org.monte.media.math
Class LinearEquations

java.lang.Object
  org.monte.media.math.LinearEquations

public class LinearEquations
extends java.lang.Object

LinearEquations.

Reference: http://en.wikipedia.org/wiki/Cramer's_rule http://en.wikipedia.org/wiki/Determinant

Version:

$Id: LinearEquations.java 187 2012-03-28 11:49:30Z werner $

Author:

Werner Randelshofer

Method Summary

static double	det(double a, double b, double c, double d) Computes the determinant of a 3x3 matrix using Sarrus' rule.
static double	det(double a, double b, double c, double d, double e, double f, double g, double h, double i) Computes the determinant of a 2x2 matrix using Sarrus' rule.
static double[]	solve(double a, double b, double c, double d, double e, double f) Solves a linear system for x,y with cramer's rule.
static double[]	solve(double a, double b, double c, double d, double e, double f, double g, double h, double i, double j, double k, double l) Solves a linear system for x,y,z with cramer's rule.

Methods inherited from class java.lang.Object

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

Method Detail

solve

public static double[] solve(double a,
                             double b,
                             double c,
                             double d,
                             double e,
                             double f)

Solves a linear system for x,y with cramer's rule.

 a*x + b*y = e
 c*x + d*y = f
 

Parameters:

a -

b -

c -

d -

e -

f -

solve

public static double[] solve(double a,
                             double b,
                             double c,
                             double d,
                             double e,
                             double f,
                             double g,
                             double h,
                             double i,
                             double j,
                             double k,
                             double l)

Solves a linear system for x,y,z with cramer's rule.

 a*x + b*y + c*z = j
 d*x + e*y + f*z = k
 g*x + h*y + i*z = l
 

Parameters:

a -

b -

c -

d -

e -

f -

det

public static double det(double a,
                         double b,
                         double c,
                         double d,
                         double e,
                         double f,
                         double g,
                         double h,
                         double i)

Computes the determinant of a 2x2 matrix using Sarrus' rule.

 | a, b, c |     |e, f|   |d, f|   |d, e|
 | d, e, f | = a*|h, i|-b*|g, i|+c*|g, h|=aei+bfg+cdh-ceg-bdi-afh
 | g, h, i |
 

Parameters:

a -

b -

c -

d -

e -

f -

g -

h -

i -

Returns:

the determinant

det

public static double det(double a,
                         double b,
                         double c,
                         double d)

Computes the determinant of a 3x3 matrix using Sarrus' rule.

 | a, b |
 | c, d | = a*d - b*c
 

Parameters:

a -

b -

c -

d -

Returns:

the determinant