/// <summary>
/// モンテカルロ積分を行う。
/// </summary>
/// <param name="result"></param>
/// <param name="numerator"></param>
/// <param name="denominator"></param>
/// <param name="calculation_count"></param>
/// <param name="iscalar"></param>
/// <param name="range_max"></param>
/// <param name="range_min"></param>
/// <param name="seeds"></param>
public static void Monte_Carlo_Integration
(ref decimal result, ref decimal numerator, ref decimal denominator
, uint calculation_count
, IScalar iscalar, decimal[] range_max, decimal[] range_min
, uint[] seeds)
{
//積分区間の最大値と最小値の次元をそろえる
if (range_max.Length != range_min.Length)
{
throw new FormatException("length of " + nameof(range_max) + "(" + range_max.Length + ")"
+ " with that of " + nameof(range_min) + "(" + range_min.Length + ")");
}
//乱数の種の次元もそろえる
if (range_max.Length != seeds.Length)
{
throw new FormatException("length of " + nameof(range_max) + "(" + range_max.Length + ")"
+ " with that of " + nameof(seeds) + "(" + seeds.Length + ")");
}
//一様乱数のclassを生成する
List <Uniform_Distribution> list_ud = new List <Uniform_Distribution>();
for (int j = 0; j < range_min.Length; j++)
{
list_ud.Add(new Uniform_Distribution(seeds[j]));
}
//積分を行う
decimal[] xs = new decimal[range_min.Length];
for (uint j = 0; j < calculation_count; j++)
{
//乱数を生成する
for (int k = 0; k < list_ud.Count; k++)
{
xs[k] = list_ud[k].NextDecimal(range_max[k], range_min[k]);
}
numerator += iscalar.Calculate_f_u(xs);
denominator++;
}
result = numerator / denominator;
}
public static void Monte_Carlo_Metropolis_Hastings
(ref decimal result, ref decimal numerator, ref decimal denominator
, ref decimal partition_function
, uint calculation_count_epoch
, decimal[] initial_x, ref decimal[] final_x
, IAction iaction, decimal[] step_half_width, uint[] seeds_for_step
, uint seed_for_judge
, IScalar iscalar
)
{
//ジャンプの幅の乱数の種の次元をそろえる
if (step_half_width.Length != seeds_for_step.Length)
{
throw new FormatException("Length of " + nameof(step_half_width) + "(" + step_half_width.Length + ")"
+ " with that of " + nameof(seeds_for_step) + "(" + seeds_for_step.Length + ")");
}
//初期位置と乱数の種の次元をそろえる
if (initial_x.Length != seeds_for_step.Length)
{
throw new FormatException("Length of " + nameof(initial_x) + "(" + initial_x.Length + ")"
+ " with that of " + nameof(seeds_for_step) + "(" + seeds_for_step.Length + ")");
}
//ジャンプの幅を正の数にしておく
decimal[] abs_step_half_width = new decimal[step_half_width.Length];
for (int j = 0; j < step_half_width.Length; j++)
{
abs_step_half_width[j] = Math.Abs(step_half_width[j]);
}
//一様乱数のclassを生成する
List <Uniform_Distribution> list_ud = new List <Uniform_Distribution>();
for (int j = 0; j < step_half_width.Length; j++)
{
list_ud.Add(new Uniform_Distribution(seeds_for_step[j]));
}
Uniform_Distribution judge = new Uniform_Distribution(seed_for_judge);
//初期設定を行う
decimal[] xs = new decimal[step_half_width.Length];
decimal[] xs_candidate = new decimal[step_half_width.Length];
for (int k = 0; k < step_half_width.Length; k++)
{
xs[k] = initial_x[k];
xs_candidate[k] = xs[k];
}
decimal action = 0m;
decimal action_candidate = 0m;
action = iaction.Calculate_f_u(xs);
action_candidate = action;
//計算を行う
for (int j = 0; j < calculation_count_epoch; j++)
{
//新しいxの候補を計算する。
for (int k = 0; k < step_half_width.Length; k++)
{
//xの値を1次元だけ動かす
xs_candidate[k] = xs[k] + list_ud[k].NextDecimal(abs_step_half_width[k], -abs_step_half_width[k]);
}
action_candidate = iaction.Calculate_f_u(xs_candidate);
//更新できる場合
if (judge.NextDecimal() < Taylor_Series_Decimal.Exponential(action - action_candidate))
{
//被積分関数の値を足す
numerator += iscalar.Calculate_f_u(xs_candidate);
//分配関数に確率値を加える。
partition_function += Taylor_Series_Decimal.Exponential(-action_candidate);
for (int k = 0; k < step_half_width.Length; k++)
{
//xの値を更新する。
xs[k] = xs_candidate[k];
}
//作用を更新する。
action = action_candidate;
}
else
{
}
denominator++;
}
result = numerator / denominator;
for (int j = 0; j < initial_x.Length; j++)
{
final_x[j] = xs[j];
}
}