Package net.algart.math.functions

package net.algart.math.functions

Abstraction of any mathematical functions and operators and some their implementations.

Author:

Daniel Alievsky

Related Packages

Package	Description
net.algart.math	Some mathematical objects: ranges, multidimensional points, multidimensional rectangular areas, integers with 128-bit precision.
net.algart.math.geometry	Some geometric objects and utilities.
net.algart.math.patterns	Patterns: sets of n-dimensional points.
net.algart.math.rectangles	Special algorithms for 2-dimensional rectangles.

Class	Description
AbstractCoordinateTransformationOperator	A skeletal implementation of the CoordinateTransformationOperator interface to minimize the effort required to implement this interface.
AbstractFunc	A skeletal implementation of the Func interface to minimize the effort required to implement this interface.
ApertureFilteredFunc	A function, transformed by ApertureFilterOperator in n-dimensional Euclidean space.
ApertureFilterOperator	Aperture filtering operator in n-dimensional Euclidean space: g(x) = O f(x) = apertureFunc(f(x+a0), f(x+a1), ..., f(x+am-1)), where x is a point of the n-dimensional space, apertureFunc is some function with m arguments (the aperture function), {ai} is a set of points with (usually) little coordinates (the aperture), f is the source mathematical function and g is the result of applying the operator to f.
ConstantFunc	Trivial constant function: f(x0, x1, ..., xn-1) = c, where c is a constant.
ContrastingFunc	Contrasting function: by default, f(x0, x1, x2, x3) = M * (x0/x1) * (x−x2) / max(x3−x2,threshold), where x = (x1<x2 ? x2 : x1>x3 ? x3 : x1) is x1, truncated to x2..x3 range, M and threshold are constants.
CoordinateTransformationOperator	Coordinate transformation operator in n-dimensional Euclidean space: g(x) = O f(x) = f(map(x)), where x is a point of the n-dimensional space, map is some mapping of this space, f is the source mathematical function and g is the result of applying the operator to f.
CoordinateTransformedFunc	A function, the arguments of which are transformed by some coordinate transformation operator in n-dimensional Euclidean space.
DividingFunc	Quotient of two numbers: f(x0, x1) = scale*x0/x1 , where scale is a constant, passed to DividingFunc.getInstance(double) method.
ExpFunc	Exponent function: f(x0) = bx0 (b is the base of the exponent).
Func	Abstract mathematical function f(x0, x1, ..., xn-1), or f(x), where x is a point of the n-dimensional space.
Func.Updatable	"Updatable" mathematical function: an extension of Func interface allowing assigning values to the function result, that leads to corresponding correction of arguments.
InverseNumberFunc	Inverse function: f(x0, x1, ..., xn-1) = c/x0 (c is some constant).
InverseNumberFunc.Updatable	Updatable extension of the inverse function.
LinearFunc	Linear function: f(x0, x1, ..., xn-1) = b + a0x0 + a1x1 +...+ an-1xn-1.
LinearFunc.Updatable	Updatable extension of the linear function with one argument.
LinearOperator	Linear operator (affine transformation): O f(x) = f(Ax + b), where the numeric n x n matrix A and the n-dimensional vector b are parameters of the transformation.
LogFunc	Logarithm function: f(x0) = logb(x0) (b is the base of the logarithm).
MaxFromTwoSelectedNumbersFunc	Maximum from 2 arguments, selected by 1st argument: f(x0, x1, ..., xn-1) = max(xi+1, xj+1), i=(int)x[0] (x0 cast to integer type), j=(i−1+indexShift)%(n−1)+1, where indexShift is an integer constant, passed to MaxFromTwoSelectedNumbersFunc.getInstance(int) method.
MinFromTwoSelectedNumbersFunc	Minimum from 2 arguments, selected by 1st argument: f(x0, x1, ..., xn-1) = min(xi+1, xj+1), i=(int)x[0] (x0 cast to integer type), j=(i−1+indexShift)%(n−1)+1, where indexShift is an integer constant, passed to MinFromTwoSelectedNumbersFunc.getInstance(int) method.
MultiplyingFunc	Product from several numbers: f(x0, x1, ..., xn-1) = scale*x0x1...xn-1, where scale is a constant, passed to MultiplyingFunc.getInstance(double) method.
Operator	Abstract operator: a transformation from one mathematical function to another.
PowerFunc	Power function: f(x0, x1) = scale*x0x1 or f(x0) = scale*x0c, where c and scale are constants.
PowerFunc.Updatable	Updatable extension of the power function with one argument.
ProjectiveOperator	Projective operator (projective transformation): O f(x) = f(y), yi = (aix + bi) / (cx + d) (ai means the line i of the matrix A), where the numeric n x n matrix A, the n-dimensional vectors b and c and the number d are parameters of the transformation.
RectangularFunc	Absolute value function: f(x0) = in if min<=x0<=max and f(x0) = out in other case, where min, max, in, out are parameters of this function.
SelectConstantFunc	Selecting constant function: f(x0, x1, ..., xn-1) = values[(int)x0], where values is the given array of constants.
WeightedMeanFunc	Weighted mean of 2 numbers: f(x0, x1, x2) = scale*x0x1 + (1-scale*x0)x2, where scale is a constant, passed to WeightedMeanFunc.getInstance(double) method.