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/*
Tool chi dung trong truong hop ham f thoa man 2 dieu kien:
- Ham f bieu dien duoc duoi dang 1/2 * xT * A * x + bT * x + c
- A la ma tran xac dinh duong
 
 
 
 
Input:
- Dong dau la 'n': So chieu cua khong gian
- Dong thu hai gom (n+1)*n/2 so: Cac he so cua ham trong bieu dien phan bac 2
- Dong thu ba gom n so: Cac he so cua ham trong bieu dien phan bac 1
- Dong thu tu gom 1 so: He so tu do
- Dong thu nam gom n so: Diem xuat phat
 
Output:
- Bieu dien qua trinh thuc hien quy tac Exact Line Search/Armijo duoi dang bang
 
 
 
 
 
Vi du:
Input:
4
5 1 0 1 4 1 0 3 1 2
2 4 -7 8
6
4 2 3 7
 
-> f(x,y,z,t) = 5x^2 + 1xy  + 0xz  + 1xt
			         + 4y^2 + 1yz  + 0yt
			        	    + 3z^2 + 1zt
			        			   + 2t^2
			  + 2x   + 4y   -7z    + 8t
			  + 6
 
Xuat phat: (x0; y0; z0; t0) = (4; 2; 3; 7);
 
 
Output:
-> Nghiem toi uu cho bai toan min f(x,y,z,t) tren R4:
(0.118055555589,  -0.726851851816,  1.696759259221,  -2.453703703590)
Gia tri nho nhat dat duoc la -11.089120370370
*/
 
 
 
//------- Khoi tao ------------
#include <bits/stdc++.h>
#define up(i,a,b) for (int i = (int)a; i <= (int)b; i++)
#define PB push_back
#define ld long double
using namespace std;
 
const int maxn = 1e5 + 10;
ld epsilon;
int precision_digit;
 
template <typename T>
string to_string_precs(const T a_value, const int n = precision_digit){
    std::ostringstream out;
    out.precision(n);
    out << std::fixed << a_value;
    return std::move(out).str();
}
 
vector<ld> x[maxn];
ld t[maxn], res[maxn];
vector<string> fin[maxn];
string description[maxn];
string indent[maxn];
 
 
 
 
 
 
//--------- Cac ham quan trong ---------------
//Tich vo huong cua hai vector
ld DOT(const vector<ld>& A, const vector<ld>& B, int n){
    ld sum = 0;
    up(i, 0, n-1) sum += A[i] * B[i];
    return sum;
}
 
//Gia tri ham f doi voi ma tran A, B, C tai diem X, khong gian n chieu.
//f = 1/2 * xT * A * x + bT * x + c
ld f(const vector<vector<ld> >& A, const vector<ld>& B, const ld& C, const vector<ld>& X, const int& n){
    vector<ld> temp(n, 0);
    up(j, 0, n-1){
        for (int i = 0; i <= j; i++){
            ld H = A[i][j];
            if (i == j) H /= 2;
            temp[j] += X[i] * H;
        }
    }
 
    ld sum = DOT(temp, X, n) + DOT(B, X, n) + C;
    return sum;
}
 
//Gradient tai diem X
vector<ld> GRAD(const vector<vector<ld> >& A, const vector<ld>& B, const vector<ld>& X, const int& n){
    vector<ld> temp(n, 0);
    up(j, 0, n-1) up(i, 0, n-1){
        temp[j] += X[i] * A[i][j];
    }
    up(i, 0, n-1) temp[i] += B[i];
 
    return temp;
}
 
//Am Gradient tai diem X
vector<ld> MINUS_GRAD(const vector<vector<ld> >& A, const vector<ld>& B, const vector<ld>& X, const int& n){
    vector<ld> temp(n, 0);
    temp = GRAD(A, B, X, n);
    up(i, 0, n-1) temp[i] = -temp[i];
    return temp;
}
 
//Tich cua mot vector [1 x n] voi mot ma tran [n x n] -> vector [1 x n]
vector<ld> MXV(const vector<vector<ld> >& A, const vector<ld>& X, const int& n){
    vector<ld> temp(n, 0);
    up(j, 0, n-1) up(i, 0, n-1){
        temp[j] += X[i] * A[i][j];
    }
    return temp;
}
 
//X_(k+1) = X_(k) + t_(k)*d_(k)
vector<ld> FIND_NEXT(const vector<ld>& X, const ld& T, const vector<ld>& D, const int& n){
    vector<ld> temp(n, 0);
    up(i, 0, n-1) temp[i] = X[i] + T*D[i];
    return temp;
}
 
 
 
 
 
 
 
 
 
//------- Exact line search starts ---------
ld Exact_line_search (const vector<vector<ld> >& A, const vector<ld>& B, const ld& C, const vector<ld>& X, const vector<ld>& d, const int& n){
    return (DOT(d, d, n))/DOT(MXV(A, d, n), d, n);
}
 
//----- Armijo starts ---------
int cnt = 0;
ld t0, m, alpha, beta;
ld Armijo_step_size(const vector<vector<ld> >& A, const vector<ld>& B, const ld& C, const vector<ld>& X, const vector<ld>& d, const int& n) {
    ld t = t0;  // Reset t ve t0 cap nhat duoc gan nhat trong moi lan tim co buoc phu hop
 
    ld fx = f(A, B, C, X, n);
    ld grad_dot_d = DOT(GRAD(A, B, X, n), d, n);
    while (true) {
        vector<ld> X_new = FIND_NEXT(X, t, d, n);
        ld fx_new = f(A, B, C, X_new, n);
        if (fx_new - fx <= m * t * grad_dot_d) {
            t0 = t;
            return t;
        }
        t *= alpha;
        if (t < beta) break;
        ++cnt;
    }
    return t;
}
 
 
 
 
 
 
 
//------ GRADIENT DESCENT CONCEPT --------
void Gradient_Descent(vector<vector<ld> >& A, vector<ld>& B, ld& C, vector<ld>& X, int n, int& lim,
           ld (*kind)(const vector<vector<ld> >&, const vector<ld>&, const ld&, const vector<ld>&, const vector<ld>&, const int&)){
    x[0] = X;
    res[0] = f(A, B, C, x[0], n);
 
    for (int i = 1; i <= lim; i++){
        vector<ld> d = MINUS_GRAD(A, B, x[i-1], n);
        if (sqrt(DOT(d, d, n)) < epsilon){
            cout << "Desired stationary point found at iteration: " << i-1 << "\n\n";
            lim = i-1;
            break;
        }
 
        t[i-1] = kind(A, B, C, X, d, n);
        x[i] = FIND_NEXT(x[i-1], t[i-1], d, n);
        res[i] = f(A, B, C, x[i], n);
    }
}
 
 
 
 
 
 
 
 
//------ INPUT + PREPROCESSING ----------
void input(vector<vector<ld> >& A, vector<ld>& B, ld& C, vector<ld>& X, int& n){
    up(i, 0, n-1) up(j, i, n-1) cin >> A[i][j];
    //xx xy xz yy yz zz
 
    up(i, 0, n-1) cin >> B[i];
    //x y z
 
    cin >> C;
    //C
 
    up(i, 0, n-1) cin >> X[i];
    //x1 x2 x3
 
    up(i, 0, n-1){
        up(j, i, n-1){
            if (i == j) A[i][j] *= 2;
            else A[j][i] = A[i][j];
        }
    }
    // A in 1/2(xT*A*x)
}
 
 
 
 
 
 
 
// ------ OUTPUT ---------
void parse_indent(const vector<string>& fin, const int& max_length){
    int k = (int)fin.size();
    description[0] = "i";
    description[k-1] = "delta f";
    description[k-1 - 1] = "ti";
    description[k-1 - 2] = "f";
 
    for (int i = 1; i < k-1 - 2; i++){
        string cur_description = "x" + to_string(i);
        description[i] = cur_description;
    }
 
    up(i, 0, k-1) indent[i] = string(max_length+2, ' ');
}
 
void print_columns(const vector<string>& fin, const int& max_length){
    up(i, 0, fin.size()-1){
        cout << description[i];
        cout << indent[i];
    }
    cout << "\n";
}
 
void print_result_table(const int& lim, const int& max_length){
    up(i,0,lim){
        for (int j = 0; j < (int)fin[i].size(); j++){
            cout << fin[i][j] << " ";
            if ((int)fin[i][j].size() < max_length){
                int dotdot = max_length - (int)fin[i][j].size();
                if (j == 0) dotdot -= (max_length - 7);
                cout << string(dotdot, ' ');
            }
            cout << "|  ";
        }
        cout << "\n";
    }
    cout << "\n";
}
 
 
 
 
 
 
 
 
//--------- MAIN -------------
signed main(){
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    #define Task "A"
    if (fopen(Task".inp", "r")){
        freopen(Task".inp", "r", stdin);
        freopen(Task".out", "w", stdout);
    }
 
    cout << fixed << setprecision(12);
 
// --------- INPUT ------------
    int n;
    cin >> n;
 
    vector<vector<ld> > A(n, vector<ld>(n, 0));
    vector<ld> B(n, 0);
    ld C;
    vector<ld> X(n, 0);
    input(A, B, C, X, n);
 
 
 
 
 
 
 
 
 
 
 
// --------- ALGORITHM ----------
    /**
        int lim = 10000;            // So lan lap toi da
        ld t0 = 1;                  // t0 ban dau trong thuat toan Armijo
        ld m = 0.5;                 // He so dieu kien: nen dat trong khoang [0.5 -> 0.7]
        ld alpha = 0.9;             // Learning rate: nen dat trong khoang [0.5 -> 0.95]
        ld beta = 1e-6;             // Co buoc toi thieu: cham qua thi thoi
        ld epsilon = 1e-9;          // Gia tri toi thieu can dat duoc cua NORM(GRAD(diem dung)): cang chuan -> chay cang cham
        int precision_digit = 12;   // So chu so sau dau phay khi hien thi ket qua
    **/
    int lim = 50000;
    t0 = 1;
    m = 0.5;
    alpha = 0.8;
    beta = 1e-6;
    epsilon = 1e-5;
    precision_digit = 5;
    Gradient_Descent(A, B, C, X, n, lim, Armijo_step_size);
//     Gradient_Descent(A, B, C, X, n, lim, Exact_line_search);
 
 
 
 
 
 
 
 
 
 
 
 
 
//-------- Parsing Output -----------
    up(i, 0, lim){
        fin[i].PB(to_string_precs(i));
        up(j, 0, n-1){
            fin[i].PB(to_string_precs(x[i][j]));
        }
        fin[i].PB(to_string_precs(res[i]));
        fin[i].PB(to_string_precs(t[i]));
        fin[i].PB(to_string_precs(res[i] - res[i-1]));
    }
 
    int max_length = 0;
    up(i, 0, lim){
        for (int j = 0; j < (int)fin[i].size(); j++){
            max_length = max(max_length, (int)fin[i][j].size());
        }
    }
 
//---- Printing the result table ----
    parse_indent(fin[0], max_length);
    print_columns(fin[0], max_length);
    print_result_table(lim, max_length);
    cout << "Tong so buoc t = alpha*t trong thuat toan Armijo: " << cnt;
}

/*
Tool chi dung trong truong hop ham f thoa man 2 dieu kien:
- Ham f bieu dien duoc duoi dang 1/2 * xT * A * x + bT * x + c
- A la ma tran xac dinh duong




Input:
- Dong dau la 'n': So chieu cua khong gian
- Dong thu hai gom (n+1)*n/2 so: Cac he so cua ham trong bieu dien phan bac 2
- Dong thu ba gom n so: Cac he so cua ham trong bieu dien phan bac 1
- Dong thu tu gom 1 so: He so tu do
- Dong thu nam gom n so: Diem xuat phat

Output:
- Bieu dien qua trinh thuc hien quy tac Exact Line Search/Armijo duoi dang bang





Vi du:
Input:
4
5 1 0 1 4 1 0 3 1 2
2 4 -7 8
6
4 2 3 7

-> f(x,y,z,t) = 5x^2 + 1xy  + 0xz  + 1xt
			         + 4y^2 + 1yz  + 0yt
			        	    + 3z^2 + 1zt
			        			   + 2t^2
			  + 2x   + 4y   -7z    + 8t
			  + 6

Xuat phat: (x0; y0; z0; t0) = (4; 2; 3; 7);


Output:
-> Nghiem toi uu cho bai toan min f(x,y,z,t) tren R4:
(0.118055555589,  -0.726851851816,  1.696759259221,  -2.453703703590)
Gia tri nho nhat dat duoc la -11.089120370370
*/



//------- Khoi tao ------------
#include <bits/stdc++.h>
#define up(i,a,b) for (int i = (int)a; i <= (int)b; i++)
#define PB push_back
#define ld long double
using namespace std;

const int maxn = 1e5 + 10;
ld epsilon;
int precision_digit;

template <typename T>
string to_string_precs(const T a_value, const int n = precision_digit){
    std::ostringstream out;
    out.precision(n);
    out << std::fixed << a_value;
    return std::move(out).str();
}

vector<ld> x[maxn];
ld t[maxn], res[maxn];
vector<string> fin[maxn];
string description[maxn];
string indent[maxn];






//--------- Cac ham quan trong ---------------
//Tich vo huong cua hai vector
ld DOT(const vector<ld>& A, const vector<ld>& B, int n){
    ld sum = 0;
    up(i, 0, n-1) sum += A[i] * B[i];
    return sum;
}

//Gia tri ham f doi voi ma tran A, B, C tai diem X, khong gian n chieu.
//f = 1/2 * xT * A * x + bT * x + c
ld f(const vector<vector<ld> >& A, const vector<ld>& B, const ld& C, const vector<ld>& X, const int& n){
    vector<ld> temp(n, 0);
    up(j, 0, n-1){
        for (int i = 0; i <= j; i++){
            ld H = A[i][j];
            if (i == j) H /= 2;
            temp[j] += X[i] * H;
        }
    }

    ld sum = DOT(temp, X, n) + DOT(B, X, n) + C;
    return sum;
}

//Gradient tai diem X
vector<ld> GRAD(const vector<vector<ld> >& A, const vector<ld>& B, const vector<ld>& X, const int& n){
    vector<ld> temp(n, 0);
    up(j, 0, n-1) up(i, 0, n-1){
        temp[j] += X[i] * A[i][j];
    }
    up(i, 0, n-1) temp[i] += B[i];

    return temp;
}

//Am Gradient tai diem X
vector<ld> MINUS_GRAD(const vector<vector<ld> >& A, const vector<ld>& B, const vector<ld>& X, const int& n){
    vector<ld> temp(n, 0);
    temp = GRAD(A, B, X, n);
    up(i, 0, n-1) temp[i] = -temp[i];
    return temp;
}

//Tich cua mot vector [1 x n] voi mot ma tran [n x n] -> vector [1 x n]
vector<ld> MXV(const vector<vector<ld> >& A, const vector<ld>& X, const int& n){
    vector<ld> temp(n, 0);
    up(j, 0, n-1) up(i, 0, n-1){
        temp[j] += X[i] * A[i][j];
    }
    return temp;
}

//X_(k+1) = X_(k) + t_(k)*d_(k)
vector<ld> FIND_NEXT(const vector<ld>& X, const ld& T, const vector<ld>& D, const int& n){
    vector<ld> temp(n, 0);
    up(i, 0, n-1) temp[i] = X[i] + T*D[i];
    return temp;
}









//------- Exact line search starts ---------
ld Exact_line_search (const vector<vector<ld> >& A, const vector<ld>& B, const ld& C, const vector<ld>& X, const vector<ld>& d, const int& n){
    return (DOT(d, d, n))/DOT(MXV(A, d, n), d, n);
}

//----- Armijo starts ---------
int cnt = 0;
ld t0, m, alpha, beta;
ld Armijo_step_size(const vector<vector<ld> >& A, const vector<ld>& B, const ld& C, const vector<ld>& X, const vector<ld>& d, const int& n) {
    ld t = t0;  // Reset t ve t0 cap nhat duoc gan nhat trong moi lan tim co buoc phu hop

    ld fx = f(A, B, C, X, n);
    ld grad_dot_d = DOT(GRAD(A, B, X, n), d, n);
    while (true) {
        vector<ld> X_new = FIND_NEXT(X, t, d, n);
        ld fx_new = f(A, B, C, X_new, n);
        if (fx_new - fx <= m * t * grad_dot_d) {
            t0 = t;
            return t;
        }
        t *= alpha;
        if (t < beta) break;
        ++cnt;
    }
    return t;
}







//------ GRADIENT DESCENT CONCEPT --------
void Gradient_Descent(vector<vector<ld> >& A, vector<ld>& B, ld& C, vector<ld>& X, int n, int& lim,
           ld (*kind)(const vector<vector<ld> >&, const vector<ld>&, const ld&, const vector<ld>&, const vector<ld>&, const int&)){
    x[0] = X;
    res[0] = f(A, B, C, x[0], n);

    for (int i = 1; i <= lim; i++){
        vector<ld> d = MINUS_GRAD(A, B, x[i-1], n);
        if (sqrt(DOT(d, d, n)) < epsilon){
            cout << "Desired stationary point found at iteration: " << i-1 << "\n\n";
            lim = i-1;
            break;
        }

        t[i-1] = kind(A, B, C, X, d, n);
        x[i] = FIND_NEXT(x[i-1], t[i-1], d, n);
        res[i] = f(A, B, C, x[i], n);
    }
}








//------ INPUT + PREPROCESSING ----------
void input(vector<vector<ld> >& A, vector<ld>& B, ld& C, vector<ld>& X, int& n){
    up(i, 0, n-1) up(j, i, n-1) cin >> A[i][j];
    //xx xy xz yy yz zz

    up(i, 0, n-1) cin >> B[i];
    //x y z

    cin >> C;
    //C

    up(i, 0, n-1) cin >> X[i];
    //x1 x2 x3

    up(i, 0, n-1){
        up(j, i, n-1){
            if (i == j) A[i][j] *= 2;
            else A[j][i] = A[i][j];
        }
    }
    // A in 1/2(xT*A*x)
}







// ------ OUTPUT ---------
void parse_indent(const vector<string>& fin, const int& max_length){
    int k = (int)fin.size();
    description[0] = "i";
    description[k-1] = "delta f";
    description[k-1 - 1] = "ti";
    description[k-1 - 2] = "f";

    for (int i = 1; i < k-1 - 2; i++){
        string cur_description = "x" + to_string(i);
        description[i] = cur_description;
    }

    up(i, 0, k-1) indent[i] = string(max_length+2, ' ');
}

void print_columns(const vector<string>& fin, const int& max_length){
    up(i, 0, fin.size()-1){
        cout << description[i];
        cout << indent[i];
    }
    cout << "\n";
}

void print_result_table(const int& lim, const int& max_length){
    up(i,0,lim){
        for (int j = 0; j < (int)fin[i].size(); j++){
            cout << fin[i][j] << " ";
            if ((int)fin[i][j].size() < max_length){
                int dotdot = max_length - (int)fin[i][j].size();
                if (j == 0) dotdot -= (max_length - 7);
                cout << string(dotdot, ' ');
            }
            cout << "|  ";
        }
        cout << "\n";
    }
    cout << "\n";
}








//--------- MAIN -------------
signed main(){
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    #define Task "A"
    if (fopen(Task".inp", "r")){
        freopen(Task".inp", "r", stdin);
        freopen(Task".out", "w", stdout);
    }

    cout << fixed << setprecision(12);

// --------- INPUT ------------
    int n;
    cin >> n;

    vector<vector<ld> > A(n, vector<ld>(n, 0));
    vector<ld> B(n, 0);
    ld C;
    vector<ld> X(n, 0);
    input(A, B, C, X, n);











// --------- ALGORITHM ----------
    /**
        int lim = 10000;            // So lan lap toi da
        ld t0 = 1;                  // t0 ban dau trong thuat toan Armijo
        ld m = 0.5;                 // He so dieu kien: nen dat trong khoang [0.5 -> 0.7]
        ld alpha = 0.9;             // Learning rate: nen dat trong khoang [0.5 -> 0.95]
        ld beta = 1e-6;             // Co buoc toi thieu: cham qua thi thoi
        ld epsilon = 1e-9;          // Gia tri toi thieu can dat duoc cua NORM(GRAD(diem dung)): cang chuan -> chay cang cham
        int precision_digit = 12;   // So chu so sau dau phay khi hien thi ket qua
    **/
    int lim = 50000;
    t0 = 1;
    m = 0.5;
    alpha = 0.8;
    beta = 1e-6;
    epsilon = 1e-5;
    precision_digit = 5;
    Gradient_Descent(A, B, C, X, n, lim, Armijo_step_size);
//     Gradient_Descent(A, B, C, X, n, lim, Exact_line_search);













//-------- Parsing Output -----------
    up(i, 0, lim){
        fin[i].PB(to_string_precs(i));
        up(j, 0, n-1){
            fin[i].PB(to_string_precs(x[i][j]));
        }
        fin[i].PB(to_string_precs(res[i]));
        fin[i].PB(to_string_precs(t[i]));
        fin[i].PB(to_string_precs(res[i] - res[i-1]));
    }

    int max_length = 0;
    up(i, 0, lim){
        for (int j = 0; j < (int)fin[i].size(); j++){
            max_length = max(max_length, (int)fin[i][j].size());
        }
    }

//---- Printing the result table ----
    parse_indent(fin[0], max_length);
    print_columns(fin[0], max_length);
    print_result_table(lim, max_length);
    cout << "Tong so buoc t = alpha*t trong thuat toan Armijo: " << cnt;
}


Success #stdin #stdout 0.01s 17936KB

stdin

4
5 1 0 1 4 1 0 3 1 2
2 4 -7 8
6
4 2 3 7

3
4 1 0 3 1 2
-7 5 4
12
4 7 5

2
1 2 4
-7 5
3
4 7

stdout

Desired stationary point found at iteration: 229

i            x1            x2            x3            x4            f            ti            delta f            
0       |  4.00000    |  2.00000    |  3.00000    |  7.00000    |  341.00000  |  0.10737    |  341.00000  |  
1       |  -1.47608   |  -0.89910   |  0.85252    |  2.38291    |  39.28636   |  0.01801    |  -301.71364 |  
2       |  -1.27293   |  -0.83035   |  0.85974    |  2.07832    |  31.94151   |  0.01801    |  -7.34485   |  
3       |  -1.10213   |  -0.77530   |  0.87043    |  1.79189    |  25.87364   |  0.01801    |  -6.06787   |  
4       |  -0.95793   |  -0.73145   |  0.88414    |  1.52283    |  20.80499   |  0.01801    |  -5.06865   |  
5       |  -0.83565   |  -0.69677   |  0.90042    |  1.27031    |  16.53150   |  0.01801    |  -4.27348   |  
6       |  -0.73148   |  -0.66958   |  0.91887    |  1.03350    |  12.90062   |  0.01801    |  -3.63089   |  
7       |  -0.64229   |  -0.64851   |  0.93909    |  0.81153    |  9.79618    |  0.01801    |  -3.10444   |  
8       |  -0.56555   |  -0.63246   |  0.96076    |  0.60359    |  7.12817    |  0.01801    |  -2.66800   |  
9       |  -0.49918   |  -0.62049   |  0.98353    |  0.40887    |  4.82566    |  0.01801    |  -2.30252   |  
10      |  -0.44147   |  -0.61185   |  1.00714    |  0.22656    |  2.83182    |  0.01801    |  -1.99384   |  
11      |  -0.39103   |  -0.60592   |  1.03132    |  0.05593    |  1.10053    |  0.01801    |  -1.73130   |  
12      |  -0.34671   |  -0.60219   |  1.05586    |  -0.10375   |  -0.40618   |  0.01801    |  -1.50670   |  
13      |  -0.30756   |  -0.60024   |  1.08055    |  -0.25316   |  -1.71983   |  0.01801    |  -1.31365   |  
14      |  -0.27281   |  -0.59972   |  1.10523    |  -0.39296   |  -2.86690   |  0.01801    |  -1.14707   |  
15      |  -0.24181   |  -0.60034   |  1.12976    |  -0.52375   |  -3.86976   |  0.01801    |  -1.00287   |  
16      |  -0.21403   |  -0.60188   |  1.15400    |  -0.64613   |  -4.74747   |  0.01801    |  -0.87771   |  
17      |  -0.18902   |  -0.60413   |  1.17785    |  -0.76061   |  -5.51633   |  0.01801    |  -0.76885   |  
18      |  -0.16641   |  -0.60693   |  1.20122    |  -0.86774   |  -6.19033   |  0.01801    |  -0.67400   |  
19      |  -0.14590   |  -0.61016   |  1.22405    |  -0.96796   |  -6.78155   |  0.01801    |  -0.59122   |  
20      |  -0.12722   |  -0.61371   |  1.24628    |  -1.06175   |  -7.30045   |  0.01801    |  -0.51890   |  
21      |  -0.11015   |  -0.61748   |  1.26786    |  -1.14952   |  -7.75609   |  0.01801    |  -0.45564   |  
22      |  -0.09450   |  -0.62141   |  1.28875    |  -1.23166   |  -8.15634   |  0.01801    |  -0.40026   |  
23      |  -0.08012   |  -0.62542   |  1.30894    |  -1.30854   |  -8.50807   |  0.01801    |  -0.35173   |  
24      |  -0.06688   |  -0.62948   |  1.32840    |  -1.38050   |  -8.81726   |  0.01801    |  -0.30919   |  
25      |  -0.05465   |  -0.63355   |  1.34713    |  -1.44786   |  -9.08913   |  0.01801    |  -0.27187   |  
26      |  -0.04334   |  -0.63759   |  1.36512    |  -1.51093   |  -9.32824   |  0.01801    |  -0.23911   |  
27      |  -0.03286   |  -0.64157   |  1.38237    |  -1.56999   |  -9.53860   |  0.01801    |  -0.21035   |  
28      |  -0.02313   |  -0.64548   |  1.39890    |  -1.62528   |  -9.72368   |  0.01801    |  -0.18508   |  
29      |  -0.01408   |  -0.64930   |  1.41470    |  -1.67707   |  -9.88656   |  0.01801    |  -0.16288   |  
30      |  -0.00567   |  -0.65301   |  1.42980    |  -1.72557   |  -10.02993  |  0.01801    |  -0.14337   |  
31      |  0.00217    |  -0.65661   |  1.44421    |  -1.77100   |  -10.15613  |  0.01801    |  -0.12621   |  
32      |  0.00949    |  -0.66010   |  1.45794    |  -1.81355   |  -10.26725  |  0.01801    |  -0.11111   |  
33      |  0.01631    |  -0.66346   |  1.47102    |  -1.85342   |  -10.36508  |  0.01801    |  -0.09784   |  
34      |  0.02268    |  -0.66670   |  1.48346    |  -1.89078   |  -10.45124  |  0.01801    |  -0.08616   |  
35      |  0.02864    |  -0.66981   |  1.49529    |  -1.92578   |  -10.52712  |  0.01801    |  -0.07588   |  
36      |  0.03421    |  -0.67279   |  1.50653    |  -1.95858   |  -10.59395  |  0.01801    |  -0.06683   |  
37      |  0.03942    |  -0.67564   |  1.51720    |  -1.98932   |  -10.65281  |  0.01801    |  -0.05887   |  
38      |  0.04430    |  -0.67837   |  1.52732    |  -2.01813   |  -10.70467  |  0.01801    |  -0.05185   |  
39      |  0.04886    |  -0.68098   |  1.53691    |  -2.04514   |  -10.75035  |  0.01801    |  -0.04568   |  
40      |  0.05314    |  -0.68346   |  1.54600    |  -2.07045   |  -10.79059  |  0.01801    |  -0.04024   |  
41      |  0.05715    |  -0.68583   |  1.55461    |  -2.09418   |  -10.82605  |  0.01801    |  -0.03546   |  
42      |  0.06091    |  -0.68808   |  1.56276    |  -2.11643   |  -10.85729  |  0.01801    |  -0.03124   |  
43      |  0.06443    |  -0.69023   |  1.57047    |  -2.13729   |  -10.88481  |  0.01801    |  -0.02753   |  
44      |  0.06773    |  -0.69226   |  1.57776    |  -2.15685   |  -10.90907  |  0.01801    |  -0.02425   |  
45      |  0.07082    |  -0.69420   |  1.58465    |  -2.17519   |  -10.93044  |  0.01801    |  -0.02137   |  
46      |  0.07373    |  -0.69603   |  1.59116    |  -2.19239   |  -10.94927  |  0.01801    |  -0.01883   |  
47      |  0.07645    |  -0.69777   |  1.59732    |  -2.20852   |  -10.96587  |  0.01801    |  -0.01660   |  
48      |  0.07900    |  -0.69942   |  1.60312    |  -2.22364   |  -10.98049  |  0.01801    |  -0.01463   |  
49      |  0.08140    |  -0.70099   |  1.60861    |  -2.23783   |  -10.99338  |  0.01801    |  -0.01289   |  
50      |  0.08365    |  -0.70247   |  1.61378    |  -2.25114   |  -11.00474  |  0.01801    |  -0.01136   |  
51      |  0.08576    |  -0.70387   |  1.61866    |  -2.26362   |  -11.01475  |  0.01801    |  -0.01001   |  
52      |  0.08774    |  -0.70519   |  1.62326    |  -2.27533   |  -11.02357  |  0.01801    |  -0.00882   |  
53      |  0.08960    |  -0.70644   |  1.62760    |  -2.28631   |  -11.03135  |  0.01801    |  -0.00778   |  
54      |  0.09134    |  -0.70762   |  1.63169    |  -2.29662   |  -11.03820  |  0.01801    |  -0.00685   |  
55      |  0.09298    |  -0.70874   |  1.63555    |  -2.30628   |  -11.04424  |  0.01801    |  -0.00604   |  
56      |  0.09451    |  -0.70980   |  1.63919    |  -2.31535   |  -11.04956  |  0.01801    |  -0.00532   |  
57      |  0.09595    |  -0.71079   |  1.64261    |  -2.32386   |  -11.05426  |  0.01801    |  -0.00469   |  
58      |  0.09731    |  -0.71173   |  1.64583    |  -2.33184   |  -11.05839  |  0.01801    |  -0.00413   |  
59      |  0.09858    |  -0.71262   |  1.64887    |  -2.33933   |  -11.06203  |  0.01801    |  -0.00364   |  
60      |  0.09977    |  -0.71346   |  1.65173    |  -2.34636   |  -11.06525  |  0.01801    |  -0.00321   |  
61      |  0.10089    |  -0.71425   |  1.65442    |  -2.35295   |  -11.06808  |  0.01801    |  -0.00283   |  
62      |  0.10194    |  -0.71499   |  1.65696    |  -2.35914   |  -11.07057  |  0.01801    |  -0.00250   |  
63      |  0.10293    |  -0.71569   |  1.65934    |  -2.36495   |  -11.07277  |  0.01801    |  -0.00220   |  
64      |  0.10385    |  -0.71636   |  1.66159    |  -2.37040   |  -11.07471  |  0.01801    |  -0.00194   |  
65      |  0.10472    |  -0.71698   |  1.66370    |  -2.37551   |  -11.07642  |  0.01801    |  -0.00171   |  
66      |  0.10554    |  -0.71757   |  1.66568    |  -2.38031   |  -11.07793  |  0.01801    |  -0.00151   |  
67      |  0.10630    |  -0.71812   |  1.66755    |  -2.38481   |  -11.07925  |  0.01801    |  -0.00133   |  
68      |  0.10702    |  -0.71864   |  1.66931    |  -2.38904   |  -11.08042  |  0.01801    |  -0.00117   |  
69      |  0.10770    |  -0.71913   |  1.67097    |  -2.39300   |  -11.08145  |  0.01801    |  -0.00103   |  
70      |  0.10833    |  -0.71959   |  1.67252    |  -2.39673   |  -11.08236  |  0.01801    |  -0.00091   |  
71      |  0.10892    |  -0.72003   |  1.67398    |  -2.40022   |  -11.08316  |  0.01801    |  -0.00080   |  
72      |  0.10948    |  -0.72043   |  1.67536    |  -2.40350   |  -11.08387  |  0.01801    |  -0.00071   |  
73      |  0.11001    |  -0.72082   |  1.67665    |  -2.40658   |  -11.08449  |  0.01801    |  -0.00062   |  
74      |  0.11050    |  -0.72118   |  1.67787    |  -2.40947   |  -11.08504  |  0.01801    |  -0.00055   |  
75      |  0.11096    |  -0.72152   |  1.67901    |  -2.41218   |  -11.08553  |  0.01801    |  -0.00048   |  
76      |  0.11140    |  -0.72184   |  1.68009    |  -2.41472   |  -11.08595  |  0.01801    |  -0.00043   |  
77      |  0.11180    |  -0.72214   |  1.68109    |  -2.41711   |  -11.08633  |  0.01801    |  -0.00038   |  
78      |  0.11219    |  -0.72243   |  1.68204    |  -2.41935   |  -11.08666  |  0.01801    |  -0.00033   |  
79      |  0.11254    |  -0.72269   |  1.68294    |  -2.42146   |  -11.08695  |  0.01801    |  -0.00029   |  
80      |  0.11288    |  -0.72295   |  1.68377    |  -2.42343   |  -11.08721  |  0.01801    |  -0.00026   |  
81      |  0.11320    |  -0.72318   |  1.68456    |  -2.42529   |  -11.08743  |  0.01801    |  -0.00023   |  
82      |  0.11349    |  -0.72340   |  1.68530    |  -2.42703   |  -11.08763  |  0.01801    |  -0.00020   |  
83      |  0.11377    |  -0.72361   |  1.68600    |  -2.42866   |  -11.08781  |  0.01801    |  -0.00018   |  
84      |  0.11404    |  -0.72381   |  1.68665    |  -2.43019   |  -11.08797  |  0.01801    |  -0.00016   |  
85      |  0.11428    |  -0.72399   |  1.68727    |  -2.43163   |  -11.08810  |  0.01801    |  -0.00014   |  
86      |  0.11451    |  -0.72416   |  1.68784    |  -2.43299   |  -11.08822  |  0.01801    |  -0.00012   |  
87      |  0.11473    |  -0.72433   |  1.68838    |  -2.43425   |  -11.08833  |  0.01801    |  -0.00011   |  
88      |  0.11493    |  -0.72448   |  1.68889    |  -2.43544   |  -11.08842  |  0.01801    |  -0.00009   |  
89      |  0.11512    |  -0.72462   |  1.68937    |  -2.43656   |  -11.08851  |  0.01801    |  -0.00008   |  
90      |  0.11530    |  -0.72476   |  1.68982    |  -2.43761   |  -11.08858  |  0.01801    |  -0.00007   |  
91      |  0.11547    |  -0.72489   |  1.69024    |  -2.43860   |  -11.08864  |  0.01801    |  -0.00006   |  
92      |  0.11563    |  -0.72501   |  1.69064    |  -2.43952   |  -11.08870  |  0.01801    |  -0.00006   |  
93      |  0.11578    |  -0.72512   |  1.69101    |  -2.44039   |  -11.08875  |  0.01801    |  -0.00005   |  
94      |  0.11592    |  -0.72522   |  1.69136    |  -2.44120   |  -11.08879  |  0.01801    |  -0.00004   |  
95      |  0.11605    |  -0.72532   |  1.69169    |  -2.44197   |  -11.08883  |  0.01801    |  -0.00004   |  
96      |  0.11617    |  -0.72542   |  1.69200    |  -2.44269   |  -11.08887  |  0.01801    |  -0.00003   |  
97      |  0.11629    |  -0.72550   |  1.69229    |  -2.44336   |  -11.08890  |  0.01801    |  -0.00003   |  
98      |  0.11639    |  -0.72558   |  1.69256    |  -2.44399   |  -11.08892  |  0.01801    |  -0.00003   |  
99      |  0.11650    |  -0.72566   |  1.69282    |  -2.44459   |  -11.08895  |  0.01801    |  -0.00002   |  
100     |  0.11659    |  -0.72573   |  1.69306    |  -2.44515   |  -11.08897  |  0.01801    |  -0.00002   |  
101     |  0.11668    |  -0.72580   |  1.69328    |  -2.44567   |  -11.08899  |  0.01801    |  -0.00002   |  
102     |  0.11676    |  -0.72587   |  1.69350    |  -2.44616   |  -11.08900  |  0.01801    |  -0.00002   |  
103     |  0.11684    |  -0.72593   |  1.69370    |  -2.44662   |  -11.08902  |  0.01801    |  -0.00001   |  
104     |  0.11692    |  -0.72598   |  1.69388    |  -2.44706   |  -11.08903  |  0.01801    |  -0.00001   |  
105     |  0.11699    |  -0.72604   |  1.69406    |  -2.44746   |  -11.08904  |  0.01801    |  -0.00001   |  
106     |  0.11705    |  -0.72609   |  1.69422    |  -2.44784   |  -11.08905  |  0.01801    |  -0.00001   |  
107     |  0.11711    |  -0.72613   |  1.69438    |  -2.44820   |  -11.08906  |  0.01801    |  -0.00001   |  
108     |  0.11717    |  -0.72618   |  1.69452    |  -2.44854   |  -11.08906  |  0.01801    |  -0.00001   |  
109     |  0.11723    |  -0.72622   |  1.69466    |  -2.44886   |  -11.08907  |  0.01801    |  -0.00001   |  
110     |  0.11728    |  -0.72626   |  1.69479    |  -2.44915   |  -11.08908  |  0.01801    |  -0.00001   |  
111     |  0.11732    |  -0.72629   |  1.69491    |  -2.44943   |  -11.08908  |  0.01801    |  -0.00001   |  
112     |  0.11737    |  -0.72633   |  1.69502    |  -2.44969   |  -11.08909  |  0.01801    |  -0.00000   |  
113     |  0.11741    |  -0.72636   |  1.69513    |  -2.44994   |  -11.08909  |  0.01801    |  -0.00000   |  
114     |  0.11745    |  -0.72639   |  1.69523    |  -2.45017   |  -11.08909  |  0.01801    |  -0.00000   |  
115     |  0.11749    |  -0.72642   |  1.69532    |  -2.45038   |  -11.08910  |  0.01801    |  -0.00000   |  
116     |  0.11752    |  -0.72644   |  1.69541    |  -2.45059   |  -11.08910  |  0.01801    |  -0.00000   |  
117     |  0.11755    |  -0.72647   |  1.69549    |  -2.45078   |  -11.08910  |  0.01801    |  -0.00000   |  
118     |  0.11759    |  -0.72649   |  1.69557    |  -2.45096   |  -11.08910  |  0.01801    |  -0.00000   |  
119     |  0.11761    |  -0.72651   |  1.69564    |  -2.45112   |  -11.08911  |  0.01801    |  -0.00000   |  
120     |  0.11764    |  -0.72653   |  1.69571    |  -2.45128   |  -11.08911  |  0.01801    |  -0.00000   |  
121     |  0.11767    |  -0.72655   |  1.69577    |  -2.45143   |  -11.08911  |  0.01801    |  -0.00000   |  
122     |  0.11769    |  -0.72657   |  1.69583    |  -2.45157   |  -11.08911  |  0.01801    |  -0.00000   |  
123     |  0.11771    |  -0.72659   |  1.69589    |  -2.45170   |  -11.08911  |  0.01801    |  -0.00000   |  
124     |  0.11773    |  -0.72660   |  1.69594    |  -2.45182   |  -11.08911  |  0.01801    |  -0.00000   |  
125     |  0.11775    |  -0.72662   |  1.69599    |  -2.45194   |  -11.08911  |  0.01801    |  -0.00000   |  
126     |  0.11777    |  -0.72663   |  1.69604    |  -2.45205   |  -11.08911  |  0.01801    |  -0.00000   |  
127     |  0.11779    |  -0.72665   |  1.69608    |  -2.45215   |  -11.08912  |  0.01801    |  -0.00000   |  
128     |  0.11781    |  -0.72666   |  1.69613    |  -2.45224   |  -11.08912  |  0.01801    |  -0.00000   |  
129     |  0.11782    |  -0.72667   |  1.69616    |  -2.45233   |  -11.08912  |  0.01801    |  -0.00000   |  
130     |  0.11783    |  -0.72668   |  1.69620    |  -2.45242   |  -11.08912  |  0.01801    |  -0.00000   |  
131     |  0.11785    |  -0.72669   |  1.69623    |  -2.45249   |  -11.08912  |  0.01801    |  -0.00000   |  
132     |  0.11786    |  -0.72670   |  1.69627    |  -2.45257   |  -11.08912  |  0.01801    |  -0.00000   |  
133     |  0.11787    |  -0.72671   |  1.69630    |  -2.45264   |  -11.08912  |  0.01801    |  -0.00000   |  
134     |  0.11788    |  -0.72672   |  1.69632    |  -2.45270   |  -11.08912  |  0.01801    |  -0.00000   |  
135     |  0.11789    |  -0.72673   |  1.69635    |  -2.45276   |  -11.08912  |  0.01801    |  -0.00000   |  
136     |  0.11790    |  -0.72674   |  1.69638    |  -2.45282   |  -11.08912  |  0.01801    |  -0.00000   |  
137     |  0.11791    |  -0.72674   |  1.69640    |  -2.45288   |  -11.08912  |  0.01801    |  -0.00000   |  
138     |  0.11792    |  -0.72675   |  1.69642    |  -2.45293   |  -11.08912  |  0.01801    |  -0.00000   |  
139     |  0.11793    |  -0.72676   |  1.69644    |  -2.45297   |  -11.08912  |  0.01801    |  -0.00000   |  
140     |  0.11794    |  -0.72676   |  1.69646    |  -2.45302   |  -11.08912  |  0.01801    |  -0.00000   |  
141     |  0.11795    |  -0.72677   |  1.69648    |  -2.45306   |  -11.08912  |  0.01801    |  -0.00000   |  
142     |  0.11795    |  -0.72677   |  1.69650    |  -2.45310   |  -11.08912  |  0.01801    |  -0.00000   |  
143     |  0.11796    |  -0.72678   |  1.69651    |  -2.45314   |  -11.08912  |  0.01801    |  -0.00000   |  
144     |  0.11796    |  -0.72678   |  1.69653    |  -2.45317   |  -11.08912  |  0.01801    |  -0.00000   |  
145     |  0.11797    |  -0.72679   |  1.69654    |  -2.45320   |  -11.08912  |  0.01801    |  -0.00000   |  
146     |  0.11798    |  -0.72679   |  1.69656    |  -2.45323   |  -11.08912  |  0.01801    |  -0.00000   |  
147     |  0.11798    |  -0.72679   |  1.69657    |  -2.45326   |  -11.08912  |  0.01801    |  -0.00000   |  
148     |  0.11798    |  -0.72680   |  1.69658    |  -2.45329   |  -11.08912  |  0.01801    |  -0.00000   |  
149     |  0.11799    |  -0.72680   |  1.69659    |  -2.45332   |  -11.08912  |  0.01801    |  -0.00000   |  
150     |  0.11799    |  -0.72680   |  1.69660    |  -2.45334   |  -11.08912  |  0.01801    |  -0.00000   |  
151     |  0.11800    |  -0.72681   |  1.69661    |  -2.45336   |  -11.08912  |  0.01801    |  -0.00000   |  
152     |  0.11800    |  -0.72681   |  1.69662    |  -2.45338   |  -11.08912  |  0.01801    |  -0.00000   |  
153     |  0.11800    |  -0.72681   |  1.69663    |  -2.45340   |  -11.08912  |  0.01801    |  -0.00000   |  
154     |  0.11801    |  -0.72681   |  1.69664    |  -2.45342   |  -11.08912  |  0.01801    |  -0.00000   |  
155     |  0.11801    |  -0.72682   |  1.69664    |  -2.45344   |  -11.08912  |  0.01801    |  -0.00000   |  
156     |  0.11801    |  -0.72682   |  1.69665    |  -2.45345   |  -11.08912  |  0.01801    |  -0.00000   |  
157     |  0.11802    |  -0.72682   |  1.69666    |  -2.45347   |  -11.08912  |  0.01801    |  -0.00000   |  
158     |  0.11802    |  -0.72682   |  1.69666    |  -2.45348   |  -11.08912  |  0.01801    |  -0.00000   |  
159     |  0.11802    |  -0.72682   |  1.69667    |  -2.45350   |  -11.08912  |  0.01801    |  -0.00000   |  
160     |  0.11802    |  -0.72683   |  1.69668    |  -2.45351   |  -11.08912  |  0.01801    |  -0.00000   |  
161     |  0.11802    |  -0.72683   |  1.69668    |  -2.45352   |  -11.08912  |  0.01801    |  -0.00000   |  
162     |  0.11803    |  -0.72683   |  1.69669    |  -2.45353   |  -11.08912  |  0.01801    |  -0.00000   |  
163     |  0.11803    |  -0.72683   |  1.69669    |  -2.45354   |  -11.08912  |  0.01801    |  -0.00000   |  
164     |  0.11803    |  -0.72683   |  1.69669    |  -2.45355   |  -11.08912  |  0.01801    |  -0.00000   |  
165     |  0.11803    |  -0.72683   |  1.69670    |  -2.45356   |  -11.08912  |  0.01801    |  -0.00000   |  
166     |  0.11803    |  -0.72683   |  1.69670    |  -2.45357   |  -11.08912  |  0.01801    |  -0.00000   |  
167     |  0.11803    |  -0.72684   |  1.69671    |  -2.45358   |  -11.08912  |  0.01801    |  -0.00000   |  
168     |  0.11804    |  -0.72684   |  1.69671    |  -2.45359   |  -11.08912  |  0.01801    |  -0.00000   |  
169     |  0.11804    |  -0.72684   |  1.69671    |  -2.45359   |  -11.08912  |  0.01801    |  -0.00000   |  
170     |  0.11804    |  -0.72684   |  1.69671    |  -2.45360   |  -11.08912  |  0.01801    |  -0.00000   |  
171     |  0.11804    |  -0.72684   |  1.69672    |  -2.45361   |  -11.08912  |  0.01801    |  -0.00000   |  
172     |  0.11804    |  -0.72684   |  1.69672    |  -2.45361   |  -11.08912  |  0.01801    |  -0.00000   |  
173     |  0.11804    |  -0.72684   |  1.69672    |  -2.45362   |  -11.08912  |  0.01801    |  -0.00000   |  
174     |  0.11804    |  -0.72684   |  1.69672    |  -2.45362   |  -11.08912  |  0.01801    |  -0.00000   |  
175     |  0.11804    |  -0.72684   |  1.69673    |  -2.45363   |  -11.08912  |  0.01801    |  -0.00000   |  
176     |  0.11804    |  -0.72684   |  1.69673    |  -2.45363   |  -11.08912  |  0.01801    |  -0.00000   |  
177     |  0.11804    |  -0.72684   |  1.69673    |  -2.45364   |  -11.08912  |  0.01801    |  -0.00000   |  
178     |  0.11804    |  -0.72684   |  1.69673    |  -2.45364   |  -11.08912  |  0.01801    |  -0.00000   |  
179     |  0.11805    |  -0.72684   |  1.69673    |  -2.45365   |  -11.08912  |  0.01801    |  -0.00000   |  
180     |  0.11805    |  -0.72684   |  1.69674    |  -2.45365   |  -11.08912  |  0.01801    |  -0.00000   |  
181     |  0.11805    |  -0.72685   |  1.69674    |  -2.45365   |  -11.08912  |  0.01801    |  -0.00000   |  
182     |  0.11805    |  -0.72685   |  1.69674    |  -2.45366   |  -11.08912  |  0.01801    |  -0.00000   |  
183     |  0.11805    |  -0.72685   |  1.69674    |  -2.45366   |  -11.08912  |  0.01801    |  -0.00000   |  
184     |  0.11805    |  -0.72685   |  1.69674    |  -2.45366   |  -11.08912  |  0.01801    |  -0.00000   |  
185     |  0.11805    |  -0.72685   |  1.69674    |  -2.45366   |  -11.08912  |  0.01801    |  -0.00000   |  
186     |  0.11805    |  -0.72685   |  1.69674    |  -2.45367   |  -11.08912  |  0.01801    |  -0.00000   |  
187     |  0.11805    |  -0.72685   |  1.69674    |  -2.45367   |  -11.08912  |  0.01801    |  -0.00000   |  
188     |  0.11805    |  -0.72685   |  1.69674    |  -2.45367   |  -11.08912  |  0.01801    |  -0.00000   |  
189     |  0.11805    |  -0.72685   |  1.69675    |  -2.45367   |  -11.08912  |  0.01801    |  -0.00000   |  
190     |  0.11805    |  -0.72685   |  1.69675    |  -2.45367   |  -11.08912  |  0.01801    |  -0.00000   |  
191     |  0.11805    |  -0.72685   |  1.69675    |  -2.45368   |  -11.08912  |  0.01801    |  -0.00000   |  
192     |  0.11805    |  -0.72685   |  1.69675    |  -2.45368   |  -11.08912  |  0.01801    |  -0.00000   |  
193     |  0.11805    |  -0.72685   |  1.69675    |  -2.45368   |  -11.08912  |  0.01801    |  -0.00000   |  
194     |  0.11805    |  -0.72685   |  1.69675    |  -2.45368   |  -11.08912  |  0.01801    |  -0.00000   |  
195     |  0.11805    |  -0.72685   |  1.69675    |  -2.45368   |  -11.08912  |  0.01801    |  -0.00000   |  
196     |  0.11805    |  -0.72685   |  1.69675    |  -2.45368   |  -11.08912  |  0.01801    |  -0.00000   |  
197     |  0.11805    |  -0.72685   |  1.69675    |  -2.45368   |  -11.08912  |  0.01801    |  -0.00000   |  
198     |  0.11805    |  -0.72685   |  1.69675    |  -2.45369   |  -11.08912  |  0.01801    |  -0.00000   |  
199     |  0.11805    |  -0.72685   |  1.69675    |  -2.45369   |  -11.08912  |  0.01801    |  -0.00000   |  
200     |  0.11805    |  -0.72685   |  1.69675    |  -2.45369   |  -11.08912  |  0.01801    |  -0.00000   |  
201     |  0.11805    |  -0.72685   |  1.69675    |  -2.45369   |  -11.08912  |  0.01801    |  -0.00000   |  
202     |  0.11805    |  -0.72685   |  1.69675    |  -2.45369   |  -11.08912  |  0.01801    |  -0.00000   |  
203     |  0.11805    |  -0.72685   |  1.69675    |  -2.45369   |  -11.08912  |  0.01801    |  -0.00000   |  
204     |  0.11805    |  -0.72685   |  1.69675    |  -2.45369   |  -11.08912  |  0.01801    |  -0.00000   |  
205     |  0.11805    |  -0.72685   |  1.69675    |  -2.45369   |  -11.08912  |  0.01801    |  -0.00000   |  
206     |  0.11805    |  -0.72685   |  1.69675    |  -2.45369   |  -11.08912  |  0.01801    |  -0.00000   |  
207     |  0.11805    |  -0.72685   |  1.69675    |  -2.45369   |  -11.08912  |  0.01801    |  -0.00000   |  
208     |  0.11805    |  -0.72685   |  1.69676    |  -2.45369   |  -11.08912  |  0.01801    |  -0.00000   |  
209     |  0.11805    |  -0.72685   |  1.69676    |  -2.45369   |  -11.08912  |  0.01801    |  -0.00000   |  
210     |  0.11805    |  -0.72685   |  1.69676    |  -2.45370   |  -11.08912  |  0.01801    |  -0.00000   |  
211     |  0.11805    |  -0.72685   |  1.69676    |  -2.45370   |  -11.08912  |  0.01801    |  -0.00000   |  
212     |  0.11805    |  -0.72685   |  1.69676    |  -2.45370   |  -11.08912  |  0.01801    |  -0.00000   |  
213     |  0.11805    |  -0.72685   |  1.69676    |  -2.45370   |  -11.08912  |  0.01801    |  -0.00000   |  
214     |  0.11805    |  -0.72685   |  1.69676    |  -2.45370   |  -11.08912  |  0.01801    |  -0.00000   |  
215     |  0.11805    |  -0.72685   |  1.69676    |  -2.45370   |  -11.08912  |  0.01801    |  -0.00000   |  
216     |  0.11805    |  -0.72685   |  1.69676    |  -2.45370   |  -11.08912  |  0.01801    |  -0.00000   |  
217     |  0.11805    |  -0.72685   |  1.69676    |  -2.45370   |  -11.08912  |  0.01801    |  -0.00000   |  
218     |  0.11805    |  -0.72685   |  1.69676    |  -2.45370   |  -11.08912  |  0.01801    |  -0.00000   |  
219     |  0.11805    |  -0.72685   |  1.69676    |  -2.45370   |  -11.08912  |  0.01801    |  -0.00000   |  
220     |  0.11805    |  -0.72685   |  1.69676    |  -2.45370   |  -11.08912  |  0.01801    |  -0.00000   |  
221     |  0.11805    |  -0.72685   |  1.69676    |  -2.45370   |  -11.08912  |  0.01801    |  -0.00000   |  
222     |  0.11805    |  -0.72685   |  1.69676    |  -2.45370   |  -11.08912  |  0.01801    |  -0.00000   |  
223     |  0.11805    |  -0.72685   |  1.69676    |  -2.45370   |  -11.08912  |  0.01801    |  -0.00000   |  
224     |  0.11805    |  -0.72685   |  1.69676    |  -2.45370   |  -11.08912  |  0.01801    |  -0.00000   |  
225     |  0.11806    |  -0.72685   |  1.69676    |  -2.45370   |  -11.08912  |  0.01801    |  -0.00000   |  
226     |  0.11806    |  -0.72685   |  1.69676    |  -2.45370   |  -11.08912  |  0.01801    |  -0.00000   |  
227     |  0.11806    |  -0.72685   |  1.69676    |  -2.45370   |  -11.08912  |  0.01801    |  -0.00000   |  
228     |  0.11806    |  -0.72685   |  1.69676    |  -2.45370   |  -11.08912  |  0.01801    |  -0.00000   |  
229     |  0.11806    |  -0.72685   |  1.69676    |  -2.45370   |  -11.08912  |  0.00000    |  -0.00000   |  

Tong so buoc t = alpha*t trong thuat toan Armijo: 18

https://ideone.com/F5FwgF

Exact line search and Armijo rule for strictly convex functions

language:

C++14 (gcc 8.3)

created:

visibility:

secret

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