opt.h File Reference

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Functions
double	nextdouble (double x, double dir)
double	GradientMax (void *params, double(*F)(int, double *, void *), void(*dF)(double *, int, double *, void *), int dim, double *start, double ep=1e-6, int maxiter=100)
double	GradientOneMax (void *params, double(*F)(int, double *, void *), void(*dF)(double *, int, double *, void *), int dim, double *start, double ep, int maxiter)
double	Newton (double &x0, double(*y)(double, void *), double(*y1)(double, void *), void *params=0, double epx=1e-6, int maxiter=100, double epy=1e-256)
int	Newton (double &x0, double(*dy)(double, void *), void *params, int yshift, double epx=1e-6, int maxiter=100, double epy=1e-256, double xmin=-1e308, double xmax=1e308)
double	Newton1dmax (double &x0, double xa, double xb, double(*ddy)(double, void *), void *params, int y1shift, int yshift, double(*dy)(double, void *), int dyshift, double epx=1e-6, int maxiter=100, double epdy=1e-128, bool checkinput=true)
double	Newton2D (double &x1, double &x2, double(*dy)(double &, double &, void *), double(*ddy)(double &, double &, double &, void *), void *params=0, double epx1=1e-6, double epx2=1e-6, int maxiter=100, double epdy=1e-256)
double	rootsearchhalf (double &x1, double x2, double(*y)(double, void *), void *params=0, double epx=1e-6, int maxiter=100)
double	rootsearchsecant (double &x1, double x2, double(*y)(double, void *), void *params=0, double epx=1e-6, int maxiter=100)
double	rootsearchbisecant (double &x1, double x2, double(*y)(double, void *), void *params=0, double epx=1e-6, int maxiter=100)
double	Search1Dmax (double &x, void *params, double(*F)(double, void *), double inf, double sup, double *maxresult=0, double ep=1e-6, int maxiter=100, bool convcheck=false)
double	Search1DmaxEx (double &x, void *params, double(*F)(double, void *), double inf, double sup, double *maxresult=0, double ep=1e-6, int maxiter=100, double len=1)
double	Search1Dmaxfrom (void *params, double(*F)(int, double *, void *), int dim, double *start, double *direct, double step=1e-2, double minstep=1e-6, double maxstep=1e6, double *opt=0, double *max=0, double ep=1e-6, int maxiter=100, bool convcheck=false)

Detailed Description

• optimization routines

Function Documentation

double GradientMax	(	void *	params,
		double(*)(int, double *, void *)	F,
		void(*)(double *, int, double *, void *)	dF,
		int	dim,
		double *	start,
		double	ep,
		int	maxiter
	)

function GradientMax: gradient method maximizing F(x)

In: function F(x) and its derivative dF(x) start[dim]: initial value of x ep: a stopping threshold maxiter: maximal number of iterates Out: start[dim]: the final x

Returnx max F(final x)

double GradientOneMax	(	void *	params,
		double(*)(int, double *, void *)	F,
		void(*)(double *, int, double *, void *)	dF,
		int	dim,
		double *	start,
		double	ep,
		int	maxiter
	)

function GradientOneMax: gradient method maximizing F(x), which searches $dim dimensions one after another instead of taking the gradient descent direction.

In: function F(x) and its derivative dF(x) start[dim]: initial value of x ep: a stopping threshold maxiter: maximal number of iterates Out: start[dim]: the final x

Returnx max F(final x)

double Newton	(	double &	x0,
		double(*)(double, void *)	y,
		double(*)(double, void *)	y1,
		void *	params,
		double	epx,
		int	maxiter,
		double	epy
	)

function Newton: Newton method for finding the root of y(x)

In: function y(x) and its derivative y'(x) params: additional argument for calling y and y' x0: inital value of x epx, epy: stopping thresholds on x and y respectively maxiter: maximal number of iterates Out: x0: the root

Returns 0 if successful.

int Newton	(	double &	x0,
		double(*)(double, void *)	dy,
		void *	params,
		int	yshift,
		double	epx,
		int	maxiter,
		double	epy,
		double	xmin,
		double	xmax
	)

function Newton: Newton method for finding the root of y(x), for use when it's more efficient for y' and y to be calculated in one function call

In: function dy(x) that computes y and y' at x params: additional argument for calling dy yshift: the byte shift in params where dy(x) put the value of y(x) as double type x0: inital value of x epx, epy: stopping thresholds on x and y respectively maxiter: maximal number of iterates Out: x0: the root

Returns 0 if successful.

double Newton1dmax	(	double &	x0,
		double	xa,
		double	xb,
		double(*)(double, void *)	ddy,
		void *	params,
		int	y1shift,
		int	yshift,
		double(*)(double, void *)	dy,
		int	dyshift,
		double	epx,
		int	maxiter,
		double	epdy,
		bool	checkinput
	)

function Newton1dmax: uses init_Newton_1d_max and Newton_1d_max to search for a local maximum of y.

By default ddy and dy use the same parameter structure and returns the lower order derivatives at specific offsets within that structure. However, since the same params is used, it's possible the same variable may take different offsets when returned from ddy() and dy().

On calling xa<x0<xb, and it is assumed that y0>=ya, y0>=yb. If the conditions on y are not met, it returns a negative value showing the order of y0, ya and yb, i.e. -0.5 for ya<=y0<yb -0.6 for yb<=y0<ya -0.7 for y0<ya<yb -0.8 for y0<yb<=ya

In: function ddy(x) that computes y, y' and y" at x function dy(x) that computes y and y' at x params: additional argument for calling ddy and dy y1shift: the byte shift in params where ddy(x) put the value of y'(x) as double type yshift: the byte shift in params where ddy(x) put the value of y(x) as double type dyshift: the byte shift in params where dy(x) put the value of y(x) as double type x0: inital value of x (xa, xb): initial search range epx, epdy: stopping threshold for x and y', respectively maxiter: maximal number of iterates Out: x0: the maximum

Returns the error bound for maximum x0, or a negative value if the initial point does not satisfy relevent assumptions.

double rootsearchbisecant	(	double &	x1,
		double	x2,
		double(*)(double, void *)	y,
		void *	params,
		double	epx,
		int	maxiter
	)

function rootsearchbisecant: searches for the root of y(x) in (x1, x2) by bi-secant method. On calling given that y(x1) and y(x2) have different signs. The bound interval (x1, x2) converges to 0, as compared to standared secant method.

In: function y(x), params: additional arguments for calling y (x1, x2): inital range epx: stopping threshold on x maxiter: maximal number of iterates Out: root x1

Returns an estimated error bound if a root is found, a negative value if not.

double rootsearchhalf	(	double &	x1,
		double	x2,
		double(*)(double, void *)	y,
		void *	params,
		double	epx,
		int	maxiter
	)

function rootsearchhalf: searches for the root of y(x) in (x1, x2) by half-split method. On calling y(x1) and y(x2) must not have the same sign, or -1 is returned signaling a failure.

In: function y(x), params: additional arguments for calling y (x1, x2): inital range epx: stopping threshold on x maxiter: maximal number of iterates Out: root x1

Returns a positive error estimate if a root is found, -1 if not.

double rootsearchsecant	(	double &	x1,
		double	x2,
		double(*)(double, void *)	y,
		void *	params,
		double	epx,
		int	maxiter
	)

function rootsearchsecant: searches for the root of y(x) in (x1, x2) by secant method.

In: function y(x), params: additional arguments for calling y (x1, x2): inital range epx: stopping threshold on x maxiter: maximal number of iterates Out: root x1

Returns a positive error estimate if a root is found, -1 if not.

double Search1Dmax	(	double &	x,
		void *	params,
		double(*)(double, void *)	F,
		double	inf,
		double	sup,
		double *	maxresult,
		double	ep,
		int	maxiter,
		bool	convcheck
	)

function Search1Dmax: 1-dimensional maximum search within interval [inf, sup] using 0.618 method

In: function F(x), params: additional arguments for calling F (inf, sup): inital range epx: stopping threshold on x maxiter: maximal number of iterates convcheck: specifies if convexity is checked at each interate, false recommended. Out: x: the maximum maxresult: the maximal value, if specified

Returns an estimated error bound of x if successful, a negative value if not.

double Search1DmaxEx	(	double &	x,
		void *	params,
		double(*)(double, void *)	F,
		double	inf,
		double	sup,
		double *	maxresult,
		double	ep,
		int	maxiter,
		double	len
	)

function Search1DmaxEx: 1-dimensional maximum search using Search1Dmax, but allows setting a $len argument so that a pre-location of the maximum is performed by sampling (inf, sup) at interval $len, so that Search1Dmax will work on an interval no longer than 2*len.

In: function F(x), params: additional arguments for calling F (inf, sup): inital range len: rough sampling interval for pre-locating maximum epx: stopping threshold on x maxiter: maximal number of iterates convcheck: specifies if convexity is checked at each interate, false recommended. Out: x: the maximum maxresult: the maximal value, if specified

Returns an estimated error bound of x if successful, a negative value if not.

double Search1Dmaxfrom	(	void *	params,
		double(*)(int, double *, void *)	F,
		int	dim,
		double *	start,
		double *	direct,
		double	step,
		double	minstep,
		double	maxstep,
		double *	opt,
		double *	max,
		double	ep,
		int	maxiter,
		bool	convcheck
	)

function Search1Dmaxfrom: 1-dimensional maximum search from start[] towards start+direct[]. The function tries to locate an interval ("step") for which the 4-point convexity rule confirms the existence of a convex maximum.

In: function F(x) params: additional arguments for calling F start[dim]: initial x[] direct[dim]: search direction step: initial step size minstep: minimal step size in 4-point scheme between x0 and x3 maxstep: maximal step size in 4-point scheme between x0 and x3 Out: opt[dim]: the maximum, if specified max: maximal value, if specified

Returns x>0 that locally maximizes F(start+x*direct) or x|-x>0 that maximizes F(start-x*direct) at calculated points if convex check fails.