Class Matrices

java.lang.Object
  Matrices

public class Matrices

extends java.lang.Object

Matrices provides an assortment of Matrix utilities - add, subtract, multiply, transpose, identity.
Adds two matrices of the same order.

A			+	B			=	C
0	1	2		2	0	1		2	1	3
1	2	3	+	0	1	0	=	1	3	3
3	4	5		2	0	3		5	4	8

C[r][c] = A[r][c] + B[r][c]
C[0][0] = 0 + 2 = 2, C[0][1] = 1 + 0 = 1, C[0][2] = 2 + 1 = 3
C[1][0] = 1 + 0 = 1, C[1][1] = 2 + 1 = 3, C[1][2] = 3 + 0 = 3
C[2][0] = 3 + 2 = 5, C[2][1] = 4 + 0 = 4, C[2][2] = 5 + 3 = 8

Multiplies compatible matrices -the number of columns of the first matches the number of rows of the second.

A			*	B			=	C
0	1	2		2	0	1		4	1	6
1	2	3	*	0	1	0	=	8	2	10
3	4	5		2	0	3		16	4	18

C[r][c] = A[r][0] * B[0][c] + A[r][1] * B[1][c] + ... + A[r][k] * B[k][c]
C[0][0] = 0*2 + 1*0 + 2*2 = 4, C[0][1] = 0*0 + 1*1 + 2*0 = 1, C[0][2] = 0*1 + 1*0 + 2*3 = 6
C[1][0] = 1*2 + 2*0 + 3*2 = 8, C[1][1] = 1*0 + 2*1 + 3*0 = 2, C[1][2] = 1*1 + 2*0 + 3*3 = 10
C[2][0] = 3*2 + 4*0 + 5*2 = 16, C[2][1] = 3*0 + 4*1 + 5*0 = 4, C[2[2] = 3*1 + 4*0 + 5*3 = 18

D (3 x 2)			*	E (2 x 3)			=	F (3 x 3)
0	1			2	0	1		0	1	0
1	2		*	0	1	0	=	2	2	1
3	4							6	4	3

F[r][c] = D[r][0] * E[0][c] + D[r][1] * E[1][c] + ... + D[r][k] * E[k][c]
F[0][0] = 0*2 + 1*0 = 0, F[0][1] = 0*0 + 1*1 = 1, F[0][2] = 0*1 + 1*0 = 0
F[1][0] = 1*2 + 2*0 = 2, F[1][1] = 1*0 + 2*1 = 2, F[1][2] = 1*1 + 2*0 = 1
F[2][0] = 3*2 + 4*0 = 6, F[2][1] = 3*0 + 4*1 = 4, F[2][2] = 3*1 + 4*0 = 3

Author:

Jack Tompkins

Source Code: Matrices.java

Constructor Summary

Matrices()

Method Summary

static double[][]	add(double[][] A, double[][] B) Adds two matrices of the same order.
static double[][]	add(double[][] A, int[][] B) Adds two matrices of the same order.
static double[][]	add(int[][] A, double[][] B) Adds two matrices of the same order.
static int[][]	add(int[][] A, int[][] B) Adds two matrices of the same order.
static double[][]	identity(double n) The identity matrix of order n.
static int[][]	identity(int n) The identity matrix of order n.
static void	main(java.lang.String[] args)
static double[][]	multiply(double[][] A, double[][] B) Multiplies compatible matrices -the number of columns of the first matches the number of rows of the second.
static double[][]	multiply(double[][] A, int[][] B) Multiplies compatible matrices -the number of columns of the first matches the number of rows of the second.
static double[][]	multiply(int[][] A, double[][] B) Multiplies compatible matrices -the number of columns of the first matches the number of rows of the second.
static int[][]	multiply(int[][] A, int[][] B) Multiplies compatible matrices -the number of columns of the first matches the number of rows of the second.
static void	printArray(java.lang.String title, double[][] A) Prints each element of a double array, one row at a time.
static void	printArray(java.lang.String title, int[][] A) Prints each element of a double array, one row at a time.
static double[][]	subtract(double[][] A, double[][] B) Subtracts two matrices of the same order.
static double[][]	subtract(double[][] A, int[][] B) Subtracts two matrices of the same order.
static double[][]	subtract(int[][] A, double[][] B) Subtracts two matrices of the same order.
static int[][]	subtract(int[][] A, int[][] B) Subtracts two matrices of the same order.
static double[][]	transpose(double[][] A) interchanges the rows and columns of matrix A
static int[][]	transpose(int[][] A) interchanges the rows and columns of matrix A

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

main

public static void main(java.lang.String[] args)

printArray

public static void printArray(java.lang.String title,
                              int[][] A)

Prints each element of a double array, one row at a time.

Parameters:

title - printed before the array on a separate line.

A - double array, size m X n

printArray

public static void printArray(java.lang.String title,
                              double[][] A)

Prints each element of a double array, one row at a time.

Parameters:

title - printed before the array on a separate line.

A - double array, size m X n

multiply

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

Multiplies compatible matrices -the number of columns of the first matches the number of rows of the second.

A			*	B			=	C
0	1	2		2	0	1		4	1	6
1	2	3	*	0	1	0	=	8	2	10
3	4	5		2	0	3		16	4	18

C[r][c] = A[r][0] * B[0][c] + A[r][1] * B[1][c] + ... + A[r][k] * B[k][c]
C[0][0] = 0*2 + 1*0 + 2*2 = 4, C[0][1] = 0*0 + 1*1 + 2*0 = 1, C[0][2] = 0*1 + 1*0 + 2*3 = 6
C[1][0] = 1*2 + 2*0 + 3*2 = 8, C[1][1] = 1*0 + 2*1 + 3*0 = 2, C[1][2] = 1*1 + 2*0 + 3*3 = 10
C[2][0] = 3*2 + 4*0 + 5*2 = 16, C[2][1] = 3*0 + 4*1 + 5*0 = 4, C[2[2] = 3*1 + 4*0 + 5*3 = 18

D (3 x 2)			*	E (2 x 3)			=	F (3 x 3)
0	1			2	0	1		0	1	0
1	2		*	0	1	0	=	2	2	1
3	4							6	4	3

F[r][c] = D[r][0] * E[0][c] + D[r][1] * E[1][c] + ... + D[r][k] * E[k][c]
F[0][0] = 0*2 + 1*0 = 0, F[0][1] = 0*0 + 1*1 = 1, F[0][2] = 0*1 + 1*0 = 0
F[1][0] = 1*2 + 2*0 = 2, F[1][1] = 1*0 + 2*1 = 2, F[1][2] = 1*1 + 2*0 = 1
F[2][0] = 3*2 + 4*0 = 6, F[2][1] = 3*0 + 4*1 = 4, F[2][2] = 3*1 + 4*0 = 3

Parameters:

A - double array, size m X k of ints.

B - double array, size k X n of ints

Returns:

The product AB, a matrix size m X n

multiply

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

Multiplies compatible matrices -the number of columns of the first matches the number of rows of the second.

Parameters:

A - double array, size m X k of doubles.

B - double array, size k X n of doubles

Returns:

The product AB, a matrix size m X n

multiply

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

Multiplies compatible matrices -the number of columns of the first matches the number of rows of the second.

Parameters:

A - double array, size m X k of doubles.

B - double array, size k X n of ints

Returns:

The product AB, a matrix size m X n

multiply

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

Multiplies compatible matrices -the number of columns of the first matches the number of rows of the second.

Parameters:

A - double array, size m X k of ints.

B - double array, size k X n of doubles

Returns:

The product AB, a matrix size m X n

transpose

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

interchanges the rows and columns of matrix A

Parameters:

A - double array of ints, matrix A, an m X n matrix.

Returns:

double array of ints, matrix At, an n X m matrix - the transpose of A

transpose

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

interchanges the rows and columns of matrix A

Parameters:

A - double array of doubles, matrix A, an m X n matrix.

Returns:

double array of doubles, matrix At, an n X m matrix - the transpose of A

identity

public static int[][] identity(int n)

The identity matrix of order n.

Parameters:

n - the order of this identity matrix.

Returns:

a double array, order n, of ints - identity matrix - ones along the main diagonal, zeros elsewhere

identity

public static double[][] identity(double n)

The identity matrix of order n.

Parameters:

n - the order of this identity matrix.

Returns:

a double array, order n, of doubles - identity matrix - ones along the main diagonal, zeros elsewhere

add

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

Adds two matrices of the same order.

A			+	B			=	C
0	1	2		2	0	1		2	1	3
1	2	3	+	0	1	0	=	1	3	3
3	4	5		2	0	3		5	4	8

C[r][c] = A[r][c] + B[r][c]
C[0][0] = 0 + 2 = 2, C[0][1] = 1 + 0 = 1, C[0][2] = 2 + 1 = 3
C[1][0] = 1 + 0 = 1, C[1][1] = 2 + 1 = 3, C[1][2] = 3 + 0 = 3
C[2][0] = 3 + 2 = 5, C[2][1] = 4 + 0 = 4, C[2][2] = 5 + 3 = 8

Parameters:

A - double array, size m X n of ints.

B - double array, size m X n of ints

Returns:

the sum A + B, a double array of ints

add

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

Adds two matrices of the same order.

Parameters:

A - double array, size m X n of doubles.

B - double array, size m X n of doubles

Returns:

the sum A + B, a double array of doubles

add

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

Adds two matrices of the same order.

Parameters:

A - double array, size m X n of doubles.

B - double array, size m X n of ints

Returns:

the sum A + B, a double array of doubles

add

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

Adds two matrices of the same order.

Parameters:

A - double array, size m X n of ints.

B - double array, size m X n of doubles

Returns:

the sum A + B, a double array of doubles

subtract

public static int[][] subtract(int[][] A,
                               int[][] B)

Subtracts two matrices of the same order.

Parameters:

A - double array, size m X n of ints.

B - double array, size m X n of ints

Returns:

the difference A - B, a double array of ints

subtract

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

Subtracts two matrices of the same order.

Parameters:

A - double array, size m X n of doubles.

B - double array, size m X n of doubles

Returns:

the difference A - B, a double array of doubles

subtract

public static double[][] subtract(double[][] A,
                                  int[][] B)

Subtracts two matrices of the same order.

Parameters:

A - double array, size m X n of doubles.

B - double array, size m X n of ints

Returns:

the difference A - B, a double array of doubles

subtract

public static double[][] subtract(int[][] A,
                                  double[][] B)

Subtracts two matrices of the same order.

Parameters:

A - double array, size m X n of ints.

B - double array, size m X n of doubles

Returns:

the difference A - B, a double array of doubles