?? lequations.cs
字號:
/*
* 求解線性方程組的類 LEquations
*
* 周長發編制
*/
using System;
namespace CSharpAlgorithm.Algorithm
{
/**
* 求解線性方程組的類 LEquations
* @author 周長發
* @version 1.0
*/
public class LEquations
{
private Matrix mtxLECoef; // 系數矩陣
private Matrix mtxLEConst; // 常數矩陣
/**
* 基本構造函數
*/
public LEquations()
{
}
/**
* 指定系數和常數構造函數
*
* @param mtxCoef - 指定的系數矩陣
* @param mtxConst - 指定的常數矩陣
*/
public LEquations(Matrix mtxCoef, Matrix mtxConst)
{
Init(mtxCoef, mtxConst);
}
/**
* 初始化函數
*
* @param mtxCoef - 指定的系數矩陣
* @param mtxConst - 指定的常數矩陣
* @return bool 型，初始化是否成功
*/
public bool Init(Matrix mtxCoef, Matrix mtxConst)
{
if (mtxCoef.GetNumRows() != mtxConst.GetNumRows())
return false;
mtxLECoef = new Matrix(mtxCoef);
mtxLEConst = new Matrix(mtxConst);
return true;
}
/**
* 獲取系數矩陣
*
* @return Matrix 型，返回系數矩陣
*/
public Matrix GetCoefMatrix()
{
return mtxLECoef;
}
/**
* 獲取常數矩陣
*
* @return Matrix 型，返回系數矩陣
*/
public Matrix GetConstMatrix()
{
return mtxLEConst;
}
/**
* 獲取方程個數
*
* @return int 型，返回方程組方程的個數
*/
public int GetNumEquations()
{
return GetCoefMatrix().GetNumRows();
}
/**
* 獲取未知數個數
*
* @return int 型，返回方程組未知數的個數
*/
public int GetNumUnknowns()
{
return GetCoefMatrix().GetNumColumns();
}
/**
* 全選主元高斯消去法
*
* @param mtxResult - Matrix對象，返回方程組的解
* @return bool 型，方程組求解是否成功
*/
public bool GetRootsetGauss(Matrix mtxResult)
{
int l,k,i,j,nIs=0,p,q;
double d,t;
// 方程組的屬性，將常數矩陣賦給解矩陣
mtxResult.SetValue(mtxLEConst);
double[] pDataCoef = mtxLECoef.GetData();
double[] pDataConst = mtxResult.GetData();
int n = GetNumUnknowns();
// 臨時緩沖區，存放列數
int[] pnJs = new int[n];
// 消元
l=1;
for (k=0;k<=n-2;k++)
{
d=0.0;
for (i=k;i<=n-1;i++)
{
for (j=k;j<=n-1;j++)
{
t=Math.Abs(pDataCoef[i*n+j]);
if (t>d)
{
d=t;
pnJs[k]=j;
nIs=i;
}
}
}
if (d == 0.0)
l=0;
else
{
if (pnJs[k]!=k)
{
for (i=0;i<=n-1;i++)
{
p=i*n+k;
q=i*n+pnJs[k];
t=pDataCoef[p];
pDataCoef[p]=pDataCoef[q];
pDataCoef[q]=t;
}
}
if (nIs!=k)
{
for (j=k;j<=n-1;j++)
{
p=k*n+j;
q=nIs*n+j;
t=pDataCoef[p];
pDataCoef[p]=pDataCoef[q];
pDataCoef[q]=t;
}
t=pDataConst[k];
pDataConst[k]=pDataConst[nIs];
pDataConst[nIs]=t;
}
}
// 求解失敗
if (l==0)
{
return false;
}
d=pDataCoef[k*n+k];
for (j=k+1;j<=n-1;j++)
{
p=k*n+j;
pDataCoef[p]=pDataCoef[p]/d;
}
pDataConst[k]=pDataConst[k]/d;
for (i=k+1;i<=n-1;i++)
{
for (j=k+1;j<=n-1;j++)
{
p=i*n+j;
pDataCoef[p]=pDataCoef[p]-pDataCoef[i*n+k]*pDataCoef[k*n+j];
}
pDataConst[i]=pDataConst[i]-pDataCoef[i*n+k]*pDataConst[k];
}
}
// 求解失敗
d=pDataCoef[(n-1)*n+n-1];
if (d == 0.0)
{
return false;
}
// 求解
pDataConst[n-1]=pDataConst[n-1]/d;
for (i=n-2;i>=0;i--)
{
t=0.0;
for (j=i+1;j<=n-1;j++)
t=t+pDataCoef[i*n+j]*pDataConst[j];
pDataConst[i]=pDataConst[i]-t;
}
// 調整解的位置
pnJs[n-1]=n-1;
for (k=n-1;k>=0;k--)
{
if (pnJs[k]!=k)
{
t=pDataConst[k];
pDataConst[k]=pDataConst[pnJs[k]];
pDataConst[pnJs[k]]=t;
}
}
return true;
}
/**
* 全選主元高斯－約當消去法
*
* @param mtxResult - Matrix對象，返回方程組的解
* @return bool 型，方程組求解是否成功
*/
public bool GetRootsetGaussJordan(Matrix mtxResult)
{
int l,k,i,j,nIs=0,p,q;
double d,t;
// 方程組的屬性，將常數矩陣賦給解矩陣
mtxResult.SetValue(mtxLEConst);
double[] pDataCoef = mtxLECoef.GetData();
double[] pDataConst = mtxResult.GetData();
int n = GetNumUnknowns();
int m = mtxLEConst.GetNumColumns();
// 臨時緩沖區，存放變換的列數
int[] pnJs = new int[n];
// 消元
l=1;
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=Math.Abs(pDataCoef[i*n+j]);
if (t>d)
{
d=t;
pnJs[k]=j;
nIs=i;
}
}
}
if (d+1.0==1.0)
l=0;
else
{
if (pnJs[k]!=k)
{
for (i=0;i<=n-1;i++)
{
p=i*n+k;
q=i*n+pnJs[k];
t=pDataCoef[p];
pDataCoef[p]=pDataCoef[q];
pDataCoef[q]=t;
}
}
if (nIs!=k)
{
for (j=k;j<=n-1;j++)
{
p=k*n+j;
q=nIs*n+j;
t=pDataCoef[p];
pDataCoef[p]=pDataCoef[q];
pDataCoef[q]=t;
}
for (j=0;j<=m-1;j++)
{
p=k*m+j;
q=nIs*m+j;
t=pDataConst[p];
pDataConst[p]=pDataConst[q];
pDataConst[q]=t;
}
}
}
// 求解失敗
if (l==0)
{
return false;
}
d=pDataCoef[k*n+k];
for (j=k+1;j<=n-1;j++)
{
p=k*n+j;
pDataCoef[p]=pDataCoef[p]/d;
}
for (j=0;j<=m-1;j++)
{
p=k*m+j;
pDataConst[p]=pDataConst[p]/d;
}
for (j=k+1;j<=n-1;j++)
{
for (i=0;i<=n-1;i++)
{
p=i*n+j;
if (i!=k)
pDataCoef[p]=pDataCoef[p]-pDataCoef[i*n+k]*pDataCoef[k*n+j];
}
}
for (j=0;j<=m-1;j++)
{
for (i=0;i<=n-1;i++)
{
p=i*m+j;
if (i!=k)
pDataConst[p]=pDataConst[p]-pDataCoef[i*n+k]*pDataConst[k*m+j];
}
}
}
// 調整
for (k=n-1;k>=0;k--)
{
if (pnJs[k]!=k)
{
for (j=0;j<=m-1;j++)
{
p=k*m+j;
q=pnJs[k]*m+j;
t=pDataConst[p];
pDataConst[p]=pDataConst[q];
pDataConst[q]=t;
}
}
}
return true;
}
/**
* 復系數方程組的全選主元高斯消去法
*
* @param mtxCoefImag - 系數矩陣的虛部矩陣
* @param mtxConstImag - 常數矩陣的虛部矩陣
* @param mtxResult - Matrix對象，返回方程組解矩陣的實部矩陣
* @param mtxResultImag - Matrix對象，返回方程組解矩陣的虛部矩陣
* @return bool 型，方程組求解是否成功
*/
public bool GetRootsetGauss(Matrix mtxCoefImag, Matrix mtxConstImag, Matrix mtxResult, Matrix mtxResultImag)
{
int l,k,i,j,nIs=0,u,v;
double p,q,s,d;
// 方程組的屬性，將常數矩陣賦給解矩陣
mtxResult.SetValue(mtxLEConst);
mtxResultImag.SetValue(mtxConstImag);
double[] pDataCoef = mtxLECoef.GetData();
double[] pDataConst = mtxResult.GetData();
double[] pDataCoefImag = mtxCoefImag.GetData();
double[] pDataConstImag = mtxResultImag.GetData();
int n = GetNumUnknowns();
int m = mtxLEConst.GetNumColumns();
// 臨時緩沖區，存放變換的列數
int[] pnJs = new int[n];
// 消元
for (k=0;k<=n-2;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;
}
}
}
// 求解失敗
if (d == 0.0)
{
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];
// 求解失敗
if (d == 0.0)
{
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;
}
}
// 調整位置
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;
}
}
return true;
}
/**
* 復系數方程組的全選主元高斯－約當消去法
*
* @param mtxCoefImag - 系數矩陣的虛部矩陣
* @param mtxConstImag - 常數矩陣的虛部矩陣
* @param mtxResult - Matrix對象，返回方程組解矩陣的實部矩陣
* @param mtxResultImag - Matrix對象，返回方程組解矩陣的虛部矩陣
* @return bool 型，方程組求解是否成功
*/
public bool GetRootsetGaussJordan(Matrix mtxCoefImag, Matrix mtxConstImag, Matrix mtxResult, Matrix mtxResultImag)
{
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