为什么是辛普森';用Python重写的s集成规则给出了不同的结果?
以下源代码是集成的实现 C#源代码。为什么是辛普森';用Python重写的s集成规则给出了不同的结果?,python,c#,numerical-integration,simpsons-rule,Python,C#,Numerical Integration,Simpsons Rule,以下源代码是集成的实现 C#源代码。 using System; public class Simpson { private double Function(double x) { return 1.0 / (1.0 + Math.Pow(x, 5)); //Define the function f(x) } public double Compute(double a, double b, int n) { dou
using System;
public class Simpson
{
private double Function(double x)
{
return 1.0 / (1.0 + Math.Pow(x, 5)); //Define the function f(x)
}
public double Compute(double a, double b, int n)
{
double[] x = new double[n + 1];
double delta_x = (b - a) / n;
x[0] = a;
for (int j = 1; j <= n; j++)//calculate the values of x1, x2, ...xn
{
x[j] = a + delta_x * j;
}
double sum = Function(x[0]);
for (int j = 1; j < n; j++)
{
if (j % 2 != 0)
{
sum += 4 * Function(x[j]);
}
else
{
sum += 2 * Function(x[j]);
}
}
sum += Function(x[n]);
double integration = sum * delta_x / 3;
return integration;
}
}
public class MainClass
{
public static void Main()
{
Simpson simpson = new Simpson();
double a = 0d;//lower limit a
double b = 3d;//upper limit b
int n = 6;//Enter step-length n
if (n % 2 == 0)//n must be even
{
Console.WriteLine(simpson.Compute(a, b, n));
}
else
{
Console.WriteLine("n should be an even number");
}
Console.ReadLine();
}
}
import math
# function to be integrated
def Function(x):
return 1.0 / (1.0 + math.pow(x, 5)); #Define the function f(x)
def Simpson(a, b, n):
x = [0] * (n + 1);
delta_x = (b - a) / n;
x[0] = a;
for j in range(1,n):#calculate the values of x1, x2, ...xn
x[j] = a + delta_x * j;
sum = Function(x[0]);
for j in range( 1, n):
if (j % 2 != 0):
sum = sum + 4 * Function(x[j]);
else:
sum = sum + 2 * Function(x[j]);
sum += Function(x[n]);
integration = sum * delta_x / 3;
return integration;
# Main Program
a = 0.0; # lower limit a
b = 3.0; # upper limit b
n = 6; # Enter step-length n
if (n % 2 == 0): # n must be even
print(Simpson(a, b, n));
else:
print("n should be an even number");
Python源代码。
using System;
public class Simpson
{
private double Function(double x)
{
return 1.0 / (1.0 + Math.Pow(x, 5)); //Define the function f(x)
}
public double Compute(double a, double b, int n)
{
double[] x = new double[n + 1];
double delta_x = (b - a) / n;
x[0] = a;
for (int j = 1; j <= n; j++)//calculate the values of x1, x2, ...xn
{
x[j] = a + delta_x * j;
}
double sum = Function(x[0]);
for (int j = 1; j < n; j++)
{
if (j % 2 != 0)
{
sum += 4 * Function(x[j]);
}
else
{
sum += 2 * Function(x[j]);
}
}
sum += Function(x[n]);
double integration = sum * delta_x / 3;
return integration;
}
}
public class MainClass
{
public static void Main()
{
Simpson simpson = new Simpson();
double a = 0d;//lower limit a
double b = 3d;//upper limit b
int n = 6;//Enter step-length n
if (n % 2 == 0)//n must be even
{
Console.WriteLine(simpson.Compute(a, b, n));
}
else
{
Console.WriteLine("n should be an even number");
}
Console.ReadLine();
}
}
import math
# function to be integrated
def Function(x):
return 1.0 / (1.0 + math.pow(x, 5)); #Define the function f(x)
def Simpson(a, b, n):
x = [0] * (n + 1);
delta_x = (b - a) / n;
x[0] = a;
for j in range(1,n):#calculate the values of x1, x2, ...xn
x[j] = a + delta_x * j;
sum = Function(x[0]);
for j in range( 1, n):
if (j % 2 != 0):
sum = sum + 4 * Function(x[j]);
else:
sum = sum + 2 * Function(x[j]);
sum += Function(x[n]);
integration = sum * delta_x / 3;
return integration;
# Main Program
a = 0.0; # lower limit a
b = 3.0; # upper limit b
n = 6; # Enter step-length n
if (n % 2 == 0): # n must be even
print(Simpson(a, b, n));
else:
print("n should be an even number");
输出:
1.07491527775614
1.2408988843135185
C#程序的输出与Python的输出不同
这是为什么?范围(1,n)
表示[1,n)
。而(int j=1;j范围(1,n)
表示[1,n)
。而(int j=1;j