jhplot

Class F2D

java.lang.Object

jhplot.Plottable

jhplot.DrawOptions

jhplot.F2D

All Implemented Interfaces:

java.io.Serializable

public class F2D
extends DrawOptions

Create 2D function. The function may have up to 2 independent variables: x,y.

One can enabled fast math calculation using @see jhplot.HParam. For example, setting jhplot.HParam.setMath(true) makes calculation of elementary functions a factot 4-5 faster than using the standard Java Math, with precision of E-14.

Operators and functions

the following operators are supported:

• Addition: '2 + 2'
• Subtraction: '2 - 2'
• Multiplication: '2 * 2'
• Division: '2 / 2'
• Exponential: '2 ^ 2' or ** (raise to a power)
• Unary Minus,Plus (Sign Operators): '+2 - (-2)'
• Modulo: '2 % 2'

the following functions are supported:

• abs: absolute value
• acos: arc cosine
• asin: arc sine
• atan: arc tangent
• cbrt: cubic root
• ceil: nearest upper integer
• cos: cosine
• cosh: hyperbolic cosine
• exp: euler's number raised to the power (e^x)
• floor: nearest lower integer
• log: logarithm natural (base e)
• log10: logarithm (base 10)
• sin: sine
• sinh: hyperbolic sine
• sqrt: square root
• tan: tangent
• tanh: hyperbolic tangent

It also recognizes the pi (or Pi) values.

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor and Description
F2D(Expression calc, double Xmin, double Xmax, double Ymin, double Ymax) Create a function in 2D.
F2D(FProxy f) Initialize function from proxy.
F2D(IFunction iname) Create a F2D function from JAIDA IFunction.
F2D(IFunction iname, double Xmin, double Xmax, double Ymin, double Ymax) Create a F2D function from JAIDA IFunction.
F2D(java.lang.String name) Create a function in 2D for evaluation.
F2D(java.lang.String name, double Xmin, double Xmax, double Ymin, double Ymax) Build a 2D function.
F2D(java.lang.String title, Expression calc, double Xmin, double Xmax, double Ymin, double Ymax) Create a function in 2D.
F2D(java.lang.String title, IFunction iname, double Xmin, double Xmax, double Ymin, double Ymax) Create a F2D function from JAIDA IFunction.
F2D(java.lang.String title, java.lang.String name) Create new function.
F2D(java.lang.String title, java.lang.String name, double Xmin, double Xmax, double Ymin, double Ymax) Create a function in 2D.

Method Summary

Modifier and Type	Method and Description
void	doc() Show online documentation.
boolean	elementary() Convert this function rewrite in term of elementary functions (log, exp, frac, sqrt, implicit roots) This is useful before simplifying function.
double[][]	eval(double[] x, double[] y) Evaluate a function for an array of x-values
double	eval(double x, double y) Evaluate a function at a specific point in (x,y)
boolean	expand() Convert this function rewrite in expanded form.
boolean	factorize() Convert this function rewrite in factorized form (if can).
FProxy	get() Get the proxy of this function used for serialization and non-graphical representations.
java.lang.String	getException() If error occurs at some step, this is the way to retrieve it.
H2D	getH2D(java.lang.String hname, int hbinX, double hminX, double hmaxX, int hbinY, double hminY, double hmaxY) Generate a 2D histogram from the F2D function using a custom number of bins and given min and max values.
IFunction	getIFunction() Get Jaida function
double	getMaxX() Get Max value in X
double	getMaxY() Get Max value in Y
double	getMinX() Get Min value in X
double	getMinY() Get Min value in Y
java.lang.String	getName() Get the name of the function used for evaluation
Expression	getParse() Return parsed function.
int	getPoints() Get the number of points for evaluation of a function
double	integral() Integral using fastest trapezium rule method.
double	integral(double minX, double maxX, double minY, double maxY) Integral using fastest trapezium rule method.
double	integral(int N, double minX, double maxX, double minY, double maxY) Numerical integration using trapezium rule.
double	integral(int xSegs, int ySegs, double minX, double maxX, double minY, double maxY) Finds the volume under the surface described by the function f(x, y) for a <= x <= b, c <= y <= d.
boolean	isParsed() If the function is parsed correctly, return true.
boolean	numeric() Perform some numeric substitutions.
boolean	parse() Parse the function.
void	setMaxX(double max) Set Max value in X
void	setMaxY(double max) Set Max value in Y
void	setMinX(double min) Set Min in X
void	setMinY(double min) Set Min value in Y
void	setName(java.lang.String name) Sets a name of the function, i.e.
void	setPar(java.lang.String parameter, double value) Replace abstract parameter with the value (double).
void	setPoints(int bins) Set the number of points
boolean	simplify() Try to simplify this function.
java.lang.String	toJava() Convert the function into Java code.
java.lang.String	toMathML() Convert the function into MathML form.
java.lang.String	toString() Get this function as a string.

Methods inherited from class jhplot.DrawOptions

copyLinePars, getBinWidth, getColor, getDrawOption, getDrawOptions, getFillColor, getLegend, getLineParm, getLineStyle, getNameX, getNameY, getNameZ, getPenWidth, getSymbol, getSymbolShape, getSymbolSize, getTitle, getType, isBars, isErrX, isErrY, isFilled, printDrawOptions, printDrawOptions, setBars, setBinWidth, setColor, setDrawLine, setDrawLineKey, setDrawOption, setDrawSymbol, setErr, setErrAll, setErrColor, setErrColor, setErrColorX, setErrColorY, setErrFill, setErrFillColor, setErrFillColor, setErrSys, setErrSysFill, setErrSysFillColor, setErrSysFillColor, setErrSysX, setErrSysY, setErrTicSize, setErrX, setErrY, setFill, setFillColor, setFillColorTransparency, setGraphStyle, setLegend, setLineStyle, setNameX, setNameY, setNameZ, setPenDash, setPenDash, setPenWidth, setPenWidthErr, setPenWidthErrSys, setStyle, setSymbol, setSymbol, setSymbolSize, setTitle, setType

Methods inherited from class jhplot.Plottable

getLabelX, getLabelY, getLabelZ, is3D, set3D, setLabelX, setLabelY, setLabelZ

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

F2D

public F2D(java.lang.String name)

Create a function in 2D for evaluation. The function is not in range. The function may have up to 2 independent variables: x,y.

Operators and functions

the following operators are supported:

• Addition: '2 + 2'
• Subtraction: '2 - 2'
• Multiplication: '2 * 2'
• Division: '2 / 2'
• Exponential: '2 ^ 2' or ** (raise to a power)
• Unary Minus,Plus (Sign Operators): '+2 - (-2)'
• Modulo: '2 % 2'

the following functions are supported:

• abs: absolute value
• acos: arc cosine
• asin: arc sine
• atan: arc tangent
• cbrt: cubic root
• ceil: nearest upper integer
• cos: cosine
• cosh: hyperbolic cosine
• exp: euler's number raised to the power (e^x)
• floor: nearest lower integer
• log: logarithm natural (base e)
• sin: sine
• sinh: hyperbolic sine
• sqrt: square root
• tan: tangent
• tanh: hyperbolic tangent

It also recognizes the pi (or Pi) values.

Parameters:

name - String representing the function

F2D

public F2D(java.lang.String title,
           java.lang.String name)

Create new function.

Parameters:

title - title

name - definition

F2D

public F2D(java.lang.String title,
           java.lang.String name,
           double Xmin,
           double Xmax,
           double Ymin,
           double Ymax)

Create a function in 2D. This is a ranged function. Uses 200 points between min and max value for evaluation. The function may have up to 2 independent variables in it (x,y). Operators and functions

the following operators are supported:

• Addition: '2 + 2'
• Subtraction: '2 - 2'
• Multiplication: '2 * 2'
• Division: '2 / 2'
• Exponential: '2 ^ 2' or ** (raise to a power)
• Unary Minus,Plus (Sign Operators): '+2 - (-2)'
• Modulo: '2 % 2'

the following functions are supported:

• abs: absolute value
• acos: arc cosine
• asin: arc sine
• atan: arc tangent
• cbrt: cubic root
• ceil: nearest upper integer
• cos: cosine
• cosh: hyperbolic cosine
• exp: euler's number raised to the power (e^x)
• floor: nearest lower integer
• log: logarithm natural (base e)
• sin: sine
• sinh: hyperbolic sine
• sqrt: square root
• tan: tangent
• tanh: hyperbolic tangent

Parameters:

name - String representing the function.

Xmin - Min value in X

Xmax - Max value in X

Ymin - Min value in Y

Ymax - Max value in Y

F2D

public F2D(java.lang.String name,
           double Xmin,
           double Xmax,
           double Ymin,
           double Ymax)

Build a 2D function. Title is set to the name. This is ranged function.

Parameters:

name - Name

Xmin - X-min

Xmax - X-max

Ymin - Y-min

Ymax - Y-max

F2D

public F2D(java.lang.String title,
           IFunction iname,
           double Xmin,
           double Xmax,
           double Ymin,
           double Ymax)

Create a F2D function from JAIDA IFunction. By default, 500 points for evaluation are used. Ranged function.

Parameters:

title - Title

name - new function name

iname - input IFunction

Xmin - Min X value

Xmax - Max X value

Ymin - Min Y value

Ymax - Max Y value

F2D

public F2D(java.lang.String title,
           Expression calc,
           double Xmin,
           double Xmax,
           double Ymin,
           double Ymax)

Create a function in 2D. 500 points are used between Min and Max for evaluation. The function may have x as independent variable. Make sure that expression has 2 variables, x and y.

Parameters:

title - Title

function - Expression after parsing and building

Xmin - Min X value

Xmax - Max X value

Ymin - Min Y value

Ymax - Max Y value

F2D

public F2D(Expression calc,
           double Xmin,
           double Xmax,
           double Ymin,
           double Ymax)

Create a function in 2D. 200 points are used between Min and Max for evaluation. The function may have x as independent variable. Make sure that expression has 2 variables, x and y.

Parameters:

title - Title

function - Expression after parsing and building

Xmin - Min X value

Xmax - Max X value

Ymin - Min Y value

Ymax - Max Y value

F2D

public F2D(IFunction iname)

Create a F2D function from JAIDA IFunction. By default, 500 points for evaluation are used. Unranged function.

Parameters:

iname -

F2D

public F2D(FProxy f)

Initialize function from proxy.

Parameters:

f -

F2D

public F2D(IFunction iname,
           double Xmin,
           double Xmax,
           double Ymin,
           double Ymax)

Create a F2D function from JAIDA IFunction.

Parameters:

iname - input IFunction

Xmin - Min X value

Xmax - Max X value

Ymin - Min Y value

Ymax - Max Y value

Method Detail

eval

public double eval(double x,
                   double y)

Evaluate a function at a specific point in (x,y)

Parameters:

x - value in x for evaluation

y - value in y for evaluation

Returns:

function value at (x,y)

getIFunction

public IFunction getIFunction()

Get Jaida function

Returns:

eval

public double[][] eval(double[] x,
                       double[] y)

Evaluate a function for an array of x-values

Parameters:

x - array of values in x for evaluation

y - array of values in y for evaluation

Returns:

array of function values

setMinX

public void setMinX(double min)

Set Min in X

Parameters:

min - Min value

parse

public boolean parse()

Parse the function.

Returns:

true if parsed without problems.

getMinX

public double getMinX()

Get Min value in X

Returns:

Min value in X

setMinY

public void setMinY(double min)

Set Min value in Y

Parameters:

min - Min value in Y

doc

public void doc()

Show online documentation.

getMinY

public double getMinY()

Get Min value in Y

Returns:

Min value in Y

setMaxX

public void setMaxX(double max)

Set Max value in X

Parameters:

max - Max value in X

setName

public void setName(java.lang.String name)

Sets a name of the function, i.e. what will be used for evaluation

Parameters:

name - Name

getName

public java.lang.String getName()

Get the name of the function used for evaluation

Returns:

Name

getMaxX

public double getMaxX()

Get Max value in X

Returns:

Max value in X

setMaxY

public void setMaxY(double max)

Set Max value in Y

Parameters:

max - Max value in Y

getMaxY

public double getMaxY()

Get Max value in Y

Returns:

Max value in Y

setPoints

public void setPoints(int bins)

Set the number of points

Parameters:

bins - Number of points

setPar

public void setPar(java.lang.String parameter,
                   double value)

Replace abstract parameter with the value (double). Case sensitive!

Parameters:

parameter - parameter name

value - value to be inserted

getPoints

public int getPoints()

Get the number of points for evaluation of a function

Returns:

Number of points

integral

public double integral(int N,
                       double minX,
                       double maxX,
                       double minY,
                       double maxY)

Numerical integration using trapezium rule.

Parameters:

N - the number of strips to use for integration (in X and Y the same)

minX - the first ordinate in X.

maxX - the last ordinate in X.

minY - the first ordinate in X.

maxY - the last ordinate in Y.

Returns:

integral

integral

public double integral(double minX,
                       double maxX,
                       double minY,
                       double maxY)

Integral using fastest trapezium rule method. It uses the default number of points (500).

Parameters:

minX - the first ordinate in X.

maxX - the last ordinate in X.

minY - the first ordinate in X.

maxY - the last ordinate in Y.

simplify

public boolean simplify()

Try to simplify this function. It is often useful to rewrite an expression in term of elementary functions (log, exp, frac, sqrt, implicit roots), using the "elementary()" before simplifying it. Retrieve the simplified name as a string using getName() method.

Returns:

false if error occurs. Retrieve this error as a string using getException().

getException

public java.lang.String getException()

If error occurs at some step, this is the way to retrieve it.

Returns:

last exception happened in any method of this class.

getParse

public Expression getParse()

Return parsed function. One can evaluate it as "calculate()".

Returns:

function

getH2D

public H2D getH2D(java.lang.String hname,
                  int hbinX,
                  double hminX,
                  double hmaxX,
                  int hbinY,
                  double hminY,
                  double hmaxY)

Generate a 2D histogram from the F2D function using a custom number of bins and given min and max values.

Parameters:

hname - histogram name

hbinX - number of X bins

hminX - min value in X

hmaxX - max value in X

hbinY - number of bins in Y

hminY - min value in Y

hmaxY - max value in Y

Returns:

2D histogram from the function

integral

public double integral()

Integral using fastest trapezium rule method. This function return non-zero if it the range was defined during the initialization. The default number of points is 500. Increase it if needed more precision.

Returns:

integral in the range defined during the initialization.

integral

public double integral(int xSegs,
                       int ySegs,
                       double minX,
                       double maxX,
                       double minY,
                       double maxY)

Finds the volume under the surface described by the function f(x, y) for a <= x <= b, c <= y <= d. It uses the trapezoid rule. Using xSegs number of segments across the x axis and ySegs number of segments across the y axis.

Parameters:

xSegs - The number of segments in the x axis.

ySegs - The number of segments in the y axis.

minX - The lower bound of x.

maxX - The upper bound of x.

minX - The lower bound of y.

maxY - The upper bound of y.

Returns:

The volume under the function f(x, y).

isParsed

public boolean isParsed()

If the function is parsed correctly, return true. Use this check before drawing it.

Returns:

true if parsed.

toMathML

public java.lang.String toMathML()

Convert the function into MathML form.

Returns:

String representing this function in MathML.

toJava

public java.lang.String toJava()

Convert the function into Java code.

Returns:

String representing this function in Java.

elementary

public boolean elementary()

Convert this function rewrite in term of elementary functions (log, exp, frac, sqrt, implicit roots) This is useful before simplifying function. Retrieve the simplified name as a string using getName() method.

Returns:

false if error occurs. Retrieve this error as a string using getException().

expand

public boolean expand()

Convert this function rewrite in expanded form. Retrieve the expanded name as a string using getName() method.

Returns:

false if error occurs. Retrieve this error as a string using getException().

factorize

public boolean factorize()

Convert this function rewrite in factorized form (if can). Retrieve the expanded name as a string using getName() method.

Returns:

false if error occurs. Retrieve this error as a string using getException().

numeric

public boolean numeric()

Perform some numeric substitutions. Examples: exp(1) should be 2.71828182, "pi" should be 3.14159 etc. Retrieve the expanded name as a string using getName() method.

Returns:

false if error occurs. Retrieve this error as a string using getException().

get

public FProxy get()

Get the proxy of this function used for serialization and non-graphical representations.

Parameters:

proxy - proxy of this function.

toString

public java.lang.String toString()

Get this function as a string.

Overrides:

toString in class java.lang.Object

Returns:

Convert to string.