smithers.algorithms
Class Matrix

java.lang.Object
  smithers.algorithms.Matrix

public class Matrix
extends java.lang.Object

Implements a collection of useful matrix related algorithms. The methods of this class all require that the matrix arguments be rectangular; for efficiency they do not check this, hence if the arguments are invalid, they will likely throw ArrayIndexOutOfBoundsException or NullPointerException

Method Summary

static void	decomposeLQ(float[][] matrix, float[][] l, float[][] q) Computes an LQ decomposition of a matrix.
static float[]	product(float[][] matrix, float[] vector) Multiplies a matrix by a column vector.
static float[][]	product(float[][] matrix1, float[][] matrix2) Multiplies two matrices together.
static float[]	product(float[] vector, float[][] matrix) Multiplies a row vector by a matrix.
static void	rowReduce(float[][] matrix) Row reduce a matrix in-place.

Methods inherited from class java.lang.Object

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

Method Detail

product

public static float[][] product(float[][] matrix1,
                                float[][] matrix2)

Multiplies two matrices together. The first matrix must have as many columns as the second has rows.

Parameters:

matrix1 - a matrix

matrix2 - another matrix

Returns:

matrix1 * matrix2

product

public static float[] product(float[][] matrix,
                              float[] vector)

Multiplies a matrix by a column vector. The vector must have as many elements as the matrix has columns.

Parameters:

matrix - a matrix

vector - a vector

Returns:

matrix * vector

product

public static float[] product(float[] vector,
                              float[][] matrix)

Multiplies a row vector by a matrix. The vector must have as many elements as the matrix has rows.

Parameters:

vector - a vector

matrix - a matrix

Returns:

vector * matrix

rowReduce

public static void rowReduce(float[][] matrix)

Row reduce a matrix in-place. Uses Gauss-Jordan elimination with scaled partial pivoting.

Parameters:

matrix - the matrix to reduce

decomposeLQ

public static void decomposeLQ(float[][] matrix,
                               float[][] l,
                               float[][] q)

Computes an LQ decomposition of a matrix. The matrix must have at least as many columns as rows. This computes L and Q such that A = LQ, with L lower triangular and Q orthogonal. Uses the modified Gram-Schmidt process, further modified to still work if A is not square or if the rows of A are not linearly independant; in the latter case the matrix L will have one or more zero entries on the diagonal.

Parameters:

matrix - the matrix to decompose

l - the matrix in which to store L; must have the same dimensions as matrix

q - the matrix in which to store Q; must be square of dimension equal to the number of columns of matrix