public class Minimization extends java.lang.Object
Modified by: Joseph A. Huwaldt
| Constructor and Description |
|---|
Minimization() |
| Modifier and Type | Method and Description |
|---|---|
static void |
bracket1D(double ax,
double bx,
double[] triple,
double[] values,
Evaluatable1D eval)
Method that searches in the downhill direction (defined by the function as
evaluated at the initial points) and returns new points (in triple) that bracket
a minimum of the function.
|
static double |
find(Evaluatable1D eval,
double x1,
double x2,
double tol,
double[] output)
Method that isolates the minimum of a 1D function to a fractional precision
of about "tol".
|
static double |
find(Evaluatable1D eval,
double ax,
double bx,
double cx,
double tol,
double[] output)
Method that isolates the minimum of a 1D function to a fractional precision
of about "tol".
|
static double |
findND(ScalarFunctionND func,
double[] p,
int n,
double tol)
Method that isolates the minimum of an n-Dimensional scalar function
to a fractional precision of about "tol".
|
static void |
main(java.lang.String[] args)
Used to test out the methods in this class.
|
public Minimization()
public static double find(Evaluatable1D eval, double x1, double x2, double tol, double[] output) throws RootException
Method that isolates the minimum of a 1D function to a fractional precision of about "tol". A version of Brent's method is used with derivative information if it is available or a version without if it is not.
eval - An evaluatable 1D function that returns the
function value at x and optionally returns the
function derivative value (d(fx)/dx) at x. It is
guaranteed that "function()" will always be called
before "derivative()".x1 - The lower bracket surrounding the minimum (assumed that
minimum lies between x1 and x2).x2 - The upper bracket surrounding the root (assumed that
minimum lies between x1 and x2).tol - The root will be refined until it's accuracy is
better than this. This should generally not be smaller
than Math.sqrt(EPS)!output - An optional 2-element array that will be filled in with the abscissa (x) and
function minimum ordinate ( f(x) ) on output. output[xmin,f(xmin)].
Pass "null" if this is not required.RootException - Unable to find a minimum of the function.public static double find(Evaluatable1D eval, double ax, double bx, double cx, double tol, double[] output) throws RootException
Method that isolates the minimum of a 1D function to a fractional precision of about "tol". A version of Brent's method is used with derivative information if it is available or a version without if it is not.
eval - An evaluatable 1D function that returns the
function value at x and optionally returns the
function derivative value (d(fx)/dx) at x. It is
guaranteed that "function()" will always be called
before "derivative()". The return value from the 1st
call to "function()" is ignored.ax - The lower bracket known to surround the minimum (assumed that
minimum lies between ax and cx).bx - Abscissa point that lies between ax and cx where f(bx) is less than
both f(ax) and f(cx).cx - The upper bracket known to surround the root (assumed that
minimum lies between ax and cx).tol - The root will be refined until it's accuracy is
better than this. This should generally not be smaller
than Math.sqrt(EPS)!output - An optional 2-element array that will be filled in with the abscissa (x) and
function minimum ordinate ( f(x) ) on output. output[xmin,f(xmin)].
Pass "null" if this is not required.RootException - Unable to find a minimum of the function.public static void bracket1D(double ax, double bx, double[] triple, double[] values, Evaluatable1D eval) throws RootException
ax - The lower bracket surrounding the minimum (assumed that
minimum lies between ax and bx).bx - The upper bracket surrounding the root (assumed that
minimum lies between ax and bx).triple - A 3-element array that will be filled in with the abcissa of the
three points that bracket the minium triple[ax,bx,cx].values - A 3-element array that contains the function values that correspond
with the points ax, bx and cx in triple. Null may be passed for this
if the function values are not required.eval - An evaluatable 1D function that returns the
function value at x and optionally returns the
function derivative value (d(fx)/dx) at x. It is
guaranteed that "function()" will always be called
before "derivative()".RootExceptionpublic static double findND(ScalarFunctionND func, double[] p, int n, double tol) throws RootException
Method that isolates the minimum of an n-Dimensional scalar function to a fractional precision of about "tol". If no derivatives are available then Powell's method is used. If derivatives are available, then a Polak-Reibiere minimization is used.
func - An evaluatable n-D scalar function that returns the
function value at a point, p[1..n], and optionally returns the
function derivatives (d(fx[1..n])/dx) at p[1..n]. It is
guaranteed that "function()" will always be called
before "derivatives()".p - On input, this is the initial guess at the minimum point. On output, this
is filled in with the values that minimize the function.n - The number of variables in the array p.tol - The convergence tolerance on the function value.RootException - if unable to find a minimum of the function.public static void main(java.lang.String[] args)