Function information

optimistix.FunctionInfo

Different solvers (BFGS, Levenberg--Marquardt, ...) evaluate different quantities of the objective function. Some may compute gradient information, some may provide approximate Hessian information, etc.

This enumeration-ish object captures the different variants.

Available variants are optimistix.FunctionInfo.{Eval, EvalGrad, EvalGradHessian, EvalGradHessianInv, Residual, ResidualJac}.

as_min() -> Shaped[Array, '']

For a minimisation problem, returns f(y). For a least-squares problem, returns 0.5*residuals^2 -- i.e. its loss as a minimisation problem.

optimistix.FunctionInfo.Eval(optimistix.FunctionInfo)

Has a .f attribute describing fn(y). Used when no gradient information is available.

__init__(f: Shaped[Array, ''])

Arguments:

• f: the scalar output of a function evaluation fn(y).

optimistix.FunctionInfo.EvalGrad(optimistix.FunctionInfo)

Has a .f attribute as with optimistix.FunctionInfo.Eval. Also has a .grad attribute describing d(fn)/dy. Used with first-order solvers for minimisation problems. (E.g. gradient descent; nonlinear CG.)

__init__(f: Shaped[Array, ''], grad: ~Y)

Arguments:

• f: the scalar output of a function evaluation fn(y).
• grad: the output of a gradient evaluation grad(fn)(y).

optimistix.FunctionInfo.EvalGradHessian(optimistix.FunctionInfo)

Has .f and .grad attributes as with optimistix.FunctionInfo.EvalGrad. Also has a .hessian attribute describing (an approximation to) the Hessian of fn at y. Used with quasi-Newton minimisation algorithms, like BFGS.

__init__(f: Shaped[Array, ''], grad: ~Y, hessian: lineax.AbstractLinearOperator)

Arguments:

• f: the scalar output of a function evaluation fn(y).
• grad: the output of a gradient evaluation grad(fn)(y).
• hessian: the output of a hessian evaluation hessian(fn)(y).

optimistix.FunctionInfo.EvalGradHessianInv(optimistix.FunctionInfo)

As optimistix.FunctionInfo.EvalGradHessian, but records the (approximate) inverse-Hessian instead. Has .f and .grad and .hessian_inv attributes.

__init__(f: Shaped[Array, ''], grad: ~Y, hessian_inv: lineax.AbstractLinearOperator)

Arguments:

• f: the scalar output of a function evaluation fn(y).
• grad: the output of a gradient evaluation grad(fn)(y).
• hessian_inv: the matrix inverse of a hessian evaluation (hessian(fn)(y))^{-1}.

optimistix.FunctionInfo.Residual(optimistix.FunctionInfo)

Has a .residual attribute describing fn(y). Used with least squares problems, for which fn returns residuals.

__init__(residual: ~Out)

Arguments:

• residual: the vector output of a function evaluation fn(y). When thought of as a minimisation problem the scalar value to minimise is 0.5 * residual^T residual.

optimistix.FunctionInfo.ResidualJac(optimistix.FunctionInfo)

Records the Jacobian d(fn)/dy as a linear operator. Used for least squares problems, for which fn returns residuals. Has .residual and .jac attributes, where residual = fn(y), jac = d(fn)/dy.

__init__(residual: ~Out, jac: lineax.AbstractLinearOperator)

Arguments:

• residual: the vector output of a function evaluation fn(y). When thought of as a minimisation problem the scalar value to minimise is 0.5 * residual^T residual.
• jac: the jacobian jac(fn)(y).