Struct ExponentialFit 

pub struct ExponentialFit<V = Vec<f64>> {
    pub t: Vec<f64>,
    pub y: Vec<f64>,
    /* private fields */
}

Available on crate feature problems only.

Exponential data-fitting problem min_{a,b} ½ Σ (a·exp(b·tᵢ) − yᵢ)². Carries the data (t, y) on the struct; the generic parameter V pins the parameter-vector backend. Construct with new.

Jacobian is implemented for the feature-gated backends (nalgebra DVector<f64>, faer Col<f64>, and ndarray Array1<f64>); the default Vec<f64> backend supplies CostFunction and Residual but not Jacobian.

Fields

t: Vec<f64>

Sample abscissae tᵢ.

y: Vec<f64>

Observed values yᵢ.

Implementations

impl<V> ExponentialFit<V>

pub fn new(t: Vec<f64>, y: Vec<f64>) -> Self

Build an exponential-fit problem from data. Panics if t and y have different lengths.

pub fn sampled(a: f64, b: f64, m: usize, dt: f64) -> Self

Build the exact-data instance whose global minimum is (a, b) with f = 0: samples tᵢ = i · dt for i ∈ 0..m and sets yᵢ = a · exp(b · tᵢ). Handy for tests and benchmarks that need a known optimum.

Trait Implementations

impl CostFunction for ExponentialFit<Vec<f64>>

type Param = Vec<f64>

The parameter type the objective is defined over.

type Output = f64

Scalar cost type. In practice f64 (see CONTRIBUTING.md’s provisional choices).

type Error = Infallible

User-chosen hard-abort error. Pick std::convert::Infallible when the cost cannot fail: its niche optimization keeps Result<f64, Infallible> the same layout as bare f64 on the happy path.

fn cost(&self, x: &Vec<f64>) -> Result<f64, Infallible>

Evaluate the objective at param.

impl CostFunction for ExponentialFit<DVector<f64>>

Available on crate feature nalgebra only.

type Param = Matrix<f64, Dyn, Const<1>, VecStorage<f64, Dyn, Const<1>>>

The parameter type the objective is defined over.

type Output = f64

Scalar cost type. In practice f64 (see CONTRIBUTING.md’s provisional choices).

type Error = Infallible

User-chosen hard-abort error. Pick std::convert::Infallible when the cost cannot fail: its niche optimization keeps Result<f64, Infallible> the same layout as bare f64 on the happy path.

fn cost(&self, x: &DVector<f64>) -> Result<f64, Infallible>

Evaluate the objective at param.

impl CostFunction for ExponentialFit<Array1<f64>>

Available on crate feature ndarray only.

type Param = ArrayBase<OwnedRepr<f64>, Dim<[usize; 1]>>

The parameter type the objective is defined over.

type Output = f64

Scalar cost type. In practice f64 (see CONTRIBUTING.md’s provisional choices).

type Error = Infallible

User-chosen hard-abort error. Pick std::convert::Infallible when the cost cannot fail: its niche optimization keeps Result<f64, Infallible> the same layout as bare f64 on the happy path.

fn cost(&self, x: &Array1<f64>) -> Result<f64, Infallible>

Evaluate the objective at param.

impl CostFunction for ExponentialFit<Col<f64>>

Available on crate feature faer only.

type Param = Col<Own<f64>>

The parameter type the objective is defined over.

type Output = f64

Scalar cost type. In practice f64 (see CONTRIBUTING.md’s provisional choices).

type Error = Infallible

User-chosen hard-abort error. Pick std::convert::Infallible when the cost cannot fail: its niche optimization keeps Result<f64, Infallible> the same layout as bare f64 on the happy path.

fn cost(&self, x: &Col<f64>) -> Result<f64, Infallible>

Evaluate the objective at param.

impl<V> HasSpec for ExponentialFit<V>

const SPEC: &'static ProblemSpec

The catalog entry for this problem type.

impl Jacobian for ExponentialFit<DVector<f64>>

Available on crate feature nalgebra only.

type Jacobian = Matrix<f64, Dyn, Dyn, VecStorage<f64, Dyn, Dyn>>

The Jacobian matrix type, shape m × n.

fn jacobian(&self, x: &DVector<f64>) -> Result<DMatrix<f64>, Infallible>

Evaluate the Jacobian at param.

fn residual_and_jacobian( &self, param: &Self::Param, ) -> Result<(<Self as Residual>::Output, Self::Jacobian), <Self as Residual>::Error>

Evaluate residual and Jacobian at param in one call. The default body delegates to Residual::residual and Jacobian::jacobian; override when shared intermediate work can be amortized across the two, common in NLLS where r(x) reuses forward-mode AD state that J(x) continues from.

impl Jacobian for ExponentialFit<Array1<f64>>

Available on crate feature ndarray only.

type Jacobian = ArrayBase<OwnedRepr<f64>, Dim<[usize; 2]>>

The Jacobian matrix type, shape m × n.

fn jacobian(&self, x: &Array1<f64>) -> Result<Array2<f64>, Infallible>

Evaluate the Jacobian at param.

fn residual_and_jacobian( &self, param: &Self::Param, ) -> Result<(<Self as Residual>::Output, Self::Jacobian), <Self as Residual>::Error>

Evaluate residual and Jacobian at param in one call. The default body delegates to Residual::residual and Jacobian::jacobian; override when shared intermediate work can be amortized across the two, common in NLLS where r(x) reuses forward-mode AD state that J(x) continues from.

impl Jacobian for ExponentialFit<Col<f64>>

Available on crate feature faer only.

type Jacobian = Mat<Own<f64>>

The Jacobian matrix type, shape m × n.

fn jacobian(&self, x: &Col<f64>) -> Result<Mat<f64>, Infallible>

Evaluate the Jacobian at param.

fn residual_and_jacobian( &self, param: &Self::Param, ) -> Result<(<Self as Residual>::Output, Self::Jacobian), <Self as Residual>::Error>

Evaluate residual and Jacobian at param in one call. The default body delegates to Residual::residual and Jacobian::jacobian; override when shared intermediate work can be amortized across the two, common in NLLS where r(x) reuses forward-mode AD state that J(x) continues from.

impl Residual for ExponentialFit<Vec<f64>>

type Param = Vec<f64>

The parameter type the residual is defined over (matches CostFunction::Param).

type Output = Vec<f64>

The residual vector type. Length is the number of residuals m, independent of param.len() = n.

type Error = Infallible

User-chosen hard-abort error. Independent of CostFunction::Error: the trait families are orthogonal (NLLS solvers bind on Residual + Jacobian; first-order solvers bind on CostFunction + Gradient).

fn residual(&self, x: &Vec<f64>) -> Result<Vec<f64>, Infallible>

Evaluate the residual at param.

impl Residual for ExponentialFit<DVector<f64>>

Available on crate feature nalgebra only.

type Param = Matrix<f64, Dyn, Const<1>, VecStorage<f64, Dyn, Const<1>>>

The parameter type the residual is defined over (matches CostFunction::Param).

type Output = Matrix<f64, Dyn, Const<1>, VecStorage<f64, Dyn, Const<1>>>

The residual vector type. Length is the number of residuals m, independent of param.len() = n.

type Error = Infallible

User-chosen hard-abort error. Independent of CostFunction::Error: the trait families are orthogonal (NLLS solvers bind on Residual + Jacobian; first-order solvers bind on CostFunction + Gradient).

fn residual(&self, x: &DVector<f64>) -> Result<DVector<f64>, Infallible>

Evaluate the residual at param.

impl Residual for ExponentialFit<Array1<f64>>

Available on crate feature ndarray only.

type Param = ArrayBase<OwnedRepr<f64>, Dim<[usize; 1]>>

The parameter type the residual is defined over (matches CostFunction::Param).

type Output = ArrayBase<OwnedRepr<f64>, Dim<[usize; 1]>>

The residual vector type. Length is the number of residuals m, independent of param.len() = n.

type Error = Infallible

User-chosen hard-abort error. Independent of CostFunction::Error: the trait families are orthogonal (NLLS solvers bind on Residual + Jacobian; first-order solvers bind on CostFunction + Gradient).

fn residual(&self, x: &Array1<f64>) -> Result<Array1<f64>, Infallible>

Evaluate the residual at param.

impl Residual for ExponentialFit<Col<f64>>

Available on crate feature faer only.

type Param = Col<Own<f64>>

The parameter type the residual is defined over (matches CostFunction::Param).

type Output = Col<Own<f64>>

The residual vector type. Length is the number of residuals m, independent of param.len() = n.

type Error = Infallible

User-chosen hard-abort error. Independent of CostFunction::Error: the trait families are orthogonal (NLLS solvers bind on Residual + Jacobian; first-order solvers bind on CostFunction + Gradient).

fn residual(&self, x: &Col<f64>) -> Result<Col<f64>, Infallible>

Evaluate the residual at param.