public class CS0101
{
public static void Main()
{
System.Console.WriteLine(3 + 5);
System.Console.WriteLine(3 - 5);
System.Console.WriteLine(3 * 5);
System.Console.WriteLine(System.Math.Pow(3, 5));
System.Console.WriteLine(5 / 3);
System.Console.WriteLine(5.0 / 3);
System.Console.WriteLine(5 / 3.0);
System.Console.WriteLine(5 % 3);
System.Console.Write(3 * 5 + "\n");
System.Console.WriteLine(string.Format("{0,3:D}", 3 * 5));
System.Console.WriteLine(string.Format("{0,23:F20}", 5 / 3.0));
}
}
public class CS0102
{
public static void Main()
{
int i = 3 * 5;
System.Console.WriteLine("3 * 5 = " + i);
System.Console.WriteLine(string.Format("3 * 5 = {0}", i));
}
}
public class CS0103
{
public static void Main()
{
for (int i = 1; i < 10; i++)
{
System.Console.Write(i + ", ");
}
System.Console.WriteLine();
}
}
public class CS0104
{
public static void Main()
{
for (int i = 1; i < 10; i++)
{
if (i % 3 == 0)
{
System.Console.Write(i + ", ");
}
}
System.Console.WriteLine();
}
}
public class CS0105
{
public static void Main()
{
int sum = 0;
for (int i = 1; i < 100; i++)
{
if (i % 3 == 0)
{
sum += i;
}
}
System.Console.WriteLine(sum);
}
}
using System.Linq;
using System.Collections.Generic;
public class CS0201
{
public static void Main()
{
IEnumerable<int> squares = Enumerable.Range(1, 9);
foreach (int num in squares)
{
System.Console.Write(num + ", ");
}
System.Console.WriteLine();
}
}
using System.Linq;
using System.Collections.Generic;
public class CS0202
{
public static void Main()
{
IEnumerable<int> squares =
Enumerable.Range(1, 9).Where(num => num % 3 == 0);
foreach (int num in squares)
{
System.Console.Write(num + ", ");
}
System.Console.WriteLine();
}
}
using System.Linq;
public class CS0203
{
public static void Main()
{
int sum = Enumerable.Range(1, 99).Where(num => (num % 3 == 0)).Sum();
System.Console.WriteLine(sum);
sum = Enumerable.Range(1, 99).Where(num => (num % 3 == 0)).Aggregate((x, n) => x + n);
System.Console.WriteLine(sum);
}
}
public class CS0301
{
public static void Main()
{
// 3 の倍数の合計
System.Console.WriteLine( sn(3, 999) );
}
// 初項:a, 公差:a で, 上限:lim の数列の総和を返す関数
private static int sn(int a, int lim)
{
int n = lim / a; // 項数:n = 上限:lim / 公差:a
int l = n * a; // 末項:l = 項数:n * 公差:a
return (a + l) * n / 2; // 総和:sn = (初項:a + 末項:l) * 項数:n / 2
}
}
public class CS0302
{
public static void Main()
{
// 10000 までの 自然数の和
// 項目数 n = 10000
int n = 10000;
System.Console.WriteLine( n * (n + 1) / 2 );
}
}
public class CS0303
{
public static void Main()
{
// 10000 までの 偶数の和
// 項目数 n = 5000
int n = 10000 / 2;
System.Console.WriteLine( n * (n + 1) );
}
}
public class CS0304
{
public static void Main()
{
// 10000 までの 奇数の和
// 項目数 n = 5000
int n = 10000 / 2;
System.Console.WriteLine( System.Math.Pow(n, 2) );
}
}
public class CS0305
{
public static void Main()
{
// 1000 までの 自然数の２乗の和
int n = 1000;
System.Console.WriteLine( n * (n + 1) * (2 * n + 1) / 6 );
}
}
public class CS0306
{
public static void Main()
{
// 100 までの 自然数の３乗の和
int n = 100;
System.Console.WriteLine( System.Math.Pow(n, 2) * System.Math.Pow((n + 1), 2) / 4 );
}
}
public class CS0307
{
public static void Main()
{
// 初項 2, 公比 3, 項数 10 の等比数列の和
int n = 10;
int a = 2;
int r = 3;
System.Console.WriteLine( (a * (System.Math.Pow(r, n) - 1)) / (r - 1) );
}
}
using System;
public class CS0401
{
public static void Main()
{
int a = 5; // 初項 5
int d = 3; // 公差 3
int n = 10; // 項数 10
long p = 1; // 積
for (int i = 1; i <= n; i++)
{
int m = a + (d * (i - 1));
p *= m;
}
Console.WriteLine(p);
}
}
using System;
public class CS0402
{
public static void Main()
{
// 初項 5, 公差 3, 項数 10 の数列の積を表示する
Console.WriteLine(product(5, 3, 10));
}
private static long product(int m, int d, int n)
{
if (n == 0)
return 1;
else
return m * product(m + d, d, n - 1);
}
}
using System;
public class CS0403
{
// 階乗を求める関数
private static int Fact(int n)
{
if (n <= 1)
return 1;
else
return n * Fact(n - 1);
}
public static void Main()
{
// 10の階乗
Console.WriteLine(Fact(10));
Console.WriteLine(10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1);
}
}
using System;
public class CS0404
{
// 下降階乗冪
private static int FallingFact(int x, int n)
{
if (n <= 1)
return x;
else
return x * FallingFact(x - 1, n - 1);
}
public static void Main()
{
// 10 から 6 までの 総乗
Console.WriteLine(FallingFact(10, 5));
Console.WriteLine(10 * 9 * 8 * 7 * 6);
}
}
using System;
public class CS0405
{
// 上昇階乗冪
private static int RisingFact(int x, int n)
{
if (n <= 1)
return x;
else
return x * RisingFact(x + 1, n - 1);
}
public static void Main()
{
// 10 から 14 までの 総乗
Console.WriteLine(RisingFact(10, 5));
Console.WriteLine(10 * 11 * 12 * 13 * 14);
}
}
using System;
public class CS0406
{
// 階乗
private static int Fact(int n)
{
if (n <= 1)
return 1;
else
return n * Fact(n - 1);
}
// 下降階乗冪
private static int FallingFact(int x, int n)
{
if (n <= 1)
return x;
else
return x * FallingFact(x - 1, n - 1);
}
public static void Main()
{
// 順列 (異なる 10 個のものから 5 個取ってできる順列の総数)
int n = 10;
int r = 5;
Console.WriteLine(Fact(n) / Fact(n - r));
Console.WriteLine(FallingFact(n, r));
}
}
using System;
public class CS0407
{
public static void Main()
{
// 重複順列 (異なる 10 個のものから重複を許して 5 個取ってできる順列の総数)
int n = 10;
int r = 5;
Console.WriteLine(Math.Pow(n, r));
}
}
using System;
public class CS040101
{
// 組合せ
private static int Comb(int n, int r)
{
if (r == 0 || r == n)
return 1;
else if (r == 1)
return n;
else
return Comb(n - 1, r - 1) + Comb(n - 1, r);
}
public static void Main()
{
// 組合せ (異なる 10 個のものから 5 個取ってできる組合せの総数)
int n = 10;
int r = 5;
Console.WriteLine(Comb(n, r));
}
}
using System;
public class CS0409
{
// 組合せ
private static int Comb(int n, int r)
{
if (r == 0 || r == n)
return 1;
else if (r == 1)
return n;
else
return Comb(n - 1, r - 1) + Comb(n - 1, r);
}
public static void Main()
{
// 重複組合せ (異なる 10 個のものから重複を許して 5 個とる組合せの総数)
int n = 10;
int r = 5;
Console.WriteLine(Comb(n + r - 1, r));
}
}
using System;
public class CS0501
{
public static void Main()
{
for (int degree = 0; degree <= 360; degree += 15)
{
if (degree % 30 == 0 || degree % 45 == 0)
{
double radian = degree * Math.PI / 180.0;
// 自作の正弦関数
double d1 = mySin(radian, 1, false, radian, 1.0, radian);
// 標準の正弦関数
double d2 = Math.Sin(radian);
// 標準関数との差異
Console.WriteLine(string.Format("{0,3:D} : {1,13:F10} - {2,13:F10} = {3,13:F10}", degree, d1, d2, d1 - d2));
}
}
}
// 自作の正弦関数
private static double mySin(double x, int n, bool nega, double numerator, double denominator, double y)
{
int m = 2 * n;
denominator = denominator * (m + 1) * m;
numerator = numerator * x * x;
double a = numerator / denominator;
// 十分な精度になったら処理を抜ける
if (a <= 0.00000000001)
return y;
else
return y + mySin(x, ++n, !nega, numerator, denominator, nega ? a : -a);
}
}
using System;
public class CS0502
{
public static void Main()
{
for (int degree = 0; degree <= 360; degree += 15)
{
if (degree % 30 == 0 || degree % 45 == 0)
{
double radian = degree * Math.PI / 180.0;
// 自作の余弦関数
double d1 = myCos(radian, 1, false, 1.0, 1.0, 1.0);
// 標準の余弦関数
double d2 = Math.Cos(radian);
// 標準関数との差異
Console.WriteLine(string.Format("{0,3:D} : {1,13:F10} - {2,13:F10} = {3,13:F10}", degree, d1, d2, d1 - d2));
}
}
}
// 自作の余弦関数
private static double myCos(double x, int n, bool nega, double numerator, double denominator, double y)
{
int m = 2 * n;
denominator = denominator * m * (m - 1);
numerator = numerator * x * x;
double a = numerator / denominator;
// 十分な精度になったら処理を抜ける
if (a <= 0.00000000001)
return y;
else
return y + myCos(x, ++n, !nega, numerator, denominator, nega ? a : -a);
}
}
using System;
public class CS0503
{
public static void Main()
{
for (int degree = -90; degree <= 90; degree += 15)
{
if ((degree + 90) % 180 != 0)
{
double radian = degree * Math.PI / 180.0;
double x2 = radian * radian;
// 自作の正接関数
double d1 = myTan(radian, x2, 15, 0.0); // 15:必要な精度が得られる十分大きな奇数
// 標準の正接関数
double d2 = Math.Tan(radian);
// 標準関数との差異
Console.WriteLine(string.Format("{0,3:D} : {1,13:F10} - {2,13:F10} = {3,13:F10}", degree, d1, d2, d1 - d2));
}
}
}
// 自作の正接関数
private static double myTan(double x, double x2, int n, double t)
{
t = x2 / (n - t);
n -= 2;
if (n <= 1)
return x / (1 - t);
else
return myTan(x, x2, n, t);
}
}
using System;
public class CS0504
{
public static void Main()
{
for (int i = -10; i <= 10; i++)
{
double x = i / 4.0;
// 標準の指数関数
double d1 = Math.Exp(x);
// 自作の指数関数
double d2 = myExp(x, 1, 1.0, 1.0, 1.0);
// 標準関数との差異
Console.WriteLine(string.Format("{0,5:F2} : {1,13:F10} - {2,13:F10} = {3,13:F10}", x, d1, d2, d1 - d2));
}
}
// 自作の指数関数
private static double myExp(double x, int n, double numerator, double denominator, double y)
{
denominator = denominator * n;
numerator = numerator * x;
double a = numerator / denominator;
// 十分な精度になったら処理を抜ける
if (Math.Abs(a) <= 0.00000000001)
return y;
else
return y + myExp(x, ++n, numerator, denominator, a);
}
}
using System;
public class CS0505
{
public static void Main()
{
for (int i = -10; i <= 10; i++)
{
double x = i / 4.0;
// 標準の指数関数
double d1 = Math.Exp(x);
// 自作の指数関数
double x2 = x * x;
double d2 = myExp(x, x2, 30, 0.0); // 30:必要な精度が得られるよう, 6から始めて4ずつ増加させる
// 標準関数との差異
Console.WriteLine(string.Format("{0,5:F2} : {1,13:F10} - {2,13:F10} = {3,13:F10}", x, d1, d2, d1 - d2));
}
}
// 自作の指数関数
private static double myExp(double x, double x2, int n, double t)
{
t = x2 / (n + t);
n -= 4;
if (n < 6)
return 1 + ((2 * x) / (2 - x + t));
else
return myExp(x, x2, n, t);
}
}
using System;
public class CS0506
{
public static void Main()
{
for (int i = 1; i <= 20; i++)
{
double x = i / 5.0;
// 標準の対数関数
double d1 = Math.Log(x);
// 自作の対数関数
double x2 = (x - 1) / (x + 1);
double d2 = 2 * myLog(x2, x2, 1.0, x2);
// 標準関数との差異
Console.WriteLine(string.Format("{0,5:F2} : {1,13:F10} - {2,13:F10} = {3,13:F10}", x, d1, d2, d1 - d2));
}
}
// 自作の対数関数
private static double myLog(double x2, double numerator, double denominator, double y)
{
denominator = denominator + 2;
numerator = numerator * x2 * x2;
double a = numerator / denominator;
// 十分な精度になったら処理を抜ける
if (Math.Abs(a) <= 0.00000000001)
return y;
else
return y + myLog(x2, numerator, denominator, a);
}
}
using System;
public class CS0507
{
public static void Main()
{
for (int i = 1; i <= 20; i++)
{
double x = i / 5.0;
// 標準の対数関数
double d1 = Math.Log(x);
// 自作の対数関数
double d2 = myLog(x - 1, 27, 0.0); // 27:必要な精度が得られる十分大きな奇数
// 標準関数との差異
Console.WriteLine(string.Format("{0,5:F2} : {1,13:F10} - {2,13:F10} = {3,13:F10}", x, d1, d2, d1 - d2));
}
}
// 自作の対数関数
private static double myLog(double x, int n, double t)
{
int n2 = n;
double x2 = x;
if (n > 3)
{
if (n % 2 == 0)
n2 = 2;
x2 = x * (n / 2);
}
t = x2 / (n2 + t);
if (n <= 2)
return x / (1 + t);
else
return myLog(x, --n, t);
}
}
using System;
public class CS0508
{
public static void Main()
{
for (int x = -10; x <= 10; x++)
{
// 自作の双曲線正弦関数
double d1 = mySinh(x, 1, x, 1.0, x);
// 標準の双曲線正弦関数
double d2 = Math.Sinh(x);
// 標準関数との差異
Console.WriteLine(string.Format("{0,3:D} : {1,17:F10} - {2,17:F10} = {3,13:F10}", x, d1, d2, d1 - d2));
}
}
// 自作の双曲線正弦関数
private static double mySinh(double x, int n, double numerator, double denominator, double y)
{
int m = 2 * n;
denominator = denominator * (m + 1) * m;
numerator = numerator * x * x;
double a = numerator / denominator;
// 十分な精度になったら処理を抜ける
if (Math.Abs(a) <= 0.00000000001)
return y;
else
return y + mySinh(x, ++n, numerator, denominator, a);
}
}
using System;
public class CS0509
{
public static void Main()
{
for (int x = -10; x <= 10; x++)
{
// 自作の双曲線余弦関数
double d1 = myCosh(x, 1, 1.0, 1.0, 1.0);
// 標準の双曲線余弦関数
double d2 = Math.Cosh(x);
// 標準関数との差異
Console.WriteLine(string.Format("{0,3:D} : {1,17:F10} - {2,17:F10} = {3,13:F10}", x, d1, d2, d1 - d2));
}
}
// 自作の双曲線余弦関数
private static double myCosh(double x, int n, double numerator, double denominator, double y)
{
int m = 2 * n;
denominator = denominator * m * (m - 1);
numerator = numerator * x * x;
double a = numerator / denominator;
// 十分な精度になったら処理を抜ける
if (Math.Abs(a) <= 0.00000000001)
return y;
else
return y + myCosh(x, ++n, numerator, denominator, a);
}
}
using System;
public class CS0510
{
public static void Main()
{
//for (int degree = -45; degree <= 45; degree += 15)
for (int max = 1000; max <= 40000; max += 1000)
{
double radian = 1; // degree * Math.PI / 180.0;
// 自作の逆正接関数
double d1 = myAtan(radian, false, radian, 1, radian, max);
// 標準の逆正接関数
double d2 = Math.Atan(radian);
// 標準関数との差異
//Console.WriteLine(string.Format("{0,3:D} : {1,13:F10} - {2,13:F10} = {3,13:F10}", degree, d1, d2, d1 - d2));
Console.WriteLine(string.Format("{0,5:D} : {1,13:F10} - {2,13:F10} = {3,13:F10}", max, d1 * 4, d2 * 4, (d1 * 4) - (d2 * 4)));
}
}
// 自作の逆正接関数
private static double myAtan(double x, bool nega, double numerator, int denominator, double y, int max)
{
denominator = denominator + 2;
numerator = numerator * x * x;
double a = numerator / denominator;
// 十分な精度になったら処理を抜ける
//if (Math.Abs(a) <= 0.00000000001)
if (denominator >= max)
return y;
else
return y + myAtan(x, !nega, numerator, denominator, nega ? a : -a, max);
}
}
/*
1000 : 3.1395926556 - 3.1415926536 = -0.0019999980
2000 : 3.1405926538 - 3.1415926536 = -0.0009999998
3000 : 3.1409259870 - 3.1415926536 = -0.0006666666
4000 : 3.1410926536 - 3.1415926536 = -0.0005000000
5000 : 3.1411926536 - 3.1415926536 = -0.0004000000
6000 : 3.1412593203 - 3.1415926536 = -0.0003333333
7000 : 3.1413069393 - 3.1415926536 = -0.0002857143
8000 : 3.1413426536 - 3.1415926536 = -0.0002500000
9000 : 3.1413704314 - 3.1415926536 = -0.0002222222
10000 : 3.1413926536 - 3.1415926536 = -0.0002000000
11000 : 3.1414108354 - 3.1415926536 = -0.0001818182
12000 : 3.1414259869 - 3.1415926536 = -0.0001666667
13000 : 3.1414388074 - 3.1415926536 = -0.0001538462
14000 : 3.1414497964 - 3.1415926536 = -0.0001428571
15000 : 3.1414593203 - 3.1415926536 = -0.0001333333
16000 : 3.1414676536 - 3.1415926536 = -0.0001250000
17000 : 3.1414750065 - 3.1415926536 = -0.0001176471
18000 : 3.1414815425 - 3.1415926536 = -0.0001111111
19000 : 3.1414873904 - 3.1415926536 = -0.0001052632
20000 : 3.1414926536 - 3.1415926536 = -0.0001000000
21000 : 3.1414974155 - 3.1415926536 = -0.0000952381
22000 : 3.1415017445 - 3.1415926536 = -0.0000909091
23000 : 3.1415056971 - 3.1415926536 = -0.0000869565
24000 : 3.1415093203 - 3.1415926536 = -0.0000833333
25000 : 3.1415126536 - 3.1415926536 = -0.0000800000
26000 : 3.1415157305 - 3.1415926536 = -0.0000769231
27000 : 3.1415185795 - 3.1415926536 = -0.0000740741
28000 : 3.1415212250 - 3.1415926536 = -0.0000714286
29000 : 3.1415236881 - 3.1415926536 = -0.0000689655
30000 : 3.1415259869 - 3.1415926536 = -0.0000666667
31000 : 3.1415281375 - 3.1415926536 = -0.0000645161
32000 : 3.1415301536 - 3.1415926536 = -0.0000625000
33000 : 3.1415320475 - 3.1415926536 = -0.0000606061
34000 : 3.1415338301 - 3.1415926536 = -0.0000588235
35000 : 3.1415355107 - 3.1415926536 = -0.0000571429
36000 : 3.1415370980 - 3.1415926536 = -0.0000555556
37000 : 3.1415385995 - 3.1415926536 = -0.0000540541
38000 : 3.1415400220 - 3.1415926536 = -0.0000526316
39000 : 3.1415413715 - 3.1415926536 = -0.0000512821
40000 : 3.1415426536 - 3.1415926536 = -0.0000500000
*/
using System;
public class CS0511
{
public static void Main()
{
for (int degree = -45; degree <= 45; degree += 15)
{
double radian = degree * Math.PI / 180.0;
double x2 = radian * radian;
// 自作の逆正接関数
double d1 = myAtan(radian, x2, 23, 0.0); // 23:必要な精度が得られる十分大きな奇数
// 標準の逆正接関数
double d2 = Math.Atan(radian);
// 標準関数との差異
Console.WriteLine(string.Format("{0,3:D} : {1,13:F10} - {2,13:F10} = {3,13:F10}", degree, d1, d2, d1 - d2));
}
}
// 自作の逆正接関数
private static double myAtan(double x, double x2, int n, double t)
{
int m = n / 2;
t = (m * m * x2) / (n + t);
n -= 2;
if (n <= 1)
return x / (1 + t);
else
return myAtan(x, x2, n, t);
}
}using System;
public class CS0512
{
public static void Main()
{
for (int i = 11; i <= 31; i += 2)
{
double radian = 1; // degree * Math.PI / 180.0;
double x2 = radian * radian;
// 自作の逆正接関数
double d1 = myAtan(radian, x2, i, 0.0); // i:必要な精度が得られる十分大きな奇数
// 標準の逆正接関数
//double d2 = Math.Atan(radian);
// 標準関数との差異
Console.WriteLine(string.Format("{0,2:D} : {1,13:F10}, {2,13:F10}", i, d1 * 4, d1 * 4 - Math.PI));
//Console.WriteLine(string.Format("{0,2D} : {1,13:F10}", i, d1));
//Console.WriteLine(string.Format("{0,2:D}", i));
//Console.WriteLine(string.Format("{0,13:F10}, {1,13:F10}, {2,13:F10}", d1 * 4, d2 * 4, Math.PI));
}
}
// 自作の逆正接関数
private static double myAtan(double x, double x2, int n, double t)
{
int m = n / 2;
t = (m * m * x2) / (n + t);
n -= 2;
if (n <= 1)
return x / (1 + t);
else
return myAtan(x, x2, n, t);
}
}using System;
public class CS0601
{
private static double f(double x)
{
return 4 / (1 + x * x);
}
public static void Main()
{
const double a = 0;
const double b = 1;
// 台形則で積分
int n = 2;
for (int j = 1; j <= 10; j++)
{
double h = (b - a) / n;
double s = 0;
double x = a;
for (int i = 1; i <= n - 1; i++)
{
x += h;
s += f(x);
}
s = h * ((f(a) + f(b)) / 2 + s);
n *= 2;
// 結果を π と比較
Console.WriteLine(string.Format("{0,2:D} : {1,13:F10}, {2,13:F10}", j, s, s - Math.PI));
}
}
}
using System;
public class CS0602
{
private static double f(double x)
{
return 4 / (1 + x * x);
}
public static void Main()
{
const double a = 0;
const double b = 1;
// 中点則で積分
int n = 2;
for (int j = 1; j <= 10; j++)
{
double h = (b - a) / n;
double s = 0;
double x = a + (h / 2);
for (int i = 1; i <= n; i++)
{
s += f(x);
x += h;
}
s *= h;
n *= 2;
// 結果を π と比較
Console.WriteLine(string.Format("{0,2:D} : {1,13:F10}, {2,13:F10}", j, s, s - Math.PI));
}
}
}
using System;
public class CS0603
{
private static double f(double x)
{
return 4 / (1 + x * x);
}
public static void Main()
{
const double a = 0;
const double b = 1;
// Simpson則で積分
int n = 2;
for (int j = 1; j <= 5; j++)
{
double h = (b - a) / n;
double s2 = 0;
double s4 = 0;
double x = a + h;
for (int i = 1; i <= n / 2; i++)
{
s4 += f(x);
x += h;
s2 += f(x);
x += h;
}
s2 = (s2 - f(b)) * 2 + f(a) + f(b);
s4 *= 4;
double s = (s2 + s4) * h / 3;
n *= 2;
// 結果を π と比較
Console.WriteLine(string.Format("{0,2:D} : {1,13:F10}, {2,13:F10}", j, s, s - Math.PI));
}
}
}
using System;
public class CS0604
{
private static double f(double x)
{
return 4 / (1 + x * x);
}
public static void Main()
{
const double a = 0;
const double b = 1;
double[,] t = new double[7,7];
// 台形則で積分
int n = 2;
for (int i = 1; i <= 6; i++)
{
double h = (b - a) / n;
double s = 0;
double x = a;
for (int j = 1; j <= n - 1; j++)
{
x += h;
s += f(x);
}
// 結果を保存
t[i,1] = h * ((f(a) + f(b)) / 2 + s);
n *= 2;
}
// Richardsonの補外法
n = 4;
for (int j = 2; j <= 6; j++)
{
for (int i = j; i <= 6; i++)
{
t[i,j] = t[i, j - 1] + (t[i, j - 1] - t[i - 1, j - 1]) / (n - 1);
if (i == j)
{
// 結果を π と比較
Console.WriteLine(string.Format("{0,2:D} : {1,13:F10}, {2,13:F10}", j, t[i,j], t[i,j] - Math.PI));
}
}
n *= 4;
}
}
}
using System;
public class CS0701
{
// データ点の数
private const int N = 7;
public static void Main()
{
double[] x = new double[N];
double[] y = new double[N];
// 1.5刻みで -4.5〜4.5 まで, ７点だけ値をセット
for (int i = 0; i < N; i++)
{
double d = i * 1.5 - 4.5;
x[i] = d;
y[i] = f(d);
}
// 0.5刻みで 与えられていない値を補間
for (int i = 0; i <= 18; i++)
{
double d = i * 0.5 - 4.5;
double d1 = f(d);
double d2 = lagrange(d, x, y);
// 元の関数と比較
Console.WriteLine(string.Format("{0,5:F2}\t{1,8:F5}\t{2,8:F5}\t{3,8:F5}", d, d1, d2, d1 - d2));
}
}
// 元の関数
private static double f(double x)
{
return x - Math.Pow(x,3) / (3 * 2) + Math.Pow(x,5) / (5 * 4 * 3 * 2);
}
// Lagrange (ラグランジュ) 補間
private static double lagrange(double d, double[] x, double[] y)
{
double sum = 0;
for (int i = 0; i < N; i++)
{
double prod = y[i];
for (int j = 0; j < N; j++)
{
if (j != i)
prod *= (d - x[j]) / (x[i] - x[j]);
}
sum += prod;
}
return sum;
}
}
using System;
public class CS0702
{
// データ点の数
private const int N = 7;
public static void Main()
{
double[] x = new double[N];
double[] y = new double[N];
// 1.5刻みで -4.5〜4.5 まで, ７点だけ値をセット
for (int i = 0; i < N; i++)
{
double d = i * 1.5 - 4.5;
x[i] = d;
y[i] = f(d);
}
// 0.5刻みで 与えられていない値を補間
for (int i = 0; i <= 18; i++)
{
double d = i * 0.5 - 4.5;
double d1 = f(d);
double d2 = neville(d, x, y);
// 元の関数と比較
Console.WriteLine(string.Format("{0,5:F2}\t{1,8:F5}\t{2,8:F5}\t{3,8:F5}", d, d1, d2, d1 - d2));
}
}
// 元の関数
private static double f(double x)
{
return x - Math.Pow(x,3) / (3 * 2) + Math.Pow(x,5) / (5 * 4 * 3 * 2);
}
// Neville (ネヴィル) 補間
private static double neville(double d, double[] x, double[] y)
{
double[,] w = new double[N,N];
for (int i = 0; i < N; i++)
w[0,i] = y[i];
for (int j = 1; j < N; j++)
{
for (int i = 0; i < N - j; i++)
w[j,i] = w[j-1,i+1] + (w[j-1,i+1] - w[j-1,i]) * (d - x[i+j]) / (x[i+j] - x[i]);
}
return w[N-1,0];
}
}
using System;
public class CS0703
{
// データ点の数
private const int N = 7;
public static void Main()
{
double[] x = new double[N];
double[] y = new double[N];
// 1.5刻みで -4.5〜4.5 まで, ７点だけ値をセット
for (int i = 0; i < N; i++)
{
double d1 = i * 1.5 - 4.5;
x[i] = d1;
y[i] = f(d1);
}
// 差分商の表を作る
double[,] d = new double[N,N];
for (int j = 0; j < N; j++)
d[0,j] = y[j];
for (int i = 1; i < N; i++)
{
for (int j = 0; j < N - i; j++)
d[i,j] = (d[i-1,j+1] - d[i-1,j]) / (x[j+i] - x[j]);
}
// ｎ階差分商
double[] a = new double[N];
for (int j = 0; j < N; j++)
a[j] = d[j,0];
// 0.5刻みで 与えられていない値を補間
for (int i = 0; i <= 18; i++)
{
double d1 = i * 0.5 - 4.5;
double d2 = f(d1);
double d3 = newton(d1, x, a);
// 元の関数と比較
Console.WriteLine(string.Format("{0,5:F2}\t{1,8:F5}\t{2,8:F5}\t{3,8:F5}", d1, d2, d3, d2 - d3));
}
}
// 元の関数
private static double f(double x)
{
return x - Math.Pow(x,3) / (3 * 2) + Math.Pow(x,5) / (5 * 4 * 3 * 2);
}
// Newton (ニュートン) 補間
private static double newton(double d, double[] x, double[] a)
{
double sum = a[0];
for (int i = 1; i < N; i++)
{
double prod = a[i];
for (int j = 0; j < i; j++)
prod *= (d - x[j]);
sum += prod;
}
return sum;
}
}
using System;
public class CS0704
{
// データ点の数
private const int N = 7;
private const int Nx2 = 14;
public static void Main()
{
double[] x = new double[N];
double[] y = new double[N];
double[] yd = new double[N];
// 1.5刻みで -4.5〜4.5 まで, ７点だけ値をセット
for (int i = 0; i < N; i++)
{
double d1 = i * 1.5 - 4.5;
x[i] = d1;
y[i] = f(d1);
yd[i] = fd(d1);
}
// 差分商の表を作る
double[] z = new double[Nx2];
double[,] d = new double[Nx2,Nx2];
for (int i = 0; i < Nx2; i++)
{
int j = i / 2;
z[i] = x[j];
d[0,i] = y[j];
}
for (int i = 1; i < Nx2; i++)
{
for (int j = 0; j < Nx2 - i; j++)
{
if (i == 1 && j % 2 == 0)
d[i,j] = yd[j / 2];
else
d[i,j] = (d[i-1,j+1] - d[i-1,j]) / (z[j+i] - z[j]);
}
}
// ｎ階差分商
double[] a = new double[Nx2];
for (int j = 0; j < Nx2; j++)
a[j] = d[j,0];
// 0.5刻みで 与えられていない値を補間
for (int i = 0; i <= 18; i++)
{
double d1 = i * 0.5 - 4.5;
double d2 = f(d1);
double d3 = hermite(d1, z, a);
// 元の関数と比較
Console.WriteLine(string.Format("{0,5:F2}\t{1,8:F5}\t{2,8:F5}\t{3,8:F5}", d1, d2, d3, d2 - d3));
}
}
// 元の関数
private static double f(double x)
{
return x - Math.Pow(x,3) / (3 * 2) + Math.Pow(x,5) / (5 * 4 * 3 * 2);
}
// 導関数
private static double fd(double x)
{
return 1 - Math.Pow(x,2) / 2 + Math.Pow(x,4) / (4 * 3 * 2);
}
// Hermite (エルミート) 補間
private static double hermite(double d, double[] z, double[] a)
{
double sum = a[0];
for (int i = 1; i < Nx2; i++)
{
double prod = a[i];
for (int j = 0; j < i; j++)
prod *= (d - z[j]);
sum += prod;
}
return sum;
}
}
using System;
public class CS0705
{
// データ点の数
private const int N = 7;
public static void Main()
{
double[] x = new double[N];
double[] y = new double[N];
// 1.5刻みで -4.5〜4.5 まで, ７点だけ値をセット
for (int i = 0; i < N; i++)
{
double d1 = i * 1.5 - 4.5;
x[i] = d1;
y[i] = f(d1);
}
// ３項方程式の係数の表を作る
double[] a = new double[N];
double[] b = new double[N];
double[] c = new double[N];
double[] d = new double[N];
for (int i = 1; i < N - 1; i++)
{
a[i] = x[i] - x[i-1];
b[i] = 2.0 * (x[i+1] - x[i-1]);
c[i] = x[i+1] - x[i];
d[i] = 6.0 * ((y[i+1] - y[i]) / (x[i+1] - x[i]) - (y[i] - y[i-1]) / (x[i] - x[i-1]));
}
// ３項方程式を解く (ト−マス法)
double[] g = new double[N];
double[] s = new double[N];
g[1] = b[1];
s[1] = d[1];
for (int i = 2; i < N - 1; i++)
{
g[i] = b[i] - a[i] * c[i-1] / g[i-1];
s[i] = d[i] - a[i] * s[i-1] / g[i-1];
}
double[] z = new double[N];
z[0] = 0;
z[N-1] = 0;
z[N-2] = s[N-2] / g[N-2];
for (int i = N - 3; i >= 1; i--)
{
z[i] = (s[i] - c[i] * z[i+1]) / g[i];
}
// 0.5刻みで 与えられていない値を補間
for (int i = 0; i <= 18; i++)
{
double d1 = i * 0.5 - 4.5;
double d2 = f(d1);
double d3 = spline(d1, x, y, z);
// 元の関数と比較
Console.WriteLine(string.Format("{0,5:F2}\t{1,8:F5}\t{2,8:F5}\t{3,8:F5}", d1, d2, d3, d2 - d3));
}
}
// 元の関数
private static double f(double x)
{
return x - Math.Pow(x,3) / (3 * 2) + Math.Pow(x,5) / (5 * 4 * 3 * 2);
}
// Spline (スプライン) 補間
private static double spline(double d, double[] x, double[] y, double[] z)
{
// 補間関数値がどの区間にあるか
int k = -1;
for (int i = 1; i < N; i++)
{
if (d <= x[i])
{
k = i - 1;
break;
}
}
if (k < 0) k = N - 1;
double d1 = x[k+1] - d;
double d2 = d - x[k];
double d3 = x[k+1] - x[k];
return (z[k] * Math.Pow(d1,3) + z[k+1] * Math.Pow(d2,3)) / (6.0 * d3)
+ (y[k] / d3 - z[k] * d3 / 6.0) * d1
+ (y[k+1] / d3 - z[k+1] * d3 / 6.0) * d2;
}
}
using System;
public class CS0801
{
// 重力加速度
private const double g = -9.8;
// 空気抵抗係数
private const double k = -0.01;
// 時間間隔(秒)
private const double h = 0.01;
public static void Main()
{
// 角度
double degree = 45;
double radian = degree * Math.PI / 180.0;
// 初速 250 km/h -> 秒速に変換
double v = 250 * 1000 / 3600;
// 水平方向の速度
double[] vx = new double[2];
vx[0] = v * Math.Cos(radian);
// 鉛直方向の速度
double[] vy = new double[2];
vy[0] = v * Math.Sin(radian);
// 経過秒数
double t = 0.0;
// 位置
double x = 0.0;
double y = 0.0;
// Euler法
for (int i = 1; y >= 0.0; i++)
{
// 経過秒数
t = i * h;
// 位置
x += h * vx[0];
y += h * vy[0];
Console.WriteLine(string.Format("{0,4:F2}\t{1,8:F5}\t{2,9:F5}\t{3,9:F5}\t{4,8:F5}", t, vx[0], vy[0], x, y));
// 速度
vx[1] = vx[0] + h * fx(vx[0], vy[0]);
vy[1] = vy[0] + h * fy(vx[0], vy[0]);
vx[0] = vx[1];
vy[0] = vy[1];
}
}
// 空気抵抗による水平方向の減速分
private static double fx(double vx, double vy)
{
return k * Math.Sqrt(vx * vx + vy * vy) * vx;
}
// 重力と空気抵抗による鉛直方向の減速分
private static double fy(double vx, double vy)
{
return g + (k * Math.Sqrt(vx * vx + vy * vy) * vy);
}
}
using System;
public class CS0802
{
// 重力加速度
private const double g = -9.8;
// 空気抵抗係数
private const double k = -0.01;
// 時間間隔(秒)
private const double h = 0.01;
public static void Main()
{
// 角度
double degree = 45;
double radian = degree * Math.PI / 180.0;
// 初速 250 km/h -> 秒速に変換
double v = 250 * 1000 / 3600;
// 水平方向の速度
double[] vx = new double[3];
vx[0] = v * Math.Cos(radian);
// 鉛直方向の速度
double[] vy = new double[3];
vy[0] = v * Math.Sin(radian);
// 経過秒数
double t = 0.0;
// 位置
double[] x = new double[3];
x[0] = 0.0;
double[] y = new double[3];
y[0] = 0.0;
// Heun法
for (int i = 1; y[0] >= 0.0; i++)
{
// 経過秒数
t = i * h;
// 位置・速度
x[1] = x[0] + h * vx[0];
y[1] = y[0] + h * vy[0];
vx[1] = vx[0] + h * fx(vx[0], vy[0]);
vy[1] = vy[0] + h * fy(vx[0], vy[0]);
x[2] = x[0] + h * ( vx[0] + vx[1] ) / 2;
y[2] = y[0] + h * ( vy[0] + vy[1] ) / 2;
vx[2] = vx[0] + h * (fx(vx[0], vy[0]) + fx(vx[1], vy[1])) / 2;
vy[2] = vy[0] + h * (fy(vx[0], vy[0]) + fy(vx[1], vy[1])) / 2;
x[0] = x[2];
y[0] = y[2];
vx[0] = vx[2];
vy[0] = vy[2];
Console.WriteLine(string.Format("{0,4:F2}\t{1,8:F5}\t{2,9:F5}\t{3,9:F5}\t{4,8:F5}", t, vx[0], vy[0], x[0], y[0]));
}
}
// 空気抵抗による水平方向の減速分
private static double fx(double vx, double vy)
{
return k * Math.Sqrt(vx * vx + vy * vy) * vx;
}
// 重力と空気抵抗による鉛直方向の減速分
private static double fy(double vx, double vy)
{
return g + (k * Math.Sqrt(vx * vx + vy * vy) * vy);
}
}
using System;
public class CS0803
{
// 重力加速度
private const double g = -9.8;
// 空気抵抗係数
private const double k = -0.01;
// 時間間隔(秒)
private const double h = 0.01;
public static void Main()
{
// 角度
double degree = 45;
double radian = degree * Math.PI / 180.0;
// 初速 250 km/h -> 秒速に変換
double v = 250 * 1000 / 3600;
// 水平方向の速度
double[] vx = new double[2];
vx[0] = v * Math.Cos(radian);
// 鉛直方向の速度
double[] vy = new double[2];
vy[0] = v * Math.Sin(radian);
// 経過秒数
double t = 0.0;
// 位置
double[] x = new double[2];
x[0] = 0.0;
double[] y = new double[2];
y[0] = 0.0;
// 中点法
for (int i = 1; y[0] >= 0.0; i++)
{
// 経過秒数
t = i * h;
// 位置・速度
vx[1] = h * fx(vx[0], vy[0]);
vy[1] = h * fy(vx[0], vy[0]);
double wx = vx[0] + vx[1] / 2;
double wy = vy[0] + vy[1] / 2;
vx[0] = vx[0] + h * fx(wx, wy);
vy[0] = vy[0] + h * fy(wx, wy);
x[0] = x[0] + h * wx;
y[0] = y[0] + h * wy;
Console.WriteLine(string.Format("{0,4:F2}\t{1,8:F5}\t{2,9:F5}\t{3,9:F5}\t{4,8:F5}", t, vx[0], vy[0], x[0], y[0]));
}
}
// 空気抵抗による水平方向の減速分
private static double fx(double vx, double vy)
{
return k * Math.Sqrt(vx * vx + vy * vy) * vx;
}
// 重力と空気抵抗による鉛直方向の減速分
private static double fy(double vx, double vy)
{
return g + (k * Math.Sqrt(vx * vx + vy * vy) * vy);
}
}
using System;
public class CS0804
{
// 重力加速度
private const double g = -9.8;
// 空気抵抗係数
private const double k = -0.01;
// 時間間隔(秒)
private const double h = 0.01;
public static void Main()
{
// 角度
double degree = 45;
double radian = degree * Math.PI / 180.0;
// 初速 250 km/h -> 秒速に変換
double v = 250 * 1000 / 3600;
// 水平方向の速度
double[] vx = new double[5];
vx[0] = v * Math.Cos(radian);
// 鉛直方向の速度
double[] vy = new double[5];
vy[0] = v * Math.Sin(radian);
// 経過秒数
double t = 0.0;
// 位置
double[] x = new double[5];
x[0] = 0.0;
double[] y = new double[5];
y[0] = 0.0;
// Runge-Kutta法
for (int i = 1; y[0] >= 0.0; i++)
{
// 経過秒数
t = i * h;
// 位置・速度
x[1] = h * vx[0];
y[1] = h * vy[0];
vx[1] = h * fx(vx[0], vy[0]);
vy[1] = h * fy(vx[0], vy[0]);
double wx = vx[0] + vx[1] / 2;
double wy = vy[0] + vy[1] / 2;
x[2] = h * wx;
y[2] = h * wy;
vx[2] = h * fx(wx, wy);
vy[2] = h * fy(wx, wy);
wx = vx[0] + vx[2] / 2;
wy = vy[0] + vy[2] / 2;
x[3] = h * wx;
y[3] = h * wy;
vx[3] = h * fx(wx, wy);
vy[3] = h * fy(wx, wy);
wx = vx[0] + vx[3];
wy = vy[0] + vy[3];
x[4] = h * wx;
y[4] = h * wy;
vx[4] = h * fx(wx, wy);
vy[4] = h * fy(wx, wy);
x[0] += ( x[1] + x[2] * 2 + x[3] * 2 + x[4]) / 6;
y[0] += ( y[1] + y[2] * 2 + y[3] * 2 + y[4]) / 6;
vx[0] += (vx[1] + vx[2] * 2 + vx[3] * 2 + vx[4]) / 6;
vy[0] += (vy[1] + vy[2] * 2 + vy[3] * 2 + vy[4]) / 6;
Console.WriteLine(string.Format("{0,4:F2}\t{1,8:F5}\t{2,9:F5}\t{3,9:F5}\t{4,8:F5}", t, vx[0], vy[0], x[0], y[0]));
}
}
// 空気抵抗による水平方向の減速分
private static double fx(double vx, double vy)
{
return k * Math.Sqrt(vx * vx + vy * vy) * vx;
}
// 重力と空気抵抗による鉛直方向の減速分
private static double fy(double vx, double vy)
{
return g + (k * Math.Sqrt(vx * vx + vy * vy) * vy);
}
}
using System;
public class CS0805
{
// 重力加速度
private const double g = -9.8;
// 空気抵抗係数
private const double k = -0.01;
// 時間間隔(秒)
private const double h = 0.01;
public static void Main()
{
// 角度
double degree = 45;
double radian = degree * Math.PI / 180.0;
// 初速 250 km/h -> 秒速に変換
double v = 250 * 1000 / 3600;
// 水平方向の速度
double[] vx = new double[5];
vx[0] = v * Math.Cos(radian);
// 鉛直方向の速度
double[] vy = new double[5];
vy[0] = v * Math.Sin(radian);
// 経過秒数
double t = 0.0;
// 位置
double[] x = new double[5];
x[0] = 0.0;
double[] y = new double[5];
y[0] = 0.0;
// Runge-Kutta-Gill法
for (int i = 1; y[0] >= 0.0; i++)
{
// 経過秒数
t = i * h;
// 位置・速度
x[1] = h * vx[0];
y[1] = h * vy[0];
vx[1] = h * fx(vx[0], vy[0]);
vy[1] = h * fy(vx[0], vy[0]);
double wx = vx[0] + vx[1] / 2;
double wy = vy[0] + vy[1] / 2;
x[2] = h * wx;
y[2] = h * wy;
vx[2] = h * fx(wx, wy);
vy[2] = h * fy(wx, wy);
wx = vx[0] + vx[1] * ((Math.Sqrt(2.0) - 1) / 2) + vx[2] * (1 - 1 / Math.Sqrt(2.0));
wy = vy[0] + vy[1] * ((Math.Sqrt(2.0) - 1) / 2) + vy[2] * (1 - 1 / Math.Sqrt(2.0));
x[3] = h * wx;
y[3] = h * wy;
vx[3] = h * fx(wx, wy);
vy[3] = h * fy(wx, wy);
wx = vx[0] - vx[2] / Math.Sqrt(2.0) + vx[3] * (1 + 1 / Math.Sqrt(2.0));
wy = vy[0] - vy[2] / Math.Sqrt(2.0) + vy[3] * (1 + 1 / Math.Sqrt(2.0));
x[4] = h * wx;
y[4] = h * wy;
vx[4] = h * fx(wx, wy);
vy[4] = h * fy(wx, wy);
x[0] += ( x[1] + x[2] * (2 - Math.Sqrt(2.0)) + x[3] * (2 + Math.Sqrt(2.0)) + x[4]) / 6;
y[0] += ( y[1] + y[2] * (2 - Math.Sqrt(2.0)) + y[3] * (2 + Math.Sqrt(2.0)) + y[4]) / 6;
vx[0] += (vx[1] + vx[2] * (2 - Math.Sqrt(2.0)) + vx[3] * (2 + Math.Sqrt(2.0)) + vx[4]) / 6;
vy[0] += (vy[1] + vy[2] * (2 - Math.Sqrt(2.0)) + vy[3] * (2 + Math.Sqrt(2.0)) + vy[4]) / 6;
Console.WriteLine(string.Format("{0,4:F2}\t{1,8:F5}\t{2,9:F5}\t{3,9:F5}\t{4,8:F5}", t, vx[0], vy[0], x[0], y[0]));
}
}
// 空気抵抗による水平方向の減速分
private static double fx(double vx, double vy)
{
return k * Math.Sqrt(vx * vx + vy * vy) * vx;
}
// 重力と空気抵抗による鉛直方向の減速分
private static double fy(double vx, double vy)
{
return g + (k * Math.Sqrt(vx * vx + vy * vy) * vy);
}
}
using System;
public class CS0901
{
public static void Main()
{
double a = 1;
double b = 2;
Console.WriteLine(string.Format("{0,12:F10}", bisection(a, b)));
}
private static double bisection(double a, double b)
{
double c;
while (true)
{
// 区間 (a, b) の中点 c = (a + b) / 2
c = (a + b) / 2;
Console.WriteLine(string.Format("{0,12:F10}\t{1,13:F10}", c, c - Math.Sqrt(2)));
double fc = f(c);
if (Math.Abs(fc) < 0.0000000001) break;
if (fc < 0)
{
// f(c) < 0 であれば, 解は区間 (c, b) の中に存在
a = c;
}
else
{
// f(c) > 0 であれば, 解は区間 (a, c) の中に存在
b = c;
}
}
return c;
}
private static double f(double x)
{
return x * x - 2;
}
}
using System;
public class CS0902
{
public static void Main()
{
double a = 1;
double b = 2;
Console.WriteLine(string.Format("{0,12:F10}", falseposition(a, b)));
}
private static double falseposition(double a, double b)
{
double c;
while (true)
{
// 点 (a,f(a)) と 点 (b,f(b)) を結ぶ直線と x軸の交点 c
c = (a * f(b) - b * f(a)) / (f(b) - f(a));
Console.WriteLine(string.Format("{0,12:F10}\t{1,13:F10}", c, c - Math.Sqrt(2)));
double fc = f(c);
if (Math.Abs(fc) < 0.0000000001) break;
if (fc < 0)
{
// f(c) < 0 であれば, 解は区間 (c, b) の中に存在
a = c;
}
else
{
// f(c) > 0 であれば, 解は区間 (a, c) の中に存在
b = c;
}
}
return c;
}
private static double f(double x)
{
return x * x - 2;
}
}
using System;
public class CS0903
{
public static void Main()
{
double x = 1;
Console.WriteLine(string.Format("{0,12:F10}", iterative(x)));
}
private static double iterative(double x0)
{
double x1;
while (true)
{
x1 = g(x0);
Console.WriteLine(string.Format("{0,12:F10}\t{1,13:F10}", x1, x1 - Math.Sqrt(2)));
if (Math.Abs(x1 - x0) < 0.0000000001) break;
x0 = x1;
}
return x1;
}
private static double g(double x)
{
return (x / 2) + (1 / x);
}
}
using System;
public class CS0904
{
public static void Main()
{
double x = 2;
Console.WriteLine(string.Format("{0,12:F10}", newton(x)));
}
private static double newton(double x0)
{
double x1;
while (true)
{
x1 = x0 - (f0(x0) / f1(x0));
Console.WriteLine(string.Format("{0,12:F10}\t{1,13:F10}", x1, x1 - Math.Sqrt(2)));
if (Math.Abs(x1 - x0) < 0.0000000001) break;
x0 = x1;
}
return x1;
}
private static double f0(double x)
{
return x * x - 2;
}
private static double f1(double x)
{
return 2 * x;
}
}
using System;
public class CS0905
{
public static void Main()
{
double x = 2;
Console.WriteLine(string.Format("{0,12:F10}", bailey(x)));
}
private static double bailey(double x0)
{
double x1;
while (true)
{
x1 = x0 - (f0(x0) / (f1(x0) - (f0(x0) * f2(x0) / (2 * f1(x0)))));
Console.WriteLine(string.Format("{0,12:F10}\t{1,13:F10}", x1, x1 - Math.Sqrt(2)));
if (Math.Abs(x1 - x0) < 0.0000000001) break;
x0 = x1;
}
return x1;
}
private static double f0(double x)
{
return x * x - 2;
}
private static double f1(double x)
{
return 2 * x;
}
private static double f2(double x)
{
return 2;
}
}
using System;
public class CS0906
{
public static void Main()
{
double x0 = 1;
double x1 = 2;
Console.WriteLine(string.Format("{0,12:F10}", secant(x0, x1)));
}
private static double secant(double x0, double x1)
{
double x2;
while (true)
{
x2 = x1 - f(x1) * (x1 - x0) / (f(x1) - f(x0));
Console.WriteLine(string.Format("{0,12:F10}\t{1,13:F10}", x2, x2 - Math.Sqrt(2)));
if (Math.Abs(x2 - x1) < 0.0000000001) break;
x0 = x1;
x1 = x2;
}
return x2;
}
private static double f(double x)
{
return x * x - 2;
}
}
using System;
public class CS1001
{
private const int N = 4;
public static void Main()
{
double[,] a = {{9,2,1,1},{2,8,-2,1},{-1,-2,7,-2},{1,-1,-2,6}};
double[] b = {20,16,8,17};
double[] c = {0,0,0,0};
// ヤコビの反復法
jacobi(a,b,c);
Console.WriteLine("解");
for (int i = 0; i < N; i++)
Console.Write(string.Format("{0,14:F10}\t", c[i]));
Console.WriteLine();
}
// ヤコビの反復法
public static void jacobi(double[,] a, double[] b, double[] x0)
{
while (true)
{
double[] x1 = new double[N];
bool finish = true;
for (int i = 0; i < N; i++)
{
x1[i] = 0;
for (int j = 0; j < N; j++)
if (j != i)
x1[i] += a[i,j] * x0[j];
x1[i] = (b[i] - x1[i]) / a[i,i];
if (Math.Abs(x1[i] - x0[i]) > 0.0000000001) finish = false;
}
for (int i = 0; i < N; i++)
{
x0[i] = x1[i];
Console.Write(string.Format("{0,14:F10}\t", x0[i]));
}
Console.WriteLine();
if (finish) return;
}
}
}
using System;
public class CS1002
{
private const int N = 4;
public static void Main()
{
double[,] a = {{9,2,1,1},{2,8,-2,1},{-1,-2,7,-2},{1,-1,-2,6}};
double[] b = {20,16,8,17};
double[] c = {0,0,0,0};
// ガウス・ザイデル法
gauss(a,b,c);
Console.WriteLine("解");
for (int i = 0; i < N; i++)
Console.Write(String.Format("{0,14:F10}\t", c[i]));
Console.WriteLine();
}
// ガウス・ザイデル法
private static void gauss(double[,] a, double[] b, double[] x0)
{
while (true)
{
double x1;
bool finish = true;
for (int i = 0; i < N; i++)
{
x1 = 0;
for (int j = 0; j < N; j++)
if (j != i)
x1 += a[i,j] * x0[j];
x1 = (b[i] - x1) / a[i,i];
if (Math.Abs(x1 - x0[i]) > 0.0000000001) finish = false;
x0[i] = x1;
}
for (int i = 0; i < N; i++)
Console.Write(String.Format("{0,14:F10}\t", x0[i]));
Console.WriteLine();
if (finish) return;
}
}
}
using System;
public class CS1003
{
private const int N = 4;
// ガウスの消去法
public static void Main()
{
double[,] a = {{-1,-2,7,-2},{1,-1,-2,6},{9,2,1,1},{2,8,-2,1}};
double[] b = {8,17,20,16};
// ピボット選択
pivoting(a,b);
Console.WriteLine("ピボット選択後");
disp_progress(a,b);
// 前進消去
forward_elimination(a,b);
Console.WriteLine("前進消去後");
disp_progress(a,b);
// 後退代入
backward_substitution(a,b);
Console.WriteLine("解");
for (int i = 0; i < N; i++)
Console.Write(String.Format("{0,14:F10}\t", b[i]));
Console.WriteLine();
}
// 前進消去
private static void forward_elimination(double[,] a, double[] b)
{
for (int pivot = 0; pivot < N - 1; pivot++)
{
for (int row = pivot + 1; row < N; row++)
{
double s = a[row,pivot] / a[pivot,pivot];
for (int col = pivot; col < N; col++)
a[row,col] -= a[pivot,col] * s;
b[row] -= b[pivot] * s;
}
}
}
// 後退代入
private static void backward_substitution(double[,] a, double[] b)
{
for (int row = N - 1; row >= 0; row--)
{
for (int col = N - 1; col > row; col--)
b[row] -= a[row,col] * b[col];
b[row] /= a[row,row];
}
}
// ピボット選択
private static void pivoting(double[,] a, double[] b)
{
for(int pivot = 0; pivot < N; pivot++)
{
// 各列で 一番値が大きい行を 探す
int max_row = pivot;
double max_val = 0;
for (int row = pivot; row < N; row++)
{
if (Math.Abs(a[row,pivot]) > max_val)
{
// 一番値が大きい行
max_val = Math.Abs(a[row,pivot]);
max_row = row;
}
}
// 一番値が大きい行と入れ替え
if (max_row != pivot) {
double tmp;
for (int col = 0; col < N; col++)
{
tmp = a[max_row,col];
a[max_row,col] = a[pivot,col];
a[pivot,col] = tmp;
}
tmp = b[max_row];
b[max_row] = b[pivot];
b[pivot] = tmp;
}
}
}
// 状態を確認
private static void disp_progress(double[,] a, double[] b)
{
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
Console.Write(String.Format("{0,14:F10}\t", a[i,j]));
Console.WriteLine(String.Format("{0,14:F10}\t", b[i]));
}
Console.WriteLine();
}
}
using System;
public class CS1004
{
private const int N = 4;
// ガウス・ジョルダン法
public static void Main()
{
double[,] a = {{-1,-2,7,-2},{1,-1,-2,6},{9,2,1,1},{2,8,-2,1}};
double[] b = {8,17,20,16};
// ピボット選択
pivoting(a,b);
Console.WriteLine("ピボット選択後");
disp_progress(a,b);
// 前進消去
forward_elimination(a,b);
Console.WriteLine("前進消去後");
disp_progress(a,b);
// 後退代入
backward_substitution(a,b);
Console.WriteLine("解");
for (int i = 0; i < N; i++)
Console.Write(String.Format("{0,14:F10}\t", b[i]));
Console.WriteLine();
}
// 前進消去
private static void forward_elimination(double[,] a, double[] b)
{
// 対角線上の係数を 1 にする
for (int pivot = 0; pivot < N; pivot++)
{
double s = a[pivot,pivot];
for (int col = 0; col < N; col++)
a[pivot,col] /= s;
b[pivot] /= s;
}
Console.WriteLine("対角線上の係数を 1 にする");
disp_progress(a,b);
// 対角行列にする
for (int pivot = 0; pivot < N; pivot++)
{
for (int row = 0; row < N; row++)
{
if (row == pivot) continue;
double s = a[row,pivot] / a[pivot,pivot];
for (int col = pivot; col < N; col++)
a[row,col] -= a[pivot,col] * s;
b[row] -= b[pivot] * s;
}
}
}
// 後退代入
private static void backward_substitution(double[,] a, double[] b)
{
for (int pivot = 0; pivot < N; pivot++)
b[pivot] /= a[pivot,pivot];
}
// ピボット選択
private static void pivoting(double[,] a, double[] b)
{
for(int pivot = 0; pivot < N; pivot++)
{
// 各列で 一番値が大きい行を 探す
int max_row = pivot;
double max_val = 0;
for (int row = pivot; row < N; row++)
{
if (Math.Abs(a[row,pivot]) > max_val)
{
// 一番値が大きい行
max_val = Math.Abs(a[row,pivot]);
max_row = row;
}
}
// 一番値が大きい行と入れ替え
if (max_row != pivot) {
double tmp;
for (int col = 0; col < N; col++)
{
tmp = a[max_row,col];
a[max_row,col] = a[pivot,col];
a[pivot,col] = tmp;
}
tmp = b[max_row];
b[max_row] = b[pivot];
b[pivot] = tmp;
}
}
}
// 状態を確認
private static void disp_progress(double[,] a, double[] b)
{
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
Console.Write(String.Format("{0,14:F10}\t", a[i,j]));
Console.WriteLine(String.Format("{0,14:F10}\t", b[i]));
}
Console.WriteLine();
}
}
using System;
public class CS1005
{
private const int N = 4;
// LU分解
public static void Main()
{
double[,] a = {{-1,-2,7,-2},{1,-1,-2,6},{9,2,1,1},{2,8,-2,1}};
double[] b = {8,17,20,16};
// ピボット選択
pivoting(a,b);
Console.WriteLine("ピボット選択後");
disp_progress(a,b);
// LU分解
double[] x = {0,0,0,0};
decomp(a,b,x);
Console.WriteLine("X");
for (int i = 0; i < N; i++)
Console.Write(String.Format("{0,14:F10}\t", x[i]));
Console.WriteLine();
}
// LU分解
private static void decomp(double[,] a, double[] b, double[] x)
{
// 前進消去
forward_elimination(a,b);
// 下三角行列を確認
Console.WriteLine("L");
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
if (i > j)
Console.Write(String.Format("{0,14:F10}\t", a[i,j]));
else if (i == j)
Console.Write(String.Format("{0,14:F10}\t", 1.0));
else
Console.Write(String.Format("{0,14:F10}\t", 0.0));
Console.WriteLine();
}
Console.WriteLine();
// 上三角行列を確認
Console.WriteLine("U");
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
if (i <= j)
Console.Write(String.Format("{0,14:F10}\t", a[i,j]));
else
Console.Write(String.Format("{0,14:F10}\t", 0.0));
Console.WriteLine();
}
Console.WriteLine();
// Ly=b から y を求める (前進代入)
double[] y = {0,0,0,0};
for (int row = 0; row < N; row++)
{
for (int col = 0; col < row; col++)
b[row] -= a[row,col] * y[col];
y[row] = b[row];
}
// y の 値 を確認
Console.WriteLine("Y");
for (int i = 0; i < N; i++)
Console.Write(String.Format("{0,14:F10}\t", y[i]));
Console.WriteLine("\n");
// Ux=y から x を求める (後退代入)
for (int row = N - 1; row >= 0; row--)
{
for (int col = N - 1; col > row; col--)
y[row] -= a[row,col] * x[col];
x[row] = y[row] / a[row,row];
}
}
// 前進消去
private static void forward_elimination(double[,] a, double[] b)
{
for (int pivot = 0; pivot < N - 1; pivot++)
{
for (int row = pivot + 1; row < N; row++)
{
double s = a[row,pivot] / a[pivot,pivot];
for (int col = pivot; col < N; col++)
a[row,col] -= a[pivot,col] * s; // これが 上三角行列
a[row,pivot] = s; // これが 下三角行列
// b[row] -= b[pivot] * s; // この値は変更しない
}
}
}
// ピボット選択
private static void pivoting(double[,] a, double[] b)
{
for(int pivot = 0; pivot < N; pivot++)
{
// 各列で 一番値が大きい行を 探す
int max_row = pivot;
double max_val = 0;
for (int row = pivot; row < N; row++)
{
if (Math.Abs(a[row,pivot]) > max_val)
{
// 一番値が大きい行
max_val = Math.Abs(a[row,pivot]);
max_row = row;
}
}
// 一番値が大きい行と入れ替え
if (max_row != pivot)
{
double tmp;
for (int col = 0; col < N; col++)
{
tmp = a[max_row,col];
a[max_row,col] = a[pivot,col];
a[pivot,col] = tmp;
}
tmp = b[max_row];
b[max_row] = b[pivot];
b[pivot] = tmp;
}
}
}
// 状態を確認
private static void disp_progress(double[,] a, double[] b)
{
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
Console.Write(String.Format("{0,14:F10}\t", a[i,j]));
Console.WriteLine(String.Format("{0,14:F10}\t", b[i]));
}
Console.WriteLine();
}
}
using System;
public class CS1006
{
private const int N = 4;
// コレスキー法
public static void Main()
{
double[,] a = {{5,2,3,4},{2,10,6,7},{3,6,15,9},{4,7,9,20}};
double[] b = {34,68,96,125};
Console.WriteLine("A");
disp_progress(a);
// LL^T分解
double[] x = {0,0,0,0};
decomp(a,b,x);
Console.WriteLine("X");
for (int i = 0; i < N; i++)
Console.Write(String.Format("{0,14:F10}\t", x[i]));
Console.WriteLine();
}
// LL^T分解
private static void decomp(double[,] a, double[] b, double[] x)
{
// 前進消去
forward_elimination(a,b);
Console.WriteLine("L と L^T");
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
if (j <= i)
Console.Write(String.Format("{0,14:F10}\t", a[i,j]));
else
Console.Write(String.Format("{0,14:F10}\t", a[j,i]));
Console.WriteLine();
}
Console.WriteLine();
// Ly=b から y を求める (前進代入)
double[] y = {0,0,0,0};
for (int row = 0; row < N; row++)
{
for (int col = 0; col < row; col++)
b[row] -= a[row,col] * y[col];
y[row] = b[row] / a[row,row];
}
// y の 値 を確認
Console.WriteLine("Y");
for (int i = 0; i < N; i++)
Console.Write(String.Format("{0,14:F10}\t", y[i]));
Console.WriteLine("\n");
// Ux=y から x を求める (後退代入)
for (int row = N - 1; row >= 0; row--)
{
for (int col = N - 1; col > row; col--)
y[row] -= a[col,row] * x[col];
x[row] = y[row] / a[row,row];
}
}
// 前進消去
private static void forward_elimination(double[,] a, double[] b)
{
for (int pivot = 0; pivot < N; pivot++)
{
double s = 0;
for (int col = 0; col < pivot; col++)
s += a[pivot,col] * a[pivot,col];
// ここで根号の中が負の値になると計算できない！
a[pivot,pivot] = Math.Sqrt(a[pivot,pivot] - s);
for (int row = pivot + 1; row < N; row++)
{
s = 0;
for (int col = 0; col < pivot; col++)
s += a[row,col] * a[pivot,col];
a[row,pivot] = (a[row,pivot] - s) / a[pivot,pivot];
}
}
}
// 状態を確認
private static void disp_progress(double[,] a)
{
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
Console.Write(String.Format("{0,14:F10}\t", a[i,j]));
Console.WriteLine();
}
Console.WriteLine();
}
}
using System;
public class CS1006
{
private const int N = 4;
// 修正コレスキー法
public static void Main()
{
double[,] a = {{5,2,3,4},{2,10,6,7},{3,6,15,9},{4,7,9,20}};
double[] b = {34,68,96,125};
Console.WriteLine("A");
disp_progress(a);
// LDL^T分解
double[] x = {0,0,0,0};
decomp(a,b,x);
Console.WriteLine("X");
for (int i = 0; i < N; i++)
Console.Write(String.Format("{0,14:F10}\t", x[i]));
Console.WriteLine();
}
// LDL^T分解
private static void decomp(double[,] a, double[] b, double[] x)
{
// 前進消去
forward_elimination(a,b);
Console.WriteLine("L と D");
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
if (j <= i)
Console.Write(String.Format("{0,14:F10}\t", a[i,j]));
else
Console.Write(String.Format("{0,14:F10}\t", a[j,i]));
Console.WriteLine();
}
Console.WriteLine();
// Ly=b から y を求める (前進代入)
double[] y = {0,0,0,0};
for (int row = 0; row < N; row++)
{
for (int col = 0; col < row; col++)
b[row] -= a[row,col] * y[col];
y[row] = b[row];
}
// y の 値 を確認
Console.WriteLine("Y");
for (int i = 0; i < N; i++)
Console.Write(String.Format("{0,14:F10}\t", y[i]));
Console.WriteLine("\n");
// DL^Tx=y から x を求める (後退代入)
for (int row = N - 1; row >= 0; row--)
{
for (int col = N - 1; col > row; col--)
y[row] -= a[col,row] * a[row,row] * x[col];
x[row] = y[row] / a[row,row];
}
}
// 前進消去
private static void forward_elimination(double[,] a, double[] b)
{
for (int pivot = 0; pivot < N; pivot++)
{
double s;
// pivot < k の場合
for (int col = 0; col < pivot; col++)
{
s = a[pivot,col];
for (int k = 0; k < col; k++)
s -= a[pivot,k] * a[col,k] * a[k,k];
a[pivot,col] = s / a[col,col];
}
// pivot == k の場合
s = a[pivot,pivot];
for (int k = 0; k < pivot; k++)
s -= a[pivot,k] * a[pivot,k] * a[k,k];
a[pivot,pivot] = s;
}
}
// 状態を確認
private static void disp_progress(double[,] a)
{
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
Console.Write(String.Format("{0,14:F10}\t", a[i,j]));
Console.WriteLine();
}
Console.WriteLine();
}
}
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