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

#include <time.h>

using namespace std;

#define PI 3.1415

double x(double t,double A[],double B[],double w);


int main(){

    int i,n;
    double j,l,dx,xa,xb,w;
    double N;
    double a[5],b[5],sa[6],sb[6];

    srand((unsigned int) time(NULL));

    for(i=0;i<5;i++){
        a[i]=rand()%100+1.0;
        b[i]=rand()%100+1.0;
    }

    w=(double)((rand()%50)/50.0+0.01);

    for(i=0;i<=5;i++) {
        sa[i]=0.0;
        sb[i]=0.0;
    }

    ofstream out("fourier1.txt");
    for(j=10.0;j<=10.0+6.0*PI/w;j+=0.01){
        out << j<<' '<<x(j,a,b,w)<<endl;
    }
    out.close();

    cout <<"角速度:"<<w<<endl;
    cout<<"周期:"<<2*PI/w<<endl;

    cout <<"x(10.0):    "

        <<x(10.0,a,b,w)<<endl
         <<"=x(10.0+"<<2*PI/w<<"):  "
         <<x(10.0+2*PI/w,a,b,w)<<endl;

    l=PI/w;
    N=1000.0/w;
    dx=2*l/N;

    for(n=1;n<=5;n++){
        for(j=0.0;j<N;j++) {
            xa=10.0+dx*j;
            xb=10.0+dx*(j+1.0);
            sa[n]+=(x(xa,a,b,w)*cos(n*PI*xa/l)+x(xb,a,b,w)*cos(n*PI*xb/l))*dx/2.0;
            

        }
    }

    for(n=1;n<=5;n++){
        for(j=0.0;j<N;j++) {
            xa=10.0+dx*j;
            xb=10.0+dx*(j+1);
            sb[n]+=(x(xa,a,b,w)*sin(n*PI*xa/l)+x(xb,a,b,w)*sin(n*PI*xb/l))*dx/2.0;
            

        }
    }

    cout <<"-------フーリエ変換によるa[i]----------"<<endl;

    for(n=1;n<=5;n++) {
        cout <<"a["<<n<<"]="<<sa[n]/l<<endl;
    }
    
    cout <<"-------実際のa[i]---------"<<endl;

    for(i=0;i<5;i++){
    cout << "a[" << i+1 << "]=" << a[i] <<endl;
    }

    cout <<"-------フーリエ変換によるb[i]----------"<<endl;

    for(n=1;n<=5;n++) {
        cout <<"b["<<n<<"]="<<sb[n]/l<<endl;
    }
    
    cout <<"-------実際のb[i]---------"<<endl;

    for(i=0;i<5;i++){
    cout << "b[" << i+1 << "]=" << b[i] <<endl;
    }

    return 0;
}


double x(double t,double A[],double B[],double w){      //x(t)

    
    int i;
    double k=0.0;
    
    for(i=1;i<=5;i++){
        k+=A[i-1]*cos(i*w*t)+B[i-1]*sin(i*w*t);
    }
    
    return (k);
}

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

#include <time.h>

using namespace std;

#define PI 3.1415

double x(double t,double A[],double B[],double w,double r[]);


int main(){

    int i;
    double j,k,dx,xa,xb,w,sum;
    double N;
    double a[3],b[3],r[3];

    srand((unsigned int) time(NULL));

    for(i=0;i<3;i++){
        a[i]=rand()%100+1.0;
        b[i]=rand()%100+1.0;
        r[i]=(double)((rand()%50)/50.0+0.1);
        cout <<"r["<<i+1<<"]="<<r[i]<<endl;
    }
    w=(double)((rand()%50)/80.0+1);
    


    ofstream out1("fourier1.txt");
    for(j=0;j<=4.0*PI/w;j+=0.02){
        out1 << j<<' '<<x(j,a,b,w,r)<<endl;
    }
    out1.close();

    cout <<"角速度:"<<w<<endl;

    N=pow(10.0,4);
    dx=0.01;

    ofstream out2("fourier2.txt");
    
    //フーリエ余弦変換

    for(k=0;k<=6.0;k+=0.02){
        sum=0.0;
        for(j=0.0;j<N;j+=1.0) {
            xa=0+dx*j;
            xb=0+dx*(j+1.0);
            sum+=(x(xa,a,b,w,r)*cos(k*xa)+x(xb,a,b,w,r)*cos(k*xb))*dx/2.0;
        }
        sum*=pow(2.0/PI,0.50);
        out2<<k<<' '<<sum<<endl;
    }
    out2.close();

    ofstream out3("fourier3.txt");
    
    //フーリエ正弦変換
    for(k=0;k<=6;k+=0.02){
        sum=0.0;
        for(j=0.0;j<N;j+=1.0) {
            xa=0+dx*j;
            xb=0+dx*(j+1.0);
            sum+=(x(xa,a,b,w,r)*sin(k*xa)+x(xb,a,b,w,r)*sin(k*xb))*dx/2.0;
        }
        sum*=pow(2.0/PI,0.50);
        out3<<k<<' '<<sum<<endl;
    }
    out3.close();

    return 0;
}


double x(double t,double A[],double B[],double w,double r[]){       //x(t)

    
    int i;
    double k=0.0;
    
    for(i=1;i<=3;i++){
        k+=A[i-1]*exp(-r[i-1]*t)*cos(i*w*t)+B[i-1]*exp(-r[i-1]*t)*sin(i*w*t);
    }
    
    return (k);
}