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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::< i32> () as f32;
let count = data.len();
let mean = match count {
positive if positive > 0 => Some(sum / count as f32),
_ => None
};
println!(" Mean of the data is {:?}" , 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: & [i32]) -> Option< (Vec< i32> , i32, Vec< i32> )> {
match data.len() {
0 => None,
_ => {
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) = & mut splits;
if next < & pivot {
left.push(*next);
} else {
right.push(*next);
}
}
splits
});
Some((left, pivot, right))
}
}
}
fn select(data: & [i32], k: usize) -> Option< i32> {
let part = partition(data);
match part {
None => None,
Some((left, pivot, right)) => {
let pivot_idx = left.len();
match pivot_idx.cmp(& k) {
Ordering::Equal => Some(pivot),
Ordering::Greater => select(& left, k),
Ordering::Less => select(& right, k - (pivot_idx + 1)),
}
},
}
}
fn median(data: & [i32]) -> Option< f32> {
let size = data.len();
match size {
even if even % 2 == 0 => {
let fst_med = select(data, (even / 2) - 1);
let snd_med = select(data, even / 2);
match (fst_med, snd_med) {
(Some(fst), Some(snd)) => Some((fst + snd) as f32 / 2.0),
_ => None
}
},
odd => 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(& data);
println!(" Partition is {:?}" , part);
let sel = select(& data, 5);
println!(" Selection at ordered index {} is {:?}" , 5, sel);
let med = median(& data);
println!(" Median is {:?}" , 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(|& (_, count)| count)
.map(|(value, _)| *value);
println!(" Mode of the data is {:?}" , 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: & [i32]) -> Option< f32> {
let sum = data.iter().sum::< i32> () as f32;
let count = data.len();
match count {
positive if positive > 0 => Some(sum / count as f32),
_ => None,
}
}
fn std_deviation(data: & [i32]) -> Option< f32> {
match (mean(data), data.len()) {
(Some(data_mean), count) if count > 0 => {
let variance = data.iter().map(|value| {
let diff = data_mean - (*value as f32);
diff * diff
}).sum::< f32> () / count as f32;
Some(variance.sqrt())
},
_ => None
}
}
fn main() {
let data = [3, 1, 6, 1, 5, 8, 1, 8, 10, 11];
let data_mean = mean(& data);
println!(" Mean is {:?}" , data_mean);
let data_std_deviation = std_deviation(& data);
println!(" Standard deviation is {:?}" , data_std_deviation);
let zscore = match (data_mean, data_std_deviation) {
(Some(mean), Some(std_deviation)) => {
let diff = data[4] as f32 - mean;
Some(diff / std_deviation)
},
_ => None
};
println!(" Z-score of data at index 4 (with value {}) is {:?}" , data[4], zscore);
}
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