행렬연산을 위한 자료구조, Tensor, Torch 를 자바로 재구현 해보자!

본문은 아직 완성되지 않았음.

---

# 행렬연산을 위한 자료구조 Tensor, Torch 

 - 1차원 배열로 구성되어있다.

 - offset, strides 의 개념으로 모든 것을 해결

 - 전치행렬을 만들때 압도적인 성능

 - 행렬의 곱셈연산은 O(n^2) 로 추정 (직접 구현하고 추후 수정예정)

 

# 크기가 n인 정방행렬을 전치행렬로 만들때 Brute-force 시간복잡도 

 - 3중포문, O(n^3)

 

# Tensor 구조로 전치행렬 시간복잡도

 - O(1)

 - 2차원 배열로 바꿀때, O(n^2) - 데이터 복사 시간

 

---

 

# Tensor.class

public class Tensor {

    public int[] tensor;
    public int offset;

    public int[] strides;
    public int rowLen;
    public int colLen;
    public int rowOriginLen;
    public int colOriginLen;



    public Tensor(int[][] arr) {
        this.rowLen = arr.length;
        this.rowOriginLen = arr.length;
        this.colLen = arr[0].length;
        this.colOriginLen = arr[0].length;
        this.tensor = new int[this.rowLen*this.colLen];
        this.offset = 0;
        this.strides = new int[]{colLen,1};
        for(int i=0, cnt=0; i<this.rowLen;i++){
            for(int j=0;j<this.colLen;j++){
                this.tensor[cnt++]=arr[i][j];
            }
        }
    }

    public void printTensorStorage(){
        System.out.print("tf.Storage[");
        for(int i=0; i<tensor.length; i++){
            System.out.print(tensor[i]+" ");
        }
        System.out.println("]");
    }

    @Override
    public String toString() {
        return getTensorToString();
    }

    public String getTensorToString(){
        int i=0; String result="";
        int idx;
        for(i=0; i<rowLen;i++){
            result+="(";
            for(int j=0; j<colLen; j++){
                idx = this.offset + strides[0]*i +strides[1]*j;
                if(j==colLen-1 && i!=rowLen-1) result+=tensor[idx]+")\n";
                else if(j==colLen-1 && i==rowLen-1) result+=tensor[idx]+"";
                else result+=tensor[idx]+" ";
            }
        }
        result+=")";
        return result;
    }

    public int trickSwap(int a, int b){
        return a;
    }

    public void slicing(int rowStart, int rowEnd, int colStart, int colEnd){
        if(colEnd>colLen) colEnd=colOriginLen;
        if(rowEnd>rowLen) rowEnd=rowOriginLen;

        this.offset = strides[0]*(rowStart) +strides[1]*(colStart);
        this.colLen = colEnd-colStart;
        this.rowLen = rowEnd-rowStart;
    }

    public int[][] to2DArray(){
        int i=0; int[][] result=new int[rowLen][colLen];
        int idx;
        for(i=0; i<rowLen;i++){
            for(int j=0; j<colLen; j++){
                idx = this.offset + strides[0]*i +strides[1]*j;
                result[i][j]=tensor[idx];
            }
        }
        return result;
    }

    public void transpose(){
        strides[1]=trickSwap(strides[0],strides[0]=strides[1]);
        colLen = trickSwap(rowLen,rowLen=colLen);
        colOriginLen =colLen;
        rowOriginLen =rowLen;
    }



}

 

 

# Test

public class TensorTest {

    public static void print2DArray(int[][] arr){
        for(int i=0;i<arr.length;i++){
            for(int j=0;j<arr[0].length;j++){
                System.out.print(arr[i][j]+ " ");
            }
            System.out.println();
        }
    }

    public static void main(String[] args) {
        int[][] arr1 = {
                {1,2,3,4},
                {5,6,7,8},
                {9,10,11,12},
        };
        Tensor tf = new Tensor(arr1);
        System.out.println("# This is a storage of tensor.");
        tf.printTensorStorage();
        System.out.println("# Offset : "+tf.offset);
        System.out.println("# Strides : ("+tf.strides[0]+","+tf.strides[1]+")");
        System.out.println("# This is tensor.");
        System.out.println(tf);


        //transpose
        System.out.println("# Transpose");
        tf.transpose();
        tf.printTensorStorage();
        System.out.println("# Strides : ("+tf.strides[0]+","+tf.strides[1]+")");
        System.out.println(tf);


        //slicing 1
        tf.slicing(1,3,1,3);
        System.out.println("# Slicing(tf[1:3, 1:3])");
        tf.printTensorStorage();
        System.out.println("# SlicingOffset : "+tf.offset);
        System.out.println("# Strides : ("+tf.strides[0]+","+tf.strides[1]+")");
        System.out.println("# len(row,col) : ("+tf.rowLen+","+tf.colLen+")");
        System.out.println(tf);

        //slicing 2
        tf.slicing(2,100,1,4);
        System.out.println("# Slicing(tf[2:100, 1:4])");
        tf.printTensorStorage();
        System.out.println("# SlicingOffset : "+tf.offset);
        System.out.println("# Strides : ("+tf.strides[0]+","+tf.strides[1]+")");
        System.out.println("# len(row,col) : ("+tf.rowLen+","+tf.colLen+")");
        System.out.println(tf);

        //transpose again
        System.out.println("# Transpose");
        tf.transpose();
        tf.printTensorStorage();
        System.out.println("# Strides : ("+tf.strides[0]+","+tf.strides[1]+")");
        System.out.println(tf);

        //to2DArray
        System.out.println("# 2D array Transformation");
        int[][] arr = tf.to2DArray();
        print2DArray(arr);


    }
}