uk.ac.starlink.ttools.plot
Class Matrices

java.lang.Object
  uk.ac.starlink.ttools.plot.Matrices

public class Matrices
extends Object

Utility class for linear algebra in 3-dimensional space. The array arguments to the methods here are either 3-element arrays representing 3-d vectors

    ( v[0], v[1], v[2] )
 

or 9-element arrays representing 3-d matrices:

    ( m[0], m[1], m[2],
      m[3], m[4], m[5],
      m[6], m[7], m[8] )
 

Since:

25 Nov 2005

Author:

Mark Taylor

Constructor Summary

Matrices()

Method Summary

static double[]	adj(double[] m) Calculates the adjoint of a matrix.
static double[]	cross(double[] a, double[] b) Calculates the vector (cross) product of two vectors.
static double	det(double[] m) Calculates the determinant of a matrix.
static double	dot(double[] a, double[] b) Calclulates the scalar (dot) product of two vectors.
static double[]	fromPal(double[][] m) Converts a 3-d matrix from Pal-friendly form (3x3) to the form used elsewhere in this class (flat 9-element array).
static double[]	invert(double[] m) Inverts a matrix.
static double[]	mmMult(double[] a, double[] b) Multiplies two matrices together.
static double	mod(double[] v) Calculates the modulus of a vector.
static double[]	mult(double[] v, double c) Multiplies a vector by a constant.
static double[]	mvMult(double[] m, double[] v) Multiplies a matrix by a vector.
static double[]	normalise(double[] v) Normalises a vector.
static double[][]	toPal(double[] m) Converts a 3-d matrix from the form used in this class (flat 9-element array) to Pal-friendly form (3x3).
static String	toString(double[] a) Returns a string giving the contents of an arbitrary length vector.
static double[]	transpose(double[] a) Returns the transpose of a 3x3 matrix.
static double[]	unit(int iaxis) Returns a unit vector along an indicated axis.

Methods inherited from class java.lang.Object

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

Constructor Detail

Matrices

public Matrices()

Method Detail

adj

public static double[] adj(double[] m)

Calculates the adjoint of a matrix.

Parameters:

m - input matrix as 9-element array

Returns:

adj(m) as 9-element array

det

public static double det(double[] m)

Calculates the determinant of a matrix.

Parameters:

m - input matrix as 9-element array

Returns:

det(m)

invert

public static double[] invert(double[] m)

Inverts a matrix.

Parameters:

m - input matrix as 9-element array

Returns:

m^-1 as 9-element array

dot

public static double dot(double[] a,
                         double[] b)

Calclulates the scalar (dot) product of two vectors.

Parameters:

a - vector 1

b - vector 2

Returns:

a.b

cross

public static double[] cross(double[] a,
                             double[] b)

Calculates the vector (cross) product of two vectors.

Parameters:

a - vector 1

b - vector 2

Returns:

a x b

transpose

public static double[] transpose(double[] a)

Returns the transpose of a 3x3 matrix.

Parameters:

a - input matrix

Returns:

transpose of a

unit

public static double[] unit(int iaxis)

Returns a unit vector along an indicated axis.

Parameters:

iaxis - index of axis (0, 1 or 2)

Returns:

unit vector iaxis

mod

public static double mod(double[] v)

Calculates the modulus of a vector.

Parameters:

v - input vector

Returns:

|v|

normalise

public static double[] normalise(double[] v)

Normalises a vector.

Parameters:

v - input vector

Returns:

|v|

mult

public static double[] mult(double[] v,
                            double c)

Multiplies a vector by a constant.

Parameters:

v - vector of arbitrary length

c - constant factor

Returns:

v * c

mvMult

public static double[] mvMult(double[] m,
                              double[] v)

Multiplies a matrix by a vector.

Parameters:

m - input matrix as 9-element array

v - input vector as 3-element array

Returns:

m * v

mmMult

public static double[] mmMult(double[] a,
                              double[] b)

Multiplies two matrices together.

Parameters:

a - input matrix 1 as 9-element array

b - input matrix 2 as 9-element array

Returns:

a * b as 9-element array

toString

public static String toString(double[] a)

Returns a string giving the contents of an arbitrary length vector.

Parameters:

a - array

Returns:

stringified a

fromPal

public static double[] fromPal(double[][] m)

Converts a 3-d matrix from Pal-friendly form (3x3) to the form used elsewhere in this class (flat 9-element array).

Parameters:

m - flat matrix

Returns:

pal-friendly matrix

toPal

public static double[][] toPal(double[] m)

Converts a 3-d matrix from the form used in this class (flat 9-element array) to Pal-friendly form (3x3).

Parameters:

m - flat matrix

Returns:

pal-friendly matrix