jabble
Class MathUtils

java.lang.Object
  jabble.MathUtils

public class MathUtils
extends java.lang.Object

A toolkit class containing a set of mathematical functions typically used for initial conditions (gaussian, pulse, step, ...).

Method Summary

static double	gaussian(double x, double centerX, double width) 1D gaussian, centered on centerX and with the specified width.
static double	gaussian(double x, double y, double centerX, double centerY, double width) 2D gaussian, centered on centerX/Y and with the specified width.
static double	gaussian(double x, double y, double z, double centerX, double centerY, double centerZ, double width) 3D gaussian, centered on centerX/Y/Z and with the specified width.
static double	module(double a, double b) Returns the modulus from the two components.
static double	module2(double a, double b) Returns the modulus square of a complex number given the real and imaginary part.
static double	modulus(double... components) Calculates the modulus given the components of a vector.
static double	phase(double a, double b) Returns the phase of a complex number given the real and imaginary part.
static double	phaseDiff(double theta1, double theta2) Returns the difference of the two angles, taking into account periodicity.
static double	reverseStep(double x, double stepX) Reverse step function, returns 1.0 before stepX and 1.0 afterwards.
static double	squarePulse(double x, double lowerX, double upperX) 1D pulse, returns 1.0 within the range and 0.0 outside.
static double	squarePulse(double x, double y, double lowerX, double upperX, double lowerY, double upperY) 2D pulse, returns 1.0 within the range and 0.0 outside.
static double	squarePulse(double x, double y, double z, double lowerX, double upperX, double lowerY, double upperY, double lowerZ, double upperZ) 3D pulse, returns 1.0 within the range and 0.0 outside.
static double	step(double x, double stepX) Step funtion, returns 0.0 before stepX and 1.0 afterwards.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

phase

public static double phase(double a,
                           double b)

Returns the phase of a complex number given the real and imaginary part.

Parameters:

a - real part of a complex number

b - imaginary part of a complex number

Returns:

the phase of a complex number

module2

public static double module2(double a,
                             double b)

Returns the modulus square of a complex number given the real and imaginary part.

Parameters:

a - real part of a complex number

b - imaginary part of a complex number

Returns:

the modulus square

module

public static double module(double a,
                            double b)

Returns the modulus from the two components.

Parameters:

a - real part of a complex number

b - imaginary part of a complex number

Returns:

the modulus

modulus

public static double modulus(double... components)

Calculates the modulus given the components of a vector.

Parameters:

components - the components

Returns:

the modulus

phaseDiff

public static double phaseDiff(double theta1,
                               double theta2)

Returns the difference of the two angles, taking into account periodicity.

Parameters:

theta1 - an angle

theta2 - anothe angle

Returns:

the difference between the two

gaussian

public static double gaussian(double x,
                              double y,
                              double z,
                              double centerX,
                              double centerY,
                              double centerZ,
                              double width)

3D gaussian, centered on centerX/Y/Z and with the specified width.

Parameters:

x - coordinate x

y - coordinate y

z - coordinate z

centerX - center of the gaussian on x

centerY - center of the gaussian on y

centerZ - center of the gaussian on z

width - width of the gaussian in all directions

Returns:

the value of the function at the given coordinates

gaussian

public static double gaussian(double x,
                              double y,
                              double centerX,
                              double centerY,
                              double width)

2D gaussian, centered on centerX/Y and with the specified width.

Parameters:

x - coordinate x

y - coordinate y

centerX - center of the gaussian on x

centerY - center of the gaussian on y

width - width of the gaussian in all directions

Returns:

the value of the function at the given coordinates

gaussian

public static double gaussian(double x,
                              double centerX,
                              double width)

1D gaussian, centered on centerX and with the specified width.

Parameters:

x - coordinate x

centerX - center of the gaussian on x

width - width of the gaussian in all directions

Returns:

the value of the function at the given coordinates

squarePulse

public static double squarePulse(double x,
                                 double lowerX,
                                 double upperX)

1D pulse, returns 1.0 within the range and 0.0 outside.

Parameters:

x - coordinate x

lowerX - lower boundary for the pulse

upperX - upper boundary for the pulse

Returns:

the value of the function at the given coordinates

squarePulse

public static double squarePulse(double x,
                                 double y,
                                 double lowerX,
                                 double upperX,
                                 double lowerY,
                                 double upperY)

2D pulse, returns 1.0 within the range and 0.0 outside.

Parameters:

x - coordinate x

y - coordinate y

lowerX - lower boundary for the pulse on x

upperX - upper boundary for the pulse on x

lowerY - lower boundary for the pulse on y

upperY - upper boundary for the pulse on y

Returns:

the value of the function at the given coordinates

squarePulse

public static double squarePulse(double x,
                                 double y,
                                 double z,
                                 double lowerX,
                                 double upperX,
                                 double lowerY,
                                 double upperY,
                                 double lowerZ,
                                 double upperZ)

3D pulse, returns 1.0 within the range and 0.0 outside.

Parameters:

x - coordinate x

y - coordinate y

z - coordinate z

lowerX - lower boundary for the pulse on x

upperX - upper boundary for the pulse on x

lowerY - lower boundary for the pulse on y

upperY - upper boundary for the pulse on y

lowerZ - lower boundary for the pulse on z

upperZ - upper boundary for the pulse on z

Returns:

the value of the function at the given coordinates

step

public static double step(double x,
                          double stepX)

Step funtion, returns 0.0 before stepX and 1.0 afterwards.

Parameters:

x - coordinate x

stepX - value at which the function changes

Returns:

the value of the function at the given coordinates

reverseStep

public static double reverseStep(double x,
                                 double stepX)

Reverse step function, returns 1.0 before stepX and 1.0 afterwards.

Parameters:

x - coordinate x

stepX - value at which the function changes

Returns:

the value of the function at the given coordinates