public static double MathApprox_4_Compute_2(double arg, double error)
{
int L = 1;
int M = 1;
//finding the appropriate L and M for the approximation to meet the adjusted error
for (;;)
{
if (error > CMathApprox_4.MathApprox_4_2_CheckError(L, M))
{
break;
}
M++;
L++;
}
double[] C = new double[L + M + 1];
int p = 0;
C[0] = Math.PI / 2;
for (int i = 1; i < L + M + 1; i++)
{
if ((i % 2) == 0)
{
C[i] = 0;
}
else
{
C[i] = 1.0 / i * Math.Pow(-1, p + 1);
p++;
}
}
double[] Numer = new double[L + 1];
double[] Denom = new double[M + 1];
CFind_Pade.Find_Denominator(Denom, C, L, M);
CFind_Pade.Find_Numerator(Numer, Denom, C, L, M);
double P0 = 0;
double P1 = 0;
for (int j = 0; j < M + 1; j++)
{
double Tmp = Math.Pow(arg, j);
if (j <= L)
{
P0 += Numer[j] * Tmp;
}
P1 += Denom[j] * Tmp;
}
double Res = P0 / P1;
return(Res);
}
public static double MathApprox_4_2_CheckError(int L, int M)
{
double[] C = new double[L + M + 1];
int p = 0;
C[0] = Math.PI / 2;
for (int i = 1; i < L + M + 1; i++)
{
if ((i % 2) == 0)
{
C[i] = 0;
}
else
{
C[i] = 1.0 / i * Math.Pow(-1, p + 1);
p++;
}
}
double[] Numer = new double[L + 1];
double[] Denom = new double[M + 1];
CFind_Pade.Find_Denominator(Denom, C, L, M);
CFind_Pade.Find_Numerator(Numer, Denom, C, L, M);
double error = 0;
Random rnd = new Random();
for (int i = 0; i < 10000; i++)
{
double arg = 0.001 * rnd.Next(500);
double P0 = 0;
double P1 = 0;
for (int j = 0; j < M + 1; j++)
{
double Tmp = Math.Pow(arg, j);
if (j <= L)
{
P0 += Numer[j] * Tmp;
}
P1 += Denom[j] * Tmp;
}
double Res = P0 / P1;
double Temp = Math.Abs((Math.PI / 2 - Math.Atan(arg)) - Res);
if (error < Temp)
{
error = Temp;
}
}
return(error);
}
public static double MathApprox_1_Compute_2(double arg, double error)
{
int L = 0;
int M = 1;
//finding the appropriate L and M for the approximation to meet the adjusted error
for (;;)
{
if (error > CMathApprox_1.MathApprox_1_2_CheckError(L, M))
{
break;
}
if (L == M)
{
M++;
}
else
{
L++;
}
}
//creating suitable approximation;
//Ln_Numer is the numerator, Ln_Denom is the denominator, C is the Taylor approximation
double[] C = new double[L + M + 1];
C[0] = 0;
for (int i = 1; i < L + M + 1; i++)
{
C[i] = 1.0 / i * Math.Pow(-1, i + 1);
}
double[] Numer = new double[L + 1];
double[] Denom = new double[M + 1];
CFind_Pade.Find_Denominator(Denom, C, L, M);
CFind_Pade.Find_Numerator(Numer, Denom, C, L, M);
double P0 = 0;
double P1 = 1;
for (int j = 1; j < M + 1; j++)
{
double Tmp = Math.Pow(arg, j);
if (j <= L)
{
P0 += Numer[j] * Tmp;
}
P1 += Denom[j] * Tmp;
}
double Res = P0 / P1;
return(Res);
}
public static double MathApprox_3_2_CheckError(int L, int M)
{
double[] C = new double[L + M + 1];
C[0] = 0; C[1] = 1;
for (int i = 2; i < L + M + 1; i++)
{
if ((i % 2) == 0)
{
C[i] = 0;
}
else
{
C[i] = C[i - 2] * (i - 2) * (i - 2) / i / (i - 1);
}
}
double[] Numer = new double[L + 1];
double[] Denom = new double[M + 1];
CFind_Pade.Find_Denominator(Denom, C, L, M);
CFind_Pade.Find_Numerator(Numer, Denom, C, L, M);
double error = 0;
Random rnd = new Random();
for (int i = 0; i < 10000; i++)
{
double arg = 0.001 * rnd.Next(500);
double P0 = 0;
double P1 = 1;
for (int j = 1; j < M + 1; j++)
{
double Tmp = Math.Pow(arg, j);
if (j <= L)
{
P0 += Numer[j] * Tmp;
}
P1 += Denom[j] * Tmp;
}
double Res = P0 / P1;
double Temp = Math.Abs(Math.Asin(arg) - Res);
if (error < Temp)
{
error = Temp;
}
}
return(error);
}
public static double MathApprox_1_2_CheckError(int L, int M)
{
if ((L == 1) && (M == 2))
{
return(0.005);
}
double[] C = new double[L + M + 1];
C[0] = 0;
for (int i = 1; i < L + M + 1; i++)
{
C[i] = 1.0 / i * Math.Pow(-1, i + 1);
}
double[] Numer = new double[L + 1];
double[] Denom = new double[M + 1];
CFind_Pade.Find_Denominator(Denom, C, L, M);
CFind_Pade.Find_Numerator(Numer, Denom, C, L, M);
double error = 0;
Random rnd = new Random();
for (int i = 0; i < 10000; i++)
{
double arg = 0.001 * rnd.Next(1000);
double P0 = 0;
double P1 = 1;
for (int j = 1; j < M + 1; j++)
{
double Tmp = Math.Pow(arg, j);
if (j <= L)
{
P0 += Numer[j] * Tmp;
}
P1 += Denom[j] * Tmp;
}
double Res = P0 / P1;
double Temp = Math.Abs(Math.Log(arg + 1) - Res);
if (error < Temp)
{
error = Temp;
}
}
return(error);
}
public static string MathApprox_1_2(string PathName, double error)
{
int L = 0;
int M = 1;
//finding the appropriate L and M for the approximation to meet the adjusted error
for (;;)
{
if (error > MathApprox_1_2_CheckError(L, M))
{
break;
}
if (L == M)
{
M++;
}
else
{
L++;
}
}
//creating suitable approximation;
//Ln_Numer is the numerator, Ln_Denom is the denominator, C is the Taylor approximation
double[] C = new double[L + M + 1];
C[0] = 0;
for (int i = 1; i < L + M + 1; i++)
{
C[i] = 1.0 / i * Math.Pow(-1, i + 1);
}
double[] Numer = new double[L + 1];
double[] Denom = new double[M + 1];
CFind_Pade.Find_Denominator(Denom, C, L, M);
CFind_Pade.Find_Numerator(Numer, Denom, C, L, M);
//creating program with found approximation
string FileName = PathName + "MathApprox_1_2" + "_" + error.ToString() + ".cs";
System.IO.StreamWriter FileWriter = CMakeProgram.MakeBeginning(PathName, "MathApprox_1_2", error);
//!!!
//Необходимо заменить Ln_Numer и Ln_Denom на реально полученные коэффициенты !!!
FileWriter.WriteLine(" double P0 = 0;");
FileWriter.WriteLine(" double P1 = 1;");
FileWriter.WriteLine(" double[] Denom = new double[" + (M + 1).ToString() + "];");
FileWriter.WriteLine(" double[] Numer = new double[" + (L + 1).ToString() + "];");
for (int i = 0; i < M + 1; i++)
{
FileWriter.WriteLine(" Denom[" + i.ToString() + "] = " + Denom[i].ToString().Replace(",", ".") + ";");
}
for (int i = 0; i < L + 1; i++)
{
FileWriter.WriteLine(" Numer[" + i.ToString() + "] = " + Numer[i].ToString().Replace(",", ".") + ";");
}
FileWriter.WriteLine(" Console.Write(\"Input argument for ln(1 + x): \");");
FileWriter.WriteLine(" double arg = double.Parse(Console.ReadLine());");
FileWriter.WriteLine(" for (int j = 1; j < " + (M + 1).ToString() + "; j++)");
FileWriter.WriteLine(" {");
FileWriter.WriteLine(" double Tmp = Math.Pow(arg, j);");
FileWriter.WriteLine(" P0 += Numer[j] * Tmp;");
FileWriter.WriteLine(" P1 += Denom[j] * Tmp;");
FileWriter.WriteLine(" }");
FileWriter.WriteLine(" double Res = P0 / P1;");
FileWriter.WriteLine(" ");
FileWriter.WriteLine(" Console.Write(\"Ln(1 + \" + arg.ToString() + \") = \");");
FileWriter.WriteLine(" Console.WriteLine(Res);");
FileWriter.WriteLine(" Console.Write(\"Target value: \" + Math.Log(arg + 1).ToString());");
FileWriter.WriteLine(" Console.WriteLine();");
FileWriter.WriteLine(" }");
FileWriter.WriteLine(" }");
FileWriter.WriteLine("}");
FileWriter.Close();
return(FileName);
}