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  1. using System;
  2. using System.Globalization;
  3. namespace NamespaceName
  4. {
  5. 	public class ClassName
  6. 	{
  7. 		const int maxiter = 1000;
  8. 		const double eps = 1e-12;
  9. 		public static void PrintMatrix(int m,int n,double[,] A)
  10. 		{
  11. 			NumberFormatInfo nfi = new NumberFormatInfo();
  12. 			nfi.NumberDecimalDigits = 12;
  13. 			double p = 0;
  14. 			for(int i=0;i<m;i++)
  15. 			{
  16. 				for(int j=0;j < n; j++)
  17. 					if(Math.Abs(A[i,j]) > eps)
  18. 						Console.Write("{0} , ",A[i,j].ToString("N",nfi));
  19. 					else
  20. 						Console.Write("{0} , ",p.ToString("N",nfi)); 
  21. 				Console.WriteLine();
  22. 			}
  23. 			Console.WriteLine();
  24. 		}
  25. 		public static double Hypot(double a,double b)
  26. 		{
  27. 			double absa,absb;
  28. 			absa = Math.Abs(a);
  29. 			absb = Math.Abs(b);
  30. 			if(absa > absb) return absa * Math.Sqrt(1 + ((double) absb / absa) * ((double) absb / absa));
  31. 			else return (absb == 0 ? 0 : absb * Math.Sqrt(1 + ((double) absa / absb) * ((double) absa / absb)));
  32. 		}
  33. 		public static void QRdecomp(int m,int n,double[,] A,double[,] Q)
  34. 		{
  35. 			for(int i = 0; i < m; i++)
  36. 				for(int j = 0;j < m;j++)
  37. 					Q[i,j] = (i == j ? 1 : 0);
  38. 				int min = (m < n ? m : n);
  39. 				for(int i = 0; i < min; i++)
  40. 					for(int j = i + 1; j < m; j++)
  41. 						if(A[j,i] != 0)
  42. 						{
  43. 							double r = Hypot(A[i,i],A[j,i]);
  44. 							double c = (double) A[i,i] / r;
  45. 							double s = (double) A[j,i] / r;
  46. 							for(int k = 0; k < n; k++)
  47. 							{
  48. 								double temp = A[i,k];
  49. 								A[i,k] = c * A[i,k] + s * A[j,k];
  50. 								A[j,k] = -s * temp + c * A[j,k];
  51. 							}
  52. 							for(int k = 0;k < m;k++)
  53. 							{
  54. 								double temp = Q[k,i];
  55. 								Q[k,i] = c * Q[k,i] + s * Q[k,j];
  56. 								Q[k,j] = -s * temp + c * Q[k,j];
  57. 							}
  58. 						}
  59.  
  60. 		}
  61.  
  62. 		public static void MultiplyMatrix(int m,int n,int p,double[,] A,double[,] B,double[,] C)
  63. 		{
  64. 			for(int i = 0;i < m;i++)
  65. 				for(int k=0;k < p;k++)
  66. 				{
  67. 					C[i,k] = 0;
  68. 					for(int j=0;j < n;j++)
  69. 						C[i,k] += A[i,j] * B[j,k];
  70. 				}
  71. 		}
  72. 		public static void CopyMatrix(int m,int n,double[,] A,double[,] B)
  73. 		{
  74. 			for(int i=0;i<m;i++)
  75. 				for(int j=0;j<n;j++)
  76. 					B[i,j] = A[i,j];
  77. 		}
  78. 		public static void Main(string[] args)
  79. 		{
  80. 			int deg;
  81. 			double[,] A;
  82. 			double[,] Q;
  83. 			double[,] R;
  84. 			double[] c;
  85. 			Console.WriteLine("Obliczanie przyblizonych pierwiastkow rownania wielomianowego za pomoca wartosci wlasnych macierzy stowarzyszonej");
  86. 				Console.WriteLine("Podaj stopien wielomianu ktorego pierwiastki chcesz policzyc");
  87. 				int.TryParse(Console.ReadLine(),out deg);
  88. 				A = new double[deg,deg];
  89. 				Q = new double[deg,deg];
  90. 				R = new double[deg,deg];
  91. 				c = new double[deg+1];
  92. 				for(int i = deg; i >= 0;i--)
  93. 				{
  94. 					Console.Write("c[{0}]=",i);
  95. 					double.TryParse(Console.ReadLine(),out c[i]);
  96. 				}
  97. 				for(int i=0;i<deg;i++)
  98. 					A[0,i] = (double)(-c[deg-1-i])/c[deg];
  99.  
  100. 				for(int i=1;i<deg;i++)
  101. 					for(int j = 0;j < deg;j++)
  102. 						A[i,j] = (j+1 == i ? 1: 0);
  103. 				Console.WriteLine("Macierz stowarzyszona");
  104. 				PrintMatrix(deg,deg,A);
  105. 				for(int i = 0;i<maxiter;i++)
  106. 				{
  107. 					QRdecomp(deg,deg,A,Q);
  108. 					CopyMatrix(deg,deg,A,R);
  109. 					MultiplyMatrix(deg,deg,deg,R,Q,A);
  110. 				}
  111. 				Console.WriteLine("Macierz stowarzyszona po iteracyjnym sprowadzeniu do postaci Schura");
  112. 				PrintMatrix(deg,deg,A);
  113. 				int k = 0;
  114. 				NumberFormatInfo nfi = new NumberFormatInfo();
  115. 				nfi.NumberDecimalDigits = 12;
  116. 				while(k < deg)
  117. 				{
  118. 					if(k + 1 < deg && Math.Abs(A[k+1,k]) > eps)
  119. 					{
  120. 						/* Tutaj zalozylem ze w postaci Schura klatka 2x2 pojawia sie
  121. 						 na diagonali gdy macierz posiada zespolone wartosci wlasne
  122. 						 */
  123. 						double p = 0.5 * (A[k,k] + A[k + 1,k + 1]);
  124. 						double q = A[k,k] * A[k+1,k+1] - A[k,k+1] * A[k+1,k];
  125. 						double d = Math.Sqrt(Math.Abs(q - p * p));
  126. 						Console.WriteLine("x[{0}] = {1} - {2}*i",k,p.ToString("N",nfi),d.ToString("N",nfi));
  127. 						Console.WriteLine("x[{0}] = {1} + {2}*i",k+1,p.ToString("N",nfi),d.ToString("N",nfi));
  128. 						k += 2;
  129. 					}
  130. 					else
  131. 					{
  132. 						Console.WriteLine("x[{0}] = {1}",k,A[k,k]);
  133. 						k++;
  134. 					}
  135. 				}		
  136. 		}
  137. 	}
  138. }
  139.  
Success #stdin #stdout 0.03s 23240KB
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stdout
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Obliczanie przyblizonych pierwiastkow rownania wielomianowego za pomoca wartosci wlasnych macierzy stowarzyszonej
Podaj stopien wielomianu ktorego pierwiastki chcesz policzyc
c[6]=c[5]=c[4]=c[3]=c[2]=c[1]=c[0]=Macierz stowarzyszona
0.000000000000 , -5.000000000000 , 0.000000000000 , -7.000000000000 , 0.000000000000 , -6.000000000000 , 
1.000000000000 , 0.000000000000 , 0.000000000000 , 0.000000000000 , 0.000000000000 , 0.000000000000 , 
0.000000000000 , 1.000000000000 , 0.000000000000 , 0.000000000000 , 0.000000000000 , 0.000000000000 , 
0.000000000000 , 0.000000000000 , 1.000000000000 , 0.000000000000 , 0.000000000000 , 0.000000000000 , 
0.000000000000 , 0.000000000000 , 0.000000000000 , 1.000000000000 , 0.000000000000 , 0.000000000000 , 
0.000000000000 , 0.000000000000 , 0.000000000000 , 0.000000000000 , 1.000000000000 , 0.000000000000 , 

Macierz stowarzyszona po iteracyjnym sprowadzeniu do postaci Schura
0.000000000000 , -3.485583997689 , 0.000000000000 , -6.781350173503 , 0.000000000000 , -6.672653481939 , 
1.000000000000 , 0.000000000000 , 0.000000000000 , 0.000000000000 , 0.000000000000 , 0.000000000000 , 
0.000000000000 , 0.000000000000 , 0.000000000000 , -1.894700247594 , 0.000000000000 , -2.044006628719 , 
0.000000000000 , 0.000000000000 , 1.000000000000 , 0.000000000000 , 0.000000000000 , 0.000000000000 , 
0.000000000000 , 0.000000000000 , 0.000000000000 , 1.194663674708 , 0.000000000000 , 0.380284245283 , 
0.000000000000 , 0.000000000000 , 0.000000000000 , 0.000000000000 , 1.000000000000 , 0.000000000000 , 

x[0] = 0.000000000000 - 1.866971879191*i
x[1] = 0.000000000000 + 1.866971879191*i
x[2] = 0.000000000000 - 1.376481110511*i
x[3] = 0.000000000000 + 1.376481110511*i
x[4] = 0.000000000000 - 0.616671910567*i
x[5] = 0.000000000000 + 0.616671910567*i
https://ideone.com/jcmdLu
language:
C# (gmcs 5.20.1)
created:
2 years ago
visibility:
secret

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