Class Map1DFunction

java.lang.Object
   |
   +----Map1DFunction

public class Map1DFunction
extends Object

Class to return nf'th iterate of map function.
To be subclassed by specific functions, which must provide:

a method evaluateFunction(double x) to return the function which must map the interval 0 a method evaluateDerivative(double x) to return the derivative at x
an int variable nParameters giving the number of map parameters (1 or 2)
the initialization of a[nParamters] and aDefault[nParameters]

Optional parameters are:

double aMinimum giving a constant minimum value of a
double aMaximum giving a constant maximum value of a
boolean enforceARange true if the range is to be enforced (i.e. user cannot override it
double bMinimum giving a constant minimum value of b (if nParameters=2)
double bMaximum giving a constant maximum value of b
boolean enforceBRange true if the range is to be enforced
double x0Default giving the default value of the initial value of x
String title giving the name of the function to use as a graph title
double[] aDefault(nParameters] giving default values for the map parameters

Optional methods area:

getAMainmum(double d) gives the minimum value allowed for a (default returns aMinimum, but may be overridden.
getAMaximum(double d) gives the maximum value allowed for a (default returns aMaximum, but may be overridden.
boolean showWinding set to true if winding number to be displayed

a
array giving map paramters
aDefault
array giving default values of map parameters
aMaximum
maximum value of a
aMinimum
minimum value of a
bMaximum
maximum value of b
bMinimum
minimum value of b
enforceARange
true if the maximum is to be enforced
enforceBRange
true if the minimum is to be enforced
nParameters
number of map parameters (1 or 2)
showWinding
true if winding number to be shown
slope
accumulates the product of the slopes at the nf iteration points
title
the name of the function to use as a graph title
total
number of iterations contributing to winding
winding
winding number for circle map
windingAdd
set to zero in transients so winding number not updated
x0Default
the default value of the initial value of x

Map1DFunction()

evaluateDerivative(double)
evaluates the derivative of the map function at x
evaluateFunction(double)
evaluates map function
evaluateSlope(double)
iterates the map function nf times: calls evaluateDerivative and evaluates the product of the slopes
getAMaximum(double)
Returns the maximum value of a allowed (may depend on parameter d, usually the second map parameter).
getAMinimum(double)
Returns the minimum value of a allowed (may depend on parameter d, usually the second map parameter).
getNParameters()
Returnd the number of paraemters defining the map
iterate(double)
iterates the map function nf times: calls evaluateFunction
mod(double)
Shifts x to 0 setCompose(int)
Sets the compose value nf
setParameters(double[])
Sets the map paramters

nParameters
```
 int nParameters
```
number of map parameters (1 or 2)

a
```
 double a[]
```
array giving map paramters

aDefault
```
 double aDefault[]
```
array giving default values of map parameters

aMinimum
```
 double aMinimum
```
minimum value of a

aMaximum
```
 double aMaximum
```
maximum value of a

enforceARange
```
 boolean enforceARange
```
true if the maximum is to be enforced

bMinimum
```
 double bMinimum
```
minimum value of b

bMaximum
```
 double bMaximum
```
maximum value of b

enforceBRange
```
 boolean enforceBRange
```
true if the minimum is to be enforced

x0Default
```
 double x0Default
```
the default value of the initial value of x

title
```
 String title
```
the name of the function to use as a graph title

slope
```
 public double slope
```
accumulates the product of the slopes at the nf iteration points

winding
```
 public int winding
```
winding number for circle map

windingAdd
```
 public int windingAdd
```
set to zero in transients so winding number not updated

total
```
 public int total
```
number of iterations contributing to winding

showWinding
```
 public boolean showWinding
```
true if winding number to be shown

Map1DFunction
```
 public Map1DFunction()
```
setParameters
```
 public void setParameters(double parameters[])
```
Sets the map paramters

Parameters:
paramters - the array of input paramters

iterate
```
 public double iterate(double x)
```
iterates the map function nf times: calls evaluateFunction

Parameters:
x - input value
Returns:
iterated value

evaluateSlope
```
 public double evaluateSlope(double x)
```
iterates the map function nf times: calls evaluateDerivative and evaluates the product of the slopes

Parameters:
x - input value
Returns:
iterated value

evaluateFunction
```
 public double evaluateFunction(double x)
```
evaluates map function

Parameters:
x - input value

evaluateDerivative
```
 public double evaluateDerivative(double x)
```
evaluates the derivative of the map function at x

Parameters:
x - input value

setCompose
```
 public void setCompose(int inNf)
```
Sets the compose value nf

Parameters:
inNf - the input value of nf

getNParameters
```
 public int getNParameters()
```
Returnd the number of paraemters defining the map

Returns:
number of parameters

getAMaximum
```
 public double getAMaximum(double d)
```
Returns the maximum value of a allowed (may depend on parameter d, usually the second map parameter).

Returns:
maximum value of a

getAMinimum
```
 public double getAMinimum(double d)
```
Returns the minimum value of a allowed (may depend on parameter d, usually the second map parameter).

Returns:
minimum value of a

mod
```
 double mod(double x)
```
Shifts x to 0

Parameters:
x - input value
Returns:
value shifted to between 0 and 1