optimize

type ActiveBound int8

type Constraint struct {
	Fn   func(x []float64) float64
	Grad func(x []float64) []float64
	Type ConstraintType
}

type ConstraintType int

type LeastSquaresOptions struct {
	// MaxIter caps the outer iterations (one per accepted step, the
	// damping retries inside an iteration not counted). 0 means 2000;
	// negative is refused.
	MaxIter int
	// CostTol stops the run when an accepted step lowers the cost by at
	// most CostTol·cost. 0 means 1e-13; a negative or non-finite value is
	// refused.
	CostTol float64
	// StepTol stops the run when an accepted step moves every parameter
	// by at most StepTol·(1+|x_i|). 0 means 1e-10; a negative or
	// non-finite value is refused.
	StepTol float64
}

type LeastSquaresResult struct {
	// X is the final parameter vector; Cost is ½·Σ r_i² there.
	X    []float64
	Cost float64
	// JTJ is JᵀJ at X over every parameter (bound-held ones included),
	// so a caller forms the Gauss–Newton covariance σ²·(JᵀJ)⁻¹ from it
	// (linalg.InverseSPD), with σ² = 2·Cost / (m − n), after dropping the
	// rows and columns of parameters held on a bound.
	JTJ *linalg.Sym
	// Active marks, per parameter, the bound it sits EXACTLY on: a step
	// that crosses a bound is projected onto it, so a parameter bounded
	// at 0 reaches 0.
	Active     []ActiveBound
	Status     LeastSquaresStatus
	Iterations int
	FuncEvals  int
	JacEvals   int
}

type LeastSquaresStatus int

type MinimizeOptions struct {
	// Lower and Upper are per-variable bounds: nil, or exactly len(x0)
	// entries. An infinite or NaN entry marks that side unbounded; a
	// finite Lower[i] above Upper[i] is refused.
	Lower, Upper []float64
	// Constraints are the general constraints, in any mix of Eq and
	// Ineq; MinimizeResult.Multipliers follows this order.
	Constraints []Constraint
	// Acc is SLSQP's accuracy goal (SciPy's ftol): the stop on the
	// objective change, step length and constraint violation. 0 means
	// 1e-6; a negative or non-finite value is refused.
	Acc float64
	// MaxIter caps the major iterations. 0 means 100; negative is refused.
	MaxIter int
}

type MinimizeResult struct {
	// X is the final decision vector; F is the objective there.
	X []float64
	F float64
	// Multipliers holds one Lagrange multiplier per Constraint, in
	// MinimizeOptions.Constraints order, from the last QP subproblem. At
	// a solution ∇f = Σ Multipliers[i]·∇Fn_i on the free variables, so
	// a multiplier is the rate the optimal objective moves as its
	// constraint's right-hand side is relaxed; an Ineq multiplier is ≥ 0
	// when its constraint binds and 0 when it is slack.
	Multipliers []float64
	// Active marks, per variable, the bound it sits on: within
	// sqrt(machine epsilon)·(1+|bound|) of it.
	Active []ActiveBound
	// MaxViolation is the largest constraint violation at X: |Fn| for an
	// Eq constraint, max(−Fn, 0) for an Ineq one (0 with no constraints).
	MaxViolation float64
	Status       Status
	Iterations   int
	FuncEvals    int
	GradEvals    int
}

type Status int