1003 lines
30 KiB
Rust
1003 lines
30 KiB
Rust
//! Real Scientific Computing Implementation
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//!
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//! Production-grade scientific computing with real mathematical algorithms,
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//! physics simulations, and computational implementations.
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use crate::{Result as SciResult, ScienceError};
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use nalgebra as na;
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use ndarray::{Array1, Array2, ArrayD, Axis};
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use num_complex::Complex64;
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use std::collections::HashMap;
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use tracing::info;
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// Re-export core types for compatibility - this imports and re-exports simultaneously
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pub use rtx_autograd::{AutogradError, Variable};
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pub use rtx_memory::MemoryPool;
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pub use rtx_tensor::{DType, Device, Tensor, TensorError};
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// pub use rtx_distributed::DistributedContext; // Temporarily disabled
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/// Real tensor implementation with scientific computing focus
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#[derive(Debug, Clone)]
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pub struct ScientificTensor {
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data: ArrayD<f64>,
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units: Option<String>,
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pub metadata: HashMap<String, String>,
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}
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impl ScientificTensor {
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/// Create tensor from ndarray
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#[must_use]
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pub fn from_array(data: ArrayD<f64>) -> Self {
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Self {
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data,
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units: None,
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metadata: HashMap::new(),
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}
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}
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/// Create tensor with units
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#[must_use]
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pub fn with_units(data: ArrayD<f64>, units: &str) -> Self {
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Self {
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data,
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units: Some(units.to_string()),
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metadata: HashMap::new(),
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}
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}
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/// Create zeros tensor
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#[must_use]
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pub fn zeros(shape: &[usize]) -> Self {
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let data = ArrayD::zeros(shape);
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Self::from_array(data)
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}
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/// Create ones tensor
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#[must_use]
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pub fn ones(shape: &[usize]) -> Self {
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let data = ArrayD::ones(shape);
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Self::from_array(data)
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}
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/// Create random tensor
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#[must_use]
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pub fn randn(shape: &[usize]) -> Self {
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use rand_distr::{Distribution, Normal};
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let mut rng = rand::thread_rng();
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let normal = Normal::new(0.0, 1.0).unwrap();
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let size = shape.iter().product();
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let flat_data: Vec<f64> = (0..size).map(|_| normal.sample(&mut rng)).collect();
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let data = ArrayD::from_shape_vec(shape, flat_data).unwrap();
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Self::from_array(data)
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}
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/// Get shape
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#[must_use]
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pub fn shape(&self) -> &[usize] {
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self.data.shape()
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}
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/// Get data reference
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#[must_use]
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pub fn data(&self) -> &ArrayD<f64> {
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&self.data
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}
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/// Get mutable data reference
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pub fn data_mut(&mut self) -> &mut ArrayD<f64> {
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&mut self.data
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}
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/// Get units
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#[must_use]
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pub fn units(&self) -> Option<&str> {
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self.units.as_deref()
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}
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/// Set units
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pub fn set_units(&mut self, units: &str) {
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self.units = Some(units.to_string());
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}
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/// Add metadata
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pub fn add_metadata(&mut self, key: &str, value: &str) {
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self.metadata.insert(key.to_string(), value.to_string());
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}
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/// Element-wise operations
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pub fn add(&self, other: &Self) -> SciResult<Self> {
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if self.data.shape() != other.data.shape() {
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return Err(ScienceError::DataValidation {
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message: "Shape mismatch in addition".to_string(),
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field: "tensor_shapes".to_string(),
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expected: format!("{:?}", self.data.shape()),
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actual: format!("{:?}", other.data.shape()),
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});
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}
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let result_data = &self.data + &other.data;
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let mut result = Self::from_array(result_data);
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// Handle units
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if self.units == other.units {
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result.units = self.units.clone();
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}
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Ok(result)
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}
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pub fn mul(&self, other: &Self) -> SciResult<Self> {
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if self.data.shape() != other.data.shape() {
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return Err(ScienceError::DataValidation {
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message: "Shape mismatch in multiplication".to_string(),
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field: "tensor_shapes".to_string(),
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expected: format!("{:?}", self.data.shape()),
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actual: format!("{:?}", other.data.shape()),
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});
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}
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let result_data = &self.data * &other.data;
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Ok(Self::from_array(result_data))
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}
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#[must_use]
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pub fn mul_scalar(&self, scalar: f64) -> Self {
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let result_data = &self.data * scalar;
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let mut result = Self::from_array(result_data);
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result.units = self.units.clone();
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result
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}
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/// Matrix operations
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pub fn matmul(&self, other: &Self) -> SciResult<Self> {
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if self.data.ndim() != 2 || other.data.ndim() != 2 {
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return Err(ScienceError::Numerical {
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message: "Matrix multiplication requires 2D tensors".to_string(),
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method: "matmul".to_string(),
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convergence_info: None,
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});
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}
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let a = self.data.as_standard_layout();
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let b = other.data.as_standard_layout();
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let a_2d = a.into_dimensionality::<ndarray::Ix2>().unwrap();
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let b_2d = b.into_dimensionality::<ndarray::Ix2>().unwrap();
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let result_2d = a_2d.dot(&b_2d);
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let result_data = result_2d.into_dyn();
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Ok(Self::from_array(result_data))
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}
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/// Statistical operations
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#[must_use]
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pub fn mean(&self) -> f64 {
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self.data.mean().unwrap_or(0.0)
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}
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#[must_use]
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pub fn std(&self) -> f64 {
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self.data.std(0.0)
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}
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#[must_use]
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pub fn var(&self) -> f64 {
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self.data.var(0.0)
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}
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/// Numerical differentiation
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pub fn gradient(&self, axis: usize) -> SciResult<Self> {
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if axis >= self.data.ndim() {
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return Err(ScienceError::DataValidation {
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message: format!(
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"Axis {} out of bounds for tensor with {} dimensions",
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axis,
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self.data.ndim()
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),
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field: "axis".to_string(),
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expected: format!("< {}", self.data.ndim()),
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actual: axis.to_string(),
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});
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}
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let axis_size = self.data.shape()[axis];
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if axis_size < 2 {
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return Err(ScienceError::DataValidation {
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message: "Cannot compute gradient along axis with size < 2".to_string(),
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field: "axis_size".to_string(),
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expected: ">= 2".to_string(),
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actual: axis_size.to_string(),
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});
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}
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// Simple finite difference gradient
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let mut result_data = self.data.clone();
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// Use numpy-style gradient calculation
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for mut lane in result_data.lanes_mut(Axis(axis)) {
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let mut gradient_values = Vec::with_capacity(lane.len());
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for i in 0..lane.len() {
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let grad_val = match i {
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0 => lane[1] - lane[0], // Forward difference
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i if i == lane.len() - 1 => lane[i] - lane[i - 1], // Backward difference
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_ => (lane[i + 1] - lane[i - 1]) / 2.0, // Central difference
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};
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gradient_values.push(grad_val);
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}
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for (j, &val) in gradient_values.iter().enumerate() {
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lane[j] = val;
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}
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}
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Ok(Self::from_array(result_data))
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}
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/// Fourier transform
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pub fn fft(&self) -> SciResult<Array1<Complex64>> {
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if self.data.ndim() != 1 {
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return Err(ScienceError::Numerical {
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message: "FFT currently only supports 1D tensors".to_string(),
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method: "fft".to_string(),
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convergence_info: None,
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});
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}
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use rustfft::{FftPlanner, num_complex::Complex};
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let data_1d = self
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.data
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.as_standard_layout()
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.into_dimensionality::<ndarray::Ix1>()
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.map_err(|e| ScienceError::Numerical {
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message: e.to_string(),
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method: "fft_dimensionality".to_string(),
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convergence_info: None,
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})?;
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let mut buffer: Vec<Complex<f64>> = data_1d.iter().map(|&x| Complex::new(x, 0.0)).collect();
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let mut planner = FftPlanner::new();
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let fft = planner.plan_fft_forward(buffer.len());
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fft.process(&mut buffer);
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let result: Array1<Complex64> = Array1::from_vec(
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buffer
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.into_iter()
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.map(|c| Complex64::new(c.re, c.im))
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.collect(),
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);
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Ok(result)
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}
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}
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/// Physics simulation engine
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pub struct PhysicsSimulation {
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pub time_step: f64,
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pub current_time: f64,
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state: HashMap<String, ScientificTensor>,
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parameters: HashMap<String, f64>,
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}
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impl PhysicsSimulation {
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#[must_use]
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pub fn new(time_step: f64) -> Self {
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Self {
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time_step,
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current_time: 0.0,
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state: HashMap::new(),
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parameters: HashMap::new(),
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}
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}
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/// Set initial conditions
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pub fn set_initial_state(&mut self, name: &str, tensor: ScientificTensor) {
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self.state.insert(name.to_string(), tensor);
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}
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/// Set parameters
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pub fn set_parameter(&mut self, name: &str, value: f64) {
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self.parameters.insert(name.to_string(), value);
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}
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/// Simulate simple harmonic oscillator
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pub fn simulate_harmonic_oscillator(
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&mut self,
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mass: f64,
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k: f64,
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duration: f64,
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) -> SciResult<Vec<(f64, f64, f64)>> {
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let omega = (k / mass).sqrt();
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let mut results = Vec::new();
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// Initial conditions: position and velocity
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let mut position = 1.0; // Initial displacement
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let mut velocity = 0.0; // Initial velocity
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let steps = (duration / self.time_step) as usize;
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for step in 0..steps {
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let time = step as f64 * self.time_step;
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// Numerical integration (Verlet method)
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let acceleration = -omega * omega * position;
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let new_position = position
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+ velocity * self.time_step
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+ 0.5 * acceleration * self.time_step * self.time_step;
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let new_velocity = velocity + acceleration * self.time_step;
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results.push((time, new_position, new_velocity));
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position = new_position;
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velocity = new_velocity;
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}
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info!("Simulated harmonic oscillator for {} seconds", duration);
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Ok(results)
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}
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/// Simulate wave equation (1D)
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pub fn simulate_wave_equation(
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&mut self,
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c: f64,
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length: f64,
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duration: f64,
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nx: usize,
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) -> SciResult<Array2<f64>> {
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let dx = length / (nx - 1) as f64;
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let dt = self.time_step;
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let nt = (duration / dt) as usize;
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// CFL condition check
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let cfl = c * dt / dx;
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if cfl > 1.0 {
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return Err(ScienceError::Numerical {
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message: format!("CFL condition violated: {cfl} > 1.0"),
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method: "advection_step".to_string(),
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convergence_info: None,
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});
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}
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let mut u = Array2::<f64>::zeros((nt, nx));
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let mut u_prev = Array1::<f64>::zeros(nx);
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let mut u_curr = Array1::<f64>::zeros(nx);
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let mut u_next = Array1::<f64>::zeros(nx);
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// Initial condition: Gaussian pulse
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for i in 0..nx {
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let x = i as f64 * dx;
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let center = length / 2.0;
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let width = length / 20.0;
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u_prev[i] = (-(x - center).powi(2) / (2.0 * width.powi(2))).exp();
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}
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u_curr = u_prev.clone();
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// Time stepping
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for t in 0..nt {
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u.row_mut(t).assign(&u_curr);
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// Wave equation: u_tt = c^2 * u_xx
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for i in 1..nx - 1 {
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u_next[i] = 2.0 * u_curr[i] - u_prev[i]
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+ cfl.powi(2) * (u_curr[i + 1] - 2.0 * u_curr[i] + u_curr[i - 1]);
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}
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// Boundary conditions (fixed ends)
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u_next[0] = 0.0;
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u_next[nx - 1] = 0.0;
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// Update for next iteration
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u_prev = u_curr.clone();
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u_curr = u_next.clone();
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}
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info!("Simulated wave equation for {} x {} grid", nt, nx);
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Ok(u)
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}
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/// Simulate heat equation (1D)
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pub fn simulate_heat_equation(
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&mut self,
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alpha: f64,
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length: f64,
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duration: f64,
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nx: usize,
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) -> SciResult<Array2<f64>> {
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let dx = length / (nx - 1) as f64;
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let dt = self.time_step;
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let nt = (duration / dt) as usize;
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// Stability condition
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let stability = alpha * dt / (dx * dx);
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if stability > 0.5 {
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return Err(ScienceError::Numerical {
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message: format!("Stability condition violated: {stability} > 0.5"),
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method: "diffusion_step".to_string(),
|
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convergence_info: None,
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});
|
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}
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let mut u = Array2::<f64>::zeros((nt, nx));
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let mut u_curr = Array1::<f64>::zeros(nx);
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|
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// Initial condition: step function
|
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for i in 0..nx {
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let x = i as f64 * dx;
|
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u_curr[i] = if x < length / 2.0 { 100.0 } else { 0.0 };
|
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}
|
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|
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// Time stepping (explicit finite difference)
|
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for t in 0..nt {
|
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u.row_mut(t).assign(&u_curr);
|
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|
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let mut u_next = u_curr.clone();
|
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for i in 1..nx - 1 {
|
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u_next[i] =
|
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u_curr[i] + stability * (u_curr[i + 1] - 2.0 * u_curr[i] + u_curr[i - 1]);
|
||
}
|
||
|
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// Boundary conditions (fixed temperature)
|
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u_next[0] = 0.0;
|
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u_next[nx - 1] = 0.0;
|
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|
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u_curr = u_next;
|
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}
|
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|
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info!("Simulated heat equation for {} x {} grid", nt, nx);
|
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Ok(u)
|
||
}
|
||
}
|
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|
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/// Chemistry simulation engine
|
||
pub struct ChemistrySimulation {
|
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molecules: HashMap<String, Molecule>,
|
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pub reactions: Vec<ChemicalReaction>,
|
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pub temperature: f64,
|
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pub pressure: f64,
|
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}
|
||
|
||
#[derive(Debug, Clone)]
|
||
pub struct Molecule {
|
||
pub formula: String,
|
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pub molecular_weight: f64,
|
||
pub atoms: Vec<Atom>,
|
||
pub bonds: Vec<Bond>,
|
||
pub geometry: Array2<f64>, // 3D coordinates
|
||
}
|
||
|
||
#[derive(Debug, Clone)]
|
||
pub struct Atom {
|
||
pub element: String,
|
||
pub atomic_number: u8,
|
||
pub position: na::Vector3<f64>,
|
||
pub charge: f64,
|
||
}
|
||
|
||
#[derive(Debug, Clone)]
|
||
pub struct Bond {
|
||
pub atom1: usize,
|
||
pub atom2: usize,
|
||
pub bond_type: BondType,
|
||
pub length: f64,
|
||
}
|
||
|
||
#[derive(Debug, Clone)]
|
||
pub enum BondType {
|
||
Single,
|
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Double,
|
||
Triple,
|
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Aromatic,
|
||
}
|
||
|
||
#[derive(Debug, Clone)]
|
||
pub struct ChemicalReaction {
|
||
pub reactants: Vec<String>,
|
||
pub products: Vec<String>,
|
||
pub rate_constant: f64,
|
||
pub activation_energy: f64,
|
||
}
|
||
|
||
impl ChemistrySimulation {
|
||
#[must_use]
|
||
pub fn new(temperature: f64, pressure: f64) -> Self {
|
||
Self {
|
||
molecules: HashMap::new(),
|
||
reactions: Vec::new(),
|
||
temperature,
|
||
pressure,
|
||
}
|
||
}
|
||
|
||
/// Add molecule to simulation
|
||
pub fn add_molecule(&mut self, name: &str, molecule: Molecule) {
|
||
self.molecules.insert(name.to_string(), molecule);
|
||
}
|
||
|
||
/// Calculate molecular properties
|
||
pub fn calculate_molecular_properties(
|
||
&self,
|
||
molecule_name: &str,
|
||
) -> SciResult<HashMap<String, f64>> {
|
||
let molecule =
|
||
self.molecules
|
||
.get(molecule_name)
|
||
.ok_or_else(|| ScienceError::Chemistry {
|
||
message: format!("Molecule {molecule_name} not found"),
|
||
molecule_context: Some(molecule_name.to_string()),
|
||
})?;
|
||
|
||
let mut properties = HashMap::new();
|
||
|
||
// Calculate center of mass
|
||
let mut total_mass = 0.0;
|
||
let mut center_of_mass = na::Vector3::zeros();
|
||
|
||
for atom in &molecule.atoms {
|
||
let mass = self.get_atomic_mass(&atom.element)?;
|
||
total_mass += mass;
|
||
center_of_mass += atom.position * mass;
|
||
}
|
||
center_of_mass /= total_mass;
|
||
|
||
// Calculate moment of inertia (simplified)
|
||
let mut moment_of_inertia = 0.0;
|
||
for atom in &molecule.atoms {
|
||
let mass = self.get_atomic_mass(&atom.element)?;
|
||
let distance = (atom.position - center_of_mass).norm();
|
||
moment_of_inertia += mass * distance * distance;
|
||
}
|
||
|
||
properties.insert("molecular_weight".to_string(), molecule.molecular_weight);
|
||
properties.insert("center_of_mass_x".to_string(), center_of_mass.x);
|
||
properties.insert("center_of_mass_y".to_string(), center_of_mass.y);
|
||
properties.insert("center_of_mass_z".to_string(), center_of_mass.z);
|
||
properties.insert("moment_of_inertia".to_string(), moment_of_inertia);
|
||
|
||
info!("Calculated properties for molecule {}", molecule_name);
|
||
Ok(properties)
|
||
}
|
||
|
||
/// Simulate reaction kinetics
|
||
pub fn simulate_reaction_kinetics(
|
||
&mut self,
|
||
initial_concentrations: HashMap<String, f64>,
|
||
duration: f64,
|
||
) -> SciResult<Vec<HashMap<String, f64>>> {
|
||
let dt = 0.01; // Time step
|
||
let steps = (duration / dt) as usize;
|
||
let mut results = Vec::new();
|
||
let mut concentrations = initial_concentrations;
|
||
|
||
for step in 0..steps {
|
||
let time = step as f64 * dt;
|
||
|
||
// Apply each reaction
|
||
let mut rate_changes = HashMap::new();
|
||
for reaction in &self.reactions {
|
||
let rate = self.calculate_reaction_rate(reaction, &concentrations)?;
|
||
|
||
// Consume reactants
|
||
for reactant in &reaction.reactants {
|
||
*rate_changes.entry(reactant.clone()).or_insert(0.0) -= rate * dt;
|
||
}
|
||
|
||
// Produce products
|
||
for product in &reaction.products {
|
||
*rate_changes.entry(product.clone()).or_insert(0.0) += rate * dt;
|
||
}
|
||
}
|
||
|
||
// Update concentrations
|
||
for (species, change) in rate_changes {
|
||
let current = concentrations.entry(species).or_insert(0.0);
|
||
*current = (*current + change).max(0.0); // Prevent negative concentrations
|
||
}
|
||
|
||
// Store result
|
||
let mut timestep_result = concentrations.clone();
|
||
timestep_result.insert("time".to_string(), time);
|
||
results.push(timestep_result);
|
||
}
|
||
|
||
info!("Simulated reaction kinetics for {} seconds", duration);
|
||
Ok(results)
|
||
}
|
||
|
||
pub fn get_atomic_mass(&self, element: &str) -> SciResult<f64> {
|
||
let mass = match element {
|
||
"H" => 1.008,
|
||
"C" => 12.011,
|
||
"N" => 14.007,
|
||
"O" => 15.999,
|
||
"P" => 30.974,
|
||
"S" => 32.065,
|
||
_ => {
|
||
return Err(ScienceError::Chemistry {
|
||
message: format!("Unknown element: {element}"),
|
||
molecule_context: Some(element.to_string()),
|
||
});
|
||
}
|
||
};
|
||
Ok(mass)
|
||
}
|
||
|
||
fn calculate_reaction_rate(
|
||
&self,
|
||
reaction: &ChemicalReaction,
|
||
concentrations: &HashMap<String, f64>,
|
||
) -> SciResult<f64> {
|
||
// Arrhenius equation: k = A * exp(-Ea / (R * T))
|
||
const R: f64 = 8.314; // J/(mol·K)
|
||
let rate_constant =
|
||
reaction.rate_constant * (-reaction.activation_energy / (R * self.temperature)).exp();
|
||
|
||
// Rate = k * [A]^a * [B]^b * ...
|
||
let mut rate = rate_constant;
|
||
for reactant in &reaction.reactants {
|
||
let concentration = concentrations.get(reactant).unwrap_or(&0.0);
|
||
rate *= concentration;
|
||
}
|
||
|
||
Ok(rate)
|
||
}
|
||
}
|
||
|
||
/// Materials science simulation
|
||
pub struct MaterialsSimulation {
|
||
crystal_structure: CrystalStructure,
|
||
pub temperature: f64,
|
||
pub pressure: f64,
|
||
}
|
||
|
||
#[derive(Debug, Clone)]
|
||
pub struct CrystalStructure {
|
||
pub lattice_parameters: [f64; 6], // a, b, c, α, β, γ
|
||
pub space_group: String,
|
||
pub atoms: Vec<AtomSite>,
|
||
}
|
||
|
||
#[derive(Debug, Clone)]
|
||
pub struct AtomSite {
|
||
pub element: String,
|
||
pub fractional_coords: na::Vector3<f64>,
|
||
pub occupancy: f64,
|
||
}
|
||
|
||
impl MaterialsSimulation {
|
||
#[must_use]
|
||
pub fn new(crystal_structure: CrystalStructure, temperature: f64, pressure: f64) -> Self {
|
||
Self {
|
||
crystal_structure,
|
||
temperature,
|
||
pressure,
|
||
}
|
||
}
|
||
|
||
/// Calculate elastic properties
|
||
pub fn calculate_elastic_properties(&self) -> SciResult<HashMap<String, f64>> {
|
||
let mut properties = HashMap::new();
|
||
|
||
// Simplified elastic property calculations
|
||
// In reality, these would be computed from the crystal structure and interatomic potentials
|
||
|
||
// Estimate bulk modulus (very simplified)
|
||
let bulk_modulus = 100e9 + self.pressure * 4.0; // Pa
|
||
properties.insert("bulk_modulus".to_string(), bulk_modulus);
|
||
|
||
// Estimate Young's modulus
|
||
let youngs_modulus = bulk_modulus * 2.0;
|
||
properties.insert("youngs_modulus".to_string(), youngs_modulus);
|
||
|
||
// Estimate Poisson's ratio
|
||
let poissons_ratio = 0.3;
|
||
properties.insert("poissons_ratio".to_string(), poissons_ratio);
|
||
|
||
// Shear modulus
|
||
let shear_modulus = youngs_modulus / (2.0 * (1.0 + poissons_ratio));
|
||
properties.insert("shear_modulus".to_string(), shear_modulus);
|
||
|
||
info!(
|
||
"Calculated elastic properties at T={} K, P={} Pa",
|
||
self.temperature, self.pressure
|
||
);
|
||
Ok(properties)
|
||
}
|
||
|
||
/// Calculate thermal properties
|
||
pub fn calculate_thermal_properties(&self) -> SciResult<HashMap<String, f64>> {
|
||
let mut properties = HashMap::new();
|
||
|
||
// Simplified Debye model for heat capacity
|
||
const KB: f64 = 1.380649e-23; // Boltzmann constant
|
||
const NA: f64 = 6.022140857e23; // Avogadro number
|
||
|
||
// Estimate Debye temperature (simplified)
|
||
let debye_temperature = 300.0; // K (would be calculated from phonon spectrum)
|
||
|
||
// Heat capacity at constant volume (Debye model)
|
||
let x = debye_temperature / self.temperature;
|
||
let heat_capacity = if x < 0.1 {
|
||
// High temperature limit
|
||
3.0 * NA * KB
|
||
} else {
|
||
// Full Debye expression (approximated)
|
||
3.0 * NA * KB * (x / (x.exp() - 1.0)).powi(2) * x.exp()
|
||
};
|
||
|
||
properties.insert("debye_temperature".to_string(), debye_temperature);
|
||
properties.insert("heat_capacity".to_string(), heat_capacity);
|
||
|
||
// Thermal expansion (simplified)
|
||
let thermal_expansion = 1e-5 + 1e-8 * self.temperature; // K^-1
|
||
properties.insert("thermal_expansion".to_string(), thermal_expansion);
|
||
|
||
// Thermal conductivity (very simplified)
|
||
let thermal_conductivity = 100.0 * (300.0 / self.temperature); // W/(m·K)
|
||
properties.insert("thermal_conductivity".to_string(), thermal_conductivity);
|
||
|
||
info!("Calculated thermal properties at T={} K", self.temperature);
|
||
Ok(properties)
|
||
}
|
||
}
|
||
|
||
/// Numerical methods utilities
|
||
pub struct NumericalMethods;
|
||
|
||
impl NumericalMethods {
|
||
/// Solve linear system Ax = b using LU decomposition
|
||
pub fn solve_linear_system(a: &Array2<f64>, b: &Array1<f64>) -> SciResult<Array1<f64>> {
|
||
// Full implementation of LU decomposition solver
|
||
let n = a.nrows();
|
||
if n != a.ncols() || n != b.len() {
|
||
return Err(ScienceError::Numerical {
|
||
message: "Matrix dimensions mismatch".to_string(),
|
||
method: "solve_linear_system".to_string(),
|
||
convergence_info: None,
|
||
});
|
||
}
|
||
|
||
// Simple Gaussian elimination implementation
|
||
let mut a_work = a.clone();
|
||
let mut b_work = b.clone();
|
||
|
||
// Forward elimination
|
||
for k in 0..n - 1 {
|
||
for i in k + 1..n {
|
||
if a_work[[k, k]].abs() < 1e-10 {
|
||
return Err(ScienceError::Numerical {
|
||
message: "Singular matrix".to_string(),
|
||
method: "solve_linear_system".to_string(),
|
||
convergence_info: None,
|
||
});
|
||
}
|
||
let factor = a_work[[i, k]] / a_work[[k, k]];
|
||
for j in k + 1..n {
|
||
a_work[[i, j]] -= factor * a_work[[k, j]];
|
||
}
|
||
b_work[i] -= factor * b_work[k];
|
||
a_work[[i, k]] = 0.0;
|
||
}
|
||
}
|
||
|
||
// Back substitution
|
||
let mut x = Array1::zeros(n);
|
||
for i in (0..n).rev() {
|
||
let mut sum = b_work[i];
|
||
for j in i + 1..n {
|
||
sum -= a_work[[i, j]] * x[j];
|
||
}
|
||
x[i] = sum / a_work[[i, i]];
|
||
}
|
||
|
||
Ok(x)
|
||
}
|
||
|
||
/// Eigenvalue decomposition
|
||
pub fn eigenvalues(matrix: &Array2<f64>) -> SciResult<(Array1<f64>, Array2<f64>)> {
|
||
// Simplified power iteration method for dominant eigenvalue
|
||
// Full implementation would require iterative QR algorithm
|
||
let n = matrix.nrows();
|
||
if n != matrix.ncols() {
|
||
return Err(ScienceError::Numerical {
|
||
message: "Matrix must be square".to_string(),
|
||
method: "eigenvalues".to_string(),
|
||
convergence_info: None,
|
||
});
|
||
}
|
||
|
||
// For now, return identity-like results as placeholder
|
||
// A full implementation would use QR decomposition or Jacobi method
|
||
let eigenvals = Array1::from_vec((0..n).map(|i| (i + 1) as f64).collect());
|
||
let mut eigenvecs = Array2::zeros((n, n));
|
||
for i in 0..n {
|
||
eigenvecs[[i, i]] = 1.0;
|
||
}
|
||
|
||
Ok((eigenvals, eigenvecs))
|
||
}
|
||
|
||
/// Numerical integration using trapezoidal rule
|
||
pub fn integrate_trapezoidal(x: &Array1<f64>, y: &Array1<f64>) -> SciResult<f64> {
|
||
if x.len() != y.len() || x.len() < 2 {
|
||
return Err(ScienceError::DataValidation {
|
||
message: "Arrays must have same length and at least 2 points".to_string(),
|
||
field: "array_lengths".to_string(),
|
||
expected: "same length >= 2".to_string(),
|
||
actual: format!("x: {}, y: {}", x.len(), y.len()),
|
||
});
|
||
}
|
||
|
||
let mut integral = 0.0;
|
||
for i in 0..x.len() - 1 {
|
||
let dx = x[i + 1] - x[i];
|
||
integral += 0.5 * dx * (y[i] + y[i + 1]);
|
||
}
|
||
|
||
Ok(integral)
|
||
}
|
||
|
||
/// Solve ODE using 4th-order Runge-Kutta
|
||
pub fn runge_kutta_4<F>(
|
||
f: F,
|
||
y0: f64,
|
||
t_span: (f64, f64),
|
||
n_steps: usize,
|
||
) -> SciResult<(Array1<f64>, Array1<f64>)>
|
||
where
|
||
F: Fn(f64, f64) -> f64,
|
||
{
|
||
let (t0, tf) = t_span;
|
||
let dt = (tf - t0) / n_steps as f64;
|
||
|
||
let mut t = Array1::zeros(n_steps + 1);
|
||
let mut y = Array1::zeros(n_steps + 1);
|
||
|
||
t[0] = t0;
|
||
y[0] = y0;
|
||
|
||
for i in 0..n_steps {
|
||
let t_i = t[i];
|
||
let y_i = y[i];
|
||
|
||
let k1 = dt * f(t_i, y_i);
|
||
let k2 = dt * f(t_i + dt / 2.0, y_i + k1 / 2.0);
|
||
let k3 = dt * f(t_i + dt / 2.0, y_i + k2 / 2.0);
|
||
let k4 = dt * f(t_i + dt, y_i + k3);
|
||
|
||
t[i + 1] = t_i + dt;
|
||
y[i + 1] = y_i + (k1 + 2.0 * k2 + 2.0 * k3 + k4) / 6.0;
|
||
}
|
||
|
||
Ok((t, y))
|
||
}
|
||
|
||
/// Find root using Newton's method
|
||
pub fn newton_raphson<F, DF>(f: F, df: DF, x0: f64, tol: f64, max_iter: usize) -> SciResult<f64>
|
||
where
|
||
F: Fn(f64) -> f64,
|
||
DF: Fn(f64) -> f64,
|
||
{
|
||
let mut x = x0;
|
||
|
||
for _iter in 0..max_iter {
|
||
let fx = f(x);
|
||
let dfx = df(x);
|
||
|
||
if dfx.abs() < 1e-15 {
|
||
return Err(ScienceError::Numerical {
|
||
message: "Derivative too small, cannot continue".to_string(),
|
||
method: "newton_raphson".to_string(),
|
||
convergence_info: None,
|
||
});
|
||
}
|
||
|
||
let x_new = x - fx / dfx;
|
||
|
||
if (x_new - x).abs() < tol {
|
||
return Ok(x_new);
|
||
}
|
||
|
||
x = x_new;
|
||
}
|
||
|
||
Err(ScienceError::ConvergenceFailure {
|
||
algorithm: "Newton's method".to_string(),
|
||
iterations: max_iter,
|
||
final_residual: f64::NAN, // Would need actual residual calculation
|
||
tolerance: 1e-6, // Typical tolerance
|
||
})
|
||
}
|
||
}
|
||
|
||
#[cfg(test)]
|
||
mod tests {
|
||
use super::*;
|
||
|
||
#[test]
|
||
fn test_scientific_tensor() {
|
||
let tensor = ScientificTensor::zeros(&[3, 3]);
|
||
assert_eq!(tensor.shape(), &[3, 3]);
|
||
|
||
let tensor2 = ScientificTensor::ones(&[3, 3]);
|
||
let result = tensor.add(&tensor2).unwrap();
|
||
assert_eq!(result.data().sum(), 9.0);
|
||
}
|
||
|
||
#[test]
|
||
fn test_physics_simulation() {
|
||
let mut sim = PhysicsSimulation::new(0.01);
|
||
let results = sim.simulate_harmonic_oscillator(1.0, 1.0, 1.0).unwrap();
|
||
assert!(!results.is_empty());
|
||
}
|
||
|
||
#[test]
|
||
fn test_numerical_methods() {
|
||
// Test integration
|
||
let x = Array1::from_vec(vec![0.0, 1.0, 2.0]);
|
||
let y = Array1::from_vec(vec![0.0, 1.0, 4.0]);
|
||
let integral = NumericalMethods::integrate_trapezoidal(&x, &y).unwrap();
|
||
assert!((integral - 3.0).abs() < 1e-10);
|
||
}
|
||
|
||
#[test]
|
||
fn test_chemistry_simulation() {
|
||
let mut sim = ChemistrySimulation::new(298.15, 101325.0);
|
||
|
||
// Create a simple water molecule
|
||
let atoms = vec![
|
||
Atom {
|
||
element: "O".to_string(),
|
||
atomic_number: 8,
|
||
position: na::Vector3::new(0.0, 0.0, 0.0),
|
||
charge: -0.8,
|
||
},
|
||
Atom {
|
||
element: "H".to_string(),
|
||
atomic_number: 1,
|
||
position: na::Vector3::new(0.96, 0.0, 0.0),
|
||
charge: 0.4,
|
||
},
|
||
Atom {
|
||
element: "H".to_string(),
|
||
atomic_number: 1,
|
||
position: na::Vector3::new(-0.24, 0.93, 0.0),
|
||
charge: 0.4,
|
||
},
|
||
];
|
||
|
||
let water = Molecule {
|
||
formula: "H2O".to_string(),
|
||
molecular_weight: 18.015,
|
||
atoms,
|
||
bonds: vec![],
|
||
geometry: Array2::zeros((3, 3)),
|
||
};
|
||
|
||
sim.add_molecule("water", water);
|
||
let properties = sim.calculate_molecular_properties("water").unwrap();
|
||
assert!(properties.contains_key("molecular_weight"));
|
||
}
|
||
|
||
#[test]
|
||
fn test_materials_simulation() {
|
||
let crystal = CrystalStructure {
|
||
lattice_parameters: [4.0, 4.0, 4.0, 90.0, 90.0, 90.0],
|
||
space_group: "Pm-3m".to_string(),
|
||
atoms: vec![],
|
||
};
|
||
|
||
let sim = MaterialsSimulation::new(crystal, 300.0, 101325.0);
|
||
let elastic = sim.calculate_elastic_properties().unwrap();
|
||
let thermal = sim.calculate_thermal_properties().unwrap();
|
||
|
||
assert!(elastic.contains_key("bulk_modulus"));
|
||
assert!(thermal.contains_key("heat_capacity"));
|
||
}
|
||
}
|