jhplot

Class F1D

java.lang.Object

jhplot.Plottable

jhplot.DrawOptions

jhplot.F1D

All Implemented Interfaces:

Serializable

public class F1D
extends DrawOptions

Create a function in one dimension using "x" as a variable. The function name could have parameters named in unique way as P0, P1, P2. In this case, the function should not be parsed. Parameters have to be replaced with values using setPar(x) method for evaluation. The function may have one independent variable: x

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
F1D(Expression calc) Create a function in 1D.
F1D(ExpressionBuilder function) Build a function.
F1D(Expression calc, double min, double max) Create a function from the expression.
F1D(FProxy f) Initialize function from proxy.
F1D(hep.aida.IFunction iname) Create a F1D function from JAIDA IFunction.
F1D(hep.aida.IFunction iname, double min, double max) Create a F1D function from JAIDA IFunction in ranges.
F1D(String name) Create a function in 1D.
F1D(String name, boolean parse) Build a function.
F1D(String title, double[] pars, boolean parse) Create a polynomial analytical function using a list of values.
F1D(String name, double min, double max) Create a new function in pre-defined range for plotting.
F1D(String name, double min, double max, boolean parsed) Define a ranged function.
F1D(String title, Expression calc) Create a function in 1D.
F1D(String title, ExpressionBuilder function) Create a function in 1D.
F1D(String title, Expression calc, double min, double max) Create a function in 1D.
F1D(String title, hep.aida.IFunction iname) Create F1D function from JAIDA IFunction.
F1D(String title, hep.aida.IFunction iname, double min, double max) Create F1D function from JAIDA IFunction.
F1D(String title, String name) Create new function.
F1D(String title, String name, boolean parsed) Create a new function in pre-defined range for plotting.
F1D(String title, String name, double min, double max) Create a new function.
F1D(String title, String name, double min, double max, boolean parse) Create a new function.

Method Summary

Modifier and Type	Method and Description
double[]	differentiate() Numerical differentiation of a function.
double[]	differentiate(int N, double min, double max) Numerical differentiation.
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.
void	eval() Evaluate a function for graphic representation.
double	eval(double x) Evaluate a function at a specific point in x
double[]	eval(double[] x) Evaluate a function for an array of x-values
void	eval(double xMin, double xMax) Evaluate a function for graphic representation.
void	eval(double min, double max, int Npoints) Evaluate a function for graphic representation.
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.
double[]	getArrayX() Get array of X-values after function after evaluation using the default number of points
double[]	getArrayY() Get array of Y-values after function after evaluation using the default number of points
String	getException() If error occurs at some step, this is the way to retrieve it.
H1D	getH1D() Return H1D histogram from F1D function.
H1D	getH1D(double min, double max) Return H1D histogram from F1D function.
H1D	getH1D(String hname, int bins, double hmin, double hmax) Return a Histogram given by the F1D function.
hep.aida.IFunction	getIFunction() Get Jaida function
double	getMax() Get the maximum value in X
double	getMin() Get the minimum value in X
String	getName() Get the name of the function used for evaluation
Expression	getParse() Return parsed function.
int	getPoints() Get the number of points used for plotting, integration and differentiation.
double	getX(int i) Get value in X-axis
double	getY(int i) Get value in Y-axis
double	integral() Integral using fastest trapezium rule method.
double	integral(double min, double max) Integral using fastest trapezium rule method.
double	integral(int N, double min, double max) Numerical integration using trapezium rule.
double	integral(String type, int N, double min, double max) Numerical integration.
boolean	isParsed() If the function is parsed correctly, return true.
boolean	numeric() Perform some numeric substitutions.
boolean	parse() Parse the function.
void	set(FProxy f) Set proxy function
void	setMax(double max) Set the maximum value in X
void	setMin(double min) Set Min value in X
void	setName(String name) Sets a name of the function, i.e.
void	setPar(String parameter, double value) Replace abstract parameter with the value (double).
void	setPar(String parameter, int value) Replace abstract parameter with the value (integer).
void	setPoints(int bins) Sets the number points between Min and Max for evaluation
boolean	simplify() Try to simplify this function.
String	toJava() Convert the function into Java code.
String	toMathML() Convert the function into MathML form.
String	toString() Get this function as a string.
void	toTable() Print the F1D function to a Table in a separate Frame.

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

F1D

public F1D(String name)

Create a function in 1D. 500 points are used between Min and Max for evaluation. The title is set to the function's definition.

A function can be ranged (range min and max is included) or unranged (min and max are not defined). Ranged function determines the plot ranges, integration range etc. The function may have one independent variable: x. Example: x*x 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's definition

F1D

public F1D(FProxy f)

Initialize function from proxy.

Parameters:

f -

F1D

public F1D(String title,
           String name)

Create new function. The function is unranged (nor range is defined).

Parameters:

title - title

name - definition

F1D

public F1D(String title,
           String name,
           double min,
           double max)

Create a new function. Do not parse it when using parameters. You should apply substitution first and create a function with one variable "x". If min=0 and max=0, the ranges are determined by plotting canvases. The function is ranged. The function is parsed. The function may have one independent variable: x

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 10 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:

title - title

name - definition

min - minimum value for plotting

max - maximum value for plotting

F1D

public F1D(String name,
           double min,
           double max,
           boolean parsed)

Define a ranged function.

Parameters:

name - name

min - min value

max - max value

parsed - is parsed?

F1D

public F1D(String title,
           hep.aida.IFunction iname,
           double min,
           double max)

Create F1D function from JAIDA IFunction. By default 500 points are used. The function is ranged.

Parameters:

title - Title

iname - input IFunction

min - Min X values

max - Max X values

F1D

public F1D(String title,
           String name,
           double min,
           double max,
           boolean parse)

Create a new function. Do not parse it when using parameters. You should apply substitution first and create a function with one variable "x". If min=0 and max=0, the ranges are determined by plotting canvases. The function is ranged. The function may have one independent variable: x

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 10 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:

title - title

name - definition

min - minimum value for plotting

max - maximum value for plotting

parse - parse or not. Do not parse when using parameters.

F1D

public F1D(hep.aida.IFunction iname,
           double min,
           double max)

Create a F1D function from JAIDA IFunction in ranges. By default, 500 points for evaluation are used

Parameters:

iname - input IFunction

min - Min value

max - Max value

F1D

public F1D(String name,
           double min,
           double max)

Create a new function in pre-defined range for plotting. Do not parse it when using parameters. You should apply substitution first and create a function with one variable "x". If min=0 and max=0, ranges are determined by plotting canvaces. The function may have one independent variable: x

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 10 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 - definition

min - min value for plotting

max - max value for plotting

parse - parse or not. Do not parse when using parameters.

F1D

public F1D(String title,
           String name,
           boolean parsed)

Create a new function in pre-defined range for plotting. Do not parse it when using parameters. You should apply substitution first and create a function with one variable "x". Ranges for the function are not defined. The function may have one independent variable: x

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 10 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:

title - title

name - definition

parse - parse or not. Do not parse when using parameters.

F1D

public F1D(String title,
           double[] pars,
           boolean parse)

Create a polynomial analytical function using a list of values. Example: pars[0]+pars[1]*x+pars[2]*x*x +pars[3]*x*x*x

Parameters:

title - Title of this function

pars - array of coefficients for polynomial function

parse - set true if it should be parsed

F1D

public F1D(String name,
           boolean parse)

Build a function. The function may have one independent variable: x. Function can have parameters, in which case set parsing to false. You can parse this function later after substitution of numeric parameter.

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 - name

parse - is parsed or not?

F1D

public F1D(String title,
           ExpressionBuilder function)

Create a function in 1D. 500 points are used between Min and Max for evaluation. The function may have x as independent variable.

Parameters:

title - Title

function - ExpressionBuilder

min - Min value

max - Max value

F1D

public F1D(Expression calc,
           double min,
           double max)

Create a function from the expression. The function is in the range.

Parameters:

calc - expression

min - Min value

max - Max value

F1D

public F1D(String title,
           Expression calc,
           double min,
           double max)

Create a function in 1D. 500 points are used between Min and Max for evaluation. The function may have x as independent variable.

Parameters:

title - Title

function - Expression after parsing and building

F1D

public F1D(String title,
           Expression calc)

Create a function in 1D. 500 points are used between Min and Max for evaluation. The function may have x as independent variable.

Parameters:

title - Title

function - Expression after parsing and building

F1D

public F1D(Expression calc)

Create a function in 1D. The function may have x as independent variable.

Parameters:

function - expression

F1D

public F1D(ExpressionBuilder function)

Build a function.

Parameters:

function - input of expression

F1D

public F1D(hep.aida.IFunction iname)

Create a F1D function from JAIDA IFunction. By default, 500 points for evaluation are used. No ranges are set.

Parameters:

iname - input IFunction

F1D

public F1D(String title,
           hep.aida.IFunction iname)

Create F1D function from JAIDA IFunction. By default 500 points are used

Parameters:

title - Title

iname - input IFunction

min - Min X values

max - Max X values

Method Detail

get

public FProxy get()

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

Parameters:

proxy - proxy of this function.

parse

public boolean parse()

Parse the function.

Returns:

true if parsed without problems.

eval

public double eval(double x)

Evaluate a function at a specific point in x

Parameters:

x - value in x for evaluation

Returns:

function value at x

eval

public double[] eval(double[] x)

Evaluate a function for an array of x-values

Parameters:

x - array of values in x for evaluation

Returns:

array of function values

eval

public void eval(double xMin,
                 double xMax)

Evaluate a function for graphic representation. Number of points for evaluations is 500.

Parameters:

XMin - value in x

XMax - value in x

eval

public void eval()

Evaluate a function for graphic representation. The function is assumed to me ranged (the range is defined during the initialization).

eval

public void eval(double min,
                 double max,
                 int Npoints)

Evaluate a function for graphic representation. Number of points for evaluations is 500.

Parameters:

Min - value in x

Max - value in x

Number - of evaluation points

doc

public void doc()

Show online documentation.

toTable

public void toTable()

Print the F1D function to a Table in a separate Frame. The numbers are formatted to scientific format. One can sort and search the data in this table (data cannot be modified)

Parameters:

min -

max -

setPar

public void setPar(String parameter,
                   double value)

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

Parameters:

parameter - parameter name

value - value to be inserted

getH1D

public H1D getH1D()

Return H1D histogram from F1D function. The number of points are given by setPoints() method, but the default 500 is used if not given. Min and Max values are given during the function initialisation (ranged function) The number of points is 500 by default.

Returns:

histogram

getH1D

public H1D getH1D(double min,
                  double max)

Return H1D histogram from F1D function. The number of points are given by setPoints() method, but the default 500 is used if not given. Min and Max values are given by the values used to parse the function.

Parameters:

min - value

max - value

Returns:

histogram

getH1D

public H1D getH1D(String hname,
                  int bins,
                  double hmin,
                  double hmax)

Return a Histogram given by the F1D function. All statistical characteristics of such histogram are meaningless. Bins and Min and Max values are user defined. The function is evaluated at the bin center which is important for small number of bins.

Parameters:

hname - Name of the histogram

bins - number of bins for histogram

hmin - min value of histogram

hmax - max value of histogram

Returns:

H1D histogram

setPar

public void setPar(String parameter,
                   int value)

Replace abstract parameter with the value (integer). Case sensitive. You will need to call parse() to finish this function.

Parameters:

parameter - parameter name

value - integer value to be inserted.

getX

public double getX(int i)

Get value in X-axis

Parameters:

i - index

Returns:

value in X

getY

public double getY(int i)

Get value in Y-axis

Parameters:

i - index

Returns:

value in Y

setName

public void setName(String name)

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

Parameters:

name - Name

getName

public String getName()

Get the name of the function used for evaluation

Returns:

Name

getParse

public Expression getParse()

Return parsed function. One can evaluate Y as: y =function.getResult(x), where function is what returned by this method.

Returns:

function

setPoints

public void setPoints(int bins)

Sets the number points between Min and Max for evaluation

Parameters:

bins - Number of points

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 pecision.

Returns:

integral in the range defined during the initisliazation.

integral

public double integral(double min,
                       double max)

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

Parameters:

min - the first ordinate.

max - the last ordinate.

integral

public double integral(String type,
                       int N,
                       double min,
                       double max)

Numerical integration. Define types as:
type="gauss4" - Gaussian integration formula (4 points)
type="gauss8" - Gaussian integration formula (8 points)
type="richardson" - Richardson extrapolation
type="simpson" - using Simpson's rule.
type="trapezium" - trapezium rule.

Parameters:

type - type of algorithm. Can be: "gauss4","gauss8","richardson","simpson","trapezium".

N - the number of strips to use for integration

min - the first ordinate.

max - the last ordinate.

Returns:

integral

integral

public double integral(int N,
                       double min,
                       double max)

Numerical integration using trapezium rule.

Parameters:

N - the number of strips to use for integration

min - the first ordinate.

max - the last ordinate.

Returns:

integral

getIFunction

public hep.aida.IFunction getIFunction()

Get Jaida function

Returns:

getArrayX

public double[] getArrayX()

Get array of X-values after function after evaluation using the default number of points

Returns:

X-values

getArrayY

public double[] getArrayY()

Get array of Y-values after function after evaluation using the default number of points

Returns:

Y-values

isParsed

public boolean isParsed()

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

Returns:

true if parsed.

toMathML

public String toMathML()

Convert the function into MathML form.

Returns:

String representing this function in MathML.

toJava

public String toJava()

Convert the function into Java code.

Returns:

String representing this function in Java.

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().

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().

differentiate

public double[] differentiate(int N,
                              double min,
                              double max)

Numerical differentiation.

Parameters:

N - the number of points to use.

min - the first ordinate.

max - the last ordinate.

Returns:

array with differentials

differentiate

public double[] differentiate()

Numerical differentiation of a function. Range of the function is given during the initisalisation (ranged function)

Returns:

array with differentials

getPoints

public int getPoints()

Get the number of points used for plotting, integration and differentiation.

Returns:

Number of points

getException

public 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.

setMin

public void setMin(double min)

Set Min value in X

Parameters:

min - Minimum value

getMin

public double getMin()

Get the minimum value in X

Returns:

min Minimum value

setMax

public void setMax(double max)

Set the maximum value in X

Parameters:

max - Maximal value

set

public void set(FProxy f)

Set proxy function

Parameters:

f -

getMax

public double getMax()

Get the maximum value in X

Returns:

Maximal value

toString

public String toString()

Get this function as a string.

Overrides:

toString in class Object

Returns:

Convert to string.