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Expand Down 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
0.615011 0.653053 0.667677 0.849528 0.409837
0.165128 0.335078 0.4295 0.0483559 0.00943597
0.371067 0.440276 0.305891 0.377394 0.27311
0.714239 0.528475 0.754844 0.842399 0.377717
0.850673 0.151194 0.564335 0.665783 0.366963
0.742039 0.586452 0.881275 0.553423 0.959277
0.800695 0.0409674 0.614942 0.577694 0.746121
0.801573 0.0147857 0.710935 0.15881 0.0500568
0.532702 0.730838 0.280543 0.352134 0.623975
0.823049 0.89349 0.42974 0.198846 0.971429
</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>0.1651280275570669
<div class="highlight"><pre><span></span><code>0.8006954109006309
</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}
0.81563 0.989289 0.560372 0.55302 0.245637
0.0494841 0.132329 0.50417 0.217977 0.798952
0.258137 0.743077 0.649988 0.460808 0.277386
0.672347 0.720251 0.491559 0.330121 0.819383
0.603059 0.438958 0.562114 0.979535 0.843235
0.302168 0.962407 0.293022 0.542257 0.312674
0.732169 0.0288436 0.0185259 0.416337 0.685471
0.144793 0.684657 0.330945 0.148742 0.858339
0.0381463 0.825872 0.936292 0.569627 0.352894
0.965438 0.746857 0.00207353 0.706275 0.4701
</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>0.2773860138618044
<div class="highlight"><pre><span></span><code>0.8583394102078234
</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 0.330429 0.816163
20 0.241814 0.766346
30 0.826847 0.486748
40 0.107968 0.253838
50 0.103568 … 0.12739
60 0.0854633 0.251501
70 0.563859 0.855956
80 0.57229 0.661141
90 0.491513 0.219145
100 0.828801 … 0.889994
10 0.0529236 0.246815
20 0.0794562 0.610772
30 0.323582 0.920826
40 0.626518 0.0270199
50 0.0960106 … 0.934671
60 0.0386 0.838448
70 0.949423 0.196701
80 0.846502 0.847099
90 0.922264 0.820609
100 0.449165 … 0.467115
</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
10 … 90 100
2001-01-01T00:00:00 0.7252 0.708448 0.151508
2001-02-01T00:00:00 0.0865807 0.411089 0.44746
2001-03-01T00:00:00 0.265197 0.86882 0.408719
2001-04-01T00:00:00 0.293093 0.228115 0.792358
2001-05-01T00:00:00 0.216107 … 0.307123 0.477806
2001-06-01T00:00:00 0.99614 0.111172 0.15801
2001-07-01T00:00:00 0.662801 0.0342727 0.241335
2001-08-01T00:00:00 0.424399 0.542106 0.643702
2001-09-01T00:00:00 0.648135 0.127682 0.812149
2001-10-01T00:00:00 0.666797 … 0.819095 0.333216
2001-11-01T00:00:00 0.173364 0.633557 0.000201314
2001-12-01T00:00:00 0.385952 0.735422 0.735445
… 80 90 100
2001-01-01T00:00:00 0.919996 0.240232 0.27883
2001-02-01T00:00:00 0.743756 0.966851 0.458265
2001-03-01T00:00:00 0.530674 0.0885089 0.34007
2001-04-01T00:00:00 0.19191 0.516862 0.263621
2001-05-01T00:00:00 … 0.639087 0.933271 0.114815
2001-06-01T00:00:00 0.147117 0.140322 0.739686
2001-07-01T00:00:00 0.346512 0.428956 0.527013
2001-08-01T00:00:00 0.393688 0.808105 0.43755
2001-09-01T00:00:00 0.665723 0.650276 0.220515
2001-10-01T00:00:00 … 0.725377 0.661739 0.913668
2001-11-01T00:00:00 0.622399 0.502721 0.725586
2001-12-01T00:00:00 0.317769 0.37146 0.24139
</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 0.330429 0.382967
40 0.107968 0.964364
70 0.563859 0.915145
100 0.828801 0.682227
10 0.0529236 0.655993
40 0.626518 0.00454459
70 0.949423 0.932173
100 0.449165 0.266214
</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 0.330429 0.816163
40 0.107968 0.253838
70 0.563859 0.855956
100 0.828801 0.889994
10 0.0529236 0.246815
40 0.626518 0.0270199
70 0.949423 0.196701
100 0.449165 0.467115
</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">$</span><span class="n">A2</span><span class="p">[</span><span class="n">X</span><span class="p">(</span><span class="mi">1</span><span class="p">),</span><span class="w"> </span><span class="n">Y</span><span class="p">(</span><span class="mi">2</span><span class="p">)])</span>
</code></pre></div>
<div class="highlight"><pre><span></span><code> 38.710 ns (0 allocations: 0 bytes)
<div class="highlight"><pre><span></span><code> 47.315 ns (0 allocations: 0 bytes)
1.0
</code></pre></div>
<p>and</p>
<div class="highlight"><pre><span></span><code><span class="n">println</span><span class="p">(</span><span class="nd">@btime</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="o">$</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> 4.300 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]
1.91945 2.52143 2.21734 3.26048
3.01172 2.30549 1.6219 1.89255
2.4388 1.76976 2.55045 1.95759
3.74892 4.09716 2.35979 2.62055
2.09455 2.97429 2.27608 3.24993
2.04749 2.13523 2.55579 4.00008
</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]
0.383889 0.504286 0.443468 0.652095
0.602344 0.461098 0.324381 0.378511
0.487759 0.353953 0.510089 0.391517
0.749784 0.819431 0.471957 0.52411
0.418909 0.594857 0.455217 0.649986
0.409498 0.427047 0.511158 0.800015
</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 0.416228 0.432139
30 0.133104 0.360829
20 0.513671 0.213113
30 0.42402 0.853681
</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>0.6493324348671289
<div class="highlight"><pre><span></span><code>0.2606972536712586
</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 0.24344
21 m 0.0608659
31 m 0.804227
41 m 0.505891
11 m 0.6536
21 m 0.383142
31 m 0.714299
41 m 0.067355
</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}:
0.18384414807081062
0.9293537605351444
0.35459708870494655
0.18231216643483794
0.8683146311961011
0.48851863344942437
0.9087352104876705
0.3381744056289252
0.4501830151197299
0.3725632661799382
</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>
Expand Down
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