微软公司内部培训程序员资料---操作复数类
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/* * 操作复数的类Complex * * 周长发编制 */using System;namespace MSAlgorithm{ /** * 操作复数的类Complex * @author 周长发 * @version 1.0 */ public class Complex { /// <summary> /// 复数实部 /// </summary> private double real = 0.0; /// <summary> /// 复数虚部 /// </summary> private double imaginary = 0.0; /// <summary> /// 缺省精度 /// </summary> private double eps = 0.0; /// <summary> /// 实部 /// </summary> public double Real { get { return real; } set { real = value; } } /// <summary> /// 虚部 /// </summary> public double Imaginary { get { return imaginary; } set { imaginary = value; } } /// <summary> /// 精度 /// </summary> public double Eps { get { return eps; } set { eps = value; } } /// <summary> /// 构造函数 /// </summary> public Complex() { } /// <summary> /// 指定值构造函数 /// </summary> /// <param name="dblX">指定的实部</param> /// <param name="dblY">指定的虚部</param> public Complex(double dblX, double dblY) { real = dblX; imaginary = dblY; } /// <summary> /// 拷贝构造函数 /// </summary> /// <param name="other">源复数</param> public Complex(Complex other) { real = other.real; imaginary = other.imaginary; } /// <summary> /// 根据"a,b"形式的字符串来构造复数，以a为复数的实部，b为复数的虚部 /// </summary> /// <param name="s">"a,b"形式的字符串，a为复数的实部，b为复数的虚部</param> /// <param name="sDelim">a, b之间的分隔符</param> public Complex(string s, string sDelim) { SetValue(s, sDelim); } /// <summary> /// 设置复数运算的精度 /// </summary> /// <param name="newEps">新的精度值</param> public void SetEps(double newEps) { eps = newEps; } /// <summary> /// 取复数的精度值 /// </summary> /// <returns>复数的精度值</returns> public double GetEps() { return eps; } /// <summary> /// 指定复数的实部 /// </summary> /// <param name="dblX">复数的实部</param> public void SetReal(double dblX) { real = dblX; } /// <summary> /// 指定复数的虚部 /// </summary> /// <param name="dblY">复数的虚部</param> public void SetImag(double dblY) { imaginary = dblY; } /// <summary> /// 取复数的实部 /// </summary> /// <returns>复数的实部</returns> public double GetReal() { return real; } /// <summary> /// 取复数的虚部 /// </summary> /// <returns>复数的虚部</returns> public double GetImag() { return imaginary; } /// <summary> /// 指定复数的实部和虚部值 /// </summary> /// <param name="real">指定的实部</param> /// <param name="imag">指定的虚部</param> public void SetValue(double real, double imag) { SetReal(real); SetImag(imag); } /// <summary> /// 将"a,b"形式的字符串转化为复数，以a为复数的实部，b为复数的虚部 /// </summary> /// <param name="s">"a,b"形式的字符串，a为复数的实部，b为复数的虚部</param> /// <param name="sDelim">a, b之间的分隔符</param> public void SetValue(string s, string sDelim) { int nPos = s.IndexOf(sDelim); if (nPos == -1) { s = s.Trim(); real = double.Parse(s); imaginary = 0; } else { int nLen = s.Length; string sLeft = s.Substring(0, nPos); string sRight = s.Substring(nPos + 1, nLen - nPos - 1); sLeft = sLeft.Trim(); sRight = sRight.Trim(); real = double.Parse(sLeft); imaginary = double.Parse(sRight); } } /// <summary> /// 重载 + 运算 /// </summary> /// <param name="cpx1">指定的复数1</param> /// <param name="cpx2">指定的复数2</param> /// <returns>Complex对象</returns> public static Complex operator +(Complex cpx1, Complex cpx2) { return cpx1.Add(cpx2); } /// <summary> /// 重载 - 运算符 /// </summary> /// <param name="cpx1">指定的复数1</param> /// <param name="cpx2">指定的复数2</param> /// <returns>Complex对象</returns> public static Complex operator -(Complex cpx1, Complex cpx2) { return cpx1.Subtract(cpx2); } /// <summary> /// 重载 * 运算符 /// </summary> /// <param name="cpx1">指定的复数1</param> /// <param name="cpx2">指定的复数2</param> /// <returns>Complex对象</returns> public static Complex operator *(Complex cpx1, Complex cpx2) { return cpx1.Multiply(cpx2); } /// <summary> /// 重载 / 运算符 /// </summary> /// <param name="cpx1">指定的复数1</param> /// <param name="cpx2">指定的复数2</param> /// <returns></returns> public static Complex operator /(Complex cpx1, Complex cpx2) { return cpx1.Divide(cpx2); } /// <summary> /// 重载 double 运算符 /// </summary> /// <param name="cpx">指定的复数</param> /// <returns>double值</returns> public static implicit operator double(Complex cpx) { return cpx.Abs(); } /// <summary> /// 将复数转化为"a+bj"形式的字符串 /// </summary> /// <returns>string 型，"a+bj"形式的字符串</returns> public override string ToString() { string s; if (real != 0.0) { if (imaginary > 0) s = real.ToString("F") + "+" + imaginary.ToString("F") + "j"; else if (imaginary < 0) { double absImag = -1 * imaginary; s = real.ToString("F") + "-" + absImag.ToString("F") + "j"; } else s = real.ToString("F"); } else { if (imaginary > 0) s = imaginary.ToString("F") + "j"; else if (imaginary < 0) { double absImag = -1 * imaginary; s = absImag.ToString("F") + "j"; } else s = real.ToString("F"); } return s; } /// <summary> /// 比较两个复数是否相等 /// </summary> /// <param name="other">用于比较的复数</param> /// <returns> bool型，相等则为true，否则为false</returns> public override bool Equals(object other) { Complex cpxX = other as Complex; if (cpxX == null) return false; return Math.Abs(real - cpxX.real) <= eps && Math.Abs(imaginary - cpxX.imaginary) <= eps; } /// <summary> /// 因为重写了Equals，因此必须重写GetHashCode /// </summary> /// <returns>int型，返回复数对象散列码</returns> public override int GetHashCode() { return (int)Math.Sqrt(real * real + imaginary * imaginary); } /// <summary> /// 给复数赋值 /// </summary> /// <param name="cpxX">用于给复数赋值的源复数</param> /// <returns>Complex型，与cpxX相等的复数</returns> public Complex SetValue(Complex cpxX) { real = cpxX.real; imaginary = cpxX.imaginary; return this; } /// <summary> /// 实现复数的加法 /// </summary> /// <param name="cpxX">与指定复数相加的复数</param> /// <returns>指定复数与cpxX相加之和</returns> public Complex Add(Complex cpxX) { double x = real + cpxX.real; double y = imaginary + cpxX.imaginary; return new Complex(x, y); } /// <summary> /// 实现复数的减法 /// </summary> /// <param name="cpxX">与指定复数相减的复数</param> /// <returns>指定复数减去cpxX之差</returns> public Complex Subtract(Complex cpxX) { double x = real - cpxX.real; double y = imaginary - cpxX.imaginary; return new Complex(x, y); } /// <summary> /// 实现复数的乘法 /// </summary> /// <param name="cpxX">与指定复数相乘的复数</param> /// <returns>指定复数与cpxX相乘之积</returns> public Complex Multiply(Complex cpxX) { double x = real * cpxX.real - imaginary * cpxX.imaginary; double y = imaginary * cpxX.real + real * cpxX.imaginary; return new Complex(x, y); } /// <summary> /// 实现复数的除法 /// </summary> /// <param name="cpxX">与指定复数相除的复数</param> /// <returns>指定复数除与cpxX之商</returns> public Complex Divide(Complex cpxX) { double e, f, x, y; if (Math.Abs(cpxX.real) >= Math.Abs(cpxX.imaginary)) { e = cpxX.imaginary / cpxX.real; f = cpxX.real + e * cpxX.imaginary; x = (real + imaginary * e) / f; y = (imaginary - real * e) / f; } else { e = cpxX.real / cpxX.imaginary; f = cpxX.imaginary + e * cpxX.real; x = (real * e + imaginary) / f; y = (imaginary * e - real) / f; } return new Complex(x, y); } /// <summary> /// 计算复数的模 /// </summary> /// <returns>double型，指定复数的模</returns> public double Abs() { //求取实部和虚部的绝对值 double x = Math.Abs(real); double y = Math.Abs(imaginary); if (real == 0) return y; if (imaginary == 0) return x; //计算模 if (x > y) return (x * Math.Sqrt(1 + (y / x) * (y / x))); return (y * Math.Sqrt(1 + (x / y) * (x / y))); } /// <summary> /// 计算复数的根 /// </summary> /// <param name="n">待求根的根次</param> /// <param name="cpxR">Complex型数组，长度为n，返回复数的所有根</param> public void Root(int n, Complex[] cpxR) { if (n < 1) return; double q = Math.Atan2(imaginary, real); double r = Math.Sqrt(real * real + imaginary * imaginary); if (r != 0) { r = (1.0 / n) * Math.Log(r); r = Math.Exp(r); } for (int k = 0; k <= n - 1; k++) { double t = (2.0 * k * 3.1415926 + q) / n; cpxR[k] = new Complex(r * Math.Cos(t), r * Math.Sin(t)); } } /// <summary> /// 计算复数的实幂指数 /// </summary> /// <param name="dblW">待求实幂指数的幂次</param> /// <returns>Complex型，复数的实幂指数值</returns> public Complex Pow(double dblW) { //常量 const double PI = 3.14159265358979; double r, t; //特殊值处理 if ((real == 0) && (imaginary == 0)) return new Complex(0, 0); //幂运算公式中的三角函数运算 if (real == 0) { if (imaginary > 0) t = 1.5707963268; else t = -1.5707963268; } else { if (real > 0) t = Math.Atan2(imaginary, real); else { if (imaginary >= 0) t = Math.Atan2(imaginary, real) + PI; else t = Math.Atan2(imaginary, real) - PI; } } //模的幂 r = Math.Exp(dblW * Math.Log(Math.Sqrt(real * real + imaginary * imaginary))); //复数的实幂指数 return new Complex(r * Math.Cos(dblW * t), r * Math.Sin(dblW * t)); } /// <summary> /// 计算复数的复幂指数 /// </summary> /// <param name="cpxW">待求复幂指数的幂次</param> /// <param name="n">控制参数，默认值为0。当n=0时，求得的结果为复幂指数的主值</param> /// <returns>Complex型，复数的复幂指数值</returns> public Complex Pow(Complex cpxW, int n) { //常量 const double PI = 3.14159265358979; double r, s, u, v; //特殊值处理 if (real == 0) { if (imaginary == 0) return new Complex(0, 0); s = 1.5707963268 * (Math.Abs(imaginary) / imaginary + 4 * n); } else { s = 2 * PI * n + Math.Atan2(imaginary, real); if (real < 0) { if (imaginary > 0) s = s + PI; else s = s - PI; } } //求幂运算公式 r = 0.5 * Math.Log(real * real + imaginary * imaginary); v = cpxW.real * r + cpxW.imaginary * s; u = Math.Exp(cpxW.real * r - cpxW.imaginary * s); return new Complex(u * Math.Cos(v), u * Math.Sin(v)); } /// <summary> /// 计算复数的自然对数 /// </summary> /// <returns>Complex型，复数的自然对数值</returns> public Complex Log() { double p = Math.Log(Math.Sqrt(real * real + imaginary * imaginary)); return new Complex(p, Math.Atan2(imaginary, real)); } /// <summary> /// 计算复数的正弦 /// </summary> /// <returns>Complex型，复数的正弦值</returns> public Complex Sin() { int i; double x, y, y1, br, b1, b2; double[] c = new double[6]; //切比雪夫公式的常数系数 c[0] = 1.13031820798497; c[1] = 0.04433684984866; c[2] = 0.00054292631191; c[3] = 0.00000319843646; c[4] = 0.00000001103607; c[5] = 0.00000000002498; y1 = Math.Exp(imaginary); x = 0.5 * (y1 + 1 / y1); br = 0; if (Math.Abs(imaginary) >= 1) y = 0.5 * (y1 - 1 / y1); else { b1 = 0; b2 = 0; y1 = 2 * (2 * imaginary * imaginary - 1); for (i = 5; i >= 0; --i) { br = y1 * b1 - b2 - c[i]; if (i != 0) { b2 = b1; b1 = br; } } y = imaginary * (br - b1); } //组合计算结果 x = x * Math.Sin(real); y = y * Math.Cos(real); return new Complex(x, y); } /// <summary> /// 计算复数的余弦 /// </summary> /// <returns>Complex型，复数的余弦值</returns> public Complex Cos() { int i; double x, y, y1, br, b1, b2; double[] c = new double[6]; //切比雪夫公式的常数系数 c[0] = 1.13031820798497; c[1] = 0.04433684984866; c[2] = 0.00054292631191; c[3] = 0.00000319843646; c[4] = 0.00000001103607; c[5] = 0.00000000002498; y1 = Math.Exp(imaginary); x = 0.5 * (y1 + 1 / y1); br = 0; if (Math.Abs(imaginary) >= 1) y = 0.5 * (y1 - 1 / y1); else { b1 = 0; b2 = 0; y1 = 2 * (2 * imaginary * imaginary - 1); for (i = 5; i >= 0; i--) { br = y1 * b1 - b2 - c[i]; if (i != 0) { b2 = b1; b1 = br; } } y = imaginary * (br - b1); } //组合计算结果 x = x * Math.Cos(real); y = -y * Math.Sin(real); return new Complex(x, y); } /// <summary> /// 计算复数的正切 /// </summary> /// <returns>Complex型，复数的正切值</returns> public Complex Tan() { return Sin().Divide(Cos()); } }}注：本代码为原作者所有，本人只是摘录，如有侵犯作者，请与本人联系
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