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   1:  #ifndef CHASEMETHORD_H
   2:  #define CHASEMETHORD_H
   3:  #include <assert.h>
   4:  #define NULL 0
   5:  /************************************************************************/
   6:  /* 功 能:追赶法接矩阵方程:Ax = y.
   7:  /*        其中A必须是三对角矩阵,即非零元素分布在主对角线及其相邻两条次对角
   8:  /*        线上。
   9:  /* 参 数:size_t n,    矩阵对角线元素个数[in]
  10:  /*        T*     a,    主对角线以下元素[in]
  11:  /*        T*     b,    主对角线以上元素[in]
  12:  /*        T*     c,    主对角线元素[in]
  13:  /*        T*     x,    矩阵的解集[out]
  14:  /*        T*     y,    y集[in]      
  15:  /************************************************************************/
  16:  template <typename T>
  17:  void ChaseMethord(size_t n, T* a, T *b, T* c, T* x, T* f)
  18:  {
  19:      assert(a != NULL && b != NULL && c != NULL && x != NULL && f !=  NULL);
  20:      
  21:      //Ax = f => A = LU,即L(Ux) = f,又:令y = Ux,所以Ly = f;
  22:      //其中,L是下二对角矩阵,U是单位上二对角矩阵
  23:      T *l = new T[n];
  24:      T *u = new T[n];
  25:      T *y = new T[n];
  26:      
  27:      assert(l != NULL);
  28:      assert(u != NULL);
  29:      assert(y != NULL);
  30:      
  31:      l[0] = b[0]; 
  32:      if (l[0] == 0)
  33:      {
  34:          return;
  35:      }
  36:      y[0] = f[0] / l[0];
  37:      
  38:      size_t i;
  39:      
  40:      //依次求出l[0]->u[0]->l[1]->u[1]->...->l[n-1],y[i]
  41:      for (i = 1; i < n; i++)
  42:      {
  43:          if (l[i] == 0)
  44:          {
  45:              return;
  46:          }
  47:          
  48:          u[i - 1] = c[i - 1] / l[i - 1];
  49:          l[i] = b[i] - a[i - 1] * u[i - 1];
  50:          y[i] = (f[i] - a[i - 1] * y[i - 1]) / l[i];
  51:      }
  52:      
  53:      //逆序求x[i]
  54:      x[i-1] = y[i-1];
  55:      for (int k = i - 2; k >= 0; k--)
  56:      {
  57:          x[k] = y[k] - u[k] * x[k + 1];
  58:      }
  59:      
  60:      if (l != NULL)
  61:      {
  62:          delete [] l;
  63:          l = NULL;
  64:      }
  65:      
  66:      if (u != NULL)
  67:      {
  68:          delete [] u;
  69:          u = NULL;
  70:      }
  71:      
  72:      if (y != NULL)
  73:      {
  74:          delete [] y;
  75:          y = NULL;
  76:      }
  77:  }
  78:   
  79:   
  80:  #endif

测试程序:

   1:  #include "ChaseMethord.h"
   2:  #include <iostream>
   3:  using namespace std;
   4:   
   5:  int main()
   6:  {
   7:      float a[]  = {1,1,2};
   8:      float b[]  = {2,3,1,1};
   9:      float c[]  = {1,1,1};
  10:      float f[]  = {1,2,2,0};
  11:      
  12:      float *x = new float[4];
  13:      
  14:      ChaseMethord(4, a, b, c, x,f);
  15:      
  16:      for (int i = 0; i < 4; i ++)
  17:      {
  18:          cout << x[i] << endl;
  19:      }
  20:      
  21:      delete [] x;    
  22:    
  23:      return 0;
  24:  }
posted on 2010-03-23 14:01 The cpper 阅读(1068) 评论(1)  编辑 收藏 引用

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# re: 追赶法解矩阵方程(c++实现) 2014-12-06 11:15 zc02051126
运行结果全是零,您测试过您的程序吗  回复  更多评论
  


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