, 'fs37', 81)" class="f">s1s</span> <span onmouseout="hideTip(event, 'fs34', 82)" onmouseover="showTip(event, 'fs34', 82)" class="i">rng</span> <span class="o">=</span> <span class="i">Sample</span><span class="o">.</span><span class="i">mapSeq</span> <span onmouseout="hideTip(event, 'fs35', 83)" onmouseover="showTip(event, 'fs35', 83)" class="i">tanh</span> (<span class="i">Sample</span><span class="o">.</span><span class="i">normalSeq</span> <span class="n">2.0</span> <span class="n">0.5</span>) <span onmouseout="hideTip(event, 'fs34', 84)" onmouseover="showTip(event, 'fs34', 84)" class="i">rng</span>
<span class="c">/// Now with multiple distributions, e.g. their product:</span>
<span class="k">let</span> <span class="i">s2</span> <span class="i">rng</span> <span class="o">=</span> (<span class="i">Sample</span><span class="o">.</span><span class="i">normal</span> <span class="n">2.0</span> <span class="n">1.5</span> <span class="i">rng</span>) <span class="o">*</span> (<span class="i">Sample</span><span class="o">.</span><span class="i">cauchy</span> <span class="n">2.0</span> <span class="n">0.5</span> <span class="i">rng</span>)
<span class="k">let</span> <span class="i">s2f</span> <span class="i">rng</span> <span class="o">=</span> <span class="i">Sample</span><span class="o">.</span><span class="i">map2</span> <span class="o">(*)</span> (<span class="i">Sample</span><span class="o">.</span><span class="i">normal</span> <span class="n">2.0</span> <span class="n">1.5</span>) (<span class="i">Sample</span><span class="o">.</span><span class="i">cauchy</span> <span class="n">2.0</span> <span class="n">0.5</span>) <span class="i">rng</span>
<span class="k">let</span> <span class="i">s2s</span> <span class="i">rng</span> <span class="o">=</span> <span class="i">Sample</span><span class="o">.</span><span class="i">mapSeq2</span> <span class="o">(*)</span> (<span class="i">Sample</span><span class="o">.</span><span class="i">normalSeq</span> <span class="n">2.0</span> <span class="n">1.5</span>) (<span class="i">Sample</span><span class="o">.</span><span class="i">cauchySeq</span> <span class="n">2.0</span> <span class="n">0.5</span>) <span class="i">rng</span>
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs38', 85)" onmouseover="showTip(event, 'fs38', 85)" class="f">s2</span> <span onmouseout="hideTip(event, 'fs34', 86)" onmouseover="showTip(event, 'fs34', 86)" class="i">rng</span> <span class="o">=</span> (<span class="i">Sample</span><span class="o">.</span><span onmouseout="hideTip(event, 'fs1', 87)" onmouseover="showTip(event, 'fs1', 87)" class="i">normal</span> <span class="n">2.0</span> <span class="n">1.5</span> <span onmouseout="hideTip(event, 'fs34', 88)" onmouseover="showTip(event, 'fs34', 88)" class="i">rng</span>) <span class="o">*</span> (<span class="i">Sample</span><span class="o">.</span><span onmouseout="hideTip(event, 'fs4', 89)" onmouseover="showTip(event, 'fs4', 89)" class="i">cauchy</span> <span class="n">2.0</span> <span class="n">0.5</span> <span onmouseout="hideTip(event, 'fs34', 90)" onmouseover="showTip(event, 'fs34', 90)" class="i">rng</span>)
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs39', 91)" onmouseover="showTip(event, 'fs39', 91)" class="f">s2f</span> <span onmouseout="hideTip(event, 'fs34', 92)" onmouseover="showTip(event, 'fs34', 92)" class="i">rng</span> <span class="o">=</span> <span class="i">Sample</span><span class="o">.</span><span class="i">map2</span> <span class="o">(*)</span> (<span class="i">Sample</span><span class="o">.</span><span onmouseout="hideTip(event, 'fs1', 93)" onmouseover="showTip(event, 'fs1', 93)" class="i">normal</span> <span class="n">2.0</span> <span class="n">1.5</span>) (<span class="i">Sample</span><span class="o">.</span><span onmouseout="hideTip(event, 'fs4', 94)" onmouseover="showTip(event, 'fs4', 94)" class="i">cauchy</span> <span class="n">2.0</span> <span class="n">0.5</span>) <span onmouseout="hideTip(event, 'fs34', 95)" onmouseover="showTip(event, 'fs34', 95)" class="i">rng</span>
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs40', 96)" onmouseover="showTip(event, 'fs40', 96)" class="f">s2s</span> <span onmouseout="hideTip(event, 'fs34', 97)" onmouseover="showTip(event, 'fs34', 97)" class="i">rng</span> <span class="o">=</span> <span class="i">Sample</span><span class="o">.</span><span class="i">mapSeq2</span> <span class="o">(*)</span> (<span class="i">Sample</span><span class="o">.</span><span class="i">normalSeq</span> <span class="n">2.0</span> <span class="n">1.5</span>) (<span class="i">Sample</span><span class="o">.</span><span class="i">cauchySeq</span> <span class="n">2.0</span> <span class="n">0.5</span>) <span onmouseout="hideTip(event, 'fs34', 98)" onmouseover="showTip(event, 'fs34', 98)" class="i">rng</span>
<span class="c">// Taking some samples from the composed function</span>
<span class="i">Seq</span><span class="o">.</span><span class="i">take</span> <span class="n">10</span> (<span class="i">s2s</span> (<span class="i">Random</span><span class="o">.</span><span class="i">system</span>())) <span class="o">|&gt;</span> <span class="i">Seq</span><span class="o">.</span><span class="i">toArray</span>
<span onmouseout="hideTip(event, 'fs11', 99)" onmouseover="showTip(event, 'fs11', 99)" class="t">Seq</span><span class="o">.</span><span onmouseout="hideTip(event, 'fs12', 100)" onmouseover="showTip(event, 'fs12', 100)" class="f">take</span> <span class="n">10</span> (<span onmouseout="hideTip(event, 'fs40', 101)" onmouseover="showTip(event, 'fs40', 101)" class="f">s2s</span> (<span class="i">Random</span><span class="o">.</span><span class="i">system</span>())) <span class="o">|&gt;</span> <span onmouseout="hideTip(event, 'fs11', 102)" onmouseover="showTip(event, 'fs11', 102)" class="t">Seq</span><span class="o">.</span><span onmouseout="hideTip(event, 'fs13', 103)" onmouseover="showTip(event, 'fs13', 103)" class="f">toArray</span>
</code></pre></td>
</tr>
</table>
<div class="tip" id="fs1">val normal : obj<br /><br />Full name: Probability.normal</div>
<div class="tip" id="fs2">val exponential : obj<br /><br />Full name: Probability.exponential</div>
<div class="tip" id="fs3">val gamma : obj<br /><br />Full name: Probability.gamma</div>
<div class="tip" id="fs4">val cauchy : obj<br /><br />Full name: Probability.cauchy</div>
<div class="tip" id="fs5">val poisson : obj<br /><br />Full name: Probability.poisson</div>
<div class="tip" id="fs6">val geometric : obj<br /><br />Full name: Probability.geometric</div>
<div class="tip" id="fs7">val estimation : obj<br /><br />Full name: Probability.estimation</div>
<div class="tip" id="fs8">val mean : obj<br /><br />Full name: Probability.mean</div>
<div class="tip" id="fs9">val variance : obj<br /><br />Full name: Probability.variance</div>
<div class="tip" id="fs10">val moreSamples : obj []<br /><br />Full name: Probability.moreSamples</div>
<div class="tip" id="fs11">module Seq<br /><br />from Microsoft.FSharp.Collections</div>
<div class="tip" id="fs12">val take : count:int -&gt; source:seq&lt;&#39;T&gt; -&gt; seq&lt;&#39;T&gt;<br /><br />Full name: Microsoft.FSharp.Collections.Seq.take</div>
<div class="tip" id="fs13">val toArray : source:seq&lt;&#39;T&gt; -&gt; &#39;T []<br /><br />Full name: Microsoft.FSharp.Collections.Seq.toArray</div>
<div class="tip" id="fs14">val continuous : obj list<br /><br />Full name: Probability.continuous</div>
<div class="tip" id="fs15">val discrete : obj list<br /><br />Full name: Probability.discrete</div>
<div class="tip" id="fs16">val w : obj<br /><br />Full name: Probability.w</div>
<div class="tip" id="fs17">val x : obj<br /><br />Full name: Probability.x</div>
<div class="tip" id="fs18">val u : obj<br /><br />Full name: Probability.u</div>
<div class="tip" id="fs19">val v : obj list<br /><br />Full name: Probability.v</div>
<div class="tip" id="fs20">Multiple items<br />module List<br /><br />from Microsoft.FSharp.Collections<br /><br />--------------------<br />type List&lt;&#39;T&gt; =<br />&#160;&#160;| ( [] )<br />&#160;&#160;| ( :: ) of Head: &#39;T * Tail: &#39;T list<br />&#160;&#160;interface IEnumerable<br />&#160;&#160;interface IEnumerable&lt;&#39;T&gt;<br />&#160;&#160;member GetSlice : startIndex:int option * endIndex:int option -&gt; &#39;T list<br />&#160;&#160;member Head : &#39;T<br />&#160;&#160;member IsEmpty : bool<br />&#160;&#160;member Item : index:int -&gt; &#39;T with get<br />&#160;&#160;member Length : int<br />&#160;&#160;member Tail : &#39;T list<br />&#160;&#160;static member Cons : head:&#39;T * tail:&#39;T list -&gt; &#39;T list<br />&#160;&#160;static member Empty : &#39;T list<br /><br />Full name: Microsoft.FSharp.Collections.List&lt;_&gt;</div>
<div class="tip" id="fs21">val ofSeq : source:seq&lt;&#39;T&gt; -&gt; &#39;T list<br /><br />Full name: Microsoft.FSharp.Collections.List.ofSeq</div>
<div class="tip" id="fs22">val scan : folder:(&#39;State -&gt; &#39;T -&gt; &#39;State) -&gt; state:&#39;State -&gt; source:seq&lt;&#39;T&gt; -&gt; seq&lt;&#39;State&gt;<br /><br />Full name: Microsoft.FSharp.Collections.Seq.scan</div>
<div class="tip" id="fs23">val gammaStats : obj * obj * obj * obj * obj * obj<br /><br />Full name: Probability.gammaStats</div>
<div class="tip" id="fs24">val nd : obj<br /><br />Full name: Probability.nd</div>
<div class="tip" id="fs25">val ndLn : obj<br /><br />Full name: Probability.ndLn</div>
<div class="tip" id="fs26">val nc : obj<br /><br />Full name: Probability.nc</div>
<div class="tip" id="fs27">val nic : obj<br /><br />Full name: Probability.nic</div>
<div class="tip" id="fs28">val nd2 : obj<br /><br />Full name: Probability.nd2</div>
<div class="tip" id="fs29">val sqrt : value:&#39;T -&gt; &#39;U (requires member Sqrt)<br /><br />Full name: Microsoft.FSharp.Core.Operators.sqrt</div>
<div class="tip" id="fs30">val ndLn2 : obj<br /><br />Full name: Probability.ndLn2</div>
<div class="tip" id="fs31">val nc2 : obj<br /><br />Full name: Probability.nc2</div>
<div class="tip" id="fs32">val nic2 : obj<br /><br />Full name: Probability.nic2</div>
<div class="tip" id="fs33">val s1 : rng:&#39;a -&gt; float<br /><br />Full name: Probability.s1<br /><em><br /><br />&#160;Transform a sample from a distribution</em></div>
<div class="tip" id="fs34">val rng : &#39;a</div>
<div class="tip" id="fs35">val tanh : value:&#39;T -&gt; &#39;T (requires member Tanh)<br /><br />Full name: Microsoft.FSharp.Core.Operators.tanh</div>
<div class="tip" id="fs36">val s1f : rng:&#39;a -&gt; &#39;b<br /><br />Full name: Probability.s1f<br /><em><br /><br />&#160;But we really want to transform the function, not the resulting sample:</em></div>
<div class="tip" id="fs37">val s1s : rng:&#39;a -&gt; &#39;b<br /><br />Full name: Probability.s1s<br /><em><br /><br />&#160;Exactly the same also works with functions generating full sequences</em></div>
<div class="tip" id="fs38">val s2 : rng:&#39;a -&gt; obj<br /><br />Full name: Probability.s2<br /><em><br /><br />&#160;Now with multiple distributions, e.g. their product:</em></div>
<div class="tip" id="fs39">val s2f : rng:&#39;a -&gt; &#39;b<br /><br />Full name: Probability.s2f</div>
<div class="tip" id="fs40">val s2s : rng:&#39;a -&gt; &#39;b<br /><br />Full name: Probability.s2s</div>
</div>
<div class="span3">

67
Random.html
View File

@ -124,18 +124,18 @@ System.Random rng <span class="o">=</span> SystemRandomSource.Default;
<span class="l">11: </span>
<span class="l">12: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="k">let</span> <span class="i">samples</span> <span class="o">=</span> <span class="i">Random</span><span class="o">.</span><span class="i">doubles</span> <span class="n">1000</span>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="k">let</span> <span onmouseout="hideTip(event, 'fs1', 1)" onmouseover="showTip(event, 'fs1', 1)" class="i">samples</span> <span class="o">=</span> <span class="i">Random</span><span class="o">.</span><span class="i">doubles</span> <span class="n">1000</span>
<span class="c">// overwrite the whole array with new random values</span>
<span class="i">Random</span><span class="o">.</span><span class="i">doubleFill</span> <span class="i">samples</span>
<span class="i">Random</span><span class="o">.</span><span class="i">doubleFill</span> <span onmouseout="hideTip(event, 'fs1', 2)" onmouseover="showTip(event, 'fs1', 2)" class="i">samples</span>
<span class="c">// create an infinite sequence:</span>
<span class="k">let</span> <span class="i">sampleSeq</span> <span class="o">=</span> <span class="i">Random</span><span class="o">.</span><span class="i">doubleSeq</span> ()
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs2', 3)" onmouseover="showTip(event, 'fs2', 3)" class="i">sampleSeq</span> <span class="o">=</span> <span class="i">Random</span><span class="o">.</span><span class="i">doubleSeq</span> ()
<span class="c">// take a single random value</span>
<span class="k">let</span> <span class="i">rng</span> <span class="o">=</span> <span class="i">Random</span><span class="o">.</span><span class="i">shared</span>
<span class="k">let</span> <span class="i">sample</span> <span class="o">=</span> <span class="i">rng</span><span class="o">.</span><span class="i">NextDouble</span>()
<span class="k">let</span> <span class="i">sampled</span> <span class="o">=</span> <span class="i">rng</span><span class="o">.</span><span class="i">NextDecimal</span>()
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs3', 4)" onmouseover="showTip(event, 'fs3', 4)" class="i">rng</span> <span class="o">=</span> <span class="i">Random</span><span class="o">.</span><span class="i">shared</span>
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs4', 5)" onmouseover="showTip(event, 'fs4', 5)" class="i">sample</span> <span class="o">=</span> <span onmouseout="hideTip(event, 'fs3', 6)" onmouseover="showTip(event, 'fs3', 6)" class="i">rng</span><span class="o">.</span><span class="i">NextDouble</span>()
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs5', 7)" onmouseover="showTip(event, 'fs5', 7)" class="i">sampled</span> <span class="o">=</span> <span onmouseout="hideTip(event, 'fs3', 8)" onmouseover="showTip(event, 'fs3', 8)" class="i">rng</span><span class="o">.</span><span class="i">NextDecimal</span>()
</code></pre></td>
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</table>
@ -187,9 +187,9 @@ or else a combination of a random number from a shared RNG, the time and a Guid
<span class="l">2: </span>
<span class="l">3: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="k">let</span> <span class="i">someTimeSeed</span> <span class="o">=</span> <span class="i">RandomSeed</span><span class="o">.</span><span class="i">Time</span>() <span class="c">// not recommended</span>
<span class="k">let</span> <span class="i">someGuidSeed</span> <span class="o">=</span> <span class="i">RandomSeed</span><span class="o">.</span><span class="i">Guid</span>()
<span class="k">let</span> <span class="i">someRobustSeed</span> <span class="o">=</span> <span class="i">RandomSeed</span><span class="o">.</span><span class="i">Robust</span>() <span class="c">// recommended, used by default</span>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="k">let</span> <span onmouseout="hideTip(event, 'fs6', 9)" onmouseover="showTip(event, 'fs6', 9)" class="i">someTimeSeed</span> <span class="o">=</span> <span class="i">RandomSeed</span><span class="o">.</span><span class="i">Time</span>() <span class="c">// not recommended</span>
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs7', 10)" onmouseover="showTip(event, 'fs7', 10)" class="i">someGuidSeed</span> <span class="o">=</span> <span class="i">RandomSeed</span><span class="o">.</span><span class="i">Guid</span>()
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs8', 11)" onmouseover="showTip(event, 'fs8', 11)" class="i">someRobustSeed</span> <span class="o">=</span> <span class="i">RandomSeed</span><span class="o">.</span><span class="i">Robust</span>() <span class="c">// recommended, used by default</span>
</code></pre></td>
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</table>
@ -198,9 +198,9 @@ or else a combination of a random number from a shared RNG, the time and a Guid
<span class="l">2: </span>
<span class="l">3: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="k">let</span> <span class="i">samplesSeeded</span> <span class="o">=</span> <span class="i">Random</span><span class="o">.</span><span class="i">doublesSeed</span> <span class="n">42</span> <span class="n">1000</span>
<span class="i">Random</span><span class="o">.</span><span class="i">doubleFillSeed</span> <span class="n">42</span> <span class="i">samplesSeeded</span>
<span class="k">let</span> <span class="i">samplesSeqSeeded</span> <span class="o">=</span> <span class="i">Random</span><span class="o">.</span><span class="i">doubleSeqSeed</span> <span class="n">42</span>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="k">let</span> <span onmouseout="hideTip(event, 'fs9', 12)" onmouseover="showTip(event, 'fs9', 12)" class="i">samplesSeeded</span> <span class="o">=</span> <span class="i">Random</span><span class="o">.</span><span class="i">doublesSeed</span> <span class="n">42</span> <span class="n">1000</span>
<span class="i">Random</span><span class="o">.</span><span class="i">doubleFillSeed</span> <span class="n">42</span> <span onmouseout="hideTip(event, 'fs9', 13)" onmouseover="showTip(event, 'fs9', 13)" class="i">samplesSeeded</span>
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs10', 14)" onmouseover="showTip(event, 'fs10', 14)" class="i">samplesSeqSeeded</span> <span class="o">=</span> <span class="i">Random</span><span class="o">.</span><span class="i">doubleSeqSeed</span> <span class="n">42</span>
</code></pre></td>
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</table>
@ -269,18 +269,18 @@ In case of the latter, all objects will be cast to their common base type <code>
<span class="l">13: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="c">// By using the normal constructor (random1 has type MersenneTwister) </span>
<span class="k">let</span> <span class="i">random1</span> <span class="o">=</span> <span class="i">MersenneTwister</span>()
<span class="k">let</span> <span class="i">random1b</span> <span class="o">=</span> <span class="i">MersenneTwister</span>(<span class="n">42</span>) <span class="c">// with seed</span>
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs11', 15)" onmouseover="showTip(event, 'fs11', 15)" class="i">random1</span> <span class="o">=</span> <span class="i">MersenneTwister</span>()
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs12', 16)" onmouseover="showTip(event, 'fs12', 16)" class="i">random1b</span> <span class="o">=</span> <span class="i">MersenneTwister</span>(<span class="n">42</span>) <span class="c">// with seed</span>
<span class="c">// By using the Random module (random2 has type System.Random)</span>
<span class="k">let</span> <span class="i">random2</span> <span class="o">=</span> <span class="i">Random</span><span class="o">.</span><span class="i">mersenneTwister</span> ()
<span class="k">let</span> <span class="i">random2b</span> <span class="o">=</span> <span class="i">Random</span><span class="o">.</span><span class="i">mersenneTwisterSeed</span> <span class="n">42</span> <span class="c">// with seed</span>
<span class="k">let</span> <span class="i">random2c</span> <span class="o">=</span> <span class="i">Random</span><span class="o">.</span><span class="i">mersenneTwisterWith</span> <span class="n">42</span> <span class="k">false</span> <span class="c">// opt-out of thread-safety</span>
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs13', 17)" onmouseover="showTip(event, 'fs13', 17)" class="i">random2</span> <span class="o">=</span> <span class="i">Random</span><span class="o">.</span><span class="i">mersenneTwister</span> ()
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs14', 18)" onmouseover="showTip(event, 'fs14', 18)" class="i">random2b</span> <span class="o">=</span> <span class="i">Random</span><span class="o">.</span><span class="i">mersenneTwisterSeed</span> <span class="n">42</span> <span class="c">// with seed</span>
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs15', 19)" onmouseover="showTip(event, 'fs15', 19)" class="i">random2c</span> <span class="o">=</span> <span class="i">Random</span><span class="o">.</span><span class="i">mersenneTwisterWith</span> <span class="n">42</span> <span class="k">false</span> <span class="c">// opt-out of thread-safety</span>
<span class="c">// Using some other algorithms:</span>
<span class="k">let</span> <span class="i">random3</span> <span class="o">=</span> <span class="i">Random</span><span class="o">.</span><span class="i">crypto</span> ()
<span class="k">let</span> <span class="i">random4</span> <span class="o">=</span> <span class="i">Random</span><span class="o">.</span><span class="i">xorshift</span> ()
<span class="k">let</span> <span class="i">random5</span> <span class="o">=</span> <span class="i">Random</span><span class="o">.</span><span class="i">wh2006</span> ()
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs16', 20)" onmouseover="showTip(event, 'fs16', 20)" class="i">random3</span> <span class="o">=</span> <span class="i">Random</span><span class="o">.</span><span class="i">crypto</span> ()
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs17', 21)" onmouseover="showTip(event, 'fs17', 21)" class="i">random4</span> <span class="o">=</span> <span class="i">Random</span><span class="o">.</span><span class="i">xorshift</span> ()
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs18', 22)" onmouseover="showTip(event, 'fs18', 22)" class="i">random5</span> <span class="o">=</span> <span class="i">Random</span><span class="o">.</span><span class="i">wh2006</span> ()
</code></pre></td>
</tr>
</table>
@ -314,11 +314,11 @@ unless explicitly disabled by a constructor argument or by setting <code>Control
<span class="l">4: </span>
<span class="l">5: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="k">let</span> <span class="i">a</span> <span class="o">=</span> <span class="i">Random</span><span class="o">.</span><span class="i">systemShared</span>
<span class="k">let</span> <span class="i">b</span> <span class="o">=</span> <span class="i">Random</span><span class="o">.</span><span class="i">mersenneTwisterShared</span>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="k">let</span> <span onmouseout="hideTip(event, 'fs19', 23)" onmouseover="showTip(event, 'fs19', 23)" class="i">a</span> <span class="o">=</span> <span class="i">Random</span><span class="o">.</span><span class="i">systemShared</span>
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs20', 24)" onmouseover="showTip(event, 'fs20', 24)" class="i">b</span> <span class="o">=</span> <span class="i">Random</span><span class="o">.</span><span class="i">mersenneTwisterShared</span>
<span class="c">// or if you don&#39;t care, simply</span>
<span class="k">let</span> <span class="i">c</span> <span class="o">=</span> <span class="i">Random</span><span class="o">.</span><span class="i">shared</span>;
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs21', 25)" onmouseover="showTip(event, 'fs21', 25)" class="i">c</span> <span class="o">=</span> <span class="i">Random</span><span class="o">.</span><span class="i">shared</span>;
</code></pre></td>
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</table>
@ -351,6 +351,27 @@ Normal.Samples(c, <span class="n">0.0</span>, <span class="n">1.0</span>);
</code></pre></td></tr></table>
<p>See <a href="Probability.html">Probability Distributions</a> for details.</p>
<div class="tip" id="fs1">val samples : obj<br /><br />Full name: Random.samples</div>
<div class="tip" id="fs2">val sampleSeq : obj<br /><br />Full name: Random.sampleSeq</div>
<div class="tip" id="fs3">val rng : obj<br /><br />Full name: Random.rng</div>
<div class="tip" id="fs4">val sample : obj<br /><br />Full name: Random.sample</div>
<div class="tip" id="fs5">val sampled : obj<br /><br />Full name: Random.sampled</div>
<div class="tip" id="fs6">val someTimeSeed : obj<br /><br />Full name: Random.someTimeSeed</div>
<div class="tip" id="fs7">val someGuidSeed : obj<br /><br />Full name: Random.someGuidSeed</div>
<div class="tip" id="fs8">val someRobustSeed : obj<br /><br />Full name: Random.someRobustSeed</div>
<div class="tip" id="fs9">val samplesSeeded : obj<br /><br />Full name: Random.samplesSeeded</div>
<div class="tip" id="fs10">val samplesSeqSeeded : obj<br /><br />Full name: Random.samplesSeqSeeded</div>
<div class="tip" id="fs11">val random1 : obj<br /><br />Full name: Random.random1</div>
<div class="tip" id="fs12">val random1b : obj<br /><br />Full name: Random.random1b</div>
<div class="tip" id="fs13">val random2 : obj<br /><br />Full name: Random.random2</div>
<div class="tip" id="fs14">val random2b : obj<br /><br />Full name: Random.random2b</div>
<div class="tip" id="fs15">val random2c : obj<br /><br />Full name: Random.random2c</div>
<div class="tip" id="fs16">val random3 : obj<br /><br />Full name: Random.random3</div>
<div class="tip" id="fs17">val random4 : obj<br /><br />Full name: Random.random4</div>
<div class="tip" id="fs18">val random5 : obj<br /><br />Full name: Random.random5</div>
<div class="tip" id="fs19">val a : obj<br /><br />Full name: Random.a</div>
<div class="tip" id="fs20">val b : obj<br /><br />Full name: Random.b</div>
<div class="tip" id="fs21">val c : obj<br /><br />Full name: Random.c</div>
</div>
<div class="span3">

4
Regression.html
View File

@ -89,7 +89,7 @@ Tuple&lt;<span class="k">double</span>, <span class="k">double</span>&gt; p <spa
<p>Or in F#:</p>
<table class="pre"><tr><td class="lines"><pre class="fssnip"><span class="l">1: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="k">let</span> <span class="i">a</span>, <span class="i">b</span> <span class="o">=</span> <span class="i">Fit</span><span class="o">.</span><span class="i">Line</span> ([|<span class="n">10.0</span>;<span class="n">20.0</span>;<span class="n">30.0</span>|], [|<span class="n">15.0</span>;<span class="n">20.0</span>;<span class="n">25.0</span>|])
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="k">let</span> <span onmouseout="hideTip(event, 'fs1', 1)" onmouseover="showTip(event, 'fs1', 1)" class="i">a</span>, <span onmouseout="hideTip(event, 'fs2', 2)" onmouseover="showTip(event, 'fs2', 2)" class="i">b</span> <span class="o">=</span> <span class="i">Fit</span><span class="o">.</span><span class="i">Line</span> ([|<span class="n">10.0</span>;<span class="n">20.0</span>;<span class="n">30.0</span>|], [|<span class="n">15.0</span>;<span class="n">20.0</span>;<span class="n">25.0</span>|])
</code></pre></td>
</tr>
</table>
@ -285,6 +285,8 @@ are dependent on the point of interest <span class="math">\(t\)</span>.</p>
<h2><a name="Regularization" class="anchor" href="#Regularization">Regularization</a></h2>
<h2><a name="Iterative-Methods" class="anchor" href="#Iterative-Methods">Iterative Methods</a></h2>
<div class="tip" id="fs1">val a : obj<br /><br />Full name: Regression.a</div>
<div class="tip" id="fs2">val b : obj<br /><br />Full name: Regression.b</div>
</div>
<div class="span3">

2
ReleaseNotes-MKL.html
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@ -58,7 +58,7 @@
<div class="span9" id="main">
<h1><a name="MKL-Provider-Release-Notes" class="anchor" href="#MKL-Provider-Release-Notes">MKL Provider Release Notes</a></h1>
<p><a href="ReleaseNotes.html">Math.NET Numerics</a> | <a href="ReleaseNotes-MKL.html">MKL Provider</a> | <a href="ReleaseNotes-OpenBLAS.html">OpenBLAS Provider</a> | <a href="ReleaseNotes-Data.html">Data Extensions</a></p>
<p><a href="ReleaseNotes.html">Math.NET Numerics</a> | <a href="ReleaseNotes-MKL.html">MKL Provider</a> | <a href="ReleaseNotes-OpenBLAS.html">OpenBLAS Provider</a></p>
<h3><a name="2-5-0-2021-01-01" class="anchor" href="#2-5-0-2021-01-01">2.5.0 - 2021-01-01</a></h3>
<ul>
<li>r14 with Intel MKL 2020 Update 4</li>

2
ReleaseNotes-OpenBLAS.html
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@ -58,7 +58,7 @@
<div class="span9" id="main">
<h1><a name="OpenBLAS-Provider-Release-Notes" class="anchor" href="#OpenBLAS-Provider-Release-Notes">OpenBLAS Provider Release Notes</a></h1>
<p><a href="ReleaseNotes.html">Math.NET Numerics</a> | <a href="ReleaseNotes-MKL.html">MKL Provider</a> | <a href="ReleaseNotes-OpenBLAS.html">OpenBLAS Provider</a> | <a href="ReleaseNotes-Data.html">Data Extensions</a></p>
<p><a href="ReleaseNotes.html">Math.NET Numerics</a> | <a href="ReleaseNotes-MKL.html">MKL Provider</a> | <a href="ReleaseNotes-OpenBLAS.html">OpenBLAS Provider</a></p>
<h3><a name="0-2-0-2015-09-26" class="anchor" href="#0-2-0-2015-09-26">0.2.0 - 2015-09-26</a></h3>
<ul>
<li>Initial version</li>

22
ReleaseNotes.html
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@ -58,7 +58,27 @@
<div class="span9" id="main">
<h1><a name="Math-NET-Numerics-Release-Notes" class="anchor" href="#Math-NET-Numerics-Release-Notes">Math.NET Numerics Release Notes</a></h1>
<p><a href="ReleaseNotes.html">Math.NET Numerics</a> | <a href="ReleaseNotes-MKL.html">MKL Provider</a> | <a href="ReleaseNotes-OpenBLAS.html">OpenBLAS Provider</a> | <a href="ReleaseNotes-Data.html">Data Extensions</a></p>
<p><a href="ReleaseNotes.html">Math.NET Numerics</a> | <a href="ReleaseNotes-MKL.html">MKL Provider</a> | <a href="ReleaseNotes-OpenBLAS.html">OpenBLAS Provider</a></p>
<h3><a name="5-0-0-alpha01-2021-06-27" class="anchor" href="#5-0-0-alpha01-2021-06-27">5.0.0-alpha01 - 2021-06-27</a></h3>
<ul>
<li>COMPATIBILITY: net5.0, net48 better supported with explicit builds</li>
<li>COMPATIBILITY: netstandard1.x, net40, net45 no longer supported</li>
<li>BREAKING: drop all which was marked as obsolete</li>
<li>BREAKING: all native provider adapters moved out to separate NuGet packages</li>
<li>BREAKING: switch many usages of tuples to value tuples (experimental)</li>
<li>Distributions: Logistic <em>~Bobby Ingram</em></li>
<li>Distributions: Perf: Cauchy avoid duplicate evaluation <em>~Febin</em></li>
<li>Precision: Perf: pre-compute negative powers <em>~Febin</em></li>
<li>Optimizations: Remove static properties in LevenbergMarquardtMinimizer <em>~Jong Hyun Kim</em></li>
<li>Fit.Curve and FindMinimum extended to accept two more parameters</li>
<li>Series: stable series summation</li>
<li>Providers: drop managed reference linear algebra provider</li>
<li>Providers: native providers no longer inherit managed providers, managed now sealed</li>
<li>Providers: MKL provider compilation switched to Intel oneAPI MKL</li>
<li>Lots of internal cleanup, leveraging newer language features</li>
<li>Data: now released always together with Numerics (no longer separate versioning)</li>
<li>Control.Describe now includes CPU architecture and family identifier if know</li>
</ul>
<h3><a name="4-15-0-2021-01-07" class="anchor" href="#4-15-0-2021-01-07">4.15.0 - 2021-01-07</a></h3>
<ul>
<li>Precision: Round (with integer part rounding) <em>~Jon Larborn</em></li>

11
index.html
View File

@ -119,9 +119,9 @@ idiomatic and includes arbitrary precision types (BigInteger, BigRational).</p>
<span class="l">4: </span>
</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="k">open</span> <span class="i">MathNet</span><span class="o">.</span><span class="i">Numerics</span><span class="o">.</span><span class="i">LinearAlgebra</span>
<span class="k">let</span> <span class="i">m</span> <span class="o">=</span> <span class="i">matrix</span> [[ <span class="n">1.0</span>; <span class="n">2.0</span> ]
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs1', 1)" onmouseover="showTip(event, 'fs1', 1)" class="i">m</span> <span class="o">=</span> <span class="i">matrix</span> [[ <span class="n">1.0</span>; <span class="n">2.0</span> ]
[ <span class="n">3.0</span>; <span class="n">4.0</span> ]]
<span class="k">let</span> <span class="i">m&#39;</span> <span class="o">=</span> <span class="i">m</span><span class="o">.</span><span class="i">Inverse</span>()
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs2', 2)" onmouseover="showTip(event, 'fs2', 2)" class="i">m&#39;</span> <span class="o">=</span> <span onmouseout="hideTip(event, 'fs1', 3)" onmouseover="showTip(event, 'fs1', 3)" class="i">m</span><span class="o">.</span><span class="i">Inverse</span>()
</code></pre></td>
</tr>
</table>
@ -145,8 +145,8 @@ For convenience our F# packages include a small script that sets everything up p
<span class="i">SpecialFunctions</span><span class="o">.</span><span class="i">Gamma</span>(<span class="n">0.5</span>)
<span class="k">open</span> <span class="i">MathNet</span><span class="o">.</span><span class="i">Numerics</span><span class="o">.</span><span class="i">LinearAlgebra</span>
<span class="k">let</span> <span class="i">m</span> <span class="o">:</span> <span class="i">Matrix</span><span class="o">&lt;</span><span class="i">float</span><span class="o">&gt;</span> <span class="o">=</span> <span class="i">DenseMatrix</span><span class="o">.</span><span class="i">randomStandard</span> <span class="n">50</span> <span class="n">50</span>
(<span class="i">m</span> <span class="o">*</span> <span class="i">m</span><span class="o">.</span><span class="i">Transpose</span>())<span class="o">.</span><span class="i">Determinant</span>()
<span class="k">let</span> <span onmouseout="hideTip(event, 'fs1', 4)" onmouseover="showTip(event, 'fs1', 4)" class="i">m</span> <span class="o">:</span> <span class="i">Matrix</span><span class="o">&lt;</span><span onmouseout="hideTip(event, 'fs3', 5)" onmouseover="showTip(event, 'fs3', 5)" class="i">float</span><span class="o">&gt;</span> <span class="o">=</span> <span class="i">DenseMatrix</span><span class="o">.</span><span class="i">randomStandard</span> <span class="n">50</span> <span class="n">50</span>
(<span onmouseout="hideTip(event, 'fs1', 6)" onmouseover="showTip(event, 'fs1', 6)" class="i">m</span> <span class="o">*</span> <span onmouseout="hideTip(event, 'fs1', 7)" onmouseover="showTip(event, 'fs1', 7)" class="i">m</span><span class="o">.</span><span class="i">Transpose</span>())<span class="o">.</span><span class="i">Determinant</span>()
</code></pre></td>
</tr>
</table>
@ -281,6 +281,9 @@ DenseVector 500-Double
</code></pre></td></tr></table>
<p>See <a href="MKL.html">Intel MKL</a> for details how to use native providers on Linux.</p>
<div class="tip" id="fs1">val m : obj<br /><br />Full name: index.m</div>
<div class="tip" id="fs2">val m&#39; : obj<br /><br />Full name: index.m&#39;</div>
<div class="tip" id="fs3">Multiple items<br />val float : value:&#39;T -&gt; float (requires member op_Explicit)<br /><br />Full name: Microsoft.FSharp.Core.Operators.float<br /><br />--------------------<br />type float = System.Double<br /><br />Full name: Microsoft.FSharp.Core.float<br /><br />--------------------<br />type float&lt;&#39;Measure&gt; = float<br /><br />Full name: Microsoft.FSharp.Core.float&lt;_&gt;</div>
</div>
<div class="span3">

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