public ReturnData SearchMin()
{
ReturnData results = new ReturnData(N);
// Шаг 1
f0 = f.getSum(x);
results.F += 1;
g = fg.getGrad(x);
results.F += N + 1;
g1 = new List <double>(g);
results.F += N + 1;
for (int i = 0; i < N; i++) // B0 = E
{
for (int j = 0; j < N; j++)
{
if (i == j)
{
B.Add(1);
}
else
{
B.Add(0);
}
}
}
double tmp = 0.0;
for (int i = 0; i < N; i++)
{
if (tmp < Math.Abs(x[i]))
{
tmp = Math.Abs(x[i]);
}
}
double h = Math.Sqrt(0.0001) * tmp; // Первый минимальный шаг
countIter = 0;
tmpX = new List <double>(x);
midlineX.Add(tmpX);
while (normVec(g) > epcilon && countIter <= iteration)
{
double d = 0.0;
dd = 0.0;
double ngt = 0.0;
double ng1 = 0.0;
gt = new List <double>(N);
ksi = new List <double>(N);
g0 = new List <double>(N);
x1 = new List <double>(N);
prevB = new List <double>(B);
// Градиент в преобразованном пространствен gt
for (int i = 0; i < N; i++)
{
gt.Add(0.0);
d = 0.0;
for (int j = 0; j < N; j++)
{
d += B[j + i * N] * g[j];
}
gt[i] = d;
// dd += d * g1[i];
ngt += d * d;
ng1 += g1[i] * g1[i];
}
ngt = Math.Sqrt(ngt);
ng1 = Math.Sqrt(ng1);
// dd /= ngt * ng1;
//
for (int i = 0; i < N; i++)
{
ksi.Add(gt[i] - g1[i]);
}
double nrmksi = normVec(ksi);
if (countIter > 0)
{
for (int i = 0; i < N; i++)
{
ksi[i] /= nrmksi;
}
d = 0.0;
for (int i = 0; i < N; i++)
{
d += ksi[i] * gt[i];
}
ng1 = 0.0; d *= w;
for (int i = 0; i < N; i++)
/* g1=gt+(1 / alfa - 1)*(ksi*gt')*ksi: */
{
dd = 0.0;
g1[i] = gt[i] + d * ksi[i];
ng1 += g1[i] * g1[i];
for (int j = 0; j < N; j++)
{
dd += B[j * N + i] * ksi[j];
}
dd *= w;
/* Новая матрица преобразования: B = B ( E + (1/alpha -1)ksi*ksit' ) */
for (int j = 0; j < N; j++)
{
B[j * N + i] += dd * ksi[j];
}
}
ng1 = Math.Sqrt(ng1);
}
for (int i = 0; i < N; i++)
{
gt[i] = g1[i] / ng1;
}
/* Градиент в нетрансформированом пространстве: g0 = B' * gt */
for (int i = 0; i < N; i++)
{
d = 0.0;
g0.Add(0.0);
for (int j = 0; j < N; j++)
{
d += prevB[j * N + i] * gt[j];
}
g0[i] = d;
}
adaptiveAdjustmentOfStep(results);
g = fg.getGrad(x);
results.F += N + 1;
countIter += 1;
}
results.K = countIter;
results.min = x.ToArray();
return(results);
}
public ReturnData alg_LM_adapt(int N, double[] x0, double [] csi, double eps, double Kiter, double gamma0 = 10000, double v = 10)
{
double gamma = gamma0;
double[] x_min = new double[N];
double[] x_k = new double[N];
double[] x_knew = new double[N];
double[] gradfR = new double[N];
double[] d_k = new double[N];
double[][] Gessian = new double[N][];
double[][] GessianInv = new double[N][];
ReturnData result = new ReturnData(N);
for (int i = 0; i < N; i++)
{
Gessian[i] = new double[N];
GessianInv[i] = new double[N];
x_k[i] = x0[i];
x_knew[i] = x0[i];
}
int k = 0;
while (k <= Kiter)
{
//Вычисление градиента
grad_funR(x_k, gradfR, csi, N);
result.F += 2 * N + 1;
//Проверка критерия останова
if (norma(gradfR, N) < eps)
{
//cout<<" STOP"<<endl;
for (int i = 0; i < N; i++)
{
x_min[i] = x_k[i];
}
break;
}
gessian_funR(x_k, Gessian, csi, N);
result.F += N * N + 1;
while (R_fun(x_knew, csi, N) >= R_fun(x_k, csi, N))
{
result.F += 4;
//Прибавление к главной диагонали гессиана шрафной добавки (параметра регуляяризации)
for (int i = 0; i < N; i++)
{
Gessian[i][i] += gamma;//*Gessian[i][i];
}
//Нахождение обратной матрицы
inverse(Gessian, GessianInv, N);;
//Вычисление направления поиска
d_k = Matr_x_Vect(GessianInv, gradfR, N);
Vect_x_a(d_k, -1, N);
result.D.Add(d_k);
//Вычисление новой точки x_k+1
for (int i = 0; i < N; i++)
{
x_knew[i] = x_k[i] + d_k[i];
}
//cout<<"f_k+1 >= f_k"<<endl;
if (R_fun(x_knew, csi, N) >= R_fun(x_k, csi, N))
{
gamma = v * gamma;
}
}
for (int i = 0; i < N; i++)
{
x_k[i] = x_knew[i];
}
gamma = gamma / v;
k++;
}
result.K = k;
result.min = x_min;
return(result);
}
public ReturnData SearchMin()
{
ReturnData results = new ReturnData(N);
// Шаг 1
f0 = f.getSum(x);
results.F += 1;
g = fg.getGrad(x);
results.F += N+1;
g1 = new List<double>(g);
results.F += N + 1;
for (int i = 0; i < N; i++) // B0 = E
for (int j = 0; j < N; j++)
{
if (i == j)
B.Add(1);
else
B.Add(0);
}
double tmp = 0.0;
for (int i = 0; i < N; i++)
{
if (tmp < Math.Abs(x[i]))
tmp = Math.Abs(x[i]);
}
double h = Math.Sqrt(0.0001) * tmp; // Первый минимальный шаг
countIter = 0;
tmpX = new List<double>(x);
midlineX.Add(tmpX);
while (normVec(g) > epcilon && countIter <= iteration)
{
double d = 0.0;
dd = 0.0;
double ngt = 0.0;
double ng1 = 0.0;
gt = new List<double>(N);
ksi = new List<double>(N);
g0 = new List<double>(N);
x1 = new List<double>(N);
prevB = new List<double>(B);
// Градиент в преобразованном пространствен gt
for (int i = 0; i < N; i++)
{
gt.Add(0.0);
d = 0.0;
for (int j = 0; j < N; j++)
d += B[j + i * N] * g[j];
gt[i] = d;
// dd += d * g1[i];
ngt += d * d;
ng1 += g1[i] * g1[i];
}
ngt = Math.Sqrt(ngt);
ng1 = Math.Sqrt(ng1);
// dd /= ngt * ng1;
//
for (int i = 0; i < N; i++)
{
ksi.Add(gt[i] - g1[i]);
}
double nrmksi = normVec(ksi);
if (countIter > 0)
{
for (int i = 0; i < N; i++)
ksi[i] /= nrmksi;
d = 0.0;
for (int i = 0; i < N; i++)
d += ksi[i] * gt[i];
ng1 = 0.0; d *= w;
for (int i = 0; i < N; i++)
/* g1=gt+(1 / alfa - 1)*(ksi*gt')*ksi: */
{
dd = 0.0;
g1[i] = gt[i] + d * ksi[i];
ng1 += g1[i] * g1[i];
for (int j = 0; j < N; j++)
dd += B[j * N + i] * ksi[j];
dd *= w;
/* Новая матрица преобразования: B = B ( E + (1/alpha -1)ksi*ksit' ) */
for (int j = 0; j < N; j++)
B[j * N + i] += dd * ksi[j];
}
ng1 = Math.Sqrt(ng1);
}
for (int i = 0; i < N; i++)
gt[i] = g1[i] / ng1;
/* Градиент в нетрансформированом пространстве: g0 = B' * gt */
for (int i = 0; i < N; i++)
{
d = 0.0;
g0.Add(0.0);
for (int j = 0; j < N; j++)
d += prevB[j * N + i] * gt[j];
g0[i] = d;
}
adaptiveAdjustmentOfStep(results);
g = fg.getGrad(x);
results.F += N + 1;
countIter += 1;
}
results.K = countIter;
results.min = x.ToArray();
return results;
}
private void adaptiveAdjustmentOfStep(ReturnData results)
{
for (int i = 0; i < N; i++)
{
x1.Add(x[i]);
}
double hp = h;
bool ksm = false;
double k1 = 0.0, k2 = 0.0;
double kc = 0.0;
double ii, stepvanish = 0.0;
double du20 = 2.0, du10 = 1.5, du03 = 1.05;
while (true)
{
for (int i = 0; i < N; i++)
{
x1[i] = x[i];
}
double f1 = f0;
if (f1 < 0.0)
{
dd = -1.0;
}
else
{
dd = 1.0;
}
/* Следующе испытание: */
for (int i = 0; i < N; i++)
{
x[i] -= hp * g0[i];
}
ii = 0.0;
for (int i = 0; i < N; i++)
{
if (Math.Abs(x[i] - x1[i]) < Math.Abs(x[i]) * epsnorm)
{
ii += 1;
}
}
/* Функция в текущее точке: */
f0 = f.getSum(x);
results.F += 1;
if (ii == N)
{
stepvanish += 1;
if (stepvanish >= 5)
{
return;
}
else
{
for (int i = 0; i < N; i++)
{
x[i] = x1[i];
}
f0 = f1;
hp *= 10.0;
ksm = true;
}
}
/* используем маленький шаг: */
else if (f0 > f1)
{
if (ksm)
{
return;
}
k2 += 1;
k1 = 0;
hp /= dq;
for (int i = 0; i < N; i++)
{
x[i] = x1[i];
}
f0 = f1;
if (kc >= mxtc)
{
return;
}
}
else
{
if (-1.0 * f0 <= -1.0 * f1)
{
return;
}
/* Используеем больший шаг */
k1 += 1;
if (k2 > 0)
{
kc += 1;
}
k2 = 0;
if (k1 >= 20)
{
hp *= du20;
}
else
if (k1 >= 10)
{
hp *= du10;
}
else if (k1 >= 3)
{
hp *= du03;
}
}
}
}
private void adaptiveAdjustmentOfStep(ReturnData results)
{
for (int i = 0; i < N; i++)
x1.Add(x[i]);
double hp = h;
bool ksm = false;
double k1 = 0.0, k2 = 0.0;
double kc = 0.0;
double ii, stepvanish = 0.0;
double du20 = 2.0, du10 = 1.5, du03 = 1.05;
while (true)
{
for (int i = 0; i < N; i++)
x1[i] = x[i];
double f1 = f0;
if (f1 < 0.0) dd = -1.0;
else
dd = 1.0;
/* Следующе испытание: */
for (int i = 0; i < N; i++)
x[i] -= hp * g0[i];
ii = 0.0;
for (int i = 0; i < N; i++)
{
if (Math.Abs(x[i] - x1[i]) < Math.Abs(x[i]) * epsnorm)
ii += 1;
}
/* Функция в текущее точке: */
f0 = f.getSum(x);
results.F += 1;
if (ii == N)
{
stepvanish += 1;
if (stepvanish >= 5)
return;
else
{
for (int i = 0; i < N; i++)
x[i] = x1[i];
f0 = f1;
hp *= 10.0;
ksm = true;
}
}
/* используем маленький шаг: */
else if (f0 > f1)
{
if (ksm)
return;
k2 += 1;
k1 = 0;
hp /= dq;
for (int i = 0; i < N; i++)
x[i] = x1[i];
f0 = f1;
if (kc >= mxtc)
return;
}
else
{
if (-1.0 * f0 <= -1.0 * f1)
return;
/* Используеем больший шаг */
k1 += 1;
if (k2 > 0) kc += 1;
k2 = 0;
if (k1 >= 20) hp *= du20;
else
if (k1 >= 10) hp *= du10;
else if (k1 >= 3) hp *= du03;
}
}
}
private void test2()
{
int N = 10;
Random rand = new Random();
int[] Ntest = { 2, 3, 5, 10, 30, 50, 100 };
double[] eps = { 0.1, 0.01, 0.001, 0.0001, 0.00001, 0.000001, 0.0000001 };
double[][] Delta = new double[7][];
int[][] Kstop = new int[7][];
for (int i = 0; i < 7; i++)
{
Delta[i] = new double[7];
Kstop[i] = new int[7];
}
int K = 50;
double[] sred = new double[K];
int[] sredK = new int[K];
for (int n = 0; n < 7; n++) //для каждого N
{
N = Ntest[n];
ReturnData result1 = new ReturnData(N);
double[] x0 = new double[N];
double[] _x0 = new double[N];
double[] del = new double[N];
double[] csi = new double[N];
for (int i = 0; i < 7; i++) //изменяем eps
{
for (int j = 0; j < N; j++)
{
csi[j] = rand.NextDouble() + 000.1;
x0[j] = rand.Next(-10, -5);
}
for (int k = 0; k < K; k++) //несколько итераций для усреднения
{
ShorMethod method1 = new ShorMethod(eps[i], new List <double>(x0), N, 2, new List <double>(csi), Klimitation);
result1 = method1.SearchMin();
sredK[k] = result1.K;
Console.WriteLine(N);
for (int j = 0; j < N; j++)
{
del[j] = 1 - result1.min[j];
}
sred[k] = method1.normVec(new List <double>(del));
}
for (int j = 0; j < K; j++)
{
Delta[i][n] += sred[j];
Kstop[i][n] += sredK[j];
}
Delta[i][n] /= K;
Kstop[i][n] /= K;
}
}
CreateLineGraph2();
Graw_Draw2(eps, Delta);
CreateLineGraph3(Klimitation);
Graw_Draw3(eps, Kstop);
}
public ReturnData alg_LM_adapt(int N, double[] x0, double []csi, double eps, double Kiter, double gamma0 = 10000, double v = 10)
{
double gamma = gamma0;
double[] x_min = new double[N];
double[] x_k = new double[N];
double[] x_knew = new double[N];
double[] gradfR = new double[N];
double[] d_k = new double[N];
double[][] Gessian = new double[N][];
double[][] GessianInv = new double[N][];
ReturnData result = new ReturnData(N);
for (int i = 0; i < N; i++)
{
Gessian[i] = new double[N];
GessianInv[i] = new double[N];
x_k[i] = x0[i];
x_knew[i] = x0[i];
}
int k = 0;
while (k <= Kiter)
{
//Вычисление градиента
grad_funR(x_k, gradfR, csi, N);
result.F += 2*N + 1;
//Проверка критерия останова
if (norma(gradfR, N) < eps)
{
//cout<<" STOP"<<endl;
for (int i = 0; i < N; i++)
{
x_min[i] = x_k[i];
}
break;
}
gessian_funR(x_k, Gessian, csi, N);
result.F += N * N + 1;
while (R_fun(x_knew, csi, N) >= R_fun(x_k, csi, N))
{
result.F += 4;
//Прибавление к главной диагонали гессиана шрафной добавки (параметра регуляяризации)
for (int i = 0; i < N; i++)
Gessian[i][i] += gamma;//*Gessian[i][i];
//Нахождение обратной матрицы
inverse(Gessian, GessianInv, N); ;
//Вычисление направления поиска
d_k = Matr_x_Vect(GessianInv, gradfR, N);
Vect_x_a(d_k, -1, N);
result.D.Add(d_k);
//Вычисление новой точки x_k+1
for (int i = 0; i < N; i++)
{
x_knew[i] = x_k[i] + d_k[i];
}
//cout<<"f_k+1 >= f_k"<<endl;
if (R_fun(x_knew, csi, N) >= R_fun(x_k, csi, N))
gamma = v * gamma;
}
for (int i = 0; i < N; i++)
x_k[i] = x_knew[i];
gamma = gamma / v;
k++;
}
result.K = k;
result.min = x_min;
return result;
}
private void test2()
{
int N = 10;
Random rand = new Random();
int[] Ntest = { 2, 3, 5, 10, 30, 50, 100 };
double[] eps = { 0.1, 0.01, 0.001, 0.0001, 0.00001, 0.000001, 0.0000001 };
double[][] Delta = new double[7][];
int[][] Kstop = new int[7][];
for (int i = 0; i < 7; i++)
{
Delta[i] = new double[7];
Kstop[i] = new int[7];
}
int K = 50;
double[] sred = new double[K];
int[] sredK = new int[K];
for (int n = 0; n < 7; n++) //для каждого N
{
N = Ntest[n];
ReturnData result1 = new ReturnData(N);
double[] x0 = new double[N];
double[] _x0 = new double[N];
double[] del = new double[N];
double[] csi = new double[N];
for (int i = 0; i < 7; i++) //изменяем eps
{
for (int j = 0; j < N; j++)
{
csi[j] = rand.NextDouble() + 000.1;
x0[j] = rand.Next(-10, -5);
}
for (int k = 0; k < K; k++) //несколько итераций для усреднения
{
ShorMethod method1 = new ShorMethod(eps[i], new List<double>(x0), N, 2, new List<double>(csi), Klimitation);
result1 = method1.SearchMin();
sredK[k] = result1.K;
Console.WriteLine(N);
for (int j = 0; j < N; j++)
{
del[j] = 1 - result1.min[j];
}
sred[k] = method1.normVec(new List<double>(del));
}
for (int j = 0; j < K; j++)
{
Delta[i][n] += sred[j];
Kstop[i][n] += sredK[j];
}
Delta[i][n] /= K;
Kstop[i][n] /= K;
}
}
CreateLineGraph2();
Graw_Draw2(eps, Delta);
CreateLineGraph3(Klimitation);
Graw_Draw3(eps, Kstop);
}
private void test1()
{
int N = 0;
Random rand = new Random();
int[] Ntest = { 2, 3, 5, 10, 30, 50, 100 };
int[] Kstop = new int[7];
int K = 50; //Количество повторений
int[] sredK = new int[K];
int[] sredF = new int[K];
int[] F = new int[7];
double a = 0.0;
for (int i = 0; i < 7; i++)
{
Kstop[i] = 0;
N = Ntest[i];
ReturnData result1 = new ReturnData(N);
double[] x0 = new double[N];
double[] _x0 = new double[N];
double[] csi = new double[N];
for (int j = 0; j < K; j++)
{
for (int k = 0; k < N; k++)
{
csi[k] = rand.NextDouble() + 000.1;
x0[k] = rand.Next(-10, -5);
}
ShorMethod method1 = new ShorMethod(epsilon, new List<double>(x0), N, 2, new List<double>(csi), Klimitation);
result1 = method1.SearchMin();
sredK[j] = result1.K;
sredF[j] = result1.F;
Console.WriteLine(N);
}
for (int j = 0; j < K; j++)
{
Kstop[i] += sredK[j];
F[i] += sredF[j];
}
Kstop[i] /= K;
F[i] /= K;
}
CreateLineGraph1(Klimitation);
Graw_Draw1(Ntest, Kstop);
for (int i = 0; i < 6; i++)
a = Math.Max(F[i], F[i + 1]);
CreateLineGraph4(a);
Graw_Draw4(Ntest, F);
}
