public class Java0101 { public static void main(String []args) { System.out.println(3 + 5); System.out.println(3 - 5); System.out.println(3 * 5); System.out.println(Math.pow(3, 5)); System.out.println(5 / 3); System.out.println(5.0 / 3); System.out.println(5 / 3.0); System.out.println(5 % 3); System.out.print(3 * 5 + "\n"); System.out.println(String.format("%3d", 3 * 5)); System.out.println(String.format("%23.20f", 5 / 3.0)); } } public class Java0102 { public static void main(String []args) { int i = 3 * 5; System.out.println("3 * 5 = " + i); System.out.printf("3 * 5 = %d\n", i); } } public class Java0103 { public static void main(String []args) { for (int i = 1; i < 10; i++) { System.out.print(i + ", "); } System.out.println(); } } public class Java0104 { public static void main(String []args) { for (int i = 1; i < 10; i++) { if (i % 3 == 0) { System.out.print(i + ", "); } } System.out.println(); } } public class Java0105 { public static void main(String []args) { int sum = 0; for (int i = 1; i < 100; i++) { if (i % 3 == 0) { sum += i; } } System.out.println(sum); } } public class Java0301 { public static void main(String []args) { // 3 の倍数の合計 System.out.println( 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 Java0302{ public static void main(String []args){ // 10000 までの 自然数の和 // 項目数 n = 10000 int n = 10000; System.out.println( n * (n + 1) / 2 ); } } public class Java0303{ public static void main(String []args){ // 10000 までの 偶数の和 // 項目数 n = 5000 int n = 10000 / 2; System.out.println( n * (n + 1) ); } } public class Java0304{ public static void main(String []args){ // 10000 までの 奇数の和 // 項目数 n = 5000 int n = 10000 / 2; System.out.println((int) Math.pow(n, 2) ); } } public class Java0305{ public static void main(String []args){ // 1000 までの 自然数の2乗の和 int n = 1000; System.out.println( n * (n + 1) * (2 * n + 1) / 6 ); } } public class Java0306{ public static void main(String []args){ // 100 までの 自然数の3乗の和 int n = 100; System.out.println((int) (Math.pow(n, 2) * Math.pow((n + 1), 2) / 4 ) ); } } public class Java0307{ public static void main(String []args){ // 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.out.println((int) (a * (Math.pow(r, n) - 1)) / (r - 1) ); } } public class Java0401 { public static void main(String []args) { 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; } System.out.println(p); } } public class Java0402 { public static void main(String []args) { // 初項 5, 公差 3, 項数 10 の数列の積を表示する System.out.println(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); } } public class Java0403 { // 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(String []args) { // 10の階乗 System.out.println(Fact(10)); System.out.println(10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1); } } public class Java0404 { // 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(String []args) { // 10 から 6 までの 総乗 System.out.println(FallingFact(10, 5)); System.out.println(10 * 9 * 8 * 7 * 6); } } public class Java0405 { // 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(String []args) { // 10 から 14 までの 総乗 System.out.println(RisingFact(10, 5)); System.out.println(10 * 11 * 12 * 13 * 14); } } public class Java0406 { // 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(String []args) { // 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; System.out.println(Fact(n) / Fact(n - r)); System.out.println(FallingFact(n, r)); } } public class Java0407 { public static void main(String []args) { // 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; System.out.println(Math.pow(n, r)); } } public class Java040101 { // 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(String []args) { // 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; System.out.println(Comb(n, r)); } } public class Java0409 { // 組合せ private static int Comb(int n, int r) { if (r == 0 || r == n) return 1; else if (r == 1) return n; elsereturn Comb(n - 1, r - 1) + Comb(n - 1, r); } public static void main(String []args) { // 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; System.out.println(Comb(n + r - 1, r)); } } public class Java0501 { public static void main(String []args) { for (int degree = 0; degree <= 360; degree += 15) { if (degree % 30 == 0 || degree % 45 == 0) { double radian = Math.toRadians(degree); // 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 System.out.println(String.format("%3d : %13.10f - %13.10f = %13.10f", degree, d1, d2, d1 - d2)); } } } // 自作の正弦関数 private static double mySin(double x, int n, boolean 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); } } public class Java0502 { public static void main(String []args) { for (int degree = 0; degree <= 360; degree += 15) { if (degree % 30 == 0 || degree % 45 == 0) { double radian = Math.toRadians(degree); // 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 System.out.println(String.format("%3d : %13.10f - %13.10f = %13.10f", degree, d1, d2, d1 - d2)); } } } // 自作の余弦関数 private static double myCos(double x, int n, boolean 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); } } public class Java0503 { public static void main(String []args) { for (int degree = -90; degree <= 90; degree += 15) { if ((degree + 90) % 180 != 0) { double radian = Math.toRadians(degree); 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 System.out.println(String.format("%3d : %13.10f - %13.10f = %13.10f", 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); } } public class Java0504 { public static void main(String []args) { 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 System.out.println(String.format("%5.2f : %13.10f - %13.10f = %13.10f", 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); } } public class Java0505 { public static void main(String []args) { 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 System.out.println(String.format("%5.2f : %13.10f - %13.10f = %13.10f", 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); } } public class Java0506 { public static void main(String []args) { 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 System.out.println(String.format("%5.2f : %13.10f - %13.10f = %13.10f", 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); } } public class Java0507 { public static void main(String []args) { 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 System.out.println(String.format("%5.2f : %13.10f - %13.10f = %13.10f", 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); } } public class Java0508 { public static void main(String []args) { 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 System.out.println(String.format("%3d : %17.10f - %17.10f = %13.10f", 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); } } public class Java0509 { public static void main(String []args) { 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 System.out.println(String.format("%3d : %17.10f - %17.10f = %13.10f", 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); } } public class Java0601 { private static double f(double x) { return 4 / (1 + x * x); } public static void main(String []args) { final double a = 0; final 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 System.out.println(String.format("%2d : %13.10f, %13.10f", j, s, s - Math.PI)); } } } public class Java0602 { private static double f(double x) { return 4 / (1 + x * x); } public static void main(String []args) { final double a = 0; final 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 System.out.println(String.format("%2d : %13.10f, %13.10f", j, s, s - Math.PI)); } } } public class Java0603 { private static double f(double x) { return 4 / (1 + x * x); } public static void main(String []args) { final double a = 0; final 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 System.out.println(String.format("%2d : %13.10f, %13.10f", j, s, s - Math.PI)); } } } public class Java0604 { private static double f(double x) { return 4 / (1 + x * x); } public static void main(String []args) { final double a = 0; final 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 System.out.println(String.format("%2d : %13.10f, %13.10f", j, t[i][j], t[i][j] - Math.PI)); } } n *= 4; } } } public class Java0701 { // データ点の数 private static final int N = 7; public static void main(String []args) { 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 System.out.println(String.format("%5.2f\t%8.5f\t%8.5f\t%8.5f", 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; } } public class Java0702 { // データ点の数 private static final int N = 7; public static void main(String []args) { 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 System.out.println(String.format("%5.2f\t%8.5f\t%8.5f\t%8.5f", 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]; } } public class Java0703 { // データ点の数 private static final int N = 7; public static void main(String []args) { 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 System.out.println(String.format("%5.2f\t%8.5f\t%8.5f\t%8.5f", 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; } } public class Java0704 { // データ点の数 private static final int N = 7; private static final int Nx2 = 14; public static void main(String []args) { 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 System.out.println(String.format("%5.2f\t%8.5f\t%8.5f\t%8.5f", 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; } } public class Java0705 { // データ点の数 private static final int N = 7; public static void main(String []args) { 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 System.out.println(String.format("%5.2f\t%8.5f\t%8.5f\t%8.5f", 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; } } import static java.lang.System.out; public class Java0801 { // 重力加速度 private static final double g = -9.8; // 空気抵抗係数 private static final double k = -0.01; // 時間間隔(秒) private static final double h = 0.01; public static void main(String []args) { // 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]; out.println(String.format("%4.2f\t%8.5f\t%9.5f\t%9.5f\t%8.5f", 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); } } import static java.lang.System.out; public class Java0802 { // 重力加速度 private static final double g = -9.8; // 空気抵抗係数 private static final double k = -0.01; // 時間間隔(秒) private static final double h = 0.01; public static void main(String []args) { // 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]; out.println(String.format("%4.2f\t%8.5f\t%9.5f\t%9.5f\t%8.5f", 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); } } import static java.lang.System.out; public class Java0803 { // 重力加速度 private static final double g = -9.8; // 空気抵抗係数 private static final double k = -0.01; // 時間間隔(秒) private static final double h = 0.01; public static void main(String []args) { // 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; out.println(String.format("%4.2f\t%8.5f\t%9.5f\t%9.5f\t%8.5f", 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); } } import static java.lang.System.out; public class Java0804 { // 重力加速度 private static final double g = -9.8; // 空気抵抗係数 private static final double k = -0.01; // 時間間隔(秒) private static final double h = 0.01; public static void main(String []args) { // 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; out.println(String.format("%4.2f\t%8.5f\t%9.5f\t%9.5f\t%8.5f", 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); } } import static java.lang.System.out; public class Java0805 { // 重力加速度 private static final double g = -9.8; // 空気抵抗係数 private static final double k = -0.01; // 時間間隔(秒) private static final double h = 0.01; public static void main(String []args) { // 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; out.println(String.format("%4.2f\t%8.5f\t%9.5f\t%9.5f\t%8.5f", 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); } } import static java.lang.System.out; public class Java0901 { public static void main(String []args) { double a = 1; double b = 2; out.println(String.format("%12.10f", 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; out.println(String.format("%12.10f\t%13.10f", 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; } } import static java.lang.System.out; public class Java0902 { public static void main(String []args) { double a = 1; double b = 2; out.println(String.format("%12.10f", 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 = (a * f(b) - b * f(a)) / (f(b) - f(a)); out.println(String.format("%12.10f\t%13.10f", 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; } } import static java.lang.System.out; public class Java0903 { public static void main(String []args) { double x = 1; out.println(String.format("%12.10f", iterative(x))); } private static double iterative(double x0) { double x1; while (true) { x1 = g(x0); out.println(String.format("%12.10f\t%13.10f", 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); } } import static java.lang.System.out; public class Java0904 { public static void main(String []args) { double x = 2; out.println(String.format("%12.10f", newton(x))); } private static double newton(double x0) { double x1; while (true) { x1 = x0 - (f0(x0) / f1(x0)); out.println(String.format("%12.10f\t%13.10f", 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; } } import static java.lang.System.out; public class Java0905 { public static void main(String []args) { double x = 2; out.println(String.format("%12.10f", 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))))); out.println(String.format("%12.10f\t%13.10f", 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; } } import static java.lang.System.out; public class Java0906 { public static void main(String []args) { double x0 = 1; double x1 = 2; out.println(String.format("%12.10f", 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)); out.println(String.format("%12.10f\t%13.10f", 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; } } import java.lang.*; public class Java1001 { private static final int N = 4; public static void main(String []args) { 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); System.out.println("解"); for (int i = 0; i < N; i++) System.out.print(String.format("%14.10f\t", c[i])); System.out.println(); } // ヤコビの反復法 private static void jacobi(double[][] a, double[] b, double[] x0) { while (true) { double[] x1 = new double[N]; boolean 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]; System.out.print(String.format("%14.10f\t", x0[i])); } System.out.println(); if (finish) return; } } } import java.lang.*; public class Java1002 { private static final int N = 4; public static void main(String []args) { 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); System.out.println("解"); for (int i = 0; i < N; i++) System.out.print(String.format("%14.10f\t", c[i])); System.out.println(); } // ガウス・ザイデル法 private static void gauss(double[][] a, double[] b, double[] x0) { while (true) { double x1; boolean 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++) System.out.print(String.format("%14.10f\t", x0[i])); System.out.println(); if (finish) return; } } } import java.lang.*; public class Java1003 { private static final int N = 4; // ガウスの消去法 public static void main(String []args) { 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); System.out.println("ピボット選択後"); disp_progress(a,b); // 前進消去 forward_elimination(a,b); System.out.println("前進消去後"); disp_progress(a,b); // 後退代入 backward_substitution(a,b); System.out.println("解"); for (int i = 0; i < N; i++) System.out.print(String.format("%14.10f\t", b[i])); System.out.println(); } // 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++) System.out.print(String.format("%14.10f\t", a[i][j])); System.out.println(String.format("%14.10f\t", b[i])); } System.out.println(); } } import java.lang.*; public class Java1004 { private static final int N = 4; // ガウス・ジョルダン法 public static void main(String []args) { 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); System.out.println("ピボット選択後"); disp_progress(a,b); // 前進消去 forward_elimination(a,b); System.out.println("前進消去後"); disp_progress(a,b); // 後退代入 backward_substitution(a,b); System.out.println("解"); for (int i = 0; i < N; i++) System.out.print(String.format("%14.10f\t", b[i])); System.out.println(); } // 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; } System.out.println("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++) System.out.print(String.format("%14.10f\t", a[i][j])); System.out.println(String.format("%14.10f\t", b[i])); } System.out.println(); } } import java.lang.*; public class Java1005 { private static final int N = 4; // LU分解 public static void main(String []args) { 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); System.out.println("ピボット選択後"); disp_progress(a,b); // LU分解 double[] x = {0,0,0,0}; decomp(a,b,x); System.out.println("X"); for (int i = 0; i < N; i++) System.out.print(String.format("%14.10f\t", x[i])); System.out.println(); } // 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 System.out.println("L"); for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) if (i > j) System.out.print(String.format("%14.10f\t", a[i][j])); else if (i == j) System.out.print(String.format("%14.10f\t", 1.0)); else System.out.print(String.format("%14.10f\t", 0.0)); System.out.println(); } System.out.println(); // 上三角行列を確認 System.out.println("U"); for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) if (i <= j) System.out.print(String.format("%14.10f\t", a[i][j])); else System.out.print(String.format("%14.10f\t", 0.0)); System.out.println(); } System.out.println(); // 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 System.out.println("Y"); for (int i = 0; i < N; i++) System.out.print(String.format("%14.10f\t", y[i])); System.out.println("\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++) System.out.print(String.format("%14.10f\t", a[i][j])); System.out.println(String.format("%14.10f\t", b[i])); } System.out.println(); } } public class Java1006 { private static final int N = 4; // コレスキー法 public static void main(String []args) { double[][] a = {{5,2,3,4},{2,10,6,7},{3,6,15,9},{4,7,9,20}}; double[] b = {34,68,96,125}; System.out.println("A"); disp_progress(a); // LL^T分解 double[] x = {0,0,0,0}; decomp(a,b,x); System.out.println("X"); for (int i = 0; i < N; i++) System.out.print(String.format("%14.10f\t", x[i])); System.out.println(); } // LL^T分解 private static void decomp(double[][] a, double[] b, double[] x) { // 前進消去 forward_elimination(a,b); System.out.println("L と L^T"); for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) if (j <= i) System.out.print(String.format("%14.10f\t", a[i][j])); else System.out.print(String.format("%14.10f\t", a[j][i])); System.out.println(); } System.out.println(); // 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 System.out.println("Y"); for (int i = 0; i < N; i++) System.out.print(String.format("%14.10f\t", y[i])); System.out.println("\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++) System.out.print(String.format("%14.10f\t", a[i][j])); System.out.println(); } System.out.println(); } } public class Java1007 { private static final int N = 4; // 修正コレスキー法 public static void main(String []args) { double[][] a = {{5,2,3,4},{2,10,6,7},{3,6,15,9},{4,7,9,20}}; double[] b = {34,68,96,125}; System.out.println("A"); disp_progress(a); // LDL^T分解 double[] x = {0,0,0,0}; decomp(a,b,x); System.out.println("X"); for (int i = 0; i < N; i++) System.out.print(String.format("%14.10f\t", x[i])); System.out.println(); } // LDL^T分解 private static void decomp(double[][] a, double[] b, double[] x) { // 前進消去 forward_elimination(a,b); System.out.println("L と D"); for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) if (j <= i) System.out.print(String.format("%14.10f\t", a[i][j])); else System.out.print(String.format("%14.10f\t", a[j][i])); System.out.println(); } System.out.println(); // 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 System.out.println("Y"); for (int i = 0; i < N; i++) System.out.print(String.format("%14.10f\t", y[i])); System.out.println("\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++) System.out.print(String.format("%14.10f\t", a[i][j])); System.out.println(); } System.out.println(); } } |