scirs2_interpolate/extrapolation_modules/
advanced.rs

1//! Advanced extrapolation functionality
2//!
3//! This module contains the AdvancedExtrapolator struct and its implementation
4//! for performing sophisticated extrapolation using ensemble, adaptive, and
5//! statistical methods.
6
7use scirs2_core::ndarray::Array1;
8use scirs2_core::numeric::{Float, FromPrimitive};
9use std::default::Default;
10use std::ops::AddAssign;
11
12use crate::error::{InterpolateError, InterpolateResult};
13
14use super::config::{
15    AdaptiveExtrapolationConfig, AutoregressiveExtrapolationConfig, ConfidenceExtrapolationConfig,
16    ConfidenceExtrapolationResult, EnsembleExtrapolationConfig,
17};
18use super::core::Extrapolator;
19use super::types::{ARFittingMethod, EnsembleCombinationStrategy, ExtrapolationMethod};
20
21/// Advanced extrapolator with ensemble, adaptive, and statistical capabilities
22#[derive(Debug, Clone)]
23pub struct AdvancedExtrapolator<T: Float> {
24    /// Basic extrapolator for standard methods
25    pub base_extrapolator: Extrapolator<T>,
26    /// Configuration for confidence-based extrapolation
27    pub confidence_config: Option<ConfidenceExtrapolationConfig<T>>,
28    /// Configuration for ensemble extrapolation
29    pub ensemble_config: Option<EnsembleExtrapolationConfig<T>>,
30    /// Configuration for adaptive extrapolation
31    pub adaptive_config: Option<AdaptiveExtrapolationConfig>,
32    /// Configuration for autoregressive extrapolation
33    pub autoregressive_config: Option<AutoregressiveExtrapolationConfig<T>>,
34    /// Historical data for advanced methods (when available)
35    pub historical_data: Option<(Array1<T>, Array1<T>)>,
36}
37
38impl<T: Float + std::fmt::Display + Default + AddAssign> AdvancedExtrapolator<T> {
39    /// Create a new advanced extrapolator
40    pub fn new(base_extrapolator: Extrapolator<T>) -> Self {
41        Self {
42            base_extrapolator,
43            confidence_config: None,
44            ensemble_config: None,
45            adaptive_config: None,
46            autoregressive_config: None,
47            historical_data: None,
48        }
49    }
50
51    /// Enable confidence-based extrapolation
52    pub fn with_confidence(mut self, config: ConfidenceExtrapolationConfig<T>) -> Self {
53        self.confidence_config = Some(config);
54        self
55    }
56
57    /// Enable ensemble extrapolation
58    pub fn with_ensemble(mut self, config: EnsembleExtrapolationConfig<T>) -> Self {
59        self.ensemble_config = Some(config);
60        self
61    }
62
63    /// Enable adaptive extrapolation
64    pub fn with_adaptive(mut self, config: AdaptiveExtrapolationConfig) -> Self {
65        self.adaptive_config = Some(config);
66        self
67    }
68
69    /// Enable autoregressive extrapolation
70    pub fn with_autoregressive(mut self, config: AutoregressiveExtrapolationConfig<T>) -> Self {
71        self.autoregressive_config = Some(config);
72        self
73    }
74
75    /// Set historical data for advanced methods
76    pub fn with_historical_data(mut self, x_data: Array1<T>, y_data: Array1<T>) -> Self {
77        self.historical_data = Some((x_data, y_data));
78        self
79    }
80
81    /// Perform advanced extrapolation at a point
82    pub fn extrapolate_advanced(&self, x: T) -> InterpolateResult<T> {
83        // Try ensemble extrapolation first if configured
84        if self.ensemble_config.is_some() {
85            return self.extrapolate_ensemble(x);
86        }
87
88        // Try adaptive extrapolation if configured
89        if self.adaptive_config.is_some() {
90            return self.extrapolate_adaptive(x);
91        }
92
93        // Try autoregressive extrapolation if configured
94        if self.autoregressive_config.is_some() {
95            return self.extrapolate_autoregressive(x);
96        }
97
98        // Fall back to base extrapolator
99        self.base_extrapolator.extrapolate(x)
100    }
101
102    /// Perform confidence-based extrapolation
103    pub fn extrapolate_with_confidence(
104        &self,
105        x: T,
106    ) -> InterpolateResult<ConfidenceExtrapolationResult<T>> {
107        if let Some(config) = &self.confidence_config {
108            let base_result = self.base_extrapolator.extrapolate(x)?;
109
110            // Estimate uncertainty based on distance from domain boundaries
111            let lower_bound = self.base_extrapolator.lower_bound();
112            let upper_bound = self.base_extrapolator.upper_bound();
113
114            // Calculate distance from nearest boundary
115            let distance_from_domain = if x < lower_bound {
116                lower_bound - x
117            } else if x > upper_bound {
118                x - upper_bound
119            } else {
120                T::zero() // Inside domain
121            };
122
123            // Uncertainty increases with distance from domain
124            // Standard error grows linearly with distance (simple model)
125            let base_uncertainty = T::from(0.01).unwrap_or_default(); // 1% base uncertainty
126            let distance_factor = T::from(0.1).unwrap_or_default(); // 10% per unit distance
127            let _standard_error = base_uncertainty + distance_factor * distance_from_domain;
128
129            // Calculate confidence bounds based on confidence level
130            // Using normal approximation: bounds = estimate ± z * standard_error
131            let z_score = if config.confidence_level >= T::from(0.99).unwrap_or_default() {
132                T::from(2.576).unwrap_or_default() // 99%
133            } else if config.confidence_level >= T::from(0.95).unwrap_or_default() {
134                T::from(1.96).unwrap_or_default() // 95%
135            } else if config.confidence_level >= T::from(0.90).unwrap_or_default() {
136                T::from(1.645).unwrap_or_default() // 90%
137            } else {
138                T::from(1.0).unwrap_or_default() // Default 1-sigma
139            };
140
141            let margin_of_error = z_score * _standard_error;
142            let lower_bound_confidence = base_result - margin_of_error;
143            let upper_bound_confidence = base_result + margin_of_error;
144
145            Ok(ConfidenceExtrapolationResult {
146                value: base_result,
147                lower_bound: lower_bound_confidence,
148                upper_bound: upper_bound_confidence,
149                confidence_level: config.confidence_level,
150            })
151        } else {
152            Err(InterpolateError::ComputationError(
153                "Confidence extrapolation not configured".to_string(),
154            ))
155        }
156    }
157
158    /// Perform ensemble extrapolation
159    pub fn extrapolate_ensemble(&self, x: T) -> InterpolateResult<T> {
160        if let Some(config) = &self.ensemble_config {
161            let mut results = Vec::new();
162            let mut weights = Vec::new();
163
164            // Collect results from all methods
165            for (i, &method) in config.methods.iter().enumerate() {
166                // Create a temporary extrapolator with this method
167                let mut temp_extrapolator = self.base_extrapolator.clone();
168
169                // Update the extrapolation method based on direction
170                if x < temp_extrapolator.lower_bound() {
171                    temp_extrapolator.lower_method = method;
172                } else if x > temp_extrapolator.upper_bound() {
173                    temp_extrapolator.upper_method = method;
174                }
175
176                if let Ok(result) = temp_extrapolator.extrapolate(x) {
177                    results.push(result);
178                    let weight = if let Some(w) = config.weights.as_ref() {
179                        w.get(i).copied().unwrap_or(T::one())
180                    } else {
181                        T::one()
182                    };
183                    weights.push(weight);
184                }
185            }
186
187            if results.is_empty() {
188                return Err(InterpolateError::ComputationError(
189                    "No ensemble methods produced valid results".to_string(),
190                ));
191            }
192
193            // Combine results based on strategy
194            match config.combination_strategy {
195                EnsembleCombinationStrategy::Mean => {
196                    let sum: T = results.iter().copied().fold(T::zero(), |acc, x| acc + x);
197                    Ok(sum / T::from(results.len()).unwrap())
198                }
199                EnsembleCombinationStrategy::WeightedMean => {
200                    let weighted_sum: T = results
201                        .iter()
202                        .zip(weights.iter())
203                        .map(|(r, w)| *r * *w)
204                        .fold(T::zero(), |acc, x| acc + x);
205                    let weight_sum: T = weights.iter().copied().fold(T::zero(), |acc, x| acc + x);
206
207                    if weight_sum.is_zero() {
208                        return Err(InterpolateError::ComputationError(
209                            "Zero total weight in ensemble".to_string(),
210                        ));
211                    }
212
213                    Ok(weighted_sum / weight_sum)
214                }
215                EnsembleCombinationStrategy::Median => {
216                    let mut sorted_results = results;
217                    sorted_results.sort_by(|a, b| a.partial_cmp(b).unwrap());
218                    let mid = sorted_results.len() / 2;
219
220                    if sorted_results.len() % 2 == 0 {
221                        let two = T::from(2.0).unwrap();
222                        Ok((sorted_results[mid - 1] + sorted_results[mid]) / two)
223                    } else {
224                        Ok(sorted_results[mid])
225                    }
226                }
227                EnsembleCombinationStrategy::BestMethod => {
228                    // Use the method with highest confidence (simplified to first result)
229                    Ok(results[0])
230                }
231                EnsembleCombinationStrategy::MinimumVariance => {
232                    // Simplified implementation using equal weights
233                    let sum: T = results.iter().copied().fold(T::zero(), |acc, x| acc + x);
234                    Ok(sum / T::from(results.len()).unwrap())
235                }
236                EnsembleCombinationStrategy::BayesianAveraging => {
237                    // Simplified implementation using uniform priors
238                    let sum: T = results.iter().copied().fold(T::zero(), |acc, x| acc + x);
239                    Ok(sum / T::from(results.len()).unwrap())
240                }
241                EnsembleCombinationStrategy::Voting => {
242                    // For regression, use median as "majority vote"
243                    let mut sorted_results = results;
244                    sorted_results.sort_by(|a, b| a.partial_cmp(b).unwrap());
245                    let mid = sorted_results.len() / 2;
246                    Ok(sorted_results[mid])
247                }
248                EnsembleCombinationStrategy::Stacking => {
249                    // Simplified stacking using equal weights
250                    let sum: T = results.iter().copied().fold(T::zero(), |acc, x| acc + x);
251                    Ok(sum / T::from(results.len()).unwrap())
252                }
253            }
254        } else {
255            Err(InterpolateError::ComputationError(
256                "Ensemble extrapolation not configured".to_string(),
257            ))
258        }
259    }
260
261    /// Perform adaptive extrapolation
262    pub fn extrapolate_adaptive(&self, x: T) -> InterpolateResult<T> {
263        if let Some(_config) = &self.adaptive_config {
264            // Simplified adaptive extrapolation
265            // In a full implementation, this would analyze local data characteristics
266            // and select the best method based on the selection criterion
267
268            let candidate_methods = vec![
269                ExtrapolationMethod::Linear,
270                ExtrapolationMethod::Quadratic,
271                ExtrapolationMethod::Cubic,
272                ExtrapolationMethod::Exponential,
273            ];
274
275            let mut best_result = None;
276            let mut _best_score = T::infinity();
277
278            // Try each candidate method and select the best one
279            for &method in &candidate_methods {
280                let mut temp_extrapolator = self.base_extrapolator.clone();
281
282                // Update the extrapolation method based on direction
283                if x < temp_extrapolator.lower_bound() {
284                    temp_extrapolator.lower_method = method;
285                } else if x > temp_extrapolator.upper_bound() {
286                    temp_extrapolator.upper_method = method;
287                }
288
289                if let Ok(result) = temp_extrapolator.extrapolate(x) {
290                    if best_result.is_none() {
291                        best_result = Some(result);
292                        // In a full implementation, we'd compute a quality score here
293                    }
294                }
295            }
296
297            best_result.ok_or_else(|| {
298                InterpolateError::ComputationError(
299                    "No adaptive methods produced valid results".to_string(),
300                )
301            })
302        } else {
303            Err(InterpolateError::ComputationError(
304                "Adaptive extrapolation not configured".to_string(),
305            ))
306        }
307    }
308
309    /// Perform autoregressive extrapolation
310    pub fn extrapolate_autoregressive(&self, x: T) -> InterpolateResult<T> {
311        if let Some(config) = &self.autoregressive_config {
312            if let Some((x_data, y_data)) = &self.historical_data {
313                // Fit AR model and predict
314                let ar_coeffs = self.fit_ar_model(x_data, y_data, config.ar_order)?;
315                self.ar_predict(&ar_coeffs, x_data, y_data, x, config)
316            } else {
317                Err(InterpolateError::ComputationError(
318                    "Historical data required for autoregressive extrapolation".to_string(),
319                ))
320            }
321        } else {
322            Err(InterpolateError::ComputationError(
323                "Autoregressive extrapolation not configured".to_string(),
324            ))
325        }
326    }
327
328    /// Fit autoregressive model to historical data
329    fn fit_ar_model(
330        &self,
331        _x_data: &Array1<T>,
332        y_data: &Array1<T>,
333        order: usize,
334    ) -> InterpolateResult<Array1<T>> {
335        if y_data.len() < order + 1 {
336            return Err(InterpolateError::ComputationError(
337                "Insufficient data for AR model fitting".to_string(),
338            ));
339        }
340
341        // Simple AR fitting using Yule-Walker equations (simplified version)
342        let n = y_data.len();
343        let mut coeffs = Array1::zeros(order);
344
345        // For simplicity, use least squares approach
346        // In practice, you'd use more sophisticated methods like Burg's method
347
348        // Calculate autocorrelations
349        let mut autocorr = Array1::zeros(order + 1);
350        for lag in 0..=order {
351            let mut sum = T::zero();
352            let mut count = 0;
353
354            for i in lag..n {
355                sum += y_data[i] * y_data[i - lag];
356                count += 1;
357            }
358
359            if count > 0 {
360                autocorr[lag] = sum / T::from(count).unwrap_or(T::one());
361            }
362        }
363
364        // Solve Yule-Walker equations (simplified)
365        // For a proper implementation, you'd solve the full Toeplitz system
366        for i in 0..order {
367            if autocorr[0] != T::zero() {
368                coeffs[i] = autocorr[i + 1] / autocorr[0];
369            }
370        }
371
372        Ok(coeffs)
373    }
374
375    /// Make AR prediction
376    fn ar_predict(
377        &self,
378        coeffs: &Array1<T>,
379        x_data: &Array1<T>,
380        y_data: &Array1<T>,
381        x: T,
382        _config: &AutoregressiveExtrapolationConfig<T>,
383    ) -> InterpolateResult<T> {
384        let order = coeffs.len();
385
386        if y_data.len() < order {
387            return Err(InterpolateError::ComputationError(
388                "Insufficient data for AR prediction".to_string(),
389            ));
390        }
391
392        // Use the last 'order' values to predict
393        let mut prediction = T::zero();
394        let start_idx = y_data.len() - order;
395
396        for i in 0..order {
397            prediction += coeffs[i] * y_data[start_idx + i];
398        }
399
400        // Adjust prediction based on distance from domain
401        // This is a simplified approach - in practice you'd interpolate the time series
402        let last_x = x_data[x_data.len() - 1];
403        let extrapolation_distance = x - last_x;
404
405        // Apply simple trend adjustment (very basic)
406        if extrapolation_distance != T::zero() && y_data.len() >= 2 {
407            let trend = (y_data[y_data.len() - 1] - y_data[y_data.len() - 2])
408                / (x_data[x_data.len() - 1] - x_data[x_data.len() - 2]);
409            prediction += trend * extrapolation_distance;
410        }
411
412        Ok(prediction)
413    }
414
415    /// Get access to the base extrapolator
416    pub fn base(&self) -> &Extrapolator<T> {
417        &self.base_extrapolator
418    }
419
420    /// Get mutable access to the base extrapolator
421    pub fn base_mut(&mut self) -> &mut Extrapolator<T> {
422        &mut self.base_extrapolator
423    }
424
425    /// Check if confidence estimation is enabled
426    pub fn has_confidence(&self) -> bool {
427        self.confidence_config.is_some()
428    }
429
430    /// Check if ensemble methods are enabled
431    pub fn has_ensemble(&self) -> bool {
432        self.ensemble_config.is_some()
433    }
434
435    /// Check if adaptive selection is enabled
436    pub fn has_adaptive(&self) -> bool {
437        self.adaptive_config.is_some()
438    }
439
440    /// Check if autoregressive modeling is enabled
441    pub fn has_autoregressive(&self) -> bool {
442        self.autoregressive_config.is_some()
443    }
444
445    /// Check if historical data is available
446    pub fn has_historical_data(&self) -> bool {
447        self.historical_data.is_some()
448    }
449
450    /// Get the number of available AR coefficients
451    pub fn ar_model_order(&self) -> Option<usize> {
452        self.autoregressive_config.as_ref().map(|c| c.ar_order)
453    }
454
455    /// Perform multiple extrapolations efficiently
456    pub fn extrapolate_batch(&self, x_values: &[T]) -> Vec<InterpolateResult<T>> {
457        x_values
458            .iter()
459            .map(|&x| self.extrapolate_advanced(x))
460            .collect()
461    }
462
463    /// Get extrapolation method recommendations based on data characteristics
464    pub fn recommend_methods(&self, x: T) -> Vec<ExtrapolationMethod> {
465        let mut recommendations = Vec::new();
466
467        // Basic recommendations based on position relative to domain
468        let distance_from_lower = if x < self.base_extrapolator.lower_bound() {
469            self.base_extrapolator.lower_bound() - x
470        } else {
471            T::zero()
472        };
473
474        let distance_from_upper = if x > self.base_extrapolator.upper_bound() {
475            x - self.base_extrapolator.upper_bound()
476        } else {
477            T::zero()
478        };
479
480        let domain_width = self.base_extrapolator.domain_width();
481
482        // For small extrapolation distances, recommend higher-order methods
483        if distance_from_lower < domain_width * T::from(0.1).unwrap_or(T::one())
484            || distance_from_upper < domain_width * T::from(0.1).unwrap_or(T::one())
485        {
486            recommendations.push(ExtrapolationMethod::Cubic);
487            recommendations.push(ExtrapolationMethod::Quadratic);
488        }
489
490        // For moderate distances, recommend robust methods
491        recommendations.push(ExtrapolationMethod::Linear);
492
493        // For large distances, recommend asymptotic methods
494        if distance_from_lower > domain_width * T::from(0.5).unwrap_or(T::one())
495            || distance_from_upper > domain_width * T::from(0.5).unwrap_or(T::one())
496        {
497            recommendations.push(ExtrapolationMethod::Exponential);
498            recommendations.push(ExtrapolationMethod::PowerLaw);
499        }
500
501        recommendations
502    }
503}
scirs2_interpolate/extrapolation_modules/advanced.rs

scirs2_interpolate/extrapolation_modules/
advanced.rs
