imagingbook.lib.math

Class Matrix

java.lang.Object

imagingbook.lib.math.Matrix

public abstract class Matrix
extends Object

This class contains a collection of static methods for calculations with vectors and matrices using native Java arrays without any enclosing objects structures. Matrices are simply two-dimensional array M[r][c], where r is the row index and c is the column index (as common in linear algebra). This means that matrices are really vectors of row vectors. TODO: need to differentiate functional and side-effect methods! TODO: add JavaDoc comments.

Version:

2016/11/28

Constructor Summary

Constructors

Constructor and Description
Matrix()

Method Summary

Modifier and Type	Method and Description
static double[][]	add(double[][] A, double[][] B)
static double[]	add(double[] a, double[] b)
static int[]	add(int[] a, int[] b)
static double[]	concatenate(double[]... xs)
static float[]	concatenate(float[]... xs)
static double[][]	createDoubleMatrix(int rows, int columns)
static double[]	createDoubleVector(int length)
static float[][]	createFloatMatrix(int rows, int columns)
static float[]	createFloatVector(int length)
static double	determinant2x2(double[][] A)
static float	determinant2x2(float[][] A)
static double	determinant3x3(double[][] A)
static float	determinant3x3(float[][] A)
static double	dotProduct(double[] A, double[] B)
static double[]	duplicate(double[] A)
static double[][]	duplicate(double[][] A)
static float[]	duplicate(float[] A)
static float[][]	duplicate(float[][] A)
static double[][]	duplicateToDouble(float[][] A)
static float[][]	duplicateToFloat(double[][] A)
static int[]	floor(double[] a)
static double	froebeniusNorm(double[][] A)
static double[]	getColumn(double[][] A, int c)
static int	getNumberOfColumns(double[][] A)
static int	getNumberOfColumns(float[][] A)
static int	getNumberOfRows(double[][] A)
static int	getNumberOfRows(float[][] A)
static double[]	getRow(double[][] A, int r)
static double[][]	idMatrix(int size)
static double[][]	inverse(double[][] A)
static float[][]	inverse(float[][] A)
static double[][]	inverse2x2(double[][] A) Deprecated.
static float[][]	inverse2x2(float[][] A) Deprecated.
static void	main(String[] args)
static double	max(double[] A)
static float	max(float[] A)
static double	min(double[] A)
static float	min(float[] A)
static double[]	multiply(double[][] A, double[] x)
static double[][]	multiply(double[][] A, double[][] B)
static double[]	multiply(double[] x, double[][] A)
static double[]	multiply(double s, double[] a)
static double[][]	multiply(double s, double[][] A)
static float[]	multiply(float[][] A, float[] x)
static float[][]	multiply(float[][] A, float[][] B)
static void	multiply(float[][] A, float[][] B, float[][] C)
static float[]	multiply(float s, float[] A)
static float[][]	multiply(float s, float[][] A)
static void	multiplyD(double[][] A, double[][] B, double[][] C)
static void	multiplyD(double[][] A, double[] x, double[] y)
static void	multiplyD(double[] x, double[][] A, double[] y)
static void	multiplyD(double s, double[] a)
static void	multiplyD(double s, double[][] A)
static void	multiplyD(float[][] A, float[] x, float[] y) Matrix-vector product: A .
static void	multiplyD(float s, float[] A)
static void	multiplyD(float s, float[][] A)
static double	normL1(double[] A)
static float	normL1(float[] A)
static double	normL2(double[] A)
static float	normL2(float[] A)
static double	normL2squared(double[] A)
static float	normL2squared(float[] A)
static double[][]	outerProduct(double[] A, double[] B)
static void	printToStream(double[][] A, PrintStream strm)
static void	printToStream(double[] A, PrintStream strm)
static void	printToStream(float[][] A, PrintStream strm)
static void	printToStream(float[] A, PrintStream strm)
static double[]	solve(double[][] A, double[] b)
static double[]	subtract(double[] a, double[] b)
static double[]	subtract(double[] a, int[] b)
static double	sum(double[] A)
static double	sum(double[][] A)
static float	sum(float[] A)
static double	sum(float[][] A)
static String	toString(double[] x)
static String	toString(double[][] A)
static String	toString(float[] A)
static String	toString(float[][] A)
static double	trace(double[][] A)
static double[][]	transpose(double[][] A)
static float[][]	transpose(float[][] A)
static double[]	zeroVector(int size)

Methods inherited from class java.lang.Object

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

Constructor Detail

Matrix

public Matrix()

Method Detail

createDoubleVector

public static double[] createDoubleVector(int length)

createFloatVector

public static float[] createFloatVector(int length)

createDoubleMatrix

public static double[][] createDoubleMatrix(int rows,
                                            int columns)

createFloatMatrix

public static float[][] createFloatMatrix(int rows,
                                          int columns)

zeroVector

public static double[] zeroVector(int size)

idMatrix

public static double[][] idMatrix(int size)

getNumberOfRows

public static int getNumberOfRows(double[][] A)

getNumberOfColumns

public static int getNumberOfColumns(double[][] A)

getNumberOfRows

public static int getNumberOfRows(float[][] A)

getNumberOfColumns

public static int getNumberOfColumns(float[][] A)

getRow

public static double[] getRow(double[][] A,
                              int r)

getColumn

public static double[] getColumn(double[][] A,
                                 int c)

duplicate

public static double[] duplicate(double[] A)

duplicate

public static float[] duplicate(float[] A)

duplicate

public static double[][] duplicate(double[][] A)

duplicateToFloat

public static float[][] duplicateToFloat(double[][] A)

duplicate

public static float[][] duplicate(float[][] A)

duplicateToDouble

public static double[][] duplicateToDouble(float[][] A)

add

public static int[] add(int[] a,
                        int[] b)

add

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

add

public static double[][] add(double[][] A,
                             double[][] B)

subtract

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

subtract

public static double[] subtract(double[] a,
                                int[] b)

floor

public static int[] floor(double[] a)

multiply

public static double[] multiply(double s,
                                double[] a)

multiplyD

public static void multiplyD(double s,
                             double[] a)

multiply

public static double[][] multiply(double s,
                                  double[][] A)

multiplyD

public static void multiplyD(double s,
                             double[][] A)

multiply

public static float[] multiply(float s,
                               float[] A)

multiplyD

public static void multiplyD(float s,
                             float[] A)

multiply

public static float[][] multiply(float s,
                                 float[][] A)

multiplyD

public static void multiplyD(float s,
                             float[][] A)

multiply

public static double[] multiply(double[] x,
                                double[][] A)

multiplyD

public static void multiplyD(double[] x,
                             double[][] A,
                             double[] y)

multiply

public static double[] multiply(double[][] A,
                                double[] x)

multiplyD

public static void multiplyD(double[][] A,
                             double[] x,
                             double[] y)

multiply

public static float[] multiply(float[][] A,
                               float[] x)

multiplyD

public static void multiplyD(float[][] A,
                             float[] x,
                             float[] y)

Matrix-vector product: A . x = y All arguments must be appropriately sized. destructive

Parameters:

A - matrix of size m,n (input)

x - vector of length n (input)

y - vector of length m (result)

multiply

public static double[][] multiply(double[][] A,
                                  double[][] B)

multiplyD

public static void multiplyD(double[][] A,
                             double[][] B,
                             double[][] C)

multiply

public static float[][] multiply(float[][] A,
                                 float[][] B)

multiply

public static void multiply(float[][] A,
                            float[][] B,
                            float[][] C)

dotProduct

public static double dotProduct(double[] A,
                                double[] B)

outerProduct

public static double[][] outerProduct(double[] A,
                                      double[] B)

normL1

public static double normL1(double[] A)

normL2

public static double normL2(double[] A)

normL2squared

public static double normL2squared(double[] A)

normL1

public static float normL1(float[] A)

normL2

public static float normL2(float[] A)

normL2squared

public static float normL2squared(float[] A)

sum

public static double sum(double[] A)

sum

public static double sum(double[][] A)

sum

public static float sum(float[] A)

sum

public static double sum(float[][] A)

min

public static float min(float[] A)

min

public static double min(double[] A)

max

public static float max(float[] A)

max

public static double max(double[] A)

concatenate

public static float[] concatenate(float[]... xs)

concatenate

public static double[] concatenate(double[]... xs)

determinant2x2

public static float determinant2x2(float[][] A)

determinant2x2

public static double determinant2x2(double[][] A)

determinant3x3

public static float determinant3x3(float[][] A)

determinant3x3

public static double determinant3x3(double[][] A)

transpose

public static float[][] transpose(float[][] A)

transpose

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

froebeniusNorm

public static double froebeniusNorm(double[][] A)

trace

public static double trace(double[][] A)

inverse

public static double[][] inverse(double[][] A)

Parameters:

A - a square matrix.

Returns:

the inverse of A or null if A is non-square or singular.

inverse

public static float[][] inverse(float[][] A)

inverse2x2

@Deprecated
public static float[][] inverse2x2(float[][] A)

Deprecated.

inverse2x2

@Deprecated
public static double[][] inverse2x2(double[][] A)

Deprecated.

solve

public static double[] solve(double[][] A,
                             double[] b)

toString

public static String toString(double[] x)

printToStream

public static void printToStream(double[] A,
                                 PrintStream strm)

toString

public static String toString(double[][] A)

printToStream

public static void printToStream(double[][] A,
                                 PrintStream strm)

toString

public static String toString(float[] A)

printToStream

public static void printToStream(float[] A,
                                 PrintStream strm)

toString

public static String toString(float[][] A)

printToStream

public static void printToStream(float[][] A,
                                 PrintStream strm)

main

public static void main(String[] args)