scirs2_stats/

property_based_validation.rs

//! Property-based testing framework for mathematical invariants
//!
//! This module provides comprehensive property-based testing to validate
//! mathematical properties and invariants of statistical functions.
//!
//! ## Features
//!
//! - Automated generation of test cases with edge conditions
//! - Validation of mathematical properties and invariants
//! - Regression testing with statistical significance
//! - Cross-platform consistency validation
//! - Numerical stability analysis

use crate::error::{StatsError, StatsResult};
use scirs2_core::ndarray::Array1;
use serde::{Deserialize, Serialize};
use std::collections::HashMap;
use std::fmt::Debug;

/// Property-based testing framework for mathematical validation
#[derive(Debug)]
pub struct PropertyBasedValidator {
    config: PropertyTestConfig,
    test_results: HashMap<String, PropertyTestResult>,
}

/// Configuration for property-based testing
#[derive(Debug, Clone)]
pub struct PropertyTestConfig {
    /// Number of test cases to generate per property
    pub test_cases_per_property: usize,
    /// Random seed for reproducible tests
    pub seed: u64,
    /// Tolerance for floating-point comparisons
    pub tolerance: f64,
    /// Enable testing of edge cases (inf, nan, zero)
    pub test_edge_cases: bool,
    /// Enable cross-platform consistency tests
    pub test_cross_platform: bool,
    /// Enable numerical stability analysis
    pub test_numerical_stability: bool,
}

/// Result of a property test
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct PropertyTestResult {
    /// Property name being tested
    pub property_name: String,
    /// Function name being tested
    pub function_name: String,
    /// Number of test cases run
    pub test_cases_run: usize,
    /// Number of test cases that passed
    pub test_cases_passed: usize,
    /// Number of test cases that failed
    pub test_cases_failed: usize,
    /// List of failures with details
    pub failures: Vec<PropertyTestFailure>,
    /// Overall test status
    pub status: PropertyTestStatus,
    /// Statistical significance of results
    pub statistical_significance: Option<f64>,
}

/// Details of a property test failure
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct PropertyTestFailure {
    /// Test case that failed
    pub test_case: String,
    /// Expected result or property
    pub expected: String,
    /// Actual result observed
    pub actual: String,
    /// Error or discrepancy magnitude
    pub error_magnitude: f64,
    /// Input data that caused the failure
    pub inputdata: Vec<f64>,
}

/// Status of a property test
#[derive(Debug, Clone, Copy, Serialize, Deserialize, PartialEq, Eq)]
pub enum PropertyTestStatus {
    /// All test cases passed
    Pass,
    /// Some test cases failed but within acceptable bounds
    Warning,
    /// Significant number of test cases failed
    Fail,
    /// Test could not be completed due to errors
    Error,
}

/// Mathematical property to be tested
pub trait MathematicalProperty<T> {
    /// Name of the property
    fn name(&self) -> &str;

    /// Test the property for given input
    fn test(&self, input: &T) -> PropertyTestResult;

    /// Generate test cases for this property
    fn generate_test_cases(&self, config: &PropertyTestConfig) -> Vec<T>;
}

impl Default for PropertyTestConfig {
    fn default() -> Self {
        Self {
            test_cases_per_property: 1000,
            seed: 42,
            tolerance: 1e-12,
            test_edge_cases: true,
            test_cross_platform: true,
            test_numerical_stability: true,
        }
    }
}

impl PropertyBasedValidator {
    /// Create a new property-based validator
    pub fn new(config: PropertyTestConfig) -> Self {
        Self {
            config,
            test_results: HashMap::new(),
        }
    }

    /// Create validator with default configuration
    pub fn default() -> Self {
        Self::new(PropertyTestConfig::default())
    }

    /// Test a specific mathematical property
    pub fn test_property<T, P>(&mut self, property: P) -> StatsResult<PropertyTestResult>
    where
        P: MathematicalProperty<T>,
    {
        let test_cases = property.generate_test_cases(&self.config);
        let mut passed = 0;
        let mut failed = 0;
        let mut failures = Vec::new();

        for (i, test_case) in test_cases.iter().enumerate() {
            let result = property.test(test_case);

            if result.status == PropertyTestStatus::Pass {
                passed += 1;
            } else {
                failed += 1;
                // Store failure details (simplified)
                failures.push(PropertyTestFailure {
                    test_case: format!("test_case_{}", i),
                    expected: "property_holds".to_string(),
                    actual: "property_violated".to_string(),
                    error_magnitude: 0.0, // Would be calculated from actual test
                    inputdata: vec![],    // Would contain actual input data
                });
            }
        }

        let total_cases = test_cases.len();
        let status = if failed == 0 {
            PropertyTestStatus::Pass
        } else if (failed as f64 / total_cases as f64) < 0.05 {
            PropertyTestStatus::Warning
        } else {
            PropertyTestStatus::Fail
        };

        let result = PropertyTestResult {
            property_name: property.name().to_string(),
            function_name: "unknown".to_string(), // Would be set by caller
            test_cases_run: total_cases,
            test_cases_passed: passed,
            test_cases_failed: failed,
            failures,
            status,
            statistical_significance: self.calculate_statistical_significance(passed, failed),
        };

        self.test_results
            .insert(property.name().to_string(), result.clone());
        Ok(result)
    }

    /// Calculate statistical significance of test results
    fn calculate_statistical_significance(&self, passed: usize, failed: usize) -> Option<f64> {
        let total = passed + failed;
        if total == 0 {
            return None;
        }

        let success_rate = passed as f64 / total as f64;

        // Simple statistical significance calculation
        // In practice, this would use proper statistical tests
        if success_rate >= 0.99 {
            Some(0.001) // Very significant
        } else if success_rate >= 0.95 {
            Some(0.05) // Significant
        } else {
            Some(0.1) // Not significant
        }
    }

    /// Generate comprehensive validation report
    pub fn generate_validation_report(&self) -> ValidationReport {
        let results: Vec<_> = self.test_results.values().cloned().collect();

        let total_properties = results.len();
        let passed_properties = results
            .iter()
            .filter(|r| r.status == PropertyTestStatus::Pass)
            .count();
        let failed_properties = results
            .iter()
            .filter(|r| r.status == PropertyTestStatus::Fail)
            .count();
        let warning_properties = results
            .iter()
            .filter(|r| r.status == PropertyTestStatus::Warning)
            .count();

        ValidationReport {
            total_properties,
            passed_properties,
            failed_properties,
            warning_properties,
            overall_status: if failed_properties == 0 {
                if warning_properties == 0 {
                    PropertyTestStatus::Pass
                } else {
                    PropertyTestStatus::Warning
                }
            } else {
                PropertyTestStatus::Fail
            },
            property_results: results,
            generated_at: chrono::Utc::now(),
        }
    }
}

/// Comprehensive validation report
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct ValidationReport {
    /// Total number of properties tested
    pub total_properties: usize,
    /// Number of properties that passed all tests
    pub passed_properties: usize,
    /// Number of properties that failed tests
    pub failed_properties: usize,
    /// Number of properties with warnings
    pub warning_properties: usize,
    /// Overall validation status
    pub overall_status: PropertyTestStatus,
    /// Detailed results for each property
    pub property_results: Vec<PropertyTestResult>,
    /// Timestamp when report was generated
    pub generated_at: chrono::DateTime<chrono::Utc>,
}

// Specific mathematical properties for statistical functions

/// Property: Mean is invariant under translation
pub struct MeanTranslationInvariance;

impl MathematicalProperty<Array1<f64>> for MeanTranslationInvariance {
    fn name(&self) -> &str {
        "mean_translation_invariance"
    }

    fn test(&self, input: &Array1<f64>) -> PropertyTestResult {
        use crate::descriptive::mean;

        let original_mean = mean(&input.view());
        let translation = 100.0;
        let translated = input.mapv(|x| x + translation);
        let translated_mean = mean(&translated.view());

        let property_holds = match (original_mean, translated_mean) {
            (Ok(orig), Ok(trans)) => {
                let diff = (trans - orig - translation).abs();
                let scale = 1.0 + orig.abs() + translation.abs();
                diff < 1e-9 * scale
            }
            _ => false,
        };

        PropertyTestResult {
            property_name: self.name().to_string(),
            function_name: "mean".to_string(),
            test_cases_run: 1,
            test_cases_passed: if property_holds { 1 } else { 0 },
            test_cases_failed: if property_holds { 0 } else { 1 },
            failures: if property_holds {
                vec![]
            } else {
                vec![PropertyTestFailure {
                    test_case: "translation_test".to_string(),
                    expected: "mean(x + c) = mean(x) + c".to_string(),
                    actual: "property_violated".to_string(),
                    error_magnitude: 0.0,
                    inputdata: input.to_vec(),
                }]
            },
            status: if property_holds {
                PropertyTestStatus::Pass
            } else {
                PropertyTestStatus::Fail
            },
            statistical_significance: Some(if property_holds { 0.001 } else { 0.1 }),
        }
    }

    fn generate_test_cases(&self, config: &PropertyTestConfig) -> Vec<Array1<f64>> {
        use scirs2_core::random::prelude::*;
        use scirs2_core::random::{Distribution, Normal};

        let mut rng = StdRng::seed_from_u64(config.seed);
        let normal = Normal::new(0.0, 1.0).expect("Operation failed");
        let mut test_cases = Vec::new();

        for _ in 0..config.test_cases_per_property {
            let size = rng.random_range(10..1000);
            let mut data = Array1::zeros(size);

            for val in data.iter_mut() {
                *val = normal.sample(&mut rng);
            }

            test_cases.push(data);
        }

        // Add edge cases (avoid extreme magnitudes like f64::MAX/MIN or 1e100 since
        // adding the translation constant (100.0) to values near the f64 range limits
        // causes overflow or cancellation that would invalidate the property check)
        if config.test_edge_cases {
            test_cases.push(Array1::from_vec(vec![0.0]));
            test_cases.push(Array1::from_vec(vec![-1e6_f64, 1e6_f64]));
            test_cases.push(Array1::from_vec(vec![-1.0, 1.0]));
        }

        test_cases
    }
}

/// Property: Variance is invariant under translation
pub struct VarianceTranslationInvariance;

impl MathematicalProperty<Array1<f64>> for VarianceTranslationInvariance {
    fn name(&self) -> &str {
        "variance_translation_invariance"
    }

    fn test(&self, input: &Array1<f64>) -> PropertyTestResult {
        use crate::descriptive::var;

        let original_var = var(&input.view(), 1, None);
        let translation = 50.0;
        let translated = input.mapv(|x| x + translation);
        let translated_var = var(&translated.view(), 1, None);

        let property_holds = match (original_var, translated_var) {
            (Ok(orig), Ok(trans)) => {
                let diff = (trans - orig).abs();
                let scale = 1.0 + orig.abs();
                diff < 1e-9 * scale
            }
            // If both fail (e.g., insufficient data for ddof=1), the property is
            // vacuously satisfied — we cannot test it on this degenerate input.
            (Err(_), Err(_)) => true,
            // One succeeded and the other didn't — unexpected asymmetry; fail.
            _ => false,
        };

        PropertyTestResult {
            property_name: self.name().to_string(),
            function_name: "variance".to_string(),
            test_cases_run: 1,
            test_cases_passed: if property_holds { 1 } else { 0 },
            test_cases_failed: if property_holds { 0 } else { 1 },
            failures: if property_holds {
                vec![]
            } else {
                vec![PropertyTestFailure {
                    test_case: "translation_test".to_string(),
                    expected: "var(x + c) = var(x)".to_string(),
                    actual: "property_violated".to_string(),
                    error_magnitude: 0.0,
                    inputdata: input.to_vec(),
                }]
            },
            status: if property_holds {
                PropertyTestStatus::Pass
            } else {
                PropertyTestStatus::Fail
            },
            statistical_significance: Some(if property_holds { 0.001 } else { 0.1 }),
        }
    }

    fn generate_test_cases(&self, config: &PropertyTestConfig) -> Vec<Array1<f64>> {
        // Same implementation as MeanTranslationInvariance
        let mean_prop = MeanTranslationInvariance;
        mean_prop.generate_test_cases(config)
    }
}

/// Property: Correlation coefficient is between -1 and 1
pub struct CorrelationBounds;

impl MathematicalProperty<(Array1<f64>, Array1<f64>)> for CorrelationBounds {
    fn name(&self) -> &str {
        "correlation_bounds"
    }

    fn test(&self, input: &(Array1<f64>, Array1<f64>)) -> PropertyTestResult {
        use crate::correlation::pearson_r;

        let (x, y) = input;

        // Ensure arrays have the same length
        if x.len() != y.len() {
            return PropertyTestResult {
                property_name: self.name().to_string(),
                function_name: "pearson_r".to_string(),
                test_cases_run: 1,
                test_cases_passed: 0,
                test_cases_failed: 1,
                failures: vec![],
                status: PropertyTestStatus::Error,
                statistical_significance: None,
            };
        }

        let correlation = pearson_r(&x.view(), &y.view());

        let property_holds = match correlation {
            Ok(r) => r >= -1.0 && r <= 1.0 && r.is_finite(),
            Err(_) => false,
        };

        PropertyTestResult {
            property_name: self.name().to_string(),
            function_name: "pearson_r".to_string(),
            test_cases_run: 1,
            test_cases_passed: if property_holds { 1 } else { 0 },
            test_cases_failed: if property_holds { 0 } else { 1 },
            failures: if property_holds {
                vec![]
            } else {
                vec![PropertyTestFailure {
                    test_case: "bounds_test".to_string(),
                    expected: "-1 <= correlation <= 1".to_string(),
                    actual: format!("correlation = {:?}", correlation),
                    error_magnitude: 0.0,
                    inputdata: vec![],
                }]
            },
            status: if property_holds {
                PropertyTestStatus::Pass
            } else {
                PropertyTestStatus::Fail
            },
            statistical_significance: Some(if property_holds { 0.001 } else { 0.1 }),
        }
    }

    fn generate_test_cases(&self, config: &PropertyTestConfig) -> Vec<(Array1<f64>, Array1<f64>)> {
        use scirs2_core::random::prelude::*;
        use scirs2_core::random::{Distribution, Normal};

        let mut rng = StdRng::seed_from_u64(config.seed);
        let normal = Normal::new(0.0, 1.0).expect("Operation failed");
        let mut test_cases = Vec::new();

        for _ in 0..config.test_cases_per_property {
            let size = rng.random_range(10..1000);
            let mut x = Array1::zeros(size);
            let mut y = Array1::zeros(size);

            for i in 0..size {
                x[i] = normal.sample(&mut rng);
                y[i] = normal.sample(&mut rng);
            }

            test_cases.push((x, y));
        }

        // Add edge cases
        if config.test_edge_cases {
            // Perfect positive correlation
            let x1 = Array1::from_vec(vec![1.0, 2.0, 3.0, 4.0, 5.0]);
            let y1 = Array1::from_vec(vec![1.0, 2.0, 3.0, 4.0, 5.0]);
            test_cases.push((x1, y1));

            // Perfect negative correlation
            let x2 = Array1::from_vec(vec![1.0, 2.0, 3.0, 4.0, 5.0]);
            let y2 = Array1::from_vec(vec![5.0, 4.0, 3.0, 2.0, 1.0]);
            test_cases.push((x2, y2));

            // No correlation
            let x3 = Array1::from_vec(vec![1.0, 2.0, 3.0, 4.0, 5.0]);
            let y3 = Array1::from_vec(vec![2.0, 1.0, 4.0, 3.0, 5.0]);
            test_cases.push((x3, y3));
        }

        test_cases
    }
}

/// Comprehensive test suite for all mathematical properties
#[derive(Debug)]
pub struct ComprehensivePropertyTestSuite {
    validator: PropertyBasedValidator,
}

impl ComprehensivePropertyTestSuite {
    /// Create a new comprehensive test suite
    pub fn new(config: PropertyTestConfig) -> Self {
        Self {
            validator: PropertyBasedValidator::new(config),
        }
    }

    /// Run all property tests for statistical functions
    pub fn run_all_tests(&mut self) -> StatsResult<ValidationReport> {
        // Test mean properties
        self.validator.test_property(MeanTranslationInvariance)?;

        // Test variance properties
        self.validator
            .test_property(VarianceTranslationInvariance)?;

        // Test correlation properties
        self.validator.test_property(CorrelationBounds)?;

        Ok(self.validator.generate_validation_report())
    }

    /// Run tests for a specific function
    pub fn test_function(&mut self, functionname: &str) -> StatsResult<Vec<PropertyTestResult>> {
        let mut results = Vec::new();

        match functionname {
            "mean" => {
                results.push(self.validator.test_property(MeanTranslationInvariance)?);
            }
            "variance" => {
                results.push(
                    self.validator
                        .test_property(VarianceTranslationInvariance)?,
                );
            }
            "correlation" => {
                results.push(self.validator.test_property(CorrelationBounds)?);
            }
            "standard_deviation" => {
                results.push(self.validator.test_property(StandardDeviationScale)?);
                results.push(
                    self.validator
                        .test_property(StandardDeviationNonNegativity)?,
                );
            }
            "quantile" => {
                results.push(self.validator.test_property(QuantileMonotonicity)?);
                results.push(self.validator.test_property(QuantileBounds)?);
            }
            _ => {
                return Err(StatsError::InvalidInput(format!(
                    "Unknown function: {}",
                    functionname
                )));
            }
        }

        Ok(results)
    }

    /// Run enhanced test suite with additional properties
    pub fn run_enhanced_tests(&mut self) -> StatsResult<ValidationReport> {
        // Test mean properties
        self.validator.test_property(MeanTranslationInvariance)?;

        // Test variance properties
        self.validator
            .test_property(VarianceTranslationInvariance)?;

        // Test correlation properties
        self.validator.test_property(CorrelationBounds)?;

        // Test standard deviation properties
        self.validator.test_property(StandardDeviationScale)?;
        self.validator
            .test_property(StandardDeviationNonNegativity)?;

        // Test quantile properties
        self.validator.test_property(QuantileMonotonicity)?;
        self.validator.test_property(QuantileBounds)?;

        // Test linearity properties
        self.validator.test_property(MeanLinearity)?;

        // Test symmetry properties
        self.validator.test_property(CorrelationSymmetry)?;

        Ok(self.validator.generate_validation_report())
    }
}

/// Property: Standard deviation scales with data scaling
pub struct StandardDeviationScale;

impl MathematicalProperty<Array1<f64>> for StandardDeviationScale {
    fn name(&self) -> &str {
        "standard_deviation_scale"
    }

    fn test(&self, input: &Array1<f64>) -> PropertyTestResult {
        use crate::descriptive::std;

        let original_std = std(&input.view(), 1, None);
        let scale_factor = 2.0;
        let scaled = input.mapv(|x| x * scale_factor);
        let scaled_std = std(&scaled.view(), 1, None);

        let property_holds = match (original_std, scaled_std) {
            (Ok(orig), Ok(scaled)) => {
                let expected = orig * scale_factor;
                (scaled - expected).abs() < 1e-12
            }
            _ => false,
        };

        PropertyTestResult {
            property_name: self.name().to_string(),
            function_name: "standard_deviation".to_string(),
            test_cases_run: 1,
            test_cases_passed: if property_holds { 1 } else { 0 },
            test_cases_failed: if property_holds { 0 } else { 1 },
            failures: if property_holds {
                vec![]
            } else {
                vec![PropertyTestFailure {
                    test_case: "scale_test".to_string(),
                    expected: "std(a*x) = |a| * std(x)".to_string(),
                    actual: "property_violated".to_string(),
                    error_magnitude: 0.0,
                    inputdata: input.to_vec(),
                }]
            },
            status: if property_holds {
                PropertyTestStatus::Pass
            } else {
                PropertyTestStatus::Fail
            },
            statistical_significance: Some(if property_holds { 0.001 } else { 0.1 }),
        }
    }

    fn generate_test_cases(&self, config: &PropertyTestConfig) -> Vec<Array1<f64>> {
        let mean_prop = MeanTranslationInvariance;
        mean_prop.generate_test_cases(config)
    }
}

/// Property: Standard deviation is always non-negative
pub struct StandardDeviationNonNegativity;

impl MathematicalProperty<Array1<f64>> for StandardDeviationNonNegativity {
    fn name(&self) -> &str {
        "standard_deviation_non_negativity"
    }

    fn test(&self, input: &Array1<f64>) -> PropertyTestResult {
        use crate::descriptive::std;

        let result = std(&input.view(), 1, None);

        let property_holds = match result {
            Ok(std_val) => std_val >= 0.0 && std_val.is_finite(),
            Err(_) => false,
        };

        PropertyTestResult {
            property_name: self.name().to_string(),
            function_name: "standard_deviation".to_string(),
            test_cases_run: 1,
            test_cases_passed: if property_holds { 1 } else { 0 },
            test_cases_failed: if property_holds { 0 } else { 1 },
            failures: if property_holds {
                vec![]
            } else {
                vec![PropertyTestFailure {
                    test_case: "non_negativity_test".to_string(),
                    expected: "std(x) >= 0".to_string(),
                    actual: format!("std(x) = {:?}", result),
                    error_magnitude: 0.0,
                    inputdata: input.to_vec(),
                }]
            },
            status: if property_holds {
                PropertyTestStatus::Pass
            } else {
                PropertyTestStatus::Fail
            },
            statistical_significance: Some(if property_holds { 0.001 } else { 0.1 }),
        }
    }

    fn generate_test_cases(&self, config: &PropertyTestConfig) -> Vec<Array1<f64>> {
        let mean_prop = MeanTranslationInvariance;
        mean_prop.generate_test_cases(config)
    }
}

/// Property: Quantiles are monotonic
pub struct QuantileMonotonicity;

impl MathematicalProperty<Array1<f64>> for QuantileMonotonicity {
    fn name(&self) -> &str {
        "quantile_monotonicity"
    }

    fn test(&self, input: &Array1<f64>) -> PropertyTestResult {
        use crate::quantile::quantile;

        if input.len() < 2 {
            return PropertyTestResult {
                property_name: self.name().to_string(),
                function_name: "quantile".to_string(),
                test_cases_run: 1,
                test_cases_passed: 1,
                test_cases_failed: 0,
                failures: vec![],
                status: PropertyTestStatus::Pass,
                statistical_significance: Some(0.001),
            };
        }

        let q25 = quantile(
            &input.view(),
            0.25,
            crate::quantile::QuantileInterpolation::Linear,
        );
        let q50 = quantile(
            &input.view(),
            0.50,
            crate::quantile::QuantileInterpolation::Linear,
        );
        let q75 = quantile(
            &input.view(),
            0.75,
            crate::quantile::QuantileInterpolation::Linear,
        );

        let property_holds = match (q25.clone(), q50.clone(), q75.clone()) {
            (Ok(q25_val), Ok(q50_val), Ok(q75_val)) => q25_val <= q50_val && q50_val <= q75_val,
            _ => false,
        };

        PropertyTestResult {
            property_name: self.name().to_string(),
            function_name: "quantile".to_string(),
            test_cases_run: 1,
            test_cases_passed: if property_holds { 1 } else { 0 },
            test_cases_failed: if property_holds { 0 } else { 1 },
            failures: if property_holds {
                vec![]
            } else {
                vec![PropertyTestFailure {
                    test_case: "monotonicity_test".to_string(),
                    expected: "Q25 <= Q50 <= Q75".to_string(),
                    actual: format!("Q25={:?}, Q50={:?}, Q75={:?}", q25, q50, q75),
                    error_magnitude: 0.0,
                    inputdata: input.to_vec(),
                }]
            },
            status: if property_holds {
                PropertyTestStatus::Pass
            } else {
                PropertyTestStatus::Fail
            },
            statistical_significance: Some(if property_holds { 0.001 } else { 0.1 }),
        }
    }

    fn generate_test_cases(&self, config: &PropertyTestConfig) -> Vec<Array1<f64>> {
        let mean_prop = MeanTranslationInvariance;
        mean_prop.generate_test_cases(config)
    }
}

/// Property: Quantiles are bounded by min and max
pub struct QuantileBounds;

impl MathematicalProperty<Array1<f64>> for QuantileBounds {
    fn name(&self) -> &str {
        "quantile_bounds"
    }

    fn test(&self, input: &Array1<f64>) -> PropertyTestResult {
        use crate::quantile::quantile;

        if input.is_empty() {
            return PropertyTestResult {
                property_name: self.name().to_string(),
                function_name: "quantile".to_string(),
                test_cases_run: 1,
                test_cases_passed: 0,
                test_cases_failed: 1,
                failures: vec![],
                status: PropertyTestStatus::Error,
                statistical_significance: None,
            };
        }

        let min_val = input.iter().fold(f64::INFINITY, |a, &b| a.min(b));
        let max_val = input.iter().fold(f64::NEG_INFINITY, |a, &b| a.max(b));

        let q25 = quantile(
            &input.view(),
            0.25,
            crate::quantile::QuantileInterpolation::Linear,
        );
        let q75 = quantile(
            &input.view(),
            0.75,
            crate::quantile::QuantileInterpolation::Linear,
        );

        let property_holds = match (q25.clone(), q75.clone()) {
            (Ok(q25_val), Ok(q75_val)) => {
                q25_val >= min_val && q25_val <= max_val && q75_val >= min_val && q75_val <= max_val
            }
            _ => false,
        };

        PropertyTestResult {
            property_name: self.name().to_string(),
            function_name: "quantile".to_string(),
            test_cases_run: 1,
            test_cases_passed: if property_holds { 1 } else { 0 },
            test_cases_failed: if property_holds { 0 } else { 1 },
            failures: if property_holds {
                vec![]
            } else {
                vec![PropertyTestFailure {
                    test_case: "bounds_test".to_string(),
                    expected: "min <= quantile <= max".to_string(),
                    actual: format!(
                        "min={}, max={}, Q25={:?}, Q75={:?}",
                        min_val, max_val, q25, q75
                    ),
                    error_magnitude: 0.0,
                    inputdata: input.to_vec(),
                }]
            },
            status: if property_holds {
                PropertyTestStatus::Pass
            } else {
                PropertyTestStatus::Fail
            },
            statistical_significance: Some(if property_holds { 0.001 } else { 0.1 }),
        }
    }

    fn generate_test_cases(&self, config: &PropertyTestConfig) -> Vec<Array1<f64>> {
        let mean_prop = MeanTranslationInvariance;
        mean_prop.generate_test_cases(config)
    }
}

/// Property: Mean is linear - mean(a*x + b*y) = a*mean(x) + b*mean(y)
pub struct MeanLinearity;

impl MathematicalProperty<(Array1<f64>, Array1<f64>)> for MeanLinearity {
    fn name(&self) -> &str {
        "mean_linearity"
    }

    fn test(&self, input: &(Array1<f64>, Array1<f64>)) -> PropertyTestResult {
        use crate::descriptive::mean;

        let (x, y) = input;

        if x.len() != y.len() {
            return PropertyTestResult {
                property_name: self.name().to_string(),
                function_name: "mean".to_string(),
                test_cases_run: 1,
                test_cases_passed: 0,
                test_cases_failed: 1,
                failures: vec![],
                status: PropertyTestStatus::Error,
                statistical_significance: None,
            };
        }

        let a = 2.0;
        let b = 3.0;
        let combined = x.mapv(|x_val| a * x_val) + &y.mapv(|y_val| b * y_val);

        let mean_combined = mean(&combined.view());
        let mean_x = mean(&x.view());
        let mean_y = mean(&y.view());

        let property_holds = match (mean_combined, mean_x, mean_y) {
            (Ok(combined_val), Ok(x_val), Ok(y_val)) => {
                let expected = a * x_val + b * y_val;
                (combined_val - expected).abs() < 1e-12
            }
            _ => false,
        };

        PropertyTestResult {
            property_name: self.name().to_string(),
            function_name: "mean".to_string(),
            test_cases_run: 1,
            test_cases_passed: if property_holds { 1 } else { 0 },
            test_cases_failed: if property_holds { 0 } else { 1 },
            failures: if property_holds {
                vec![]
            } else {
                vec![PropertyTestFailure {
                    test_case: "linearity_test".to_string(),
                    expected: "mean(a*x + b*y) = a*mean(x) + b*mean(y)".to_string(),
                    actual: "linearity_violated".to_string(),
                    error_magnitude: 0.0,
                    inputdata: vec![],
                }]
            },
            status: if property_holds {
                PropertyTestStatus::Pass
            } else {
                PropertyTestStatus::Fail
            },
            statistical_significance: Some(if property_holds { 0.001 } else { 0.1 }),
        }
    }

    fn generate_test_cases(&self, config: &PropertyTestConfig) -> Vec<(Array1<f64>, Array1<f64>)> {
        let corr_prop = CorrelationBounds;
        corr_prop.generate_test_cases(config)
    }
}

/// Property: Correlation is symmetric - corr(x, y) = corr(y, x)
pub struct CorrelationSymmetry;

impl MathematicalProperty<(Array1<f64>, Array1<f64>)> for CorrelationSymmetry {
    fn name(&self) -> &str {
        "correlation_symmetry"
    }

    fn test(&self, input: &(Array1<f64>, Array1<f64>)) -> PropertyTestResult {
        use crate::correlation::pearson_r;

        let (x, y) = input;

        if x.len() != y.len() {
            return PropertyTestResult {
                property_name: self.name().to_string(),
                function_name: "correlation".to_string(),
                test_cases_run: 1,
                test_cases_passed: 0,
                test_cases_failed: 1,
                failures: vec![],
                status: PropertyTestStatus::Error,
                statistical_significance: None,
            };
        }

        let corr_xy = pearson_r(&x.view(), &y.view());
        let corr_yx = pearson_r(&y.view(), &x.view());

        let property_holds = match (corr_xy.clone(), corr_yx.clone()) {
            (Ok(xy), Ok(yx)) => (xy - yx).abs() < 1e-12,
            _ => false,
        };

        PropertyTestResult {
            property_name: self.name().to_string(),
            function_name: "correlation".to_string(),
            test_cases_run: 1,
            test_cases_passed: if property_holds { 1 } else { 0 },
            test_cases_failed: if property_holds { 0 } else { 1 },
            failures: if property_holds {
                vec![]
            } else {
                vec![PropertyTestFailure {
                    test_case: "symmetry_test".to_string(),
                    expected: "corr(x, y) = corr(y, x)".to_string(),
                    actual: format!("corr(x,y)={:?}, corr(y,x)={:?}", corr_xy, corr_yx),
                    error_magnitude: 0.0,
                    inputdata: vec![],
                }]
            },
            status: if property_holds {
                PropertyTestStatus::Pass
            } else {
                PropertyTestStatus::Fail
            },
            statistical_significance: Some(if property_holds { 0.001 } else { 0.1 }),
        }
    }

    fn generate_test_cases(&self, config: &PropertyTestConfig) -> Vec<(Array1<f64>, Array1<f64>)> {
        let corr_prop = CorrelationBounds;
        corr_prop.generate_test_cases(config)
    }
}

/// Convenience function to run comprehensive property-based validation
#[allow(dead_code)]
pub fn run_comprehensive_property_validation() -> StatsResult<ValidationReport> {
    let config = PropertyTestConfig {
        test_cases_per_property: 500, // Balanced for thoroughness and speed
        seed: 42,
        tolerance: 1e-12,
        test_edge_cases: true,
        test_cross_platform: true,
        test_numerical_stability: true,
    };

    let mut suite = ComprehensivePropertyTestSuite::new(config);
    suite.run_enhanced_tests()
}

/// Convenience function to run quick property-based validation
#[allow(dead_code)]
pub fn run_quick_property_validation() -> StatsResult<ValidationReport> {
    let config = PropertyTestConfig {
        test_cases_per_property: 100, // Faster for CI/CD
        seed: 42,
        tolerance: 1e-10,
        test_edge_cases: true,
        test_cross_platform: false,
        test_numerical_stability: false,
    };

    let mut suite = ComprehensivePropertyTestSuite::new(config);
    suite.run_enhanced_tests()
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn test_property_validator_creation() {
        let validator = PropertyBasedValidator::default();
        assert_eq!(validator.config.test_cases_per_property, 1000);
        assert_eq!(validator.config.tolerance, 1e-12);
    }

    #[test]
    fn test_mean_translation_invariance() {
        let property = MeanTranslationInvariance;
        let testdata = Array1::from_vec(vec![1.0, 2.0, 3.0, 4.0, 5.0]);
        let result = property.test(&testdata);

        assert_eq!(result.property_name, "mean_translation_invariance");
        assert_eq!(result.status, PropertyTestStatus::Pass);
    }

    #[test]
    fn test_variance_translation_invariance() {
        let property = VarianceTranslationInvariance;
        let testdata = Array1::from_vec(vec![1.0, 2.0, 3.0, 4.0, 5.0]);
        let result = property.test(&testdata);

        assert_eq!(result.property_name, "variance_translation_invariance");
        assert_eq!(result.status, PropertyTestStatus::Pass);
    }

    #[test]
    fn test_correlation_bounds() {
        let property = CorrelationBounds;
        let x = Array1::from_vec(vec![1.0, 2.0, 3.0, 4.0, 5.0]);
        let y = Array1::from_vec(vec![1.0, 2.0, 3.0, 4.0, 5.0]);
        let result = property.test(&(x, y));

        assert_eq!(result.property_name, "correlation_bounds");
        assert_eq!(result.status, PropertyTestStatus::Pass);
    }

    #[test]
    fn test_comprehensive_test_suite() {
        let config = PropertyTestConfig {
            test_cases_per_property: 10, // Smaller for testing
            ..Default::default()
        };
        let mut suite = ComprehensivePropertyTestSuite::new(config);
        let report = suite.run_all_tests().expect("Operation failed");

        assert!(report.total_properties > 0);
        assert_eq!(report.overall_status, PropertyTestStatus::Pass);
    }
}