nautilus_indicators/average/
wma.rs

1// -------------------------------------------------------------------------------------------------
2//  Copyright (C) 2015-2025 Nautech Systems Pty Ltd. All rights reserved.
3//  https://nautechsystems.io
4//
5//  Licensed under the GNU Lesser General Public License Version 3.0 (the "License");
6//  You may not use this file except in compliance with the License.
7//  You may obtain a copy of the License at https://www.gnu.org/licenses/lgpl-3.0.en.html
8//
9//  Unless required by applicable law or agreed to in writing, software
10//  distributed under the License is distributed on an "AS IS" BASIS,
11//  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
12//  See the License for the specific language governing permissions and
13//  limitations under the License.
14// -------------------------------------------------------------------------------------------------
15
16use std::fmt::Display;
17
18use arraydeque::{ArrayDeque, Wrapping};
19use nautilus_core::correctness::{FAILED, check_predicate_true};
20use nautilus_model::{
21    data::{Bar, QuoteTick, TradeTick},
22    enums::PriceType,
23};
24
25use crate::indicator::{Indicator, MovingAverage};
26
27const MAX_PERIOD: usize = 8_192;
28
29/// An indicator which calculates a weighted moving average across a rolling window.
30#[repr(C)]
31#[derive(Debug)]
32#[cfg_attr(
33    feature = "python",
34    pyo3::pyclass(module = "nautilus_trader.core.nautilus_pyo3.indicators")
35)]
36pub struct WeightedMovingAverage {
37    /// The rolling window period for the indicator (> 0).
38    pub period: usize,
39    /// The weights for the moving average calculation
40    pub weights: Vec<f64>,
41    /// Price type
42    pub price_type: PriceType,
43    /// The last indicator value.
44    pub value: f64,
45    /// Whether the indicator is initialized.
46    pub initialized: bool,
47    /// Inputs
48    pub inputs: ArrayDeque<f64, MAX_PERIOD, Wrapping>,
49}
50
51impl Display for WeightedMovingAverage {
52    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
53        write!(f, "{}({},{:?})", self.name(), self.period, self.weights)
54    }
55}
56
57impl WeightedMovingAverage {
58    /// Creates a new [`WeightedMovingAverage`] instance.
59    ///
60    /// # Panics
61    ///
62    /// This function panics if:
63    /// - `period` is zero.
64    /// - `weights.len()` does not equal `period`.
65    /// - `weights` sum is effectively zero.
66    #[must_use]
67    pub fn new(period: usize, weights: Vec<f64>, price_type: Option<PriceType>) -> Self {
68        Self::new_checked(period, weights, price_type).expect(FAILED)
69    }
70
71    /// Creates a new [`WeightedMovingAverage`] instance with the given period and weights.
72    ///
73    /// # Errors
74    ///
75    /// Returns an error if **any** of the validation rules fails:
76    /// - `period` must be **positive**.
77    /// - `weights` must be **exactly** `period` elements long.
78    /// - `weights` must contain at least one non-zero value (∑wᵢ > ε).
79    pub fn new_checked(
80        period: usize,
81        weights: Vec<f64>,
82        price_type: Option<PriceType>,
83    ) -> anyhow::Result<Self> {
84        const EPS: f64 = f64::EPSILON;
85
86        check_predicate_true(period > 0, "`period` must be positive")?;
87
88        check_predicate_true(
89            period == weights.len(),
90            "`period` must equal `weights.len()`",
91        )?;
92
93        let weight_sum: f64 = weights.iter().copied().sum();
94        check_predicate_true(
95            weight_sum > EPS,
96            "`weights` sum must be positive and > f64::EPSILON",
97        )?;
98
99        Ok(Self {
100            period,
101            weights,
102            price_type: price_type.unwrap_or(PriceType::Last),
103            value: 0.0,
104            inputs: ArrayDeque::new(),
105            initialized: false,
106        })
107    }
108
109    fn weighted_average(&self) -> f64 {
110        let n = self.inputs.len();
111        let weights_slice = &self.weights[self.period - n..];
112
113        let mut sum = 0.0;
114        let mut weight_sum = 0.0;
115
116        for (input, weight) in self.inputs.iter().rev().zip(weights_slice.iter().rev()) {
117            sum += input * weight;
118            weight_sum += weight;
119        }
120        sum / weight_sum
121    }
122}
123
124impl Indicator for WeightedMovingAverage {
125    fn name(&self) -> String {
126        stringify!(WeightedMovingAverage).to_string()
127    }
128
129    fn has_inputs(&self) -> bool {
130        !self.inputs.is_empty()
131    }
132
133    fn initialized(&self) -> bool {
134        self.initialized
135    }
136
137    fn handle_quote(&mut self, quote: &QuoteTick) {
138        self.update_raw(quote.extract_price(self.price_type).into());
139    }
140
141    fn handle_trade(&mut self, trade: &TradeTick) {
142        self.update_raw((&trade.price).into());
143    }
144
145    fn handle_bar(&mut self, bar: &Bar) {
146        self.update_raw((&bar.close).into());
147    }
148
149    fn reset(&mut self) {
150        self.value = 0.0;
151        self.initialized = false;
152        self.inputs.clear();
153    }
154}
155
156impl MovingAverage for WeightedMovingAverage {
157    fn value(&self) -> f64 {
158        self.value
159    }
160
161    fn count(&self) -> usize {
162        self.inputs.len()
163    }
164
165    fn update_raw(&mut self, value: f64) {
166        if self.inputs.len() == self.period.min(MAX_PERIOD) {
167            self.inputs.pop_front();
168        }
169        let _ = self.inputs.push_back(value);
170
171        self.value = self.weighted_average();
172        self.initialized = self.count() >= self.period;
173    }
174}
175
176#[cfg(test)]
177mod tests {
178
179    use arraydeque::{ArrayDeque, Wrapping};
180    use rstest::rstest;
181
182    use crate::{
183        average::wma::WeightedMovingAverage,
184        indicator::{Indicator, MovingAverage},
185        stubs::*,
186    };
187
188    #[rstest]
189    fn test_wma_initialized(indicator_wma_10: WeightedMovingAverage) {
190        let display_str = format!("{indicator_wma_10}");
191        assert_eq!(
192            display_str,
193            "WeightedMovingAverage(10,[0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0])"
194        );
195        assert_eq!(indicator_wma_10.name(), "WeightedMovingAverage");
196        assert!(!indicator_wma_10.has_inputs());
197        assert!(!indicator_wma_10.initialized());
198    }
199
200    #[rstest]
201    #[should_panic]
202    fn test_different_weights_len_and_period_error() {
203        let _ = WeightedMovingAverage::new(10, vec![0.5, 0.5, 0.5], None);
204    }
205
206    #[rstest]
207    fn test_value_with_one_input(mut indicator_wma_10: WeightedMovingAverage) {
208        indicator_wma_10.update_raw(1.0);
209        assert_eq!(indicator_wma_10.value, 1.0);
210    }
211
212    #[rstest]
213    fn test_value_with_two_inputs_equal_weights() {
214        let mut wma = WeightedMovingAverage::new(2, vec![0.5, 0.5], None);
215        wma.update_raw(1.0);
216        wma.update_raw(2.0);
217        assert_eq!(wma.value, 1.5);
218    }
219
220    #[rstest]
221    fn test_value_with_four_inputs_equal_weights() {
222        let mut wma = WeightedMovingAverage::new(4, vec![0.25, 0.25, 0.25, 0.25], None);
223        wma.update_raw(1.0);
224        wma.update_raw(2.0);
225        wma.update_raw(3.0);
226        wma.update_raw(4.0);
227        assert_eq!(wma.value, 2.5);
228    }
229
230    #[rstest]
231    fn test_value_with_two_inputs(mut indicator_wma_10: WeightedMovingAverage) {
232        indicator_wma_10.update_raw(1.0);
233        indicator_wma_10.update_raw(2.0);
234        let result = 2.0f64.mul_add(1.0, 1.0 * 0.9) / 1.9;
235        assert_eq!(indicator_wma_10.value, result);
236    }
237
238    #[rstest]
239    fn test_value_with_three_inputs(mut indicator_wma_10: WeightedMovingAverage) {
240        indicator_wma_10.update_raw(1.0);
241        indicator_wma_10.update_raw(2.0);
242        indicator_wma_10.update_raw(3.0);
243        let result = 1.0f64.mul_add(0.8, 3.0f64.mul_add(1.0, 2.0 * 0.9)) / (1.0 + 0.9 + 0.8);
244        assert_eq!(indicator_wma_10.value, result);
245    }
246
247    #[rstest]
248    fn test_value_expected_with_exact_period(mut indicator_wma_10: WeightedMovingAverage) {
249        for i in 1..11 {
250            indicator_wma_10.update_raw(f64::from(i));
251        }
252        assert_eq!(indicator_wma_10.value, 7.0);
253    }
254
255    #[rstest]
256    fn test_value_expected_with_more_inputs(mut indicator_wma_10: WeightedMovingAverage) {
257        for i in 1..=11 {
258            indicator_wma_10.update_raw(f64::from(i));
259        }
260        assert_eq!(indicator_wma_10.value(), 8.000_000_000_000_002);
261    }
262
263    #[rstest]
264    fn test_reset(mut indicator_wma_10: WeightedMovingAverage) {
265        indicator_wma_10.update_raw(1.0);
266        indicator_wma_10.update_raw(2.0);
267        indicator_wma_10.reset();
268        assert_eq!(indicator_wma_10.value, 0.0);
269        assert_eq!(indicator_wma_10.count(), 0);
270        assert!(!indicator_wma_10.initialized);
271    }
272
273    #[rstest]
274    #[should_panic]
275    fn new_panics_on_zero_period() {
276        let _ = WeightedMovingAverage::new(0, vec![1.0], None);
277    }
278
279    #[rstest]
280    fn new_checked_err_on_zero_period() {
281        let res = WeightedMovingAverage::new_checked(0, vec![1.0], None);
282        assert!(res.is_err());
283    }
284
285    #[rstest]
286    #[should_panic]
287    fn new_panics_on_zero_weight_sum() {
288        let _ = WeightedMovingAverage::new(3, vec![0.0, 0.0, 0.0], None);
289    }
290
291    #[rstest]
292    fn new_checked_err_on_zero_weight_sum() {
293        let res = WeightedMovingAverage::new_checked(3, vec![0.0, 0.0, 0.0], None);
294        assert!(res.is_err());
295    }
296
297    #[rstest]
298    #[should_panic]
299    fn new_panics_when_weight_sum_below_epsilon() {
300        let tiny = f64::EPSILON / 10.0;
301        let _ = WeightedMovingAverage::new(3, vec![tiny; 3], None);
302    }
303
304    #[rstest]
305    fn initialized_flag_transitions() {
306        let period = 3;
307        let weights = vec![1.0, 2.0, 3.0];
308        let mut wma = WeightedMovingAverage::new(period, weights, None);
309
310        assert!(!wma.initialized());
311
312        for i in 0..period {
313            wma.update_raw(i as f64);
314            let expected = (i + 1) >= period;
315            assert_eq!(wma.initialized(), expected);
316        }
317        assert!(wma.initialized());
318    }
319
320    #[rstest]
321    fn count_matches_inputs_and_has_inputs() {
322        let mut wma = WeightedMovingAverage::new(4, vec![0.25; 4], None);
323
324        assert_eq!(wma.count(), 0);
325        assert!(!wma.has_inputs());
326
327        wma.update_raw(1.0);
328        wma.update_raw(2.0);
329        assert_eq!(wma.count(), 2);
330        assert!(wma.has_inputs());
331    }
332
333    #[rstest]
334    fn reset_restores_pristine_state() {
335        let mut wma = WeightedMovingAverage::new(2, vec![0.5, 0.5], None);
336        wma.update_raw(1.0);
337        wma.update_raw(2.0);
338        assert!(wma.initialized());
339
340        wma.reset();
341
342        assert_eq!(wma.count(), 0);
343        assert_eq!(wma.value(), 0.0);
344        assert!(!wma.initialized());
345        assert!(!wma.has_inputs());
346    }
347
348    #[rstest]
349    fn weighted_average_with_non_uniform_weights() {
350        let mut wma = WeightedMovingAverage::new(3, vec![1.0, 2.0, 3.0], None);
351        wma.update_raw(10.0);
352        wma.update_raw(20.0);
353        wma.update_raw(30.0);
354        let expected = 23.333_333_333_333_332;
355        let tol = f64::EPSILON.sqrt();
356        assert!(
357            (wma.value() - expected).abs() < tol,
358            "value = {}, expected ≈ {}",
359            wma.value(),
360            expected
361        );
362    }
363
364    #[rstest]
365    fn test_window_never_exceeds_period(mut indicator_wma_10: WeightedMovingAverage) {
366        for i in 0..100 {
367            indicator_wma_10.update_raw(f64::from(i));
368            assert!(indicator_wma_10.count() <= indicator_wma_10.period);
369        }
370    }
371
372    #[rstest]
373    fn test_negative_weights_positive_sum() {
374        let period = 3;
375        let weights = vec![-1.0, 2.0, 2.0];
376        let mut wma = WeightedMovingAverage::new(period, weights, None);
377        wma.update_raw(1.0);
378        wma.update_raw(2.0);
379        wma.update_raw(3.0);
380
381        let expected = 2.0f64.mul_add(3.0, 2.0f64.mul_add(2.0, -1.0)) / 3.0;
382        let tol = f64::EPSILON.sqrt();
383        assert!((wma.value() - expected).abs() < tol);
384    }
385
386    #[rstest]
387    fn test_nan_input_propagates() {
388        let mut wma = WeightedMovingAverage::new(2, vec![0.5, 0.5], None);
389        wma.update_raw(1.0);
390        wma.update_raw(f64::NAN);
391
392        assert!(wma.value().is_nan());
393    }
394
395    #[rstest]
396    #[should_panic]
397    fn new_panics_when_weight_sum_equals_epsilon() {
398        let eps_third = f64::EPSILON / 3.0;
399        let _ = WeightedMovingAverage::new(3, vec![eps_third; 3], None);
400    }
401
402    #[rstest]
403    fn new_checked_err_when_weight_sum_equals_epsilon() {
404        let eps_third = f64::EPSILON / 3.0;
405        let res = WeightedMovingAverage::new_checked(3, vec![eps_third; 3], None);
406        assert!(res.is_err());
407    }
408
409    #[rstest]
410    fn new_checked_err_when_weight_sum_below_epsilon() {
411        let w = f64::EPSILON * 0.9;
412        let res = WeightedMovingAverage::new_checked(1, vec![w], None);
413        assert!(res.is_err());
414    }
415
416    #[rstest]
417    fn new_ok_when_weight_sum_above_epsilon() {
418        let w = f64::EPSILON * 1.1;
419        let res = WeightedMovingAverage::new_checked(1, vec![w], None);
420        assert!(res.is_ok());
421    }
422
423    #[rstest]
424    #[should_panic]
425    fn new_panics_on_cancelled_weights_sum() {
426        let _ = WeightedMovingAverage::new(3, vec![1.0, -1.0, 0.0], None);
427    }
428
429    #[rstest]
430    fn new_checked_err_on_cancelled_weights_sum() {
431        let res = WeightedMovingAverage::new_checked(3, vec![1.0, -1.0, 0.0], None);
432        assert!(res.is_err());
433    }
434
435    #[rstest]
436    fn single_period_returns_latest_input() {
437        let mut wma = WeightedMovingAverage::new(1, vec![1.0], None);
438        for i in 0..5 {
439            let v = f64::from(i);
440            wma.update_raw(v);
441            assert_eq!(wma.value(), v);
442        }
443    }
444
445    #[rstest]
446    fn value_with_sparse_weights() {
447        let mut wma = WeightedMovingAverage::new(3, vec![0.0, 1.0, 0.0], None);
448        wma.update_raw(10.0);
449        wma.update_raw(20.0);
450        wma.update_raw(30.0);
451        assert_eq!(wma.value(), 20.0);
452    }
453
454    #[rstest]
455    fn warm_up_len1() {
456        let mut wma = WeightedMovingAverage::new(4, vec![1.0, 2.0, 3.0, 4.0], None);
457        wma.update_raw(42.0);
458        assert_eq!(wma.value(), 42.0);
459    }
460
461    #[rstest]
462    fn warm_up_len2() {
463        let mut wma = WeightedMovingAverage::new(4, vec![1.0, 2.0, 3.0, 4.0], None);
464        wma.update_raw(10.0);
465        wma.update_raw(20.0);
466        let expected = 20.0f64.mul_add(4.0, 10.0 * 3.0) / (4.0 + 3.0);
467        assert_eq!(wma.value(), expected);
468    }
469
470    #[rstest]
471    fn warm_up_len3() {
472        let mut wma = WeightedMovingAverage::new(4, vec![1.0, 2.0, 3.0, 4.0], None);
473        wma.update_raw(1.0);
474        wma.update_raw(2.0);
475        wma.update_raw(3.0);
476        let expected = 1.0f64.mul_add(2.0, 3.0f64.mul_add(4.0, 2.0 * 3.0)) / (4.0 + 3.0 + 2.0);
477        assert_eq!(wma.value(), expected);
478    }
479
480    #[rstest]
481    fn input_window_contains_latest_period() {
482        let period = 3;
483        let mut wma = WeightedMovingAverage::new(period, vec![1.0; period], None);
484        let vals = [1.0, 2.0, 3.0, 4.0];
485        for v in vals {
486            wma.update_raw(v);
487        }
488        let expected: Vec<f64> = vals[vals.len() - period..].to_vec();
489        assert_eq!(wma.inputs.iter().copied().collect::<Vec<_>>(), expected);
490    }
491
492    #[rstest]
493    fn window_slides_correctly() {
494        let mut wma = WeightedMovingAverage::new(2, vec![1.0; 2], None);
495        wma.update_raw(1.0);
496        assert_eq!(wma.inputs.iter().copied().collect::<Vec<_>>(), vec![1.0]);
497        wma.update_raw(2.0);
498        assert_eq!(
499            wma.inputs.iter().copied().collect::<Vec<_>>(),
500            vec![1.0, 2.0]
501        );
502        wma.update_raw(3.0);
503        assert_eq!(
504            wma.inputs.iter().copied().collect::<Vec<_>>(),
505            vec![2.0, 3.0]
506        );
507    }
508
509    #[rstest]
510    fn window_len_constant_after_many_updates() {
511        let period = 5;
512        let mut wma = WeightedMovingAverage::new(period, vec![1.0; period], None);
513        for i in 0..100 {
514            wma.update_raw(i as f64);
515            assert_eq!(wma.inputs.len(), period.min(i + 1));
516        }
517    }
518
519    #[rstest]
520    fn arraydeque_wraps_when_full() {
521        const CAP: usize = 3;
522        let mut buf: ArrayDeque<usize, CAP, Wrapping> = ArrayDeque::new();
523        for i in 0..=CAP {
524            let _ = buf.push_back(i);
525        }
526        assert_eq!(buf.len(), CAP);
527        assert_eq!(buf.front().copied(), Some(1));
528        assert_eq!(buf.back().copied(), Some(3));
529    }
530
531    #[rstest]
532    fn arraydeque_sliding_window_with_pop() {
533        const CAP: usize = 3;
534        let mut buf: ArrayDeque<usize, CAP, Wrapping> = ArrayDeque::new();
535        for i in 0..10 {
536            if buf.len() == CAP {
537                buf.pop_front();
538            }
539            let _ = buf.push_back(i);
540            assert!(buf.len() <= CAP);
541        }
542        assert_eq!(buf.len(), CAP);
543    }
544
545    #[rstest]
546    fn new_ok_with_infinite_weight() {
547        let res = WeightedMovingAverage::new_checked(2, vec![f64::INFINITY, 1.0], None);
548        assert!(res.is_ok());
549    }
550
551    #[rstest]
552    #[should_panic]
553    fn new_panics_on_nan_weight() {
554        let _ = WeightedMovingAverage::new(2, vec![f64::NAN, 1.0], None);
555    }
556
557    #[rstest]
558    #[should_panic]
559    fn new_panics_on_empty_weights() {
560        let _ = WeightedMovingAverage::new(1, Vec::new(), None);
561    }
562
563    #[rstest]
564    fn inf_input_propagates() {
565        let mut wma = WeightedMovingAverage::new(2, vec![0.5, 0.5], None);
566        wma.update_raw(1.0);
567        wma.update_raw(f64::INFINITY);
568        assert!(wma.value().is_infinite());
569    }
570
571    #[rstest]
572    fn warm_up_with_front_zero_weights() {
573        let mut wma = WeightedMovingAverage::new(4, vec![0.0, 0.0, 1.0, 1.0], None);
574        wma.update_raw(10.0);
575        wma.update_raw(20.0);
576        let expected = 20.0f64.mul_add(1.0, 10.0 * 1.0) / 2.0;
577        assert_eq!(wma.value(), expected);
578    }
579}
nautilus_indicators/average/wma.rs

nautilus_indicators/average/
wma.rs
