1782 lines
39 KiB
C++
1782 lines
39 KiB
C++
//////////////////////////////////////////////////////////////////////
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// LEquations.cpp
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//
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// 求解线性方程组的类 CLEquations 的实现代码
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//
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// 编制, 2002/8
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//////////////////////////////////////////////////////////////////////
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#include "LEquations.h"
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#include<complex>
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//////////////////////////////////////////////////////////////////////
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// Construction/Destruction
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//////////////////////////////////////////////////////////////////////
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//////////////////////////////////////////////////////////////////////
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// 基本构造函数
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//////////////////////////////////////////////////////////////////////
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CLEquations::CLEquations()
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{
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}
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//////////////////////////////////////////////////////////////////////
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// 指定系数和常数构造函数
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//
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// 参数：
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// 1. const CMatrix1& mtxCoef - 指定的系数矩阵
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// 2. const CMatrix1& mtxConst - 指定的常数矩阵
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//////////////////////////////////////////////////////////////////////
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CLEquations::CLEquations(const CMatrix1& mtxCoef, const CMatrix1& mtxConst)
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{
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//ASSERT(Init(mtxCoef, mtxConst));
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//whp change 2011.12.6 for :ASSERT仅在调试版中有效，如果是release，ASSERT(Init(mtxCoef, mtxConst));不被执行，也就无法进行初始化
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//在发行版本中，可以用VERIFY代替ASSERT
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//BOOL bSuccess = Init(mtxCoef, mtxConst);
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//ASSERT(bSuccess);
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// VERIFY
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(Init(mtxCoef, mtxConst));
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}
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//////////////////////////////////////////////////////////////////////
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// 析构函数
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//////////////////////////////////////////////////////////////////////
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CLEquations::~CLEquations()
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{
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}
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//////////////////////////////////////////////////////////////////////
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// 初始化函数
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//
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// 参数：
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// 1. const CMatrix1& mtxCoef - 指定的系数矩阵
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// 2. const CMatrix1& mtxConst - 指定的常数矩阵
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//
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// 返回值：BOOL 型，初始化是否成功
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//////////////////////////////////////////////////////////////////////
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BOOL CLEquations::Init(const CMatrix1& mtxCoef, const CMatrix1& mtxConst)
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{
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if (mtxCoef.GetNumRows() != mtxConst.GetNumRows())
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return FALSE;
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m_mtxCoef = mtxCoef;
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m_mtxConst = mtxConst;
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return TRUE;
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}
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//////////////////////////////////////////////////////////////////////
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// 获取系数矩阵
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//
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// 参数：无
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//
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// 返回值：CMatrix1 型，返回系数矩阵
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//////////////////////////////////////////////////////////////////////
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inline CMatrix1 CLEquations::GetCoefMatrix() const
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{
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return m_mtxCoef;
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}
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//////////////////////////////////////////////////////////////////////
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// 获取常数矩阵
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//
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// 参数：无
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//
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// 返回值：CMatrix1 型，返回常数矩阵
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//////////////////////////////////////////////////////////////////////
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inline CMatrix1 CLEquations::GetConstMatrix() const
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{
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return m_mtxConst;
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}
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//////////////////////////////////////////////////////////////////////
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// 获取方程个数
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//
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// 参数：无
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//
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// 返回值：int 型，返回方程组方程的个数
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//////////////////////////////////////////////////////////////////////
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inline int CLEquations::GetNumEquations() const
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{
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return GetCoefMatrix().GetNumRows();
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}
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//////////////////////////////////////////////////////////////////////
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// 获取未知数个数
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//
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// 参数：无
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//
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// 返回值：int 型，返回方程组未知数的个数
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//////////////////////////////////////////////////////////////////////
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inline int CLEquations::GetNumUnknowns() const
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{
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return GetCoefMatrix().GetNumColumns();
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}
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//////////////////////////////////////////////////////////////////////
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// 全选主元高斯消去法
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//
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// 参数：
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// 1. CMatrix1& mtxResult - CMatrix1引用对象，返回方程组的解
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//
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// 返回值：BOOL 型，方程组求解是否成功
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//////////////////////////////////////////////////////////////////////
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BOOL CLEquations::GetRootsetGauss(CMatrix1& mtxResult)
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{
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int *pnJs,l,k,i,j,nIs,p,q;
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float d,t;
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// 方程组的属性，将常数矩阵赋给解矩阵
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mtxResult = m_mtxConst;
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float *pDataCoef = m_mtxCoef.GetData();
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float *pDataConst = mtxResult.GetData();
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int n = GetNumUnknowns();
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// 临时缓冲区，存放列数
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pnJs = new int[n];
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// 消元
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l=1;
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for (k=0;k<=n-2;k++)
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{
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d=0.0;
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for (i=k;i<=n-1;i++)
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{
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for (j=k;j<=n-1;j++)
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{
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t=fabs(pDataCoef[i*n+j]);
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if (t>d)
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{
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d=t;
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pnJs[k]=j;
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nIs=i;
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}
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}
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}
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if (d == 0.0)
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l=0;
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else
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{
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if (pnJs[k]!=k)
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{
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for (i=0;i<=n-1;i++)
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{
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p=i*n+k;
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q=i*n+pnJs[k];
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t=pDataCoef[p];
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pDataCoef[p]=pDataCoef[q];
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pDataCoef[q]=t;
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}
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}
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if (nIs!=k)
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{
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for (j=k;j<=n-1;j++)
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{
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p=k*n+j;
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q=nIs*n+j;
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t=pDataCoef[p];
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pDataCoef[p]=pDataCoef[q];
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pDataCoef[q]=t;
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}
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t=pDataConst[k];
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pDataConst[k]=pDataConst[nIs];
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pDataConst[nIs]=t;
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}
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}
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// 求解失败
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if (l==0)
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{
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delete[] pnJs;
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return FALSE;
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}
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d=pDataCoef[k*n+k];
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for (j=k+1;j<=n-1;j++)
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{
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p=k*n+j;
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pDataCoef[p]=pDataCoef[p]/d;
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}
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pDataConst[k]=pDataConst[k]/d;
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for (i=k+1;i<=n-1;i++)
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{
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for (j=k+1;j<=n-1;j++)
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{
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p=i*n+j;
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pDataCoef[p]=pDataCoef[p]-pDataCoef[i*n+k]*pDataCoef[k*n+j];
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}
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pDataConst[i]=pDataConst[i]-pDataCoef[i*n+k]*pDataConst[k];
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}
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}
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// 求解失败
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d=pDataCoef[(n-1)*n+n-1];
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if (d == 0.0)
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{
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delete[] pnJs;
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return FALSE;
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}
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// 求解
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pDataConst[n-1]=pDataConst[n-1]/d;
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for (i=n-2;i>=0;i--)
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{
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t=0.0;
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for (j=i+1;j<=n-1;j++)
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t=t+pDataCoef[i*n+j]*pDataConst[j];
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pDataConst[i]=pDataConst[i]-t;
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}
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// 调整解的位置
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pnJs[n-1]=n-1;
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for (k=n-1;k>=0;k--)
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{
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if (pnJs[k]!=k)
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{
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t=pDataConst[k];
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pDataConst[k]=pDataConst[pnJs[k]];
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pDataConst[pnJs[k]]=t;
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}
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}
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// 清理内存
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delete[] pnJs;
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return TRUE;
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}
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//////////////////////////////////////////////////////////////////////
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// 全选主元高斯－约当消去法
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//
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// 参数：
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// 1. CMatrix1& mtxResult - CMatrix1引用对象，返回方程组的解
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//
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// 返回值：BOOL 型，方程组求解是否成功
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//////////////////////////////////////////////////////////////////////
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BOOL CLEquations::GetRootsetGaussJordan(CMatrix1& mtxResult)
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{
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int *pnJs,l,k,i,j,nIs,p,q;
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float d,t;
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// 方程组的属性，将常数矩阵赋给解矩阵
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mtxResult = m_mtxConst;
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float *pDataCoef = m_mtxCoef.GetData();
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float *pDataConst = mtxResult.GetData();
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int n = GetNumUnknowns();
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int m = m_mtxConst.GetNumColumns();
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// 临时缓冲区，存放变换的列数
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pnJs = new int[n];
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// 消元
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l=1;
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for (k=0;k<=n-1;k++)
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{
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d=0.0;
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for (i=k;i<=n-1;i++)
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{
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for (j=k;j<=n-1;j++)
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{
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t=fabs(pDataCoef[i*n+j]);
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if (t>d)
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{
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d=t;
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pnJs[k]=j;
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nIs=i;
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}
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}
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}
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if (d+1.0==1.0)
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l=0;
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else
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{
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if (pnJs[k]!=k)
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{
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for (i=0;i<=n-1;i++)
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{
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p=i*n+k;
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q=i*n+pnJs[k];
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t=pDataCoef[p];
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pDataCoef[p]=pDataCoef[q];
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pDataCoef[q]=t;
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}
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}
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if (nIs!=k)
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{
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for (j=k;j<=n-1;j++)
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{
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p=k*n+j;
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q=nIs*n+j;
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t=pDataCoef[p];
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pDataCoef[p]=pDataCoef[q];
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pDataCoef[q]=t;
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}
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for (j=0;j<=m-1;j++)
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{
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p=k*m+j;
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q=nIs*m+j;
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t=pDataConst[p];
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pDataConst[p]=pDataConst[q];
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pDataConst[q]=t;
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}
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}
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}
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// 求解失败
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if (l==0)
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{
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delete[] pnJs;
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return FALSE;
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}
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d=pDataCoef[k*n+k];
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for (j=k+1;j<=n-1;j++)
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{
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p=k*n+j;
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pDataCoef[p]=pDataCoef[p]/d;
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}
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for (j=0;j<=m-1;j++)
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{
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p=k*m+j;
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pDataConst[p]=pDataConst[p]/d;
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}
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for (j=k+1;j<=n-1;j++)
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{
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for (i=0;i<=n-1;i++)
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{
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p=i*n+j;
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if (i!=k)
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pDataCoef[p]=pDataCoef[p]-pDataCoef[i*n+k]*pDataCoef[k*n+j];
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}
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}
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for (j=0;j<=m-1;j++)
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{
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for (i=0;i<=n-1;i++)
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{
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p=i*m+j;
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if (i!=k)
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pDataConst[p]=pDataConst[p]-pDataCoef[i*n+k]*pDataConst[k*m+j];
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}
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}
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}
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// 调整
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for (k=n-1;k>=0;k--)
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{
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if (pnJs[k]!=k)
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{
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for (j=0;j<=m-1;j++)
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{
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p=k*m+j;
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q=pnJs[k]*m+j;
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t=pDataConst[p];
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pDataConst[p]=pDataConst[q];
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pDataConst[q]=t;
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}
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}
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}
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// 清理内存
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delete[] pnJs;
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return TRUE;
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}
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//////////////////////////////////////////////////////////////////////
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// 复系数方程组的全选主元高斯消去法
|
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//
|
||
// 参数：
|
||
// 1. const CMatrix1& mtxCoefImag - 系数矩阵的虚部矩阵
|
||
// 2. const CMatrix1& mtxConstImag - 常数矩阵的虚部矩阵
|
||
// 3. CMatrix1& mtxResult - CMatrix1引用对象，返回方程组解矩阵的实部矩阵
|
||
// 4. CMatrix1& mtxResultImag - CMatrix1引用对象，返回方程组解矩阵的虚部矩阵
|
||
//
|
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// 返回值：BOOL 型，方程组求解是否成功
|
||
//////////////////////////////////////////////////////////////////////
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BOOL CLEquations::GetRootsetGauss(const CMatrix1& mtxCoefImag, const CMatrix1& mtxConstImag, CMatrix1& mtxResult, CMatrix1& mtxResultImag)
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{
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int *pnJs,l,k,i,j,nIs,u,v;
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float p,q,s,d;
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// 方程组的属性，将常数矩阵赋给解矩阵
|
||
mtxResult = m_mtxConst;
|
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mtxResultImag = mtxConstImag;
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float *pDataCoef = m_mtxCoef.GetData();
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float *pDataConst = mtxResult.GetData();
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float *pDataCoefImag = mtxCoefImag.GetData();
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float *pDataConstImag = mtxResultImag.GetData();
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int n = GetNumUnknowns();
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int m = m_mtxConst.GetNumColumns();
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|
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// 临时缓冲区，存放变换的列数
|
||
pnJs = new int[n];
|
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|
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// 消元
|
||
for (k=0;k<=n-2;k++)
|
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{
|
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d=0.0;
|
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for (i=k;i<=n-1;i++)
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{
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for (j=k;j<=n-1;j++)
|
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{
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u=i*n+j;
|
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p=pDataCoef[u]*pDataCoef[u]+pDataCoefImag[u]*pDataCoefImag[u];
|
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if (p>d)
|
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{
|
||
d=p;
|
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pnJs[k]=j;
|
||
nIs=i;
|
||
}
|
||
}
|
||
}
|
||
|
||
// 求解失败
|
||
if (d == 0.0)
|
||
{
|
||
delete[] pnJs;
|
||
return FALSE;
|
||
}
|
||
|
||
if (nIs!=k)
|
||
{
|
||
for (j=k;j<=n-1;j++)
|
||
{
|
||
u=k*n+j;
|
||
v=nIs*n+j;
|
||
p=pDataCoef[u];
|
||
pDataCoef[u]=pDataCoef[v];
|
||
pDataCoef[v]=p;
|
||
p=pDataCoefImag[u];
|
||
pDataCoefImag[u]=pDataCoefImag[v];
|
||
pDataCoefImag[v]=p;
|
||
}
|
||
|
||
p=pDataConst[k];
|
||
pDataConst[k]=pDataConst[nIs];
|
||
pDataConst[nIs]=p;
|
||
p=pDataConstImag[k];
|
||
pDataConstImag[k]=pDataConstImag[nIs];
|
||
pDataConstImag[nIs]=p;
|
||
}
|
||
|
||
if (pnJs[k]!=k)
|
||
{
|
||
for (i=0;i<=n-1;i++)
|
||
{
|
||
u=i*n+k;
|
||
v=i*n+pnJs[k];
|
||
p=pDataCoef[u];
|
||
pDataCoef[u]=pDataCoef[v];
|
||
pDataCoef[v]=p;
|
||
p=pDataCoefImag[u];
|
||
pDataCoefImag[u]=pDataCoefImag[v];
|
||
pDataCoefImag[v]=p;
|
||
}
|
||
}
|
||
|
||
v=k*n+k;
|
||
for (j=k+1;j<=n-1;j++)
|
||
{
|
||
u=k*n+j;
|
||
p=pDataCoef[u]*pDataCoef[v];
|
||
q=-pDataCoefImag[u]*pDataCoefImag[v];
|
||
s=(pDataCoef[v]-pDataCoefImag[v])*(pDataCoef[u]+pDataCoefImag[u]);
|
||
pDataCoef[u]=(p-q)/d;
|
||
pDataCoefImag[u]=(s-p-q)/d;
|
||
}
|
||
|
||
p=pDataConst[k]*pDataCoef[v];
|
||
q=-pDataConstImag[k]*pDataCoefImag[v];
|
||
s=(pDataCoef[v]-pDataCoefImag[v])*(pDataConst[k]+pDataConstImag[k]);
|
||
pDataConst[k]=(p-q)/d;
|
||
pDataConstImag[k]=(s-p-q)/d;
|
||
|
||
for (i=k+1;i<=n-1;i++)
|
||
{
|
||
u=i*n+k;
|
||
for (j=k+1;j<=n-1;j++)
|
||
{
|
||
v=k*n+j;
|
||
l=i*n+j;
|
||
p=pDataCoef[u]*pDataCoef[v];
|
||
q=pDataCoefImag[u]*pDataCoefImag[v];
|
||
s=(pDataCoef[u]+pDataCoefImag[u])*(pDataCoef[v]+pDataCoefImag[v]);
|
||
pDataCoef[l]=pDataCoef[l]-p+q;
|
||
pDataCoefImag[l]=pDataCoefImag[l]-s+p+q;
|
||
}
|
||
|
||
p=pDataCoef[u]*pDataConst[k];
|
||
q=pDataCoefImag[u]*pDataConstImag[k];
|
||
s=(pDataCoef[u]+pDataCoefImag[u])*(pDataConst[k]+pDataConstImag[k]);
|
||
pDataConst[i]=pDataConst[i]-p+q;
|
||
pDataConstImag[i]=pDataConstImag[i]-s+p+q;
|
||
}
|
||
}
|
||
|
||
u=(n-1)*n+n-1;
|
||
d=pDataCoef[u]*pDataCoef[u]+pDataCoefImag[u]*pDataCoefImag[u];
|
||
|
||
// 求解失败
|
||
if (d == 0.0)
|
||
{
|
||
delete[] pnJs;
|
||
return FALSE;
|
||
}
|
||
|
||
// 求解
|
||
p=pDataCoef[u]*pDataConst[n-1]; q=-pDataCoefImag[u]*pDataConstImag[n-1];
|
||
s=(pDataCoef[u]-pDataCoefImag[u])*(pDataConst[n-1]+pDataConstImag[n-1]);
|
||
pDataConst[n-1]=(p-q)/d; pDataConstImag[n-1]=(s-p-q)/d;
|
||
|
||
for (i=n-2;i>=0;i--)
|
||
{
|
||
for (j=i+1;j<=n-1;j++)
|
||
{
|
||
u=i*n+j;
|
||
p=pDataCoef[u]*pDataConst[j];
|
||
q=pDataCoefImag[u]*pDataConstImag[j];
|
||
s=(pDataCoef[u]+pDataCoefImag[u])*(pDataConst[j]+pDataConstImag[j]);
|
||
pDataConst[i]=pDataConst[i]-p+q;
|
||
pDataConstImag[i]=pDataConstImag[i]-s+p+q;
|
||
}
|
||
}
|
||
|
||
// 调整位置
|
||
pnJs[n-1]=n-1;
|
||
for (k=n-1;k>=0;k--)
|
||
{
|
||
if (pnJs[k]!=k)
|
||
{
|
||
p=pDataConst[k];
|
||
pDataConst[k]=pDataConst[pnJs[k]];
|
||
pDataConst[pnJs[k]]=p;
|
||
p=pDataConstImag[k];
|
||
pDataConstImag[k]=pDataConstImag[pnJs[k]];
|
||
pDataConstImag[pnJs[k]]=p;
|
||
}
|
||
}
|
||
|
||
// 清理内存
|
||
delete[] pnJs;
|
||
|
||
return TRUE;
|
||
}
|
||
|
||
//////////////////////////////////////////////////////////////////////
|
||
// 复系数方程组的全选主元高斯－约当消去法
|
||
//
|
||
// 参数：
|
||
// 1. const CMatrix1& mtxCoefImag - 系数矩阵的虚部矩阵
|
||
// 2. const CMatrix1& mtxConstImag - 常数矩阵的虚部矩阵
|
||
// 3. CMatrix1& mtxResult - CMatrix1引用对象，返回方程组解矩阵的实部矩阵
|
||
// 4. CMatrix1& mtxResultImag - CMatrix1引用对象，返回方程组解矩阵的虚部矩阵
|
||
//
|
||
// 返回值：BOOL 型，方程组求解是否成功
|
||
//////////////////////////////////////////////////////////////////////
|
||
BOOL CLEquations::GetRootsetGaussJordan(const CMatrix1& mtxCoefImag, const CMatrix1& mtxConstImag, CMatrix1& mtxResult, CMatrix1& mtxResultImag)
|
||
{
|
||
int *pnJs,l,k,i,j,nIs,u,v;
|
||
float p,q,s,d;
|
||
|
||
// 方程组的属性，将常数矩阵赋给解矩阵
|
||
mtxResult = m_mtxConst;
|
||
mtxResultImag = mtxConstImag;
|
||
float *pDataCoef = m_mtxCoef.GetData();
|
||
float *pDataConst = mtxResult.GetData();
|
||
float *pDataCoefImag = mtxCoefImag.GetData();
|
||
float *pDataConstImag = mtxResultImag.GetData();
|
||
int n = GetNumUnknowns();
|
||
int m = m_mtxConst.GetNumColumns();
|
||
|
||
// 临时缓冲区，存放变换的列数
|
||
pnJs = new int[n];
|
||
|
||
// 消元
|
||
for (k=0;k<=n-1;k++)
|
||
{
|
||
d=0.0;
|
||
for (i=k;i<=n-1;i++)
|
||
{
|
||
for (j=k;j<=n-1;j++)
|
||
{
|
||
u=i*n+j;
|
||
p=pDataCoef[u]*pDataCoef[u]+pDataCoefImag[u]*pDataCoefImag[u];
|
||
if (p>d)
|
||
{
|
||
d=p;
|
||
pnJs[k]=j;
|
||
nIs=i;
|
||
}
|
||
}
|
||
}
|
||
|
||
// 求解失败
|
||
if (d == 0.0)
|
||
{
|
||
delete[] pnJs;
|
||
return FALSE;
|
||
}
|
||
|
||
if (nIs!=k)
|
||
{
|
||
for (j=k;j<=n-1;j++)
|
||
{
|
||
u=k*n+j;
|
||
v=nIs*n+j;
|
||
p=pDataCoef[u];
|
||
pDataCoef[u]=pDataCoef[v];
|
||
pDataCoef[v]=p;
|
||
p=pDataCoefImag[u];
|
||
pDataCoefImag[u]=pDataCoefImag[v];
|
||
pDataCoefImag[v]=p;
|
||
}
|
||
|
||
for (j=0;j<=m-1;j++)
|
||
{
|
||
u=k*m+j;
|
||
v=nIs*m+j;
|
||
p=pDataConst[u];
|
||
pDataConst[u]=pDataConst[v];
|
||
pDataConst[v]=p;
|
||
p=pDataConstImag[u];
|
||
pDataConstImag[u]=pDataConstImag[v];
|
||
pDataConstImag[v]=p;
|
||
}
|
||
}
|
||
|
||
if (pnJs[k]!=k)
|
||
{
|
||
for (i=0;i<=n-1;i++)
|
||
{
|
||
u=i*n+k;
|
||
v=i*n+pnJs[k];
|
||
p=pDataCoef[u];
|
||
pDataCoef[u]=pDataCoef[v];
|
||
pDataCoef[v]=p;
|
||
p=pDataCoefImag[u];
|
||
pDataCoefImag[u]=pDataCoefImag[v];
|
||
pDataCoefImag[v]=p;
|
||
}
|
||
}
|
||
|
||
v=k*n+k;
|
||
for (j=k+1;j<=n-1;j++)
|
||
{
|
||
u=k*n+j;
|
||
p=pDataCoef[u]*pDataCoef[v];
|
||
q=-pDataCoefImag[u]*pDataCoefImag[v];
|
||
s=(pDataCoef[v]-pDataCoefImag[v])*(pDataCoef[u]+pDataCoefImag[u]);
|
||
pDataCoef[u]=(p-q)/d;
|
||
pDataCoefImag[u]=(s-p-q)/d;
|
||
}
|
||
|
||
for (j=0;j<=m-1;j++)
|
||
{
|
||
u=k*m+j;
|
||
p=pDataConst[u]*pDataCoef[v];
|
||
q=-pDataConstImag[u]*pDataCoefImag[v];
|
||
s=(pDataCoef[v]-pDataCoefImag[v])*(pDataConst[u]+pDataConstImag[u]);
|
||
pDataConst[u]=(p-q)/d;
|
||
pDataConstImag[u]=(s-p-q)/d;
|
||
}
|
||
|
||
for (i=0;i<=n-1;i++)
|
||
{
|
||
if (i!=k)
|
||
{
|
||
u=i*n+k;
|
||
for (j=k+1;j<=n-1;j++)
|
||
{
|
||
v=k*n+j;
|
||
l=i*n+j;
|
||
p=pDataCoef[u]*pDataCoef[v];
|
||
q=pDataCoefImag[u]*pDataCoefImag[v];
|
||
s=(pDataCoef[u]+pDataCoefImag[u])*(pDataCoef[v]+pDataCoefImag[v]);
|
||
pDataCoef[l]=pDataCoef[l]-p+q;
|
||
pDataCoefImag[l]=pDataCoefImag[l]-s+p+q;
|
||
}
|
||
|
||
for (j=0;j<=m-1;j++)
|
||
{
|
||
l=i*m+j;
|
||
v=k*m+j;
|
||
p=pDataCoef[u]*pDataConst[v]; q=pDataCoefImag[u]*pDataConstImag[v];
|
||
s=(pDataCoef[u]+pDataCoefImag[u])*(pDataConst[v]+pDataConstImag[v]);
|
||
pDataConst[l]=pDataConst[l]-p+q;
|
||
pDataConstImag[l]=pDataConstImag[l]-s+p+q;
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
// 求解调整
|
||
for (k=n-1;k>=0;k--)
|
||
{
|
||
if (pnJs[k]!=k)
|
||
{
|
||
for (j=0;j<=m-1;j++)
|
||
{
|
||
u=k*m+j;
|
||
v=pnJs[k]*m+j;
|
||
p=pDataConst[u];
|
||
pDataConst[u]=pDataConst[v];
|
||
pDataConst[v]=p;
|
||
p=pDataConstImag[u];
|
||
pDataConstImag[u]=pDataConstImag[v];
|
||
pDataConstImag[v]=p;
|
||
}
|
||
}
|
||
}
|
||
|
||
// 清理内存
|
||
delete[] pnJs;
|
||
|
||
return TRUE;
|
||
}
|
||
|
||
//////////////////////////////////////////////////////////////////////
|
||
// 求解三对角线方程组的追赶法
|
||
//
|
||
// 参数：
|
||
// 1. CMatrix1& mtxResult - CMatrix1引用对象，返回方程组解矩阵
|
||
//
|
||
// 返回值：BOOL 型，方程组求解是否成功
|
||
//////////////////////////////////////////////////////////////////////
|
||
BOOL CLEquations::GetRootsetTriDiagonal(CMatrix1& mtxResult)
|
||
{
|
||
int k,j;
|
||
float s;
|
||
|
||
// 将常数矩阵赋给解矩阵
|
||
mtxResult = m_mtxConst;
|
||
float *pDataConst = mtxResult.GetData();
|
||
|
||
int n = GetNumUnknowns();
|
||
// ASSERT(m_mtxCoef.GetNumRows() == n);
|
||
|
||
// 为系数矩阵对角线数组分配内存
|
||
float* pDiagData = new float[3*n-2];
|
||
|
||
// 构造系数矩阵对角线元素数组
|
||
k = j = 0;
|
||
if (k == 0)
|
||
{
|
||
pDiagData[j++] = m_mtxCoef.GetElement(k, k);
|
||
pDiagData[j++] = m_mtxCoef.GetElement(k, k+1);
|
||
}
|
||
for (k=1; k<n-1; ++k)
|
||
{
|
||
pDiagData[j++] = m_mtxCoef.GetElement(k, k-1);
|
||
pDiagData[j++] = m_mtxCoef.GetElement(k, k);
|
||
pDiagData[j++] = m_mtxCoef.GetElement(k, k+1);
|
||
}
|
||
if (k == n-1)
|
||
{
|
||
pDiagData[j++] = m_mtxCoef.GetElement(k, k-1);
|
||
pDiagData[j++] = m_mtxCoef.GetElement(k, k);
|
||
}
|
||
|
||
// 求解
|
||
for (k=0;k<=n-2;k++)
|
||
{
|
||
j=3*k;
|
||
s=pDiagData[j];
|
||
|
||
// 求解失败
|
||
if (fabs(s)+1.0==1.0)
|
||
{
|
||
delete[] pDiagData;
|
||
return FALSE;
|
||
}
|
||
|
||
pDiagData[j+1]=pDiagData[j+1]/s;
|
||
pDataConst[k]=pDataConst[k]/s;
|
||
pDiagData[j+3]=pDiagData[j+3]-pDiagData[j+2]*pDiagData[j+1];
|
||
pDataConst[k+1]=pDataConst[k+1]-pDiagData[j+2]*pDataConst[k];
|
||
}
|
||
|
||
s=pDiagData[3*n-3];
|
||
if (s == 0.0)
|
||
{
|
||
delete[] pDiagData;
|
||
return FALSE;
|
||
}
|
||
|
||
// 调整
|
||
pDataConst[n-1]=pDataConst[n-1]/s;
|
||
for (k=n-2;k>=0;k--)
|
||
pDataConst[k]=pDataConst[k]-pDiagData[3*k+1]*pDataConst[k+1];
|
||
|
||
// 释放内存
|
||
delete[] pDiagData;
|
||
|
||
return TRUE;
|
||
}
|
||
|
||
//////////////////////////////////////////////////////////////////////
|
||
// 一般带型方程组的求解
|
||
//
|
||
// 参数：
|
||
// 1. int nBandWidth - 带宽
|
||
// 2. CMatrix1& mtxResult - CMatrix1引用对象，返回方程组解矩阵
|
||
//
|
||
// 返回值：BOOL 型，方程组求解是否成功
|
||
//////////////////////////////////////////////////////////////////////
|
||
BOOL CLEquations::GetRootsetBand(int nBandWidth, CMatrix1& mtxResult)
|
||
{
|
||
int ls,k,i,j,is,u,v;
|
||
float p,t;
|
||
|
||
// 带宽必须为奇数
|
||
if ((nBandWidth-1)%2 != 0)
|
||
return FALSE;
|
||
|
||
// 将常数矩阵赋给解矩阵
|
||
mtxResult = m_mtxConst;
|
||
float *pDataConst = mtxResult.GetData();
|
||
|
||
// 方程组属性
|
||
int m = m_mtxConst.GetNumColumns();
|
||
int n = GetNumUnknowns();
|
||
// ASSERT(m_mtxCoef.GetNumRows() == n);
|
||
|
||
// 带宽数组：带型矩阵的有效数据
|
||
float* pBandData = new float[nBandWidth*n];
|
||
|
||
// 半带宽
|
||
ls = (nBandWidth-1)/2;
|
||
|
||
// 构造带宽数组
|
||
for (i=0; i<n; ++i)
|
||
{
|
||
j = 0;
|
||
for (k=max(0, i-ls); k<max(0, i-ls)+nBandWidth; ++k)
|
||
{
|
||
if (k < n)
|
||
pBandData[i*nBandWidth+j++] = m_mtxCoef.GetElement(i, k);
|
||
else
|
||
pBandData[i*nBandWidth+j++] = 0;
|
||
}
|
||
}
|
||
|
||
// 求解
|
||
for (k=0;k<=n-2;k++)
|
||
{
|
||
p=0.0;
|
||
for (i=k;i<=ls;i++)
|
||
{
|
||
t=fabs(pBandData[i*nBandWidth]);
|
||
if (t>p)
|
||
{
|
||
p=t;
|
||
is=i;
|
||
}
|
||
}
|
||
|
||
if (p == 0.0)
|
||
{
|
||
delete[] pBandData;
|
||
return FALSE;
|
||
}
|
||
|
||
for (j=0;j<=m-1;j++)
|
||
{
|
||
u=k*m+j;
|
||
v=is*m+j;
|
||
t=pDataConst[u];
|
||
pDataConst[u]=pDataConst[v];
|
||
pDataConst[v]=t;
|
||
}
|
||
|
||
for (j=0;j<=nBandWidth-1;j++)
|
||
{
|
||
u=k*nBandWidth+j;
|
||
v=is*nBandWidth+j;
|
||
t=pBandData[u];
|
||
pBandData[u]=pBandData[v];
|
||
pBandData[v]=t;
|
||
}
|
||
|
||
for (j=0;j<=m-1;j++)
|
||
{
|
||
u=k*m+j;
|
||
pDataConst[u]=pDataConst[u]/pBandData[k*nBandWidth];
|
||
}
|
||
|
||
for (j=1;j<=nBandWidth-1;j++)
|
||
{
|
||
u=k*nBandWidth+j;
|
||
pBandData[u]=pBandData[u]/pBandData[k*nBandWidth];
|
||
}
|
||
|
||
for (i=k+1;i<=ls;i++)
|
||
{
|
||
t=pBandData[i*nBandWidth];
|
||
for (j=0;j<=m-1;j++)
|
||
{
|
||
u=i*m+j;
|
||
v=k*m+j;
|
||
pDataConst[u]=pDataConst[u]-t*pDataConst[v];
|
||
}
|
||
|
||
for (j=1;j<=nBandWidth-1;j++)
|
||
{
|
||
u=i*nBandWidth+j;
|
||
v=k*nBandWidth+j;
|
||
pBandData[u-1]=pBandData[u]-t*pBandData[v];
|
||
}
|
||
|
||
u=i*nBandWidth+nBandWidth-1; pBandData[u]=0.0;
|
||
}
|
||
|
||
if (ls!=(n-1))
|
||
ls=ls+1;
|
||
}
|
||
|
||
p=pBandData[(n-1)*nBandWidth];
|
||
if (p == 0.0)
|
||
{
|
||
delete[] pBandData;
|
||
return FALSE;
|
||
}
|
||
|
||
for (j=0;j<=m-1;j++)
|
||
{
|
||
u=(n-1)*m+j;
|
||
pDataConst[u]=pDataConst[u]/p;
|
||
}
|
||
|
||
ls=1;
|
||
for (i=n-2;i>=0;i--)
|
||
{
|
||
for (k=0;k<=m-1;k++)
|
||
{
|
||
u=i*m+k;
|
||
for (j=1;j<=ls;j++)
|
||
{
|
||
v=i*nBandWidth+j;
|
||
is=(i+j)*m+k;
|
||
pDataConst[u]=pDataConst[u]-pBandData[v]*pDataConst[is];
|
||
}
|
||
}
|
||
|
||
if (ls!=(nBandWidth-1))
|
||
ls=ls+1;
|
||
}
|
||
|
||
// 释放内存
|
||
delete[] pBandData;
|
||
|
||
return TRUE;
|
||
}
|
||
|
||
//////////////////////////////////////////////////////////////////////
|
||
// 求解对称方程组的分解法
|
||
//
|
||
// 参数：
|
||
// 1. CMatrix1& mtxResult - CMatrix1引用对象，返回方程组解矩阵
|
||
//
|
||
// 返回值：BOOL 型，方程组求解是否成功
|
||
//////////////////////////////////////////////////////////////////////
|
||
BOOL CLEquations::GetRootsetDjn(CMatrix1& mtxResult)
|
||
{
|
||
int i,j,l,k,u,v,w,k1,k2,k3;
|
||
float p;
|
||
|
||
// 方程组属性，将常数矩阵赋给解矩阵
|
||
CMatrix1 mtxCoef = m_mtxCoef;
|
||
mtxResult = m_mtxConst;
|
||
int n = mtxCoef.GetNumColumns();
|
||
int m = mtxResult.GetNumColumns();
|
||
float* pDataCoef = mtxCoef.GetData();
|
||
float* pDataConst = mtxResult.GetData();
|
||
|
||
// 非对称系数矩阵，不能用本方法求解
|
||
if (pDataCoef[0] == 0.0)
|
||
return FALSE;
|
||
|
||
for (i=1; i<=n-1; i++)
|
||
{
|
||
u=i*n;
|
||
pDataCoef[u]=pDataCoef[u]/pDataCoef[0];
|
||
}
|
||
|
||
for (i=1; i<=n-2; i++)
|
||
{
|
||
u=i*n+i;
|
||
for (j=1; j<=i; j++)
|
||
{
|
||
v=i*n+j-1;
|
||
l=(j-1)*n+j-1;
|
||
pDataCoef[u]=pDataCoef[u]-pDataCoef[v]*pDataCoef[v]*pDataCoef[l];
|
||
}
|
||
|
||
p=pDataCoef[u];
|
||
if (p == 0.0)
|
||
return FALSE;
|
||
|
||
for (k=i+1; k<=n-1; k++)
|
||
{
|
||
u=k*n+i;
|
||
for (j=1; j<=i; j++)
|
||
{
|
||
v=k*n+j-1;
|
||
l=i*n+j-1;
|
||
w=(j-1)*n+j-1;
|
||
pDataCoef[u]=pDataCoef[u]-pDataCoef[v]*pDataCoef[l]*pDataCoef[w];
|
||
}
|
||
|
||
pDataCoef[u]=pDataCoef[u]/p;
|
||
}
|
||
}
|
||
|
||
u=n*n-1;
|
||
for (j=1; j<=n-1; j++)
|
||
{
|
||
v=(n-1)*n+j-1;
|
||
w=(j-1)*n+j-1;
|
||
pDataCoef[u]=pDataCoef[u]-pDataCoef[v]*pDataCoef[v]*pDataCoef[w];
|
||
}
|
||
|
||
p=pDataCoef[u];
|
||
if (p == 0.0)
|
||
return FALSE;
|
||
|
||
for (j=0; j<=m-1; j++)
|
||
{
|
||
for (i=1; i<=n-1; i++)
|
||
{
|
||
u=i*m+j;
|
||
for (k=1; k<=i; k++)
|
||
{
|
||
v=i*n+k-1;
|
||
w=(k-1)*m+j;
|
||
pDataConst[u]=pDataConst[u]-pDataCoef[v]*pDataConst[w];
|
||
}
|
||
}
|
||
}
|
||
|
||
for (i=1; i<=n-1; i++)
|
||
{
|
||
u=(i-1)*n+i-1;
|
||
for (j=i; j<=n-1; j++)
|
||
{
|
||
v=(i-1)*n+j;
|
||
w=j*n+i-1;
|
||
pDataCoef[v]=pDataCoef[u]*pDataCoef[w];
|
||
}
|
||
}
|
||
|
||
for (j=0; j<=m-1; j++)
|
||
{
|
||
u=(n-1)*m+j;
|
||
pDataConst[u]=pDataConst[u]/p;
|
||
for (k=1; k<=n-1; k++)
|
||
{
|
||
k1=n-k;
|
||
k3=k1-1;
|
||
u=k3*m+j;
|
||
for (k2=k1; k2<=n-1; k2++)
|
||
{
|
||
v=k3*n+k2;
|
||
w=k2*m+j;
|
||
pDataConst[u]=pDataConst[u]-pDataCoef[v]*pDataConst[w];
|
||
}
|
||
|
||
pDataConst[u]=pDataConst[u]/pDataCoef[k3*n+k3];
|
||
}
|
||
}
|
||
|
||
return TRUE;
|
||
}
|
||
|
||
//////////////////////////////////////////////////////////////////////
|
||
// 求解对称正定方程组的平方根法
|
||
//
|
||
// 参数：
|
||
// 1. CMatrix1& mtxResult - CMatrix1引用对象，返回方程组解矩阵
|
||
//
|
||
// 返回值：BOOL 型，方程组求解是否成功
|
||
//////////////////////////////////////////////////////////////////////
|
||
BOOL CLEquations::GetRootsetCholesky(CMatrix1& mtxResult)
|
||
{
|
||
int i,j,k,u,v;
|
||
|
||
// 方程组属性，将常数矩阵赋给解矩阵
|
||
CMatrix1 mtxCoef = m_mtxCoef;
|
||
mtxResult = m_mtxConst;
|
||
int n = mtxCoef.GetNumColumns();
|
||
int m = mtxResult.GetNumColumns();
|
||
float* pDataCoef = mtxCoef.GetData();
|
||
float* pDataConst = mtxResult.GetData();
|
||
|
||
// 非对称正定系数矩阵，不能用本方法求解
|
||
if (pDataCoef[0] <= 0.0)
|
||
return FALSE;
|
||
|
||
pDataCoef[0]=sqrt(pDataCoef[0]);
|
||
for (j=1; j<=n-1; j++)
|
||
pDataCoef[j]=pDataCoef[j]/pDataCoef[0];
|
||
|
||
for (i=1; i<=n-1; i++)
|
||
{
|
||
u=i*n+i;
|
||
for (j=1; j<=i; j++)
|
||
{
|
||
v=(j-1)*n+i;
|
||
pDataCoef[u]=pDataCoef[u]-pDataCoef[v]*pDataCoef[v];
|
||
}
|
||
|
||
if (pDataCoef[u] <= 0.0)
|
||
return FALSE;
|
||
|
||
pDataCoef[u]=sqrt(pDataCoef[u]);
|
||
if (i!=(n-1))
|
||
{
|
||
for (j=i+1; j<=n-1; j++)
|
||
{
|
||
v=i*n+j;
|
||
for (k=1; k<=i; k++)
|
||
pDataCoef[v]=pDataCoef[v]-pDataCoef[(k-1)*n+i]*pDataCoef[(k-1)*n+j];
|
||
pDataCoef[v]=pDataCoef[v]/pDataCoef[u];
|
||
}
|
||
}
|
||
}
|
||
|
||
for (j=0; j<=m-1; j++)
|
||
{
|
||
pDataConst[j]=pDataConst[j]/pDataCoef[0];
|
||
for (i=1; i<=n-1; i++)
|
||
{
|
||
u=i*n+i;
|
||
v=i*m+j;
|
||
for (k=1; k<=i; k++)
|
||
pDataConst[v]=pDataConst[v]-pDataCoef[(k-1)*n+i]*pDataConst[(k-1)*m+j];
|
||
pDataConst[v]=pDataConst[v]/pDataCoef[u];
|
||
}
|
||
}
|
||
|
||
for (j=0; j<=m-1; j++)
|
||
{
|
||
u=(n-1)*m+j;
|
||
pDataConst[u]=pDataConst[u]/pDataCoef[n*n-1];
|
||
for (k=n-1; k>=1; k--)
|
||
{
|
||
u=(k-1)*m+j;
|
||
for (i=k; i<=n-1; i++)
|
||
{
|
||
v=(k-1)*n+i;
|
||
pDataConst[u]=pDataConst[u]-pDataCoef[v]*pDataConst[i*m+j];
|
||
}
|
||
|
||
v=(k-1)*n+k-1;
|
||
pDataConst[u]=pDataConst[u]/pDataCoef[v];
|
||
}
|
||
}
|
||
|
||
return TRUE;
|
||
}
|
||
|
||
//////////////////////////////////////////////////////////////////////
|
||
// 求解大型稀疏方程组的全选主元高斯－约去消去法
|
||
//
|
||
// 参数：
|
||
// 1. CMatrix1& mtxResult - CMatrix1引用对象，返回方程组解矩阵
|
||
//
|
||
// 返回值：BOOL 型，方程组求解是否成功
|
||
//////////////////////////////////////////////////////////////////////
|
||
BOOL CLEquations::GetRootsetGgje(CMatrix1& mtxResult)
|
||
{
|
||
int *pnJs,i,j,k,nIs,u,v;
|
||
float d,t;
|
||
|
||
// 方程组属性，将常数矩阵赋给解矩阵
|
||
CMatrix1 mtxCoef = m_mtxCoef;
|
||
mtxResult = m_mtxConst;
|
||
int n = mtxCoef.GetNumColumns();
|
||
float* pDataCoef = mtxCoef.GetData();
|
||
float* pDataConst = mtxResult.GetData();
|
||
|
||
// 临时缓冲区，存放变换的列数
|
||
pnJs = new int[n];
|
||
|
||
// 消元
|
||
for (k=0; k<=n-1; k++)
|
||
{
|
||
d=0.0;
|
||
for (i=k; i<=n-1; i++)
|
||
{
|
||
for (j=k; j<=n-1; j++)
|
||
{
|
||
t=fabs(pDataCoef[i*n+j]);
|
||
if (t>d)
|
||
{
|
||
d=t;
|
||
pnJs[k]=j;
|
||
nIs=i;
|
||
}
|
||
}
|
||
}
|
||
|
||
if (d == 0.0)
|
||
{
|
||
delete[] pnJs;
|
||
return FALSE;
|
||
}
|
||
|
||
if (nIs!=k)
|
||
{
|
||
for (j=k; j<=n-1; j++)
|
||
{
|
||
u=k*n+j;
|
||
v=nIs*n+j;
|
||
t=pDataCoef[u];
|
||
pDataCoef[u]=pDataCoef[v];
|
||
pDataCoef[v]=t;
|
||
}
|
||
|
||
t=pDataConst[k];
|
||
pDataConst[k]=pDataConst[nIs];
|
||
pDataConst[nIs]=t;
|
||
}
|
||
|
||
if (pnJs[k]!=k)
|
||
{
|
||
for (i=0; i<=n-1; i++)
|
||
{
|
||
u=i*n+k;
|
||
v=i*n+pnJs[k];
|
||
t=pDataCoef[u];
|
||
pDataCoef[u]=pDataCoef[v];
|
||
pDataCoef[v]=t;
|
||
}
|
||
}
|
||
|
||
t=pDataCoef[k*n+k];
|
||
for (j=k+1; j<=n-1; j++)
|
||
{
|
||
u=k*n+j;
|
||
if (pDataCoef[u]!=0.0)
|
||
pDataCoef[u]=pDataCoef[u]/t;
|
||
}
|
||
|
||
pDataConst[k]=pDataConst[k]/t;
|
||
for (j=k+1; j<=n-1; j++)
|
||
{
|
||
u=k*n+j;
|
||
if (pDataCoef[u]!=0.0)
|
||
{
|
||
for (i=0; i<=n-1; i++)
|
||
{
|
||
v=i*n+k;
|
||
if ((i!=k)&&(pDataCoef[v]!=0.0))
|
||
{
|
||
nIs=i*n+j;
|
||
pDataCoef[nIs]=pDataCoef[nIs]-pDataCoef[v]*pDataCoef[u];
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
for (i=0; i<=n-1; i++)
|
||
{
|
||
u=i*n+k;
|
||
if ((i!=k)&&(pDataCoef[u]!=0.0))
|
||
pDataConst[i]=pDataConst[i]-pDataCoef[u]*pDataConst[k];
|
||
}
|
||
}
|
||
|
||
// 调整
|
||
for (k=n-1; k>=0; k--)
|
||
{
|
||
if (k!=pnJs[k])
|
||
{
|
||
t=pDataConst[k];
|
||
pDataConst[k]=pDataConst[pnJs[k]];
|
||
pDataConst[pnJs[k]]=t;
|
||
}
|
||
}
|
||
|
||
// 释放内存
|
||
delete[] pnJs;
|
||
|
||
return TRUE;
|
||
}
|
||
|
||
//////////////////////////////////////////////////////////////////////
|
||
// 求解托伯利兹方程组的列文逊方法
|
||
//
|
||
// 参数：
|
||
// 1. CMatrix1& mtxResult - CMatrix1引用对象，返回方程组解矩阵
|
||
//
|
||
// 返回值：BOOL 型，方程组求解是否成功
|
||
//////////////////////////////////////////////////////////////////////
|
||
BOOL CLEquations::GetRootsetTlvs(CMatrix1& mtxResult)
|
||
{
|
||
int i,j,k;
|
||
float a,beta,q,c,h,*y,*s;
|
||
|
||
// 未知数个数
|
||
int n = m_mtxCoef.GetNumColumns();
|
||
|
||
// 初始化解解向量
|
||
mtxResult.Init(n, 1);
|
||
float* x = mtxResult.GetData();
|
||
|
||
// 常数数组
|
||
float* pDataConst = m_mtxConst.GetData();
|
||
|
||
// 建立T数组
|
||
float* t = new float[n];
|
||
|
||
// 构造T数组
|
||
for (i=0; i<n; ++i)
|
||
t[i] = m_mtxCoef.GetElement(0, i);
|
||
|
||
// 临时数组
|
||
s = new float[n];
|
||
y = new float[n];
|
||
|
||
// 非托伯利兹方程组，不能用本方法求解
|
||
a=t[0];
|
||
if (a == 0.0)
|
||
{
|
||
delete[] s;
|
||
delete[] y;
|
||
delete[] t;
|
||
return FALSE;
|
||
}
|
||
|
||
// 列文逊方法求解
|
||
y[0]=1.0;
|
||
x[0]=pDataConst[0]/a;
|
||
for (k=1; k<=n-1; k++)
|
||
{
|
||
beta=0.0;
|
||
q=0.0;
|
||
for (j=0; j<=k-1; j++)
|
||
{
|
||
beta=beta+y[j]*t[j+1];
|
||
q=q+x[j]*t[k-j];
|
||
}
|
||
|
||
if (a == 0.0)
|
||
{
|
||
delete[] s;
|
||
delete[] y;
|
||
delete[] t;
|
||
return FALSE;
|
||
}
|
||
|
||
c=-beta/a;
|
||
s[0]=c*y[k-1];
|
||
y[k]=y[k-1];
|
||
if (k!=1)
|
||
{
|
||
for (i=1; i<=k-1; i++)
|
||
s[i]=y[i-1]+c*y[k-i-1];
|
||
}
|
||
|
||
a=a+c*beta;
|
||
if (a == 0.0)
|
||
{
|
||
delete[] s;
|
||
delete[] y;
|
||
delete[] t;
|
||
return FALSE;
|
||
}
|
||
|
||
h=(pDataConst[k]-q)/a;
|
||
for (i=0; i<=k-1; i++)
|
||
{
|
||
x[i]=x[i]+h*s[i];
|
||
y[i]=s[i];
|
||
}
|
||
|
||
x[k]=h*y[k];
|
||
}
|
||
|
||
// 释放内存
|
||
delete[] s;
|
||
delete[] y;
|
||
delete[] t;
|
||
|
||
return TRUE;
|
||
}
|
||
|
||
//////////////////////////////////////////////////////////////////////
|
||
// 高斯－赛德尔迭代法
|
||
//
|
||
// 参数：
|
||
// 1. CMatrix1& mtxResult - CMatrix1引用对象，返回方程组解矩阵
|
||
// 2. float eps - 控制精度，默认值为0.000001
|
||
//
|
||
// 返回值：BOOL 型，方程组求解是否成功
|
||
//////////////////////////////////////////////////////////////////////
|
||
BOOL CLEquations::GetRootsetGaussSeidel(CMatrix1& mtxResult, float eps /*= 0.000001*/)
|
||
{
|
||
int i,j,u,v;
|
||
float p,t,s,q;
|
||
|
||
// 未知数个数
|
||
int n = m_mtxCoef.GetNumColumns();
|
||
|
||
// 初始化解向量
|
||
mtxResult.Init(n, 1);
|
||
float* x = mtxResult.GetData();
|
||
|
||
// 系数与常数
|
||
float* pDataCoef = m_mtxCoef.GetData();
|
||
float* pDataConst = m_mtxConst.GetData();
|
||
|
||
// 求解
|
||
for (i=0; i<=n-1; i++)
|
||
{
|
||
u=i*n+i;
|
||
p=0.0;
|
||
x[i]=0.0;
|
||
for (j=0; j<=n-1; j++)
|
||
{
|
||
if (i!=j)
|
||
{
|
||
v=i*n+j;
|
||
p=p+fabs(pDataCoef[v]);
|
||
}
|
||
}
|
||
|
||
if (p>=fabs(pDataCoef[u]))
|
||
return FALSE;
|
||
}
|
||
|
||
// 精度控制
|
||
p=eps+1.0;
|
||
while (p>=eps)
|
||
{
|
||
p=0.0;
|
||
for (i=0; i<=n-1; i++)
|
||
{
|
||
t=x[i];
|
||
s=0.0;
|
||
for (j=0; j<=n-1; j++)
|
||
if (j!=i)
|
||
s=s+pDataCoef[i*n+j]*x[j];
|
||
|
||
x[i]=(pDataConst[i]-s)/pDataCoef[i*n+i];
|
||
q=fabs(x[i]-t)/(1.0+fabs(x[i]));
|
||
if (q>p)
|
||
p=q;
|
||
}
|
||
}
|
||
|
||
return TRUE;
|
||
}
|
||
|
||
//////////////////////////////////////////////////////////////////////
|
||
// 求解对称正定方程组的共轭梯度法
|
||
//
|
||
// 参数：
|
||
// 1. CMatrix1& mtxResult - CMatrix1引用对象，返回方程组解矩阵
|
||
// 2. float eps - 控制精度，默认值为0.000001
|
||
//
|
||
// 返回值：BOOL 型，方程组求解是否成功
|
||
//////////////////////////////////////////////////////////////////////
|
||
void CLEquations::GetRootsetGrad(CMatrix1& mtxResult, float eps /*= 0.000001*/)
|
||
{
|
||
int i,k;
|
||
float *p,*r,*s,*q,alpha,beta,d,e;
|
||
|
||
// 未知数个数
|
||
int n = GetNumUnknowns();
|
||
|
||
// 初始化解向量
|
||
mtxResult.Init(n, 1);
|
||
float* x = mtxResult.GetData();
|
||
|
||
// 构造临时矩阵
|
||
CMatrix1 mtxP(n, 1);
|
||
p = mtxP.GetData();
|
||
|
||
float* pDataCoef = m_mtxCoef.GetData();
|
||
float* pDataConst = m_mtxConst.GetData();
|
||
|
||
r = new float[n];
|
||
|
||
for (i=0; i<=n-1; i++)
|
||
{
|
||
x[i]=0.0;
|
||
p[i]=pDataConst[i];
|
||
r[i]=pDataConst[i];
|
||
}
|
||
|
||
i=0;
|
||
while (i<=n-1)
|
||
{
|
||
CMatrix1 mtxS = m_mtxCoef * mtxP;
|
||
s = mtxS.GetData();
|
||
|
||
d=0.0;
|
||
e=0.0;
|
||
for (k=0; k<=n-1; k++)
|
||
{
|
||
d=d+p[k]*pDataConst[k];
|
||
e=e+p[k]*s[k];
|
||
}
|
||
|
||
alpha=d/e;
|
||
for (k=0; k<=n-1; k++)
|
||
x[k]=x[k]+alpha*p[k];
|
||
|
||
CMatrix1 mtxQ = m_mtxCoef * mtxResult;
|
||
q = mtxQ.GetData();
|
||
|
||
d=0.0;
|
||
for (k=0; k<=n-1; k++)
|
||
{
|
||
r[k]=pDataConst[k]-q[k];
|
||
d=d+r[k]*s[k];
|
||
}
|
||
|
||
beta=d/e; d=0.0;
|
||
for (k=0; k<=n-1; k++)
|
||
d=d+r[k]*r[k];
|
||
|
||
// 满足精度，求解结束
|
||
d=sqrt(d);
|
||
if (d<eps)
|
||
break;
|
||
|
||
for (k=0; k<=n-1; k++)
|
||
p[k]=r[k]-beta*p[k];
|
||
|
||
i=i+1;
|
||
}
|
||
|
||
delete[] r;
|
||
}
|
||
|
||
//////////////////////////////////////////////////////////////////////
|
||
// 求解线性最小二乘问题的豪斯荷尔德变换法
|
||
//
|
||
// 参数：
|
||
// 1. CMatrix1& mtxResult - CMatrix1引用对象，返回方程组解矩阵
|
||
// 2. CMatrix1& mtxQ - CMatrix1引用对象，返回豪斯荷尔德变换的Q矩阵
|
||
// 3. CMatrix1& mtxR - CMatrix1引用对象，返回豪斯荷尔德变换的R矩阵
|
||
//
|
||
// 返回值：BOOL 型，方程组求解是否成功
|
||
//////////////////////////////////////////////////////////////////////
|
||
BOOL CLEquations::GetRootsetMqr(CMatrix1& mtxResult, CMatrix1& mtxQ, CMatrix1& mtxR)
|
||
{
|
||
int i,j;
|
||
float d;
|
||
|
||
// 方程组的方程数和未知数个数
|
||
int m = m_mtxCoef.GetNumRows();
|
||
int n = m_mtxCoef.GetNumColumns();
|
||
// 奇异方程组
|
||
if (m < n)
|
||
return FALSE;
|
||
|
||
// 将解向量初始化为常数向量
|
||
mtxResult = m_mtxConst;
|
||
float* pDataConst = mtxResult.GetData();
|
||
|
||
// 构造临时矩阵，用于QR分解
|
||
mtxR = m_mtxCoef;
|
||
float* pDataCoef = mtxR.GetData();
|
||
|
||
// QR分解
|
||
if (! mtxR.SplitQR(mtxQ))
|
||
return FALSE;
|
||
|
||
// 临时缓冲区
|
||
float* c = new float[n];
|
||
float* q = mtxQ.GetData();
|
||
|
||
// 求解
|
||
for (i=0; i<=n-1; i++)
|
||
{
|
||
d=0.0;
|
||
for (j=0; j<=m-1; j++)
|
||
d=d+q[j*m+i]*pDataConst[j];
|
||
|
||
c[i]=d;
|
||
}
|
||
|
||
pDataConst[n-1]=c[n-1]/pDataCoef[n*n-1];
|
||
for (i=n-2; i>=0; i--)
|
||
{
|
||
d=0.0;
|
||
for (j=i+1; j<=n-1; j++)
|
||
d=d+pDataCoef[i*n+j]*pDataConst[j];
|
||
|
||
pDataConst[i]=(c[i]-d)/pDataCoef[i*n+i];
|
||
}
|
||
|
||
// 释放内存
|
||
delete[] c;
|
||
|
||
return TRUE;
|
||
}
|
||
|
||
//////////////////////////////////////////////////////////////////////
|
||
// 求解线性最小二乘问题的广义逆法
|
||
//
|
||
// 参数：
|
||
// 1. CMatrix1& mtxResult - CMatrix1引用对象，返回方程组解矩阵
|
||
// 2. CMatrix1& mtxAP - CMatrix1引用对象，返回系数矩阵的广义逆矩阵
|
||
// 3. CMatrix1& mtxU - CMatrix1引用对象，返回U矩阵
|
||
// 4. CMatrix1& mtxV - CMatrix1引用对象，返回V矩阵
|
||
// 5. float eps - 控制精度，默认值为0.000001
|
||
//
|
||
// 返回值：BOOL 型，方程组求解是否成功
|
||
//////////////////////////////////////////////////////////////////////
|
||
BOOL CLEquations::GetRootsetGinv(CMatrix1& mtxResult, CMatrix1& mtxAP, CMatrix1& mtxU, CMatrix1& mtxV, float eps /*= 0.000001*/)
|
||
{
|
||
int i,j;
|
||
|
||
// 方程个数和未知数个数
|
||
int m = m_mtxCoef.GetNumRows();
|
||
int n = m_mtxCoef.GetNumColumns();
|
||
|
||
// 初始化解向量
|
||
mtxResult.Init(n, 1);
|
||
|
||
float* pDataConst = m_mtxConst.GetData();
|
||
float* x = mtxResult.GetData();
|
||
|
||
// 临时矩阵
|
||
CMatrix1 mtxA = m_mtxCoef;
|
||
|
||
// 求广义逆矩阵
|
||
if (! mtxA.GInvertUV(mtxAP, mtxU, mtxV, eps))
|
||
return FALSE;
|
||
|
||
float* pAPData = mtxAP.GetData();
|
||
|
||
// 求解
|
||
for (i=0; i<=n-1; i++)
|
||
{
|
||
x[i]=0.0;
|
||
for (j=0; j<=m-1; j++)
|
||
x[i]=x[i]+pAPData[i*m+j]*pDataConst[j];
|
||
}
|
||
|
||
return TRUE;
|
||
}
|
||
|
||
//////////////////////////////////////////////////////////////////////
|
||
// 病态方程组的求解
|
||
//
|
||
// 参数：
|
||
// 1. CMatrix1& mtxResult - CMatrix1引用对象，返回方程组解矩阵
|
||
// 2. int nMaxIt - 叠加次数，默认值为60
|
||
// 3. float eps - 控制精度，默认值为0.000001
|
||
//
|
||
// 返回值：BOOL 型，方程组求解是否成功
|
||
//////////////////////////////////////////////////////////////////////
|
||
BOOL CLEquations::GetRootsetMorbid(CMatrix1& mtxResult, int nMaxIt /*= 60*/, float eps /*= 0.000001*/)
|
||
{
|
||
int i, k;
|
||
float q, qq;
|
||
|
||
// 方程的阶数
|
||
int n = GetNumUnknowns();
|
||
|
||
// 设定迭代次数, 缺省为60
|
||
i = nMaxIt;
|
||
|
||
// 用全选主元高斯消元法求解
|
||
CLEquations leqs(m_mtxCoef, m_mtxConst);
|
||
if (! leqs.GetRootsetGauss(mtxResult))
|
||
return FALSE;
|
||
float* x = mtxResult.GetData();
|
||
|
||
q=1.0+eps;
|
||
while (q>=eps)
|
||
{
|
||
// 迭代次数已达最大值，仍为求得结果，求解失败
|
||
if (i==0)
|
||
return FALSE;
|
||
|
||
// 迭代次数减1
|
||
i=i-1;
|
||
|
||
// 矩阵运算
|
||
CMatrix1 mtxE = m_mtxCoef*mtxResult;
|
||
CMatrix1 mtxR = m_mtxConst - mtxE;
|
||
|
||
// 用全选主元高斯消元法求解
|
||
CLEquations leqs(m_mtxCoef, mtxR);
|
||
CMatrix1 mtxRR;
|
||
if (! leqs.GetRootsetGauss(mtxRR))
|
||
return FALSE;
|
||
|
||
float* r = mtxRR.GetData();
|
||
|
||
q=0.0;
|
||
for ( k=0; k<=n-1; k++)
|
||
{
|
||
qq=fabs(r[k])/(1.0+fabs(x[k]+r[k]));
|
||
if (qq>q)
|
||
q=qq;
|
||
}
|
||
|
||
for ( k=0; k<=n-1; k++)
|
||
x[k]=x[k]+r[k];
|
||
|
||
}
|
||
|
||
// 求解成功
|
||
return TRUE;
|
||
}
|
||
|
||
/*
|
||
complex<float> waveseparate( float s[int p],float d,complex<float> w[N],int N,int n)
|
||
{
|
||
|
||
|
||
int i,j;
|
||
complex<float> h[p],H[2*p];
|
||
float Z[N][p],matrixA[4*p*N];
|
||
float *f;
|
||
for(i=0;i<N;i++)
|
||
{
|
||
for(j=0;j<p;j++)
|
||
{
|
||
Z[i][j]=cos((i-n)*w*s[j]*d);
|
||
}
|
||
}
|
||
for(i=N;i<2*N;i++)
|
||
{
|
||
for(j=0;j<p;j++)
|
||
{
|
||
Z[i][j]=sin((i-n)*w*s[j]*d);
|
||
}
|
||
}
|
||
for(i=0;i<N;i++)
|
||
{
|
||
for(j=p;j<2*p;j++)
|
||
{
|
||
Z[i][j]=-sin((i-n)*w*s[j]*d);
|
||
}
|
||
}
|
||
for(i=N;i<2*N;i++)
|
||
{
|
||
for(j=p;j<2*p;j++)
|
||
{
|
||
Z[i][j]=cos((i-n)*w*s[j]*d);
|
||
}
|
||
}//////////////////////////////////////////////////////////////////////
|
||
*/
|
||
|