C#数值计算算法编程矩阵类Matrix的设计.doc

C#数值计算算法编程矩阵类Matrix的设计namespace CSharpAlgorithm.Algorithm/* 操作矩阵的类Matrix* author 周长发* version 1.0*/public class Matrix private intnumColumns = 0;/ 矩阵列数private intnumRows = 0;/ 矩阵行数private double eps = 0.0;/ 缺省精度private double elements = null;/ 矩阵数据缓冲区/* * 属性: 矩阵列数 */public int Columnsgetreturn numColumns;/* * 属性: 矩阵行数 */public int Rowsgetreturn numRows;/* * 索引器: 访问矩阵元素 * param row - 元素的行 * param col - 元素的列 */public double thisint row, int colgetreturn elementscol + row * numColumns; setelementscol + row * numColumns = value;/* * 属性: Eps */public double Epsgetreturn eps;seteps = value;/* * 基本构造函数 */public Matrix()numColumns = 1;numRows = 1;Init(numRows, numColumns);/* * 指定行列构造函数 * * param nRows - 指定的矩阵行数 * param nCols - 指定的矩阵列数 */public Matrix(int nRows, int nCols)numRows = nRows;numColumns = nCols;Init(numRows, numColumns);/* * 指定值构造函数 * * param value - 二维数组，存储矩阵各元素的值 */public Matrix(double, value)numRows = value.GetLength(0);numColumns = value.GetLength(1);double data = new doublenumRows * numColumns;int k = 0;for (int i=0; inumRows; +i)for (int j=0; jnumColumns; +j)datak+ = valuei, j; Init(numRows, numColumns);SetData(data);/* * 指定值构造函数 * * param nRows - 指定的矩阵行数 * param nCols - 指定的矩阵列数 * param value - 一维数组，长度为nRows*nCols，存储矩阵各元素的值 */public Matrix(int nRows, int nCols, double value)numRows = nRows;numColumns = nCols;Init(numRows, numColumns);SetData(value);/* * 方阵构造函数 * * param nSize - 方阵行列数 */public Matrix(int nSize)numRows = nSize;numColumns = nSize;Init(nSize, nSize);/* * 方阵构造函数 * * param nSize - 方阵行列数 * param value - 一维数组，长度为nRows*nRows，存储方阵各元素的值 */public Matrix(int nSize, double value)numRows = nSize;numColumns = nSize;Init(nSize, nSize);SetData(value);/* * 拷贝构造函数 * * param other - 源矩阵 */public Matrix( Matrix other)numColumns = other.GetNumColumns();numRows = other.GetNumRows();Init(numRows, numColumns);SetData(other.elements);/* * 初始化函数 * * param nRows - 指定的矩阵行数 * param nCols - 指定的矩阵列数 * return bool, 成功返回true, 否则返回false */public bool Init(int nRows, int nCols)numRows = nRows;numColumns = nCols;int nSize = nCols*nRows;if (nSize 0)return false;/ 分配内存elements = new doublenSize;return true;/* * 设置矩阵运算的精度 * * param newEps - 新的精度值 */public void SetEps(double newEps)eps = newEps;/* * 取矩阵的精度值 * * return double型，矩阵的精度值 */public double GetEps()return eps;/* * 重载+ 运算符 * * return Matrix对象 */public static Matrix operator +(Matrix m1, Matrix m2)return m1.Add(m2);/* * 重载- 运算符 * * return Matrix对象 */public static Matrix operator -(Matrix m1, Matrix m2)return m1.Subtract(m2);/* * 重载* 运算符 * * return Matrix对象 */public static Matrix operator *(Matrix m1, Matrix m2)return m1.Multiply(m2);/* * 重载double 运算符 * * return double对象 */public static implicit operator double(Matrix m)return m.elements;/* * 将方阵初始化为单位矩阵 * * param nSize - 方阵行列数 * return bool 型，初始化是否成功 */public bool MakeUnitMatrix(int nSize)if (! Init(nSize, nSize)return false;for (int i=0; inSize; +i)for (int j=0; jnSize; +j)if (i = j)SetElement(i, j, 1);return true;/* * 将矩阵各元素的值转化为字符串, 元素之间的分隔符为, 行与行之间有回车换行符 * return string 型，转换得到的字符串 */public override string ToString() return ToString(, true);/* * 将矩阵各元素的值转化为字符串 * * param sDelim - 元素之间的分隔符 * param bLineBreak - 行与行之间是否有回车换行符 * return string 型，转换得到的字符串 */public string ToString(string sDelim, bool bLineBreak) string s=;for (int i=0; inumRows; +i)for (int j=0; j= numRows)return s;for (int j=0; j= numColumns)return s;for (int i=0; inumRows; +i)string ss = GetElement(i, nCol).ToString(F);s += ss;if (i != numRows-1)s += sDelim;return s;/* * 设置矩阵各元素的值 * * param value - 一维数组，长度为numColumns*numRows，存储 * 矩阵各元素的值 */public void SetData(double value)elements = (double)value.Clone();/* * 设置指定元素的值 * * param nRow - 元素的行 * param nCol - 元素的列 * param value - 指定元素的值 * return bool 型，说明设置是否成功 */public bool SetElement(int nRow, int nCol, double value)if (nCol = numColumns | nRow = numRows)return false;/ array bounds errorelementsnCol + nRow * numColumns = value;return true;/* * 获取指定元素的值 * * param nRow - 元素的行 * param nCol - 元素的列 * return double 型，指定元素的值 */public double GetElement(int nRow, int nCol) return elementsnCol + nRow * numColumns ;/* * 获取矩阵的列数 * * return int 型，矩阵的列数 */public intGetNumColumns() return numColumns;/* * 获取矩阵的行数 * return int 型，矩阵的行数 */public intGetNumRows() return numRows;/* * 获取矩阵的数据 * * return double型数组，指向矩阵各元素的数据缓冲区 */public double GetData() return elements;/* * 获取指定行的向量 * * param nRow - 向量所在的行 * param pVector - 指向向量中各元素的缓冲区 * return int 型，向量中元素的个数，即矩阵的列数 */public int GetRowVector(int nRow, double pVector) for (int j=0; jnumColumns; +j)pVectorj = GetElement(nRow, j);return numColumns;/* * 获取指定列的向量 * * param nCol - 向量所在的列 * param pVector - 指向向量中各元素的缓冲区 * return int 型，向量中元素的个数，即矩阵的行数 */public int GetColVector(int nCol, double pVector) for (int i=0; inumRows; +i)pVectori = GetElement(i, nCol);return numRows;/* * 给矩阵赋值 * * param other - 用于给矩阵赋值的源矩阵 * return Matrix型，阵与other相等 */public Matrix SetValue(Matrix other)if (other != this)Init(other.GetNumRows(), other.GetNumColumns();SetData(other.elements);/ finally return a reference to ourselvesreturn this ;/* * 判断矩阵否相等 * * param other - 用于比较的矩阵 * return bool 型，两个矩阵相等则为true，否则为false */public override bool Equals(object other) Matrix matrix = other as Matrix;if (matrix = null)return false;/ 首先检查行列数是否相等if (numColumns != matrix.GetNumColumns() | numRows != matrix.GetNumRows()return false;for (int i=0; inumRows; +i)for (int j=0; j eps)return false;return true;/* * 因为重写了Equals，因此必须重写GetHashCode * * return int型，返回复数对象散列码 */public override int GetHashCode()double sum = 0;for (int i=0; inumRows; +i)for (int j=0; jnumColumns; +j)sum += Math.Abs(GetElement(i, j);return (int)Math.Sqrt(sum);/* * 实现矩阵的加法 * * param other - 与指定矩阵相加的矩阵 * return Matrix型，指定矩阵与other相加之和 * 如果矩阵的行/列数不匹配，则会抛出异常 */public Matrix Add(Matrix other) / 首先检查行列数是否相等if (numColumns != other.GetNumColumns() |numRows != other.GetNumRows()throw new Exception(矩阵的行/列数不匹配。);/ 构造结果矩阵Matrixresult = new Matrix(this) ;/ 拷贝构造/ 矩阵加法for (int i = 0 ; i numRows ; +i)for (int j = 0 ; j numColumns; +j)result.SetElement(i, j, result.GetElement(i, j) + other.GetElement(i, j) ;return result ;/* * 实现矩阵的减法 * * param other - 与指定矩阵相减的矩阵 * return Matrix型，指定矩阵与other相减之差 * 如果矩阵的行/列数不匹配，则会抛出异常 */public Matrix Subtract(Matrix other) if (numColumns != other.GetNumColumns() |numRows != other.GetNumRows()throw new Exception(矩阵的行/列数不匹配。);/ 构造结果矩阵Matrixresult = new Matrix(this) ;/ 拷贝构造/ 进行减法操作for (int i = 0 ; i numRows ; +i)for (int j = 0 ; j numColumns; +j)result.SetElement(i, j, result.GetElement(i, j) - other.GetElement(i, j) ;return result ;/* * 实现矩阵的数乘 * * param value - 与指定矩阵相乘的实数 * return Matrix型，指定矩阵与value相乘之积 */public Matrix Multiply(double value) / 构造目标矩阵Matrixresult = new Matrix(this) ;/ copy ourselves/ 进行数乘for (int i = 0 ; i numRows ; +i)for (int j = 0 ; j numColumns; +j)result.SetElement(i, j, result.GetElement(i, j) * value) ;return result ;/* * 实现矩阵的乘法 * * param other - 与指定矩阵相乘的矩阵 * return Matrix型，指定矩阵与other相乘之积 * 如果矩阵的行/列数不匹配，则会抛出异常 */public Matrix Multiply(Matrix other) / 首先检查行列数是否符合要求if (numColumns != other.GetNumRows()throw new Exception(矩阵的行/列数不匹配。);/ ruct the object we are going to returnMatrixresult = new Matrix(numRows, other.GetNumColumns();/ 矩阵乘法，即/ ABC GH A*G + B*I + C*KA*H + B*J + C*L/ DEF * IJ = D*G + E*I + F*KD*H + E*J + F*L/ KL/doublevalue ;for (int i = 0 ; i result.GetNumRows() ; +i)for (int j = 0 ; j other.GetNumColumns() ; +j)value = 0.0 ;for (int k = 0 ; k numColumns ; +k)value += GetElement(i, k) * other.GetElement(k, j) ;result.SetElement(i, j, value) ;return result ;/* * 复矩阵的乘法 * * param AR - 左边复矩阵的实部矩阵 * param AI - 左边复矩阵的虚部矩阵 * param BR - 右边复矩阵的实部矩阵 * param BI - 右边复矩阵的虚部矩阵 * param CR - 乘积复矩阵的实部矩阵 * param CI - 乘积复矩阵的虚部矩阵 * return bool型，复矩阵乘法是否成功 */public bool Multiply(Matrix AR, Matrix AI, Matrix BR, Matrix BI, Matrix CR, Matrix CI) / 首先检查行列数是否符合要求if (AR.GetNumColumns() != AI.GetNumColumns() |AR.GetNumRows() != AI.GetNumRows() |BR.GetNumColumns() != BI.GetNumColumns() |BR.GetNumRows() != BI.GetNumRows() |AR.GetNumColumns() != BR.GetNumRows()return false;/ 构造乘积矩阵实部矩阵和虚部矩阵Matrix mtxCR = new Matrix(AR.GetNumRows(), BR.GetNumColumns();Matrix mtxCI = new Matrix(AR.GetNumRows(), BR.GetNumColumns();/ 复矩阵相乘for (int i=0; iAR.GetNumRows(); +i)for (int j=0; jBR.GetNumColumns(); +j)double vr = 0;double vi = 0;for (int k =0; kAR.GetNumColumns(); +k)double p = AR.GetElement(i, k) * BR.GetElement(k, j);double q = AI.GetElement(i, k) * BI.GetElement(k, j);double s = (AR.GetElement(i, k) + AI.GetElement(i, k) * (BR.GetElement(k, j) + BI.GetElement(k, j);vr += p - q;vi += s - p - q;mtxCR.SetElement(i, j, vr);mtxCI.SetElement(i, j, vi);CR = mtxCR;CI = mtxCI;return true;/* * 矩阵的转置 * * return Matrix型，指定矩阵转置矩阵 */public Matrix Transpose() / 构造目标矩阵MatrixTrans = new Matrix(numColumns, numRows);/ 转置各元素for (int i = 0 ; i numRows ; +i)for (int j = 0 ; j numColumns ; +j)Trans.SetElement(j, i, GetElement(i, j) ;return Trans;/* * 实矩阵求逆的全选主元高斯约当法 * * return bool型，求逆是否成功 */public bool InvertGaussJordan()int i,j,k,l,u,v;double d = 0, p = 0;/ 分配内存int pnRow = new intnumColumns;int pnCol = new intnumColumns;/ 消元for (k=0; k=numColumns-1; k+) d=0.0;for (i=k; i=numColumns-1; i+)for (j=k; jd) d=p; pnRowk=i; pnColk=j; / 失败if (d = 0.0)return false;if (pnRowk != k)for (j=0; j=numColumns-1; j+) u=k*numColumns+j; v=pnRowk*numColumns+j;p=elementsu; elementsu=elementsv; elementsv=p; if (pnColk != k)for (i=0; i=numColumns-1; i+) u=i*numColumns+k; v=i*numColumns+pnColk;p=elementsu; elementsu=elementsv; elementsv=p;l=k*numColumns+k;elementsl=1.0/elementsl;for (j=0; j=numColumns-1; j+)if (j != k) u=k*numColumns+j; elementsu=elementsu*elementsl;for (i=0; i=numColumns-1; i+)if (i!=k)for (j=0; j=numColumns-1; j+)if (j!=k) u=i*numColumns+j;elementsu=elementsu-elementsi*numColumns+k*elementsk*numColumns+j;for (i=0; i=0; k-) if (pnColk!=k)for (j=0; j=numColumns-1; j+) u=k*numColumns+j; v=pnColk*numColumns+j;p=elementsu; elementsu=elementsv; elementsv=p;if (pnRowk!=k)for (i=0; i=numColumns-1; i+) u=i*numColumns+k; v=i*numColumns+pnRowk;p=elementsu; elementsu=elementsv; elementsv=p;/ 成功返回return true;/* * 复矩阵求逆的全选主元高斯约当法 * * param mtxImag - 复矩阵的虚部矩阵，当前矩阵为复矩阵的实部 * return bool型，求逆是否成功 */public bool InvertGaussJordan(Matrix mtxImag)int i,j,k,l,u,v,w;double p,q,s,t,d,b;/ 分配内存int pnRow = new intnumColumns;int pnCol = new intnumColumns;/ 消元for (k=0; k=numColumns-1; k+) d=0.0;for (i=k; i=numColumns-1; i+)for (j=k; jd) d=p; pnRowk=i; pnColk=j;/ 失败if (d = 0.0) return false;if (pnRowk!=k)for (j=0; j=numColumns-1; j+) u=k*numColumns+j; v=pnRowk*numColumns+j;t=elementsu; elementsu=elementsv; elementsv=t;t=mtxImag.elementsu; mtxImag.elementsu=mtxImag.elementsv; mtxImag.elementsv=t;if (pnColk!=k)for (i=0; i=numColumns-1; i+) u=i*numColumns+k; v=i*numColumns+pnColk;t=elementsu; elementsu=elementsv; elementsv=t;t=mtxImag.elementsu; mtxImag.elementsu=mtxImag.elementsv; mtxImag.elementsv=t;l=k*numColumns+k;elementsl=elementsl/d; mtxImag.elementsl=-mtxImag.elementsl/d;for (j=0; j=numColumns-1; j+)if (j!=k) u=k*numColumns+j;p=elementsu*elementsl; q=mtxImag.elementsu*mtxImag.elementsl;s=(elementsu+mtxImag.elementsu)*(elementsl+mtxImag.elementsl);elementsu=p-q; mtxImag.elementsu=s-p-q;for (i=0; i=numColumns-1; i+)if (i!=k) v=i*n