Multiway arrays

In many situations when designing statistical software, the number of variables a dis-crete distribution will have is not known in advance (at compilation time). There existsa need to generate discrete multidimensional distributions on the fly.

Multi-way arraysOne obvious way to store these multidimensional probabilities is to put them in a multi-way array. Let us say that we want to create a one-dimensional array with four elementsof type double using Java. This is easily done asdouble[] X = new double[4];To declare and create a 2x3-matrix and a 4x3x3-dimensional array with elements of typedouble one can writedouble[][]X = new double[2][3];double[][][] Y = new double[4][3][3];In Java, which has zero-based indices on arrays, Y[1][0][2] refers to the elementwith at position(one-based) in the multi-way array .This is no problem at all, but these examples deals with situations when the rank (num-ber of dimensions) of an array is known at compilation time. But what if one wants tocreate an array with rankat run-time? In programming languages such as Java, Cand Pascal, there is no easy way to do it. Just think about it and consider the followingdesperate attempt§ ¦double[][]...[] X = new double[2][4]...[6];

An easy way around this problem is to use the vec-operator. The vec-operator is anoperator that takes a multi-way array, e.g. a matrix, and puts the elements in a columnvector. In the case of a matrix the columns are stacked on top of each other creating acolumn vector.

这里我只在类里实现了两种数据结构间坐标的转换

#pragma once

using namespace std;

class multi_array
{
        protected:
                        int rank;
                        int *base;
                        int *shape;
                        int *node_i;    //coordinate of each node               
                        int value;
        public:
                        multi_array( int new_rank, int *new_shape );
                        multi_array( int new_value );
                        ~multi_array( void );
                        int get_rank();
                        int *get_shape();
                        int *get_base();
                        int *get_node_i();
                        int get_index_vector( int *node_index );
                        void get_i( int index );

};

#include "multi_array.h"
#include <iostream>
using namespace std;

multi_array::multi_array( int new_rank, int *new_shape )
{
        rank = new_rank;
        shape = new int[rank];
        base = new int[rank];
        node_i = new int[rank];

        int i;
        for ( i = 0; i < rank; ++i )
        {
                *( shape + i ) = *( new_shape + i );
        }

        for ( i = 0; i < rank; ++i )
        {
                if ( 0 == i )
                        *base = 1;
                else
                        *( base + i ) = *( base + i - 1 ) * (*( shape + i - 1 ));
        }


        for ( i = 0; i < rank; ++i )
        {
                *( node_i + i ) = 0;
        }
}

multi_array::multi_array( int new_value )
{
        value = new_value;
}

multi_array::~multi_array( void )
{
        delete[] shape;
        delete[] base;

}

/* get the rank */
int multi_array::get_rank()
{
        return rank;
}

/* get the shape */
int* multi_array::get_shape()
{
        return shape;
}

/* get the base */
int* multi_array::get_base()
{
        return base;
}

/* get the i */
int *multi_array::get_node_i()
{
        return node_i;
}

/* get the index_vector */
int multi_array::get_index_vector( int *node_index )
{
        //node_i = new int[ rank ];

        int i, temp = 1;
        for ( i = 0; i < rank; ++i )
        {
                *( node_i + i ) = *( node_index + i );
        }

        for ( i = 0; i < rank; ++i )
        {
                temp += (*( node_i + i ) - 1) * (*( base + i ));
        }

        delete[] node_i;

        return temp;
}

/* get the i of each rank */
void multi_array::get_i( int index )
{
        for ( int i = 0; i < rank; ++i )
        {
                if ( i == (rank - 1) )
                {
                        *( base + i + 1 ) = ( *( base + i ) ) * ( *( shape + i ) );
                }

                /* just for debug */
                //cout << *( base + i ) << "       "  << *( base + i + 1 ) << endl;
                *( node_i + i ) = 1 + ( ( index - 1 ) % (*( base + i + 1)) ) / (*(base + i  )) ;
        }

}

我写的一个例子

#include "multi_array.h"
#include <iostream>

using namespace std;

int main( void )
{
        int a[] = { 4, 3, 3 };
        //multi_array newarray = new multi_array;

        multi_array newarray( 3, a );

        /*for ( int i = 0 ; i < 3; ++i )
        {
                cout << *( newarray.get_base() + i ) << endl;
        }*/

        /*int b[] = { 1, 3, 2 };
        cout << newarray.get_index_vector( b ) << endl;*/

        newarray.get_i( 21 );

        for ( int i = 0; i < 3; i++ )
                cout << *( newarray.get_node_i() + i ) << endl;

        return 0;
}