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<main>
<h1 id="统计"><a class="header" href="#统计">统计</a></h1>
<h3 id="测量中心趋势"><a class="header" href="#测量中心趋势">测量中心趋势</a></h3>
<p>下面的一些例子为 Rust 数组中的数据计算它们的中心趋势。</p>
<h4 id="平均值"><a class="header" href="#平均值">平均值</a></h4>
<p>首先计算的是平均值。</p>
<pre><pre class="playground"><code class="language-rust editable edition2021">fn main() {
let data = [3, 1, 6, 1, 5, 8, 1, 8, 10, 11];
let sum = data.iter().sum::&lt;i32&gt;() as f32;
let count = data.len();
let mean = match count {
positive if positive &gt; 0 =&gt; Some(sum / count as f32),
_ =&gt; None
};
println!(&quot;Mean of the data is {:?}&quot;, mean);
}
</code></pre></pre>
<h4 id="中位数"><a class="header" href="#中位数">中位数</a></h4>
<p>下面使用快速选择算法来计算中位数。该算法只会对可能包含中位数的数据分区进行排序，从而避免了对所有数据进行全排序。</p>
<pre><pre class="playground"><code class="language-rust editable edition2021">use std::cmp::Ordering;
fn partition(data: &amp;[i32]) -&gt; Option&lt;(Vec&lt;i32&gt;, i32, Vec&lt;i32&gt;)&gt; {
match data.len() {
0 =&gt; None,
_ =&gt; {
let (pivot_slice, tail) = data.split_at(1);
let pivot = pivot_slice[0];
let (left, right) = tail.iter()
.fold((vec![], vec![]), |mut splits, next| {
{
let (ref mut left, ref mut right) = &amp;mut splits;
if next &lt; &amp;pivot {
left.push(*next);
} else {
right.push(*next);
}
}
splits
});
Some((left, pivot, right))
}
}
}
fn select(data: &amp;[i32], k: usize) -&gt; Option&lt;i32&gt; {
let part = partition(data);
match part {
None =&gt; None,
Some((left, pivot, right)) =&gt; {
let pivot_idx = left.len();
match pivot_idx.cmp(&amp;k) {
Ordering::Equal =&gt; Some(pivot),
Ordering::Greater =&gt; select(&amp;left, k),
Ordering::Less =&gt; select(&amp;right, k - (pivot_idx + 1)),
}
},
}
}
fn median(data: &amp;[i32]) -&gt; Option&lt;f32&gt; {
let size = data.len();
match size {
even if even % 2 == 0 =&gt; {
let fst_med = select(data, (even / 2) - 1);
let snd_med = select(data, even / 2);
match (fst_med, snd_med) {
(Some(fst), Some(snd)) =&gt; Some((fst + snd) as f32 / 2.0),
_ =&gt; None
}
},
odd =&gt; select(data, odd / 2).map(|x| x as f32)
}
}
fn main() {
let data = [3, 1, 6, 1, 5, 8, 1, 8, 10, 11];
let part = partition(&amp;data);
println!(&quot;Partition is {:?}&quot;, part);
let sel = select(&amp;data, 5);
println!(&quot;Selection at ordered index {} is {:?}&quot;, 5, sel);
let med = median(&amp;data);
println!(&quot;Median is {:?}&quot;, med);
}
</code></pre></pre>
<h4 id="众数-mode-"><a class="header" href="#众数-mode-">众数( mode )</a></h4>
<p>下面使用了 <code>HashMap</code> 对不同数字出现的次数进行了分别统计。</p>
<pre><pre class="playground"><code class="language-rust editable edition2021">use std::collections::HashMap;
fn main() {
let data = [3, 1, 6, 1, 5, 8, 1, 8, 10, 11];
let frequencies = data.iter().fold(HashMap::new(), |mut freqs, value| {
*freqs.entry(value).or_insert(0) += 1;
freqs
});
let mode = frequencies
.into_iter()
.max_by_key(|&amp;(_, count)| count)
.map(|(value, _)| *value);
println!(&quot;Mode of the data is {:?}&quot;, mode);
}
</code></pre></pre>
<h3 id="标准偏差"><a class="header" href="#标准偏差">标准偏差</a></h3>
<p>下面一起来看看该如何计算一组测量值的标准偏差和 z-score。</p>
<pre><pre class="playground"><code class="language-rust editable edition2021">fn mean(data: &amp;[i32]) -&gt; Option&lt;f32&gt; {
let sum = data.iter().sum::&lt;i32&gt;() as f32;
let count = data.len();
match count {
positive if positive &gt; 0 =&gt; Some(sum / count as f32),
_ =&gt; None,
}
}
fn std_deviation(data: &amp;[i32]) -&gt; Option&lt;f32&gt; {
match (mean(data), data.len()) {
(Some(data_mean), count) if count &gt; 0 =&gt; {
let variance = data.iter().map(|value| {
let diff = data_mean - (*value as f32);
diff * diff
}).sum::&lt;f32&gt;() / count as f32;
Some(variance.sqrt())
},
_ =&gt; None
}
}
fn main() {
let data = [3, 1, 6, 1, 5, 8, 1, 8, 10, 11];
let data_mean = mean(&amp;data);
println!(&quot;Mean is {:?}&quot;, data_mean);
let data_std_deviation = std_deviation(&amp;data);
println!(&quot;Standard deviation is {:?}&quot;, data_std_deviation);
let zscore = match (data_mean, data_std_deviation) {
(Some(mean), Some(std_deviation)) =&gt; {
let diff = data[4] as f32 - mean;
Some(diff / std_deviation)
},
_ =&gt; None
};
println!(&quot;Z-score of data at index 4 (with value {}) is {:?}&quot;, data[4], zscore);
}
</code></pre></pre>
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