lequations.cs

csharp版常见数值计算源码

		{
			int l,k,i,j,nIs=0,u,v;
			double p,q,s,d;

			// 方程组的属性，将常数矩阵赋给解矩阵
			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();

			// 临时缓冲区，存放变换的列数
			int[] 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)
				{
					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;
					}
				}
			}

			return true;
		}

		/**
		 * 求解三对角线方程组的追赶法
		 * 
		 * @param mtxResult - Matrix对象，返回方程组解矩阵
		 * @return bool 型，方程组求解是否成功
		 */
		public bool GetRootsetTriDiagonal(Matrix mtxResult)
		{ 
			int k,j;
			double s;
	    
			// 将常数矩阵赋给解矩阵
			mtxResult.SetValue(mtxLEConst);
			double[] pDataConst = mtxResult.GetData();

			int n = GetNumUnknowns();
			if (mtxLECoef.GetNumRows() != n)
				return false;

			// 为系数矩阵对角线数组分配内存
			double[] pDiagData = new double[3*n-2];

			// 构造系数矩阵对角线元素数组
			k = j = 0;
			if (k == 0)
			{
				pDiagData[j++] = mtxLECoef.GetElement(k, k);
				pDiagData[j++] = mtxLECoef.GetElement(k, k+1);
			}
			for (k=1; k<n-1; ++k)
			{
				pDiagData[j++] = mtxLECoef.GetElement(k, k-1);
				pDiagData[j++] = mtxLECoef.GetElement(k, k);
				pDiagData[j++] = mtxLECoef.GetElement(k, k+1);
			}
			if (k == n-1)
			{
				pDiagData[j++] = mtxLECoef.GetElement(k, k-1);
				pDiagData[j++] = mtxLECoef.GetElement(k, k);
			}

			// 求解
			for (k=0;k<=n-2;k++)
			{ 
				j=3*k; 
				s=pDiagData[j];

				// 求解失败
				if (Math.Abs(s)+1.0==1.0)
				{
					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)
			{
				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];
	    
			return true;
		}

		/**
		 * 一般带型方程组的求解
		 * 
		 * @param nBandWidth - 带宽
		 * @param mtxResult - Matrix对象，返回方程组解矩阵
		 * @return bool 型，方程组求解是否成功
		 */
		public bool GetRootsetBand(int nBandWidth, Matrix mtxResult)
		{ 
			int ls,k,i,j,nis=0,u,v;
			double 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.SetValue(mtxLEConst);
			double[] pDataConst = mtxResult.GetData();

			// 方程组属性
			int m = mtxLEConst.GetNumColumns();
			int n = GetNumUnknowns();
			if (mtxLECoef.GetNumRows() != n)
				return false;

			// 带宽数组：带型矩阵的有效数据
			double[] pBandData = new double[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=Math.Max(0, i-ls); k<Math.Max(0, i-ls)+nBandWidth; ++k)
				{
					if (k < n)
						pBandData[i*nBandWidth+j++] = mtxLECoef.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=Math.Abs(pBandData[i*nBandWidth]);
					if (t>p) 
					{
						p=t; 
						nis=i;
					}
				}
	        
				if (p == 0.0)
				{
					return false;
				}

				for (j=0;j<=m-1;j++)
				{ 
					u=k*m+j; 
					v=nis*m+j;
					t=pDataConst[u]; 
					pDataConst[u]=pDataConst[v]; 
					pDataConst[v]=t;
				}
	        
				for (j=0;j<=nBandWidth-1;j++)
				{ 
					u=k*nBandWidth+j; 
					v=nis*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)
			{
				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; 
						nis=(i+j)*m+k;
						pDataConst[u]=pDataConst[u]-pBandData[v]*pDataConst[nis];
					}
				}
	        
				if (ls!=(nBandWidth-1)) 
					ls=ls+1;
			}
	    
			return true;
		}

		/**
		 * 求解对称方程组的分解法
		 * 
		 * @param mtxResult - CMatrix引用对象，返回方程组解矩阵
		 * @return bool 型，方程组求解是否成功
		 */
		public bool GetRootsetDjn(Matrix mtxResult)
		{ 
			int i,j,l,k,u,v,w,k1,k2,k3;
			double p;

			// 方程组属性，将常数矩阵赋给解矩阵
			Matrix mtxCoef = new Matrix(mtxLECoef);
			mtxResult.SetValue(mtxLEConst);
			int n = mtxCoef.GetNumColumns();
			int m = mtxResult.GetNumColumns();
			double[] pDataCoef = mtxCoef.GetData();
			double[] 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
		 * 
		 * @param mtxResult - CMatrix引用对象，返回方程组解矩阵
		 * @return bool 型，方程组求解是否成功
		 */
		public bool GetRootsetCholesky(Matrix mtxResult)
		{ 
			int i,j,k,u,v;
	    
			// 方程组属性，将常数矩阵赋给解矩阵
			Matrix mtxCoef = new Matrix(mtxLECoef);
			mtxResult.SetValue(mtxLEConst);
			int n = mtxCoef.GetNumColumns();
			int m = mtxResult.GetNumColumns();
			double[] pDataCoef = mtxCoef.GetData();
			double[] 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]=Math.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]=Math.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];
					}
				}
			}