数值计算 第六章

import xiaodeng.method.Matrix;/*** @author邓仕军* @time 2012-06-04* @version0.1* @function:Gauss-Seidel迭代法解线性方程组*/class Program6_1 {Matrix coefficientMatrix;// 系数矩阵Matrix constantMatrix;// 常数矩阵double[] result;// 结果集double precious = 10E-5;int size = 0;// result也即结果集的长度public Program6_1(Matrix coefficientMatrix, Matrix constantMatrix, double precious) {this.coefficientMatrix = coefficientMatrix;this.constantMatrix = constantMatrix;this.precious = precious;this.size = coefficientMatrix.getNumColumns();result = newdouble[size];}// 返回result中的最大值double maxValueOfDiffer(double[] d1, double[] d2) {double max = 0d;for (int i = 0; i<this.size; i++) {double temp = Math.abs(d1[i] - d2[i]);if (i == 0 || max < temp) {max = temp;}}return max;}// 根据当前的result,计算一次,得到新的resultpublicdouble[] calculate() {for (int i = 1; i<= constantMatrix.getNumRows(); i++) {double sum = constantMatrix.getElementAt(i, 1);for (int j = 1; j <= constantMatrix.getNumRows(); j++) { if (j != i)sum -= coefficientMatrix.getElementAt(i, j) * result[j - 1];}// for-2result[i - 1] = sum / coefficientMatrix.getElementAt(i, i);}// for-1return result.clone();//}// calculate// 根据精度,调用calculate,得到在精度范围内的结果集publicvoid function() {double[] temp1, temp2;// 虽然java会自动初始化result为0，但是为了程序的可读性、可移植性、扩展性,还是在这里手动初始化一下for (int i = 0; i<this.size; i++) {result[i] = 0d;}temp1 = calculate();temp2 = calculate();while (maxValueOfDiffer(temp1, temp2) >this.precious) { temp1 = temp2;temp2 = calculate();}// while}// functiondouble getPrecious() {return precious;}void setPrecious(double precious) {this.precious = precious;}int getSize() {return size;}void setSize(int size) {this.size = size;}Matrix getCoefficientMatrix() {return coefficientMatrix;}Matrix getConstantMatrix() {return constantMatrix;}double[] getResult() {return result.clone();}}import xiaodeng.method.Matrix;publicclass TestProgram6_1 {publicstaticvoid main(String[] args) {Program6_1 p6_1 = new Program6_1(new Matrix(3, 3, newdouble[][] {{ 8, -3, 2 }, { 4, 11, -1 }, { 2, 1, 4 } }), new Matrix(3, 1,newdouble[][] { { 20 }, { 33 }, { 12 } }), 10E-5);p6_1.function();// 解方程System.out.println("方程组为：");for(int i = 1; i<= p6_1.getCoefficientMatrix().getNumRows(); i++) {for (int j = 1; j <=p6_1.getCoefficientMatrix().getNumColumns(); j++)if (j != p6_1.getCoefficientMatrix().getNumColumns())System.out.print(p6_1.getCoefficientMatrix().getElementAt(i, j)+ "x" + j + " + ");else {System.out.print(p6_1.getCoefficientMatrix().getElementAt(i, j)+ "x"+ j+ " = "+ p6_1.getConstantMatrix().getElementAt(i, 1));}System.out.println();}System.out.println("解得：");for (int i = 0; i< p6_1.getSize(); i++) {System.out.println("x"+ (i + 1) + "="+ p6_1.getResult()[i]);}}}import ng.reflect.InvocationTargetException;import ng.reflect.Method;/*** @author邓仕军* @time 2012-06-07* @version 0.2* Newton迭代法*/class Program6_2 {Method f;double x0;double precious;Derivative derivaFx;// 导数public Program6_2(Method f, double x0, double precious) { this.f = f;this.x0 = x0;this.precious = precious;derivaFx = new Derivative(this, this.f);derivaFx.setPrecision(this.precious);}publicdouble function() {double Xk = 0d, Xk1 = 0d;try {Xk = this.x0 - (Double) this.f.invoke(null, this.x0)/ this.derivaFx.getDerivative(this.x0);Xk1 = Xk - (Double) this.f.invoke(null, Xk)/ this.derivaFx.getDerivative(Xk);while (Math.abs(Xk - Xk1) >this.precious) {Xk = Xk1;Xk1 = Xk - (Double) this.f.invoke(null, Xk)/ this.derivaFx.getDerivative(Xk);}// while} catch (IllegalAccessException | IllegalArgumentException | InvocationTargetException e) {e.printStackTrace();}return (Xk + Xk1) / 2;}// functionpublicdouble getX0() {return x0;}publicvoid setX0(double x0) {this.x0 = x0;}publicdouble getPrecious() {return precious;}publicvoid setPrecious(double precious) {this.precious = precious;}}/***@author邓仕军*@version 0.1*@time 2012-05-03* Derivative:求一个函数的导数，运用反射机制*/class Derivative {Method method;Object obj;double Dx = 1;// 增量△Xdouble precision = 10E-10;// 精度public Derivative(Object obj, Method f) {this.method = f;this.obj = obj;}strictfpdouble getDerivative(double x) {double deriva1 = 0d, deriva2 = 0d;boolean flag = true;double dx = this.Dx;try {deriva1 = ((Double) this.method.invoke(obj, x + dx) - (Double) method.invoke(obj, x)) / dx;dx /= 2;while (flag) {deriva1 = ((Double) this.method.invoke(obj, x + dx) - (Double) method.invoke(obj, x)) / dx;if (Math.abs(deriva1 - deriva2) <this.precision)flag = false;else {deriva2 = deriva1;dx /= 2;}}// while} catch (IllegalAccessException | IllegalArgumentException| InvocationTargetException e) {e.printStackTrace();}return (deriva1 + deriva2) / 2;}// getDerivativepublicdouble getDx() {return Dx;}publicvoid setDx(double dx) {Dx = dx;}publicdouble getPrecision() {return precision;}publicvoid setPrecision(double precision) {this.precision = precision;}}publicclass TestProgram6_2 {staticdouble fX(double x) {return Math.pow(Math.E, 5 * x) - Math.sin(x) + Math.pow(x, 3) - 20;}publicstaticvoid main(String[] args) {double x0 = 1;double precious = 10E-8;try {Program6_2 p6_2 = new Program6_2(TestProgram6_2.class.getDeclaredMethod("fX", double.class),x0, precious);System.out.printf("方程为：e^(5x)-sinx+x^3-20=0 ,精度 ");System.out.println(precious);System.out.println("取 x0=" + x0 + ",解得x=" +p6_2.function());--x0;p6_2.setX0(x0);System.out.println("取 x0=" + x0 + ",解得x=" +p6_2.function());} catch (NoSuchMethodException | SecurityException e) {e.printStackTrace();}}}。