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TaylorExpand

oxiphysics_core::autodiff

Struct TaylorExpand 

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pub struct TaylorExpand {
    pub center: f64,
    pub f0: f64,
    pub f1: f64,
    pub f2: f64,
    pub f3: f64,
}
Expand description

Stores the value of a function and its first three derivatives at a point, enabling Taylor polynomial evaluation.

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§center: f64

The expansion center x₀.

§f0: f64

f(x₀).

§f1: f64

f'(x₀).

§f2: f64

f''(x₀) (second derivative).

§f3: f64

f'''(x₀) (third derivative).

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impl TaylorExpand

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pub fn build<F>(f: F, x0: f64) -> Self
where F: Fn(Dual) -> Dual + Copy,

Build a TaylorExpand by numerically estimating derivatives via forward-mode AD and central finite differences.

  • f1 — exact via autodiff.
  • f2 — via central difference of f'.
  • f3 — via central difference of f''.
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pub fn eval(&self, x: f64) -> f64

Evaluate the Taylor polynomial at x: f0 + f1*(x-x0) + f2/2*(x-x0)² + f3/6*(x-x0)³

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impl Clone for TaylorExpand

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fn clone(&self) -> TaylorExpand

Returns a duplicate of the value. Read more
1.0.0 (const: unstable) · Source§

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source. Read more
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impl Debug for TaylorExpand

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fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter. Read more

Auto Trait Implementations§

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impl<T> Any for T
where 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 T
where 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 T
where 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> CloneToUninit for T
where T: Clone,

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unsafe fn clone_to_uninit(&self, dest: *mut u8)

🔬This is a nightly-only experimental API. (clone_to_uninit)
Performs copy-assignment from self to dest. 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 T
where 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 SP
where 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> ToOwned for T
where T: Clone,

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type Owned = T

The resulting type after obtaining ownership.
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fn to_owned(&self) -> T

Creates owned data from borrowed data, usually by cloning. Read more
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fn clone_into(&self, target: &mut T)

Uses borrowed data to replace owned data, usually by cloning. Read more
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impl<T, U> TryFrom<U> for T
where 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 T
where 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.