Arrays - A Concise and Practical Introduction to Programming Algorithms in Java - page 94

This index remapping 5 is quite cumbersome to use in practice and may
yield various insidious bugs. Fortunately in Java, we can also create multi-
dimensional arrays easily; Java will perform the necessary index remapping
accordingly. A regular bi-dimensional array consists of n lines, each line being
itselfanarrayof m elements. A 2D matrix of integers has type int [] [] and
is declared, created and initialized as follows:
int[][]matrix;
matrix=new int[n][m];

By default at the initialization stage, the array matrix is filled up with all zero
elements. We can change the contents of this 2D array using two nested loops,
as follows:

for(int i=0; i<n; i++)
for(int j=0; j<m;j++)
matrix[i][j]=i*j+1;

These constructions extend to arbitrary array dimensions. For example, a 3D
array may be defined as follows:

int[][][]volume;
volume=new double[depth][height][width];

Let us illustrate the manipulations of linear and bi-dimensional arrays by imple-
menting the matrix vector product operation. Observe the declaration/creation
and initialization of a 2D array by enumerating all its elements:
int [][] M={{1, 2, 3}, {4,5,6}, {7,8,9}};

Program 4.11 Matrix-vector product function
class MatrixVectorProduct {
static int [] MultiplyMatrixVector ( int [][] mat, int [] v)
{ int [] result;
result= new i n t [mat. length ];

for ( int i=0;i < result . length ; i++)
{ result [ i ]=0;
for ( int j=0;j < v. length ; j++)
result [ i]+= mat[ i ][ j ]

∗ v[ j ];

} return result ;
} public static void main( String [ ]

args )

{ int [][] M= {{ 1, 2, 3 } ,

{ 4,5,6 } , { 7,8,9 }} ;

int [] v= { 1,2,3 } ;

5 We arbitrarily chose row major order. We can also choose the column major order.