bool SimpleReductor::reduceStep (Polynomial& r, const Polynomial& p) {
Polynomial t;
r.copy(p);
Monomial lm = r.lm();
int i, i0 = -1;
for (i = 0; i < g.size(); ++i) {
Monomial m = g[i].lm();
if (MP.divides(lm, m)) {
t.mul(g[i], MP.div(lm, m));
Cf f;
Ring::neg(f, r.lc());
r.add(t, t.lc(), f);
return true;
}
}
return false;
}
int main()
{
double df0 = 1.86548, dfn = -0.046115;
int n = 18;
double x[19] = {0.52, 3.1, 8, 17.95, 28.65, 39.62, 50.65, 78, 104.6, 156.6, 208.6, 260.7, 312.5, 364.4, 416.3, 468, 494, 507, 520};
double y[19] = {5.288, 9.4, 13.84, 20.2, 24.9, 28.44, 31.1, 35, 36.9, 36.6, 34.6, 31, 26.34, 20.9, 14.8, 7.8, 3.7, 1.5, 0.2};
double h[19], u[19], lamda[19], d[20];
for (int i = 0; i < n; i++)
h[i] = x[i+1] - x[i];
for (int i = 1; i < n; i++)
u[i] = h[i-1]/(h[i-1]+h[i]);
u[n] = 1;
lamda[1] = 1;
for (int i = 2; i <= n; i++)
lamda[i] = h[i-1]/(h[i-2]+h[i-1]);
d[1] = 6.0/h[0]*((y[1]-y[0])/h[0] - df0);
d[n+1] = 6.0/h[n-1]*(dfn - (y[n] - y[n-1])/h[n-1]);
for (int i = 2; i <= n; i++)
d[i] = 6.0*((y[i] - y[i-1])/h[i-1] - (y[i-1]-y[i-2])/h[i-2])/(h[i-2]+h[i-1]);
Matrix mat(n+1);
mat.setM(u, lamda);
mat.setB(d);
double *M = mat.getSolution();
for (int i = 0; i <= n; i++)
M[i] = M[i+1];
int _j[6] = {0,4,8,13,15,17};
double _x[6] = {2,30,133,390,470,515};
Polynomial *tmp1 = new Polynomial(), *tmp2 = new Polynomial();
for (int i = 0; i < 6; i++)
{
int j = _j[i];
Polynomial S;
tmp1->set1();
tmp2->set1ci(-x[j+1]);
for (int _i = 0; _i < 3; _i++)
tmp1->multiply(tmp2);
tmp1->multiply_number(-M[j]/6/h[j]);
S.add(tmp1);
tmp2->multiply_number((M[j]*h[j]*h[j]/6-y[j])/h[j]);
S.add(tmp2);
tmp1->set1();
tmp2->set1ci(-x[j]);
for (int _i = 0; _i < 3; _i++)
tmp1->multiply(tmp2);
tmp1->multiply_number(M[j+1]/6/h[j]);
S.add(tmp1);
tmp2->multiply_number((-M[j+1]*h[j]*h[j]/6+y[j+1])/h[j]);
S.add(tmp2);
cout << "f(" << _x[i] <<") = " << S.value(_x[i]) << '\n';
cout << "f'(" << _x[i] <<") = " << S.d1(_x[i]) << '\n';
cout << "f''(" << _x[i] <<") = " << S.d2(_x[i]) << '\n';
}
delete tmp1;
delete tmp2;
delete[] M;
return 0;
}
int main(int argc, char *argv[])
{
// ################### file IO ###################
ifstream fin; // for reading file
ofstream fout; // for writing file
string temp;
// argv[0] 為程式路徑，所以要讀第二個參數，也就是 argv[1]。
if (argc == 2){
// 開檔 input1.txt
fin.open(argv[1]);
}
// 如果沒有在 command line 輸入參數，則從程式裡面輸入。
else{
cout << "Please input file name: ";
cin >> temp;
// 開檔 input1.txt
fin.open(temp.c_str()); // c_str() : string to char string
}
// 若開檔 input1.txt 失敗，可能是檔案不存在。
if (fin.fail()){
cout << "Fail to open file\n";
exit(1); // 非正常結束程式
}
// 建新檔 output1.txt，預設為覆蓋。
string output_fileName = "output";
output_fileName = output_fileName + argv[1][5] + ".txt";
fout.open(output_fileName.c_str());
// 若開檔 output1.txt 失敗
if (fout.fail()){
cout << "Fail to open file\n";
exit(1); // 非正常結束程式
}
// ################### file parse ###################
char m;
char cur_operator, next_operator;
int a, b;
int polyNumber = 1;
Polynomial polyResult;
// string operator = "+";
while (!fin.eof()){ // not End-of-file，尚未讀到結尾。
Polynomial poly;
// set each Polynomial block
while(true){
fin >> a >> b; // '>>' 等同 get()，character by character
poly.set(b, a); // Polynomial set()
fin.get(); // 把換行符號吃掉。
m = fin.get(); // 嘗試吃一個 character
// 如果 m 是 operator
if( m == '+' || m == '*'){
next_operator = m;
break;
}
else if( m == EOF ){ // end-of-file
break;
}
else{
fin.putback(m); // 呃，吃錯了，吐回去。
}
}
//print every poly 寫進 output file
fout << "Polynomial " << polyNumber << ":" << poly.getPoly() << endl;
fout << "Degree:"<< poly.getDegree() << endl;
fout << "# of nonzero var: " << poly.getNonZero() << endl<< endl;
if( polyNumber == 1 ){
polyResult.add(poly);
}
else if( cur_operator == '+'){
polyResult.add(poly);
}
else if( cur_operator == '*'){
polyResult.multiplies(poly);
}
cur_operator = next_operator;
polyNumber++;
}
//printPolyResult
fout << "Result Polynomial:" << polyResult.getPoly() << endl;
fout << "Degree:"<< polyResult.getDegree() << endl;
fout << "# of nonzero var: " << polyResult.getNonZero();
// file close
fin.close();
fout.close();
}
