C-矩阵基本运算代码

©#矩阵的运算代码#region矩阵运算///<summary>〃/矩阵对应行列式的值///</summary>///<param></param>///<returns></returns>privatedoubleMatrixValue(double[,]MatrixList)(intLevel=MatrixList.GetLength(1);double[,]dMatrix=newdouble[Level,Level];for(inti=0;i<Level;i++)(for(intj=0;j<Level;j++)(dMatrix[i,j]=MatrixList[i,j];))intsign=1;for(inti=0,j=0;i<Level&&j<Level;i++,j++)(〃判断改行dMatrix[i,j]是否为0,若是，则寻找i后的行(m,m>i,切dMatrix[m,j]!=0)进行交换if(dMatrix[i,j]==0)(if(i==Level-1)(return0;)intm=i+1;〃获取一个dMatrix[m,j]不为为0的行for(;dMatrix[m,j]==0;m++)(if(m==Level-1)(return0;))//判断是否达到矩阵的最大行，若是，则返回0〃把i行和m行调换doubletemp;for(intn=j;n<Level;n++)(temp=dMatrix[i,n];dMatrix[i,n]=dMatrix[m,n];dMatrix[m,n]=temp;sign*=(-1);//把当前行以后的行所对应的列变成0doubletmp;for(ints=Level-1;s>i;s--)tmp=dMatrix[s,j];//j行后面的所有行for(intt=j;t<Level;t++)'…";doubleresult=1;for(inti=0;i<Level;i++)if(dMatrix[i,i]!=0)result*=dMatrix[i,i];elsereturn0;returnsign*result;///<summary>///矩阵减法///</summary>///<param></param>///<param></param>///<param></param>///<param></param>privatedouble[]SubMatrix(double[]A1,double[]A2)//判断矩阵的长短是否一致inta1=A1.GetLength(0);inta2=A2.GetLength(0);if(a1!=a2)(returnnull;)〃矩阵相减double[]B=newdouble[a1];for(inti=0;i<a1;i++)(B[i]=A1[i]-A2[i];)returnB;)///<summary>///矩阵乘法///</summary>///<param></param>///<param></param>///<returns></returns>privatedouble[,]MultiplyMatrix(double[,]firstMatrix,double[,]secondMatrix)(double[,]resultMatrix=newdouble[firstMatrix.GetLength(0),secondMatrix.GetLength(1)];〃判断相乘矩阵是否合法，即第一个矩阵的列要等于第二个矩阵的行if(firstMatrix.GetLength(1)!=secondMatrix.GetLength(0))(returnnull;)//求结果矩阵for(introwIndex=0;rowIndex<firstMatrix.GetLength(0);rowIndex++)(for(intcolIndex=0;colIndex<secondMatrix.GetLength(1);colIndex++)(〃初始化结果矩阵的元素resultMatrix[rowIndex,colIndex]=0;for(inti=0;i<firstMatrix.GetLength(1);i++)(//求结果矩阵的元素值resultMatrix[rowIndex,colIndex]+=firstMatrix[rowIndex,i]*secondMatrix[i,colIndex];)))returnresultMatrix;)///<summary>///求逆矩阵///</summary>III<param></param>///<returns></returns>privatedouble[,]Athwart(double[,]dMatrix)〃获取矩阵的行数intLevel=dMatrix.GetLength(l);double[,]dReverseMatrix=newdouble[Level,2*Level];//初始化矩阵Levelx(2*Level)for(inti=0;i<Level;i++)for(intj=0;j<2*Level;j++)if(j<Level)dReverseMatrix[i,j]=dMatrix[i,j];elseif(j-Level==i)dReverseMatrix[i,j]=1;else丁…。for(inti=0,j=0;i<Level&&j<Level;i++,j++)if(dReverseMatrix[i,j]==0)if(i==Level-1)returnnull;intm=i+1;for(;dMatrix[m,j]==0;m++)if(m==Level-1)returnnull;if(m==Level)returnnull;else〃把i行和m行相加for(intn=j;n<2*Level;n++) doubletemp=dReverseMatrix[i,j];if(temp!=1)〃把i行数据，变成以1开始的一行数据for(intn=j;n<2*Level;n++)if(dReverseMatrix[i,n]!=0)di…心〃把i行后的所有行的j列变成0for(ints=Level-1;s>i;s--)temp=dReverseMatrix[s,j];for(intt=j;t<2*Level;t++)[—〃把矩阵Levelx(2*Level)前LevelxLevel转变为单位矩阵for(inti=Level-2;i>=0;i--)for(intj=i+1;j<Level;j++)if(dReverseMatrix[i,j]!=0)(doubletmp=dReverseMatrix[i,j];for(intn=j;n<2*Level;n++)(dReverseMatrix[i,n]-=(tmp*dReverseMatrix[j,n])))))//返回逆矩阵double[,]dReturn=newdouble[Level,Level];for(inti=0;i<Level;i++)for(intj=0;j<Level;j++)dReturn[i,j]=dReverseMatrix[i,j+Level];returndReturn;)#endregion第二份:usingSystem;usingSystem.IO;usingSystem.Diagnostics;6namespaceAdjust7日田｛8韩///<summary>9I///Matrix的摘要说明id///实现矩阵的基本运算11卜///</summary>121publicclassMatrix13中申(1415I〃构造方阵161publicMatrix(introw)17中申(181m_data=newdouble[row,row];1920卜)21IpublicMatrix(introw,intcol)22中申(231m_data=newdouble[row,col];24卜)25I〃复制构造函数261publicMatrix(Matrixm)27中申(281introw=m.Row;291intcol=m.Col;301m_data=newdouble[row,col];31321for(inti=0;i<row;i++)331for(intj=0;j<col;j++)341m_data[i,j]=m[i,j];3536卜)3738中申/*I〃分配方阵的大小I〃对于已含有内存的矩阵，将清空数据IpublicvoidSetSize(introw)I(431m_data=newdouble[row,row];441)4546I〃分配矩阵的大小〃对于已含有内存的矩阵，将清空数据491publicvoidSetSize(introw,intcol)501{Im_data=newdouble[row,col];I)卜*/54551//unitmatrix:设为单位阵561publicvoidSetUnit()57中申｛581for(inti=0;i<m_data.GetLength(0);i++)591for(intj=0;j<m_data.GetLength(1);j++)601m_data[i,j]=((i==j)?1:0);61卜)62631〃设置元素值641publicvoidSetValue(doubled)65中申｛661for(inti=0;i<m_data.GetLength(0);i++)671for(intj=0;j<m_data.GetLength(1);j++)681m_data[i,j]=d;69卜)7071I//Valueextraction：返中行数721publicintRow73申申｛741get75中申｛76returnm_data.GetLength（0）;78卜）79卜）8081I〃返回列数821publicintCol83中申（841get85申申｛861returnm_data.GetLength（1）;87卜）88卜）8990I〃重载索引91〃存取数据成员921publicdoublethis[introw,intcol]93中申｛941get95申申｛961returnm_data[row,col];97卜）981set99中申(100Im_data[row,col]=value;101卜｝102卜｝103104I//primarychange1051//初等变换对调两行：ri<-->rj106IpublicMatrixExchange(inti,intj)107申申｛108Idoubletemp;109110Ifor(intk=0;k<Col;k++)111中申｛112Itemp=m_data[i,k];113Im_data[i,k]=m_data[j,k];114Im_data[j,k]=temp;115卜｝1161returnthis;117卜｝118119120I〃初等变换第index行乘以mul121IMatrixMultiple(intindex,doublemul)122中申(1231for(intj=0;j<Col;j++)124申申｛125Im_data[index,j]*=mul;126卜｝127Ireturnthis;128卜｝129130131I〃初等变换第src行乘以mul加到第index行132IMatrixMultipleAdd(intindex,intsrc,doublemul)133中申｛134Ifor(intj=0;j<Col;j++)135中申｛136Im_data[index,j]+=m_data[src,j]*mul;137卜｝138139Ireturnthis;140卜｝141142I//transpose转置143IpublicMatrixTranspose()144中申(145IMatrixret=newMatrix(Col,Row);146147Ifor(inti=0;i<Row;i++)148Ifor(intj=0;j<Col;j++)149中申(150Iret[j,i]=m_data[i,j];151卜｝152Ireturnret;153卜｝154155I//binaryaddition矩阵力口156IpublicstaticMatrixoperator+(Matrixlhs,Matrixrhs)157中申｛158Iif(lhs.Row!=rhs.Row)〃异常159中申｛160ISystem.Exceptione=newException("相加的两个矩阵的行数不等");161Ithrowe;162卜｝163Iif(lhs.Col!=rhs.Col)//异常164中申｛ISystem.Exceptione=newException("相加的两个矩阵的歹ij数不等");Ithrowe;卜)168169Iintrow=lhs.Row;170Iintcol=lhs.Col;171IMatrixret=newMatrix(row,col);172173Ifor(inti=0;i<row;i++)174Ifor(intj=0;j<col;j++)175中申｛176Idoubled=lhs[i,j]+rhs[i,j];177Iret[i,j]=d;178卜｝179Ireturnret;180181卜｝182183I//binarysubtraction矩阵减184IpublicstaticMatrixoperator-(Matrixlhs,Matrixrhs)185中申｛186Iif(lhs.Row!=rhs.Row)〃异常187中申(188ISystem.Exceptione=newException("相减的两个矩阵的行数不等");189Ithrowe;190卜｝191Iif(lhs.Col!=rhs.Col)〃异常192中申(193ISystem.Exceptione=newException("相减的两个矩阵的列数不等");194Ithrowe;195卜｝196197Iintrow=lhs.Row;198Iintcol=lhs.Col;199IMatrixret=newMatrix(row,col);200201Ifor(inti=0;i<row;i++)202Ifor(intj=0;j<col;j++)203中申(204Idoubled=lhs[i,j]-rhs[i,j];205Iret[i,j]=d;206卜｝207Ireturnret;208卜)209210211I//binarymultiple矩阵乘212IpublicstaticMatrixoperator*(Matrixlhs,Matrixrhs)213中年｛214Iif(lhs.Col!=rhs.Row)〃异常215中申｛216ISystem.Exceptione=newException。,相乘的两个矩阵的行歹ij数不匹配");217Ithrowe;218卜)219220IMatrixret=newMatrix(lhs.Row,rhs.Col);221Idoubletemp;222Ifor(inti=0;i<lhs.Row;i++)223中申｛224Ifor(intj=0;j<rhs.Col;j++)225中申｛226Itemp=0;227Ifor(intk=0;k<lhs.Col;k++)228中申｛229Itemp+=lhs[i,k]*rhs[k,j];230卜)231Iret[i,j]=temp;232卜｝233卜｝234235Ireturnret;236卜｝237238239I//binarydivision矩阵除240IpublicstaticMatrixoperator/(Matrixlhs,Matrixrhs)241中申(242Ireturnlhs*rhs.Inverse();243卜｝244245I//unaryaddition单目加246IpublicstaticMatrixoperator+(Matrixm)247中申(248IMatrixret=newMatrix(m);249Ireturnret;250卜｝251252I//unarysubtraction单目减253IpublicstaticMatrixoperator-(Matrixm)254中申(255IMatrixret=newMatrix(m);256Ifor(inti=0;i<ret.Row;i++)257Ifor(intj=0;j<ret.Col;j++)258中申(259Iret[i,j]=-ret[i,j];260卜)261262Ireturnret;263卜｝264265I//numbermultiple数乘266IpublicstaticMatrixoperator*(doubled,Matrixm)267中申｛268IMatrixret=newMatrix(m);269Ifor(inti=0;i<ret.Row;i++)270Ifor(intj=0;j<ret.Col;j++)271Iret[i,j]*=d;272273Ireturnret;274卜)275276I//numberdivision数除277IpublicstaticMatrixoperator/(doubled,Matrixm)278申申｛279Ireturnd*m.Inverse();280卜｝281282I〃功能：返回列主元素的行号2831〃参数：row为开始查找的行号2841〃说明：在行号[row,Col)范围内查找第row列中绝对值最大的元素，返回所在行号285IintPivot(introw)286中申｛287Iintindex=row;288289Ifor(inti=row+1;i<Row;i++)290中申｛291Iif(m_data[i,row]>m_data[index,row])292Iindex=i;293卜｝294295Ireturnindex;296卜)2972981//inversion逆阵：使用矩阵的初等变换，列主元素消去法299IpublicMatrixInverse()300申申｛301Iif(Row!=Col)//异常,非方阵302中申｛303ISystem.Exceptione=newException("求逆的矩阵不是方阵")；304Ithrowe;305卜｝306IStreamWritersw=newStreamWriter("..\\annex\\close_matrix.txt");307IMatrixtmp=newMatrix(this);308IMatrixret=newMatrix(Row);//单位阵3091ret.SetUnit();310311IintmaxIndex;312IdoubledMul;313314Ifor(inti=0;i<Row;i++)315申申｛316ImaxIndex=tmp.Pivot(i);317318Iif(tmp.m_data[maxlndex,i]==0)3199申(320ISystem.Exceptione=newException("求逆的矩阵的行歹ij式的值等于0,");321Ithrowe;322卜｝3233241if(maxIndex!=i)//下三角阵中此列的最大值不在当前行，交换325中申(326Itmp.Exchange(i,maxIndex);327Iret.Exchange(i,maxIndex);328329卜｝330331Iret.Multiple(i,1/tmp[i,i]);332333Itmp.Multiple(i,1/tmp[i,i]);334335Ifor(intj=i+1;j<Row;j++)336中申｛337IdMul=-tmp[j,i]/tmp[i,i];338Itmp.MultipleAdd(j,i,dMul);339Iret.MultipleAdd(j,i,dMul);340341卜｝342Isw.WriteLine("tmp=\r\n"+tmp);343Isw.WriteLine("ret=\r\n"+ret);344卜｝//endfor345346347Isw.WriteLine("**=\r\n"+this*ret);348349Ifor(inti=Row-1;i>0;i--)350中申｛351Ifor(intj=i-1;j>=0;j--)352中申｛353IdMul=-tmp[j,i]/tmp[i,i];354Itmp.MultipleAdd(j,i,dMul);355Iret.MultipleAdd(j,i,dMul);356卜｝357卜｝//endfor358359360Isw.WriteLine("tmp=\r\n"+tmp);361Isw.WriteLine("ret=\r\n"+ret);362Isw.WriteLine("***=\r\n"+this*ret);363Isw.Close();364365Ireturnret;366367卜}//endInverse368369中中#region370中申/*371I//inversion逆阵：使用矩阵的初等变换，列主元素消去法372IpublicMatrixInverse()373I(374Iif(Row!=Col)〃异常,非方阵375I(376ISystem.Exceptione=newException("求逆的矩阵不是方阵")；377Ithrowe;3781}379I///////////////380IStreamWritersw=newStreamWriter("..\\annex\\matrix_mul.txt");381I////////////////////382I///383IMatrixtmp=newMatrix(this);384IMatrixret=newMatrix(Row);//单位阵3851ret.SetUnit();386387IintmaxIndex;3881doubledMul;389390Ifor(inti=0;i<Row;i++)391I(392393ImaxIndex=tmp.Pivot(i);394395Iif(tmp.m_data[maxIndex,i]==0)3961{397ISystem.Exceptione=newException("求逆的矩阵的行歹ij式的值等于0,");398Ithrowe;399I)400401Iif(maxIndex!=i)〃下三角阵中此列的最大值不在当前行，交换4021{403Itmp.Exchange(i,maxIndex);404Iret.Exchange(i,maxIndex);4054061)407408Iret.Multiple(i,1/tmp[i,i]);409410I/////////////////////////411I//sw.WriteLine("nul\t"+tmp[i,i]+"\t"+ret[i,i]);412I////////////////413Itmp.Multiple(i,1/tmp[i,i]);414I//sw.WriteLine("mmm\t"+tmp[i,i]+"\t"+ret[i,i]);415Isw.WriteLine("111111111tmp=\r\n"+tmp);416Ifor(intj=i+1;j<Row;j++)417l(418IdMul=-tmp[j,i];419Itmp.MultipleAdd(j,i,dMul);420Iret.MultipleAdd(j,i,dMul);421422I}423Isw.WriteLine("222222222222=\r\n"+tmp);424425I}//endfor426427428429Ifor(inti=Row-1;i>0;i--)430I(431Ifor(intj=i-1;j>=0;j--)432I(433IdMul=-tmp[j,i];434Itmp.MultipleAdd(j,i,dMul);435Iret.MultipleAdd(j,i,dMul);4361)437I}//endfor438439I//////////////////////////440441442Isw.WriteLine("tmp=\r\n"+tmp.ToString());443444Isw.Close();445I///////////////////////////////////////446I///447Ireturnret;448449I}//endInverse450451卜*/452453卜#endregion454455I//determineifthematrixissquare:方阵456IpublicboolIsSquare()457中申(458IreturnRow==Col;459卜｝460461I//determineifthematrixissymmetric对称阵462IpublicboolIsSymmetric()463中申｛464465Iif(Row!=Col)466Ireturnfalse;467468Ifor(inti=0;i<Row;i++)469Ifor(intj=i+1;j<Col;j++)470Iif(m_data[i,j]!=m_data[j,i])471Ireturnfalse;472473Ireturntrue;474卜｝475476I〃一阶矩阵，实数477IpublicdoubleToDouble()478中申(479ITrace.Assert(Row==1&&Col==1);480481Ireturnm_data[0,0];482卜｝483484I//conerttostring485IpublicoverridestringToString()486申申｛487488Istrings="";489Ifor(inti=0;i<Row;i++)490中申｛491Ifor(intj=0;j<Col;j++)492Is+=string.Format("｛0｝",m_data[i,j]);493494Is+="\r\n";495卜｝496Ireturns;497498卜｝499500501 〃私有数据成员502Iprivatedouble[,]m_data;503504卜｝//endclassMatrix505｝///矩阵的乘publicboolMatrixMultiply(double[,]a,double。]b,refdouble。]c)(if(a.GetLength(1)!=b.GetLength(0))returnfalse;if(a.GetLength(0)!=c.GetLength(0)||b.GetLength(1)!=c.GetLength(1))returnfalse;for(inti=0;i<a.GetLength(0);i++)(for(intj=0;j<b.GetLength(1);j++)(c[i,j]=0;for(intk=0;k<b.GetLength(0);k++)(c[i,j]+=a[i,k]*b[k,j];returntrue;///矩阵的加publicboolMatrixAdd(double[,]a,double[,]b,refdouble[,]c)(if(a.GetLength(0)!=b.GetLength(0)||a.GetLength(1)!=b.GetLength(1)||a.GetLength(0)!=c.GetLength(0)||a.GetLength(1)!=c.GetLength(1))returnfalse;for(inti=0;i<a.GetLength(0);i++)(for(intj=0;j<a.GetLength(1);j++)(c[i,j]=a[i,j]+b[i,j];))returntrue;)///矩阵的减publicboolMatrixSubtration(double[,]a,double[,]b,refdouble[,]c)(if(a.GetLength(0)!=b.GetLength(0)||a.GetLength(1)!=b.GetLength(1)||a.GetLength(0)!=c.GetLength(0)||a.GetLength(1)!=c.GetLength(1))returnfalse;for(inti=0;i<a.GetLength(0);i++)(for(intj=0;j<a.GetLength(1);j++)(c[i,j]=a[i,j]-b[i,j];))returntrue;)///矩阵的行列式的值publicdoubleMatrixSurplus(double[,]a)(inti,j,k,p,r,m,n;m=a.GetLength(0);n=