# Struct ode_solvers::rk4::Rk4

``````pub struct Rk4<T, V, F>where
F: System<T, V>,
T: FloatNumber,{ /* private fields */ }``````
Expand description

Structure containing the parameters for the numerical integration.

## Implementations§

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### impl<T, D: Dim, F> Rk4<T, OVector<T, D>, F>where T: FloatNumber, F: System<T, OVector<T, D>>, OVector<T, D>: Mul<T, Output = OVector<T, D>>, DefaultAllocator: Allocator<T, D>,

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#### pub fn new(f: F, x: T, y: OVector<T, D>, x_end: T, step_size: T) -> Self

Default initializer for the structure

##### Arguments
• `f` - Structure implementing the System trait
• `x` - Initial value of the independent variable (usually time)
• `y` - Initial value of the dependent variable(s)
• `x_end` - Final value of the independent variable
• `step_size` - Step size used in the method
##### Examples found in repository?
examples/bouncing_ball.rs (line 31)
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```
``````fn main() {
// Initial state: At 10m with zero velocity
let mut y0 = State::new(10.0, 0., 0.);
let mut num_bounces = 0;
let mut combined_solver_results = Result::default();

while num_bounces < MAX_BOUNCES && y0[0] >= 0.001 {
// Create the structure containing the ODEs.
let system = BouncingBall;

// Create a stepper and run the integration.
// Use comments to see differences with Dopri
//let mut stepper = Dopri5::new(system, 0., 10.0, 0.01, y0, 1.0e-2, 1.0e-6);
let mut stepper = Rk4::new(system, 0f32, y0, 10f32, 0.01f32);
let res = stepper.integrate();

// Handle result.
match res {
Ok(stats) => println!("{}", stats),
Err(e) => println!("An error occured: {}", e),
}

num_bounces = num_bounces + 1;

// solout may not be called and therefore end not "smooth" when observing dense values with dopri5 or dop853
// Therefore we seach for the point where the results turn zero
let (_, y_out) = stepper.results().get();
let f = y_out.iter().find(|y| y[0] <= 0.);
if f.is_none() {
// that should not happen...
break;
}

let last_state = f.unwrap();
println!("Last state: {:?}", last_state);

y0[0] = last_state[0].abs();
y0[1] = -1. * last_state[1] * BOUNCE;

// beware in the case of dopri5 or dop853 the results contain a lot of invalid data with y[0] < 0
combined_solver_results.append(stepper.into());
}

let path = Path::new("./outputs/bouncing_ball.dat");

save(
combined_solver_results.get().0,
combined_solver_results.get().1,
path,
);
}``````
source

#### pub fn integrate(&mut self) -> Result<Stats, IntegrationError>

Core integration method.

##### Examples found in repository?
examples/bouncing_ball.rs (line 32)
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```
``````fn main() {
// Initial state: At 10m with zero velocity
let mut y0 = State::new(10.0, 0., 0.);
let mut num_bounces = 0;
let mut combined_solver_results = Result::default();

while num_bounces < MAX_BOUNCES && y0[0] >= 0.001 {
// Create the structure containing the ODEs.
let system = BouncingBall;

// Create a stepper and run the integration.
// Use comments to see differences with Dopri
//let mut stepper = Dopri5::new(system, 0., 10.0, 0.01, y0, 1.0e-2, 1.0e-6);
let mut stepper = Rk4::new(system, 0f32, y0, 10f32, 0.01f32);
let res = stepper.integrate();

// Handle result.
match res {
Ok(stats) => println!("{}", stats),
Err(e) => println!("An error occured: {}", e),
}

num_bounces = num_bounces + 1;

// solout may not be called and therefore end not "smooth" when observing dense values with dopri5 or dop853
// Therefore we seach for the point where the results turn zero
let (_, y_out) = stepper.results().get();
let f = y_out.iter().find(|y| y[0] <= 0.);
if f.is_none() {
// that should not happen...
break;
}

let last_state = f.unwrap();
println!("Last state: {:?}", last_state);

y0[0] = last_state[0].abs();
y0[1] = -1. * last_state[1] * BOUNCE;

// beware in the case of dopri5 or dop853 the results contain a lot of invalid data with y[0] < 0
combined_solver_results.append(stepper.into());
}

let path = Path::new("./outputs/bouncing_ball.dat");

save(
combined_solver_results.get().0,
combined_solver_results.get().1,
path,
);
}``````
source

#### pub fn x_out(&self) -> &Vec<T>

Getter for the independent variable’s output.

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#### pub fn y_out(&self) -> &Vec<OVector<T, D>>

Getter for the dependent variables’ output.

source

#### pub fn results(&self) -> &SolverResult<T, OVector<T, D>>

Getter for the results type, a pair of independent and dependent variables

##### Examples found in repository?
examples/bouncing_ball.rs (line 44)
```18
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```
``````fn main() {
// Initial state: At 10m with zero velocity
let mut y0 = State::new(10.0, 0., 0.);
let mut num_bounces = 0;
let mut combined_solver_results = Result::default();

while num_bounces < MAX_BOUNCES && y0[0] >= 0.001 {
// Create the structure containing the ODEs.
let system = BouncingBall;

// Create a stepper and run the integration.
// Use comments to see differences with Dopri
//let mut stepper = Dopri5::new(system, 0., 10.0, 0.01, y0, 1.0e-2, 1.0e-6);
let mut stepper = Rk4::new(system, 0f32, y0, 10f32, 0.01f32);
let res = stepper.integrate();

// Handle result.
match res {
Ok(stats) => println!("{}", stats),
Err(e) => println!("An error occured: {}", e),
}

num_bounces = num_bounces + 1;

// solout may not be called and therefore end not "smooth" when observing dense values with dopri5 or dop853
// Therefore we seach for the point where the results turn zero
let (_, y_out) = stepper.results().get();
let f = y_out.iter().find(|y| y[0] <= 0.);
if f.is_none() {
// that should not happen...
break;
}

let last_state = f.unwrap();
println!("Last state: {:?}", last_state);

y0[0] = last_state[0].abs();
y0[1] = -1. * last_state[1] * BOUNCE;

// beware in the case of dopri5 or dop853 the results contain a lot of invalid data with y[0] < 0
combined_solver_results.append(stepper.into());
}

let path = Path::new("./outputs/bouncing_ball.dat");

save(
combined_solver_results.get().0,
combined_solver_results.get().1,
path,
);
}``````

## Trait Implementations§

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### impl<T, D: Dim, F> Into<SolverResult<T, Matrix<T, D, Const<1>, <DefaultAllocator as Allocator<T, D>>::Buffer>>> for Rk4<T, OVector<T, D>, F>where T: FloatNumber, F: System<T, OVector<T, D>>, DefaultAllocator: Allocator<T, D>,

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#### fn into(self) -> SolverResult<T, OVector<T, D>>

Converts this type into the (usually inferred) input type.

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## Blanket Implementations§

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### impl<T> Any for Twhere T: 'static + ?Sized,

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#### fn type_id(&self) -> TypeId

Gets the `TypeId` of `self`. Read more
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### impl<T> Borrow<T> for Twhere T: ?Sized,

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#### fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more
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### impl<T> BorrowMut<T> for Twhere T: ?Sized,

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#### fn borrow_mut(&mut self) -> &mut T

Mutably borrows from an owned value. Read more
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### impl<T> From<T> for T

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#### fn from(t: T) -> T

Returns the argument unchanged.

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### impl<T, U> Into<U> for Twhere U: From<T>,

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#### fn into(self) -> U

Calls `U::from(self)`.

That is, this conversion is whatever the implementation of `From<T> for U` chooses to do.

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### impl<T> Same for T

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#### type Output = T

Should always be `Self`
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### impl<SS, SP> SupersetOf<SS> for SPwhere SS: SubsetOf<SP>,

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#### fn to_subset(&self) -> Option<SS>

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more
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#### fn is_in_subset(&self) -> bool

Checks if `self` is actually part of its subset `T` (and can be converted to it).
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#### fn to_subset_unchecked(&self) -> SS

Use with care! Same as `self.to_subset` but without any property checks. Always succeeds.
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#### fn from_subset(element: &SS) -> SP

The inclusion map: converts `self` to the equivalent element of its superset.
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### impl<T, U> TryFrom<U> for Twhere U: Into<T>,

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#### type Error = Infallible

The type returned in the event of a conversion error.
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#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

Performs the conversion.
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### impl<T, U> TryInto<U> for Twhere U: TryFrom<T>,

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#### type Error = <U as TryFrom<T>>::Error

The type returned in the event of a conversion error.
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#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.