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Documenter.jl committed Sep 26, 2023
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Expand Up @@ -551,32 +551,32 @@ <h2 id="dimensions-and-dimarrays">Dimensions and DimArrays<a class="headerlink"
<span class="n">A</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rand</span><span class="p">(</span><span class="n">X</span><span class="p">(</span><span class="mi">5</span><span class="p">),</span><span class="w"> </span><span class="n">Y</span><span class="p">(</span><span class="mi">5</span><span class="p">))</span>
</code></pre></div>
<div class="highlight"><pre><span></span><code>5×5 DimArray{Float64,2} with dimensions: X, Y
0.443704 0.843622 0.34243 0.0860598 0.183114
0.0752773 0.947195 0.982413 0.0808838 0.718821
0.216591 0.332958 0.413919 0.614533 0.643519
0.936548 0.608591 0.993979 0.632012 0.774091
0.921102 0.597758 0.471268 0.44848 0.189913
0.48135 0.978319 0.228828 0.983446 0.729521
0.76172 0.527223 0.857313 0.53394 0.681473
0.89158 0.868622 0.189245 0.209467 0.719734
0.528462 0.454164 0.806445 0.153103 0.919654
0.201973 0.0397331 0.021962 0.953818 0.196
</code></pre></div>
<p>get value</p>
<div class="highlight"><pre><span></span><code><span class="n">A</span><span class="p">[</span><span class="n">Y</span><span class="p">(</span><span class="mi">1</span><span class="p">),</span><span class="w"> </span><span class="n">X</span><span class="p">(</span><span class="mi">2</span><span class="p">)]</span>
</code></pre></div>
<div class="highlight"><pre><span></span><code>0.07527733648430668
<div class="highlight"><pre><span></span><code>0.7617200536589341
</code></pre></div>
<p>As shown above, <code>Dimension</code>s can be used to construct arrays in <code>rand</code>, <code>ones</code>, <code>zeros</code> and <code>fill</code> with either a range for a lookup index or a number for the dimension length.</p>
<p>Or we can use the <code>Dim{X}</code> dims by using <code>Symbol</code>s, and indexing with keywords:</p>
<div class="highlight"><pre><span></span><code><span class="n">A</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">DimArray</span><span class="p">(</span><span class="n">rand</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">),</span><span class="w"> </span><span class="p">(</span><span class="ss">:a</span><span class="p">,</span><span class="w"> </span><span class="ss">:b</span><span class="p">))</span>
</code></pre></div>
<div class="highlight"><pre><span></span><code>5×5 DimArray{Float64,2} with dimensions: Dim{:a}, Dim{:b}
0.448924 0.895802 0.9393 0.434738 0.146974
0.629053 0.502591 0.94497 0.0414907 0.93782
0.704831 0.821436 0.201252 0.334099 0.394146
0.21254 0.809432 0.56053 0.0007233 0.825827
0.61466 0.934774 0.163232 0.347305 0.971311
0.28643 0.758018 0.478748 0.180741 0.350359
0.68089 0.213346 0.463813 0.462992 0.378621
0.415218 0.772892 0.91939 0.957064 0.8147
0.731256 0.434278 0.537681 0.0190308 0.878032
0.340219 0.494343 0.160785 0.651715 0.349443
</code></pre></div>
<p>get value</p>
<div class="highlight"><pre><span></span><code><span class="n">A</span><span class="p">[</span><span class="n">a</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="o">=</span><span class="mi">5</span><span class="p">]</span>
</code></pre></div>
<div class="highlight"><pre><span></span><code>0.39414606919368145
<div class="highlight"><pre><span></span><code>0.814699751412053
</code></pre></div>
<p>Often, we want to provide a lookup index for the dimension:</p>
<div class="highlight"><pre><span></span><code><span class="k">using</span><span class="w"> </span><span class="n">Dates</span>
Expand All @@ -588,16 +588,16 @@ <h2 id="dimensions-and-dimarrays">Dimensions and DimArrays<a class="headerlink"
X Sampled{Int64} 10:10:100 ForwardOrdered Regular Points,
Ti Sampled{DateTime} DateTime(&quot;2001-01-01T00:00:00&quot;):Month(1):DateTime(&quot;2001-12-01T00:00:00&quot;) ForwardOrdered Regular Points
2001-01-01T00:00:00 … 2001-12-01T00:00:00
10 0.467609 0.337445
20 0.497484 0.846887
30 0.67703 0.273286
40 0.41209 0.760816
50 0.613971 … 0.873646
60 0.167046 0.340064
70 0.110016 0.392416
80 0.451012 0.322358
90 0.31334 0.0210354
100 0.119262 … 0.937963
10 0.298533 0.074927
20 0.056447 0.231851
30 0.02653 0.472181
40 0.242324 0.449711
50 0.937423 … 0.593995
60 0.272843 0.406561
70 0.187017 0.221236
80 0.568283 0.150875
90 0.653039 0.448353
100 0.598894 … 0.835608
</code></pre></div>
<p>Here both <code>X</code> and <code>Ti</code> are dimensions from <code>DimensionalData</code>. The currently exported dimensions are <code>X, Y, Z, Ti</code> (<code>Ti</code> is shortening of <code>Time</code>).</p>
<p>The length of each dimension index has to match the size of the corresponding array axis.</p>
Expand All @@ -607,19 +607,19 @@ <h2 id="dimensions-and-dimarrays">Dimensions and DimArrays<a class="headerlink"
<div class="highlight"><pre><span></span><code>12×10 DimArray{Float64,2} with dimensions:
Dim{:time} Sampled{DateTime} DateTime(&quot;2001-01-01T00:00:00&quot;):Month(1):DateTime(&quot;2001-12-01T00:00:00&quot;) ForwardOrdered Regular Points,
Dim{:distance} Sampled{Int64} 10:10:100 ForwardOrdered Regular Points
… 80 90 100
2001-01-01T00:00:00 0.104897 0.491119 0.20384
2001-02-01T00:00:00 0.709097 0.75495 0.0243176
2001-03-01T00:00:00 0.34763 0.496163 0.837822
2001-04-01T00:00:00 0.547706 0.676455 0.314979
2001-05-01T00:00:00 … 0.282009 0.753827 0.22235
2001-06-01T00:00:00 0.0344018 0.807664 0.353797
2001-07-01T00:00:00 0.524993 0.0823056 0.303352
2001-08-01T00:00:00 0.446344 0.387634 0.4294
2001-09-01T00:00:00 0.911411 0.0365052 0.360169
2001-10-01T00:00:00 … 0.113159 0.463131 0.225023
2001-11-01T00:00:00 0.121446 0.809872 0.799467
2001-12-01T00:00:00 0.780634 0.591061 0.226829
… 80 90 100
2001-01-01T00:00:00 0.936142 0.564259 0.0476195
2001-02-01T00:00:00 0.425588 0.371164 0.00256587
2001-03-01T00:00:00 0.0902057 0.867566 0.775466
2001-04-01T00:00:00 0.126659 0.588218 0.70741
2001-05-01T00:00:00 … 0.0988372 0.339753 0.598956
2001-06-01T00:00:00 0.720355 0.115282 0.424257
2001-07-01T00:00:00 0.540312 0.968827 0.175213
2001-08-01T00:00:00 0.335117 0.952392 0.0996448
2001-09-01T00:00:00 0.374017 0.722374 0.0101426
2001-10-01T00:00:00 … 0.804599 0.352696 0.00436976
2001-11-01T00:00:00 0.563097 0.802047 0.830552
2001-12-01T00:00:00 0.100013 0.834432 0.247845
</code></pre></div>
<p>Symbols can be more convenient to use than defining custom dims with <code>@dim</code>, but have some downsides. They don't inherit from a specific <code>Dimension</code> type, so plots will not know what axis to put them on. They also cannot use the basic constructor methods like <code>rand</code> or <code>zeros</code>, as we cannot dispatch on <code>Symbol</code> for Base methods without "type-piracy".</p>
<p><a id='Indexing-the-array-by-name-and-index'></a></p>
Expand All @@ -633,10 +633,10 @@ <h2 id="indexing-the-array-by-name-and-index">Indexing the array by name and ind
X Sampled{Int64} 10:30:100 ForwardOrdered Regular Points,
Ti Sampled{DateTime} DateTime(&quot;2001-01-01T00:00:00&quot;):Month(2):DateTime(&quot;2001-11-01T00:00:00&quot;) ForwardOrdered Regular Points
2001-01-01T00:00:00 … 2001-11-01T00:00:00
10 0.467609 0.310971
40 0.41209 0.185501
70 0.110016 0.434044
100 0.119262 0.428509
10 0.298533 0.507098
40 0.242324 0.559531
70 0.187017 0.178191
100 0.598894 0.6313
</code></pre></div>
<p>When specifying only one dimension, all elements of the other dimensions are assumed to be included:</p>
<div class="highlight"><pre><span></span><code><span class="n">A</span><span class="p">[</span><span class="n">X</span><span class="p">(</span><span class="mi">1</span><span class="o">:</span><span class="mi">3</span><span class="o">:</span><span class="mi">10</span><span class="p">)]</span>
Expand All @@ -645,10 +645,10 @@ <h2 id="indexing-the-array-by-name-and-index">Indexing the array by name and ind
X Sampled{Int64} 10:30:100 ForwardOrdered Regular Points,
Ti Sampled{DateTime} DateTime(&quot;2001-01-01T00:00:00&quot;):Month(1):DateTime(&quot;2001-12-01T00:00:00&quot;) ForwardOrdered Regular Points
2001-01-01T00:00:00 … 2001-12-01T00:00:00
10 0.467609 0.337445
40 0.41209 0.760816
70 0.110016 0.392416
100 0.119262 0.937963
10 0.298533 0.074927
40 0.242324 0.449711
70 0.187017 0.221236
100 0.598894 0.835608
</code></pre></div>
<div class="admonition info">
<p class="admonition-title">Indexing</p>
Expand Down Expand Up @@ -708,13 +708,13 @@ <h2 id="indexing-performance">Indexing Performance<a class="headerlink" href="#i

<span class="n">println</span><span class="p">(</span><span class="nd">@btime</span><span class="w"> </span><span class="o">$</span><span class="n">A2</span><span class="p">[</span><span class="n">X</span><span class="p">(</span><span class="mi">1</span><span class="p">),</span><span class="w"> </span><span class="n">Y</span><span class="p">(</span><span class="mi">2</span><span class="p">)])</span>
</code></pre></div>
<div class="highlight"><pre><span></span><code> 38.609 ns (0 allocations: 0 bytes)
<div class="highlight"><pre><span></span><code> 46.309 ns (0 allocations: 0 bytes)
1.0
</code></pre></div>
<p>and</p>
<div class="highlight"><pre><span></span><code><span class="n">println</span><span class="p">(</span><span class="nd">@btime</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="o">$</span><span class="n">A2</span><span class="p">)[</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">])</span>
</code></pre></div>
<div class="highlight"><pre><span></span><code> 4.000 ns (0 allocations: 0 bytes)
<div class="highlight"><pre><span></span><code> 4.800 ns (0 allocations: 0 bytes)
1.0
</code></pre></div>
<p><a id='Specifying-dims-keyword-arguments-with-Dimension'></a></p>
Expand All @@ -726,19 +726,19 @@ <h2 id="specifying-dims-keyword-arguments-with-dimension">Specifying <code>dims<
</code></pre></div>
<div class="highlight"><pre><span></span><code>3×4×1 DimArray{Float64,3} with dimensions: X, Y, Ti
[:, :, 1]
1.88606 3.04244 1.92404 2.31928
3.41461 1.4024 2.79498 1.96727
2.66682 3.10908 3.12866 2.57577
1.55284 3.45784 3.16844 1.28791
2.19929 1.62084 1.97105 2.69379
2.97629 2.28414 2.65022 2.22
</code></pre></div>
<p>This also works in methods from <code>Statistics</code>:</p>
<div class="highlight"><pre><span></span><code><span class="k">using</span><span class="w"> </span><span class="n">Statistics</span>
<span class="n">mean</span><span class="p">(</span><span class="n">A3</span><span class="p">;</span><span class="w"> </span><span class="n">dims</span><span class="o">=</span><span class="n">Ti</span><span class="p">)</span>
</code></pre></div>
<div class="highlight"><pre><span></span><code>3×4×1 DimArray{Float64,3} with dimensions: X, Y, Ti
[:, :, 1]
0.377212 0.608489 0.384808 0.463856
0.682922 0.28048 0.558995 0.393453
0.533364 0.621816 0.625733 0.515153
0.310569 0.691568 0.633687 0.257582
0.439858 0.324168 0.39421 0.538759
0.595258 0.456827 0.530044 0.444
</code></pre></div>
<p><a id='Methods-where-dims,-dim-types,-or-Symbols-can-be-used-to-indicate-the-array-dimension:'></a></p>
<p><a id='Methods-where-dims,-dim-types,-or-Symbols-can-be-used-to-indicate-the-array-dimension:-1'></a></p>
Expand Down Expand Up @@ -805,8 +805,8 @@ <h2 id="lookuparrays-and-selectors">LookupArrays and Selectors<a class="headerli
X Sampled{Int64} 20:10:30 ForwardOrdered Regular Points,
Ti Sampled{DateTime} DateTime(&quot;2001-05-01T00:00:00&quot;):Month(1):DateTime(&quot;2001-07-01T00:00:00&quot;) ForwardOrdered Regular Points
2001-05-01T00:00:00 … 2001-07-01T00:00:00
20 0.849013 0.939958
30 0.0802733 0.151849
20 0.708489 0.517171
30 0.603833 0.433236
</code></pre></div>
<p>To select intervals in DimArrays (e.g. <code>A2</code>) you need to specify <code>dimname=a .. b</code>:</p>
<div class="highlight"><pre><span></span><code><span class="n">A2</span><span class="p">[</span><span class="n">distance</span><span class="o">=</span><span class="mi">12</span><span class="w"> </span><span class="o">..</span><span class="w"> </span><span class="mi">35</span><span class="p">,</span><span class="w"> </span><span class="n">time</span><span class="o">=</span><span class="n">Date</span><span class="p">(</span><span class="mi">2001</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">)</span><span class="w"> </span><span class="o">..</span><span class="w"> </span><span class="n">Date</span><span class="p">(</span><span class="mi">2001</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">)]</span>
Expand All @@ -823,7 +823,7 @@ <h2 id="lookuparrays-and-selectors">LookupArrays and Selectors<a class="headerli
<span class="n">A4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rand</span><span class="p">(</span><span class="n">Ti</span><span class="p">(</span><span class="n">timespan</span><span class="p">),</span><span class="w"> </span><span class="n">X</span><span class="p">(</span><span class="mi">10</span><span class="o">:</span><span class="mi">10</span><span class="o">:</span><span class="mi">100</span><span class="p">))</span>
<span class="n">A4</span><span class="p">[</span><span class="n">X</span><span class="p">(</span><span class="n">Near</span><span class="p">(</span><span class="mi">35</span><span class="p">)),</span><span class="w"> </span><span class="n">Ti</span><span class="p">(</span><span class="n">At</span><span class="p">(</span><span class="n">DateTime</span><span class="p">(</span><span class="mi">2001</span><span class="p">,</span><span class="mi">5</span><span class="p">)))]</span>
</code></pre></div>
<div class="highlight"><pre><span></span><code>0.9658105940391629
<div class="highlight"><pre><span></span><code>0.06067191029280128
</code></pre></div>
<p>Without dim wrappers selectors must be in the right order, and specify all axes:</p>
<div class="highlight"><pre><span></span><code><span class="k">using</span><span class="w"> </span><span class="n">Unitful</span>
Expand All @@ -834,20 +834,20 @@ <h2 id="lookuparrays-and-selectors">LookupArrays and Selectors<a class="headerli
Y Sampled{Quantity{Int64, 𝐋, Unitful.FreeUnits{(m,), 𝐋, nothing}}} (11:10:41) m ForwardOrdered Regular Points
and reference dimensions:
Ti Sampled{Quantity{Int64, 𝐓, Unitful.FreeUnits{(s,), 𝐓, nothing}}} (21:5:21) s ForwardOrdered Regular Points
11 m 0.139313
21 m 0.581051
31 m 0.32695
41 m 0.0712766
11 m 0.588332
21 m 0.406067
31 m 0.120844
41 m 0.493258
</code></pre></div>
<p>We can also use Linear indices as in standard <code>Array</code>:</p>
<div class="highlight"><pre><span></span><code><span class="n">A5</span><span class="p">[</span><span class="mi">1</span><span class="o">:</span><span class="mi">5</span><span class="p">]</span>
</code></pre></div>
<div class="highlight"><pre><span></span><code>5-element Vector{Float64}:
0.16739381618042604
0.7240138348167
0.3087344490479902
0.38819112498465214
0.6527135191754502
0.2325303617446588
0.5197757717212687
0.4498418170918361
0.25027789256361377
0.882486935621261
</code></pre></div>
<p>But unless the <code>DimArray</code> is one dimensional, this will return a regular <code>Array</code>. It is not possible to keep the <code>LookupArray</code> or even <code>Dimension</code>s after linear indexing is used.</p>
<p><a id='LookupArrays-and-traits'></a></p>
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