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#include <iostream>
#include <fstream>
#include <math.h>
#include <Dense>
#include <SVD>

using Eigen::MatrixXf;
using Eigen::JacobiSVD;
using namespace std;

#define POINT 4

int main()
{
    fstream input;
    int length;
    int i,j,p,pixel;

    int avg[POINT];
    int sum;

    float cov[POINT][POINT]={};
    float x,y=0;
    float KLT_eff,DCT_eff;
    float r;

    unsigned char X[POINT][512*512/POINT];

    input.open("baboon.bmp", ios::in | ios::binary);

    //get the file size.
    input.seekg(0, ios::end);
    length = input.tellg();
    input.seekg(0, ios::beg);

    char *data = new char[length];
    input.read(data, length);        //read the input file and write into the array.

    //build the four vector X1, X2, X3, X4
    for (i=0, pixel=1078; i<512*512/POINT; i++){
        for (p=0; p<POINT;p++){
            X[p][i]=data[pixel++];
        }
    }

    //find each mean of X1, X2, X3, X4
    for (p=0; p<POINT; p++){
        for (i=0, sum=0; i<512*512/POINT; i++){
            sum=X[p][i]+sum;
        }
        avg[p]=sum/(512*512/POINT);
    }

    //Covariance Matrix
    for (i=0; i<POINT; i++){
        for (j=0; j<POINT; j++){
            for (p=0; p<512*512/POINT; p++){
                cov[i][j]=(X[i][p]-avg[i])*(X[j][p]-avg[j])+cov[i][j];
            }
            cov[i][j]=cov[i][j]/((512*512/POINT)-1);
        }
    }

    //print the matrix
    cout<<"Covariance Matrix:"<<endl;
    for (i=0;i<POINT;i++){
        for (j=0;j<POINT;j++){
            cout <<cov[i][j]<<"  ";
        }
        cout <<endl;
    }

    //KLT basis vectors
    MatrixXf m(POINT,POINT);
    for (i=0; i<POINT; i++){
        for (j=0; j<POINT; j++){
            m(i,j)=cov[i][j];
        }
    }

    //std::cout << "Here is the matrix m:" << std::endl << m << std::endl;
    JacobiSVD<MatrixXf> svd(m, Eigen::ComputeThinU | Eigen::ComputeThinV);
    std::cout <<endl<< "Its singular values are:" << std::endl << svd.singularValues() << std::endl;

    //Tdct    //inv_Tdct
    MatrixXf Tdct(POINT,POINT);
    MatrixXf inv_Tdct(POINT,POINT);

    for (i=0; i<POINT; i++){
        for (j=0; j<POINT; j++){
            if (i==0)
                Tdct(i,j)=1/(sqrt((float)POINT));
            else
                Tdct(i,j)=sqrt(2/(float)POINT)*cos((M_PI*(2*j+1)*i)/(2*POINT));
        }

    }

    //cout<<endl<<"Tdct matrix:"<<endl<<Tdct<<endl;
    //build the matrix to calculate inverse matrix
    MatrixXf tmp(POINT,2*POINT);
    for (i=0; i<POINT; i++){
        for (j=0; j<POINT; j++){
            tmp(i,j)=Tdct(i,j);
        }
    }
    for (i=0; i<POINT; i++){
        for (j=POINT; j<2*POINT; j++){
            if ((j-POINT)==i) tmp(i,j)=1.0;
            else tmp(i,j)=0;
        }
    }

    //calculating the inverse matrix
    for (i=0; i<POINT; i++){        //which row is standard to be one and elimate the other rows to be zero
        float beone=tmp(i,i);
        //let standard row (i,i) to be one, other col elements need to be resized.
        for (j=0; j<2*POINT; j++){  //col
            tmp(i,j)=tmp(i,j)/beone;
        }

        //elimating others row
        for (int m=0; m<POINT; m++){    //row
            r=tmp(m,i);     //ref
            for (int l=0; l<2*POINT; l++){  //col
                if (m!=i){
                    tmp(m,l)=tmp(m,l)-tmp(i,l)*r;
                }
            }
        }
    }

    //build inv_Tdct matrix
    for (i=0;i<POINT;i++){
        for (j=0;j<POINT;j++){
            inv_Tdct(i,j)=tmp(i,j+POINT);
        }
    }

    MatrixXf tmp2(POINT,POINT);
    MatrixXf D(POINT,POINT);

    //DCT matrix: D=Tdct*Cov*inv_Tdct
    for (i=0; i<POINT; i++){
        for (j=0; j<POINT; j++){
            float buf=0;
            for (int k=0; k<POINT; k++){
                buf=buf+Tdct(i,k)*m(k,j);      //tmp2 matrix = Tdct matrix* Covariance matrix; tmp2=Tdct*Czm
            }
            tmp2(i,j)=buf;
        }
    }

    for (i=0; i<POINT; i++){
        for (j=0; j<POINT; j++){
            float buf=0;
            for (int k=0; k<POINT; k++){
                buf=buf+tmp2(i,k)*inv_Tdct(k,j);      //D matrix = tmp2 matrix* inverse Tdct matrix; D=tmp2*inv_Tdct
            }
            D(i,j)=buf;
        }
    }

    cout<<endl<<"D matrix:"<<endl<<D<<endl<<endl;

    //De-correlation Efficiency for KLT
    //Y
    for (i=0,y=0;i<POINT;i++)
        y=0;
    //X
    for (i=0,x=0;i<POINT;i++){
        for (j=0;j<POINT;j++){
            if (i!=j)
                x=x+m(i,j);
        }
    }

    KLT_eff=1-y/x;
    cout <<"Decorrelation Efficiency: "<<endl<<"KLT: "<<KLT_eff*100<<"%"<<endl;

    //De-correlation Efficiency for DCT
    //Y
    for (i=0,y=0;i<POINT;i++){
        for (j=0;j<POINT;j++){
            if (i!=j)
                y=y+abs(D(i,j));
        }
    }
    //X
    for (i=0,x=0;i<POINT;i++){
        for (j=0;j<POINT;j++){
            if (i!=j)
                x=x+abs(m(i,j));
        }
    }

    DCT_eff=1-y/x;
    cout<<"DCT: "<<DCT_eff*100<<"%"<<endl;



    return 0;

}

參考:http://www.ewdna.com/2012/02/css-block.html

HTML encoder:http://formatmysourcecode.blogspot.tw/
會需要用到HTML encoder主要的原因就是一些符號在HTML裡是有特殊意義的(像是 > < &)
都需要轉換才能夠使用 否則code內的< > 就會被當成HTML的特殊意義使用 

網頁設計(HTML學習):http://www.phd.com.tw/knowledge/html/typesetting/
將code轉成HTML:http://formatmysourcecode.blogspot.tw/

8/31 2015