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// Copyright (c) by Gleb E. Zaslavkiy
//MIT License
#![allow(non_snake_case)]
use crate::symbolic::symbolic_engine::Expr;
use crate::numerical::BE::BE;
use crate::numerical::NR_for_ODE::NRODE;
use crate::numerical::ODE_api::ODEsolver;
use nalgebra::DVector;
#[allow(dead_code)]
pub fn ivp_examples(example: usize) {
match example {
0 => {
/*
//use the shortest way to solve system of equations
// first define system of equations and initial guess
let mut NR_instanse = NR::new();
let vec_of_expressions = vec!["x^2+y^2-10".to_string(), "x-y-4".to_string()];
let initial_guess = vec![1.0, 1.0];
// solve
NR_instanse.eq_generate_from_str(
vec_of_expressions,
None,
initial_guess,
1e-6,
100,
None,
);
NR_instanse.main_loop();
println!("result = {:?} \n", NR_instanse.get_result().unwrap());
// or more verbose way...
// first define system of equations
let vec_of_expressions = vec!["x^2+y^2-10", "x-y-4"];
let initial_guess = vec![1.0, 1.0];
let mut NR_instanse = NR::new();
let vec_of_expr = Expr::parse_vector_expression(vec_of_expressions.clone());
let values = vec!["x".to_string(), "y".to_string()];
NR_instanse.set_equation_system(
vec_of_expr,
Some(values.clone()),
initial_guess,
1e-6,
100,
);
NR_instanse.eq_generate();
NR_instanse.solver();
println!("result = {:?} \n", NR_instanse.get_result().unwrap());
*/
}
1 => {
//create instance of structure for symbolic equation system and Jacobian
// define argument and unknown variables
let y = Expr::Var("y".to_string());
let z: Expr = Expr::Var("z".to_string());
//define equation system
let eq1: Expr =
Expr::Const(-1.0f64) * z.clone() + (Expr::Const(-1.0) * 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();
let _ = ODE_instance.save_result();
}
2 => {
//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();
}
3 => {
let eq1 = Expr::parse_expression("z^2+y^2-10.0*x");
let eq2 = Expr::parse_expression("z-y-4.0*x");
let eq_system = vec![eq1, eq2];
println!("eq_system = {:?}", eq_system);
let initial_guess = DVector::from_vec(vec![1.0, 1.0]);
let values = vec!["z".to_string(), "y".to_string()];
let arg = "x".to_string();
let tolerance = 1e-6;
let max_iterations = 100;
let max_error = 0.0;
assert_eq!(&eq_system.len(), &2);
let mut nr = NRODE::new(
eq_system,
initial_guess,
values,
arg,
tolerance,
max_iterations,
max_error,
);
nr.eq_generate();
assert_eq!(nr.eq_system.len(), 2);
nr.set_t(1.0);
let _ = nr.solve().unwrap();
}
4 => {
// Backward Euler method: linear ODE
let eq1 = Expr::parse_expression("z+y");
let eq2 = Expr::parse_expression("z");
let eq_system = vec![eq1, eq2];
println!("eq_system = {:?}", eq_system);
let y0 = DVector::from_vec(vec![1.0, 1.0]);
let values = vec!["z".to_string(), "y".to_string()];
let arg = "x".to_string();
let tolerance = 1e-2;
let max_iterations = 100;
let h = Some(1e-3);
let t0 = 0.0;
let t_bound = 1.0;
let mut solver = BE::new();
solver.set_initial(
eq_system,
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 1 = {:?}", result.1);
println!("result = {:?}", result.1.unwrap().shape());
solver.plot_result();
// println!("result = {:?}", result);
}
5 => {
// 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();
#[allow(unused_variables)]
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();
}
6 => {
// Backward Euler method: slightly non-linear ODE: adaptative time step
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 = None;
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();
#[allow(unused_variables)]
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();
}
7 => {
//Non-stiff equations: use ODE general api ODEsolver
// RK45 and Dormand-Prince methods are available
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();
}
_ => {
println!("example not found");
}
}
//_________________________________________________
}