Collaboration diagram for Reduction operations:

Functions
value_type	AbstractLinAlgPack::max_element (const Vector &v)
	Compute the maximum element in a vector. More...

std::pair< value_type, value_type >	AbstractLinAlgPack::max_near_feas_step (const Vector &x, const Vector &d, const Vector &xl, const Vector &xu, value_type max_bnd_viol)
	Computes the maximum positive and negative step that can be taken that are within the relaxed bounds. More...

value_type	AbstractLinAlgPack::max_rel_step (const Vector &x, const Vector &d)
	Computes the maximum relative step of `x = x + d`. More...

value_type	AbstractLinAlgPack::fraction_to_boundary (const value_type tau, const Vector &x, const Vector &d, const Vector &xl, const Vector &xu)

value_type	AbstractLinAlgPack::fraction_to_zero_boundary (const value_type tau, const Vector &x, const Vector &d)

size_type	AbstractLinAlgPack::num_bounded (const Vector &xl, const Vector &xu, value_type inf_bound)
	Count the number of finitly bounded elements in `xl <= x <= xu`. More...

value_type	AbstractLinAlgPack::log_bound_barrier (const Vector &x, const Vector &xl, const Vector &xu)
	Computes the log barrier term: More...

value_type	AbstractLinAlgPack::combined_nu_comp_err (const Vector &v, const Vector &x, const Vector &xl, const Vector &xu)
	Computes an estimate of the complementarity error. More...

value_type	AbstractLinAlgPack::combined_nu_comp_err_lower (const Vector &v, const Vector &x, const Vector &xl)
	Computes an estimate of the complementarity error when only the lower bounds are non-infinite. More...

value_type	AbstractLinAlgPack::combined_nu_comp_err_upper (const Vector &v, const Vector &x, const Vector &xu)
	Computes an estimate of the complementarity error when only the upper bounds are non-infinite. More...

value_type	AbstractLinAlgPack::IP_comp_err_with_mu (const value_type mu, const value_type inf_bound, const Vector &x, const Vector &xl, const Vector &xu, const Vector &vl, const Vector &vu)
	Computes the complementarity error for a primal/dual interior point algorithm using inf norm. More...

bool	AbstractLinAlgPack::max_inequ_viol (const AbstractLinAlgPack::Vector &v, const AbstractLinAlgPack::Vector &vL, const AbstractLinAlgPack::Vector &vU, AbstractLinAlgPack::size_type max_viol_i, AbstractLinAlgPack::value_type max_viol, AbstractLinAlgPack::value_type v_i, int bnd_type, AbstractLinAlgPack::value_type *vLU_i)
	Compute the maximum violation from a set of inequality constraints `vL <= v <= vU`. More...

Detailed Description

Function Documentation

AbstractLinAlgPack::value_type AbstractLinAlgPack::max_element ( const Vector & v )

Compute the maximum element in a vector.

Returns:

max{ v(i), i = 1...n }

Definition at line 173 of file AbstractLinAlgPack_VectorAuxiliaryOps.cpp.

std::pair< AbstractLinAlgPack::value_type, AbstractLinAlgPack::value_type > AbstractLinAlgPack::max_near_feas_step	(	const Vector &	x,
		const Vector &	d,
		const Vector &	xl,
		const Vector &	xu,
		value_type	max_bnd_viol
	)

Computes the maximum positive and negative step that can be taken that are within the relaxed bounds.

This function computes and returns the maximum (in magnitude) postive (return.first >= 0.0) and negative (return.second <= 0.0) steps u that can be taken such that the relaxed bounds:

xl - max_bnd_viol <= x + u * d <= xu - max_bnd_viol

are strictly satisfied.

If return.first < 0.0 then this is a flag that x is not in the relaxed bounds to begin with. In this case return.second has no meaning.

Definition at line 184 of file AbstractLinAlgPack_VectorAuxiliaryOps.cpp.

AbstractLinAlgPack::value_type AbstractLinAlgPack::max_rel_step	(	const Vector &	x,
		const Vector &	d
	)

Computes the maximum relative step of x = x + d.

return = max{ |d|/(1.0+|x(i)|), for i = 1...n }

Definition at line 204 of file AbstractLinAlgPack_VectorAuxiliaryOps.cpp.

AbstractLinAlgPack::value_type AbstractLinAlgPack::fraction_to_boundary	(	const value_type	tau,
		const Vector &	x,
		const Vector &	d,
		const Vector &	xl,
		const Vector &	xu
	)

Computes alpha_max by the fraction to boundary rule.

ToDo: Finish documentation!

Definition at line 220 of file AbstractLinAlgPack_VectorAuxiliaryOps.cpp.

AbstractLinAlgPack::value_type AbstractLinAlgPack::fraction_to_zero_boundary	(	const value_type	tau,
		const Vector &	x,
		const Vector &	d
	)

Computes alpha_max by the fraction to boundary rule assuming only a lower bound of zero

ToDo: Finish documentation!

Definition at line 240 of file AbstractLinAlgPack_VectorAuxiliaryOps.cpp.

AbstractLinAlgPack::size_type AbstractLinAlgPack::num_bounded	(	const Vector &	xl,
		const Vector &	xu,
		value_type	inf_bound
	)

Count the number of finitly bounded elements in xl <= x <= xu.

ToDo: Finish documentation!

Definition at line 258 of file AbstractLinAlgPack_VectorAuxiliaryOps.cpp.

AbstractLinAlgPack::value_type AbstractLinAlgPack::log_bound_barrier	(	const Vector &	x,
		const Vector &	xl,
		const Vector &	xu
	)

Computes the log barrier term:

sum{ log( x(i) - xl(i) ) + log( xu(i) - x(i) ) , for i = 1...n }

Definition at line 275 of file AbstractLinAlgPack_VectorAuxiliaryOps.cpp.

AbstractLinAlgPack::value_type AbstractLinAlgPack::combined_nu_comp_err	(	const Vector &	v,
		const Vector &	x,
		const Vector &	xl,
		const Vector &	xu
	)

Computes an estimate of the complementarity error.

  for every i...
     comp_err = max(comp_err, v(i)*(xu(i)-x(i), -v(i)*(x(i)-xl(i))));

Definition at line 294 of file AbstractLinAlgPack_VectorAuxiliaryOps.cpp.

AbstractLinAlgPack::value_type AbstractLinAlgPack::combined_nu_comp_err_lower	(	const Vector &	v,
		const Vector &	x,
		const Vector &	xl
	)

Computes an estimate of the complementarity error when only the lower bounds are non-infinite.

  for every i...
     comp_err = max(comp_err, v(i)*(xl(i)-x(i))));

NOTE: equivalent to 
     comp_err = max(comp_err, -v(i)*(x(i)-xl(i))));

Definition at line 313 of file AbstractLinAlgPack_VectorAuxiliaryOps.cpp.

AbstractLinAlgPack::value_type AbstractLinAlgPack::combined_nu_comp_err_upper	(	const Vector &	v,
		const Vector &	x,
		const Vector &	xu
	)

Computes an estimate of the complementarity error when only the upper bounds are non-infinite.

  for every i...
     comp_err = max(comp_err, v(i)*(xu(i)-x(i))));

Definition at line 332 of file AbstractLinAlgPack_VectorAuxiliaryOps.cpp.

AbstractLinAlgPack::value_type AbstractLinAlgPack::IP_comp_err_with_mu	(	const value_type	mu,
		const value_type	inf_bound,
		const Vector &	x,
		const Vector &	xl,
		const Vector &	xu,
		const Vector &	vl,
		const Vector &	vu
	)

Computes the complementarity error for a primal/dual interior point algorithm using inf norm.

  for every i...
     comp_err = max(comp_err, 
                  ( fabs(vu(i)*(xu(i)-x(i)) - mu) ),
          ( fabs(vl(i)*(x(i)-xl(i)) - mu) )
          );

Definition at line 350 of file AbstractLinAlgPack_VectorAuxiliaryOps.cpp.

bool AbstractLinAlgPack::max_inequ_viol	(	const AbstractLinAlgPack::Vector &	v,
		const AbstractLinAlgPack::Vector &	vL,
		const AbstractLinAlgPack::Vector &	vU,
		AbstractLinAlgPack::size_type *	max_viol_i,
		AbstractLinAlgPack::value_type *	max_viol,
		AbstractLinAlgPack::value_type *	v_i,
		int *	bnd_type,
		AbstractLinAlgPack::value_type *	vLU_i
	)

Compute the maximum violation from a set of inequality constraints vL <= v <= vU.

Parameters

v	[in] Inequality value vector.
vL	[in] Lower inequality bounds (may be -infinity (i.e. very large negative number))
vU	[in] Upper inequality bounds (may be +infinity (i.e. very large positive number))
max_viol_i	[out] Gives the index of the inequality with the maximum (scaled) violation. If `*max_viol_i == 0` on output then no inequality was violated.
max_viol	[out] The maximum (scaled violation). Only significant if `*max_viol_i > 0`.
v_i	[out] Set to `v.get_ele(max_viol_i)`. Only significant if `max_viol_i > 0`.
bnd_type	[out] The type of bound with the maximum violation. -1 : LOWER 0 : EQUALITY +1 : UPPER Only significant if `*max_viol_i > 0`.
vLU_i	[out] Set to: `vL.get_ele(max_viol_i)` if `bnd_type <= 0` `vU.get_ele(max_viol_i)` if `bnd_type > 0` Only significant if `*max_viol_i > 0`.

Returns: Returns true if some constraint was violated.

Preconditions:

ToDo: Spell these out!

Postconditions:

ToDo: Spell these out!

In order to make the result unique if more than one inequality vL(i) <= v(i) <= vL(i) have the same maximum violation then the inequality with the lowest i is returned.

Definition at line 372 of file AbstractLinAlgPack_VectorAuxiliaryOps.cpp.

Functions

Detailed Description

Function Documentation