RustedSciThe 0.4.1

#![allow(non_camel_case_types)]
#![allow(non_snake_case)]
//! solvers of BVPs and IVPs, optization, nonlinear algeraic systems and more
/// #########################ODEs SECTION######################
///
/// SOLVER OF STIFF IVPs (initial value problems)
/// direct rewrite to Rust python code from SciPy
///
/// Example#1
/// ```
///use RustedSciThe::symbolic::symbolic_engine::Expr;
/// use RustedSciThe::symbolic::symbolic_functions::Jacobian;
/// use RustedSciThe::numerical::ODE_api::ODEsolver;
///             // set RHS of system as vector of strings
///            let RHS = vec!["-z-exp(-y)", "y"];
///            // parse RHS as symbolic expressions
///            let Equations = Expr::parse_vector_expression(RHS.clone());
///            let values = vec!["z".to_string(), "y".to_string()];
///            println!("Equations = {:?}", Equations);
///            // set argument
///            let arg = "x".to_string();
///            // set method
///            let method = "BDF".to_string();
///            // set initial conditions
///            let t0 = 0.0;
///            let y0 = vec![1.0, 1.0];
///            let t_bound = 1.0;
///            // set solver parameters (optional)
///            let first_step = None;
///            let atol = 1e-5;
///            let rtol = 1e-5;
///            let max_step = 1e-3;
///            let jac_sparsity = None;
///            let vectorized = false;
///            // create instance of ODE solver and solve the system
///            let mut ODE_instance = ODEsolver::new_complex(
///                Equations,
///                values,
///                arg,
///                method,
///                t0,
///                y0.into(),
///                t_bound,
///                max_step,
///                rtol,
///                atol,
///                jac_sparsity,
///                vectorized,
///                first_step,
///            );
///
///            ODE_instance.solve();
///            ODE_instance.plot_result();
/// ```
pub mod BDF;

/// Backward Euler method (good for stiff ODEs)
///
/// Example#1
/// ```
///         use RustedSciThe::symbolic::symbolic_engine::Expr;
///         use RustedSciThe::numerical::BE::BE;
///         use nalgebra::DVector;
///          //  Backward Euler method: slightly non-linear ODE
///          let RHS = vec!["-z-exp(-y)", "y"];
///          // parse RHS as symbolic expressions
///          let Equations = Expr::parse_vector_expression(RHS.clone());
///          let values = vec![  "z".to_string(), "y".to_string()];
///          println!("eq_system = {:?}",  Equations);
///          let y0 = DVector::from_vec(vec![1.0, 1.0]);
///          let arg = "x".to_string();
///          let tolerance = 1e-2;
///          let max_iterations = 500;
///          let h = Some(1e-3);
///          let t0 = 0.0;
///          let t_bound = 1.0;
///          let mut solver = BE::new();
///          solver.set_initial( Equations, values, arg, tolerance, max_iterations, h, t0, t_bound, y0);
///          println!("y = {:?}, initial_guess = {:?}", solver.newton.y,solver.newton.initial_guess);
///          solver.newton.eq_generate();
///          solver.solve();
///          let result = solver.get_result();
///        //  println!("\n result 0 = {:?}", result.0);
///         // println!("\n result 1 = {:?}", result.1);
///         // println!("result = {:?}", result.1.unwrap().shape());
///          solver.plot_result();
/// ```
pub mod BE;
/// Newton Raphson solver for Backward Euler method
pub mod NR_for_Euler;
pub mod NR_for_ODE;

/// Boundary value problems solvers for stiff nonlinear ODEs
///
/// solver NR_Damp_solver_frozen implements NR method with damping
/// but without adaptive grid.
/// Frozen jacobian strategy - recalculating jacobian on condition:
/// Description of strategy                                                                 key of strategy        value user must provude for strategy
/// 1. only first time:                                                                      "Frozen_naive"                   None
/// 2. every m-th time, where m is a parameter of the strategy:                                "every_m"                    m
/// 3. every time when the solution norm greater than a certain threshold A:                   "at_high_norm".               A
/// 4. when norm of (i-1) iter multiplied by certain value B(<1) is lower than norm of i-th iter : "at_low_speed".            B
/// 5. complex - combined strategies 2,3,4                                                         "complex"              vec of  parameters [m, A, B]
///
///
/// Example#1
/// ```
///      use nalgebra::DMatrix;
///      use nalgebra::DVector;
///      use std::collections::HashMap;
///     use  RustedSciThe::symbolic::symbolic_engine::Expr;
///      use RustedSciThe::numerical::BVP_Damp::NR_Damp_solver_frozen::NRBVP;
///    let eq1 = Expr::parse_expression("y-z");
///        let eq2 = Expr::parse_expression("-z^2");
///        let eq_system = vec![eq1, eq2];

///
///        let values = vec!["z".to_string(), "y".to_string()];
///        let arg = "x".to_string();
///        let tolerance = 1e-5;
///        let max_iterations = 1500;
///       
///        let t0 = 0.0;
///        let t_end = 1.0;
///        let n_steps = 100; // Dense: 200 -300ms, 400 - 2s, 800 - 22s, 1600 - 2 min,
///        let strategy =   "Frozen".to_string();//
///        let  strategy_params = Some(HashMap::from([("complex".to_string(),
///       Some(Vec::from( [2f64, 5.0, 1e-1, ]  ))
///      )]));
/// //
///  // or
/// // Some(HashMap::from([("Frozen_naive".to_string(), None)]));
/// //  or
/// //  Some(HashMap::from([("every_m".to_string(),
/// //        Some(Vec::from( [ 5 as f64]  ))
/// //        )]));
/// //  or
/// //  Some(HashMap::from([("at_high_morm".to_string(),
/// // Some(Vec::from( [ 5 as f64]  ))
/// //)]));
/// //or
/// //Some(HashMap::from([("at_low_speed".to_string(),
/// // Some(Vec::from( [ 1e-2]  ))
/// //)]));
/// //or
/// // Some(HashMap::from([("complex".to_string(),
/// // Some(Vec::from( [ 2.0, 5.0, 1e-, ]  ))
/// //)]));
/// //  */
///        let method =   "Sparse".to_string();// or  "Dense"
///        let linear_sys_method = None;
///        let ones = vec![0.0; values.len()*n_steps];
///        let initial_guess: DMatrix<f64> = DMatrix::from_column_slice(values.len(), n_steps, DVector::from_vec(ones).as_slice());
///        let mut BorderConditions = HashMap::new();
///        BorderConditions.insert("z".to_string(), vec![(0usize, 1.0f64)]);
///        BorderConditions.insert("y".to_string(), vec![(1usize, 1.0f64)]);
///        assert_eq!(&eq_system.len(), &2);
///        let mut nr =  NRBVP::new(eq_system,
///             initial_guess,
///             values,
///             arg,
///             BorderConditions, t0, t_end, n_steps,strategy, strategy_params, linear_sys_method, method, tolerance, max_iterations);

///        println!("solving system");
///        #[allow(unused_variables)]
///        let solution = nr.solve().unwrap();
///       // println!("result = {:?}", solution);
///        nr.plot_result();
///    ```
///
/// NR_Damp_solver_damped solver implements
/// Modified Newton method or Damped Newton method with adaptive grid for solving Boundary value problems for systems of nonlinear ordinary differential equations.
///
/// The code mostly inspired by sources listed below:
/// Cantera MultiNewton solver (MultiNewton.cpp )
/// TWOPNT fortran solver (see "The Twopnt Program for Boundary Value Problems" by J. F. Grcar and Chemkin Theory Manual p.261)
///

/// Example#2
/// ```
/// use nalgebra::DMatrix;
///  use nalgebra::DVector;
///      use std::collections::HashMap;
///     use  RustedSciThe::symbolic::symbolic_engine::Expr;
/// use RustedSciThe::numerical::BVP_Damp::NR_Damp_solver_damped::SolverParams;
///     use  RustedSciThe::numerical::BVP_Damp::NR_Damp_solver_damped::NRBVP as NRBDVPd;
///     let eq1 = Expr::parse_expression("y-z");
///        let eq2 = Expr::parse_expression("-z^3");
///        let eq_system = vec![eq1, eq2];
///        let values = vec!["z".to_string(), "y".to_string()];
///        let arg = "x".to_string();
///        let tolerance = 1e-5;
///        let max_iterations = 20;
///        let t0 = 0.0;
///        let t_end = 1.0;
///        let n_steps = 50; // Dense: 200 -300ms, 400 - 2s, 800 - 22s, 1600 - 2 min,
///        let strategy =   "Damped".to_string();//
///        let  strategy_params = SolverParams::default();
/// let scheme = "forward".to_string();
///        let method =   "Sparse".to_string();// or  "Dense"
///        let linear_sys_method = None;
///        let ones = vec![0.0; values.len()*n_steps];
///        let initial_guess: DMatrix<f64> = DMatrix::from_column_slice(values.len(), n_steps, DVector::from_vec(ones).as_slice());
///        let mut BorderConditions = HashMap::new();
///        BorderConditions.insert("z".to_string(), vec![(0usize, 1.0f64)]);
///        BorderConditions.insert("y".to_string(), vec![(1usize, 1.0f64)]);
///        let Bounds = HashMap::from([  ("z".to_string(), (-10.0, 10.0),    ), ("y".to_string(), (-7.0, 7.0),    ) ]);
///        let rel_tolerance =  HashMap::from([  ("z".to_string(), 1e-4    ), ("y".to_string(), 1e-4,    ) ]);
///        assert_eq!(&eq_system.len(), &2);
///        let mut nr =  NRBDVPd::new(eq_system,
///             initial_guess,
///             values,
///             arg,
///             BorderConditions, t0, t_end, n_steps,scheme, strategy, Some(strategy_params), linear_sys_method, method, tolerance, Some(rel_tolerance), max_iterations,  Some(Bounds),None);

///        println!("solving system");
///        #[allow(unused_variables)]
///        let solution = nr.solve().unwrap();
///       // println!("result = {:?}", solution);
///        nr.plot_result();
///    ```
/// API for both solvers
/// Example#3
/// ```
///  use nalgebra::DMatrix;
///  use nalgebra::DVector;
///      use std::collections::HashMap;
/// use RustedSciThe::numerical::BVP_api::BVP;
///     use  RustedSciThe::symbolic::symbolic_engine::Expr;
///     let eq1 = Expr::parse_expression("y-z");
///  let eq2 = Expr::parse_expression("-z^3");
/// let eq_system = vec![eq1, eq2];
///
///
/// let values = vec!["z".to_string(), "y".to_string()];
/// let arg = "x".to_string();
/// let tolerance = 1e-5;
/// let max_iterations = 20;
///
/// let t0 = 0.0;
/// let t_end = 1.0;
/// let n_steps = 50; // Dense: 200 -300ms, 400 - 2s, 800 - 22s, 1600 - 2 min,
///  let strategy =   "Damped".to_string();//
///
/// let  strategy_params =
/// match strategy.as_str() {
///     "Naive" => None,
///     "Damped"=> Some(HashMap::from([("max_jac".to_string(),
///     None,    ), ("maxDampIter".to_string(),
///    None,    ), ("DampFacor".to_string(),
///     None,    )   , ("adaptive".to_string(),
///           None,    )
///
///    ])),
///    "Frozen" => Some(HashMap::from([("every_m".to_string(),
///   Some(Vec::from( [ 5 as f64]  ))
///    )])),
///     &_=>panic!("Invalid strategy!")
///
///
/// };
/// let scheme = "forward".to_string();
/// let method =   "Sparse".to_string();// or  "Dense"
/// let linear_sys_method = None;
/// let ones = vec![0.0; values.len()*n_steps];
/// let initial_guess: DMatrix<f64> = DMatrix::from_column_slice(values.len(), n_steps, DVector::from_vec(ones).as_slice());
/// let mut BorderConditions = HashMap::new();
/// BorderConditions.insert("z".to_string(), vec![(0usize, 1.0f64)]);
/// BorderConditions.insert("y".to_string(), vec![(1usize, 1.0f64)]);
/// let Bounds = HashMap::from([  ("z".to_string(), (-10.0, 10.0),    ), ("y".to_string(), (-7.0, 7.0),    ) ]);
/// let rel_tolerance =  HashMap::from([  ("z".to_string(), 1e-4    ), ("y".to_string(), 1e-4,    ) ]);
/// assert_eq!(&eq_system.len(), &2);
/// let mut nr =  BVP::new(eq_system,
///      initial_guess,
///      values,
///      arg,
///      BorderConditions, t0, t_end, n_steps, scheme, strategy, strategy_params, linear_sys_method, method, tolerance,
///        max_iterations,  Some(rel_tolerance),Some(Bounds), None);
///
/// println!("solving system");
/// nr.solve();
/// nr.plot_result();
/// nr.save_to_file(None);
///    ```
pub mod BVP_Damp;
//
pub mod BVP_api;
/// BVP solver with collocation method
/// rewritten in Rust from Python code from SciPy
pub mod BVP_sci;
///  a collection of test examples of exect solutions of BVPs for testing purposes
pub mod Examples_and_utils;

pub mod LSODE2;
/// RK45 and Dormand-Prince methods
pub mod NonStiff_api;
/// solvers of nonlinear algebraic equations
pub mod Nonlinear_systems;
///  general api for ODE solvers  (BDF, RK4, etc.)
///
/// Example#1
/// ```
///use RustedSciThe::symbolic::symbolic_engine::Expr;
/// use RustedSciThe::symbolic::symbolic_functions::Jacobian;
/// use RustedSciThe::numerical::ODE_api::ODEsolver;
///
///       //create instance of structure for symbolic equation system and Jacobian
/// let mut Jacobian_instance = Jacobian::new();
// define argument andunknown variables
/// let x = Expr::Var("x".to_string()); // argument
/// let y = Expr::Var("y".to_string());
/// let z:Expr = Expr::Var("z".to_string());
//define equation system
///  let eq1:Expr = Expr::Const(-1.0 as f64)*z.clone() - (Expr::Const(-1.0 as f64)*y.clone() ).exp();
/// let eq2:Expr = y;
/// let eq_system = vec![eq1, eq2];
// set unkown variables
/// let values = vec![  "z".to_string(), "y".to_string()];
// set argument
/// let arg = "x".to_string();
// set method
/// let method = "BDF".to_string();
// set initial conditions
/// let t0 = 0.0;
/// let y0 = vec![1.0, 1.0];
/// let t_bound = 1.0;
/// // set solver parameters (optional)
/// let first_step = None;
/// let atol = 1e-5;
/// let rtol = 1e-5;
/// let max_step = 1e-3;
/// let jac_sparsity = None;
/// let vectorized = false;
// create instance of ODE solver and solve the system
///let mut ODE_instance = ODEsolver::new_complex(
///    eq_system,
///    values,
///    arg,
///    method,
///    t0,
///    y0.into(),
///    t_bound,
///    max_step,
///    rtol,
///    atol,
///    jac_sparsity,
///    vectorized,
///   first_step);
/// ODE_instance.solve();
/// // plot the solution
/// ODE_instance.plot_result();
/// ODE_instance.save_result();
/// ```
/// Non-stiff equations: use ODE general api ODEsolver
/// RK45 and Dormand-Prince methods are available
/// Example#2
/// ```
/// use RustedSciThe::symbolic::symbolic_engine::Expr;
///  use RustedSciThe::numerical::ODE_api::ODEsolver;
///          //Example 2 the laziest way to solve ODE
///    // set RHS of system as vector of strings
///    let RHS = vec!["-z-exp(-y)", "y"];
///    // parse RHS as symbolic expressions
///    let Equations = Expr::parse_vector_expression(RHS.clone());
///    let values = vec![  "z".to_string(), "y".to_string()];
///    println!("Equations = {:?}", Equations);   
///    // set argument
///    let arg = "x".to_string();
///      // set method
///      let method = "BDF".to_string();
///      // set initial conditions
///      let t0 = 0.0;
///      let y0 = vec![1.0, 1.0];
///      let t_bound = 1.0;
///      // set solver parameters (optional)
///      let first_step = None;
///      let atol = 1e-5;
///      let rtol = 1e-5;
///      let max_step = 1e-3;
///      let jac_sparsity = None;
///      let vectorized = false;
///      // create instance of ODE solver and solve the system
///      let mut ODE_instance = ODEsolver::new_complex(
///        Equations,
///        values,
///        arg,
///        method,
///        t0,
///        y0.into(),
///        t_bound,
///        max_step,
///        rtol,
///        atol,   
///        jac_sparsity,
///        vectorized,
///        first_step
///    );
///    ODE_instance.solve();
///    ODE_instance.plot_result();
///    ODE_instance.save_result();
///  ```
/// Example#3
/// ```
/// use RustedSciThe::symbolic::symbolic_engine::Expr;
///  use RustedSciThe::numerical::ODE_api::ODEsolver;
///   let RHS = vec!["-z-y", "y"];
// parse RHS as symbolic expressions
///   let Equations = Expr::parse_vector_expression(RHS.clone());
///   let values = vec![  "z".to_string(), "y".to_string()];
///   println!("Equations = {:?}", Equations);   
///   // set argument
///   let arg = "x".to_string();
///     // set method
///     let method = "DOPRI".to_string();
///     // set initial conditions
///     let t0 = 0.0;
///     let y0 = vec![1.0, 1.0];
///    let t_bound = 1.0;
///    // set solver parameters (optional)
///
///     let max_step = 1e-3;
///
///     // create instance of ODE solver and solve the system
///     let mut ODE_instance = ODEsolver::new_easy(
///       Equations,
///       values,
///       arg,
///       method,
///       t0,
///       y0.into(),
///       t_bound,
///       max_step,
///  );
///   ODE_instance.solve();
///   ODE_instance.plot_result();
///  ```
pub mod ODE_api;
/// better universal api for all IVP solvers on board
/// use universal syntax with "new" function and choise of solvers with enum "SolverType"
/// ```
///  use RustedSciThe::numerical::ODE_api2::{UniversalODESolver, SolverType};
///  use RustedSciThe::numerical::Radau::Radau_main::RadauOrder;
/// use RustedSciThe::symbolic::symbolic_engine::Expr;
///
/// use nalgebra::DVector;
///         let eq1 = Expr::parse_expression("-y");
///        let eq_system = vec![eq1];
///        let values = vec!["y".to_string()];
///        let arg = "t".to_string();
///        let t0 = 0.0;
///        let y0 = DVector::from_vec(vec![1.0]);
///        let t_bound = 0.5;
///
///        let mut solver = UniversalODESolver::new(
///            eq_system,
///            values,
///            arg,
///            SolverType::Radau(RadauOrder::Order3),
///            t0,
///            y0,
///            t_bound,
///        );
///        solver.set_max_iterations(100);
///        solver.set_tolerance(1e-6);
///        solver.set_step_size(1e-3);
///        solver.initialize();
///        solver.solve();
///        let (t_result, y_result) = solver.get_result();
///  ```
///  or use shortcuts for every solver
/// ```
///  use RustedSciThe::numerical::ODE_api2::UniversalODESolver;
///  use RustedSciThe::numerical::Radau::Radau_main::RadauOrder;
/// use RustedSciThe::symbolic::symbolic_engine::Expr;
/// use nalgebra::DVector;
///        let eq1 = Expr::parse_expression("-y");
///        let eq_system = vec![eq1];
///        let values = vec!["y".to_string()];
///        let arg = "t".to_string();
///        let t0 = 0.0;
///        let y0 = DVector::from_vec(vec![1.0]);
///        let t_bound = 0.5;
///
///        let mut solver = UniversalODESolver::radau(
///            eq_system,
///            values,
///            arg,
///            RadauOrder::Order3,
///            t0,
///            y0,
///            t_bound,
///            1e-6,
///            50,
///            Some(1e-3),
///        );
///
///        solver.solve();
///        let (t_result, y_result) = solver.get_result();
///  ```        
pub mod ODE_api2;
/// Radau solver (good for nonlinear ODEs)
/// #############################END OF ODEs SECTIONS#####
///
/// Example#1
/// ```
///   use RustedSciThe::symbolic::symbolic_engine::Expr;
///
///    use RustedSciThe::numerical::Radau::Radau_main::{Radau, RadauOrder};
///    use approx::assert_relative_eq;
///    use nalgebra::DMatrix;
///    use nalgebra::DVector;
///    use simplelog::*;
///   // Test system: y1' = -2*y1 + y2, y2' = y1 - 2*y2
///        // Initial conditions: y1(0) = 1, y2(0) = 0
///        // solution: y1(t) =  1/2 e^(-3 x) (e^(2 x) + 1)
///        // y2(t) = 1/2 e^(-3 x) (-1 + e^(2 x))
///        let eq1 = Expr::parse_expression("-2*y1+y2");
///        let eq2 = Expr::parse_expression("y1-2*y2");
///        let eq_system = vec![eq1, eq2];
///
///        let values = vec!["y1".to_string(), "y2".to_string()];
///        let arg = "t".to_string();
///        let tolerance = 1e-6;
///        let max_iterations = 50;
///        let h = Some(1e-3);
///        let t0 = 0.0;
///        let t_bound = 1.0;
///        let y0 = DVector::from_vec(vec![1.0, 0.0]);
///
///        let mut radau = Radau::new(RadauOrder::Order3);
///        radau.set_initial(
///            eq_system,
///            values,
///            arg,
///            tolerance,
///            max_iterations,
///            h,
///            t0,
///            t_bound,
///            y0,
///        );
///
///        radau.solve();
///
///        assert_eq!(radau.status, "finished");
///        let (_, y_result) = radau.get_result();
///        let y_res = y_result.unwrap();
///
///    ```
pub mod Radau;
pub mod Rosenbrock;
/// shooting method for solving BVP
pub mod ShootingBVP;
pub mod data_processing;
/// collection of optimization algorithms
pub mod optimization;