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Expand Down Expand Up @@ -591,32 +591,32 @@ <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
0.0789236 0.650018 0.874569 0.751282 0.286408
0.0747493 0.779612 0.953417 0.703704 0.849392
0.196648 0.993902 0.360195 0.852405 0.0839513
0.610024 0.525136 0.047042 0.0968304 0.668431
0.995686 0.961022 0.11152 0.328018 0.75627
0.623645 0.819318 0.000103591 0.798421 0.772365
0.741807 0.505694 0.430631 0.000399393 0.553339
0.409008 0.451821 0.693726 0.119201 0.682385
0.305206 0.894956 0.76347 0.918992 0.227188
0.0256477 0.133485 0.0970211 0.83807 0.73643
</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>0.07474928390590019
<div class="highlight"><pre><span></span><code>0.7418070003725661
</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}
0.0834937 0.213629 0.859079 0.0476227 0.100811
0.897406 0.102106 0.745417 0.686758 0.121953
0.808041 0.671183 0.547184 0.16629 0.158972
0.151024 0.439586 0.665088 0.577256 0.794193
0.935746 0.965257 0.79616 0.482317 0.172634
0.878181 0.498553 0.291119 0.737893 0.113497
0.278783 0.669269 0.307199 0.0298804 0.483271
0.245612 0.105502 0.991102 0.204864 0.536161
0.661738 0.868053 0.804687 0.789028 0.184389
0.0917761 0.738769 0.455028 0.855006 0.0920598
</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>0.15897206053395518
<div class="highlight"><pre><span></span><code>0.5361606933522421
</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 @@ -628,16 +628,16 @@ <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 0.585923 0.135135
20 0.291391 0.0155094
30 0.591679 0.000103421
40 0.254514 0.110521
50 0.725676 … 0.630714
60 0.192738 0.845039
70 0.315251 0.772994
80 0.809028 0.136398
90 0.906746 0.949487
100 0.492945 … 0.984901
10 0.878526 0.934068
20 0.0285024 0.836981
30 0.701669 0.870343
40 0.593933 0.317004
50 0.225922 … 0.472496
60 0.176543 0.72953
70 0.650019 0.162719
80 0.0444856 0.42386
90 0.730238 0.958508
100 0.0636773 … 0.615951
</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 @@ -647,19 +647,19 @@ <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 0.239872 0.32517 0.289872
2001-02-01T00:00:00 0.891392 0.597682 0.802818
2001-03-01T00:00:00 0.990028 0.782468 0.432693
2001-04-01T00:00:00 0.584583 0.447184 0.871942
2001-05-01T00:00:00 … 0.305998 0.794288 0.806409
2001-06-01T00:00:00 0.358406 0.120138 0.291032
2001-07-01T00:00:00 0.588813 0.791255 0.656966
2001-08-01T00:00:00 0.00529894 0.832337 0.896358
2001-09-01T00:00:00 0.194777 0.26824 0.203421
2001-10-01T00:00:00 … 0.818109 0.965595 0.0835779
2001-11-01T00:00:00 0.0436395 0.904873 0.0323937
2001-12-01T00:00:00 0.00698632 0.528758 0.247285
… 80 90 100
2001-01-01T00:00:00 0.915547 0.125075 0.666621
2001-02-01T00:00:00 0.723063 0.348108 0.0529588
2001-03-01T00:00:00 0.811437 0.729164 0.167957
2001-04-01T00:00:00 0.697365 0.316709 0.284936
2001-05-01T00:00:00 … 0.270475 0.431269 0.507973
2001-06-01T00:00:00 0.897969 0.905865 0.690749
2001-07-01T00:00:00 0.650473 0.330753 0.421689
2001-08-01T00:00:00 0.334844 0.31939 0.50905
2001-09-01T00:00:00 0.182784 0.387667 0.260002
2001-10-01T00:00:00 … 0.619726 0.656784 0.112406
2001-11-01T00:00:00 0.0201157 0.175242 0.585819
2001-12-01T00:00:00 0.394302 0.106406 0.612673
</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 @@ -673,10 +673,10 @@ <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 0.585923 0.364535
40 0.254514 0.773826
70 0.315251 0.259705
100 0.492945 0.645361
10 0.878526 0.905333
40 0.593933 0.555514
70 0.650019 0.797431
100 0.0636773 0.51555
</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 @@ -685,10 +685,10 @@ <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 0.585923 0.135135
40 0.254514 0.110521
70 0.315251 0.772994
100 0.492945 0.984901
10 0.878526 0.934068
40 0.593933 0.317004
70 0.650019 0.162719
100 0.0636773 0.615951
</code></pre></div>
<div class="admonition info">
<p class="admonition-title">Indexing</p>
Expand Down Expand Up @@ -748,7 +748,7 @@ <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> 43.738 ns (0 allocations: 0 bytes)
<div class="highlight"><pre><span></span><code> 43.273 ns (0 allocations: 0 bytes)
1.0
</code></pre></div>
<p>and</p>
Expand All @@ -766,19 +766,19 @@ <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]
2.86962 2.25425 2.84076 3.01107
2.03591 2.68038 3.13627 2.07446
2.80898 2.16497 1.58681 2.48702
2.97989 2.38612 3.14715 2.51754
2.50736 3.69819 1.32951 1.91699
1.60841 3.71155 2.91778 2.42099
</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]
0.573925 0.450849 0.568153 0.602214
0.407182 0.536076 0.627253 0.414892
0.561796 0.432995 0.317362 0.497404
0.595979 0.477223 0.62943 0.503508
0.501471 0.739638 0.265903 0.383398
0.321682 0.742309 0.583557 0.484198
</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 @@ -845,8 +845,8 @@ <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 0.164418 0.228931
30 0.374765 0.373156
20 0.285046 0.271226
30 0.797472 0.922055
</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 @@ -863,7 +863,7 @@ <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>0.34006798846801756
<div class="highlight"><pre><span></span><code>0.6540468712382891
</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 @@ -874,20 +874,20 @@ <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 0.0838112
21 m 0.835421
31 m 0.174326
41 m 0.198397
11 m 0.0248315
21 m 0.699965
31 m 0.453597
41 m 0.781408
</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}:
0.6694471401547952
0.8228615945886772
0.8129189111358263
0.054620637199614186
0.005965196727489852
0.5489970409391682
0.10818854340064032
0.47112576675151363
0.40345209967170736
0.5967611421132145
</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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