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variance.rs
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variance.rs
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use no_nulls::{rolling_apply_agg_window, RollingAggWindowNoNulls};
use num_traits::pow::Pow;
use super::mean::MeanWindow;
use super::*;
pub(super) struct SumSquaredWindow<'a, T> {
slice: &'a [T],
sum_of_squares: T,
last_start: usize,
last_end: usize,
// if we don't recompute every 'n' iterations
// we get a accumulated error/drift
last_recompute: u8,
}
impl<'a, T: NativeType + IsFloat + std::iter::Sum + AddAssign + SubAssign + Mul<Output = T>>
RollingAggWindowNoNulls<'a, T> for SumSquaredWindow<'a, T>
{
fn new(slice: &'a [T], start: usize, end: usize) -> Self {
let sum = slice[start..end].iter().map(|v| *v * *v).sum::<T>();
Self {
slice,
sum_of_squares: sum,
last_start: start,
last_end: end,
last_recompute: 0,
}
}
unsafe fn update(&mut self, start: usize, end: usize) -> T {
// if we exceed the end, we have a completely new window
// so we recompute
let recompute_sum = if start >= self.last_end || self.last_recompute > 128 {
self.last_recompute = 0;
true
} else {
self.last_recompute += 1;
// remove elements that should leave the window
let mut recompute_sum = false;
for idx in self.last_start..start {
// safety
// we are in bounds
let leaving_value = self.slice.get_unchecked(idx);
if T::is_float() && leaving_value.is_nan() {
recompute_sum = true;
break;
}
self.sum_of_squares -= *leaving_value * *leaving_value;
}
recompute_sum
};
self.last_start = start;
// we traverse all values and compute
if T::is_float() && recompute_sum {
self.sum_of_squares = self
.slice
.get_unchecked(start..end)
.iter()
.map(|v| *v * *v)
.sum::<T>();
} else {
for idx in self.last_end..end {
let entering_value = *self.slice.get_unchecked(idx);
self.sum_of_squares += entering_value * entering_value;
}
}
self.last_end = end;
self.sum_of_squares
}
}
// E[(xi - E[x])^2]
// can be expanded to
// E[x^2] - E[x]^2
pub struct VarWindow<'a, T> {
mean: MeanWindow<'a, T>,
sum_of_squares: SumSquaredWindow<'a, T>,
}
impl<
'a,
T: NativeType
+ IsFloat
+ std::iter::Sum
+ AddAssign
+ SubAssign
+ Div<Output = T>
+ NumCast
+ One
+ Zero
+ PartialOrd
+ Sub<Output = T>,
> RollingAggWindowNoNulls<'a, T> for VarWindow<'a, T>
{
fn new(slice: &'a [T], start: usize, end: usize) -> Self {
Self {
mean: MeanWindow::new(slice, start, end),
sum_of_squares: SumSquaredWindow::new(slice, start, end),
}
}
unsafe fn update(&mut self, start: usize, end: usize) -> T {
let count = NumCast::from(end - start).unwrap();
let sum_of_squares = self.sum_of_squares.update(start, end);
let mean_of_squares = sum_of_squares / count;
let mean = self.mean.update(start, end);
let var = mean_of_squares - mean * mean;
if end - start == 1 {
T::zero()
} else {
// apply Bessel's correction
let out = var / (count - T::one()) * count;
// variance cannot be negative.
// if it is negative it is due to numeric instability
if out < T::zero() {
T::zero()
} else {
out
}
}
}
}
pub fn rolling_var<T>(
values: &[T],
window_size: usize,
min_periods: usize,
center: bool,
weights: Option<&[f64]>,
) -> ArrayRef
where
T: NativeType
+ Float
+ IsFloat
+ std::iter::Sum
+ AddAssign
+ SubAssign
+ Div<Output = T>
+ NumCast
+ One
+ Zero
+ Sub<Output = T>,
{
match (center, weights) {
(true, None) => rolling_apply_agg_window::<VarWindow<_>, _, _>(
values,
window_size,
min_periods,
det_offsets_center,
),
(false, None) => rolling_apply_agg_window::<VarWindow<_>, _, _>(
values,
window_size,
min_periods,
det_offsets,
),
(true, Some(weights)) => {
let weights = coerce_weights(weights);
super::rolling_apply_weights(
values,
window_size,
min_periods,
det_offsets_center,
compute_var_weights,
&weights,
)
}
(false, Some(weights)) => {
let weights = coerce_weights(weights);
super::rolling_apply_weights(
values,
window_size,
min_periods,
det_offsets,
compute_var_weights,
&weights,
)
}
}
}
// E[(xi - E[x])^2]
// can be expanded to
// E[x^2] - E[x]^2
pub struct StdWindow<'a, T> {
var: VarWindow<'a, T>,
}
impl<
'a,
T: NativeType
+ IsFloat
+ std::iter::Sum
+ AddAssign
+ SubAssign
+ Div<Output = T>
+ NumCast
+ One
+ Zero
+ Sub<Output = T>
+ PartialOrd
+ Pow<T, Output = T>,
> RollingAggWindowNoNulls<'a, T> for StdWindow<'a, T>
{
fn new(slice: &'a [T], start: usize, end: usize) -> Self {
Self {
var: VarWindow::new(slice, start, end),
}
}
unsafe fn update(&mut self, start: usize, end: usize) -> T {
let var = self.var.update(start, end);
var.pow(NumCast::from(0.5).unwrap())
}
}
pub fn rolling_std<T>(
values: &[T],
window_size: usize,
min_periods: usize,
center: bool,
weights: Option<&[f64]>,
) -> ArrayRef
where
T: NativeType
+ Float
+ IsFloat
+ std::iter::Sum
+ AddAssign
+ SubAssign
+ Div<Output = T>
+ NumCast
+ One
+ Zero
+ Sub<Output = T>
+ Pow<T, Output = T>,
{
match (center, weights) {
(true, None) => rolling_apply_agg_window::<StdWindow<_>, _, _>(
values,
window_size,
min_periods,
det_offsets_center,
),
(false, None) => rolling_apply_agg_window::<StdWindow<_>, _, _>(
values,
window_size,
min_periods,
det_offsets,
),
(_, Some(_)) => {
panic!("weights not yet supported for rolling_std")
}
}
}
#[cfg(test)]
mod test {
use super::*;
#[test]
fn test_rolling_var() {
let values = &[1.0f64, 5.0, 3.0, 4.0];
let out = rolling_var(values, 2, 2, false, None);
let out = out.as_any().downcast_ref::<PrimitiveArray<f64>>().unwrap();
let out = out.into_iter().map(|v| v.copied()).collect::<Vec<_>>();
assert_eq!(out, &[None, Some(8.0), Some(2.0), Some(0.5)]);
let out = rolling_var(values, 2, 1, false, None);
let out = out.as_any().downcast_ref::<PrimitiveArray<f64>>().unwrap();
let out = out
.into_iter()
.map(|v| v.copied().unwrap())
.collect::<Vec<_>>();
// we cannot compare nans, so we compare the string values
assert_eq!(
format!("{:?}", out.as_slice()),
format!("{:?}", &[0.0, 8.0, 2.0, 0.5])
);
// test nan handling.
let values = &[-10.0, 2.0, 3.0, f64::nan(), 5.0, 6.0, 7.0];
let out = rolling_var(values, 3, 3, false, None);
let out = out.as_any().downcast_ref::<PrimitiveArray<f64>>().unwrap();
let out = out.into_iter().map(|v| v.copied()).collect::<Vec<_>>();
// we cannot compare nans, so we compare the string values
assert_eq!(
format!("{:?}", out.as_slice()),
format!(
"{:?}",
&[
None,
None,
Some(52.33333333333333),
Some(f64::nan()),
Some(f64::nan()),
Some(f64::nan()),
Some(0.9999999999999964)
]
)
);
}
}