/*
* 操作複數的類Complex
*
* 周長發編制
*/
using System;
namespace MSAlgorithm
{
/**
* 操作複數的類Complex
* @author 周長發
* @version 1.0
*/
public class Complex
{
/// <summary>
/// 複數實部
/// </summary>
private double real = 0.0;
/// <summary>
/// 複數虛部
/// </summary>
private double imaginary = 0.0;
/// <summary>
/// 缺省精度
/// </summary>
private double eps = 0.0;
/// <summary>
/// 實部
/// </summary>
public double Real
{
get { return real; }
set { real = value; }
}
/// <summary>
/// 虛部
/// </summary>
public double Imaginary
{
get { return imaginary; }
set { imaginary = value; }
}
/// <summary>
/// 精度
/// </summary>
public double Eps
{
get { return eps; }
set { eps = value; }
}
/// <summary>
/// 構造函數
/// </summary>
public Complex()
{ }
/// <summary>
/// 指定值構造函數
/// </summary>
/// <param name="dblX">指定的實部</param>
/// <param name="dblY">指定的虛部</param>
public Complex(double dblX, double dblY)
{
real = dblX;
imaginary = dblY;
}
/// <summary>
/// 拷貝構造函數
/// </summary>
/// <param name="other">源複數</param>
public Complex(Complex other)
{
real = other.real;
imaginary = other.imaginary;
}
/// <summary>
/// 根據"a,b"形式的字符串來構造複數，以a爲複數的實部，b爲複數的虛部
/// </summary>
/// <param name="s">"a,b"形式的字符串，a爲複數的實部，b爲複數的虛部</param>
/// <param name="sDelim">a, b之間的分隔符</param>
public Complex(string s, string sDelim)
{
SetValue(s, sDelim);
}
/// <summary>
/// 設置複數運算的精度
/// </summary>
/// <param name="newEps">新的精度值</param>
public void SetEps(double newEps)
{
eps = newEps;
}
/// <summary>
/// 取複數的精度值
/// </summary>
/// <returns>複數的精度值</returns>
public double GetEps()
{
return eps;
}
/// <summary>
/// 指定複數的實部
/// </summary>
/// <param name="dblX">複數的實部</param>
public void SetReal(double dblX)
{
real = dblX;
}
/// <summary>
/// 指定複數的虛部
/// </summary>
/// <param name="dblY">複數的虛部</param>
public void SetImag(double dblY)
{
imaginary = dblY;
}
/// <summary>
/// 取複數的實部
/// </summary>
/// <returns>複數的實部</returns>
public double GetReal()
{
return real;
}
/// <summary>
/// 取複數的虛部
/// </summary>
/// <returns>複數的虛部</returns>
public double GetImag()
{
return imaginary;
}
/// <summary>
/// 指定複數的實部和虛部值
/// </summary>
/// <param name="real">指定的實部</param>
/// <param name="imag">指定的虛部</param>
public void SetValue(double real, double imag)
{
SetReal(real);
SetImag(imag);
}
/// <summary>
/// 將"a,b"形式的字符串轉化爲複數，以a爲複數的實部，b爲複數的虛部
/// </summary>
/// <param name="s">"a,b"形式的字符串，a爲複數的實部，b爲複數的虛部</param>
/// <param name="sDelim">a, b之間的分隔符</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>
/// 重載 + 運算
/// </summary>
/// <param name="cpx1">指定的複數1</param>
/// <param name="cpx2">指定的複數2</param>
/// <returns>Complex對象</returns>
public static Complex operator +(Complex cpx1, Complex cpx2)
{
return cpx1.Add(cpx2);
}
/// <summary>
/// 重載 - 運算符
/// </summary>
/// <param name="cpx1">指定的複數1</param>
/// <param name="cpx2">指定的複數2</param>
/// <returns>Complex對象</returns>
public static Complex operator -(Complex cpx1, Complex cpx2)
{
return cpx1.Subtract(cpx2);
}
/// <summary>
/// 重載 * 運算符
/// </summary>
/// <param name="cpx1">指定的複數1</param>
/// <param name="cpx2">指定的複數2</param>
/// <returns>Complex對象</returns>
public static Complex operator *(Complex cpx1, Complex cpx2)
{
return cpx1.Multiply(cpx2);
}
/// <summary>
/// 重載 / 運算符
/// </summary>
/// <param name="cpx1">指定的複數1</param>
/// <param name="cpx2">指定的複數2</param>
/// <returns></returns>
public static Complex operator /(Complex cpx1, Complex cpx2)
{
return cpx1.Divide(cpx2);
}
/// <summary>
/// 重載 double 運算符
/// </summary>
/// <param name="cpx">指定的複數</param>
/// <returns>double值</returns>
public static implicit operator double(Complex cpx)
{
return cpx.Abs();
}
/// <summary>
/// 將複數轉化爲"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>
/// 比較兩個複數是否相等
/// </summary>
/// <param name="other">用於比較的複數</param>
/// <returns> bool型，相等則爲true，否則爲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>
/// 因爲重寫了Equals，因此必須重寫GetHashCode
/// </summary>
/// <returns>int型，返回複數對象散列碼</returns>
public override int GetHashCode()
{
return (int)Math.Sqrt(real * real + imaginary * imaginary);
}
/// <summary>
/// 給複數賦值
/// </summary>
/// <param name="cpxX">用於給複數賦值的源複數</param>
/// <returns>Complex型，與cpxX相等的複數</returns>
public Complex SetValue(Complex cpxX)
{
real = cpxX.real;
imaginary = cpxX.imaginary;
return this;
}
/// <summary>
/// 實現複數的加法
/// </summary>
/// <param name="cpxX">與指定複數相加的複數</param>
/// <returns>指定複數與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>
/// 實現複數的減法
/// </summary>
/// <param name="cpxX">與指定複數相減的複數</param>
/// <returns>指定複數減去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>
/// 實現複數的乘法
/// </summary>
/// <param name="cpxX">與指定複數相乘的複數</param>
/// <returns>指定複數與cpxX相乘之積</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>
/// 實現複數的除法
/// </summary>
/// <param name="cpxX">與指定複數相除的複數</param>
/// <returns>指定複數除與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>
/// 計算複數的模
/// </summary>
/// <returns>double型，指定複數的模</returns>
public double Abs()
{
//求取實部和虛部的絕對值
double x = Math.Abs(real);
double y = Math.Abs(imaginary);
if (real == 0)
return y;
if (imaginary == 0)
return x;
//計算模
if (x > y)
return (x * Math.Sqrt(1 + (y / x) * (y / x)));
return (y * Math.Sqrt(1 + (x / y) * (x / y)));
}
/// <summary>
/// 計算複數的根
/// </summary>
/// <param name="n">待求根的根次</param>
/// <param name="cpxR">Complex型數組，長度爲n，返回複數的所有根</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>
/// 計算複數的實冪指數
/// </summary>
/// <param name="dblW">待求實冪指數的冪次</param>
/// <returns>Complex型，複數的實冪指數值</returns>
public Complex Pow(double dblW)
{
//常量
const double PI = 3.14159265358979;
double r, t;
//特殊值處理
if ((real == 0) && (imaginary == 0))
return new Complex(0, 0);
//冪運算公式中的三角函數運算
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;
}
}
//模的冪
r = Math.Exp(dblW * Math.Log(Math.Sqrt(real * real + imaginary * imaginary)));
//複數的實冪指數
return new Complex(r * Math.Cos(dblW * t), r * Math.Sin(dblW * t));
}
/// <summary>
/// 計算複數的復冪指數
/// </summary>
/// <param name="cpxW">待求復冪指數的冪次</param>
/// <param name="n">控制參數，默認值爲0。當n=0時，求得的結果爲復冪指數的主值</param>
/// <returns>Complex型，複數的復冪指數值</returns>
public Complex Pow(Complex cpxW, int n)
{
//常量
const double PI = 3.14159265358979;
double r, s, u, v;
//特殊值處理
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;
}
}
//求冪運算公式
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>
/// 計算複數的自然對數
/// </summary>
/// <returns>Complex型，複數的自然對數值</returns>
public Complex Log()
{
double p = Math.Log(Math.Sqrt(real * real + imaginary * imaginary));
return new Complex(p, Math.Atan2(imaginary, real));
}
/// <summary>
/// 計算複數的正弦
/// </summary>
/// <returns>Complex型，複數的正弦值</returns>
public Complex Sin()
{
int i;
double x, y, y1, br, b1, b2;
double[] c = new double[6];
//切比雪夫公式的常數係數
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);
}
//組合計算結果
x = x * Math.Sin(real);
y = y * Math.Cos(real);
return new Complex(x, y);
}
/// <summary>
/// 計算複數的餘弦
/// </summary>
/// <returns>Complex型，複數的餘弦值</returns>
public Complex Cos()
{
int i;
double x, y, y1, br, b1, b2;
double[] c = new double[6];
//切比雪夫公式的常數係數
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);
}
//組合計算結果
x = x * Math.Cos(real);
y = -y * Math.Sin(real);
return new Complex(x, y);
}
/// <summary>
/// 計算複數的正切
/// </summary>
/// <returns>Complex型，複數的正切值</returns>
public Complex Tan()
{
return Sin().Divide(Cos());
}
}
}
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