Struct NumericalDiff

pub struct NumericalDiff<const PWR: i32 = 6>;

Forward mode differentiator

It operates on functions with regular dtype inputs and outputs, no dual numbers required. The generic parameter PWR is used to specify the power of the step size, it PWR=6 uses 1e-6 as a step size.

This struct is used to compute the Jacobian of a function using forward mode differentiation via dual-numbers. It can operate on functions with up to 6 inputs and with vector-valued outputs.

use factrs::{
    linalg::{vectorx, DiffResult, NumericalDiff, VectorX},
    traits::*,
    variables::SO2,
};

// We can also be generic over Numeric as in [ForwardProp] as well if desired
fn f(x: SO2, y: SO2) -> VectorX {
    x.ominus(&y)
}

let x = SO2::from_theta(2.0);
let y = SO2::from_theta(1.0);

// 2 as the generic since we have 2 dimensions going in
let DiffResult { value, diff } = NumericalDiff::<6>::jacobian_2(f, &x, &y);
assert_eq!(value, vectorx![1.0]);

Implementations

impl<const PWR: i32> NumericalDiff<PWR>

pub fn jacobian_variable_1<V1: VariableDtype, VOut: VariableDtype, F: Fn(V1) -> VOut>( f: F, v1: &V1, ) -> DiffResult<VOut, MatrixX>

pub fn jacobian_variable_2<V1: VariableDtype, V2: VariableDtype, VOut: VariableDtype, F: Fn(V1, V2) -> VOut>( f: F, v1: &V1, v2: &V2, ) -> DiffResult<VOut, MatrixX>

pub fn jacobian_variable_3<V1: VariableDtype, V2: VariableDtype, V3: VariableDtype, VOut: VariableDtype, F: Fn(V1, V2, V3) -> VOut>( f: F, v1: &V1, v2: &V2, v3: &V3, ) -> DiffResult<VOut, MatrixX>

pub fn jacobian_variable_4<V1: VariableDtype, V2: VariableDtype, V3: VariableDtype, V4: VariableDtype, VOut: VariableDtype, F: Fn(V1, V2, V3, V4) -> VOut>( f: F, v1: &V1, v2: &V2, v3: &V3, v4: &V4, ) -> DiffResult<VOut, MatrixX>

pub fn jacobian_variable_5<V1: VariableDtype, V2: VariableDtype, V3: VariableDtype, V4: VariableDtype, V5: VariableDtype, VOut: VariableDtype, F: Fn(V1, V2, V3, V4, V5) -> VOut>( f: F, v1: &V1, v2: &V2, v3: &V3, v4: &V4, v5: &V5, ) -> DiffResult<VOut, MatrixX>

pub fn jacobian_variable_6<V1: VariableDtype, V2: VariableDtype, V3: VariableDtype, V4: VariableDtype, V5: VariableDtype, V6: VariableDtype, VOut: VariableDtype, F: Fn(V1, V2, V3, V4, V5, V6) -> VOut>( f: F, v1: &V1, v2: &V2, v3: &V3, v4: &V4, v5: &V5, v6: &V6, ) -> DiffResult<VOut, MatrixX>

Trait Implementations

impl<const PWR: i32> Diff for NumericalDiff<PWR>

type T = f64

The dtype of the variables

fn jacobian_1<V1: VariableDtype, F: Fn(V1) -> VectorX>( f: F, v1: &V1, ) -> DiffResult<VectorX, MatrixX>

fn jacobian_2<V1: VariableDtype, V2: VariableDtype, F: Fn(V1, V2) -> VectorX>( f: F, v1: &V1, v2: &V2, ) -> DiffResult<VectorX, MatrixX>

fn jacobian_3<V1: VariableDtype, V2: VariableDtype, V3: VariableDtype, F: Fn(V1, V2, V3) -> VectorX>( f: F, v1: &V1, v2: &V2, v3: &V3, ) -> DiffResult<VectorX, MatrixX>

fn jacobian_4<V1: VariableDtype, V2: VariableDtype, V3: VariableDtype, V4: VariableDtype, F: Fn(V1, V2, V3, V4) -> VectorX>( f: F, v1: &V1, v2: &V2, v3: &V3, v4: &V4, ) -> DiffResult<VectorX, MatrixX>

fn jacobian_5<V1: VariableDtype, V2: VariableDtype, V3: VariableDtype, V4: VariableDtype, V5: VariableDtype, F: Fn(V1, V2, V3, V4, V5) -> VectorX>( f: F, v1: &V1, v2: &V2, v3: &V3, v4: &V4, v5: &V5, ) -> DiffResult<VectorX, MatrixX>

fn jacobian_6<V1: VariableDtype, V2: VariableDtype, V3: VariableDtype, V4: VariableDtype, V5: VariableDtype, V6: VariableDtype, F: Fn(V1, V2, V3, V4, V5, V6) -> VectorX>( f: F, v1: &V1, v2: &V2, v3: &V3, v4: &V4, v5: &V5, v6: &V6, ) -> DiffResult<VectorX, MatrixX>

fn gradient_1<V1: VariableDtype, F: Fn(V1::Alias<Self::T>) -> Self::T>( f: F, v1: &V1, ) -> DiffResult<dtype, VectorX>

fn gradient_2<V1: VariableDtype, V2: VariableDtype, F: Fn(V1::Alias<Self::T>, V2::Alias<Self::T>) -> Self::T>( f: F, v1: &V1, v2: &V2, ) -> DiffResult<dtype, VectorX>

fn gradient_3<V1: VariableDtype, V2: VariableDtype, V3: VariableDtype, F: Fn(V1::Alias<Self::T>, V2::Alias<Self::T>, V3::Alias<Self::T>) -> Self::T>( f: F, v1: &V1, v2: &V2, v3: &V3, ) -> DiffResult<dtype, VectorX>

fn gradient_4<V1: VariableDtype, V2: VariableDtype, V3: VariableDtype, V4: VariableDtype, F: Fn(V1::Alias<Self::T>, V2::Alias<Self::T>, V3::Alias<Self::T>, V4::Alias<Self::T>) -> Self::T>( f: F, v1: &V1, v2: &V2, v3: &V3, v4: &V4, ) -> DiffResult<dtype, VectorX>

fn gradient_5<V1: VariableDtype, V2: VariableDtype, V3: VariableDtype, V4: VariableDtype, V5: VariableDtype, F: Fn(V1::Alias<Self::T>, V2::Alias<Self::T>, V3::Alias<Self::T>, V4::Alias<Self::T>, V5::Alias<Self::T>) -> Self::T>( f: F, v1: &V1, v2: &V2, v3: &V3, v4: &V4, v5: &V5, ) -> DiffResult<dtype, VectorX>

fn gradient_6<V1: VariableDtype, V2: VariableDtype, V3: VariableDtype, V4: VariableDtype, V5: VariableDtype, V6: VariableDtype, F: Fn(V1::Alias<Self::T>, V2::Alias<Self::T>, V3::Alias<Self::T>, V4::Alias<Self::T>, V5::Alias<Self::T>, V6::Alias<Self::T>) -> Self::T>( f: F, v1: &V1, v2: &V2, v3: &V3, v4: &V4, v5: &V5, v6: &V6, ) -> DiffResult<dtype, VectorX>